Cable Sizing Calculation 2 1m2c2n

Cable Sizing Calculation Contents [hide]

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1 Introduction

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1.1 Why do the calculation?

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1.2 When to do the calculation?

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2 General Methodology 2.1 Step 1: Data Gathering

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2.1.1 Load Details

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2.1.2 Cable Construction

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2.1.3 Installation Conditions 2.2 Step 2: Cable Selection Based on Current Rating

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2.2.1 Base Current Ratings

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2.2.2 Installed Current Ratings

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2.2.3 Cable Selection and Coordination with Protective Devices

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2.2.3.1 Feeders

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2.2.3.2 Motors 2.3 Step 3: Voltage Drop

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2.3.1 Cable Impedances

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2.3.2 Calculating Voltage Drop

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2.3.3 Maximum Permissible Voltage Drop

2.3.4 Calculating Maximum Cable Length due to Voltage Drop

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2.4 Step 4: Short Circuit Temperature Rise

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2.4.1 Minimum Cable Size Due to Short Circuit Temperature Rise

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2.4.2 Initial and Final Conductor Temperatures

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2.4.3 Short Circuit Energy 2.5 Step 5: Earth Fault Loop Impedance

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2.5.1 The Earth Fault Loop

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2.5.2 Maximum Cable Length 3 Worked Example

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3.1 Step 1: Data Gathering

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3.2 Step 2: Cable Selection Based on Current Rating

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3.3 Step 3: Voltage Drop

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3.4 Step 4: Short Circuit Temperature Rise

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3.5 Step 5: Earth Fault Loop Impedance

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4 Waterfall Charts

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5 Template

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6 International Standards

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6.1 IEC

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6.2 NEC

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6.3 BS

6.4 AS/NZS

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Introduction

This article examines the sizing of electrical cables (i.e. cross-sectional area) and its implementation in various international standards. Cable sizing methods do differ across international standards (e.g. IEC, NEC, BS, etc) and some standards emphasise certain things over others. However the general principles underlying any cable sizing calculation do not change. In this article, a general methodology for sizing cables is first presented and then the specific international standards are introduced.

Why do the calculation? The proper sizing of an electrical (load bearing) cable is important to ensure that the cable can: 

Operate continuously under full load without being damaged

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Withstand the worst short circuits currents flowing through the cable

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Provide the load with a suitable voltage (and avoid excessive voltage drops)

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(optional) Ensure operation of protective devices during an earth fault

When to do the calculation? This calculation can be done individually for each power cable that needs to be sized, or alternatively, it can be used to produce cable sizing waterfall charts for groups of cables with similar characteristics (e.g. cables installed on ladder feeding induction motors).

General Methodology All cable sizing methods more or less follow the same basic six step process: 1) Gathering data about the cable, its installation conditions, the load that it will carry, etc 2) Determine the minimum cable size based on continuous current carrying capacity 3) Determine the minimum cable size based on voltage drop considerations 4) Determine the minimum cable size based on short circuit temperature rise 5) Determine the minimum cable size based on earth fault loop impedance 6) Select the cable based on the highest of the sizes calculated in step 2, 3, 4 and 5

Step 1: Data Gathering The first step is to collate the relevant information that is required to perform the sizing calculation. Typically, you will need to obtain the following data:

Load Details The characteristics of the load that the cable will supply, which includes: 

Load type: motor or feeder

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Three phase, single phase or DC

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System / source voltage

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Full load current (A) - or calculate this if the load is defined in of power (kW)

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Full load power factor (pu)

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Locked rotor or load starting current (A)

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Starting power factor (pu)

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Distance / length of cable run from source to load - this length should be as close as possible to the actual route of the cable and include enough contingency for vertical drops / rises and termination of the cable tails

Cable Construction The basic characteristics of the cable's physical construction, which includes: 

Conductor material - normally copper or aluminium

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Conductor shape - e.g. circular or shaped

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Conductor type - e.g. stranded or solid

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Conductor surface coating - e.g. plain (no coating), tinned, silver or nickel

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Insulation type - e.g. PVC, XLPE, EPR

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Number of cores - single core or multicore (e.g. 2C, 3C or 4C)

Installation Conditions How the cable will be installed, which includes:

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Above ground or underground

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Installation / arrangement - e.g. for underground cables, is it directly buried or buried in conduit? for above ground cables, is it installed on cable tray / ladder, against a wall, in air, etc.

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Ambient or soil temperature of the installation site

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Cable bunching, i.e. the number of cables that are bunched together

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Cable spacing, i.e. whether cables are installed touching or spaced

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Soil thermal resistivity (for underground cables)

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Depth of laying (for underground cables)

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For single core three-phase cables, are the cables installed in trefoil or laid flat?

Step 2: Cable Selection Based on Current Rating Current flowing through a cable generates heat through the resistive losses in the conductors, dielectric losses through the insulation and resistive losses from current flowing through any cable screens / shields and armouring. The component parts that make up the cable (e.g. conductors, insulation, bedding, sheath, armour, etc) must be capable of withstanding the temperature rise and heat emanating from the cable. The current carrying capacity of a cable is the maximum current that can flow continuously through a cable without damaging the cable's insulation and other components (e.g. bedding, sheath, etc). It is sometimes also referred to as the continuous current rating or ampacity of a cable. Cables with larger conductor cross-sectional areas (i.e. more copper or aluminium) have lower resistive losses and are able to dissipate the heat better than smaller cables. Therefore a 16 mm2 cable will have a higher current carrying capacity than a 4 mm2 cable.

Base Current Ratings

Table 1. Example of base current rating table (Excerpt from IEC 60364-5-52)

International standards and manufacturers of cables will quote base current ratings of different types of cables in tables such as the one shown on the right. Each of these tables pertain to a specific type of cable construction (e.g. copper conductor, PVC insulated, 0.6/1kV voltage grade, etc) and a base set of installation conditions (e.g. ambient temperature, installation method, etc). It is important to note that the current ratings are only valid for the quoted types of cables and base installation conditions. In the absence of any guidance, the following reference based current ratings may be used.

Installed Current Ratings When the proposed installation conditions differ from the base conditions, derating (or correction) factors can be applied to the base current ratings to obtain the actual installed current ratings. International standards and cable manufacturers will provide derating factors for a range of installation conditions, for example ambient / soil temperature, grouping or bunching of cables, soil thermal resistivity, etc. The installed current rating is calculated by multiplying the base current rating with each of the derating factors, i.e.

where

is the installed current rating (A) is the base current rating (A) are the product of all the derating factors

For example, suppose a cable had an ambient temperature derating factor of kamb = 0.94 and a grouping derating factor of kg = 0.85, then the overall derating factor kd =

0.94x0.85 = 0.799. For a cable with a base current rating of 42A, the installed current rating would be Ic = 0.799x42 = 33.6A. In the absence of any guidance, the following reference derating factors may be used.

Cable Selection and Coordination with Protective Devices Feeders When sizing cables for non-motor loads, the upstream protective device (fuse or circuit breaker) is typically selected to also protect the cable against damage from thermal overload. The protective device must therefore be selected to exceed the full load current, but not exceed the cable's installed current rating, i.e. this inequality must be met:

Where

is the full load current (A)

is the protective device rating (A) is the installed cable current rating (A) Motors Motors are normally protected by a separate thermal overload (TOL) relay and therefore the upstream protective device (e.g. fuse or circuit breaker) is not required to protect the cable against overloads. As a result, cables need only to be sized to cater for the full load current of the motor, i.e.

Where

is the full load current (A)

is the installed cable current rating (A) Of course, if there is no separate thermal overload protection on the motor, then the protective device needs to be taken into as per the case for feeders above.

Step 3: Voltage Drop A cable's conductor can be seen as an impedance and therefore whenever current flows through a cable, there will be a voltage drop across it, which can be derived by Ohm’s Law (i.e. V = IZ). The voltage drop will depend on two things: 

Current flow through the cable – the higher the current flow, the higher the voltage drop

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Impedance of the conductor – the larger the impedance, the higher the voltage drop

Cable Impedances The impedance of the cable is a function of the cable size (cross-sectional area) and the length of the cable. Most cable manufacturers will quote a cable’s resistance and reactance

in Ω/km. The following typical cable impedances for low voltage AC and DC single core and multicore cables can be used in the absence of any other data.

Calculating Voltage Drop For AC systems, the method of calculating voltage drops based on load power factor is commonly used. Full load currents are normally used, but if the load has high startup currents (e.g. motors), then voltage drops based on starting current (and power factor if applicable) should also be calculated. For a three phase system:

Where

is the three phase voltage drop (V)

is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu) is the length of the cable (m) For a single phase system:

Where

is the single phase voltage drop (V)

is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu) is the length of the cable (m) For a DC system:

Where

is the dc voltage drop (V)

is the nominal full load or starting current as applicable (A) is the dc resistance of the cable (Ω/km) is the length of the cable (m)

Maximum Permissible Voltage Drop

It is customary for standards (or clients) to specify maximum permissible voltage drops, which is the highest voltage drop that is allowed across a cable. Should your cable exceed this voltage drop, then a larger cable size should be selected. Maximum voltage drops across a cable are specified because load consumers (e.g. appliances) will have an input voltage tolerance range. This means that if the voltage at the appliance is lower than its rated minimum voltage, then the appliance may not operate correctly. In general, most electrical equipment will operate normally at a voltage as low as 80% nominal voltage. For example, if the nominal voltage is 230VAC, then most appliances will run at >184VAC. Cables are typically sized for a more conservative maximum voltage drop, in the range of 5 – 10% at full load.

Calculating Maximum Cable Length due to Voltage Drop It may be more convenient to calculate the maximum length of a cable for a particular conductor size given a maximum permissible voltage drop (e.g. 5% of nominal voltage at full load) rather than the voltage drop itself. For example, by doing this it is possible to construct tables showing the maximum lengths corresponding to different cable sizes in order to speed up the selection of similar type cables. The maximum cable length that will achieve this can be calculated by re-arranging the voltage drop equations and substituting the maximum permissible voltage drop (e.g. 5% of 415V nominal voltage = 20.75V). For a three phase system:

Where

is the maximum length of the cable (m)

is the maximum permissible three phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu) For a single phase system:

Where

is the maximum length of the cable

(m) is the maximum permissible single phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km)

is the ac reactance of the cable (Ω/km) is the load power factor (pu) For a DC system:

Where

is the maximum length of the cable (m) is the maximum permissible dc voltage drop (V)

is the nominal full load or starting current as applicable (A) is the dc resistance of the cable (Ω/km) is the length of the cable (m)

Step 4: Short Circuit Temperature Rise During a short circuit, a high amount of current can flow through a cable for a short time. This surge in current flow causes a temperature rise within the cable. High temperatures can trigger unwanted reactions in the cable insulation, sheath materials and other components, which can prematurely degrade the condition of the cable. As the cross-sectional area of the cable increases, it can dissipate higher fault currents for a given temperature rise. Therefore, cables should be sized to withstand the largest short circuit that it is expected to see.

Minimum Cable Size Due to Short Circuit Temperature Rise The minimum cable size due to short circuit temperature rise is typically calculated with an equation of the form:

Where

is the minimum cross-sectional area of the cable (mm2)

is the prospective short circuit current (A) is the duration of the short circuit (s) is a short circuit temperature rise constant The temperature rise constant is calculated based on the material properties of the conductor and the initial and final conductor temperatures (see the derivation here). Different international standards have different treatments of the temperature rise constant, but by way of example, IEC 60364-5-54 calculates it as follows:

(for copper conductors)

(for aluminium conductors) Where

is the initial conductor temperature (deg C) is the final conductor temperature (deg C)

Initial and Final Conductor Temperatures The initial conductor temperature is typically chosen to be the maximum operating temperature of the cable. The final conductor temperature is typically chosen to be the limiting temperature of the insulation. In general, the cable's insulation will determine the maximum operating temperature and limiting temperatures. As a rough guide, the following temperatures are common for the different insulation materials: Material

Max Operating Temperature oC

Limiting TemperatureoC

PVC

75

160

EPR

90

250

XLPE

90

250

Short Circuit Energy The short circuit energy

is normally chosen as the maximum short circuit that the cable

could potentially experience. However for circuits with current limiting devices (such as HRC fuses), then the short circuit energy chosen should be the maximum prospective let-through energy of the protective device, which can be found from manufacturer data.

Step 5: Earth Fault Loop Impedance Sometimes it is desirable (or necessary) to consider the earth fault loop impedance of a circuit in the sizing of a cable. Suppose a bolted earth fault occurs between an active conductor and earth. During such an earth fault, it is desirable that the upstream protective device acts to interrupt the fault within a maximum disconnection time so as to protect against any inadvertent to exposed live parts. Ideally the circuit will have earth fault protection, in which case the protection will be fast acting and well within the maximum disconnection time. The maximum disconnection time is chosen so that a dangerous touch voltage does not persist for long enough to cause injury or death. For most circuits, a maximum disconnection time of 5s is sufficient, though for portable equipment and socket outlets, a faster disconnection time is desirable (i.e. <1s and will definitely require earth fault protection). However for circuits that do not have earth fault protection, the upstream protective device (i.e. fuse or circuit breaker) must trip within the maximum disconnection time. In order for the protective device to trip, the fault current due to a bolted short circuit must exceed the value that will cause the protective device to act within the maximum disconnection time. For example, suppose a circuit is protected by a fuse and the maximum disconnection time is 5s, then the fault

current must exceed the fuse melting current at 5s (which can be found by cross-referencing the fuse time-current curves). By simple application of Ohm's law:

Where

is the earth fault current required to trip the protective device within the

minimum disconnection time (A) is the phase to earth voltage at the protective device (V) is the impedance of the earth fault loop (Ω) It can be seen from the equation above that the impedance of the earth fault loop must be sufficiently low to ensure that the earth fault current can trip the upstream protection.

The Earth Fault Loop The earth fault loop can consist of various return paths other than the earth conductor, including the cable armour and the static earthing connection of the facility. However for practical reasons, the earth fault loop in this calculation consists only of the active conductor and the earth conductor. The earth fault loop impedance can be found by:

Where

is the earth fault loop impedance (Ω)

is the impedance of the active conductor (Ω) is the impedance of the earth conductor (Ω) Assuming that the active and earth conductors have identical lengths, the earth fault loop impedance can be calculated as follows:

Where and

is the length of the cable (m)

are the ac resistances of the active and earth conductors respectively

(Ω/km) and

are the reactances of the active and earth conductors respectively (Ω/km)

Maximum Cable Length The maximum earth fault loop impedance can be found by re-arranging the equation above:

Where

is the maximum earth fault loop impedance (Ω) is the phase to earth voltage at the protective device (V) is the earth fault current required to trip the protective device within the minimum disconnection time (A)

The maximum cable length can therefore be calculated by the following:

Where

is the maximum cable length (m) is the phase to earth voltage at the protective device (V) is the earth fault current required to trip the protective device within the minimum disconnection time (A) and

are the ac resistances of the active and earth conductors respectively

(Ω/km) and

are the reactances of the active and earth conductors respectively (Ω/km)

Note that the voltage V0 at the protective device is not necessarily the nominal phase to earth voltage, but usually a lower value as it can be downstream of the main busbars. This voltage is commonly represented by applying some factor of

to the nominal voltage. A conservative value

= 0.8 can be used so that:

Where Vn is the nominal phase to earth voltage (V)

Worked Example In this example, we will size a cable for a 415V, 37kW three-phase motor from the MCC to the field.

Step 1: Data Gathering The following data was collected for the cable to be sized: 

Cable type: Cu/PVC/GSWB/PVC, 3C+E, 0.6/1kV

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Operating temperature: 75C

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Cable installation: above ground on cable ladder bunched together with 3 other cables on a single layer and at 30C ambient temperature

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Cable run: 90m (including tails)

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Motor load: 37kW, 415V three phase, full load current = 61A, power factor = 0.85

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Protection: aM fuse of rating = 80A, max prospective fault I2t = 90 A2s , 5s melt time = 550A

Step 2: Cable Selection Based on Current Rating Suppose the ambient temperature derating is 0.89 and the grouping derating for 3 bunched cables on a single layer is 0.82. The overall derating factor is 0.89 0.82 = 0.7298. Given that a 16 mm2 and 25 mm2 have base current ratings of 80A and 101A respectively (based on Reference Method E), which cable should be selected based on current rating considerations? The installed current ratings for 16 mm2 and 25 mm2 is 0.7298

80A = 58.38A and 0.7298

101A = 73.71A respectively. Given that the full load current of the motor is 61A, then the installed current rating of the 16 mm2 cable is lower than the full load current and is not suitable for continuous use with the motor. The 25 mm2 cable on the other hand has an installed current rating that exceeds the motor full load current, and is therefore the cable that should be selected.

Step 3: Voltage Drop Suppose a 25 mm2 cable is selected. If the maximum permissible voltage drop is 5%, is the cable suitable for a run length of 90m? A 25 mm2 cable has an ac resistance of 0.884 Ω/km and an ac reactance of 0.0895 Ω/km. The voltage drop across the cable is:

A voltage drop of 7.593V is equivalent to

which is lower than the

maximum permissible voltage dorp of 5%. Therefore the cable is suitable for the motor based on voltage drop considerations.

Step 4: Short Circuit Temperature Rise The cable is operating normally at 75C and has a prospective fault capacity (I2t) of 90,000 A2s. What is the minimum size of the cable based on short circuit temperature rise? PVC has a limiting temperature of 160C. Using the IEC formula, the short circuit temperature rise constant is 111.329. The minimum cable size due to short circuit temperature rise is therefore:

In this example, we also use the fuse for earth fault protection and it needs to trip within 5s, which is at the upper end of the adiabatic period where the short circuit temperature rise equation is still valid. Therefore, it's a good idea to also check that the cable can withstand the short circuit temperature rise for for a 5s fault. The 80A motor fuse has a 5s melting current of 550A. The short circuit temperature rise is thus:

Therefore, our 25 mm2 cable is still suitable for this application.

Step 5: Earth Fault Loop Impedance Suppose there is no special earth fault protection for the motor and a bolted single phase to earth fault occurs at the motor terminals. Suppose that the earth conductor for our 25 mm2 cable is 10 mm2. If the maximum disconnection time is 5s, is our 90m long cable suitable based on earth fault loop impedance? The 80A motor fuse has a 5s melting current of 550A. The ac resistances of the active and earth conductors are 0.884 Ω/km and 2.33 Ω/km) respectively. The reactances of the active and earth conductors are 0.0895 Ω/km and 0.0967 Ω/km) respectively. The maximum length of the cable allowed is calculated as:

The cable run is 90m and the maximum length allowed is 108m, therefore our cable is suitable based on earth fault loop impedance. In fact, our 25 mm2 cable has ed all the tests and is the size that should be selected.

Waterfall Charts

Table 2. Example of a cable waterfall chart

Sometimes it is convenient to group together similar types of cables (for example, 415V PVC motor cables installed on cable ladder) so that instead of having to go through the laborious exercise of sizing each cable separately, one can select a cable from a pre-calculated chart.

These charts are often called "waterfall charts" and typically show a list of load ratings and the maximum of length of cable permissible for each cable size. Where a particular cable size fails to meet the requirements for current carrying capacity or short circuit temperature rise, it is blacked out on the chart (i.e. meaning that you can't choose it). Preparing a waterfall chart is common practice when having to size many like cables and substantially cuts down the time required for cable selection.

Template A professional, fully customisable Excel spreadsheet template for cable sizing waterfall charts can be purchased from Tradebit. The template is based on the calculation procedure described in this page and includes waterfall charts for: 

Three-phase motor loads

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Three-phase feeder loads

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Single-phase feeder loads

International Standards IEC IEC 60364-5-52 (2009) "Electrical installations in buildings - Part 5-52: Selection and erection of electrical equipment - Wiring systems" is the IEC standard governing cable sizing.

NEC NFPA 70 (2011) "National Electricity Code" is the equivalent standard for IEC 60364 in North America and includes a section covering cable sizing in Article 300.

BS BS 7671 (2008) "Requirements for Electrical Installations - IEE Wiring Regulations" is the equivalent standard for IEC 60364 in the United Kingdom.

AS/NZS AS/NZS 3008.1 (2009) "Electrical installations - Selection of cables - Cables for alternating voltages up to and including 0.6/1 kV" is the standard governing low voltage cable sizing in Australia and New Zealand. AS/NZS 3008.1.1 is for Australian conditions and AS/NZS 3008.1.2 is for New Zealand conditions.

Computer Software Cablesizer is a free online application for sizing cables to NEC and IEC standards. Most of the major power systems analysis software packages (e.g. ETAP, PTW, etc) have a cable sizing module. There also exists other (offline) software packages that include cable sizing (for example from Solutions Electrical UK).

Android application

Cablesizer for Android is a free (beta) version of the cable sizing tool "Cablesizer".

Earthing Calculation Contents 

1 Introduction

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1.1 Why do the calculation?

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1.2 When to do the calculation?

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1.3 When is the calculation unnecessary?

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2 Calculation Methodology

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2.1 Prerequisites

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2.2 Earthing Grid Conductor Sizing

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2.3 Touch and Step Potential Calculations

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2.3.1 Step 1: Soil Resistivity

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2.3.2 Step 2: Surface Layer Materials

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2.3.3 Step 3: Earthing Grid Resistance

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2.3.3.1 Simplified Method

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2.3.3.2 Schwarz Equations 2.3.4 Step 4: Maximum Grid Current

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2.3.4.1 Current Division Factor

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2.3.4.2 Decrement Factor

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2.3.5 Step 5: Touch and Step Potential Criteria

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2.3.6 Step 6: Ground Potential Rise (GPR)

2.3.7 Step 7: Earthing Grid Design Verification

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2.3.7.1 Mesh Voltage Calculation

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2.3.7.1.1 Geometric Spacing Factor Km

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2.3.7.1.2 Geometric Factor n

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2.3.7.1.3 Irregularity Factor Ki

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2.3.7.1.4 Effective Buried Length LM 2.3.7.2 Step Voltage Calculation

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2.3.7.2.1 Geometric Spacing Factor Ks

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2.3.7.2.2 Effective Buried Length LS 2.3.7.3 What Now?

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3 Worked Example

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3.1 Step 1: Soil Resistivity

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3.2 Step 2: Surface Layer Materials

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3.3 Step 3: Earthing Grid Resistance

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3.4 Step 4: Maximum Grid Current

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3.5 Step 5: Touch and Step Potential Criteria

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3.6 Step 6: Ground Potential Rise (GPR)

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3.7 Step 7: Earthing Grid Design Verification

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3.7.1 Mesh Voltage Calculation

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3.7.2 Step Voltage Calculation

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4 Computer Based Tools

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5 What next?

Introduction The earthing system in a plant / facility is very important for a few reasons, all of which are related to either the protection of people and equipment and/or the optimal operation of the electrical system. These include: 

Equipotential bonding of conductive objects (e.g. metallic equipment, buildings, piping etc) to the earthing system prevent the presence of dangerous voltages between objects (and earth).



The earthing system provides a low resistance return path for earth faults within the plant, which protects both personnel and equipment



For earth faults with return paths to offsite generation sources, a low resistance earthing grid relative to remote earth prevents dangerous ground potential rises (touch and step potentials)



The earthing system provides a low resistance path (relative to remote earth) for voltage transients such as lightning and surges / overvoltages



Equipotential bonding helps prevent electrostatic buildup and discharge, which can cause sparks with enough energy to ignite flammable atmospheres



The earthing system provides a reference potential for electronic circuits and helps reduce electrical noise for electronic, instrumentation and communication systems

This calculation is based primarily on the guidelines provided by IEEE Std 80 (2000), "Guide for safety in AC substation grounding". Lightning protection is excluded from the scope of this calculation (refer to the specific lightning protection calculation for more details).

Why do the calculation? The earthing calculation aids in the proper design of the earthing system. Using the results of this calculation, you can: 

Determine the minimum size of the earthing conductors required for the main earth grid



Ensure that the earthing design is appropriate to prevent dangerous step and touch potentials (if this is necessary)

When to do the calculation? This calculation should be performed when the earthing system is being designed. It could also be done after the preliminary design has been completed to confirm that the earthing system is adequate, or highlight the need for improvement / redesign. Ideally, soil resistivity test results from the site will be available for use in touch and step potential calculations (if necessary).

When is the calculation unnecessary? The sizing of earthing conductors should always be performed, but touch and step potential calculations (per IEEE Std 80 for earth faults with a return path through remote earth) are not always necessary. For example, when all electricity is generated on-site and the HV/MV/LV earthing systems are interconnected, then there is no need to do a touch and step potential calculation. In such a case, all earth faults would return to the source via the earthing system (notwithstanding some small leakage through earth). However, where there are decoupled networks (e.g. long transmission lines to remote areas of the plant), then touch and step potential calculations should be performed for the remote area only.

Calculation Methodology This calculation is based on IEEE Std 80 (2000), "Guide for safety in AC substation grounding". There are two main parts to this calculation: 

Earthing grid conductor sizing



Touch and step potential calculations

IEEE Std 80 is quite descriptive, detailed and easy to follow, so only an overview will be presented here and IEEE Std 80 should be consulted for further details (although references will be given herein).

Prerequisites The following information is required / desirable before starting the calculation: 

A layout of the site



Maximum earth fault current into the earthing grid



Maximum fault clearing time



Ambient (or soil) temperature at the site



Soil resistivity measurements at the site (for touch and step only)



Resistivity of any surface layers intended to be laid (for touch and step only)

Earthing Grid Conductor Sizing Determining the minimum size of the earthing grid conductors is necessary to ensure that the earthing grid will be able to withstand the maximum earth fault current. Like a normal power cable under fault, the earthing grid conductors experience an adiabatic short circuit temperature rise. However unlike a fault on a normal cable, where the limiting temperature is that which would cause permanent damage to the cable's insulation, the temperature limit for earthing grid conductors is the melting point of the conductor. In other words, during the worst case earth fault, we don't want the earthing grid conductors to start melting! The minimum conductor size capable of withstanding the adiabatic temperature rise associated with an earth fault is given by re-arranging IEEE Std 80 Equation 37:

Where

is the minimum cross-sectional area of the earthing grid conductor (mm2) is the energy of the maximum earth fault (A2s) is the maximum allowable (fusing) temperature (ºC) is the ambient temperature (ºC) is the thermal coefficient of resistivity (ºC - 1) is the resistivity of the earthing conductor (μΩ.cm)

is is the thermal capacity of the conductor per unit volume(Jcm - 3ºC - 1) The material constants Tm, αr, ρr and TCAP for common conductor materials can be found in IEEE Std 80 Table 1. For example. commercial hard-drawn copper has material constants: 

Tm = 1084 ºC



αr = 0.00381 ºC - 1



ρr = 1.78 μΩ.cm



TCAP = 3.42 Jcm - 3ºC - 1.

As described in IEEE Std 80 Section 11.3.1.1, there are alternative methods to formulate this equation, all of which can also be derived from first principles).

There are also additional factors that should be considered (e.g. taking into future growth in fault levels), as discussed in IEEE Std 80 Section 11.3.3.

Touch and Step Potential Calculations When electricity is generated remotely and there are no return paths for earth faults other than the earth itself, then there is a risk that earth faults can cause dangerous voltage gradients in the earth around the site of the fault (called ground potential rises). This means that someone standing near the fault can receive a dangerous electrical shock due to: 

Touch voltages - there is a dangerous potential difference between the earth and a metallic object that a person is touching



Step voltages - there is a dangerous voltage gradient between the feet of a person standing on earth

The earthing grid can be used to dissipate fault currents to remote earth and reduce the voltage gradients in the earth. The touch and step potential calculations are performed in order to assess whether the earthing grid can dissipate the fault currents so that dangerous touch and step voltages cannot exist.

Step 1: Soil Resistivity The resistivity properties of the soil where the earthing grid will be laid is an important factor in determining the earthing grid's resistance with respect to remote earth. Soils with lower resistivity lead to lower overall grid resistances and potentially smaller earthing grid configurations can be designed (i.e. that comply with safe step and touch potentials). It is good practice to perform soil resistivity tests on the site. There are a few standard methods for measuring soil resistivity (e.g. Wenner four-pin method). A good discussion on the interpretation of soil resistivity test measurements is found in IEEE Std 80 Section 13.4. Sometimes it isn't possible to conduct soil resistivity tests and an estimate must suffice. When estimating soil resistivity, it goes without saying that one should err on the side of caution and select a higher resistivity. IEEE Std 80 Table 8 gives some guidance on range of soil resistivities based on the general characteristics of the soil (i.e. wet organic soil = 10 Ω.m, moist soil = 100 Ω.m, dry soil = 1,000 Ω.m and bedrock = 10,000 Ω.m).

Step 2: Surface Layer Materials Applying a thin layer (0.08m - 0.15m) of high resistivity material (such as gravel, blue metal, crushed rock, etc) over the surface of the ground is commonly used to help protect against dangerous touch and step voltages. This is because the surface layer material increases the resistance between the soil (i.e. earth) and the feet of a person standing on it, thereby lowering the current flowing through the person in the event of a fault. IEEE Std 80 Table 7 gives typical values for surface layer material resistivity in dry and wet conditions (e.g. 40mm crushed granite = 4,000 Ω.m (dry) and 1,200 Ω.m (wet)). The effective resistance of a person's feet (with respect to earth) when standing on a surface layer is not the same as the surface layer resistance because the layer is not thick enough to have uniform resistivity in all directions. A surface layer derating factor needs to be applied in

order to compute the effective foot resistance (with respect to earth) in the presence of a finite thickness of surface layer material. This derating factor can be approximated by an empirical formula as per IEEE Std 80 Equation 27:

Where

is the surface layer derating factor

is the soil resistivity (Ω.m) is the resistivity of the surface layer material (Ω.m) is the thickness of the surface layer (m) This derating factor will be used later in Step 5 when calculating the maximum allowable touch and step voltages.

Step 3: Earthing Grid Resistance A good earthing grid has low resistance (with respect to remote earth) to minimise ground potential rise (GPR) and consequently avoid dangerous touch and step voltages. Calculating the earthing grid resistance usually goes hand in hand with earthing grid design - that is, you design the earthing grid to minimise grid resistance. The earthing grid resistance mainly depends on the area taken up by the earthing grid, the total length of buried earthing conductors and the number of earthing rods / electrodes. IEEE Std 80 offers two alternative options for calculating the earthing grid resistance (with respect to remote earth) - 1) the simplified method (Section 14.2) and 2) the Schwarz equations (Section 14.3), both of which are outlined briefly below. IEEE Std 80 also includes methods for reducing soil resistivity (in Section 14.5) and a treatment for concrete-encased earthing electrodes (in Section 14.6). Simplified Method IEEE Std 80 Equation 52 gives the simplified method as modified by Sverak to include the effect of earthing grid depth:

Where

is the earthing grid resistance with respect to remote earth (Ω) is the soil resistivitiy (Ω.m) is the total length of buried conductors (m) is the total area occupied by the earthing grid (m2) is the depth of the earthing grid (m) Schwarz Equations

The Schwarz equations are a series of equations that are more accurate in modelling the effect of earthing rods / electrodes. The equations are found in IEEE Std 80 Equations 53, 54, 55(footnote) and 56, as follows:

Where

is the earthing grid resistance with respect to remote earth (Ω) is the earth resistance of the grid conductors (Ω) is the earth resistance of the earthing electrodes (Ω) is the mutual earth resistance between the grid conductors and earthing electrodes (Ω)

And the grid, earthing electrode and mutual earth resistances are:

Where

is the soil resistivity (Ω.m)

is the total length of buried grid conductors (m) is radius

for conductors buried at depth metres, or simply

metres and with cross-sectional

for grid conductors on the surface

is the total area covered by the grid conductors (m2) is the length of each earthing electrode (m) is number of earthing electrodes in area is the cross-sectional radius of an earthing electrode (m) and The coefficient

are constant coefficients depending on the geometry of the grid can be approximated by the following:



(1) For depth



(2) For depth

:

:



(3) For depth

The coefficient

:

can be approximated by the following:



(1) For depth



(2) For depth



(3) For depth

Where in both cases,

:

:

: is the length-to-width ratio of the earthing grid.

Step 4: Maximum Grid Current The maximum grid current is the worst case earth fault current that would flow via the earthing grid back to remote earth. To calculate the maximum grid current, you firstly need to calculate the worst case symmetrical earth fault current at the facility that would have a return path through remote earth (call this

). This can be found from the power systems studies or from

manual calculation. Generally speaking, the highest relevant earth fault level will be on the primary side of the largest distribution transformer (i.e. either the terminals or the delta windings). Current Division Factor Not all of the earth fault current will flow back through remote earth. A portion of the earth fault current may have local return paths (e.g. local generation) or there could be alternative return paths other than remote earth (e.g. overhead earth return cables, buried pipes and cables, etc). Therefore a current division factor

must be applied to for the proportion of the fault

current flowing back through remote earth. Computing the current division factor is a task that is specific to each project and the fault location and it may incorporate some subjectivity (i.e. "engineeing judgement"). In any case, IEEE Std 80 Section 15.9 has a good discussion on calculating the current division factor. In the most conservative case, a current division factor of

can be applied, meaning that 100%

of earth fault current flows back through remote earth. The symmetrical grid current

is calculated by:

Decrement Factor The symmetrical grid current is not the maximum grid current because of asymmetry in short circuits, namely a dc current offset. This is captured by the decrement factor, which can be calculated from IEEE Std 80 Equation 79:

Where

is the decrement factor is the duration of the fault (s) is the dc time offset constant (see below)

The dc time offset constant is derived from IEEE Std 80 Equation 74:

Where

is the X/R ratio at the fault location is the system frequency (Hz)

The maximum grid current

is lastly calculated by:

Step 5: Touch and Step Potential Criteria One of the goals of a safe earthing grid is to protect people against lethal electric shocks in the event of an earth fault. The magnitude of ac electric current (at 50Hz or 60Hz) that a human body can withstand is typically in the range of 60 to 100mA, when ventricular fibrillation and heart stoppage can occur. The duration of an electric shock also contributes to the risk of mortality, so the speed at which faults are cleared is also vital. Given this, we need to prescribe maximum tolerable limits for touch and step voltages that do not lead to lethal shocks. The maximum tolerable voltages for step and touch scenarios can be calculated empirically from IEEE Std Section 8.3 for body weights of 50kg and 70kg: Touch voltage limit - the maximum potential difference between the surface potential and the potential of an earthed conducting structure during a fault (due to ground potential rise):



50kg person:



70kg person:

Step voltage limit - is the maximum difference in surface potential experience by a person bridging a distance of 1m with the feet without to any earthed object:



50kg person:



70kg person: Where

is the touch voltage limit (V)

is the step voltage limit (V) is the surface layer derating factor (as calculated in Step 2) is the soil resistivity (Ω.m) is the maximum fault clearing time (s) The choice of body weight (50kg or 70kg) depends on the expected weight of the personnel at the site. Typically, where women are expected to be on site, the conservative option is to choose 50kg.

Step 6: Ground Potential Rise (GPR) Normally, the potential difference between the local earth around the site and remote earth is considered to be zero (i.e. they are at the same potential). However an earth fault (where the fault current flows back through remote earth), the flow of current through the earth causes local potential gradients in and around the site. The maximum potential difference between the site and remote earth is known as the ground potential rise (GPR). It is important to note that this is a maximum potential potential difference and that earth potentials around the site will vary relative to the point of fault. The maximum GPR is calculated by:

Where

is the maximum ground potential rise (V) is the maximum grid current found earlier in Step 4 (A) is the earthing grid resistance found earlier in Step 3 (Ω)

Step 7: Earthing Grid Design Verification Now we just need to that the earthing grid design is safe for touch and step potential. If the maximum GPR calculated above does not exceed either of the touch and step voltage limits (from Step 5), then the grid design is safe. However if it does exceed the touch and step voltage limits, then some further analysis is required to the design, namely the calculation of the maximum mesh and step voltages as per IEEE Std 80 Section 16.5. Mesh Voltage Calculation The mesh voltage is the maximum touch voltage within a mesh of an earthing grid and is derived from IEEE Std 80 Equation 80:

Where ::

is the soil resistivity (Ω.m)

is the maximum grid current found earlier in Step 4 (A) is the geometric spacing factor (see below) is the irregularity factor (see below) is the effective buried length of the grid (see below) Geometric Spacing Factor Km

The geometric spacing factor

Where

is calculated from IEEE Std 80 Equation 81:

is the spacing between parallel grid conductors (m)

is the depth of buried grid conductors (m) is the cross-sectional diameter of a grid conductor (m) is a weighting factor for depth of burial = is a weighting factor for earth electrodes /rods on the corner mesh for grids with earth electrodes along the grid perimeter or corners



for grids with no earth electrodes on the corners or on the perimeter



is a geometric factor (see below) Geometric Factor n

The geometric factor

is calculated from IEEE Std 80 Equation 85:

With

for square grids, or otherwise

for square and rectangular grids, or otherwise

for square, rectangular and L-shaped grids, or otherwise Where

is the total length of horizontal grid conductors (m)

is the length of grid conductors on the perimeter (m) is the total area of the grid (m2) and

are the maximum length of the grids in the x and y directions (m)

is the maximum distance between any two points on the grid (m) Irregularity Factor Ki

The irregularity factor

Where

is calculated from IEEE Std 80 Equation 89:

is the geometric factor derived above

Effective Buried Length LM

The effective buried length 

is found as follows:

For grids with few or no earthing electrodes (and none on corners or along the perimeter):

Where

is the total length of horizontal grid conductors (m)

is the total length of earthing electrodes / rods (m) 

For grids with earthing electrodes on the corners and along the perimeter:

Where

is the total length of horizontal grid conductors

(m) is the total length of earthing electrodes / rods (m) is the length of each earthing electrode / rod (m) and

are the maximum length of the grids in the x and y directions (m) Step Voltage Calculation The maximum allowable step voltage is calculated from IEEE Std 80 Equation 92:

Where ::

is the soil resistivity (Ω.m)

is the maximum grid current found earlier in Step 4 (A)

is the geometric spacing factor (see below) is the irregularity factor (as derived above in the mesh voltage calculation) is the effective buried length of the grid (see below) Geometric Spacing Factor Ks

The geometric spacing factor

based on IEEE Std 80 Equation 81 is applicable for burial

depths between 0.25m and 2.5m:

Where

is the spacing between parallel grid conductors (m) is the depth of buried grid conductors (m) is a geometric factor (as derived above in the mesh voltage calculation)

Effective Buried Length LS

The effective buried length

Where

for all cases can be calculated by IEEE Std 80 Equation 93:

is the total length of horizontal grid conductors (m) is the total length of earthing electrodes / rods (m)

What Now? Now that the mesh and step voltages are calculated, compare them to the maximum tolerable touch and step voltages respectively. If: 

, and

 then the earthing grid design is safe. If not, however, then further work needs to be done. Some of the things that can be done to make the earthing grid design safe: 

Redesign the earthing grid to lower the grid resistance (e.g. more grid conductors, more earthing electrodes, increasing cross-sectional area of conductors, etc). Once this is done, re-compute the earthing grid resistance (see Step 3) and re-do the touch and step potential calculations.



Limit the total earth fault current or create alternative earth fault return paths



Consider soil treatments to lower the resistivity of the soil



Greater use of high resistivity surface layer materials

Worked Example In this example, the touch and step potential calculations for an earthing grid design will be performed. The proposed site is a small industrial facility with a network connection via a transmission line and a delta-wye connected transformer.

Step 1: Soil Resistivity The soil resistivity around the site was measured with a Wenner four-pin probe and found to be approximately 300 Ω.m.

Step 2: Surface Layer Materials A thin 100mm layer of blue metal (3,000 Ω.m) is proposed to be installed on the site. The surface layer derating factor is:

Step 3: Earthing Grid Resistance

Figure 1. Proposed rectangular earthing grid

A rectangular earthing grid (see the figure right) with the following parameters is proposed: 

Length of 90m and a width of 50m



6 parallel rows and 7 parallel columns



Grid conductors will be 120 mm2 and buried at a depth of 600mm



22 earthing rods will be installed on the corners and perimeter of the grid



Each earthing rod will be 3m long

Using the simplified equation, the resistance of the earthing grid with respect to remote earth is:

Step 4: Maximum Grid Current Suppose that the maximum single phase to earth fault at the HV winding of the transformer is 3.1kA and that the current division factor is 1 (all the fault current flows back to remote earth). The X/R ratio at the fault is approximately 15, the maximum fault duration 150ms and the system nominal frequency is 50Hz. The DC time offset is therefore:

The decrement factor is then:

Fianlly, the maximum grid current is:

kA

Step 5: Touch and Step Potential Criteria

Based on the average weight of the workers on the site, a body weight of 70kg is assumed for the maximum touch and step potential. A maximum fault clearing time of 150ms is also assumed. The maximum allowable touch potential is:

V The maximum allowable step potential is:

V

Step 6: Ground Potential Rise (GPR) The maximum ground potential rise is:

V The GPR far exceeds the maximum allowable touch and step potentials, and further analysis of mesh and step voltages need to be performed.

Step 7: Earthing Grid Design Verification Mesh Voltage Calculation The components of the geometric factor

,

,

and

for the rectangular grid are:

Therefore the geometric factor

is:

The average spacing between parallel grid conductors

where

is:

and

are the width and length of the grid respectively (e.g. 50m and 90m)

and

is the number of parallel rows and columns respectively (e.g. 6 and 7) The geometric spacing factor

The irregularity factor

The effective buried length

is:

is:

is:

m Finally, the maximum mesh voltage is:

V The maximum allowable touch potential is 1,720V, which exceeds the mesh voltage calculated above and the earthing system es the touch potential criteria (although it is quite marginal).

Step Voltage Calculation The geometric spacing factor

The effective buried length

is:

is:

m Finally, the maximum allowable step voltage is:

V The maximum allowable step potential is 5,664V, which exceeds the step voltage calculated above and the earthing system es the step potential criteria. Having ed both touch and step potential criteria, we can conclude that the earthing system is safe.

Computer Based Tools

Figure 2. PTW GroundMat software output (courtesy of SKM Systems Analysis Inc)

As can be seen from above, touch and step potential calculations can be quite a tedious and laborious task, and one that could conceivably be done much quicker by a computer. Even IEEE Std 80 recommends the use of computer software to calculate grid resistances, and mesh and step voltages, and also to create potential gradient visualisations of the site. Computer software packages can be used to assist in earthing grid design by modeling and simulation of different earthing grid configurations. The tools either come as standalone packages or plug-in modules to power system analysis software (such as PTW's GroundMat or ETAP's Ground Grid Design Assessment. Examples of standalone packages include SES Autogrid and SafeGrid.

What next? The minimum size for the earthing grid conductors can be used to specify the earthing grid conductor sizes in the material take-offs and earthing drawings. The touch and step potential calculations (where necessary) that the earthing grid design is safe for the worst earth faults to remote earth. The earthing drawings can therefore be approved for the next stage of reviews.

Load Schedule Contents 

1 Introduction

o

1.1 Why do the calculation?

1.2 When to do the calculation?

o 

2 Calculation Methodology

o

2.1 Step 1: Collect list of loads

o

2.2 Step 2: Collect electrical load parameters

o

2.3 Step 3: Classify the loads 2.3.1 Voltage Level



2.3.2 Load duty



2.3.3 Load criticality

o

2.4 Step 4: Calculate consumed load

o

2.5 Step 5: Calculate operating, peak and design loads









2.5.1 Operating load



2.5.2 Peak load



2.5.3 Design load 3 Worked Example

o

3.1 Step 1: Collect list of loads

o

3.2 Step 2: Collect electrical load parameters

o

3.3 Step 3: Classify the loads

o

3.4 Step 4: Calculate consumed load

o

3.5 Step 5: Calculate operating, peak and design loads 4 Operating Scenarios



5 Computer Software



6 What Next?

 Introduction Figure 1. Example of an electrical load schedule



The electrical load schedule is an estimate of the instantaneous electrical loads operating in a facility, in of active, reactive and apparent power (measured in kW, kVAR and kVA respectively). The load schedule is usually categorised by switchboard or occasionally by sub-facility / area.

 Why do the calculation? 

Preparing the load schedule is one of the earliest tasks that needs to be done as it is essentially a pre-requisite for some of the key electrical design activities (such as equipment sizing and power system studies).

 When to do the calculation? 

The electrical load schedule can typically be started with a preliminary key single line diagram (or at least an idea of the main voltage levels in the system) and any preliminary details of process / building / facility loads. It is recommended that the load schedule is started as soon as practically possible.

Calculation Methodology There are no standards governing load schedules and therefore this calculation is based on generally accepted industry practice. The following methodology assumes that the load schedule is being created for the first time and is also biased towards industrial plants. The basic steps for creating a load schedule are: 

Step 1: Collect a list of the expected electrical loads in the facility



Step 2: For each load, collect the electrical parameters, e.g. nominal / absorbed ratings, power factor, efficiency, etc



Step 3: Classify each of the loads in of switchboard location, load duty and load criticality



Step 4: For each load, calculate the expected consumed load



Step 5: For each switchboard and the overall system, calculate operating, peak and design load

Step 1: Collect list of loads The first step is to gather a list of all the electrical loads that will be supplied by the power system affected by the load schedule. There are generally two types of loads that need to be collected: 

Process loads - are the loads that are directly relevant to the facility. In factories and industrial plants, process loads are the motors, heaters, compressors, conveyors, etc that form the main business of the plant. Process loads can normally be found on either Mechanical Equipment Lists or Process and Instrumentation Diagrams (P&ID's).



Non-process loads - are the auxiliary loads that are necessary to run the facility, e.g. lighting, HVAC, utility systems (power and water), DCS/PLC control systems, fire safety systems, etc. These loads are usually taken from a number of sources, for example HVAC engineers, instruments, telecoms and control systems engineers, safety engineers, etc. Some loads such as lighting, UPS, power generation auxiliaries, etc need to be estimated by the electrical engineer.

Step 2: Collect electrical load parameters A number of electrical load parameters are necessary to construct the load schedule:



Rated power is the full load or nameplate rating of the load and represents the maximum continuous power output of the load. For motor loads, the rated power corresponds to the standard motor size (e.g. 11kW, 37kW, 75kW, etc). For load items that contain sub-loads (e.g. distribution boards, package equipment, etc), the rated power is typically the maximum power output of the item (i.e. with all its sub-loads in service).



Absorbed power is the expected power that will be drawn by the load. Most loads will not operate at its rated capacity, but at a lower point. For example, absorbed motor loads are based on the mechanical power input to the shaft of the driven equipment at its duty point. The motor is typically sized so that the rated capacity of the motor exceeds the expected absorbed load by some conservative design margin. Where information regarding the absorbed loads is not available, then a load factor of between 0.8 and 0.9 is normally applied.



Power factor of the load is necessary to determine the reactive components of the load schedule. Normally the load power factor at full load is used, but the power factor at the duty point can also be used for increased accuracy. Where power factors are not readily available, then estimates can be used (typically 0.85 for motor loads >7.5kW, 1.0 for heater loads and 0.8 for all other loads).



Efficiency s for the losses incurred when converting electrical energy to mechanical energy (or whatever type of energy the load outputs). Some of the electrical power drawn by the load is lost, usually in the form of heat to the ambient environment. Where information regarding efficiencies is not available, then estimates of between 0.8 and 1 can be used (typically 0.85 or 0.9 is used when efficiencies are unknown).

Step 3: Classify the loads Once the loads have been identified, they need to be classified accordingly:

Voltage Level What voltage level and which switchboard should the load be located? Large loads may need to be on MV or HV switchboards depending on the size of the load and how many voltage levels are available. Typically, loads <150kW tend to be on the LV system (400V - 690V), loads between 150kW and 10MW tend to be on an intermediate MV system (3.3kV - 6.6kV) where available and loads >10MW are usually on the HV distribution system (11kV - 33kV). Some consideration should also be made for grouping the loads on a switchboard in of sub-facilities, areas or sub-systems (e.g. a switchboard for the compression train sub-system or the drying area).

Load duty Loads are classified according to their duty as either continuous, intermittent and standby loads: 1) Continuous loads are those that normally operate continuously over a 24 hour period, e.g. process loads, control systems, lighting and small power distribution boards, UPS systems, etc 2) Intermittent loads that only operate a fraction of a 24 hour period, e.g. intermittent pumps and process loads, automatic doors and gates, etc 3) Standby loads are those that are on standby or rarely operate under normal conditions, e.g. standby loads, emergency systems, etc Note that for redundant loads (e.g. 2 x 100% duty / standby motors), one is usually classified as continuous and the other classified as standby. This if purely for the purposes of the load schedule and does not reflect the actual operating conditions of the loads, i.e. both redundant loads will be equally used even though one is classified as a standby load.

Load criticality Loads are typically classified as either normal, essential and critical: 1) Normal loads are those that run under normal operating conditions, e.g. main process loads, normal lighting and small power, ordinary office and workshop loads, etc 2) Essential loads are those necessary under emergency conditions, when the main power supply is disconnected and the system is being ed by an emergency generator, e.g. emergency lighting, key process loads that operate during emergency conditions, fire and safety systems, etc 3) Critical are those critical for the operation of safety systems and for facilitating or assisting evacuation from the plant, and would normally be supplied from a UPS or battery system, e.g. safety-critical shutdown systems, escape lighting, etc

Step 4: Calculate consumed load The consumed load is the quantity of electrical power that the load is expected to consume. For each load, calculate the consumed active and reactive loading, derived as follows:

Where

is the consumed active load (kW)

is the consumed reactive load (kVAr) is the absorbed load (kW)

is the load efficiency (pu) is the load power factor (pu) Notice that the loads have been categorised into three columns depending on their load duty (continuous, intermittent or standby). This is done in order to make it visually easier to see the load duty and more importantly, to make it easier to sum the loads according to their duty (e.g. sum of all continuous loads), which is necessary to calculate the operating, peak and design loads.

Step 5: Calculate operating, peak and design loads Many organisations / clients have their own distinct method for calculating operating, peak and design loads, but a generic method is presented as follows:

Operating load The operating load is the expected load during normal operation. The operating load is calculated as follows:

Where

is the operating load (kW or kVAr) is the sum of all continuous loads (kW or kVAr) is the sum of all intermittent loads (kW or kVAr)

Peak load The peak load is the expected maximum load during normal operation. Peak loading is typically infrequent and of short duration, occurring when standby loads are operated (e.g. for changeover of redundant machines, testing of safety equipment, etc). The peak load is calculated as the larger of either:

or

Where

is the peak load (kW or kVAr) is the sum of all continuous loads (kW or kVAr) is the sum of all intermittent loads (kW or kVAr) is the sum of all standby loads (kW or kVAr) is the largest standby load (kW or kVAr)

Design load

The design load is the load to be used for the design for equipment sizing, electrical studies, etc. The design load is generically calculated as the larger of either:

or

Where

is the design load (kW or kVAr) is the operating load (kW or kVAr) is the sum of all standby loads (kW or kVAr) is the largest standby load (kW or kVAr

The design load includes a margin for any errors in load estimation, load growth or the addition of unforeseen loads that may appear after the design phase. The load schedule is thus more conservative and robust to errors. On the other hand however, equipment is often over-sized as a result. Sometimes the design load is not calculated and the peak load is used for design purposes.

Worked Example Step 1: Collect list of loads Consider a small facility with the following loads identified: 

2 x 100% vapour recovery compressors (process)



2 x 100% recirculation pumps (process)



1 x 100% sump pump (process)



2 x 50% firewater pumps (safety)



1 x 100% HVAC unit (HVAC)



1 x 100% AC UPS system (electrical)



1 x Normal lighting distribution board (electrical)



1 x Essential lighting distribution board (electrical)

Step 2: Collect electrical load parameters The following electrical load parameters were collected for the loads identified in Step 1:

Load Description

Abs. Load

Rated Load

PF

Eff.

Vapour recovery compressor A

750kW

800kW

0.87

0.95

Vapour recovery compressor B

750kW

800kW

0.87

0.95

Recirculation pump A

31kW

37kW

0.83

0.86

Recirculation pump B

31kW

37kW

0.83

0.86

Sump pump

9kW

11kW

0.81

0.83

Firewater pump A

65kW

75kW

0.88

0.88

Firewater pump B

65kW

75kW

0.88

0.88

HVAC unit

80kW

90kW

0.85

0.9

AC UPS System

9kW

12kW

0.85

0.9

Normal lighting distribution board

7kW

10kW

0.8

0.9

Essential lighting distribution board

4kW

5kW

0.8

0.9

Step 3: Classify the loads Suppose we have two voltage levels, 6.6kV and 415V. The loads can be classified as follows: Load Description

Rated Load

Voltage

Duty

Criticality

Vapour recovery compressor A

800kW

6.6kV

Continuous

Normal

Vapour recovery compressor B

800kW

6.6kV

Standby

Normal

Recirculation pump A

37kW

415V

Continuous

Normal

Recirculation pump B

37kW

415V

Standby

Normal

Sump pump

11kW

415V

Intermittent

Normal

Firewater pump A

75kW

415V

Standby

Essential

Firewater pump B

75kW

415V

Standby

Essential

HVAC unit

90kW

415V

Continuous

Normal

AC UPS System

12kW

415V

Continuous

Critical

Normal lighting distribution board

10kW

415V

Continuous

Normal

Essential lighting distribution board

5kW

415V

Continuous

Essential

Step 4: Calculate consumed load Calculating the consumed loads for each of the loads in this example gives: Continuous Load

Abs

Description

Load

Vapour recovery

PF

Eff.

Intermittent

Standby

P

Q

P

Q

P

Q

(kW)

(kVAr)

(kW)

(kVAr)

(kW)

(kVAr)

750kW

0.87

0.95

789.5

447.4

-

-

-

-

750kW

0.87

0.95

-

-

-

-

789.5

447.4

31kW

0.83

0.86

36.0

24.2

-

-

-

-

31kW

0.83

0.86

-

-

-

-

36.0

24.2

9kW

0.81

0.83

-

-

10.8

7.9

-

-

65kW

0.88

0.88

-

-

-

-

73.9

39.9

65kW

0.88

0.88

-

-

-

-

73.9

39.9

HVAC unit

80kW

0.85

0.9

88.9

55.1

-

-

-

-

AC UPS System

9kW

0.85

0.9

10.0

6.2

-

-

-

-

7kW

0.8

0.9

7.8

5.8

-

-

-

-

4kW

0.8

0.9

4.4

3.3

-

-

-

-

936.6

542.0

10.8

7.9

973.3

551.4

compressor A Vapour recovery compressor B Recirculation pump A Recirculation pump B Sump pump Firewater pump A Firewater pump B

Normal lighting distribution board Essential lighting distribution board SUM TOTAL

Step 5: Calculate operating, peak and design loads The operating, peak and design loads are calculated as follows:

Sum of continuous loads

P (kW)

Q (kW)

936.6

542.0

50% x Sum of intermittent loads

5.4

4.0

10% x Sum of standby loads

97.3

55.1

Largest standby load

789.5

447.4

Operating load

942

546.0

Peak load

1,731.5

993.4

Design load

1,825.7

1,047.9

Normally you would separate the loads by switchboard and calculate operating, peak and design loads for each switchboard and one for the overall system. However for the sake of simplicity, the loads in this example are all lumped together and only one set of operating, peak and design loads are calculated.

Operating Scenarios It may be necessary to construct load schedules for different operating scenarios. For example, in order to size an emergency diesel generator, it would be necessary to construct a load schedule for emergency scenarios. The classification of the loads by criticality will help in constructing alternative scenarios, especially those that use alternative power sources.

Computer Software In the past, the load schedule has typically been done manually by hand or with the help of an Excel spreadsheet. However, this type of calculation is extremely well-suited for database driven software packages (such as Smartplant Electrical), especially for very large projects. For smaller projects, it may be far easier to simply perform this calculation manually.

What Next? The electrical load schedule is the basis for the sizing of most major electrical equipment, from generators to switchgear to transformers. Using the load schedule, major equipment sizing can be started, as well as the power system studies. A preliminary load schedule will also indicate if there will be problems with available power supply / generation, and whether alternative power sources or even process designs will need to be investigated.

Motor Starting Contents [hide]

1 Introduction

o

1.1 Why do the calculation?

o

1.2 When to do the calculation? 2 Calculation Methodology

o

2.1 Step 1: Construct System Model and Collect Equipment Parameters

o

2.2 Step 2: Calculate Equipment Impedances



2.2.1 Network Feeders



2.2.2 Synchronous Generators



2.2.3 Transformers



2.2.4 Cables



2.2.5 Standing Loads



2.2.6 Motors

o

2.3 Step 3: Referring Impedances

o

2.4 Step 4: Construct the Equivalent Circuit

o

2.5 Step 5: Calculate the Initial Source EMF

o

2.6 Step 6: Calculate System Voltages During Motor Start 3 Worked Example

o

3.1 Step 1: Construct System Model and Collect Equipment Parameters

o

3.2 Step 2: Calculate Equipment Impedances

o

3.3 Step 3: Referring Impedances

o

3.4 Step 4: Construct the Equivalent Circuit

o

3.5 Step 5: Calculate the Initial Source EMF

o

3.6 Step 6: Calculate System Voltages During Motor Start 4 Computer Software 5 What Next?

Introduction

Figure 1. High voltage motor (courtesy of ABB)

This article considers the transient effects of motor starting on the system voltage. Usually only the largest motor on a bus or system is modelled, but the calculation can in principle be used for any motor. It's important to note that motor starting is a transient power flow problem and is normally done iteratively by computer software. However a static method is shown here for first estimates only.

Why do the calculation? When a motor is started, it typically draws a current 6-7 times its full load current for a short duration (commonly called the locked rotor current). During this transient period, the source impedance is generally assumed to be fixed and therefore, a large increase in current will result in a larger voltage drop across the source impedance. This means that there can be large momentary voltage drops system-wide, from the power source (e.g. transformer or generator) through the intermediary buses, all the way to the motor terminals. A system-wide voltage drop can have a number of adverse effects, for example:



Equipment with minimum voltage tolerances (e.g. electronics) may malfunction or behave aberrantly



Undervoltage protection may be tripped



The motor itself may not start as torque is proportional to the square of the stator voltage, so a reduced voltage equals lower torque. Induction motors are typically designed to start with a terminal voltage >80%

When to do the calculation? This calculation is more or less done to that the largest motor does not cause system wide problems upon starting. Therefore it should be done after preliminary system design is complete. The following prerequisite information is required: 

Key single line diagrams



Preliminary load schedule



Tolerable voltage drop limits during motor starting, which are typically prescribed by the client

Calculation Methodology This calculation is based on standard impedance formulae and Ohm's law. To the author's knowledge, there are no international standards that govern voltage drop calculations during motor start. It should be noted that the proposed method is not 100% accurate because it is a static calculation. In reality, the voltage levels are fluctuating during a transient condition, and therefore so are the load currents drawn by the standing loads. This makes it essentially a load flow problem and a more precise solution would solve the load flow problem iteratively, for example using the Newton-Rhapson or Gauss-Siedel algorithms. Notwithstanding, the proposed method is suitably accurate for a first solution. The calculation has the following six general steps: 

Step 1: Construct the system model and assemble the relevant equipment parameters



Step 2: Calculate the relevant impedances for each equipment item in the model



Step 3: Refer all impedances to a reference voltage



Step 4: Construct the equivalent circuit for the voltage levels of interest



Step 5: Calculate the initial steady-state source emf before motor starting



Step 6: Calculate the system voltages during motor start

Step 1: Construct System Model and Collect Equipment Parameters The first step is to construct a simplified model of the system single line diagram, and then collect the relevant equipment parameters. The model of the single line diagram need only show the buses of interest in the motor starting calculation, e.g. the upstream source bus, the motor bus and possibly any intermediate or downstream buses that may be affected. All running loads are shown as lumped loads except for the motor to be started as it is assumed that the system is in a steady-state before motor start. The relevant equipment parameters to be collected are as follows: 

Network feeders: fault capacity of the network (VA), X/R ratio of the network



Generators: per-unit transient reactance, rated generator capacity (VA)



Transformers: transformer impedance voltage (%), rated transformer capacity (VA), rated current (A), total copper loss (W)



Cables: length of cable (m), resistance and reactance of cable (

)



Standing loads: rated load capacity (VA), average load power factor (pu)



Motor: full load current (A), locked rotor current (A), rated power (W), full load power factor (pu), starting power factor (pu)

Step 2: Calculate Equipment Impedances Using the collected parameters, each of the equipment item impedances can be calculated for later use in the motor starting calculations.

Network Feeders Given the approximate fault level of the network feeder at the connection point (or point of common coupling), the impedance, resistance and reactance of the network feeder is calculated as follows:

Where

is impedance of the network feeder (Ω)

is resistance of the network feeder (Ω) is reactance of the network feeder (Ω) is the nominal voltage at the connection point (Vac) is the fault level of the network feeder (VA) is a voltage factor which s for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages >1kV)

is X/R ratio of the network feeder (pu)

Synchronous Generators The transient resistance and reactance of a synchronous generator can be estimated by the following:

Where

is the transient reactance of the generator (Ω) is the resistance of the generator (Ω) is a voltage correction factor (pu) is the per-unit transient reactance of the generator (pu) is the nominal generator voltage (Vac) is the nominal system voltage (Vac) is the rated generator capacity (VA)

is the X/R ratio, typically 20 for

100MVA, 14.29 for

6.67 for all generators with nominal voltage

100MVA, and

1kV

is a voltage factor which s for the maximum system voltage (1.05 for voltages <1kV, 1.1 for voltages >1kV) is the power factor of the generator (pu)

Transformers The impedance, resistance and reactance of two-winding transformers can be calculated as follows:

Where

is the impedance of the transformer (Ω) is the resistance of the transformer (Ω) is the reactance of the transformer (Ω) is the impedance voltage of the transformer (pu) is the rated capacity of the transformer (VA) is the nominal voltage of the transformer at the high or low voltage side (Vac) is the rated current of the transformer at the high or low voltage side (I) is the total copper loss in the transformer windings (W)

Cables Cable impedances are usually quoted by manufacturers in of Ohms per km. These need to be converted to Ohms based on the length of the cables:

Where

is the resistance of the cable {Ω) is the reactance of the cable {Ω) is the quoted resistance of the cable {Ω / km)

is the quoted reactance of the cable {Ω / km) is the length of the cable {m)

Standing Loads Standing loads are lumped loads comprising all loads that are operating on a particular bus, excluding the motor to be started. Standing loads for each bus need to be calculated. The impedance, resistance and reactance of the standing load is calculated by:

Where

is the impedance of the standing load {Ω) is the resistance of the standing load {Ω) is the reactance of the standing load {Ω) is the standing load nominal voltage (Vac) is the standing load apparent power (VA) is the average load power factor (pu)

Motors The motor's transient impedance, resistance and reactance is calculated as follows:

Where

is transient impedance of the motor (Ω) is transient resistance of the motor (Ω) is transient reactance of the motor (Ω) is ratio of the locked rotor to full load current is the motor locked rotor current (A) is the motor nominal voltage (Vac) is the motor rated power (W) is the motor full load power factor (pu) is the motor starting power factor (pu)

Step 3: Referring Impedances Where there are multiple voltage levels, the equipment impedances calculated earlier need to be converted to a reference voltage (typically the HV side) in order for them to be used in a single equivalent circuit. The winding ratio of a transformer can be calculated as follows:

Where

is the transformer winding ratio is the transformer nominal secondary voltage at the principal tap (Vac) is the transformer nominal primary voltage (Vac) is the specified tap setting (%)

Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV) side of the transformer by the following relation:

Where

is the impedance referred to the primary (HV) side (Ω) is the impedance at the secondary (LV) side (Ω) is the transformer winding ratio (pu)

Conversely, by re-arranging the equation above, impedances can be referred to the LV side:

Step 4: Construct the Equivalent Circuit

Figure 2. "Near" Thévenin equivalent circuit

The equivalent circuit essentially consists of a voltage source (from a network feeder or generator) plus a set of complex impedances representing the power system equipment and load impedances.

The next step is to simplify the circuit into a form that is nearly the Thévenin equivalent circuit, with a circuit containing only a voltage source ( load impedance (

), source impedance (

) and equivalent

).

This can be done using the standard formulae for series and parallel impedances, keeping in mind that the rules of complex arithmetic must be used throughout. This simplification to a "Near" Thévenin equivalent circuit should be done both with the motor off (open circuit) and the motor in a starting condition.

Step 5: Calculate the Initial Source EMF Assuming that the system is initially in a steady-state condition, we need to first calculate the initial emf produced by the power source (i.e. feeder connection point or generator terminals). This voltage will be used in the transient calculations (Step 6) as the initial source voltage. Assumptions regarding the steady-state condition: 

The source point of common coupling (PCC) is at its nominal voltage



The motor is switched off



All standing loads are operating at the capacity calculated in Step 2



All transformer taps are set at those specified in Step 2



The system is at a steady-state, i.e. there is no switching taking place throughout the system

Since we assume that there is nominal voltage at the PCC, the initial source emf can be calculated by voltage divider:

Where

is the initial emf of the power source (Vac) is the nominal voltage (Vac) is the source impedance (Ω) is the equivalent load impedance with the motor switched off (Ω)

Step 6: Calculate System Voltages During Motor Start It is assumed in this calculation that during motor starting, the initial source emf calculated in Step 5 remains constant; that is, the power source does not react during the transient period. This is a simplifying assumption in order to avoid having to model the transient behaviour of the power source.

Next, we need to calculate the overall system current that is supplied by the power source during the motor starting period. To do this, we use the "Near" Thevenin equivalent circuit derived earlier, but now include the motor starting impedance. A new equivalent load impedance during motor starting

will be calculated.

The current supplied by the power source is therefore:

Where

is the system current supplied by the source (A) is the initial source emf (Vac) is the equivalent load impedance during motor start (Ω) is the source impedance (Ω) The voltage at the source point of common coupling (PCC) is:

Where

is the voltage at the point of common coupling (Vac) is the initial source emf (Vac) is the system current supplied by the source (A) is the source impedance (Ω) The downstream voltages can now be calculated by voltage division and simple application of Ohm's law. Specifically, we'd like to know the voltage at the motor terminals and any buses of interest that could be affected. Ensure that the voltages are acceptably within the prescribed limits, otherwise further action needs to be taken (refer to theWhat's Next? section).

Worked Example The worked example here is a very simple power system with two voltage levels and supplied by a single generator. While unrealistic, it does manage to demonstrate the key concepts pertaining to motor starting calculations.

Step 1: Construct System Model and Collect Equipment Parameters

Figure 3. Simplified system model for motor starting example

The power system has two voltage levels, 11kV and 415V, and is fed via a single 4MVA generator (G1). The 11kV bus has a standing load of 950kVA (S1) and we want to model the effects of starting a 250kW motor (M1). There is a standing load of 600kVA at 415V (S2), supplied by a 1.6MVA transformer (TX1). The equipment and cable parameters are as follows: Equipment

Parameters

= 4,000 kVA



Generator G1

= 11,000 V





= 0.85 pu



Generator Cable C1

= 0.33 pu



Length = 50m



Size = 500 mm2

(R = 0.0522 Ω\km, X = 0.0826 Ω\km)

11kV Standing Load S1



= 950 kVA



= 11,000 V = 0.84 pu



Motor M1



= 250 kW



= 11,000 V



= 106.7 A = 6.5 pu





= 0.85 pu



= 0.30 pu

Length = 150m

 Motor Cable C2

Size = 35 mm2



(R = 0.668 Ω\km, X = 0.115 Ω\km)

= 1,600 kVA



= 11,000 V



= 415 V



Transformer TX1

= 0.06 pu



= 12,700 W





= 0%

Transformer Cable C3



Length = 60m



Size = 120 mm2

(R = 0.196 Ω\km, X = 0.096 Ω\km)

= 600 kVA

 415V Standing Load S2



= 415 V = 0.80 pu



Step 2: Calculate Equipment Impedances Using the patameters above and the equations outlined earlier in the methodology, the following impedances were calculated: Equipment

Resistance (Ω)

Reactance (Ω)

Generator G1

0.65462

9.35457

Generator Cable C1

0.00261

0.00413

11kV Standing Load S1

106.98947

69.10837

Motor M1

16.77752

61.02812

Motor Cable C2

0.1002

0.01725

Transformer TX1 (Primary Side)

0.60027

4.49762

Transformer Cable C3

0.01176

0.00576

415V Standing Load S2

0.22963

0.17223

Step 3: Referring Impedances 11kV will be used as the reference voltage. The only impedance that needs to be referred to this reference voltage is the 415V Standing Load (S2). Knowing that the transformer is set at principal tap, we can calculate the winding ratio and apply it to refer the 415V Standing Load impedance to the 11kV side:

The resistance and reactance of the standing load referred to the 11kV side is now, R = 161.33333 Ω and X = 121.00 Ω.

Step 4: Construct the Equivalent Circuit

Figure 4. Equivalent circuit for motor starting example

The equivalent circuit for the system is shown in the figure to the right. The "Near" Thevenin equivalent circuit is also shown, and we now calculate the equivalent load impedance

in the steady-state condition (i.e. without the motor and motor cable

impedances included):

Similarly the equivalent load impedance during motor starting (with the motor impedances included) can be calculated as as follows:

Step 5: Calculate the Initial Source EMF

Figure 5. "Near" Thevenin equivalent circuit for motor starting example

Assuming that there is nominal voltage at the 11kV bus in the steady-state condition, the initial generator emf can be calculated by voltage divider:

Vac

Step 6: Calculate System Voltages During Motor Start Now we can calculate the transient effects of motor starting on the system voltages. Firstly, the current supplied by the generator during motor start is calculated:

Next, the voltage at the 11kV bus can be found:

Vac (or 87.98% of nominal voltage) The voltage at the motor terminals can then be found by voltage divider:

Vac (or 87.92% of nominal voltage) The voltage at the low voltage bus is:

Vac, then referred to the LV side = 359.39Vac (or 86.60% of nominal voltage) Any other voltages of interest on the system can be determined using the same methods as above. Suppose that our maximum voltage drop at the motor terminals is 15%. From above, we have found that the voltage drop is 12.08% at the motor terminals. This is a slightly marginal result and it may be prudent to simulate the system in a software package to confirm the results.

Computer Software Motor starting is a standard component of most power systems analysis software (e.g. ETAP, PTW, ERAC, etc) and this calculation is really intended to be done using this software. The numerical calculation performed by the software should also solve the power flow problem through an iterative algorithm (e.g. such as Newton-Rhapson).

What Next?

If the results of the calculation confirm that starting the largest motor does not cause any unacceptable voltage levels within the system, then that's the end of it (or perhaps it could be simulated in a power systems analysis software package to be doubly sure!). Otherwise, the issue needs to be addressed, for example by: 

Reduce the motor starting current, e.g. via soft-starters, star-delta starters, etc



Reduce the source impedances, e.g. increase the size of the generator, transformer, supply cables, etc

The calculation should be performed iteratively until the results are acceptable.

Short Circuit Calculation Contents [hide]

1 Introduction 2 AC Short-Circuit Analysis 3 DC Short-Circuit Analysis 4 Trivia

Introduction Some of the related defined by the IEC's Electropedia:

Figure 1. 110 kV power line short-circuit

Figure 2. Short-Circuit Arc



Short-Circuit: accidental or intentional conductive path between two or more conductive parts forcing the electric potential differences between these conductive parts to be equal to or close to zero.



Short-Circuit Current: an over-current resulting from a short circuit due to a fault or an incorrect connection in an electric circuit.



Short-Circuit Operation: no-load operation with zero output voltage (Note – Zero output voltage can be obtained when the output terminals are short-circuited).



Line-to-Earth Short-Circuit: short-circuit between a line conductor and the Earth, in a solidly earthed neutral system or in an impedance earthed neutral system (Note – The shortcircuit can be established, for example, through an earthing conductor and an earth electrode).



Line-to-Line Short-Circuit: short-circuit between two or more line conductors, combined or not with a line-to-earth short-circuit at the same place



Short-Circuit Current Capability: the permissible value of the short-circuit current in a given network component for a specified duration.

AC Short-Circuit Analysis according to the IEC 60909

DC Short-Circuit Analysis according to the IEC 61660 according to the ANSI/IEEE 946

Trivia

Solar System Sizing Contents 1 Introduction o

1.1 Why do the calculation?

o

1.2 When to do the calculation? 2 Calculation Methodology 2.1 Step 1: Estimate Solar Irradiation at the Site

o 

2.1.1 Baseline Solar Irradiation Data



2.1.2 Solar Irradiation on an Inclined Plane



2.1.3 Solar Trackers



2.1.4 Non-Standard Applications

o

2.2 Step 2: Collect the Solar Power System Loads

o

2.3 Step 3: Construct a Load Profile

o

2.4 Step 4: Battery Capacity Sizing

o

2.5 Step 5: Estimate a Single PV Module's Output



2.5.1 Effective PV Cell Temperature



2.5.2 Standard Regulator

2.5.3 MPPT Regulator



2.6 Step 6: Size the PV Array

o 

2.6.1 Standard Regulator



2.6.2 MPPT Controller 3 Worked Example

o

3.1 Step 1: Estimate Solar Irradiation at the Site

o

3.2 Step 2 and 3: Collect Loads and Construct a Load Profile

o

3.3 Step 4: Battery Capacity Sizing

o

3.4 Step 5: Estimate a Single PV Module's Output

o

3.5 Step 6: Size the PV Array 4 Computer Software 5 What Next?

Introduction

Figure 1. Solar PV array

This calculation outlines the sizing of a standalone solar photovoltaic (PV) power system. Standalone PV systems are commonly used to supply power to small, remote installations (e.g. telecoms) where it isn't practical or cost-efficient to run a transmission line or have alternative generation such as diesel gensets. Although this calculation is biased towards standalone solar PV systems, it can also be used for hybrid systems that draw power from mixed sources (e.g. commercial PV, hybrid wind-PV systems, etc). Loads must be adjusted according to the desired amount that the solar PV system will supply. This calculation is based on crystalline silicon PV technology. The results may not hold for other types of solar PV technologies and the manufacturer's recommendations will need to be consulted.

Why do the calculation? This calculation should be done whenever a solar PV power system is required so that the system is able to adequately cater for the necessary loads. The results can be used to determine the ratings of the system components (e.g. PV array, batteries, etc).

When to do the calculation? The following pre-requisite information is required before performing the calculation:



Loads required to be ed by the solar PV system



Autonomy time or minimum tolerable downtime (i.e. if there is no sun, how long can the system be out of service?)



GPS coordinates of the site (or measurements of the solar insolation at the site)



Output voltage (AC or DC)

Calculation Methodology The calculation is loosely based on AS/NZS 4509.2 (2002) "Standalone power systems - System design guidelines". The methodology has the following six steps: 

Step 1: Estimate the solar irradiation available at the site (based on GPS coordinates or measurement)



Step 2: Collect the loads that will be ed by the system



Step 3: Construct a load profile and calculate design load and design energy



Step 4: Calculate the required battery capacity based on the design loads



Step 5: Estimate the output of a single PV module at the proposed site location



Step 6: Calculate size of the PV array

Step 1: Estimate Solar Irradiation at the Site

Figure 2. World solar irradiation map

The first step is to determine the solar resource availability at the site. Solar resources are typically discussed in of solar radiation, which is more or less the catch-all term for sunlight shining on a surface. Solar radiation consists of three main components: 

Direct or beam radiation is made up of beams of unscattered and unreflected light reaching the surface in a straight line directly from the sun



Diffuse radiation is scattered light reaching the surface from the whole sky (but not directly from the sun)



Albedo radiation is is light reflected onto the surface from the ground

Solar radiation can be quantitatively measured by irradiance and irradiation. Note that the are distinct - "irradiance" refers to the density of the power that falls on a surface (W / m2) and "irradiation" is the density of the energy that falls on a surface over some period of time such as an hour or a day (e.g. Wh / m2 per hour/day). In this section, we will estimate the solar radiation available at the site based on data collected in the past. However, it needs to be stressed that solar radiation is statistically random in nature and there is inherent uncertainty in using past data to predict future irradiation. Therefore, we will need to build in design margins so that the system is robust to prediction error.

Baseline Solar Irradiation Data The easiest option is to estimate the solar irradiation (or solar insolation) by inputting the GPS coordinates of the site into the NASA Surface Meteorology and Solar Resourcewebsite. For any given set of GPS coordinates, the website provides first estimates of the monthly minimum, average and maximum solar irradiation (in kWh / m2 / day) at ground level and at various tilt angles. Collect this data, choose an appropriate tilt angle and identify the best and worst months of the year in of solar irradiation. Alternatively, for US locations data from the National Solar Radiation Database can be used. The minimum, average and maximum daytime temperatures at the site can also be determined from the public databases listed above. These temperatures will be used later when calculating the effective PV cell temperature. Actual solar irradiation measurements can also be made at the site. Provided that the measurements are taken over a long enough period (or cross-referenced / combined with public data), then the measurements would provide a more accurate estimate of the solar irradiation at

the site as they would capture site specific characteristics, e.g. any obstructions to solar radiation such as large buildings, trees, mountains, etc.

Solar Irradiation on an Inclined Plane Most PV arrays are installed such that they face the equator at an incline to the horizontal (for maximum solar collection). The amount of solar irradiation collected on inclined surfaces is different to the amount collected on a horizontal surface. It is theoretically possible to accurately estimate the solar irradiation on any inclined surface given the solar irradiation on an horizontal plane and the tilt angle (there are numerous research papers on this topic, for example the work done by Liu and Jordan in 1960). However, for the practical purpose of deg a solar PV system, we'll only look at estimating the solar irradiation at the optimal tilt angle, which is the incline that collects the most solar irradiation. The optimal tilt angle largely depends on the latitude of the site. At greater latitudes, the optimal tilt angle is higher as it favours summertime radiation collection over wintertime collection. The Handbook of Photovoltaic Science and Engineering suggests a linear approximation to calculating the optimal tilt angle:

Where

is the optimal tilt angle (deg) is the latitude of the site (deg)

The handbook also suggests a polynomial approximation for the solar irradiation at the optimal tilt angle:

Where

is the solar irradiation on a surface at the optimal tilt angle (Wh / m2) is the solar irradiation on the horizontal plane (Wh / m2) is the optimal tilt angle (deg)

Alternatively, the estimated irradiation data on tilted planes can be sourced directly from the various public databases listed above.

Solar Trackers Solar trackers are mechanical devices that can track the position of the sun throughout the day and orient the PV array accordingly. The use of trackers can significantly increase the solar irradiation collected by a surface. Solar trackers typically increase irradiation by 1.2 to 1.4 times

(for 1-axis trackers) and 1.3 to 1.5 times (for 2-axis trackers) compared to a fixed surface at the optimal tilt angle.

Non-Standard Applications A solar irradiation loss factor should be used for applications where there are high tilt angles (e.g. vertical PV arrays as part of a building facade) or very low tilt angles (e.g. North-South horizontal trackers). This is because the the solar irradiation is significantly affected (detrimentally) when the angle of incidence is high or the solar radiation is mainly diffuse (i.e. no albedo effects from ground reflections). For more details on this loss factor, consult the standard ASHRAE 93, "Methods of testing to determine the thermal performance of solar collectors".

Step 2: Collect the Solar Power System Loads The next step is to determine the type and quantity of loads that the solar power system needs to . For remote industrial applications, such as metering stations, the loads are normally for control systems and instrumentation equipment. For commercial applications, such as telecommunications, the loads are the telecoms hardware and possibly some small area lighting for maintenance. For rural electrification and residential applications, the loads are typically domestic lighting and low-powered apppliances, e.g. computers, radios, small tv's, etc.

Step 3: Construct a Load Profile Refer to the Load Profile Calculation for details on how to construct a load profile and calculate the design load (

) and design energy (

). Typically, the "24 Hour Profile" method for

constructing a load profile is used for Solar Power Systems.

Step 4: Battery Capacity Sizing In a solar PV power system, the battery is used to provide backup energy storage and also to maintain output voltage stability. Refer to the Battery Sizing Calculation for details on how to size the battery for the solar power system.

Step 5: Estimate a Single PV Module's Output It is assumed that a specific PV module type (e.g Suntech STP070S-12Bb) has been selected and the following parameters collected: 

Peak module power,

(W-p)



Nominal voltage



Open circuit voltage



Optimum operating voltage

(Vdc) (Vdc) (Vdc)



Short circuit current

(A)



Optimum operating current



Peak power temperature coefficient



Manufacturer's power output tolerance

(A) (% per deg C) (%)

Manufacturers usually quote these PV module parameters based on Standard Test Conditions (STC): an irradiance of 1,000 W / m2, the standard reference spectral irradiance with Air Mass 1.5 (see the NREL site for more details) and a cell temperature of 25 deg C. Standard test conditions rarely prevail on site and when the PV module are installed in the field, the output must be derated accordingly.

Effective PV Cell Temperature Firstly, the average effective PV cell temperature at the installation site needs to be calculated (as it will be used in the subsequent calculations). It can be estimated for each month using AS\NZS 4509.2 equation 3.4.3.7:

Where

is the average effective PV cell temperature (deg C)

is the average daytime ambient temperature at the site (deg C)

Standard Regulator For a solar power system using a standard switched charge regulator / controller, the derated power output of the PV module can be calculated using AS\NZS 4509.2 equation 3.4.3.9(1):

Where

is the derated power output of the PV module using a standard switched charge

controller (W) is the daily average operating voltage (Vdc) is the module output current based on the daily average operating voltage, at the effective average cell temperature and solar irradiance at the site - more on this below (A) is the manufacturer's power output tolerance (pu) is the derating factor for dirt / soiling (Clean: 1.0, Low: 0.98, Med: 0.97, High: 0.92) To estimate

, you will need the IV characteristic curve of the PV module at the effective cell

temperature calculated above. For a switched regulator, the average PV module operating

voltage is generally equal to the average battery voltage less voltage drops across the cables and regulator.

MPPT Regulator For a solar power system using a Maximum Power Point Tracking (MPPT) charge regulator / controller, the derated power output of the PV module can be calculated using AS\NZS 4509.2 equation 3.4.3.9(2):

Where

is the derated power output of the PV module using an MPPT charge controller (W) is the nominal module power under standard test conditions (W) is the manufacturer's power output tolerance (pu) is the derating factor for dirt / soiling (Clean: 1.0, Low: 0.98, Med: 0.97, High: 0.92) is the temperature derating factor - see below (pu)

The temperature derating factor is determined from AS\NZS 4509.2 equation 3.4.3.9(1):

Where

is temperature derating factor (pu) is the Power Temperature Coefficient (% per deg C) is the average effective PV cell temperature (deg C) is the temperature under standard test conditions (typically 25 deg C)

Step 6: Size the PV Array The sizing of the PV array described below is based on the method outlined in AS/NZS 4509.2. There are alternative sizing methodologies, for example the method based on reliability in of loss of load probability (LLP), but these methods will not be further elaborated in this article. The fact that there is no commonly accepted sizing methodology reflects the difficulty of performing what is an inherently uncertain task (i.e. a prediction exercise with many random factors involved).

Standard Regulator The number of PV modules required for the PV array can be found by using AS\NZS 4509.2 equation 3.4.3.11(1):

Where

is the number of PV modules required is the derated power output of the PV module (W) is the total design daily energy (VAh)

is the oversupply co-efficient (pu) is the solar irradiation after all factors (e.g. tilt angle, tracking, etc) have been captured (kWh / m2 / day) is the coulombic efficiency of the battery (pu) The oversupply coefficient

is a design contingency factor to capture the uncertainty in

deg solar power systems where future solar irradiation is not deterministic. AS/NZS 4509.2 Table 1 recommends oversupply coefficients of between 1.3 and 2.0. A battery coulombic efficiency of approximately 95% would be typically used.

MPPT Controller The number of PV modules required for the PV array can be found by using AS\NZS 4509.2 equation 3.4.3.11(2):

Where

is the number of PV modules required is the derated power output of the PV module (W) is the total design daily energy (VAh) is the oversupply coefficient (pu) is the solar irradiation after all factors (e.g. tilt angle, tracking, etc) have been captured (kWh / m2 / day) is the efficiency of the PV sub-system (pu)

The oversupply coefficient

is a design contingency factor to capture the uncertainty in

deg solar power systems where future solar irradiation is not deterministic. AS/NZS 4509.2 Table 1 recommends oversupply coefficients of between 1.3 and 2.0. The efficiency of the PV sub-system

is the combined efficiencies of the charge regulator /

controller, battery and transmission through the cable between the PV array and the battery. This will depend on specific circumstances (for example, the PV array a large distance from the battery), though an efficiency of around 90% would be typically used.

Worked Example A small standalone solar power system will be designed for a telecommunications outpost located in the desert.

Step 1: Estimate Solar Irradiation at the Site From site measurements, the solar irradiation at the site during the worst month at the optimal title angle is 4.05 kWh/m2/day.

Step 2 and 3: Collect Loads and Construct a Load Profile

Figure 3. Load profile for this example

For this example, we shall use the same loads and load profile detailed in the Energy Load Profile Calculationexample. The load profile is shown in the figure right and the following quantities were calculated: 

Design load Sd = 768 VA



Design energy demand Ed = 3,216 VAh

Step 4: Battery Capacity Sizing For this example, we shall use the same battery sizes calculated in the Battery Sizing Calculation] worked example. The selected number of cells in series is 62 cells and the minimum battery capacity is 44.4 Ah.

Step 5: Estimate a Single PV Module's Output A PV module with the following characteristics is chosen: 

Peak module power,

W-p



Nominal voltage



Peak power temperature coefficient



Manufacturer's power output tolerance

Vdc % per deg C %

Suppose the average daytime ambient temperature is 40C. The effective PV cell temperature is:

deg C An MPPT controller will be used. The temperature derating factor is therefore:

Given a medium dirt derating factor of 0.97, the derated power output of the PV module is:

W

Step 6: Size the PV Array Given an oversupply coefficient of 1.1 and a PV sub-system efficiency of 85%, the number of PV modules required for the PV array for a MPPT regulator is:

10.9588 modules For this PV array, 12 modules are selected.

Computer Software It is recommended that the solar PV system sized in this calculation is simulated with computer software. For example, HOMER is a popular software package for simulating and optimising a distributed generation (DG) system originally developed by the National Renewable Energy Laboratory (NREL). Screenshots from HOMER software

PV Output

What Next?

Battery Output

With the sizing calculation completed, the solar PV equipment (PV array, batteries, charge controllers, etc) can be specified and a cost estimate or budget enquiry / requisition package issued. The approximate dimensions of the equipment (especially the PV array and batteries) can also be estimated and a design layout can be produced.

Low Frequency Induction Calculation Contents [hide]



1 Introduction

o

1.1 Why do the calculation?

o

1.2 When to do the calculation?



2 Calculation Methodology

o

2.1 Step 1: Data Gathering

o

2.2 Step 2: Define the Zone of Influence

o

2.3 Step 3: Define Pipeline Sections

o

2.4 Step 4: Calculate Effective Distances



2.4.1 Transmission Line Geometry



2.4.2 Effective Distances

o

2.5 Step 5: Calculate Pipeline Impedances

o

2.6 Step 6: Calculate Mutual Coupling Impedances

o

2.7 Step 7: Compute Load LFI

o



2.7.1 Allowable Load LFI Limits



2.7.2 Effect of Overhead Earth Wires and Counterpoise Earths 2.8 Step 8: Compute Fault LFI



2.8.1 Shielding Factor



2.8.2 Considerations for Calculating Mutual Coupling Impedances



2.8.3 Allowable Fault LFI Limits

o

2.9 Step 9: Analysis of Pipeline-to-Earth Touch Voltages (if necessary)

o

2.10 Step 10: Apply Mitigation Works (if necessary)



3 International Standards



4 Computer Software



5 What Next?



6 Selected References

Introduction Low frequency induction (LFI) in metal pipelines is a form of electromagnetic interference that occurs when high voltage transmission lines are run in parallel with metallic pipelines. The loaded phases on a transmission line and the pipeline act like single-turn windings on a large air-core transformer. Current flowing through the transmission line induces a voltage at the pipeline. During normal operation, each loaded phase of the transmission line induces a voltage on the pipeline. If the three-phases are balanced, then most of the induced voltage will cancel each other out, but the spatial assymetry of the phases on the transmission line will prevent the induced voltages from fully cancelling out. Thus a non-zero induced voltage results on the pipeline. This condition is usually called "Load LFI". During an earth fault condition, the phases of the transmission line are no longer balanced and as a result, a more significant voltage is induced on the pipeline. This condition is usually called "Fault LFI".

Why do the calculation? LFI calculations are typically done for personnel safety reasons, in order to ensure that induced voltages are not hazardous to someone in with the pipeline. In cases where such a situation is not possible, then an approach minimising the risk of electric shock could be followed. This could involve restricting access to the pipeline or using a probability-based methodology to estimate the risk of exposure, etc.

When to do the calculation?

The calculation should be done whenever HV transmission lines are installed in the vicinity of pipelines, and vice versa. Of particular concern is when the pipeline is run nearby and parallel to the transmission line for long distances. On the other hand, if a pipeline crosses the transmission line perpendicularly, then the magnitude of LFI would be low.

Calculation Methodology The LFI calculation has nine general steps: 

Step 1: Data Gathering



Step 2: Define the Zone of Influence



Step 3: Define Pipeline Sections



Step 4: Calculate Effective Distances



Step 5: Calculate Pipeline Impedances



Step 6: Calculate Mutual Coupling Impedances



Step 7: Compute Load LFI



Step 8: Compute Fault LFI



Step 9: Calculate Pipeline-to-Earth Touch Voltages (if necessary)



Step 10: Apply Mitigation Works (if necessary)

Step 1: Data Gathering Before beginning the calculation, the following data needs to be gathered: 

Plan layouts of pipeline(s) and transmission line(s), to scale with enough resolution to measure horizontal distances between pipeline and transmission line



General arrangement of transmission line tower or underground spatial arrangement



Pipeline data, e.g. diameter, metal resistivity, coating details, etc



Soil resistivity data around pipeline



Forecast (or actual) load currents in transmission line



Worst case prospective fault currents on transmission line

Step 2: Define the Zone of Influence Based on the plan layouts of the pipeline and transmission line routes, the first step is to define the zone(s) of influence in which you will perform the LFI study. This zone is typically a corridor where the pipeline and transmission line are run close together in parallel. As a general rule of thumb, the zone extends along this corridor until the horizontal separation between the pipeline and transmission line exceeds 1km. It is deemed that there is minimal LFI effect on the pipeline beyond a 1km pipeline-transmission line separation.

Step 3: Define Pipeline Sections Once the zone of influence has been defined, the transmission line or pipeline should be broken up into small sections and the horizontal separations calculated for each section. The length of the indivudal sections do not have to be constant and can vary along the the route, depending on the rate of change of the horizontal separation. For example, long section lengths can be applied when the pipeline and transmission line are roughly parallel. However, where the two lines converge, diverge or cross, smaller sectional lengths should be used (typically, a maximum ratio of 3:1 between the start of section and end of section separations is used to determine sectional length). A table showing the sectional lengths and horizontal distances can then be developed, for example:

Horizontal distance from phase A Section

Distance along

Section Length

pipeline (km)

(m)

to pipeline (m) Start

End

1

0.0

300

140

190

2

0.3

200

190

200

Step 4: Calculate Effective Distances The table we developed in Step 2 shows the horizontal separations between phase A and the pipeline at the start and end of each pipeline section. However, the transmission line will have three phases (and possibly two sets of conductors per phase) and the horizontal distances also do not take into the geometry of the transmission tower. Therefore, we'd like to further refine these distances. Ideally, we want a single effective distance between the pipeline and each phase (and if applicable, the earth wire). By using an effective distance, this makes it more convenient for us to calculate the induced voltages on a pipeline section. This effective distance should incorporate the following: 

The average horizontal distance along the pipeline section



The geometry of the transmission line towers (and the spatial geometry of the individual conductors on the tower)



An equivalent distance for parallel conductors of the same phase

Transmission Line Geometry

Figure 1. Double conductor tower example

In order to construct the effective distances, we first need to define the spatial geometry of the transmission line with respect to the pipeline. This could be the geometry of transmission line towers or the spatial arrangement of underground conductors. The figure to the right, showing a double conductor tower with two earth wires, gives an example of the kind of data that is required: 

L1 = Distance from pipeline to phase a



Lb = Distance from phase a to phase b



Lc = Distance from phase a to phase c



Lw = Distance from phase a to the earth wire



Laa = Distance between phase a double conductors



Lbb = Distance between phase b double conductors



Lcc = Distance between phase c double conductors



Ha = Height from pipeline to phase a



Hb = Height from pipeline to phase b



Hc = Height from pipeline to phase c



Hw = Height from pipeline to earth wire

Of course your data requirements may vary depending on the transmission line type, but you need enough data to fully describe the spatial relationships between the phase conductors and the pipeline geometrically.

Effective Distances As the horizontal distance between the transmission line and the pipeline is not necessarly constant along each section, we want to calculate an average horizontal distance for each line section. Typically, the geometric mean distance is used:

Where

is the effective horizontal distance between phase a and the pipeline is the horizontal distance (between phase a and the pipeline) at the start of the section (m) is the horizontal distance (between phase a and the pipeline) at the end of the section (m)

Similarly for double conductors arranged horizontally, we use the geomtric mean distance to obtain an effective distance between double conductors and the pipeline:

Where

is the effective horizontal distance between double conductors (of phase a) and the

pipeline (m) is the effective horizontal distance calculated above (m) is the horizontal distance between the two conductors of phase a (m) Note that the above show only horizontal distances. We can use simple Pythagoras to calculate the overall effective distance between phase a and the pipeline, taking into the vertical arrangement of the conductors (relative to the pipeline). Below, we do this for a tower line:

Where

is the overall effective distance between the phase a and the pipeline is the effective horizontal distance between double conductors (of phase a) and the pipeline (m) is the height from the pipeline to phase a (m)

The same process above is repeated to calculate the effective distances for the other phases and the earth wire (if applicable). The effective distances can be calculated also for other spatial conductor arrangements, using the geometric mean as a basis. Ultimately for each line section, we'd like to end up with only a single effective distance between the pipeline and a phase of the tower line.

Step 5: Calculate Pipeline Impedances To assess the safety of a t right-of-way installation, we want to calculate pipeline-to-earth touch voltages. However a buried pipeline cannot be treated like another overhead conductor in air because a pipeline has a finite impedance to earth that is distributed along its entire length. Therefore the open-circuit voltages induced in the pipeline that we calculated earlier are not equivalent to the pipeline-to-earth touch voltage. There are continuous leakages to earth along the pipeline and the open-circuit induced voltages can be up to 10 times higher than the pipeline-to-earth touch voltages. In order to calculate a more accurate pipeline-to-earth touch voltage, we need to consider the electrical characteristics of the pipeline. The pipeline impedances described in this section are simplified approximations of Sunde's method [5] and are based on Appendix G of CIGRE Guide 95 "Guide on the Influence of High Voltage AC Power Systems on Metallic Pipelines" [2]. Refer to Sunde's original work [5] for more details on accurately modelling pipeline and other buried conductor impedances. a) Pipeline longitudinal impedance For a buried and coated metallic pipeline, the longitudinal impedance per metre can be approximated as follows:

Where

is the pipeline longitudinal (or series) impedance (Ω / m) is the diamter of the pipeline (m) is the resistivity of the pipeline metal (Ω.m) is the resistivity of the soil (Ω.m) is the permeability of free space (H/m) is the relative permeability of the pipeline metal (H/m) is the nominal frequency of the transmission line (Hz)

b) Pipeline shunt ittance For a buried and coated metallic pipeline, the shut ittance per metre can be approximated as follows:

Where

is the pipeline shunt ittance (Ω - 1 / m) is the diameter of the pipeline (m) is the resistivity of the pipeline coating (Ω.m) is the thickness of the pipeline coating (m) is the relative permeability of the coating (H/m) is the permittivity of free space (F/m)

The pipeline shunt impedance is simply the reciprocal of the ittance ( that it is complex quantity):

c) Pipeline characteristic impedance

Where

is the pipeline characteristic impedance (Ω) is the pipeline longitudinal impedance (Ω / m) is the pipeline longitudinal conductance (Ω - 1 / m)

d) Pipeline effective length

Where

is the pipeline effective length (m) is the pipeline longitudinal impedance (Ω / m) is the pipeline longitudinal conductance (Ω - 1 / m)

Step 6: Calculate Mutual Coupling Impedances The mutual coupling impedance between a line conductor and the pipeline (with earth return) can be given by the general formula below (based on Carson's equations [4]):

Where

is the mutual impedance between the line conductor

and pipeline

is the equivalent distance between the line conductor

and pipeline

(Ω / km) (m)

is the nominal system frequency (Hz) is the depth of equivalent earth return given by:

Where

is the resistivity of the soil (Ω.m)

Where

is the resistivity of the soil (Ω.m)

Using the formula above, you can calculate the mutual impedances

,

and

,

between the pipeline and phase a, b and c of the transmission line respectively. To calculate the impedances in Ohms, multiply the mutual impedances by the sectional length of the pipeline.

Step 7: Compute Load LFI Load LFI results from either unbalanced load currents or spatial differences between the phase conductors relative to the pipeline. Given the load current phasors for the transmission line, the total open-circuit induced LFI voltage on the pipeline is simply the vector sum:

Where ,

is the overall induced load LFI voltage (V) and

are the load current for phase a, b and c respectively (A). Note that

these quantities are complex phasors ,

and

are the mutual coupling impedances between the pipeline and

phase a, b and c respectively for a section of the pipeline (Ω)

Allowable Load LFI Limits Induced voltages on pipelines represent are electric shock hazards. Because load LFI can be regarded as a continuous hazard (i.e. the hazard is always present), then the allowable pipelineto-earth touch voltage limits are lower than in the fault LFI case. Limits are typically in the range of 32V to 64V (see the section on international standards below for more guidance on allowable limits). Note that the open-circuit LFI voltage calculated earlier is higher than the pipeline-to-earth touch voltage as it doesn't take into any voltage leakages to earth along the pipeline. Therefore, if the load LFI voltage you have calculated is lower than the allowable limits, then no further analysis is necessary.

Effect of Overhead Earth Wires and Counterpoise Earths

Overhead earth wires and counterpoise earth conductors provide a shielding effect (since a voltage is induced in them and they in turn induce an opposing voltage in the pipeline). The interaction of the overhead earth wires or counterpoise earth conductors with the pipeline can be modelled and a shielding factor computed (more on this later).

Step 8: Compute Fault LFI During a balanced three-phase fault, the fault current will still be balanced across all three phases (i.e. vector sum of the faulted phase currents is close to zero). Therefore any induced voltage in the pipeline will be due primarily to the spatial assymetry of the transmission line relative to the pipeline, and this will generally be small. However, an unbalanced fault such as a line-to-earth or line-to-line fault will produce a fault current that is unbalanced and can induce much higher LFI voltages on the pipeline (until the fault is cleared). The case of a line-to-earth fault will induce the highest LFI voltage and is the type of fault that will be examined hereafter. The general formula for fault LFI is as follows:

Where

is the overall induced fault LFI voltage (V) is the earth fault current, expressed as a complex phasor (A) is the shielding factor from earth wires, counterpoise earth conductors, etc is the mutual coupling impedances between the pipeline and the faulted line for a section of the pipeline (Ω)

Shielding Factor The shielding factor is the shielding effect caused by earth wires, counterpoise earths and perhaps other metallic structures, which serves to lower the LFI voltage induced on the pipeline. There a number of mechanisms that bring about this shielding effect, for example: 

If there are overhead earth wires, then not all of the earth fault current will return to the source via the earth. Some of the fault current will return via the earth wires. The current flowing through the earth wire will induce a voltage on the pipeline opposed to the voltage induced by the faulted line.



There is the interaction between the faulted line and overhead earth wires, where the faulted line induces a voltage on the overhead earth wires, which in turn induce an opposing voltage on the pipeline.



There are similar inductive coupling interactions between the faulted line, the pipeline and counterpoise earths or other metallic structures located in the vicinity

For an overhead earth wire, the shielding factor can be calculated as follows:

Where

is the mutual coupling impedances between the faulted line and the earth wire (Ω) is the self impedance of the earth wire (Ω) is the mutual coupling impedances between the pipeline and the earth wire (Ω) is the mutual coupling impedances between the pipeline and the faulted line (Ω)

Considerations for Calculating Mutual Coupling Impedances Calculating the mutual coupling impedances between the pipeline and the faulted line,

,

depends on the phase of the faulted line and it's spatial orientation relative to the pipeline. You could calculate the mutual coupling impedance between the closest phase and the pipeline, which would represent the worst case scenario. Alternatively, you could calculate the mutual coupling impedance for a group of conductors (e.g. all three phases) by considering the geometric mean separation distance between the pipeline and the group of conductors. This will result in an induced LFI voltage that is an average of the conductor group. Similarly for groups of earth wires (e.g. two overhead earth wires), a geometric mean can be selected to represent the group rather than selecting a single wire, or modelling interactions between the wires, faulted line and the pipeline (which becomes increasingly complicated). impedances in Ohms, multiply the mutual impedances by the sectional length of the pipeline.

Allowable Fault LFI Limits Like the case with load LFI, allowable limits for fault LFI are typically stipulated to prevent electric shock hazards from injuring or killing personnel. Because fault LFI is temporary (lasting only until the fault is cleared), the allowable limits are normally higher than in the load LFI case. The limits are generally based on some kind risk analysis and are typically in the order of 500V to 1000V (see the section on international standards below for more guidance on allowable limits). Note that the open-circuit LFI voltage calculated earlier is higher than the pipeline-to-earth touch voltage as it doesn't take into any voltage leakages to earth along the pipeline. Therefore, if the fault LFI voltage you have calculated is lower than the allowable limits, then no further analysis is necessary.

Step 9: Analysis of Pipeline-to-Earth Touch Voltages (if necessary) If the open-circuit load or fault LFI voltage is above the permissible touch voltage, then the pipeline-to-earth touch voltages along each section of the pipeline need to be calculated. In order to calculate the pipeline-to-earth touch voltages, we need an equivalent circuit for the pipeline. A common approach is to model the pipeline as a lossy transmission line, with the following equivalent circuit for each pipeline section:

Where

is the induced LFI voltage on the pipeline section (Vac) is the longitudinal series ittance of the pipeline section (Ω - 1) is the shunt ittance of the pipeline section (Ω - 1)

For a pipeline with "n" linear sections, the overall equivalent circuit model is therefore:

Where

is the ittance of a pipeline shunt earthing conductor (Ω - 1). The inverse of the

pipeline characteristic impedance can be used if no shunt earthing conductors are installed at the ends of the pipeline. In the model above, shunt earthing conductors can be connected to any of the linear pipeline sections, modelled in series with the pipeline section shunt ittance. The equivalent circuit can now be readily analysed using Kirchhoff's laws and converted into a system of linear equations. The unknown pipeline-to-earth node voltages can then be solved using matrix operations. Depending on the number of line sections, you will probably need to use a computer program to solve this linear algebra problem.

Step 10: Apply Mitigation Works (if necessary) If the pipeline-to-earth touch voltages are still above the allowable limits, then the design of the right-of-way needs to be modified or mitigation works installed. Design modifications and mitigation works can include:



Installation of shunt earthing conductors on the pipeline to underground earthing systems, to allow LFI voltage to drain to earth along sections of the pipeline



Increasing the distance between the pipeline and the transmission line



Installation of overhead earth wires or counterpoise earthing conductors



Modifying the design of the pipeline, e.g. coating specification, diameter, etc



Installation of gradient control wires alongside the pipeline, typically of zinc

International Standards Most countries have their own standards for electromagnetic interference on pipelines. In Europe, EN 50443:2011 is the standard for low frequency induction, conductive coupling and capacitive coupling. This has also been adopted by the British Standard BS EN 50443:2011. In Australia, AS/NZS 4853:2000 stipulates the limits on pipeline-to-earth touch voltages. There are two main categories: Category A for pipelines with access to the public or unskilled staff, and Category B for pipelines with restricted access to skill personnel. For Category A, the load LFI limit is 32 Vac and fault LFI limit is between 32 and 350 Vac depending on the fault clearing time. For Category B, the load LFI limit is also 32 Vac, but the fault LFI limit is 1000 Vac (for faults cleared in less than 1s).

Computer Software The LFI calculation is greatly simplified by using a computer software package, especially for more complicated t rights-of-way. The following commercial software packages are among the most popular: 

SES Technologies CDEGS and in particular, the Right of Way module



PRCI Pipeline A/C Interference & Mitigation Toolbox



Elsyca IRIS

A free alternative for single pipeline and tower line rights-of-way: 

Sigma Power Low-Fi

What Next? The LFI calculation is typically done to confirm the pipeline and / or transmission line design and to determine if mitigation is required. If mitigation measures are required, then the next step would be to design and specify these mitigation works.

Selected References 

[1] AS/NZS 4853:2000, "Electrical hazards on metallic pipelines"



[2] CIGRE Guide 95, WG 36.02, "Guide on the Influence of High Voltage AC Power Systems on Metallic Pipelines", 1995



[3] Schlabbach, J., "Short-circuit Currents (IET Power and Energy Series 51)", 2005, IEE



[4] Tleis, N. D., "Power System Modelling and Fault Analysis", 2008, Elsevier Ltd



[5] Sunde, E. D., "Earth Conduction Effects in Transmission Systems", 1968, Dover Publications



[6] Carson, J., "Wave Propagation in Overhead Wires with Ground Return", 1926, Bell System Technology Journal, Vol 5, pp. 539-554

Battery Sizing Contents [hide]

1 Introduction

o

1.1 Why do the calculation?

o

1.2 When to do the calculation? 2 IEEE Definitions 3 Battery Characteristics and Types

o

3.1 Battery Components

o

3.2 Battery Lifespan

o

3.3 Battery Charging Stages



3.3.1 Depth of Discharge (DOD)

o

3.4 Determining battery state of charge

o

3.5 Amp-Hour rating & Capacity

o

3.6 Renewable Applications



3.6.1 Maintenance & Monitoring



3.6.2 Future Trends 4 Calculation Methodology

o

4.1 Step 1: Collect the battery loads

o

4.2 Step 2: Construct the Load Profile

o

4.3 Step 3: Select Battery Type

o

4.4 Step 4: Number of Cells in Series

o

4.5 Step 5: Determine Battery Capacity 5 Worked Example

o

5.1 Step 1 and 2: Collect Battery Loads and Construct Load Profile

o

5.2 Step 3: Select Battery Type

o

5.3 Step 4: Number of Cells in Series

o

5.4 Step 5: Determine Battery Capacity 6 Computer Software

o

6.1 Android App 7 What Next?

Introduction

Figure 1. Stationary batteries on a rack (courtesy of Power Battery)

This article looks at the sizing of batteries for stationary applications (i.e. they don't move). Batteries are used in many applications such as AC and DC uninterruptible power supply (UPS) systems, solar power systems, telecommunications, emergency lighting, etc. Whatever the application, batteries are seen as a mature, proven technology for storing electrical energy. In addition to storage, batteries are also used as a means for providing voltage for weak power systems (e.g. at the end of small, long transmission lines).

Why do the calculation? Sizing a stationary battery is important to ensure that the loads being supplied or the power system being ed are adequately catered for by the battery for the period of time (i.e. autonomy) for which it is designed. Improper battery sizing can lead to poor autonomy times, permanent damage to battery cells from over-discharge, low load voltages, etc.

When to do the calculation? The calculation can typically be started when the following information is known: 

Battery loads that need to be ed



Nominal battery voltage



Autonomy time(s)

IEEE Definitions IEEE Std. 485-1997 provides some definitions related to the battery sizing terminology:

battery duty cycle: The loads a battery is expected to supply for specified time periods. cell size: The rated capacity of a lead-acid cell or the number of positive plates in a cell. equalizing charge: A prolonged charge, at a rate higher than the normal float voltage, to correct any inequalities of voltage and specific gravity that may have developed between the cells during service. full float operation: Operation of a dc system with the battery, battery charger, and load all connected in parallel and with the battery charger supplying the normal dc load plus any charging current required by the battery. (The battery will deliver current only when the load exceeds the charger output.) period: An interval of time in the battery duty cycle during which the load is assumed to be constant for purposes of cell sizing calculations. rated capacity (lead-acid): The capacity assigned to a cell by its manufacturer for a given discharge rate, at a specified electrolyte temperature and specific gravity, to a given end-of-discharge voltage. valve-regulated lead-acid (VRLA) cell: A lead-acid cell that is sealed with the exception of a valve that opens to the atmosphere when the internal gas pressure in the cell exceeds atmospheric pressure by a preselected amount. VRLA cells provide a means for recombination of internally generated oxygen and the suppression of hydrogen gas evolution to limit water consumption. vented battery: A battery in which the products of electrolysis and evaporation are allowed to escape freely to the atmosphere. These batteries are commonly referred to as “flooded.”

Battery Characteristics and Types Battery Components Battery technology has not changed much in the last 100 years. The standard construction method involves flooding lead plates in sulfuric acid. The chemical reaction between the positively charged lead plate and the negatively charged acid allows the battery to store and “give” electricity. The thickness of the lead plate is closely related to the lifespan of the battery because of a factor called “Positive Grid Corrosion”. The positive lead plate gradually wears away over time. Thicker plates are used in deep cycle batteries. This usually translates to a longer battery life. Although plate thickness is not the only factor related to longer lifespan, it is the most critical variable.

Battery Lifespan Most of the loss incurred in charging and discharging batteries is due to internal resistance, which is eventually wasted as heat. Efficiency ratios are relatively high considering that most lead acid batteries are 85 to 95 percent efficient at storing the energy they receive. Deep cycle batteries used in renewable energy applications are designed to provide many years of reliable performance with proper care and maintenance. Proper maintenance and usage play a major role in battery lifespan. Toiling over your battery bank daily with complex gadgets and a gallon of distilled water, however, is not necessary. The most common causes of premature battery failure include loss of electrolyte due to heat or overcharging, undercharging, excessive vibration, freezing or extremely high temperatures, and using tap water among other factors

Battery Charging Stages There are three basic stages in charging a battery: bulk, absorption, and float. These signify different voltage and current variables involved in each stage of charging.  Bulk Charge: In the first stage of the process, current is sent to the batteries at the maximum safe rate, batteries will accept it until voltage is brought up to nearly 80-90 percent full charge level. There are limits on the amount of current the battery and/or wiring can take.  Absorption Charge: In the second stage, voltage peaks and stabilizes and current begins to taper off as internal resistance rises. The charge controller puts out maximum voltage at this stage.  Float Charge: This can also be referred to as trickle charging or a maintenance charge. In this stage, voltage is reduced to lower levels in order to reduce gassing and prolong battery life. The main purpose of this stage is basically to maintain the battery’s charge in a controlled manner. In Pulse Width Modulation (PWM) the charger sends small, short charging cycles or “pulses” when it senses small drops in voltage.

Depth of Discharge (DOD) The Depth of Discharge (DOD) is used to describe how deeply the battery is discharged. If the battery is 100% fully charged, it means the DOD of this battery is 0%. If the battery has delivered 30% of its energy, here are 70% energy reserved, the DOD of this battery is 30%. And if a battery is 100% empty, the DOD of this battery is 100%. DOD always can be treated as how much energy that the battery delivered.

Determining battery state of charge

There are a few ways to determine the state of charge on a battery, each with their own level of accuracy. As there is no direct method to measure a battery’s state of charge, there are numerous ways to go about it. One way to gauge a battery is by measuring its static voltage and comparing it to a standardized chart. This is the least accurate method, but it only involves an inexpensive digital meter. Another method of gauging the battery involves measuring the density or specific gravity of the sulfuric acid electrolyte. This is the most accurate test, yet it is only applicable to the flooded types. This method involves measuring the cell’s electrolyte density with a battery hydrometer. Electrolyte density is lower when the battery is discharged and higher as the cells are charged. The battery’s chemical reactions affect the density of the electrolyte at a constant rate that is predictable enough to get a good indication of the cell’s state of charge. Using an amp-hour meter one can also obtain an accurate indication of the battery’s state of charge. Amp-hour meters keep track of all power moving in and out of the battery by time, and the state of charge is determined by comparing flow rates.

Amp-Hour rating & Capacity All deep cycle batteries are classified and rated in amp-hours. Amp-hours is the term used to describe a standardized rate of discharge measuring current relative to time. It is calculated by multiplying amps and hours. The generally accepted rating time period for most manufacturers is 20 hours. This means that the battery will provide the rated amperage for about 20 hours until it is down to 10.5 volts or completely dead. Some battery manufacturers will use 100 hours as the standard to make them look better, yet it can be useful in long-term backup calculations.

Renewable Applications There are three main types of batteries that are commonly used in renewable energy systems, each with their own advantages and disadvantages. Flooded or “wet” batteries are the most cost efficient and the most widely used batteries in photovoltaic applications. They require regular maintenance and need to be used in a vented location, and are extremely well suited for renewable energy applications. Sealed batteries come in two varieties, the gel cell and Absorbed Glass Mat (AGM) type. The gel cell uses a silica additive in its electrolyte solution that causes it to stiffen or gel, eliminating some of the issues with venting and spillage. The Absorbed Glass Mat construction method suspends the electrolyte in close proximity with the plate’s active material. These batteries are sealed, requiring virtually no maintenance. They are more suitable for remote applications where regular maintenance is difficult, or enclosed locations where venting is an issue.  a) Flooded Lead Acid (FLA)

Flooded lead acid batteries are the most commonly used batteries, and have the longest track record in solar electric systems. They usually have the longest life and the lowest cost per amphour of any of the other choices. The downside is that they do require regular maintenance in the form of watering, equalizing charges and keeping the terminals clean. These cells are often referred to as “wet” cells, and they come in two varieties: the serviceable, and the maintenancefree type (which means they are designed to die as soon as the warranty runs out). The serviceable wet cells come with removable caps, and are the smarter choice, as they allow you to check their status with a hydrometer.  b) Gelled Electrolyte Sealed Lead Acid (GEL) Gel sealed batteries use silica to stiffen or “gel” the electrolyte solution, greatly reducing the gasses, and volatility of the cell. Since all matter expands and contracts with heat, batteries are not truly sealed, but are "valve regulated". This means that a tiny valve maintains slight positive pressure. AGM batteries are slowly phasing out gel technology, but there still are many applications for the gel cells. The recharge voltage for charging Gel cells are usually lower than the other styles of lead acid batteries, and should be charged at a slower rate. When they are charged too fast, gas pockets will form on the plates and force the gelled electrolyte away from the plate, decreasing the capacity until the gas finds its way to the top of the battery and recombines with the electrolyte.  c) Sealed Absorbed Glass Mat (AGM) Absorbed Glass Mat (AGM) is a class of valve-regulated lead acid battery (VLRA) in which the electrolyte is held in glass mats as opposed to freely flooding the plates. This is achieved by weaving very thin glass fibers into a mat to increase surface area enough to hold sufficient electrolyte for the lifetime of the cell. The advantages to using the AGM batteries are many, yet these batteries are typically twice the cost of their flooded-cell counterpart. On the plus side, these cells can hold roughly 1.5 times the amp hour capacity of a similar size flooded battery due to their higher power density. Another factor that improves their efficiency is the higher lead purity used in AGM cells. Because of their sandwich construction, each plate no longer has to its own weight. Their low internal resistance allows them to be charged and discharged much faster than other types. AGM cells function well in colder temperatures and are highly resistant to vibration. There are many advantages to using the AGM cells over their flooded counterpart that are beyond the scope of this article.

Maintenance & Monitoring

Proper maintenance and monitoring will greatly extend the life of your batteries. Flooded batteries need to be checked regularly to make sure electrolyte levels are full. The chemical reaction releases gases, as water molecules are split into hydrogen and oxygen. This, in turn, consumes water and creates the need to replace it regularly. Only distilled water should ever be used in batteries, and you should never add any kind of acid solution. The connections from battery to battery and to the charging and load circuits should always be kept clean and free of corrosion. Corrosion is created upon charging, when a slight acid mist forms as the electrolyte bubbles. Corrosion buildup will create a good deal of electrical resistance, eventually contributing to a shortened battery life and malfunctions. A good way to keep up on the terminals is to regularly clean them with a baking soda solution

Future Trends Companies world-wide are quickly adjusting to the increased global market for solar systems by developing batteries that are better suited for photovoltaic systems. At some distant point in the future, it is likely that lead-acid batteries will become extinct, as newer technologies in lithium ion and Nickel metal hydride continue to evolve. Because lead-acid batteries are under the hood of virtually every car, advancements in lead-acid technology, however are still being made. New developments in lead-acid technology usually originate in the auto industry. Efficiency ratings are constantly going up, as new sensors and improved materials are helping batteries achieve longer lifespan.

Calculation Methodology The calculation is based on a mixture of normal industry practice and technical standards IEEE Std 485 (1997, R2003) "Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications" and IEEE Std 1115 (2000, R2005) "Recommended Practice for Sizing NickelCium Batteries for Stationary Applications". The calculation is based on the ampere-hour method for sizing battery capacity (rather than sizing by positive plates). The focus of this calculation is on standard lead-acid or nickel-cium (NiCd) batteries, so please consult specific supplier information for other types of batteries (e.g. lithium-ion, nickelmetal hydride, etc). Note also that the design of the battery charger is beyond the scope of this calculation. There are five main steps in this calculation: 1) Collect the loads that the battery needs to 2) Construct a load profile and calculate the design energy (VAh) 3) Select the battery type and determine the characteristics of the cell

4) Select the number of battery cells to be connected in series 5) Calculate the required Ampere-hour (Ah) capacity of the battery

Step 1: Collect the battery loads The first step is to determine the loads that the battery will be ing. This is largely specific to the application of the battery, for example an AC UPS System or a Solar Power System.

Step 2: Construct the Load Profile Refer to the Load Profile Calculation for details on how to construct a load profile and calculate the design energy,

, in VAh.

The autonomy time is often specified by the Client (i.e. in their standards). Alternatively, IEEE 446, "IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications" has some guidance (particularly Table 3-2) for autonomy times. Note that IEEE 485 and IEEE 1115 refer to the load profile as the "duty cycle".

Step 3: Select Battery Type The next step is to select the battery type (e.g. sealed lead-acid, nickel-cium, etc). The selection process is not covered in detail here, but the following factors should be taken into (as suggested by IEEE): 

Physical characteristics, e.g. dimensions, weight, container material, intercell connections, terminals



application design life and expected life of cell



Frequency and depth of discharge



Ambient temperature



Charging characteristics



Maintenance requirements



Ventilation requirements



Cell orientation requirements (sealed lead-acid and NiCd)



Seismic factors (shock and vibration)

Next, find the characteristics of the battery cells, typically from supplier data sheets. The characteristics that should be collected include:



Battery cell capacities (Ah)



Cell temperature



Electrolyte density at full charge (for lead-acid batteries)



Cell float voltage



Cell end-of-discharge voltage (EODV).

Battery manufacturers will often quote battery Ah capacities based on a number of different EODVs. For lead-acid batteries, the selection of an EODV is largely based on an EODV that prevents damage of the cell through over-discharge (from over-expansion of the cell plates). Typically, 1.75V to 1.8V per cell is used when discharging over longer than 1 hour. For short discharge durations (i.e. <15 minutes), lower EODVs of around 1.67V per cell may be used without damaging the cell. Nickel-Cium (NiCd) don't suffer from damaged cells due to over-discharge. Typical EODVs for Ni-Cd batteries are 1.0V to 1.14V per cell.

Step 4: Number of Cells in Series The most common number of cells for a specific voltage rating is shown below: Rated Voltage

Lead-Acid

Ni-Cd

12V

6

9-10

24V

12

18-20

48V

24

36-40

125V

60

92-100

250V

120

184-200

However, the number of cells in a battery can also be calculated to more accurately match the tolerances of the load. The number of battery cells required to be connected in series must fall between the two following limits:

(1)

(2) where

is the maximum number of battery cells

is the minimum number of battery cells is the nominal battery voltage (Vdc) is the maximum load voltage tolerance (%) is the minimum load voltage tolerance (%) is the cell charging voltage (Vdc) is the cell end of discharge voltage (Vdc) The limits are based on the minimum and maximum voltage tolerances of the load. As a maximum, the battery at float voltage (or boost voltage if applicable) needs to be within the maximum voltage range of the load. Likewise as a minimum, the battery at its end of discharge voltage must be within the minimum voltage range of the load. The cell charging voltage depends on the type of charge cycle that is being used, e.g. float, boost, equalising, etc, and the maximum value should be chosen. Select the number of cells in between these two limits (more or less arbitrary, though somewhere in the middle of the min/max values would be most appropriate).

Step 5: Determine Battery Capacity The minimum battery capacity required to accommodate the design load over the specified autonomy time can be calculated as follows:

where

is the minimum battery capacity (Ah) is the design energy over the autonomy time (VAh) is the nominal battery voltage (Vdc) is a battery ageing factor (%) is a temperature correction factor (%) is a capacity rating factor (%) is the maximum depth of discharge (%)

Table 1. Temperature correction factors for vented lead-acid cells (from IEEE 485)

Select a battery Ah capacity that exceeds the minimum capacity calculated above. The battery discharge rate (C rating) should also be specified, approximately the duration of discharge (e.g. for 8 hours of discharge, use the C8 rate). The selected battery specification is therefore the Ah capacity and the discharge rate (e.g. 500Ah C10). An explanation of the different factors: Ageing factor captures the decrease in battery performance due to age. The performance of a lead-acid battery is relatively stable but drops markedly at latter stages of life. The "knee point" of its life vs performance curve is approximately when the battery can deliver 80% of its rated capacity. After this point, the battery has reached the end of its useful life and should be replaced. Therefore, to ensure that battery can meet capacity throughout its useful life, an ageing factor of 1.25 should be applied (i.e. 1 / 0.8). There are some exceptions, check with the manufacturer. For Ni-Cd batteries, the principles are similar to lead-acid cells. Please consult the battery manufacturer for suitable ageing factors, but generally, applying a factor of 1.25 is standard. For applications with high temperatures and/or frequent deep discharges, a higher factor of 1.43 may be used. For more shallower discharges, a lower factor of 1.11 can be used.



Temperature correction factor is an allowance to capture the ambient installation temperature. The capacity for battery cells are typicall quoted for a standard operating temperature of 25C and where this differs with the installation temperature, a correction factor must be applied. IEEE 485 gives guidance for vented lead-acid cells (see figure right), however for sealed lead-acid and Ni-Cd cells, please consult manufacturer recommendations. Note that high temperatures lower battery life irrespective of capacity and the correction factor is for capacity sizing only, i.e. you CANNOT increase battery life by increasing capacity.



Capacity rating factor s for voltage depressions during battery discharge. Lead-acid batteries experience a voltage dip during the early stages of discharge followed by some recovery. Ni-Cds may have lower voltages on discharge due to prolonged float charging (constant voltage). Both of these effects should be ed for by the capacity rating factor - please see the manufacturer's recommendations. For Ni-Cd cells, IEEE 1115 Annex C suggests that for float charging applications, Kt = rated capacity in Ah / discharge current in Amps (for specified discharge time and EODV).

Worked Example

Figure 2. Load profile for this example

Step 1 and 2: Collect Battery Loads and Construct Load Profile

The loads and load profile from the simple example in the Energy Load Profile Calculation will be used (see the figure right). The design energy demand calculated for this system is Ed = 3,242.8 VAh.

Step 3: Select Battery Type Vented lead acid batteries have been selected for this example.

Step 4: Number of Cells in Series Suppose that the nominal battery voltage is Vdc = 120Vdc, the cell charging voltage is Vc = 2.25Vdc/cell, the end-of-discharge voltage is Veod = 1.8Vdc/cell, and the minimum and maximum load voltage tolerances areVl,min = 10% and Vl,max = 20% respectively. The maximum number of cells in series is: The maximum number of cells in series is:

cells

cells

The minimum number of cells in series is:

cells

Step 5: Determine Battery Capacity Given a depth of discharge kdod = 80%, battery ageing factor ka = 25%, temperature correction factor for vented cells at 30 deg C of kt = 0.956 and a capacity rating factor of kc= 10%, the minimum battery capacity is:

Ah

Computer Software Some battery manufacturers (such as Alcad) also provide software programs to size batteries using basic input data such as load profiles, autonomies, etc. The software will size the batteries and will often also provide details regarding different battery rack (or enclosure) dimensions.

Android App If you have an android phone then we suggest using our app "Battery Sizing Tool".

What Next? Using the results of the battery sizing calculation, the approximate dimensions of the batteries can be estimated based on typical vendor information. This will assist in determining the size, number and dimensions of the battery racks or cabinets required, which can then be used as input into the equipment / room layouts. Preliminary budget pricing can also be estimated based on the calculation results.

Load Profile Contents [hide]

1 Introduction o

1.1 Why do the calculation?

1.2 When to do the calculation?

o

2 Calculation Methodology 2.1 Step 1: Prepare the Load List

o

2.1.1 Calculating the Consumed Load VA



o

2.2 Step 2: Construct the Load Profile

o

2.3 Step 3: Calculate Design Load and Energy Demand



2.3.1 Design Load



2.3.2 Design Energy Demand 3 Computer Software 4 What Next?

Introduction

Figure 1. Example of a load profile (using the autonomy method)

The energy load profile (hereafter referred to as simply "load profile") is an estimate of the total energy demanded from a power system or sub-system over a specific period of time (e.g. hours, days, etc). The load profile is essentially a two-dimensional chart showing the instantaneous load

(in Volt-Amperes) over time, and represents a convenient way to visualise how the system loads changes with respect to time. Note that it is distinct from the electrical load schedule - the load profile incorporates a time dimension and therefore estimates the energy demand (in kWh) instead of just the instantaneous load / power (in kW).

Why do the calculation? Estimating the energy demand is important for the sizing of energy storage devices, e.g. batteries, as the required capacity of such energy storage devices depends on the total amount of energy that will be drawn by the loads. This calculation is also useful for energy efficiency applications, where it is important to make estimates of the total energy use in a system.

When to do the calculation? A load profile needs to be constructed whenever the sizing of energy storage devices (e.g. batteries) is required. The calculation can be done once preliminary load information is available.

Calculation Methodology

Figure 2. Example of a load profile (using the 24 hour profile method)

There are two distinct methods for constructing a load profile: 1) Autonomy method is the traditional method used for backup power applications, e.g. UPS systems. In this method, the instantaneous loads are displayed over an autonomy time, which is the period of time that the loads need to be ed by a backup power system in the event of a power supply interruption.

2) 24 Hour Profile method displays the average or expected instantaneous loads over a 24 hour period. This method is more commonly associated with standalone power system applications, e.g. solar systems, or energy efficiency applications. Both methods share the same three general steps, but with some differences in the details: 

Step 1: Prepare the load list



Step 2: Construct the load profile



Step 3: Calculate the design load and design energy demand

Step 1: Prepare the Load List The first step is to transform the collected loads into a load list. It is similar in form to the electrical load schedule, but is a little simplified for the purpose of constructing a load profile. For instance, instead of categorising loads by their load duty (continuous, intermittent or standby), it is assumed that all loads are operating continuously. However, a key difference of this load list is the time period associated with each load item: In the autonomy method, the associated time period is called the "autonomy" and is the number of hours that the load needs to be ed during a power supply interruption. Some loads may only be required to ride through brief interruptions or have enough autonomy to shut down safely, while some critical systems may need to operate for as long as possible (up to several days). In the 24 hour profile method, the associated time period is represented in of "ON" and "OFF" times. These are the times in the day (in hours and minutes) that the load is expected to be switched on and then later turned off. For loads that operate continuously, the ON and OFF time would be 0:00 and 23:59 respectively. A load item may need to be entered in twice if it is expected to start and stop more than once a day.

Calculating the Consumed Load VA For this calculation, we are interested in the consumed apparent power of the loads (in VA). For each load, this can be calculated as follows:

Where

is the consumed load apparent power (VA)

is the consumed load power (W) is the load power factor (pu) is the load efficiency (pu)

Examples of load lists

24 hour profile method Autonomy method

Step 2: Construct the Load Profile The load profile is constructed from the load list and is essentially a chart that shows the distribution of the loads over time. The construction of the load profile will be explained by a simple example:

Figure 3. Load profile constructed for this example

Suppose the following loads were identified based on the Autonomy Method: Description

Load (VA)

Autonomy (h

DCS Cabinet

200

4

ESD Cabinet

200

4

Telecommunications Cabinet

150

6

Computer Console

90

2

The load profile is constructed by stacking "energy rectangles" on top of each other. An energy rectangles has the load VA as the height and the autonomy time as the width and its area is a visual representation of the load's total energy. For example, the DCS Cabinet has an energy rectangle of height 200 (VA) and width 4 (hours). The load profile is created by stacking the widest rectangles first, e.g. in this example it is the Telecommunications Cabinet that is stacked first. For the 24 Hour method, energy rectangles are constructed with the periods of time that a load is energised (i.e. the time difference between the ON and OFF times).

Step 3: Calculate Design Load and Energy Demand Design Load The design load is the instantaneous load for which the power conversion, distribution and protection devices should be rated, e.g. rectifiers, inverters, cables, fuses, circuit breakers, etc. The design can be calculated as follows:

Where

is the design load apparent power (VA) is the peak load apparent power, derived from the load profile (VA) is a contingency for future load growth (%) is a design margin (%)

It is common to make considerations for future load growth (typically somewhere between 5 and 20%), to allow future loads to be ed. If no future loads are expected, then this contingency can be ignored. A design margin is used to for any potential inaccuracies in estimating the loads, less-than-optimum operating conditions due to improper maintenance, etc. Typically, a design margin of 10% to 15% is recommended, but this may also depend on Client preferences. Example: From our simple example above, the peak load apparent power is 640VA. Given a future growth contingency of 10% and a design margin of 10%, the design load is: VA

Design Energy Demand The design energy demand is used for sizing energy storage devices. From the load profile, the total energy (in of VAh) can be computed by finding the area underneath the load profile curve (i.e. integrating instantaneous power with respect to time over the autonomy or 24h period). The design energy demand (or design VAh) can then be calculated by the following equation:

Where

is the design energy demand (VAh) is the total load energy, which is the area under the load profile (VAh) is a contingency for future load growth as defined above (%) is a design contingency as defined above (%)

Example: From our simple example above, the total load energy from the load profile is 2,680VAh. Given a future growth contingency of 10% and a design margin of 10%, the design energy demand is:

Vah

Computer Software The load profile is normally done manually with the help of a spreadsheet. Since it's such a simple calculation, it's hard to argue that special software is warranted.

What Next? The load profile is usually an intermediate step in part of a larger calculation (for example, AC UPS System or Solar Power System calculations). Alternatively, constructing a load profile may be the first step to analysing energy use, for example in energy efficiency applications.

AC UPS Sizing Contents

[hide]

1 Introduction o

1.1 Why do the calculation?

o

1.2 When to do the calculation? 2 Calculation Methodology

o

2.1 Step 1: Collect the AC UPS Loads

o

2.2 Step 2: Load Profile, Design Load and Design Energy

o

2.3 Step 3: Battery Sizing



2.3.1 Nominal Battery (or DC Link) Voltage



2.3.2 Number of Cells in Series 2.4 Step 4: UPS Sizing

o 

2.4.1 Overall UPS Sizing



2.4.2 Rectifier / Charger Sizing



2.4.3 Inverter Sizing



2.4.4 Static Switch Sizing 3 Worked Example

o

3.1 Step 1 and 2: Collect the AC UPS Loads and Construct Load Profile

o

3.2 Step 3: Battery Sizing

o

3.3 Step 4: UPS Sizing



3.3.1 Overall Sizing



3.3.2 Rectifier Sizing



3.3.3 Inverter and Static Switch Sizing 4 Template 5 Computer Software 6 What next?

Introduction This calculation deals with the sizing of an AC uninterruptible power supply (UPS) system (i.e. rectifier, battery bank and inverter). In this calculation, it is assumed that the AC UPS is a double conversion type with a basic system topology as shown in Figure 1.

Figure 1. AC UPS basic system topology

An external maintenance by switch and galvanic isolation transformers are other common additions to the basic topology, but these have been omitted from the system as they are irrelevant for the sizing calculation.

Why do the calculation?

An AC UPS system is used to critical / sensitive AC loads. It is typically a battery-backed system which will continue to operate for a specified amount of time (called the autonomy) after a main power supply interruption. AC UPS systems are also used as stable power supplies that provide a reasonably constant voltage and frequency output, independent of voltage input. This is particularly useful for sensitive electrical equipment on main power supplies that are prone to voltage / frequency fluctuations or instability. The AC UPS sizing calculation determines the ratings for the main AC UPS system components: 1) rectifier, 2) battery banks and 3) inverter. In some cases, the manufacturer will independently size the system and it is only necessary to construct the AC UPS load schedule and load profile. However the calculation results will also help determine the indicative dimensions of the equipment (e.g. size of battery banks) for preliminary layout purposes.

When to do the calculation? The AC UPS sizing calculation can be done when the following prerequisite information is known: 

UPS loads that need to be ed



Input / Output AC voltage



Autonomy time(s)



Battery type

Calculation Methodology The calculation procedure has four main steps: 1) Determine and collect the prospective AC UPS loads 2) Construct a load profile and determine the UPS design load (VA) and design energy (VAh) 3) Calculate the size of the stationary battery (number of cells in series and Ah capacity) 4) Determine the size of the inverter, rectifier/ charger and static switch

Step 1: Collect the AC UPS Loads The first step is to determine the type and quantity of loads that the AC UPS system will be expected to . For industrial facilities, this will typically be critical instrumentation and control loads such as the DCS and ESD processor and marshalling hardware, critical workstations

and HMI's, telecommunications equipment and sensitive electronics. The necessary load data should be available from the instrumentation and control engineers. For commercial facilities, UPS loads will mainly be server, data / network and telecommunications hardware.

Step 2: Load Profile, Design Load and Design Energy Refer to the Load Profile Calculation for details on how to construct a load profile, calculate the design load (

) and design energy (

). The "Autonomy method" for constructing load

profiles is typically used for AC UPS systems. The autonomy time is often specified by the Client (i.e. in their standards). Alternatively, IEEE 446, "IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications" has some guidance (particularly Table 3-2) for autonomy times. Sometimes a single autonomy time is used for the entire AC UPS load, which obviously makes the construction of the load profile easier to compute.

Step 3: Battery Sizing Refer to the Battery Sizing Calculation for details on how to size the battery for the AC UPS system. The following sections provide additional information specific to battery sizing for AC UPS applications.

Nominal Battery (or DC Link) Voltage The nominal battery / DC link voltage is often selected by the AC UPS manufacturer. However, if required to be selected, the following factors need to be considered: 

DC output voltage range of the rectifier – the rectifier must be able to output the specified DC link voltage



DC input voltage range of the inverter – the DC link voltage must be within the input voltage tolerances of the inverter. Note that the battery end of discharge voltage should be within these tolerances.



Number of battery cells required in series – this will affect the overall dimensions and size of the battery rack. If physical space is a constraint, then less batteries in series would be preferable.



Total DC link current (at full load) – this will affect the sizing of the DC cables and inter-cell battery links. Obviously the smaller the better.

In general, the DC link voltage is usually selected to be close to the nominal output voltage.

Number of Cells in Series The number of battery cells required to be connected in series must be between the two following limits:

(1)

(2) where Nmax is the maximum number of battery cells Nmin is the minimum number of battery cells Vdc is the nominal battery / DC link voltage (Vdc) Vi,max is the inverter maximum input voltage tolerance (%) Vi,min is the inverter minimum input voltage tolerance (%) Vf is the nominal cell float (or boost) voltage (Vdc) Veod is the cell end of discharge voltage (Vdc) The limits are based on the input voltage tolerance of the inverter. As a maximum, the battery at float voltage (or boost if applicable) needs to be within the maximum input voltage range of the inverter. Likewise as a minimum, the battery at its end of discharge voltage must be within the minimum input voltage range of the inverter. Select the number of cells in between these two limits (more or less arbitrary, though somewhere in the middle of the min/max values would be appropriate).

Step 4: UPS Sizing Overall UPS Sizing Most of the time, all you need to provide is the overall UPS kVA rating and the UPS vendor will do the rest. Given the design load (

in VA or kVA) calculated in Step 2, select an overall UPS

rating that exceeds the design load. Vendors typically have standard UPS ratings, so it is possible to simply select the first standard rating that exceeds the design load. For example, if the design load 12kVA, then the next size unit (e.g. 15kVA UPS) would be selected.

Rectifier / Charger Sizing The rectifier / charger should be sized to supply the inverter at full load and also charge the batteries (at the maximum charge current). The design DC load current can be calculated by:

where IL,dc is the design DC load current (full load) (A) S is the selected UPS rating (kVA) Vdc is the nominal battery / DC link voltage (Vdc) The maximum battery charging current can be computed as follows:

where Ic is the maximum DC charge current (A) C is the selected battery capacity (Ah) kl is the battery recharge efficiency / loss factor (typically 1.1) (pu) tc is the minimum battery recharge time (hours) The total minimum DC rectifier / charger current is therefore:

Select the next standard rectifier / charger rating that exceeds the total minimum DC current above.

Inverter Sizing The inverter must be rated to continuously supply the UPS loads. Therefore, the inverter can be sized using the design AC load current (based on the selected UPS kVA rating). For a three-phase UPS:

For a single-phase UPS:

where IL is the design AC load current (full load) (A) S is the selected UPS rating (kVA) Vo is the nominal output voltage (line-to-line voltage for a three phase UPS) (Vac) Select the next standard inverter rating that exceeds the design AC load current.

Static Switch Sizing

Like the inverter, the static switch must be rated to continuously supply the UPS loads. Therefore, the static switch can be sized using the design AC load current (as above for the inverter sizing).

Worked Example Step 1 and 2: Collect the AC UPS Loads and Construct Load Profile

Figure 2. Load profile for this example

For this example, we shall use the same loads and load profile detailed in the Energy Load Profile Calculationexample. The load profile is shown in the figure right and the following quantities were calculated: 

Design load Sd = 768 VA



Design energy demand Ed = 3,216 VAh

Step 3: Battery Sizing For this example, we shall use the same battery sizes calculated in the Battery Sizing Calculation worked example. The selected number of cells in series is 62 cells and the minimum battery capacity is 44.4 Ah. A battery capacity of 50 Ah is selected.

Step 4: UPS Sizing Overall Sizing Given the design load of 768 VA, then a 1 kVA UPS would be appropriate.

Rectifier Sizing Given a nominal dc link voltage of 120Vdc, the design DC load current is:

A Suppose the minimum battery recharge time is 2 hours and a recharge efficiency factor of 1.1 is used. The maximum battery charging current is:

A Therefore the total minimum DC rectifier / charger current is:

A A DC rectifier rating of 40A is selected.

Inverter and Static Switch Sizing Suppose the nominal output voltage is 240Vac. The design AC load current is:

A An inverter and static switch rating of 5A is selected.

Template A professional, fully customisable Excel spreadsheet template of the AC UPS calculation can be purchased from Tradebit. The template is based on the calculation procedure described in this page and includes the following features:



Load schedule and automatic load profile generation



Battery sizing



UPS component sizing (e.g. rectifier, inverter, etc)

UPS Conf



Computer Software Template A professional, fully customisable Excel spreadsheet template of the AC UPS calculation can be purchased from Tradebit. The template is based on the calculation procedure described in this page and includes the following features: 

Load schedule and automatic load profile generation



Battery sizing



UPS component sizing (e.g. rectifier, inverter, etc) Screenshots from AC UPS Template

UPS Configuration

Load Profile

Battery Sizing

Preliminary sizing is normally done manually. Notwithstanding this, many AC UPS manufacturers provide sizing tools as part of their service package (for example, see the APC online UPS selector tool)

What next? Using the results of the UPS sizing calculation, the approximate dimensions of the batteries and UPS cabinet can be estimated based on typical vendor information. This will assist in developing the equipment / room layouts. Preliminary budget pricing can also be estimated based on the calculation results.

AC Reactance Typical AC reactances for copper and aluminium insulated cables operating at 50Hz are based on values given in AS/NZS 3008.1.

Multicore Cables AC Reactance (Ω\km) Size (mm2)

PVC

XLPE EPR

Circular

(1)

Shaped

(1)

Circular

(1)

Shaped

(1)

1

0.119

-

0.139

0.114

-

1.5

0.111

-

0.129

0.107

-

2.5

0.102

-

0.118

0.0988

-

4

0.102

-

0.11

0.093

-

6

0.0967

-

0.104

0.0887

-

10

0.0906

-

0.0967

0.084

-

16

0.0861

0.0794

0.0913

0.0805

0.0742

25

0.0853

0.0786

0.0895

0.0808

0.0744

35

0.0826

0.0761

0.0863

0.0786

0.0725

50

0.0797

0.0734

0.0829

0.0751

0.0692

70

0.077

0.071

0.0798

0.0741

0.0683

95

0.0766

0.0706

0.079

0.0725

0.0668

120

0.0743

0.0685

0.0765

0.0713

0.0657

150

0.0745

0.0687

0.0765

0.0718

0.0662

185

0.0744

0.0686

0.0762

0.072

0.0663

240

0.0735

0.0678

0.0751

0.0709

0.0653

300

0.0732

0.0675

0.0746

0.0704

0.0649

400

0.0728

0.0671

0.074

0.0702

0.0647

500

0.0723

0.0666

0.0734

0.07

0.0645

Note (1): Circular or shaped refers to the conductor's cross-sectional shape

Single Core Cables AC Reactance (Ω\km) Size (mm2)

PVC Flat

(1)

EPR Trefoil

Flat

(1)

XLPE Trefoil

Flat

(1)

Trefoil

1

0.184

0.168

0.194

0.179

0.181

0.166

1.5

0.172

0.157

0.183

0.167

0.17

0.155

2.5

0.159

0.143

0.168

0.153

0.156

0.141

4

0.152

0.137

0.157

0.142

0.146

0.131

6

0.143

0.128

0.148

0.133

0.138

0.123

10

0.134

0.118

0.138

0.123

0.129

0.114

16

0.126

0.111

0.13

0.114

0.122

0.106

25

0.121

0.106

0.125

0.109

0.118

0.102

35

0.117

0.101

0.12

0.104

0.113

0.0982

50

0.111

0.0962

0.114

0.0988

0.108

0.0924

70

0.107

0.0917

0.109

0.0941

0.104

0.0893

95

0.106

0.0904

0.108

0.0924

0.102

0.0868

120

0.102

0.087

0.104

0.0889

0.0996

0.0844

150

0.102

0.0868

0.104

0.0885

0.0996

0.0844

185

0.101

0.0862

0.103

0.0878

0.0988

0.0835

240

0.0999

0.0847

0.101

0.0861

0.097

0.0818

300

0.0991

0.0839

0.1

0.0852

0.0961

0.0809

400

0.0982

0.0829

0.0993

0.0841

0.0955

0.0802

500

0.0973

0.082

0.0983

0.083

0.0948

0.0796

630

0.0952

0.08

0.0961

0.0809

0.094

0.0787

Note (1): Single core cables are laid flat and touching Back to Low Voltage Cable Data Reference

AC Resistance Typical AC resistances for copper and aluminium insulated cables operating at 50Hz are based on values given in AS/NZS 3008.1. Contents [hide]

1 Multicore Cables o

1.1 Copper Conductors

o

1.2 Aluminium Conductors 2 Single Core Cables

Multicore Cables Copper Conductors Note that for tinned copper conductors, a scaling factor of 1.01 should be applied. AC Resistance (Ω\km) of Multicore Copper Cables Size (mm2)

Circular Conductors

Shaped Conductors

45oC

60oC

75oC

90oC

110oC

45oC

60oC

75oC

90oC

1

23.3

24.5

25.8

27

28.7

-

-

-

-

1.5

14.9

15.7

16.5

17.3

18.4

-

-

-

-

2.5

8.14

8.57

9.01

9.45

10

-

-

-

-

4

5.06

5.33

5.61

5.88

6.24

-

-

-

-

6

3.38

3.56

3.75

3.93

4.17

-

-

-

-

10

2.01

2.12

2.23

2.33

2.48

-

-

-

-

16

1.26

1.33

1.4

1.47

1.56

1.26

1.33

1.4

1.47

25

0.799

0.842

0.884

0.927

0.984

0.799

0.842

0.884

0.927

35

0.576

0.607

0.638

0.669

0.71

0.576

0.607

0.638

0.669

50

0.426

0.449

0.471

0.494

0.524

0.426

0.448

0.471

0.494

70

0.295

0.311

0.327

0.343

0.364

0.295

0.311

0.327

0.342

95

0.214

0.225

0.236

0.248

0.262

0.213

0.224

0.236

0.247

120

0.17

0.179

0.188

0.197

0.209

0.17

0.179

0.187

0.196

150

0.139

0.146

0.153

0.16

0.17

0.138

0.145

0.153

0.16

185

0.112

0.118

0.123

0.129

0.136

0.111

0.117

0.123

0.128

240

0.087

0.0912

0.0955

0.0998

0.105

0.0859

0.0902

0.0945

0.0988

300

0.0712

0.0745

0.0778

0.0812

0.0852

0.0698

0.0732

0.0766

0.08

400

0.058

0.0605

0.063

0.0656

0.0685

0.0563

0.0589

0.0615

0.0641

500

0.0486

0.0506

0.0525

0.0544

0.0565

0.0465

0.0485

0.0508

0.0526

Aluminium Conductors AC Resistance (Ω\km) of Multicore Aluminium Cables Size (mm2)

Circular Conductors

Shaped Conductors

45oC

60oC

75oC

90oC

45oC

60oC

75oC

90oC

16

2.1

2.22

2.33

2.45

2.1

2.22

2.33

2.45

25

1.32

1.39

1.47

1.54

1.32

1.39

1.47

1.54

35

0.956

1.01

1.06

1.11

0.956

1.01

1.06

1.11

50

0.706

0.745

0.784

0.822

0.706

0.745

0.783

0.822

70

0.488

0.515

0.542

0.569

0.488

0.515

0.542

0.568

95

0.353

0.373

0.392

0.411

0.353

0.372

0.392

0.411

120

0.28

0.295

0.31

0.325

0.279

0.295

0.31

0.325

150

0.228

0.241

0.253

0.265

0.228

0.24

0.253

0.265

185

0.182

0.192

0.202

0.212

0.182

0.192

0.202

0.211

240

0.14

0.148

0.155

0.162

0.139

0.147

0.154

0.162

300

0.113

0.119

0.125

0.131

0.112

0.118

0.124

0.13

400

0.0897

0.0943

0.0988

0.103

0.0886

0.0932

0.0978

0.102

500

0.073

0.0765

0.08

0.0835

0.0716

0.0752

0.0788

0.0824

Single Core Cables AC Resistance (Ω\km) of Single Core Cables Size (mm2)

Copper Conductors (1)

Aluminium Conductors 45oC

60oC

75oC

90oC

45oC

60oC

75oC

90oC

110oC

1

-

-

-

-

23.3

24.5

25.8

27

28.7

1.5

-

-

-

-

14.9

15.7

16.5

17.3

18.4

2.5

-

-

-

-

8.14

8.57

9.01

9.45

10

4

-

-

-

-

5.06

5.33

5.61

5.88

6.24

6

-

-

-

-

3.38

3.56

3.75

3.93

4.17

10

-

-

-

-

2.01

2.12

2.23

2.33

2.48

16

2.1

2.22

2.33

2.45

1.26

1.33

1.4

1.47

1.56

25

1.32

1.39

1.47

1.54

0.799

0.842

0.884

0.927

0.984

35

0.956

1.01

1.06

1.11

0.576

0.607

0.638

0.668

0.71

50

0.706

0.745

0.783

0.822

0.426

0.448

0.471

0.494

0.524

70

0.488

0.515

0.542

0.568

0.295

0.311

0.327

0.342

0.363

95

0.353

0.372

0.392

0.411

0.213

0.225

0.236

0.247

0.262

120

0.279

0.295

0.31

0.325

0.17

0.179

0.188

0.197

0.208

150

0.228

0.24

0.253

0.265

0.138

0.145

0.153

0.16

0.169

185

0.182

0.192

0.202

0.212

0.111

0.117

0.123

0.129

0.136

240

0.14

0.147

0.155

0.162

0.0862

0.0905

0.0948

0.0991

0.105

300

0.113

0.119

0.125

0.13

0.0703

0.0736

0.077

0.0803

0.0846

400

0.089

0.0936

0.0981

0.103

0.0569

0.0595

0.062

0.0646

0.0677

500

0.0709

0.0744

0.0779

0.0813

0.0467

0.0487

0.0506

0.0525

0.0547

630

0.0571

0.0597

0.0623

0.0649

0.0389

0.0404

0.0418

0.0432

0.0448

Note (1): for tinned copper conductors, a scaling factor of 1.01 should be applied.

American Wire Gauge Area

Diameter

AWG / kcmil mm2

kcmil

mm

inch

20

0.518

1.02

0.812

0.0320

19

0.653

1.29

0.912

0.0359

18

0.823

1.62

1.024

0.0403

17

1.04

2.05

1.15

0.0453

16

1.31

2.58

1.291

0.0508

15

1.65

3.26

1.45

0.0571

14

2.08

4.11

1.628

0.0641

13

2.62

5.18

1.828

0.072

12

3.31

6.53

2.053

0.0808

11

4.17

8.23

2.305

0.0907

10

5.26

10.4

2.588

0.1019

9

6.63

13.1

2.906

0.1144

8

8.37

16.5

3.264

0.1285

7

10.5

20.8

3.665

0.1443

6

13.3

26.3

4.115

0.162

5

16.8

33.1

4.621

0.1819

4

21.2

41.7

5.189

0.2043

3

26.7

52.6

5.827

0.2294

2

33.6

66.4

6.544

0.2576

1

42.4

83.7

7.348

0.2893

1/0

53.5

106

8.252

0.3249

2/0

67.4

133

9.266

0.3648

3/0

85

168

10.404

0.4096

4/0

107

212

11.684

0.46

250

127

250

12.700

0.5000

300

152

300

13.912

0.5477

350

177

350

15.027

0.5916

400

203

400

16.064

0.6325

500

253

500

17.960

0.7071

600

304

600

19.675

0.7746

700

355

700

21.251

0.8367

750

380

750

21.997

0.8660

800

405

800

22.718

0.8944

900

456

900

24.096

0.9487

1000

507

1000

25.400

1.0000

1250

633

1250

28.398

1.1180

1500

760

1500

31.108

1.2247

1750

887

1750

33.601

1.3229

2000

1013

2000

35.921

1.4142

Category: Cables

Cable Code Designation Code designations for cables A cable code of 2 - 4 letters is used to descriebe the construction. Additional abbrevation for instrumentation cables: Collective screen = (c) Individual pair or triple screen = (i) The interpretation (per letter) can be read from the table below: 1st. letter: Insulation

2nd. letter: Bedding/Inner sheath

3rd. letter: Armouring/Screen

4th. letter: Outer sheath

A

Fibre, tight cladded

A

Aluminium (optional with corrosion protection)

A

Strength member yarn

A

Yarn + bitumen

B

Fire resistant tape + insulation (Halogenfree)

B

Corrogated aluminium (o.w.c.p.)

B

Steel tapes, 2 off

B

Hydrocarbon resistant sehath

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

C

Galvanized steel wire braid

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

D

Impregnated paper Drip free

D

Aluminium + Plastics

D

Oil filled cable reinforcement (Longitudinal / Transverse)

D

E

Polyethylene - PE Polypropylene - PP

E

Polyethylene - PE Polypropylene - PP

E

Oil filled cable reinforcement (Transverse only)

E

Polyethylene - PE Polypropylene - PP

F

PE or PP + filling compound

F

Bedding or taping (Halogen-free)

F

Flat steel wire armour

F

Semi-conducting PE

G

Polyamid - PA

G

G

G

PE + PA

H

Chlorosulphonated polyethylene - CSP

H

Chlorosulphonated polyethylene - CSP

H

Steel tape + steel wires

H

Chlorosulphonated polyethylene - CSP

I

Thermoplastic compound (Halogenfree)

I

Thermoplastic compound (Halogenfree)

I

Steel tapes, 4 off

I

Thermoplastic compound (Halogenfree)

K

Paper

K

Lead

K

Steel wire, plastics or rubber coated

K

Lead

L

Air + plastics (Coaxial cable)

L

Aluminium laminate + plastics sheath

L

Aluminium (laminated to outer jacket)

L

M

Expanded PE or PP +

M

Polyester

M

M

Polyester

filling compound N

Impregnated paper

N

Polyurethane

N

Steel (laminated to outer jacket)

N

O

Impregnated paper, oilfilled cable

O

Lead + Plastics

O

Copper wire braid (Tinned or bare)

O

P

Polyvinylchloride PVC

P

Polyvinylchloride PVC

P

Phosphorbronze wire braid

P

Q

Fibre in loose tube

Q

Q

Steel wires + counter steel tape (optional)

Q

R

Ethylenepropylene rubber - EPR

R

Ethylenepropylene rubber - EPR

R

Steel wires (round) + filling compound

R

Ethylenepropylene rubber - EPR

S

Silicone rubber

S

Bedding or taping + concentric conductor

S

Concentric conductor (Screen)

S

Silicone rubber

T

Cross-linked polyethylene XLPE

T

PE + aluminium wire + steel tape

T

T

Cross-linked polyethylene XLPE

U

Halogen-free thermoset compound EMA or EVA

U

Halogen-free thermoset compound EMA or EVA

U

U

Halogen-free thermoset compound EMA or EVA

V

Fibre, slotted core

V

Aluminium screen

V

Double wire armour (two layers)

V

Other halogen-free thermoset materials

W

Other materials

W

Other materials

W

Catenary wire

W

Other materials

X

No insulation

X

No bedding or equivalent

X

No armour

X

No sheath7

Y

Screen

Y

Y

Z

Flour plastics

Z

Z

Y Z

Flour plastics PTFE / FEP

Source: Draka Norsk Kabel

Code designation according to the VDE

Polyurethane

Polyvinylchloride PVC

Flour plastics

Cable codes according to the VDE

Cable Code Designation (according to the VDE) Code designations for cables A cable code of 2 - 4 letters is used to descriebe the construction. Additional abbrevation for instrumentation cables: Collective screen = (c) Individual pair or triple screen = (i) The interpretation (per letter) can be read from the table below: 1st. letter: Insulation

2nd. letter: Bedding/Inner sheath

3rd. letter: Armouring/Screen

4th. letter: Outer sheath

A

Fibre, tight cladded

A

Aluminium (optional with corrosion protection)

A

Strength member yarn

A

Yarn + bitumen

B

Fire resistant tape + insulation (Halogenfree)

B

Corrogated aluminium (o.w.c.p.)

B

Steel tapes, 2 off

B

Hydrocarbon resistant sehath

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

C

Galvanized steel wire braid

C

Polychloroprene (Neoprene) P, or chlorinated polyethylene - E

D

Impregnated paper Drip free

Oil filled cable reinforcement (Longitudinal / Transverse)

D

E

Polyethylene - PE Polypropylene - PP

D

Aluminium + Plastics

D

E

Polyethylene - PE Polypropylene - PP

E

Oil filled cable reinforcement

E

Polyethylene - PE Polypropylene - PP

(Transverse only) F

PE or PP + filling compound

F

Bedding or taping (Halogen-free)

Flat steel wire armour

F

Semi-conducting PE

G

Polyamid - PA

G

G

G

PE + PA

H

Chlorosulphonated polyethylene - CSP

H

Chlorosulphonated polyethylene - CSP

H

Steel tape + steel wires

H

Chlorosulphonated polyethylene - CSP

I

Thermoplastic compound (Halogenfree)

I

Thermoplastic compound (Halogenfree)

I

Steel tapes, 4 off

I

Thermoplastic compound (Halogenfree)

K

Paper

K

Lead

K

Steel wire, plastics or rubber coated

K

Lead

L

Air + plastics (Coaxial cable)

L

Aluminium laminate + plastics sheath

L

Aluminium (laminated to outer jacket)

L

M

Expanded PE or PP + filling compound

M

Polyester

M

N

Impregnated paper

N

Polyurethane

N

O

Impregnated paper, oilfilled cable

O

Lead + Plastics

P

Polyvinylchloride PVC

P

Polyvinylchloride PVC

Q

Fibre in loose tube

Q

R

Ethylenepropylene rubber - EPR

R

S

Silicone rubber

T

F

M

Polyester

Steel (laminated to outer jacket)

N

Polyurethane

O

Copper wire braid (Tinned or bare)

O

P

Phosphorbronze wire braid

P

Q

Steel wires + counter steel tape (optional)

Q

Ethylenepropylene rubber - EPR

R

Steel wires (round) + filling compound

R

Ethylenepropylene rubber - EPR

S

Bedding or taping + concentric conductor

S

Concentric conductor (Screen)

S

Silicone rubber

Cross-linked polyethylene XLPE

T

PE + aluminium wire + steel tape

T

T

Cross-linked polyethylene XLPE

U

Halogen-free thermoset compound EMA or EVA

U

Halogen-free thermoset compound EMA or EVA

U

U

Halogen-free thermoset compound EMA or EVA

V

Fibre, slotted core

V

Aluminium screen

V

Double wire armour (two layers)

V

Other halogen-free thermoset materials

W

Other materials

W

Other materials

W

Catenary wire

W

Other materials

X

No insulation

X

No bedding or equivalent

X

No armour

X

No sheath7

Polyvinylchloride PVC

Y Z

Flour plastics PTFE / FEP

Y

Screen

Y

Y

Z

Flour plastics

Z

Z

Flour plastics

Code designation according to the VDE

Cable codes according to the VDE

Cable Colour Code Power cable insulation is normally colour coded so that phase, neutral and earth conductors can be easily identified. These colour codes vary with region and / or country:

Three Phase

Single Phase

DC

Country / Region Phase A

European Union

Phase B

Phase C

Purple (1

Neutra l

Positiv e

Protectiv e Earth

Code Referenc e

IEC 60445 (2010) (4)

Neutra l

Active

Negativ e

Light Blue

Black or Brown

Light Blue

- (2)

- (2)

Green / Yellow (with blue markings at ends) (3)

Black (120V) , Red (208V) or Blue (240V)

White or Grey

-

-

Green or Green / Yellow

NFPA 70 (NEC) (5)

Red

Black

Red

Black

Green / Yellow

AS/NZS 3000 (2007)

Brown

Black

United States

Black or Brown

Red, Orange (delta) or Violet (wye)

Blue or Yellow

White or Grey

Australia n / New Zealand

Red (6)

White (6)

Dark Blue(6)

Black (6

People's Republic of China

Yellow

Green

Red

Light Blue

-

Light Blue

-

-

Green / Yellow

GB 50303 (2002)

Black or Brown

Light Blue

- (2)

- (2)

Green or Green / Yellow

IEC 60445 (2010) (4)

)

)

Japan

Brown

Black

Purple

White or Natural Grey

Russia

Brown

Black

Purple

Blue

Brown

Blue

Brown

Grey

Green / Yellow

IEC 60445 (2010) (4)

South Africa

Red

White or Yellow

Blue

Black

Red

Black

-

-

Green / Yellow

IEC 60445 (2010) (4)

Notes (1) In the UK, grey can be also be used (2) No recommendations given (3) In Denmark, Italy and Poland, light blue along the entire length with green / yellow markings at the ends (4) In 2007, IEC 60446 was merged with IEC 60445 (2010), "Basic and safety principles for man-machine interface, marking and identification – Identification of equipment terminals, conductor terminations and conductors". IEC 60446 is no longer used.

(5) Since 1975, NFPA 70, "The National Electricity Code (NEC)" has not prescribed colours for active conductors (except for orange for earthed delta). Local regulations take precedence. (6) These are preferred colours. Active conductors can be any colour except for green / yellow, green, yellow, black or light blue

Cable colors identification colors of cores in cables have been subject to developments that results in the harmonization document HD 308 S2. These rules do not apply to conductors used in the materials and sets assembled at the factory although compliance is strongly recommended. For information, old national habits are reminded in the table below. These cables are still widely present in existing installations.

Colors of rigid and flexible cable cores according to HD 324 S2 standard

Cable Conductor Materials In order to transmit electrical current with as few losses as possible, a cable conductor needs to be of low resistivity (or high conductivity). There are two main cable conductor materials used in practice, copper and aluminium, because of their low resistivity characteristics, coupled with their relatively low cost. Silver has better resistivity characteristics than either copper and aluminium, but being a precious metal, is far too costly.

Copper

The resistivity of copper is in the order of 1.7 - 1.8

Ωmm2 / m. Copper is a denser

material than aluminium and has a higher melting point, hence has better performance under short circuit conditions and is mechanically stronger. However the high density of copper makes it less flexible than aluminium. Copper conductors also need to be very pure, and small traces of impurities (e.g. phosphorous) can significantly affect conductivity. Copper is typically used more commonly in industrial plants, generating stations and portable equipment because of its mechanical properties. Furthermore, it is used in applications where space restrictions abound, e.g. offshore platforms and aircraft

Aluminium The resistivity of aluminium is around 2.8

Ωmm2 / m, which makes it roughly 60% less

conductive than copper. Therefore, aluminium conductors need to be oversized by a factor of 1.6 in order to have the equivalent resistance of copper conductors. However aluminium is also 50% lighter in mass than copper so it has a weight advantage. Additionally, it is more malleable and flexible than copper. Aluminium is inherently corrosion resistant due to the thin oxide layer that is formed when aluminium is exposed to the air. Aluminium also performs better than copper in sulfur laden environments (in of corrosion resistance). Aluminimum is typically used for overhead aerial lines because of its light weight and high conductivity. It is also used in applications where space restrictions are not a large factor, e.g. underground cables

Summary The table below summarises the pros and cons of copper and aluminium as conductor materials: Copper

 Advantages



Aluminium

High conductivity



High mechanical strength

Flexible and malleable



Good short circuit performance



Lower weight



Corrosion resistant

Disadvantages 

Heavier and less flexible



Lower conductivity than copper



Impurities have large effects on conductivity



Low mechanical strength

Category: Cables

Cable Impedance Calculations This article provides details on the calculation of cable impedances - dc resistance, ac resistance and inductive reactance. Contents [hide]

1 Cable Resistance

o

1.1 DC Resistance

o

1.2 AC Resistance 2 Cable Reactance 3 References

Cable Resistance The dc and ac resistance of cable conductors can be calculated based on IEC 60287-1 Clause 2.1.

DC Resistance The dc resistance of cable conductors is calculated as follows:

Where

is the dc resistance at the conductor operating temperature θ (Ω / m) is the resistivity of the conductor material at 20oC (Ω.m). 

For copper conductors,



For aluminium conductors,

= 1.7241 x 10-8 = 2.8264 x 10-8

is the cross-sectional area of the conductor (mm2) is the temperature coefficient of the conductor material per K at 20oC.



For copper conductors,

= 3.93 x 10-3



For aluminium conductors,

= 4.03 x 10-3

is the conductor operating temperature (oC)

AC Resistance The ac resistance of cable conductors is the dc resistance corrected for skin and proximity effects.

Where

is the ac resistance at the conductor operating temperature θ (Ω / m) is the dc resistance at the conductor operating temperature θ (Ω / m) is the skin effect factor (see below) is the proximity effect factor (see below) The skin effect factor is calculated as follows:

Where is the dc resistance at the conductor operating temperature θ (Ω / m) is the supply frequency (Hz) is a constant (see table below) Note that the formula above is accurate provided that

2.8.

The proximity effect factor varies depending on the conductor geometry. For round conductors, the following formulae apply. For 2C and 2 x 1C cables:

For 3C and 3 x 1C cables:

Where is the dc resistance at the conductor operating temperature θ (Ω / m) is the supply frequency (Hz) is the diameter of the conductor (mm) is the distance between conductor axes (mm) is a constant (see table below) Note that the formula above is accurate provided that

2.8.

For shaped conductors, the proximity effect factor is two-thirds the values calculated above, and with: equal to the diameter of an equivalent circular conductor of equal cross-sectional area and degree of compaction (mm) where

is the thickness of the insulation between conductors (mm)

Type of Conductor

Dried and Impregnated? Copper

Round, stranded

Yes

Round, stranded

No

Round, segmental

-

Sector-shaped

Yes

Sector-shaped

No Aluminium

Round, stranded

Either

Round, 4 segment

Either

Round, 5 segment

Either

Round, 6 segment

Either

Cable Reactance The series inductive reactance of a cable can be approximated by the following equation:

Where

is the conductor inductive reactance (Ω / km) is the supply frequency (Hz) is the axial spacing between conductors (mm) is the diameter of the conductor, or for shaped conductors, the diameter of an equivalent circular conductor of equal cross-sectional area and degree of compaction (mm) is a constant factor pertaining to conductor formation (see below for typical values)

No. of wire strands in conductor 3 7 19 37 >60 1 (solid) For 3C and 3 x 1C cables, the axial spacing parameter conductors:

depends on the geometry of the

References 

IEC 60287-1-1, “Electric cables – Calculation of current rating – Part 1: Current rating equations (100% load factor) and calculation of losses – Section 1: General”, 2006



G.F. Moore, “Electric Cables Handbook”, Third Edition, 1997, an excellent reference book for cables

Cable Insulation Materials The following materials are typically used for cable insulation: Contents [hide]

1 Thermoplastic 2 Thermosetting 3 Paper Based 4 Comparison of Materials

Thermoplastic Thermoplastic compounds are materials that go soft when heated and harden when cooled: 

PVC (Polyvinyl Chloride) – is the most commonly used thermoplastic insulator for cables. It is cheap, durable and widely available. However, the chlorine in PVC (a halogen) causes the production of thick, toxic, black smoke when burnt and can be a health hazard in areas where low smoke and toxicity are required (e.g. confined areas such as tunnels). Normal operating temperatures are typically between 75C and 105C (depending on PVC type). Temperature limit is 160C (<300mm2) and 140C (>300mm2).



PE (Polyethylene) – is part of a class of polymers called polyolefins. Polyethylene has lower dielectric losses than PVC and is sensitive to moisture under voltage stress (i.e. for high voltages only).

Figure 2. LV/MV cable for outdoor usage with PE sheath

Figure 1. Typical low voltage PVC cable

Thermosetting

Thermosetting compounds are polymer resins that are irreversibly cured (e.g. by heat in the vulcanization process) to form a plastic or rubber: 

XLPE (Cross-Linked Polyethylene) – has different polyethylene chains linked together (“cross-linking”) which helps prevent the polymer from melting or separating at elevated temperatures. Therefore XLPE is useful for higher temperature applications. XLPE has higher dielectric losses than PE, but has better ageing characteristics and resistance to water treeing. Normal operating temperatures are typically between 90C and 110C. Temperature limit is 250C.



EPR (Ethylene Propylene Rubber) – is a copolymer of ethylene and propylene, and commonly called an “elastomer”. EPR is more flexible than PE and XLPE, but has higher dielectric losses than both. Normal operating temperatures are typically between 90C and 110C. Temperature limit is 250C.

Figure 3. 3-phase EPR insulated cable for MV

Figure 4. MV cable with XLPE insulation, 33 kV

Paper Based Paper Based insulation is the oldest type of power cable insulation and is still used mainly for high voltage cables. The paper insulation must be impregnated with a dielectric fluid (e.g. oil resin or a synthetic fluid). A lead sheath is commonly applied over the insulation to prevent water or moisture ingress into the paper insulation, which is sensitive to moisture.

Figure 5. Oil filled paper insulated cable, 66 kV

Comparison of Materials A comparison of common insulating materials is as follows: Material

Advantages

Disadvantages

Highest dielectric losses

 

Cheap Melts at high temperatures



PVC



Durable 



Widely available

Lowest dielectric losses



PE

High initial dielectric strength



Contains halogens





Not suitable for MV / HV cables



Highly sensitive to water treeing Material breaks down at high temperatures

XLPE 

Low dielectric losses



Medium sensitivity to water treeing (although som

Improved material properties



at high temperatures XLPE polymers are water-tree resistant) Does not melt but thermal



expansion occurs



Reduced thermal expansion



EPR

Increased flexibility Medium-High dielectric losses



(relative to XLPE) Requires inorganic filler / additive

 

Low sensitivity to water treeing

High weight



Paper / Oil



Low-Medium dielectric losses

  

Not harmed by DC testing



Requires hydraulic pressure / pumps for insulatin fluid

Known history of reliability

 

Category: Cables

Cable Reference Installation Methods Contents [hide]

1 Introduction 2 Method A 3 Method B

High cost

Difficult to repair Degrades with moisture

4 Method C 5 Method D 6 Method E 7 Method F 8 Method G 9 Related topics:

Introduction The IEC 60364 standard defines a number of installation methods which represent the various installation conditions. By the following icons, they are divided into groups and defined by the letters A to G which determine how to read the table of the current-carrying capacities in conductors.

Method A



A1 - Insulated single core conductors in conduit in a thermally insulated wall



A2 - Multicore cable in conduit in a thermally insulated wall

This method also applies to single core or multicore cables installed directly in a thermally insulated wall (use methods A1 and A2 respectively), conductors installed in mouldings, architraves and window frames.

Method B



B1 - Insulated single core conductors in conduit on a wall



B2 - Multicore cable in conduit on a wall

This method applies when a conduit is installed inside a wall, against a wall or spaced less than 0.3 x D (overall diameter of the cable) from the wall. Method B also applies for cables installed in trunking / cable duct against a wall or suspended from a wall and cables installed in building cavities.

Method C



C - Single core or multi-core cable on a wooden wall

This method also applies to cables fixed directly to walls or ceilings, suspended from ceilings, installed on unperforated cable trays (run horizontally or vertically) and installed directly in a masonry wall (with thermal resistivity less than 2 K.m/W).

Method D



D1 - Multicore or single core cables installed in conduit buried in the ground



D2 - Multicore or single core cables buried directly in the ground

Method E



E - Multicore cable in free-air

This method applies to cables installed on cable ladder, perforated cable tray or cleats provided that the cable is spaced more than 0.3 x D (overall diameter of the cable) from the wall. Note that cables installed on unperforated cable trays are classified under Method C.

Method F



F - Single core cables touching in free-air

This method applies to cables installed on cable ladder, perforated cable tray or cleats provided that the cable is spaced more than 0.3 x D (overall diameter of the cable) from the wall. Note that cables installed on unperforated cable trays are classified under Method C.

Method G



G - Single-core cables laid flat and spaced in free-air

This method applies to cables installed on cable ladder, perforated cable tray or cleats provided that the cable is spaced more than 0.3 x D (overall diameter of the cable) from the wall and with at least 1 x D spacings between cables. Note that cables installed on unperforated cable trays are classified under Method C. This method also applies to cables installed in air ed by insulators.

Related topics:

Cable Sheath Materials The following materials are typically used for cable inner (bedding) and outer sheaths:

Thermoplastic Thermoplastic compounds are materials that go soft when heated and harden when cooled: 

PVC (Polyvinyl Chloride) – as a sheath material, PVC is used extensively because of its low cost and good overall properties – high physical strength, good moisture resistance, adequate oil resistance, good flame resistance and excellent resistance to weathering and to soil environments. PVC contains halogens which produces thick, black toxic smoke when burnt. Most commonly used sheath material for LV cables.



PE (Polyethylene) – is usually categorized under three different densities – 1) Low density (0.91 – 0.925 g/cm3), 2) Medium density (0.926 – 0.94 g/cm3), and 3) High density (0.941 – 0.965 g/cm3). PE sheaths have good physical strength, excellent moisture resistance, good ageing properties, but poor flame resistance. Like PVC, PE will melt at high temperatures. Does not contain halogens.



E (Chlorinated Polyethylene) – similar to PVC, but with better high temperature properties. Contains halogens.



TPE (Thermoplastic Elastomer) – provides flame resistance, good low temperature performance, good abrasion resistance and good physical strength. Does not contain halogens.



Nylon – provides good physical strength, reasonable abrasion resistance, very low friction when in with conduit materials which aids in pulling cables. Excellent resistance to oils and organic solvents, but very sensitive to strong acids and oxidizing agents.

Thermosetting Thermosetting compounds are polymer resins that are irreversibly cured (e.g. by heat in the vulcanization process) to form a plastic or rubber: 

XLPE (Cross-Linked Polyethylene) – provides a tough, moisture, chemical and weather resistant sheath material. Used mainly as an outer sheath material for “rugged” cables.



P (Polychloroprene) or trade name "Neoprene" – provides good heat resistance, flame resistance, resistance to oil, sunlight and weathering, low temperature resistance and abrasion resistance. Due to its ruggedness, neoprene is used widely in the mining industry. Does not deform with high temperatures and does not contain halogens.



CSP (Chloro-sulphanated Polyethylene) – similar properties to neoprene, though superior in resistance to heat, oxidizing chemicals, ozone and moisture, and has better dielectric properties. However CSP contains halogens.



EPR (Ethylene Propylene Rubber) – not commonly used as a sheath material, but can be useful if increased cable flexibility is required (especially in low temperature applications).

Cable Terminology List of electrical and instrumentation cable terminology and definitions. Contents [hide]

1 AWA (Aluminium Wire Armour) 2 E (Chlorinated Polyethylene) 3 CSP / CSPE (Chlorosulphanated Polyethylene) 4 Dekoron® 5 DWA (Double Wire Armour) 6 EPR (Ethylene Propylene Rubber) 7 FR (Fire Resistant / Flame Retardant) 8 GSWB (Galvanised Steel Wire Braid) 9 HDPE (High Density Polyethylene) 10 HF (Halogen Free) 11 HOFR (Heat, Oil and Flame Retardant) 12 LAS (Lead Armour Sheath) 13 LSF (Low Smoke and Fumes)

14 LSTA (Low Smoke, Toxicity and Acidity) 15 LSZH / LS0H (Low Smoke, Zero Halogen) 16 MGT (Mica Glass Tape) 17 MICC (MI, MIMS) 18 Neoprene® 19 NYL (Nylon sheath) 20 P (Polychloroprene) 21 PE (Polyethylene) 22 PETP (Polyethylene Terephthalate) 23 PVC (Polyvinyl Chloride) 24 SCN (Screen) 25 SHF2 26 SWA (Steel Wire Armour) 27 TAC (Tinned Annealed Copper) 28 TCWB (Tinned Copper Wire Braid) 29 TPE (Thermoplastic Elastomer) 30 XLPE (Cross-Linked Polyethylene)

AWA (Aluminium Wire Armour) A type of cable armouring for mechanical protection, used for 3 phase cables.

E (Chlorinated Polyethylene)

An oil, ozone and heat resistant thermoplastic sheating material.

CSP / CSPE (Chlorosulphanated Polyethylene) An oil, ozone and heat resistant elastomeric compound used as bedding and outer sheath material. DuPont manufacture this material under the ed trade name "Hypalon".

Dekoron® ed trade name for a range of instrumentation cables insulated and sheathed with a flame retardant PVC. The standard range includes up to 50 pairs and up to 36 triples in either 0.5mm2 or 1.5mm2 conductors. Larger conductors may be specified, as can options of Lead Sheathing, SWA, or HF insulation and sheath materials.

DWA (Double Wire Armour) Two layers of wire armour. Typically used in subsea cables and wrapped contra-helically for bottom stability.

EPR (Ethylene Propylene Rubber) A water and ozone resistant, flexible, cross linked high grade insulation material and sometimes as a sheating material.

FR (Fire Resistant / Flame Retardant) Fire Resistant - the property of cables to continue to function while under the influence of fire. Cables that are Fire Resistant tend to provide circuit integrity even when burned and maintains integrity after the fire has extinguished. In most cases, the cables will withstand a water spray and still provide circuit integrity. Flame Retardant - the property of cables to retard or slow the progress of fire and flame along the cable. This is achieved through the use of materials that do not readily burn and will tend to self-extinguish.

GSWB (Galvanised Steel Wire Braid) A type of cable armouring for mechanical protection.

HDPE (High Density Polyethylene) Generally used as a subsea cable sheating material where it provides high resistance to water penetration, is very hard, has low coefficient of friction, and is abrasion resistant.

HF (Halogen Free)

Halogenated plastics (ie. those that contain chlorine, fluorine, bromine, iodine and astatine) when ignited will tend to release toxic and corrosive gases, which has potential safety implications, eg. obstruction of escape routes. Halogen free plastics, as the name suggests, do not contain halogens.

HOFR (Heat, Oil and Flame Retardant) Refer to FR (flame retardant).

LAS (Lead Armour Sheath) Used for chemical protection against petrochemicals and other chemicals, that can weaken the insulation materials used. The lead sheath sits under the mechanical protection (e.g. SWA), to ensure the chemical barrier isn't compromised.

LSF (Low Smoke and Fumes) Low smoke and fume emissions when the cable is on fire. Note that it may still contain halogens.

LSTA (Low Smoke, Toxicity and Acidity) Uncommonly used term for bedding and sheathing materials with low smoke, toxicity and acidity properties. Halogen free materials such as SHF2 are more or less equivalent to LSTA materials.

LSZH / LS0H (Low Smoke, Zero Halogen) Refer to HF (halogen free).

MGT (Mica Glass Tape) A fire resistant tape usually wrapped around the insulated conductor bundle beneath the innear sheath.

MICC (MI, MIMS) Mineral-insulated copper-clad cable is a variety of electrical cable made from copper conductors inside a copper sheath, insulated by inorganic magnesium oxide powder. The name is often abbreviated to MICC or MI cable, and colloquially known as pyro (because the original manufacturer and vendor for this product in the UK is a company called Pyrotenax). A similar product sheathed with metals other than copper is called mineral insulated metal sheathed (MIMS) cable.

Neoprene® Refer to P (polychroloprene)

NYL (Nylon sheath) A nylon sheath (or sometimes described as a sock) is typically used for termite protection in underground cables and also as a sheating material.

P (Polychloroprene) This is an oil resistant, tough sheating material, that is used mainly in mining cables as an outer sheath. DuPont ed trade name for this product is "Neoprene".

PE (Polyethylene) Thermoplastic used as a insulation and sheating material.

PETP (Polyethylene Terephthalate) A polymer resin used in semi-metallic screens eg. PETP/Al

PVC (Polyvinyl Chloride) Commonly used thermoplastic insulation and sheathing material.

SCN (Screen) A tape or braid, usually metallic (copper, aluminium) or semi-metallic (PETP/Al), wrapped around the cable cores to keep out or contain unwanted radiation / interference.

SHF2 Halogen free elastomeric compound commonly used for inner sheath / bedding and outer sheating materials.

SWA (Steel Wire Armour) A type of cable armouring for mechanical protection.

TAC (Tinned Annealed Copper) Annealed copper conductors with surface tinning for rust prevention. Annealing refers to the process of gradually heating and cooling the copper making it more malleable and less brittle.

TCWB (Tinned Copper Wire Braid) Typically used for flexible cable armouring of instrument cables.

TPE (Thermoplastic Elastomer)

A plastic material compounded so it displays characteristics like an elastomer. TPE is normally tough, cut resistant, flexible, smooth, with vibrant colouring.

XLPE (Cross-Linked Polyethylene) High grade insulation material of cross-linked polyethylene chains giving good high temperature performance. Category: Cables

Current Ratings Contents [hide]

1 Table 52G 2 Table 52H 3 Table 52I 4 Table 52J

Table 52G Multi-core cables with individual screening with voltage levels from 3,6/6 (7,2) kV to 18/30 (36) kV and PR/EPR insulation. Copper (Cu)

Cross-Section

Aluminium (Al)

Air

Ground

mm2

Air

Ground

156

160

25

121

125

189

192

35

146

148

227

226

50

175

175

282

277

70

220

215

345

331

95

268

257

400

377

120

309

292

456

423

150

351

327

523

478

185

407

372

619

554

240

479

431

718

627

300

552

487

Table 52H Multi-core cables with collective screening with voltage level 6/6 (7,2) kV and PR/EPR insulation. Copper (Cu)

Cross-Section

Aluminium (Al)

Air

Ground

mm2

Air

Ground

100

110

16

79

86

130

145

25

105

110

165

170

35

125

135

205

215

50

160

165

255

260

70

195

205

310

315

95

240

245

360

360

120

280

280

410

405

150

320

315

460

450

185

360

350

550

525

240

430

410

Table 52I Multi-core cables with collective screening with voltage level 6/6 (7,2) kV and PVC insulation. Copper (Cu)

Cross-Section

Aluminium (Al)

Air

Ground

mm2

Air

Ground

81

94

16

62

72

105

120

25

82

94

130

145

35

100

115

165

185

50

130

145

205

225

70

160

175

250

270

95

195

210

290

310

120

225

240

330

345

150

255

270

370

385

185

285

300

440

445

240

345

350

Table 52J Single-core cables with individual screening with voltage levels from 3,6/6 (7,2) kV to 18/30 (36) kV and PR/EPR insulation. Copper (Cu) Air

Cross-Section

Aluminium (Al)

mm2

Ground

Trefoil

Flat

Trefoil

Flat

157

161

161

165

190

195

192

233

244

292

Air

Ground

Trefoil

Flat

Trefoil

Flat

25

122

125

125

128

197

35

147

151

149

153

225

231

50

185

189

175

179

304

276

283

70

226

236

214

220

356

369

330

338

95

266

285

252

262

409

423

375

383

120

318

330

291

299

465

478

420

430

150

360

370

325

334

533

549

474

484

185

417

430

370

379

630

646

549

559

240

490

504

428

439

724

735

619

623

300

567

579

485

492

836

838

698

703

400

662

669

554

562

959

958

786

785

500

771

776

631

637

1108

1108

887

886

630

897

905

720

727

1255

1244

980

970

800

1037

1040

810

812

1390

1366

1063

1042

1000

1165

1160

895

890

1480

1445

1117

1087

1200

1264

1252

957

945

Back to Medium Voltage Cable Data Reference

Current Ratings for Cables Contents

[hide]

1 Table B.2 2 Table B.3 3 Table B.4 4 Table B.5 5 Table B.6 6 Table B.7 7 Table B.8 8 Table B.9

Table B.2 Current ratings for single-core cables with XLPE insulation – Rated voltage 3,6/6 kV to 18/30 kV – Copper conductor Cross-Section

In ground (direct)

In ground (duct)

In air

(mm2)

Trefoil

Flat

Trefoil

Flat

Trefoil

Flat touching

Flat spaced

16

109

113

103

104

125

128

150

25

140

144

132

133

163

167

196

35

166

172

157

159

198

203

238

50

196

203

186

188

238

243

286

70

239

246

227

229

296

303

356

95

285

293

271

274

361

369

434

120

323

332

308

311

417

426

500

150

361

366

343

347

473

481

559

185

406

410

387

391

543

550

637

240

469

470

447

453

641

647

745

300

526

524

504

510

735

739

846

400

590

572

564

571

845

837

938

Table B.3 Current ratings for single-core cables with XLPE insulation – Rated voltage 3,6/6 kV to 18/30 kV – Aluminium conductor Cross-Section

In ground (direct)

In ground (duct)

In air

(mm2)

Trefoil

Flat

Trefoil

Flat

Trefoil

Flat touching

Flat spaced

16

84

88

80

81

97

99

116

25

108

112

102

103

127

130

153

35

129

134

122

123

154

157

185

50

152

157

144

146

184

189

222

70

186

192

176

178

230

236

278

95

221

229

210

213

280

287

338

120

252

260

240

242

324

332

391

150

281

288

267

271

368

376

440

185

317

324

303

307

424

432

504

240

367

373

351

356

502

511

593

300

414

419

397

402

577

586

677

400

470

466

451

457

673

676

769

Table B.4 Current ratings for single-core cables with EPR insulation – Rated voltage 3,6/6 kV to 18/30 kV – Copper conductor Cross-Section

In ground (direct)

In ground (duct)

In air

(mm2)

Trefoil

Flat

Trefoil

Flat

Trefoil

Flat touching

Flat spaced

16

106

109

99

100

116

119

138

25

136

140

128

129

153

156

181

35

162

167

153

154

186

190

221

50

192

198

181

183

224

229

266

70

234

242

222

224

280

287

334

95

280

289

266

269

343

352

409

120

319

329

303

306

398

407

474

150

357

369

341

344

454

465

540

185

403

417

386

390

522

534

621

240

467

484

449

454

619

634

736

300

526

545

509

515

712

728

843

400

597

618

580

588

825

843

977

Table B.5 Current ratings for single-core cables with EPR insulation – Rated voltage 3,6/6 kV to 18/30 kV – Aluminium conductor Cross-Section

In ground (direct)

In ground (duct)

In air

(mm2)

Trefoil

Flat

Trefoil

Flat

Trefoil

Flat touching

Flat spaced

16

82

84

77

78

90

92

107

25

105

109

99

100

119

121

141

35

126

130

118

120

144

147

171

50

149

153

140

142

174

178

207

70

182

188

172

174

218

223

259

95

217

224

206

208

266

273

317

120

247

256

235

238

309

317

368

150

277

287

264

267

352

361

419

185

314

325

300

303

406

417

484

240

364

377

350

354

483

495

575

300

411

426

397

401

556

570

659

400

471

487

456

462

651

667

770

Table B.6 Current rating for three-core XLPE insulated cables – Rated voltage 3,6/6 kV to 18/30 kV – Copper conductor, armoured and unarmoured Cross-Section

Unarmoured

Armoured

(mm2)

Buried direct

Buried in ducts

In air

Buried direct

Buried in ducts

In air

16

101

87

109

101

88

110

25

129

112

142

129

112

143

35

153

133

170

154

134

172

50

181

158

204

181

158

205

70

221

193

253

220

194

253

95

262

231

304

263

232

307

120

298

264

351

298

264

352

150

334

297

398

332

296

397

185

377

336

455

374

335

453

240

434

390

531

431

387

529

300

489

441

606

482

435

599

400

553

501

696

541

492

683

Table B.7 Current rating for three-core XLPE insulated cables – Rated voltage 3,6/6 kV to 18/30 kV – Aluminium conductor, armoured and unarmoured Cross-Section

Unarmoured

Armoured

(mm2)

Buried direct

Buried in ducts

In air

Buried direct

Buried in ducts

In air

16

78

67

84

78

68

85

25

100

87

110

100

87

111

35

119

103

132

119

104

133

50

140

122

158

140

123

159

70

171

150

196

171

150

196

95

203

179

236

204

180

238

120

232

205

273

232

206

274

150

260

231

309

259

231

309

185

294

262

355

293

262

354

240

340

305

415

338

304

415

300

384

346

475

380

343

472

400

438

398

552

432

393

545

Table B.8 Current rating for three-core EPR insulated cables – Rated voltage 3,6/6 kV to 18/30 kV – Copper conductor, armoured and unarmoured Cross-Section (mm2)

Unarmoured Buried direct

Buried in ducts

Armoured In air

Buried direct

Buried in ducts

In air

16

98

84

104

98

85

104

25

125

109

135

125

109

136

35

150

130

164

150

131

164

50

176

154

195

177

155

197

70

216

189

243

216

190

244

95

258

227

296

257

227

296

120

292

258

339

292

259

339

150

328

291

385

327

291

385

185

371

330

441

368

328

439

240

429

384

519

424

381

513

300

482

434

590

475

429

583

400

545

494

678

534

485

666

Table B.9 Current rating for three-core EPR insulated cables – Rated voltage 3,6/6 kV to 18/30 kV – Aluminium conductor, armoured and unarmoured Cross-Section

Unarmoured

Armoured

(mm2)

Buried direct

Buried in ducts

In air

Buried direct

Buried in ducts

In air

16

76

65

80

76

66

81

25

97

84

105

97

85

105

35

116

101

127

116

101

127

50

137

119

151

137

120

153

70

167

147

189

168

147

190

95

200

176

229

200

176

230

120

227

201

263

227

201

264

150

255

226

299

254

226

300

185

289

257

343

288

257

343

240

335

300

406

332

299

402

300

378

340

462

374

338

459

400

432

392

538

426

387

530

Back to Medium Voltage Cable Data Reference

DC Resistance Typical DC resistances for copper and aluminium conductors operating at 20oC are based on values given in AS/NZS 1125.1. Background information can be found in the calculation of DC resistances article. Maximum DC Resistance (Ω\km) at 20oC Copper Size (mm2)

Aluminium

Stranded Conductors

Solid Conductors Nicke l

Silve r

Tinne d

Nicke l

Stranded Conductors

Solid Conductors

Plain

Silver

Tinned

0.5

38.4

38.4

39.6

36

36.7

39.6

-

-

0.75

25.3

25.3

26

24.5

24.8

19.7

-

-

1

21.2

21.2

21.6

23.3

18.1

18.2

13.2

-

-

1.5

13.6

13.6

13.8

14.9

12.1

12.2

-

-

-

2.5

7.41

7.41

7.56

8.14

7.41

7.56

-

-

12.1

4

4.61

4.61

4.7

5.06

4.61

4.7

-

7.41

7.54

6

3.08

3.08

3.11

3.34

3.08

3.11

-

4.61

5.01

10

1.83

1.83

1.84

2

1.83

1.84

-

3.08

3.08

16

1.15

1.15

1.16

-

1.15

1.16

-

1.91

1.91

25

0.727

0.727

0.734

-

0.727

-

-

1.2

1.2

35

0.524

0.524

0.529

-

-

-

-

0.868

0.868

50

0.387

0.387

0.391

-

-

-

-

0.641

0.641

70

0.268

0.268

0.27

-

-

-

-

0.443

0.443

95

0.193

0.193

0.195

-

-

-

-

0.32

0.32

120

0.153

0.153

0.154

-

-

-

-

0.253

0.253

150

0.124

0.124

0.126

-

-

-

-

0.206

0.206

185

0.0991

0.0991

0.1

-

-

-

-

0.164

0.164

240

0.0754

0.0754

0.0762

-

-

-

-

0.125

0.125

300

0.0601

0.0601

0.0607

-

-

-

-

0.1

0.1

400

0.047

0.047

0.0475

-

-

-

-

0.0778

-

500 (1)

0.0366 /

0.0366 /

0.0369 /

-

-

-

-

0.0605 /

-

630 (1)

0.037332

0.037332

0.037638

0.0283 / 0.028866

0.0283 / 0.028866

0.0286 / 0.029172

0.06171 -

-

-

-

0.0469 / 0.047838

-

Note (1): resistance values are quoted for single core / multicore cables Back to Low Voltage Cable Data Reference

Insulation thickness Contents [hide]

1 Note 2 IEC 60502 - 1 o

2.1 Table 5 - PVC insulation

o

2.2 Table 6 - XLPE insulation

o

2.3 Table 7 - EPR insulation 3 IEC 60502 - 2

o

3.1 Table 5 - PVC insulation

o

3.2 Table 6 - XLPE insulation

o

3.3 Table 7 - EPR insulation

Note The nominal insulation thicknesses are specified in Tables 5 to 7. The thickness of any separator shall not be included in the thickness of the insulation.

IEC 60502 - 1 Typical insulation thickness (in mm) for cables 0,6/1 and 1,8/3 kV according to the IEC 60502-1. Table numbers correspond to the standard.

Table 5 - PVC insulation Cross-section (mm2)

0,6/1 kV

1,8/3 kV

1

0,8

2,2

1,5

0,8

2,2

2,5

0,8

2,2

4

1

2,2

6

1

2,2

10

1

2,2

16

1

2,2

25

1,2

2,2

35

1,2

2,2

50

1,4

2,2

70

1,4

2,2

95

1,6

2,2

120

1,6

2,2

150

1,8

2,2

185

2

2,2

240

2,2

2,2

300

2,4

2,2

400

2,6

2,6

500

2,8

2,8

630

2,8

2,8

800

2,8

2,8

1000

3

3

Cross-section (mm2)

0,6/1 kV

1,8/3 kV

1

0,7

2

1,5

0,7

2

2,5

0,7

2

4

0,7

2

6

0,7

2

10

0,7

2

Table 6 - XLPE insulation

16

0,7

2

25

0,9

2

35

0,9

2

50

1

2

70

1,1

2

95

1,1

2

120

1,2

2

150

1,4

2

185

1,6

2

240

1,7

2

300

1,8

2

400

2

2

500

2,2

2,2

630

2,4

2,4

800

2,6

2,6

1000

2,8

2,8

Cross-section (mm2)

0,6/1 kV

1,8/3 kV

1

1

2,2

1,5

1

2,2

2,5

1

2,2

4

1

2,2

6

1

2,2

10

1

2,2

16

1

2,2

25

1,2

2,2

35

1,2

2,2

50

1,4

2,2

70

1,4

2,2

95

1,6

2,4

Table 7 - EPR insulation

120

1,6

2,4

150

1,8

2,4

185

2

2,4

240

2,2

2,4

300

2,4

2,4

400

2,6

2,6

500

2,8

2,8

630

2,8

2,8

800

2,8

2,8

1000

3

3

IEC 60502 - 2 Typical insulation thickness (in mm) for cables 3,6/6, 6/10, 8,7/15, 12/20, 18/30 kV according to the IEC 60502-2. Table numbers correspond to the standard.

Table 5 - PVC insulation Cross-section (mm2)

3,6/6 kV

1

0

1,5

0

2,5

0

4

0

6

0

10

3,4

16

3,4

25

3,4

35

3,4

50

3,4

70

3,4

95

3,4

120

3,4

150

3,4

185

3,4

240

3,4

300

3,4

400

3,4

500

3,4

630

3,4

800

3,4

1000

3,4

1200

3,4

1400

3,4

1600

3,4

Table 6 - XLPE insulation Cross-section (mm2)

3,6/6 kV

6/10 kV

8,7/15 kV

12/20 kV

8/30 kV

1

0

0

0

0

0

1,5

0

0

0

0

0

2,5

0

0

0

0

0

4

0

0

0

0

0

6

0

0

0

0

0

10

2,5

0

0

0

0

16

2,5

3,4

0

0

0

25

2,5

3,4

4,5

0

0

35

2,5

3,4

4,5

5,5

0

50

2,5

3,4

4,5

5,5

8

70

2,5

3,4

4,5

5,5

8

95

2,5

3,4

4,5

5,5

8

120

2,5

3,4

4,5

5,5

8

150

2,5

3,4

4,5

5,5

8

185

2,5

3,4

4,5

5,5

8

240

2,6

3,4

4,5

5,5

8

300

2,8

3,4

4,5

5,5

8

400

3

3,4

4,5

5,5

8

500

3,2

3,4

4,5

5,5

8

630

3,2

3,4

4,5

5,5

8

800

3,2

3,4

4,5

5,5

8

1000

3,2

3,4

4,5

5,5

8

1200

3,2

3,4

4,5

5,5

8

1400

3,2

3,4

4,5

5,5

8

1600

3,2

3,4

4,5

5,5

8

Table 7 - EPR insulation Cross-section (mm2)

3,6/6 kV

6/10 kV

8,7/15 kV

12/20 kV

8/30 kV

1

0

0

0

0

0

1,5

0

0

0

0

0

2,5

0

0

0

0

0

4

0

0

0

0

0

6

0

0

0

0

0

10

3

0

0

0

0

16

3

3,4

0

0

0

25

3

3,4

4,5

0

0

35

3

3,4

4,5

5,5

0

50

3

3,4

4,5

5,5

8

70

3

3,4

4,5

5,5

8

95

3

3,4

4,5

5,5

8

120

3

3,4

4,5

5,5

8

150

3

3,4

4,5

5,5

8

185

3

3,4

4,5

5,5

8

240

3

3,4

4,5

5,5

8

300

3

3,4

4,5

5,5

8

400

3

3,4

4,5

5,5

8

500

3,2

3,4

4,5

5,5

8

630

3,2

3,4

4,5

5,5

8

800

3,2

3,4

4,5

5,5

8

1000

3,2

3,4

4,5

5,5

8

1200

3,2

3,4

4,5

5,5

8

1400

3,2

3,4

4,5

5,5

8

1600

3,2

3,4

4,5

5,5

8

Category: Cables

LV Cable Commissioning Visual Inspection 

Check cable mechanical connections



Check that cable colour codes conform to project specifications and/or national standards



cable tags / numbers

Electrical Testing 

For each test, record the testing instrument make / model and serial number.



Perform insulation-resistance test (megger) on each conductor with respect to earth and adjacent conductors. For 0.6/1kV cables, an applied voltage of 1,000 Vdc for 1 minute is appropriate, with acceptance levels of 100 MΩ for new cables and 1 MΩ for aged cables.



Perform continuity (point-to-point) tests to ensure proper cable connection and continuity. Where applicable, perform continuity tests on each phase to neutral and each phase to phase and record the readings in Ohms.

Power Cable Failures Contents [hide]

1 Introduction

2 Power Cable Systems 3 Final results of a Failure 4 Root Cause Failure Analysis o

4.1 Cracking of embrittled insulation

o

4.2 Cable wafer with extensive voids

o

4.3 Large vented water tree at a fault site

o

4.4 Cable failing from the outside in

o

4.5 Other sources 5 Summary 6 References

Introduction Almost all utilities and large industrial facilities have extensive systems of power cables. Many of these cable systems are ageing and failures are becoming common. Finding the root cause of cable failures can lead to better maintenance practices and produce more reliable operation in the future. This in turn will lead to lower operating costs. As an example, the final result of a cable failure may be that the insulation failed and the cable flashed over. The root cause may in fact be a building contractor removing thermally conducting back-fill around the ducts thereby causing local overheating. Determining the root cause of the failure can help prevent future failures. Root cause analysis requires a systems approach.

Power Cable Systems One of the fundamental aspects of the cable system is the method of installation. Cable systems can be installed in various ways including: 

In trays or troughs, either in- or out-doors



Suspended from poles, bridges, or walls of vaults or tunnels



Buried in ducts or conduits, or direct buried



Underwater as a submarine cable



In special situations as mine trailing cables, crane cable etc.

Always keep in mind the installation when looking for the cause of a failure. Cable accessories are often the most prone to failure of any part of the cable system. Accessories include terminations and ts, also called splices. Terminations are required to connect the conductor of the cable to a bus or other cable conductor. Within the termination the cable’s metallic and semiconducting shields must also be properly terminated. Splices may be simply considered two terminations, connected back to back. Another aspect of the cable system is the operating environment. Some points of the operating environment, which must be considered, are: 

Cable current loading compared to cable ampacity



Ambient temperature



Type of backfill around direct buried cables or ducts



Moisture or chemicals in with the cables and accessories



Lightning impulses and other system induced over-voltages



Switching operations.

Final results of a Failure A cable failure almost always exhibits itself as either an open circuit or a short circuit. Open circuits are more common in low voltage cables than at medium or high voltage. Open circuits are usually the result of failed connectors, or broken and/or corroded conductors. The reason that open circuit failures are rare in higher voltage systems is that arcing will occur in the conduction path, leading to overheating, failure of the insulation and a short circuit. Short circuit failures will most often cause the protection system to operate and interrupt the current flow to the load. There are times when the flash over at the fault may result in more serious consequences like fire or even explosion.

Root Cause Failure Analysis Root cause failure analysis is the process of examining a failed sample, along with the operating and environmental information, to determine the fundamental cause of the failure. During the failure analysis, various tests may be conducted on the failed sample, on pieces of nearby unfaulted cable, or on accessories removed from adjacent un-failed phases. Each bit of evidence

is looked at as an effect, which had a cause. Then each cause is looked at in turn as the possible effect of a previous cause. This cause/effect trail is followed to the fundamental or root cause. The amount of evidence that can be gathered will depend on the condition of the sample, what has happened to the sample since the failure, and the availability of information about the failure and previous conditions that the cable or accessory has undergone. Often direct evidence at the failure site is destroyed by the fault. An important factor in failure analysis is of course the amount of time and money one can spend on the analysis. Two important things that must be done in any failure analysis are a close visual examination of the sample at and near the failure site, and talking to or reading s of the failure from the personnel involved. Depending on the circumstances more investigations or tests may be required, or more information may be requested from the cable . If the failure occurred in a polymeric cable, other work may include: 

More detailed examination of the conductor including possible metallurgical examination



Dissecting the insulation close to the failure and cutting wafers



Measuring insulation resistance



Performing ac breakdown level tests on a long sample near the failure site



Performing chemical tests on the insulation



Measuring semicon resistivity at elevated temperature near the failure site



Performing metallurgical tests on the shield or sheath if present



Performing chemical tests on the jacket if present

Cracking of embrittled insulation During the examination, look for signs of overheating. These may include discolored metal, or cracked and distorted polymers. Figure 1 shows an embrittled and cracked polyethylene wafer caused by overheating. to look at samples sufficiently far from the fault site to be sure they were not damaged by the arcing fault. Overheating may indicate a possible root cause of failure of the system protection, incorrect determination of the system ampacity, thermal runaway, or lack of thermal backfill. Signs of over heating may warrant further chemical or metallurgical tests to determine the maximum temperature reached. Further investigation into system operations may be necessary to determine the true root cause of this type of failure. Examples of root causes of over heating may be poor initial ampacity calculations, improper breaker settings, removal of proper backfill, or change in ambient conditions like the adding of a steam pipe.

Cable wafer with extensive voids Voids or inclusions in the insulation, or protrusions from the semicon may be seen in the wafer examination. Figure 2 shows a cable wafer with extensive voids. Voids are simply bubbles in the insulation, while inclusions are foreign matter. Protrusions are sharp points extending into the insulation from the semicon. These are all forms of cable manufacturing defects. All cause high local electrical fields, which may lead to partial discharge at the site or rapid growth of water or electrical trees near the defect. Any of these observations indicate a manufacturing defect as the cause of failure. Unfortunately the defect, which may have caused the failure, is usually destroyed by the fault, but the presence of nearby defects may give sufficient evidence of poor manufacturing. Since modern cables can be produced with super-clean insulation and semicons, and very few defects, one might conclude that the root cause of these types of failures occurring in newly purchased cables is poor specifications or acceptance testing.

Figure 1. Cracking of embrittled insulation

Figure 2. Cable wafer with extensive voids

Water trees can grow in both polyethylene and EPR insulation. Figure 3 shows a large vented water tree growing from the insulation shield. This water tree has a fault through it. Figure 4 shows a cable with a forest of water trees, which can be seen without dissecting the insulation. Water trees require both moisture and an electric field in the insulation to grow. If the cable is an older design made and installed before or about 1980, and has extensive water tree growth, one may conclude that the root cause of failure is simply that the cable has reached its normal endoflife. If newer TR-XLPE has extensive water treeing, a manufacturing problem may be the cause. If the cable is supposed to have strand blocking, water absorbing tape, or a hermetically sealed LC shield, and develops extensive water treeing in a short time, investigate the possible root cause as a manufacturing problem, mechanical damage or shield corrosion.

Cable failing from the outside in Another type of failure is evidenced by signs of burning or arcing on the surface of the semicon. If the burning or arcing becomes extensive, the cable can fail from the outside in, as seen in Figure 5. The cause was determined to be a damaged jacket, which led to corrosive ground water entering the cable and causing severe corrosion of the metallic shield. Compounding the problem of a damaged metallic shield can be high resistivity in the semicon insulation shield. The volume resistivity of the semicon in older cables often increased with elevated temperatures. This effect was demonstrated in the lab as shown in Figure 6 Figure 6a shows a break made in the taped metallic shield. In Figure 6b, the conductor was energized and carrying current. As the current was increased the cable temperature rose. At about 50º C, the semicon resistivity had increased to the point where arcing took place across the break in the metallic shield.

Other sources To investigate a failure in an accessory, in addition to the usual visual examination and gathering of environmental and operating information, other work specific to accessory failure analysis may include: 

Comparing the failed accessory with undamaged accessories in adjacent phases



Measuring resistance in connectors



Careful dissection of the accessory comparing dimensions with assembly drawings



Looking for signs of poor workmanship



Looking for signs of surface tracking



Looking for electrically floating metal electrodes.

Problems in connectors are a common cause of accessory failure. Figure 7 shows a drawing of a load-break separable insulated connector (SIC). Within the elbow, bushing insert, and bushing well that make up the SIC, there can be up to eight electrical s. Usually problem connectors overheat, which is evidenced by a discolored or burned conductor or insulation. Root cause of the failure is often improper installation including bad connector crimps, cross threading of the elbow probe, or a broken stud in the bushing well. Some older load-break SICs had design flaws in the s in the load break mechanism. Figure 8 shows an XLPE cable end, which was removed from a failed pre-molded splice. The results of arcing can be seen on the insulation surface. When the installer penciled the insulation, burrs were left on the end of the insulation and the surface was very roughly sanded. When the insulation was inserted into the splice body, semicon material was dragged over the surface. The semicon material led to surface tracking and eventual flashover. The cause of the failure was

poor workmanship. One might conclude that the root cause is poor training, installation processes or standards. Figure 6. Lab test showing shield arcing due to elevated semicon temperature

Figure 7. Elbow and Bushing Insert Drawing

Figure 8. Poor Workmanship Leads to Failure in Pre-molded Splice Installation

Summary Determining the root cause of a cable failure can lead to better maintenance practices, produce more reliable operation, and lower operating costs. Root cause analysis requires a systems approach, which includes understanding the cables, their accessories and operating environment.

References Finding the Root Cause of Power Cable Failures By: Vern Buchholz, P.Eng., Director of Electrical Technologies, Powertech Labs Inc.

Protective Earth Conductor The protective earth (PE) conductor is defined as a conductor that is provided for safety purposes (e.g. against the risk of electric shock) and which also provides a conductive path to earth. The PE conductor can be integrated inside a multi-core cable (e.g. 3C+E cable) or can be a separate cable. Contents [hide]

1 Minimum Protective Earth Conductor Size

o

1.1 Sizing from a Table

o

1.2 Sizing by Calculation

Minimum Protective Earth Conductor Size The protective earth conductor should be sized so that during a fault, it will be able to withstand the prospective fault current. IEC 60364-5-54 provides two options for the sizing of protective earth conductors.

Sizing from a Table For protective earth conductors constructed of the same material as the phase conductors, the minimum size for protective earth conductors are as follows: Phase Conductor (mm2)

Min. PE Conductor (mm2)

0.5

0.5

0.75

0.75

1

1

1.5

1.5

2.5

2.5

4

4

6

6

10

10

16

16

26

16

35

16

50

25

70

35

95

50

120

70

150

95

185

95

240

120

300

150

400

240

500

300

630

400

800

400

1000

500

For protective earth conductors that are not of the same material as the phase conductors, a

factor

must be applied to the minimum size PE conductor in the table above.

The numerator k1 is the k value for the phase conductors and the denominator k2 is the k value for the PE conductor. Calculation of the k values are described on this page.

Sizing by Calculation As per Clause 543.1.2 of IEC 60463-5-54, the size of protective earth conductors can be calculated by the adiabatic short circuit temperature rise equation (for disconnection times <5s):

Where

is the minimum cross-sectional area of the PE conductor (mm2) is the energy of the short circuit (A2s)

is a constant term (this article has guidance for selecting the constant term) Category: Cables

Standard IEC Ratings Contents [hide]

1 Introduction 2 Transformers 3 Motors and Generators

4 Cables

Introduction Most IEC rated equipment have standard sizes that correspond to full sets or subsets of Renard numbers, especially from the four preferred series of Renard numbers outlined in ISO-3: R5, R10, R20 and R40.

Transformers For transformer ratings under 10MVA, IEC 60076-1 suggest preferred values based on the R10 series: 10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, 100, and multiples of 10 n. For example, the preferred transformer sizes from 500kVA to 4000kVA are: 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150, 4000.

Motors and Generators IEC 60072-1 Table 7 suggests the following preferred ratings (based on a subset of the R40 series) for motors (in KW) and generators (in kVA): 0. 06

0. 09

0. 12

0. 18

0. 25

0. 37

0. 55

0. 75

1. 1

1. 5

1. 8*

2. 2

3 *

3. 7

4*

5. 5

6.3 *

7. 5

1 0 *

11

1 3 *

1 5

17 *

18 .5

20 *

22

25 *

30

32 *

37

40 *

45

5 0 *

5 5

63 *

7 5

8 0 *

9 0

10 0*

11 0

12 5*

1 3 2

1 5 0

1 6 0

1 8 5

2 0 0

22 0

25 0

28 0

30 0

31 5

33 5

35 5

37 5

40 0

42 5

4 5 0

4 7 5

50 0

5 3 0

5 6 0

6 0 0

63 0

6 7 0

71 0

7 5 0

8 0 0

8 5 0

9 0 0

9 5 0

10 00

(*) Note that these are "secondary series" ratings and are only to be used in cases of special need.

Cables Standard cable sizes (in mm2) are as follows: 0. 5

0.7 5

1

1. 5

2. 5

4 6

1 0

1 6

2 5

3 5

5 0

7 0

9 5

12 0

15 0

Categories: Cables | Generators | Motors | Transformers

VSD Cable

18 5

24 0

30 0

40 0

50 0

63 0

80 0

100 0

The use of fast switching circuitry in variable speed (or frequency) drives result in output waveforms with higher levels of harmonic components. These harmonics can cause: 

High electromagnetic interference (EMI) - where the cable is the antenna and the radiated EMI from the cable can induce voltages and currents on nearby cables and electrical equipment. This can especially be a problem when EMI causes noise and crosstalk in control and instrumentation cables.



High earth currents - due to harmonics causing unbalances in the three-phase output. A portion of the unbalanced currents return to the source (i.e. inverter) via the earth conductor. Therefore, VSD cables often have the following special characteristics:



Heavy duty screen - usually copper, applied over the entire cable bundle to reduce EMI



Three earth conductors - located symmetrically in the cable cross-section so that the phase-to-earth distance is identical for each phase, and the cable is "electrically balanced". Sometimes you'll see the designation "3C + 3E" - this isn't a mistake!



Larger earth conductors - to further reduce the impedance of the earth conductor return parth and therefore reduce earth currents



Robust insulation grades - such as XLPE is commonly used over PVC, so that the cable can better withstand transient voltage spikes

Category:Control Contents [hide]

1 Control Systems definition

o

1.1 Open- and closed-loop control

o

1.2 Applications for systems

2 Types of the Control Systems

Control Systems definition According to the McGraw-Hill Encyclopedia of Science and Technology (5th edition), definition of the control system is as follows: Interconnections of components forming system configurations which will provide a desired system response as time progresses. As a colourful example is given the steering of an automobile. The driver observes the position of the car relative to the desired location and makes corrections by turning the steering wheel. The car responds by changing direction, and the driver attempts to decrease the error between the desired and actual course of travel. In this case, the controlled output is the automobile's direction of travel, and the control system includes the driver, the automobile, and the road surface. The control engineer attempts to design a steering control mechanism which will provide a desired response for the automobile's direction control. Different steering designs and automobile designs result in rapid responses, as in the case of sports cars, or relatively slow and comfortable responses, as in the case of large autos with power steering.

Open- and closed-loop control

Figure 1: Open-loop control system

The basis for analysis of a control system is the foundation provided by linear system theory, which assumes a cause-effect relationship for the components of a system. A component or process to be controlled can be represented by a block. Each block possesses an input (cause) and output (effect). The input-output relation represents the cause-and-effect relationship of the process, which in turn represents a processing of the input signal to provide an output signal variable, often with power amplification. An open-loop control system utilizes a controller or control actuator in order to obtain the desired response (Figure 1).

Figure 2: Closed-loop control system

In contrast to an open-loop control system, a closed-loop control system utilizes an additional measure of the actual output in order to compare the actual output with the desired output response (Figure 2). A standard definition of a control system is a control system which tends to maintain a prescribed relationship of one system variable to another by comparing functions of these variables and using the difference as a means of control. In the case of the driver steering an automobile, the driver uses his or her sight to visually measure and compare the actual location of the car with the desired location. The driver then serves as the controller, turning the steering wheel. The process represents the dynamics of the steering mechanism and the automobile response. A control system often uses a function of a prescribed relationship between the output and reference input to control the process. Often, the difference between the output of the process under control and the reference input is amplified and used to control the process so that the difference is continually reduced. The concept has been the foundation for control system analysis and design.

Applications for systems Familiar control systems have the basic closed-loop configuration. For example, a refrigerator has a temperature setting for desired temperature, a thermostat to measure the actual temperature and the error, and a compressor motor for power amplification. Other examples in the home are the oven, furnace, and water heater. In industry, there are controls for speed, process temperature and pressure, position, thickness, composition, and quality, among many others. control concepts have also been applied to mass transportation, electric power systems, automatic warehousing and inventory control, automatic control of agricultural

systems, biomedical experimentation and biological control systems, and social, economic, and political systems.

Types of the Control Systems Generally, all control systems are "computer" based systems, but to have more suptile feeling about those systems we can divide them into followoing groups: 

PLC (Programmable Logic Controller)



AC Drives



DC Drives



SCADA (Supervisory Control And Data Acquisition)



RTU (Remote Terminal Unit)



HMI (Human Computer Interface)

Pages in category "Control" The following 3 pages are in this category, out of 3 total.

A 

Automatic Meter Reading

D 

Droop Control

P 

PLC

Electrical Power How do the various formulae for electrical power fit together? What is the difference between DC, AC and complex power and how do they harmonise with our physical conceptions of energy and power. Contents [hide]

1 Definition 2 DC Power o

2.1 Historical Derivation

o

2.2 Alternative Derivation 3 AC Power

o

3.1 Derivation

o

3.2 Physical Interpretation

o

3.3 Power Factor

o

3.4 Relation to Energy 4 Complex Power

o

4.1 Derivation

o

4.2 Complex Power from Phasors

o

4.3 Complex Exponentials 5 Apparent Power 6 Three-Phase Power

Definition By formal definition, any form of power (e.g. electrical, mechanical, thermal, etc) is the rate at which energy or work is performed. The standard unit of power is the watt (or joules per second). Electrical power is the rate at which electrical energy is delivered to a load (via an electrical circuit) and converted into another form of energy (e.g. heat, light, sound, chemical, kinetic, etc). In of electrical quantities current and voltage, power can be calculated by the following standard formula:

Where P is power in watts, V is potential difference in volts and I is current in amperes. But how did this relationship come about?

DC Power Historical Derivation 19th century English physicist James Prescott Joule observed that the amount of heat energy (H) dissipated by a constant (DC) electrical current (I), through a material of resistance R, in time t, had the following proportional relationship:

As power is the rate of change of energy over time, Joule’s observation above can be restated in of electrical power:

since P = ∆H/∆t. Now applying Ohm’s law R = V/I we get:

Alternative Derivation The SI unit for energy is the joule. For electrical energy, one joule is defined as the work required to move an electric charge of one coloumb through a potential difference of one volt. In other words:

Where E is electrical energy (in joules), Q is charge (in coulombs) and V is potential difference (in volts). Given that electric current is defined as the amount of charge flowing per unit time (I = Q/t), then

As power is the rate of change of energy over time, this reduces to:

Which is the familiar equation for electrical power.

AC Power

In its unaltered form, the power equation P = VI is only applicable to direct current (DC) waveforms. In alternating current (AC) waveforms, the instantaneous value of the waveform is always changing with time, so AC power is slightly different conceptually to DC power.

Derivation AC waveforms in power systems are typically sinusoidal with the following general form, e.g. for a voltage waveform:

Where V is the amplitude of the voltage waveform (volts) ω is the angular frequency = 2πf φ is the phase displacement v(t) is the instantaneous value of voltage at any time t (seconds) If the current waveform i(t) had a similar form, then it can be clearly seen that the instantaneous power p(t)= v(t)i(t) also varies with time. Suppose the current and voltage waveforms are both sinusoids and have a phase difference such that the current lags the voltage by a phase angle θ. Therefore we can write voltage and current as:

The instantaneous power is therefore:

Since the root-mean-square (rms) values of voltage and current are

and

, then

We can simplify this equation further by defining the following :

and

We then get the final AC instantaneous power equation:

The term P is called the active (or real) power and the term Q is called the reactive power. Note that the term cosθ is called the power factor and refers to the proportion of active or real component of AC power being delivered. The active power is the component of power that can do real work (e.g. be converted to useful forms of energy like mechanical, heat or light).

Physical Interpretation From the basic power equation:

We can see that power flow is a sinusoidal waveform with twice the frequency of voltage and current.

From the power equation, we can also break p(t) down into two components: 

A constant term (active power),



An alternating term,

Notice that the alternating term fluctuates around zero and the constant term in the above example is positive. It turns out that the alternating term always fluctuates around zero and the constant term (active power) depends on the power factor cosθ. But what does the power factor represent?

Power Factor Power factor is defined as the cosine of the power angle

, the difference in phase between

voltage and current. People will often refer to power factor as leading or lagging. This is because the power angle can only range between -90° and +90°, and the cosine of an angle in the fourth quadrant (between 0 and -90°) is always positive. Therefore the power factor is also always positive and the only way to distinguish whether the power angle is negative or positive from the power factor is to denote it leading or lagging. 

Lagging power factor: when the current lags the voltage, this means that the current waveform comes delayed after the voltage waveform (and the power angle is positive).



Leading power factor: when the current leads the voltage, this means that the current waveform comes before the voltage waveform (and the power angle is negative).



Unity power factor: refers to the case when the current and voltage are in the same phase.

The physical significance of power factor is in the load impedance. Inductive loads (e.g. coils, motors, etc) have lagging power factors, capacitative loads (e.g. capacitors) have leading power factors and resistive loads (e.g. heaters) have close to unity power factors.

Relation to Energy By definition, power is the rate at which work is being done (or the rate at which energy is being expended). As AC power varies with time, the amount of energy delivered by a given power flow in time T is found by integrating the AC power function over the specified time:

We can see that power is made up of a constant component VrmsIrmscosθ and an alternating component VrmsIrmscos(2ωt - θ). The integration can therefore be broken up as follows:

Suppose we were to integrate over a single period of an AC power waveform (e.g.

).

The alternating component drops out and the integration is solved as follows:

From this we can see that work is done by the active power component only and the alternating component does zero net work, i.e. the positive and negative components cancel each other out.

Complex Power Books often mention AC power in of complex quantities, mainly because it has attractive properties for analysis (i.e. use of vector algebra). But often, complex power is simply defined without being derived. So how do complex numbers follow from the previous definitions of power? For more information on how complex numbers are used in electrical engineering, see the related article on complex electrical quantities. Much of the derivation below is reproduced from this article.

Derivation Back in 1897, Charles Proteus Steinmetz first suggested representing AC waveforms as complex quantities in his book "Theory and Calculation of Alternating Current Phenomena". What follows is a sketch of Steinmetz’s derivation, but specifically using AC power as the quantity under consideration. Previously, we found that AC power is a sinusoidal waveform with the general form (for lagging power factors):

Where V and I are the rms values for voltage and current (A rms) For a fixed angular frequency ω, this waveform can be fully characterized by two parameters: the rms voltage and current product VI and the lagging phase angle - θ. Using these two parameters, we can represent the AC waveform p(t) as a two-dimensional vector S which can be expressed in polar coordinates with magnitude VI and polar angle - θ:

This vector S can be converted into a pair of rectangular coordinates (x, y) such that:

It can be shown trigonometrically that the addition and subtraction of AC power vectors follow the general rules of vector arithmetic, i.e. the rectangular components of two or more sinusoids can be added and subtracted (but not multiplied or divided!). However working with each rectangular component individually can be unwieldy. Suppose we were to combine the rectangular components using a meaningless operator j to distinguish between the horizontal (x) and vertical (y) components. Our vector S now becomes:

Note that the addition sign does not denote a simple addition because x and y are orthogonal quantities in a two-dimensional space. At the moment, j is a meaningless operator to distinguish the vertical component of V. Now consider a rotation of the vector by 90°:

The rotated vector –S=-y+jx Suppose we were to define the operator j to represent a 90° rotation so that multiplying a vector V by j rotates the vector by 90°. Therefore:

Therefore using our definition of j as a 90° rotation operator, j actually turns out to be an imaginary number and the vector S=x+jy is a complex quantity. Therefore our vector S:

Therefore using our definition of j as a 90° rotation operator, j actually turns out to be an imaginary number and the vector S=x+jy is a complex quantity. Therefore our vector S:

Is referred to as complex power or sometimes apparent power (refer to the section below). It is most commonly written in this form:

(for lagging power factor)

(for leading power factor)

Where

and

are the active (or real) and reactive power

quantities defined earlier. Complex Power from Phasors Given voltage and current phasors V and I such that: and

Then the complex power S can be calculated as follows:

Where

is the power angle (i.e phase difference between voltage and current)

Complex Exponentials Using Euler’s formula, we can represent our complex power vector as a complex exponential using the original polar parameters:

The use of complex exponentials gives us an alternative way to think about complex power. We have seen that the vector S rotates around the origin when we vary the phase angle θ. The complex exponential

is actually a rotation operator used to rotate vectors around a circle in

a two-dimensional space (there's a good explanation of this atBetter Explained. Therefore

is a vector with magnitude VI rotated clockwise by angle P = θ.

In other words, complex power is a two-dimensional vector representation of AC power, which is more amenable for manipulation than the time-domain function of AC power p(t). Apparent Power In the previous section, we saw that complex power S is also sometimes called apparent power. However in practice, apparent power is often used to refer to the magnitude ofS, which is

.

Three-Phase Power

So far, we have only been talking about DC and single-phase AC power. The power transferred in a balanced three-phase system is equal to the sum of the powers in each phase, i.e.

where

is the three-phase active power (W)

is the phase-neutral voltage (Vac) is the phase current (A) is the power factor (pu) For a star (wye) connected load:

and For a delta connected load:

and where

and

are the line-to-line voltage and line current respectively.

Therefore, three-phase active power is the same for both star and delta connected loads (in of line quantities):

Similarly, three-phase reactive power and apparent power are as follows:

Feeder Short description A circuit, such as conductors in conduit or a busway run, which carries a large block of power from the service equipment (or genertor switchboard) to a subfeeder or a branch circuit or to some point at which the block power is broken into smaller circuits. Subfeeders originate at a distribution center other than the service equipment or generator switchboard and supply one or more other distribution boards, branch circuit boards, or branch circuits.

Code rules on feeders also apply to subfeeders. Feeders and subfeeders must be capable in carrying the amount of current required by the load, plus any current that may be required in the future. Selection of the size of a feeder depends upon the size and nature of the known load as computed from the branch circuits, the unknown but anticipated future loads and the voltage drop.

MV Network (10 kV) with 3 Feeders, modeled using DIgSILENT's PowerFactory

Feeder Sizing according to the NEC Sections 1.) The feeder conductor ampacity shall be at least equal to 125% of a continuous load (NEC Section 220-10b). 2.) The total load on any overcurrent device located in a board must not exceed 80% of the rating of the overcurrent device (NEC Section 384-16c). 3.) Circuit conductors shall be protected against overcurrent in accordance to their ampacities, but where the ampacity of the conductor does not correspond with the standard ampere rating of a fuse or a circuit breaker, the next higher rating shall be permitted only if this rating does not exceed 800 amperes (NEC Section 240-3). 4.) Circuit conductors shall be protected against overcurrent in accordance to their ampacities, but where the ampacity of the conductor does not correspond with the standard ampere rating of a fuse or a circuit breaker, the next higher rating shall be permitted only if this rating does not exceed 800 amperes (NEC Section 240-3). 5.) These normal ampacities may have to be reduced or derated where there are more than three conductors in a cable or raceway (Note 8 to Tables 310-16 through 310-19). This means a change in ampacities of circuit conductors. 6.) The current permitted to be carried by the branch circuit conductors or feeder may have to be reduced if the load is continuous. This does not mean a change in the ampacities of the conductors but the rule refers to a limit of the load to be carried by the conductors. The change of ampacity of conductors because more than 3 conductors are installed in a cable or raceway is distinctly different from limiting the load (NEC Section 210-22c). Parallel feeders are feeders with more than one conductor per phase. The ampacity of the parallel conductors is equal to the ampacity of one multiplied by the number of conductors in parallel. Parallel conductors shall be of the same size, length and type. Example 1 Determine the minimun size of the conductor that could be used to supply a lighting load of 30 kVA fed by a 240 V, 3-Phase, 3 wire feeder operating at 80% power factor? Following NEC Sections results are: 1.) Feeder Amps = (30,000)/(220 x 1.732) = 78.73 A 2.) Feeder Size = 1.25 x 78.73 = 98.41 (recommended 25 mm2 PVC insulated cables) 

Ampacity 100 A



Max Load Allowed = 100 x 0.80 = 80 A

3.) Feeder Protection = Feeder Ampacity = 100 A 

Use 100 A Circuit breaker or Fuse, rated 240 V, 3 poles

4.) The Busbar in the board shall have a minimum ampacity of 100 A 5.) The mains of the board shall be rated at 100 A, 3-poles, 240 V

6.) The equipment grounding (4th wire) is recommended 16 mm2 PVC insulated cable. ( Reminder: the system in this example is a 3-phase 3 wire. The 4th wire is not a current carrying conductor but is intended for equipment grounding) Category: Fundamentals

IP Rating Contents [hide] 

1 Introduction



2 Summary of IP Ratings



3 Examples



4 Important Points from IEC 60529

Introduction IP Rating refers to the International Protection or Ingress Protection of electrical enclosures, against the intrusion of solid objects, water, dust and accidental to live parts, as defined by IEC 60529. The rating comprises the letters "IP" followed by two numbers (and an optional letter), where the numbers and letters refer to conformity to levels of protection. The Wikipedia article gives a fairly detailed of IP ratings. Therefore this page is only intended to be a summary of the ratings and more importantly, highlight some key points from IEC 60529 that are commonly overlooked. Summary of IP Ratings Leve

First Number (Protected

l

against solids of size:)

0

No protection against and ingress of objects

Second Number (Proection against water)

Not protected

>50 mm - Any large surface of the 1

body, such as the back of a hand,

Dripping water - Dripping water (vertically falling

but no protection against deliberate

drops) shall have no harmful effect.

with a body part

2

>12.5 mm - Fingers or similar

Dripping water when tilted up to 15° - Vertically

objects

dripping water shall have no harmful effect when the enclosure is tilted at an angle up to 15° from

its normal position.

Spraying water - Water falling as a spray at any 3

>2.5 mm - Tools, thick wires, etc.

angle up to 60° from the vertical shall have no harmful effect.

Splashing water - Water splashing against the 4

>1 mm - Most wires, screws, etc.

enclosure from any direction shall have no harmful effect.

Dust protected - Ingress of dust is not entirely prevented, but it must 5

not enter in sufficient quantity to interfere with the satisfactory operation of the equipment;

Water jets - Water projected by a nozzle (6.3mm) against enclosure from any direction shall have no harmful effects.

complete protection against

6

Dust tight - No ingress of dust; complete protection against

Powerful water jets - Water projected in powerful jets (12.5mm nozzle) against the enclosure from any direction shall have no harmful effects.

Immersion up to 1 m - Ingress of water in harmful quantity shall not be possible when the 7

N/A

enclosure is immersed in water under defined conditions of pressure and time (up to 1 m of submersion).

Immersion beyond 1 m - The equipment is suitable for continuous immersion in water under conditions which shall be specified by the 8

N/A

manufacturer. Normally, this will mean that the equipment is hermetically sealed. However, with certain types of equipment, it can mean that water can enter but only in such a manner that produces no harmful effects.

Examples An IP54 enclosure is dust protected (1st number = 5) and protected against splashing wayer (2nd number = 4).

An IP66/67 enclosure is dual protected, both for immersion up to 1m and powerful water jets. Note that it is not always true that an enclosure with a single rating such as IP68 is suitable for use in lower IP environments, such as IP66 (for more details, see the next section below). Important Points from IEC 60529 Section 6 of IEC 60529 makes an important point about backward compliance of IP ratings for water protection, as per the extract below: "Up to and including second characteristic numeral 6, the designation implies compliance with the requirements for all lower characteristic numerals. However, the tests establishing compliance with any one of the lower degrees of protection need not necessarily be carried out provided that these tests obviously would be met if applied. An enclosure designated with second characteristic numeral 7 or 8 only is considered unsuitable for exposure to water jets (designated by second characteristic numeral 5 or 6) and need not comply with requirements for numeral 5 or 6 unless it is dual coded." Category: Fundamentals Infinite Bus The infinite bus concept is a simplifying assumption that is applied to buses or nodes with an infinite upstream fault capacity (or an equivalent upstream source impedance of zero). What this means is that the voltage at this bus or node is always constant and any downstream disturbances do not affect the voltage. Obviously, there is no such thing as an infinite bus in practice, but it is a useful approximation to make when modelling a connection to a large utility or grid network (that is, large relative to the downstream system). Such large networks are sometimes called "stiff" networks or systems. Infinite Bus Concept

Figure 1: Infinite bus f and U plot The infinite bus is a useful concept that summarizes how most people already view the power grid. It can be applied when the power grid is sufficiently large that the action of any one or generator will not affect the operation of the power grid. In an infinite bus: 

1. System frequency is constant, independent of power flow



2. System voltage is constant, independent of reactive power consumed or supplied

An infinite bus assumed in many small electrical applications. As an example, we take for granted that the voltage supply to a residential outlet will be 230 V and 50 Hz: the voltage and frequency are not changed when you turn the TV on. Frequency-power and voltage-reactive power plots for an infinite bus are shown on Figure 1. Operating a generator connected to an infinite bus

Figure 2: Infinite bus f and P plot If a generator is operated off an infinite bus: 

1. Terminal voltage and frequency (and hence speed) are constant



2. The no-load settings of the mechanical system governor can be adjusted to supply more or less power

Other impacts on operation can be best understood by considering the phasor diagram. Phasor Diagrams To simplify analysis and aid understanding, neglect armature resistance

Since voltage is constant and assuming synchronous reactance is also constant, changing the power (with the mechanical system) will set E sin δ and |E| will control the reactive power. These effects can be seen be considering two cases. 

1. Constant Excitation, Changing power



2. Constant Power, Changing Excitation

Category: Fundamentals

AC Power Transmission Contents

[hide] 

1 Introduction



2 Power-Angle Relationship



3 Steady-State Voltage Stability Limits



4 Related Topics

Introduction Consider the following model depicting the transfer of AC power between two buses across a line:

Figure 1. Simple AC power transmission model

Where

is the voltage and phase angle at the sending end is the voltage and phase angle at the receiving end

is the complex impedance of the line.

is the current phasor The complex AC power transmitted to the receiving end bus can be calculated as follows:

At this stage, the impedance is purposely undefined and in the following sections, two different line impedance models will be introduced to illustrate the following fundamental features of AC power transmission: 

The power-angle relationship



PV curves and steady-state voltage stability

Power-Angle Relationship In its simplest form, we neglect the line resistance and capacitance and represent the line as purely inductive, i.e.

. The power transfer across the line is therefore:

Where

is called the power angle, which is the phase difference between the

voltages on bus 1 and bus 2. We can see that active and reactive power transfer can be characterised as follows:

Plotting the active power transfer for various values of

, we get:

Figure 2. Active power transfer characteristic for a lossless line

The figure above is often used to articulate the Power-Angle Relationship. We can see that in this simple model, power will only flow when there is a phase difference between the voltages at the sending and receiving ends. Moreover, there is a theoretical limit to how much power can be transmitted through a line (shown here when the phase difference is 90 o). This limit will be a recurring theme in these line models, i.e. lines have natural capacity limits on how much power they can transmit. Steady-State Voltage Stability Limits The lossless (L) line model can be made more realistic by adding a resistive component, i.e.

. The power transfer across the line is therefore:

From the above equation, the active and reactive power transfer can be shown to be:

From the active power equation, we can solve for the voltage at bus 2 using the quadratic equation, i.e.:

Where

By keeping the voltage at bus 1, power angle and line impedance constant, we can plot the effect of increasing the active power on the voltage at bus 2 on a PV curve:

Anatomy of a Short Circuit

A short circuit is an electrical fault where a conductive path (usually of low impedance) is formed between two or more conductive parts of an electrical system (e.g. phase-phase, phase-earth, phase-neutral, etc). This article looks at the nature of short circuits and tries to break down and explain the constituent parts of fault currents. Note that the "short circuit" and "fault" are often used interchangeably. In most networks, a short circuit is similar to the closing transient of an RL circuit, where the R and L components are the impedances of the source(s). The transient characteristics of short circuit currents vary depending on whether they are near or far from synchronous generators. The sections below describe the two general types of short circuits: Near-to-Generator Short Circuit A fault close to a synchronous generator has the following maximum short circuit current isc(t):

Where

is the phase-to-neutral rms voltage at the generator terminals (V)

is the generator direct-axis subtransient reactance (Ω) is the generator direct-axis transient reactance (Ω) is the generator synchronous reactance (Ω) is the generator subtransient time constant (s) is the generator transient time constant (s) is the aperiodic time constant (s) From the above equation, it can be seen that the short circuit current can be broken up into an aperiodic current (dc component of the short circuit):

And a series of three damped sinusoidal waveforms corresponding to the following distinct stages:

(1) Subtransient component:

This period typically lasts 10 to 20ms from the start of the fault. The subtransient reactance is due to the flux casued by the stator currents crossing the air gap and reaching the rotor surface or amortisseur / damper windings.

(2) Transient component:

This period typically lasts 100 to 400ms after the subtransient period. The transient reactance occurs when all the damping currents in the rotor surface or amortisseur / damper windings have decayed, but while the damping currents in the field winding are still in action.

(3) Steady-state component: The steady-state occurs after the transient period when all the damping currents in the field windings have decayed, and essentially remains until the fault is cleared.

Putting these all together, we get the familiar near-to-generator short circuit waveform:

Far-from-Generator Short Circuit In short circuits occurring far from synchronous generators, we can ignore the effects of the generator subtransient behaviour. It can be shown through transient circuit analysis that the maximum far-from-generator short circuit is as follows:

Where

is the rms voltage of the circuit (V)

is the fault impedance (Ω)

is the R/X ratio at the point of fault (pu) We can see that there are two components:

(1) A decaying aperiodic component:

(2) A steady state component:

Putting these together, we get the total far-from-generator fault current:

During the transient period, the peak transient current is typically 1.5 to

Electrical Power (Redirected from Complex Power) How do the various formulae for electrical power fit together? What is the difference between DC, AC and complex power and how do they harmonise with our physical conceptions of energy and power. Contents [hide] 

1 Definition



2 DC Power





o

2.1 Historical Derivation

o

2.2 Alternative Derivation

3 AC Power o

3.1 Derivation

o

3.2 Physical Interpretation

o

3.3 Power Factor

o

3.4 Relation to Energy

4 Complex Power

o

4.1 Derivation

o

4.2 Complex Power from Phasors

o

4.3 Complex Exponentials



5 Apparent Power



6 Three-Phase Power

Definition By formal definition, any form of power (e.g. electrical, mechanical, thermal, etc) is the rate at which energy or work is performed. The standard unit of power is the watt (or joules per second). Electrical power is the rate at which electrical energy is delivered to a load (via an electrical circuit) and converted into another form of energy (e.g. heat, light, sound, chemical, kinetic, etc). In of electrical quantities current and voltage, power can be calculated by the following standard formula:

Where P is power in watts, V is potential difference in volts and I is current in amperes. But how did this relationship come about? DC Power Historical Derivation 19th century English physicist James Prescott Joule observed that the amount of heat energy (H) dissipated by a constant (DC) electrical current (I), through a material of resistance R, in time t, had the following proportional relationship:

As power is the rate of change of energy over time, Joule’s observation above can be restated in of electrical power:

since P = ∆H/∆t. Now applying Ohm’s law R = V/I we get:

Alternative Derivation The SI unit for energy is the joule. For electrical energy, one joule is defined as the work required to move an electric charge of one coloumb through a potential difference of one volt. In other words:

Where E is electrical energy (in joules), Q is charge (in coulombs) and V is potential difference (in volts). Given that electric current is defined as the amount of charge flowing per unit time (I = Q/t), then

As power is the rate of change of energy over time, this reduces to:

Which is the familiar equation for electrical power. AC Power In its unaltered form, the power equation P = VI is only applicable to direct current (DC) waveforms. In alternating current (AC) waveforms, the instantaneous value of the waveform is always changing with time, so AC power is slightly different conceptually to DC power. Derivation AC waveforms in power systems are typically sinusoidal with the following general form, e.g. for a voltage waveform:

Where V is the amplitude of the voltage waveform (volts) ω is the angular frequency = 2πf φ is the phase displacement v(t) is the instantaneous value of voltage at any time t (seconds) If the current waveform i(t) had a similar form, then it can be clearly seen that the instantaneous power p(t)= v(t)i(t) also varies with time. Suppose the current and voltage waveforms are both sinusoids and have a phase difference such that the current lags the voltage by a phase angle θ. Therefore we can write voltage and current as:

The instantaneous power is therefore:

Since the root-mean-square (rms) values of voltage and current are

and

, then

We can simplify this equation further by defining the following :

and

We then get the final AC instantaneous power equation:

The term P is called the active (or real) power and the term Q is called the reactive power. Note that the term cosθ is called the power factor and refers to the proportion of active or real component of AC power being delivered. The active power is the component of power that can do real work (e.g. be converted to useful forms of energy like mechanical, heat or light). Physical Interpretation From the basic power equation:

We can see that power flow is a sinusoidal waveform with twice the frequency of voltage and current.

From the power equation, we can also break p(t) down into two components: 

A constant term (active power),



An alternating term,

Notice that the alternating term fluctuates around zero and the constant term in the above example is positive. It turns out that the alternating term always fluctuates around zero and the

constant term (active power) depends on the power factor cosθ. But what does the power factor represent? Power Factor Power factor is defined as the cosine of the power angle

, the difference in phase between

voltage and current. People will often refer to power factor as leading or lagging. This is because the power angle can only range between -90° and +90°, and the cosine of an angle in the fourth quadrant (between 0 and -90°) is always positive. Therefore the power factor is also always positive and the only way to distinguish whether the power angle is negative or positive from the power factor is to denote it leading or lagging. 

Lagging power factor: when the current lags the voltage, this means that the current waveform comes delayed after the voltage waveform (and the power angle is positive).



Leading power factor: when the current leads the voltage, this means that the current waveform comes before the voltage waveform (and the power angle is negative).



Unity power factor: refers to the case when the current and voltage are in the same phase.

The physical significance of power factor is in the load impedance. Inductive loads (e.g. coils, motors, etc) have lagging power factors, capacitative loads (e.g. capacitors) have leading power factors and resistive loads (e.g. heaters) have close to unity power factors. Relation to Energy By definition, power is the rate at which work is being done (or the rate at which energy is being expended). As AC power varies with time, the amount of energy delivered by a given power flow in time T is found by integrating the AC power function over the specified time:

We can see that power is made up of a constant component VrmsIrmscosθ and an alternating component VrmsIrmscos(2ωt - θ). The integration can therefore be broken up as follows:

Suppose we were to integrate over a single period of an AC power waveform (e.g.

).

The alternating component drops out and the integration is solved as follows:

From this we can see that work is done by the active power component only and the alternating component does zero net work, i.e. the positive and negative components cancel each other out. Complex Power

Books often mention AC power in of complex quantities, mainly because it has attractive properties for analysis (i.e. use of vector algebra). But often, complex power is simply defined without being derived. So how do complex numbers follow from the previous definitions of power? For more information on how complex numbers are used in electrical engineering, see the related article on complex electrical quantities. Much of the derivation below is reproduced from this article. Derivation Back in 1897, Charles Proteus Steinmetz first suggested representing AC waveforms as complex quantities in his book "Theory and Calculation of Alternating Current Phenomena". What follows is a sketch of Steinmetz’s derivation, but specifically using AC power as the quantity under consideration. Previously, we found that AC power is a sinusoidal waveform with the general form (for lagging power factors):

Where V and I are the rms values for voltage and current (A rms) For a fixed angular frequency ω, this waveform can be fully characterized by two parameters: the rms voltage and current product VI and the lagging phase angle - θ. Using these two parameters, we can represent the AC waveform p(t) as a two-dimensional vector S which can be expressed in polar coordinates with magnitude VI and polar angle - θ:

This vector S can be converted into a pair of rectangular coordinates (x, y) such that:

It can be shown trigonometrically that the addition and subtraction of AC power vectors follow the general rules of vector arithmetic, i.e. the rectangular components of two or more sinusoids can be added and subtracted (but not multiplied or divided!). However working with each rectangular component individually can be unwieldy. Suppose we were to combine the rectangular components using a meaningless operator j to distinguish between the horizontal (x) and vertical (y) components. Our vector S now becomes:

Note that the addition sign does not denote a simple addition because x and y are orthogonal quantities in a two-dimensional space. At the moment, j is a meaningless operator to distinguish the vertical component of V. Now consider a rotation of the vector by 90°:

The rotated vector Suppose we were to define the operator j to represent a 90° rotation so that multiplying a vector V by j rotates the vector by 90°. Therefore:

Therefore using our definition of j as a 90° rotation operator, j actually turns out to be an imaginary number and the vector S=x+jy is a complex quantity. Therefore our vector S:

Is referred to as complex power or sometimes apparent power (refer to the section below). It is most commonly written in this form: (for lagging power factor) (for leading power factor) Where

and

are the active (or real) and reactive power

quantities defined earlier. Complex Power from Phasors Given voltage and current phasors V and I such that: and

Then the complex power S can be calculated as follows:

Where

is the power angle (i.e phase difference between voltage and current)

Complex Exponentials Using Euler’s formula, we can represent our complex power vector as a complex exponential using the original polar parameters:

The use of complex exponentials gives us an alternative way to think about complex power. We have seen that the vector S rotates around the origin when we vary the phase angle θ. The complex exponential

is actually a rotation operator used to rotate vectors around a circle in

a two-dimensional space (there's a good explanation of this at Better Explained. Therefore

is a vector with magnitude VI rotated clockwise by angle P = θ.

In other words, complex power is a two-dimensional vector representation of AC power, which is more amenable for manipulation than the time-domain function of AC power p(t). Apparent Power In the previous section, we saw that complex power S is also sometimes called apparent power. However in practice, apparent power is often used to refer to the magnitude of S, which is

.

Three-Phase Power So far, we have only been talking about DC and single-phase AC power. The power transferred in a balanced three-phase system is equal to the sum of the powers in each phase, i.e.

where

is the three-phase active power (W)

is the phase-neutral voltage (Vac) is the phase current (A) is the power factor (pu) For a star (wye) connected load:

and For a delta connected load:

and where

and

are the line-to-line voltage and line current respectively.

Therefore, three-phase active power is the same for both star and delta connected loads (in of line quantities):

Similarly, three-phase reactive power and apparent power are as follows:

Figure 3. PV Curve at Bus 2 for a RL line

The PV curve shows that the voltage at bus 2 falls as the active power loading increases. The voltage falls until it hits a critical point (around 2.7pu loading) where the quadratic equation is no longer solvable. This is referred to as the "nose point" or "point of voltage collapse", and is the theoretical steady-state stability limit of the line. Related Topics 

Power Flow



Simple Power Flow Example



Overhead Line Models

Categories: Fundamentals | Modelling/Analysis | Overhead Lines

Electrical Power (Redirected from Complex Power) How do the various formulae for electrical power fit together? What is the difference between DC, AC and complex power and how do they harmonise with our physical conceptions of energy and power. Contents [hide] 

1 Definition



2 DC Power





o

2.1 Historical Derivation

o

2.2 Alternative Derivation

3 AC Power o

3.1 Derivation

o

3.2 Physical Interpretation

o

3.3 Power Factor

o

3.4 Relation to Energy

4 Complex Power o

4.1 Derivation

o

4.2 Complex Power from Phasors

o

4.3 Complex Exponentials



5 Apparent Power



6 Three-Phase Power

Definition By formal definition, any form of power (e.g. electrical, mechanical, thermal, etc) is the rate at which energy or work is performed. The standard unit of power is the watt (or joules per second). Electrical power is the rate at which electrical energy is delivered to a load (via an electrical circuit) and converted into another form of energy (e.g. heat, light, sound, chemical, kinetic, etc). In of electrical quantities current and voltage, power can be calculated by the following standard formula:

Where P is power in watts, V is potential difference in volts and I is current in amperes. But how did this relationship come about? DC Power Historical Derivation 19th century English physicist James Prescott Joule observed that the amount of heat energy (H) dissipated by a constant (DC) electrical current (I), through a material of resistance R, in time t, had the following proportional relationship:

As power is the rate of change of energy over time, Joule’s observation above can be restated in of electrical power:

since P = ∆H/∆t. Now applying Ohm’s law R = V/I we get:

Alternative Derivation The SI unit for energy is the joule. For electrical energy, one joule is defined as the work required to move an electric charge of one coloumb through a potential difference of one volt. In other words:

Where E is electrical energy (in joules), Q is charge (in coulombs) and V is potential difference (in volts). Given that electric current is defined as the amount of charge flowing per unit time (I = Q/t), then

As power is the rate of change of energy over time, this reduces to:

Which is the familiar equation for electrical power. AC Power In its unaltered form, the power equation P = VI is only applicable to direct current (DC) waveforms. In alternating current (AC) waveforms, the instantaneous value of the waveform is always changing with time, so AC power is slightly different conceptually to DC power. Derivation AC waveforms in power systems are typically sinusoidal with the following general form, e.g. for a voltage waveform:

Where V is the amplitude of the voltage waveform (volts) ω is the angular frequency = 2πf φ is the phase displacement v(t) is the instantaneous value of voltage at any time t (seconds) If the current waveform i(t) had a similar form, then it can be clearly seen that the instantaneous power p(t)= v(t)i(t) also varies with time. Suppose the current and voltage waveforms are both sinusoids and have a phase difference such that the current lags the voltage by a phase angle θ. Therefore we can write voltage and current as:

The instantaneous power is therefore:

Since the root-mean-square (rms) values of voltage and current are

and

, then

We can simplify this equation further by defining the following :

and

We then get the final AC instantaneous power equation:

The term P is called the active (or real) power and the term Q is called the reactive power. Note that the term cosθ is called the power factor and refers to the proportion of active or real component of AC power being delivered. The active power is the component of power that can do real work (e.g. be converted to useful forms of energy like mechanical, heat or light). Physical Interpretation From the basic power equation:

We can see that power flow is a sinusoidal waveform with twice the frequency of voltage and current.

From the power equation, we can also break p(t) down into two components: 

A constant term (active power),



An alternating term,

Notice that the alternating term fluctuates around zero and the constant term in the above example is positive. It turns out that the alternating term always fluctuates around zero and the

constant term (active power) depends on the power factor cosθ. But what does the power factor represent? Power Factor Power factor is defined as the cosine of the power angle

, the difference in phase between

voltage and current. People will often refer to power factor as leading or lagging. This is because the power angle can only range between -90° and +90°, and the cosine of an angle in the fourth quadrant (between 0 and -90°) is always positive. Therefore the power factor is also always positive and the only way to distinguish whether the power angle is negative or positive from the power factor is to denote it leading or lagging. 

Lagging power factor: when the current lags the voltage, this means that the current waveform comes delayed after the voltage waveform (and the power angle is positive).



Leading power factor: when the current leads the voltage, this means that the current waveform comes before the voltage waveform (and the power angle is negative).



Unity power factor: refers to the case when the current and voltage are in the same phase.

The physical significance of power factor is in the load impedance. Inductive loads (e.g. coils, motors, etc) have lagging power factors, capacitative loads (e.g. capacitors) have leading power factors and resistive loads (e.g. heaters) have close to unity power factors. Relation to Energy By definition, power is the rate at which work is being done (or the rate at which energy is being expended). As AC power varies with time, the amount of energy delivered by a given power flow in time T is found by integrating the AC power function over the specified time:

We can see that power is made up of a constant component VrmsIrmscosθ and an alternating component VrmsIrmscos(2ωt - θ). The integration can therefore be broken up as follows:

Suppose we were to integrate over a single period of an AC power waveform (e.g.

).

The alternating component drops out and the integration is solved as follows:

From this we can see that work is done by the active power component only and the alternating component does zero net work, i.e. the positive and negative components cancel each other out. Complex Power

Books often mention AC power in of complex quantities, mainly because it has attractive properties for analysis (i.e. use of vector algebra). But often, complex power is simply defined without being derived. So how do complex numbers follow from the previous definitions of power? For more information on how complex numbers are used in electrical engineering, see the related article on complex electrical quantities. Much of the derivation below is reproduced from this article. Derivation Back in 1897, Charles Proteus Steinmetz first suggested representing AC waveforms as complex quantities in his book "Theory and Calculation of Alternating Current Phenomena". What follows is a sketch of Steinmetz’s derivation, but specifically using AC power as the quantity under consideration. Previously, we found that AC power is a sinusoidal waveform with the general form (for lagging power factors):

Where V and I are the rms values for voltage and current (A rms) For a fixed angular frequency ω, this waveform can be fully characterized by two parameters: the rms voltage and current product VI and the lagging phase angle - θ. Using these two parameters, we can represent the AC waveform p(t) as a two-dimensional vector S which can be expressed in polar coordinates with magnitude VI and polar angle - θ:

This vector S can be converted into a pair of rectangular coordinates (x, y) such that:

It can be shown trigonometrically that the addition and subtraction of AC power vectors follow the general rules of vector arithmetic, i.e. the rectangular components of two or more sinusoids can be added and subtracted (but not multiplied or divided!). However working with each rectangular component individually can be unwieldy. Suppose we were to combine the rectangular components using a meaningless operator j to distinguish between the horizontal (x) and vertical (y) components. Our vector S now becomes:

Note that the addition sign does not denote a simple addition because x and y are orthogonal quantities in a two-dimensional space. At the moment, j is a meaningless operator to distinguish the vertical component of V. Now consider a rotation of the vector by 90°:

The rotated vector Suppose we were to define the operator j to represent a 90° rotation so that multiplying a vector V by j rotates the vector by 90°. Therefore:

Therefore using our definition of j as a 90° rotation operator, j actually turns out to be an imaginary number and the vector S=x+jy is a complex quantity. Therefore our vector S:

Is referred to as complex power or sometimes apparent power (refer to the section below). It is most commonly written in this form: (for lagging power factor) (for leading power factor) Where

and

are the active (or real) and reactive power

quantities defined earlier. Complex Power from Phasors Given voltage and current phasors V and I such that: and

Then the complex power S can be calculated as follows:

Where

is the power angle (i.e phase difference between voltage and current)

Complex Exponentials Using Euler’s formula, we can represent our complex power vector as a complex exponential using the original polar parameters:

The use of complex exponentials gives us an alternative way to think about complex power. We have seen that the vector S rotates around the origin when we vary the phase angle θ. The complex exponential

is actually a rotation operator used to rotate vectors around a circle in

a two-dimensional space (there's a good explanation of this at Better Explained. Therefore

is a vector with magnitude VI rotated clockwise by angle P = θ.

In other words, complex power is a two-dimensional vector representation of AC power, which is more amenable for manipulation than the time-domain function of AC power p(t). Apparent Power In the previous section, we saw that complex power S is also sometimes called apparent power. However in practice, apparent power is often used to refer to the magnitude of S, which is

.

Three-Phase Power So far, we have only been talking about DC and single-phase AC power. The power transferred in a balanced three-phase system is equal to the sum of the powers in each phase, i.e.

where

is the three-phase active power (W)

is the phase-neutral voltage (Vac) is the phase current (A) is the power factor (pu) For a star (wye) connected load:

and For a delta connected load:

and where

and

are the line-to-line voltage and line current respectively.

Therefore, three-phase active power is the same for both star and delta connected loads (in of line quantities):

Similarly, three-phase reactive power and apparent power are as follows:

Coil

Figure 1. Rendering of a coil / solenoid In electrical engineering, a coil or solenoid refers to a current-carrying wire loop that is wound in a tight spiral (sometimes around a ferromagnetic core). Contents [hide] 

1 Magnetic Field of a Coil



2 Magnetic Flux



3 Flux Linkage



4 Inductance

Magnetic Field of a Coil

Consider a long coil such that its length is very large compared to its cross-sectional diameter. Experiments show that the magnetic field outside the coil is negligible compared with the field inside the coil. The field lines inside the coil always run perpendicular to the cross-section of the coil (since from Gauss' law, magnetic fields have zero divergence):

Figure 2. Magnetic field lines in and around a coil

Using Ampere's law, we can calculate the the magnetic field inside the coil. Suppose there is a closed rectangular loop (C) that goes parallel to the field inside the coil for length L, comes out at right angles and returns outside the coil:

Figure 3. Closed loop C around part of the coil

Ampere's law states that any closed line integral of the magnetic field is equal to the total current that the line's path encloses, i.e.

In the case of the coil, it is assumed that there is no magnetic field outside the coil, so the line integral can be evaluated simply as the magnitude of the B field times the length of the line inside the coil (note that inside the coil, the magnitude of the magnetic field is constant along any path parallel to the axis):

The total current enclosed by the path is equal to the current I flowing through the wire multiplied by the number of turns N that the path encloses:

Therefore:

The magnetic field inside the coil is thus:

Magnetic Flux

Figure 3. Magnetic flux lines through the cross-sectional surface of the coil Since we assumed that the magnetic field is negligible outside the coil, the magnetic flux is completely due to the field inside the coil ing through the cross-sectional surface of the coil. Given that the field inside the coil is always perpendicular to the cross-section of the coil, the surface integration is simply the magnitude of the field multiplied by the cross-sectional area A:

Flux Linkage Due to the additive effects of Ampere's law, the total flux through the coil can be increased by adding more turns. The flux linkage is the total amount of flux that links all the current (and by extension, turns of the coil) that generate it.

Since magnetic flux density is uniform inside a simple coil, the flux linkage is equivalent to the magnetic flux derived above:

Inductance The inductance of the coil is:

Category: Fundamentals

Power Factor Contents [hide] 

1 Introduction



2 Synchronous Machine PF Contribution o



2.1 Capability Curve

3 References

Introduction Power factor is defined as the cosine of the power angle

, the difference in phase between

voltage and current, or simplified as the ration of the real power (P) and the apparent power (S). People will often refer to power factor as leading or lagging. This is because the power angle can only range between -90° and +90°, and the cosine of an angle in the fourth quadrant (between 0 and -90°) is always positive. Therefore the power factor is also always positive and the only way to distinguish whether the power angle is negative or positive from the power factor is to denote it leading or lagging. 

Lagging power factor: when the current lags the voltage, this means that the current waveform comes delayed after the voltage waveform (and the power angle is positive). In the context of the power generation it means that the generator injects reactive power (over-excited regime), with respect to the Q-maximum defined by the capability curve (i.e. S = P + jQ).



Leading power factor: when the current leads the voltage, this means that the current waveform comes before the voltage waveform (and the power angle is negative). The generator absorbs reactive power (under-excited regime), with respect to the Q-minimum defined by the capability curve (i.e. S = P - jQ).



Unity power factor: refers to the case when the current and voltage are in the same phase.

The physical significance of power factor is in the load impedance. Inductive loads (e.g. coils, motors, etc) have lagging power factors, capacitative loads (e.g. capacitors) have leading power factors and resistive loads (e.g. heaters) have close to unity power factors. A power factor of one or "unity power factor" is the goal of any electric utility company since if the power factor is less than one, they have to supply more current to the for a given amount of power use. In doing so, they incur more line losses. They also must have larger capacity equipment in place than would be otherwise necessary. As a result, an industrial facility will be charged a penalty if its power factor is much different from 1. Industrial facilities tend to have a "lagging power factor", where the current lags the voltage (like an inductor). This is primarily the result of having a lot of electric induction motors - the windings of motors act as inductors as seen by the power supply. Capacitors have the opposite effect and can compensate for the inductive motor windings. Some industrial sites will have large banks of capacitors strictly for the purpose of correcting the power factor back toward one to save on utility company charges. Synchronous Machine PF Contribution Information about the operation of synchronous machines is often determined by analysis of the armature circuit phasor diagram. Taking the armature circuit equation:

Where;

E is the open-circtuit induced voltage, also called excitation, and delta is the load angle.

The phasor diagram is constructed by taking the terminal voltage (V) as the phase reference. Once the terminal voltage is drawn, additional phasors for current, resistive voltage drop, reactance voltage drop and induced voltage can be added. The shape of the phasor diagram is dependent on the phase of the current relative to the terminal voltage. Examples of leading, lagging and unity power factor are shown below.

Capability Curve Alternator capability curve - Green area is normal operating range of a typical synchronous machine, yellow is abnormal but not damaging and operating in red regional will cause damage or misoperation.

The ability of any generator to absorb the kVAR is termed as reverse kVAR limit. This ability is defined as reactive capability curve. Figure above shows typical generator reactive capability curve. X-axis is the kVAR produced or absorbed (positive to the right). Y-axis indicates the kW (positive going up). kVAR and kW are shown as per unit quantities based on the rating of the alternator (not necessarily the generator set, which may have a lower rating. The normal operating range of a generator set is between 0 and 100 percent of the kW rating of the alternator (positive) and between 0.8 and 1.0 power factor (green area on curve). The black lines on the curves show the operating range of a specific alternator when operating outside of normal range. Notice that as power factor drops, the machine must be de-rated to prevent overheating. On the left quadrant, you can see that near-normal output (yellow area) can be achieved with some leading power factor load, in this case, down to about 0.97 power factor, leading. At that point, the ability to absorb additional kVAR quickly drops to near zero (red area), indicating that the AVR is “turning off” and any level of reverse kVAR greater than the level shown will cause the machine to lose control of voltage. A good rule of thumb for generators is that it can absorb about 20% of its rated kVAR output in reverse kVAR without losing control of voltage. However, since this characteristic is not universal, it is advisable for a system designer to specify the reverse kVAR limit used in his design, or the magnitude of the reverse kVAR load that is expected. More in the section of the Electrical Power. References

Power factor and its importance Synchronous generator: Capability curves Capacitor banks in power system Category: Fundamentals

Power Flow Contents [hide] 

1 Introduction



2 Historical Context



3 Per Unit Representation



4 Single Phase Representation



5 Nodal Representation



6 Bus ittance Matrix



7 Calculated Bus Power Injections



8 Classical Formulation of the Power Flow Problem o

8.1 Types of Buses

o

8.2 Power Mismatch Vector

o

8.3 General Solution Procedure

o

8.4 Iteration Methods



9 References



10 Related Topics

Introduction The objective of the power flow (or load flow) calculation is to determine the steady-state operating conditions of an electrical network. The power flow problem is formulated such that at each bus in the network, the following four variables are solved so as to fully define the power flows in the network: 

Bus voltage magnitude,



Bus voltage angle,



Active power injected into (or consumed at) the bus,



Reactive power injected into (or consumed at) the bus,

Figure 1. AC power transmission between two buses In the simplest case of AC power transmission between two buses connected by a line (as shown in Figure 1), the complex AC power flow at the receiving end bus can be calculated as follows:

Similarly, the power flow at the sending end bus is:

where

is the voltage and phase angle at the sending end is the voltage and phase angle at the receiving end

is the complex impedance of the line.

is the current phasor In power flow calculations, it is generally more convenient to represent impedances as ittances, i.e.

so that the current phasors are calculated by multiplication rather

than complex division:

The equations for the two bus system above form the basis of the power flow calculations. In this article, these equations are extended to larger systems of arbitrary size and topology. Historical Context

Westinghouse network analyser circa 1950 Power flow calculations evolved from the planning departments of electricity utilities in the early 20th century, where they were (and still are) used to simulate the effects of network augmentations, different load scenarios, network configurations, etc. Early power flows were solved by AC network analyzers (or calculating boards), which were analog computers containing resistors, inductors and capacitors calibrated to be a miniature scale equivalent of the actual electrical network. For large systems, these network analysers took up the space of entire rooms. As they were physical in nature, the network analysers needed to be re-wired for each different configuration, augmentation or scenario to be studied. Starting with the seminal paper by Ward and Hale in 1956 [1], the use of digital computers would enable power flow calculations to be performed faster and in a more flexible manner. The iterative method proposed by Ward and Hale (which became known as the Gauss-Seidel method) was straightforward to implement, but exhibited poor convergence characteristics. In 1961, Van Ness and Griffin [2] introduced Newton's method for solving power flows (which later became known as the Newton-Raphson method), which had more favourable characteristics but was limited to smaller networks due to computer memory requirements. In their 1967 paper, Tinney and Hart [3] exploited the sparsity properties of the Ybus matrix (and by extension, theJacobian matrix) and in conjunction with numerical techniques such as triangular factorisation and optimal ordering, were able to make the Newton-Raphson algorithm practical for solving large networks using the computing resources available at the time. In 1974, Stott and Alsac [4] recognised that in many practical networks there was decoupling between 1) active power and voltage and 2) reactive power and phase angle. The proposed an algorithm (the fast decoupled load flow) that significantly reduced the computational

requirements to construct the Jacobian matrix and therefore led to large gains in computational speed (although at the expense of a little accuracy). Per Unit Representation To simplify the calculation of ittances / impedances across different voltage levels, it is convenient to use a per-unit representation of the network. By default, most power flow programs use a system-wide MVA base of 100MVA. Single Phase Representation In the basic power flow formulation, three-phase systems are represented in single-phase form, based on the assumption that the system is perfectly balanced (e.g. loads and generation are balanced, transmission lines are fully transposed, etc). This assumption holds relatively well for high voltage transmission systems, but begins to break down at smaller scales (e.g. low voltage distribution level), where a full three-phase power flow formulation is necessary. Using a single-phase representation is convenient as it allows impedances to be formulated as single complex quantities (R + jX) rather than a 3x3 matrix of mutually coupled impedances in a full three-phase representation. Voltages in the single-phase formulation are usually referenced to earth. Nodal Representation The electrical network needs to be represented in such a way so that the quantities of interest (e.g. voltage, power flows, etc) can be solved using either nodal analysis ormesh analysis approaches. The nodal method is the standard approach for power flow calculations for several reasons: 1) busbars in the system can be easily translated into nodes, 2) the ittance matrix (without mutual couplings) can be built from inspection, and 3) the nodal method can exploit the sparsity of the ittance matrix. For example, consider the simple system below consisting of three buses (numbered 1, 2 and 3), two generators (G1 and G2), a load (L2) and a shunt capacitor (C2) connected via transmission lines:

Figure 2. Simple three bus system

In the nodal representation, the buses are represented as nodes, the generators and load are represented as current injections while the shunt capacitor and lines are represented as ittances:

Figure 3. Single-phase nodal representation of three bus system

Note that the line at the bottom represents the reference node, usually taken to be an earth reference. All node voltages are expressed with respect to this reference node. From Kirchhoff's current law, we can see that the injected currents must equal the sum of the branch currents leaving the node. For example, at node 1:

Similarly, at node 2:

Note the negative sign for the current

indicating that it is a load and current is leaving the

bus as opposed to being injected. Note also the effect of the shunt capacitor, which appears as a self-ittance (

).

The general formulation for the current injection at node k of an n-node system is:

... Equ. (1) Bus ittance Matrix We saw in Equation 1 above an expression for the current injection at an arbitrary bus in of ittances and bus voltages. The current injections for every bus in the network can be calculated using this equation and can be expressed in matrix form as follows:

Or in compact form:

where

is the vector of bus current injections (positive values are injections, negative values

are consumptions) is the vector of bus voltage phasors is the bus ittance matrix (more on this below) The bus ittance (or Ybus) matrix is one of the fundamental building blocks of power system simulations, describing both the topology and ittances / impedances of an electrical network. The diagonal elements of the Ybus matrix are referred to as self-ittances and the offdiagonal elements are mutual ittances. The Ybus matrix can be constructed from inspection when there are no mutual couplings between branches. The procedure for building the Ybus matrix from inspection follows on readily from Equation 1: 1. Self-ittances (diagonal elements): at bus k are the sum of all branch ittances connected to the bus (including shunt ittances to earth):

2. Mutual ittances (off-diagonal elements): between buses k and i are the negative sum of branch ittances connected between buses k and i:

The Ybus matrix is our three bus example above is:

The Ybus matrix is a square and symmetric

matrix with complex values. Normally, it is

also very sparse since most practical networks are not densely interconnected and thus have few non-zero branch ittance values. Note that the Ybus matrix is non-singular only if there are shunt ittances connected (e.g. the shunt capacitor

in our three-bus example above). This is easily proved by noticing that

without shunt ittances, each row and column of the Ybus matrix sums to zero (i.e. it is a zero-sum matrix) and therefore does not have full rankand is not invertible. Calculated Bus Power Injections The power flow problem is most commonly formulated using power injections rather than current injections. Complex power injections at bus k can be calculated from current injections as follows: ... Equ. (2) Given the voltages

on each bus and the Ybus matrix

, the bus power

injections (i.e. net active and reactive power flows for the k bus) can be calculated in th

rectangular coordinates as follows:

... Equ. (3)

... Equ. (4) Where

are the elements of the Ybus matrix

Classical Formulation of the Power Flow Problem It was noted earlier that at each bus, four variables (

,

,

and

) are required to be

known to fully define the power flows in the system. To solve the power flow problem, two of the four variables need to be specified (i.e. known) a priori for each bus and the power flow calculation solves for the other two. Typically, power injections at the buses are known (e.g. measured or estimated loads or dispatched generation at the bus) and are therefore normally specified. As a result, the bus voltages and angles are generally the unknown variables to be solved.

Therefore in the classical formulation, the power flow problem is constructed as a set of nonlinear algebraic power equations for the unknown variables in the system (bus voltage magnitudes and angles). The aim of the power flow calculation is to arrive at values for bus voltages and angles such that the the mismatch error between the specified and calculated power injections at each bus are within a pre-specified error tolerance. Types of Buses As discussed earlier, two variables of the four bus variables need to be specified at each bus. The two specified variables do not have to be the same for every bus, which leads to the definition of the following common bus types: (1) Swing (or slack) bus [SW]: since network losses are not known a priori, a swing bus is required where the voltage is specified, but the active power injected into the bus is unknown. The swing bus is usually designated as the voltage reference for the system. In practice, the swing bus would be analogous to a large generator responsible for load-frequency control or the point of common coupling to a larger external grid. Specified variables:

,

(2) Voltage controlled bus [PV]: in the PV bus, the active power injected into the bus is specified along with the voltage magnitude. PV buses are typically used to represent generators where the active power injected is the generator dispatch power and an automatic voltage regulator controls the bus voltage magnitude to a specified value. PV buses can also be used for reactive power devices which control the bus voltage to a specified value e.g. SVCs, synchronous condensers, STATCOMs, etc (in such cases, the P active power injected is zero). Specified variables:

,

(3) Constant power bus [PQ]: in the PQ bus, the active and reactive power injected into (or consumed at) the bus is specified. PQ buses are typically used to represent constant power loads (e.g. residential, industrial, etc), where it is assumed that the active and reactive power injections are not affected by small variations in bus voltages (at steady state). Specified variables:

,

Power Mismatch Vector The power mismatch vector is defined as a vector of the differences between the specified and calculated power injections at each bus. The power mismatch at bus k in complex form is calculated as follows:

where

is the specified complex power injection at bus k is the calculated complex power injection at bus k (i.e. from Equation 2)

The power mismatches can also be expressed in rectangular form where the calculated active and reactive power injections are computed using Equations 3 and 4 respectively, i.e.

General Solution Procedure 1. Formulate the network Ybus matrix 2. Select a swing bus for the network 3. For all other buses, define the bus type (e.g. PQ or PV) and specify the known variables 4. Select initial voltages and angles for all buses. Commonly, a flat start is used where all voltages are initialised at

pu.

5. Calculate the power mismatch vector by using the initial voltages in Step 4 and the specified power injections in Step 3. 6. Apply an iteration method (e.g. Newton-Raphson, Gauss-Seidel, etc) to get next iteration of bus voltages 7. Re-calculate the power mismatch vector and check if the power mismatches are within a prespecified error tolerance, e.g. 0.001pu. If so, then the solution has been reached successfully. If not, then continue iterating (Step 6-7) until the solution is reached or stop after a maximum number of iterations. Iteration Methods The formulation of the power flow problem is generic, but there are a number of options for the iteration method used to solve the non-linear equations. The most common methods are as follows: 

Gauss-Seidel method



Newton-Raphson method



Decoupled Newton-Raphson method



DC power flow method



Newton-Krylov methods

References 

[1] Ward, J. B., and Hale, H. W., "Digital Computer Solution of Power Flow Problems", AIEE Tansactions on Power Apparatus and Systems, vol PAS-75, pp. 398-404, June 1956



[2] Van Ness, J. E., and Griffin, J. H., "Elimination methods for flow studies" Trans. IEEE Transactions on Power Apparatus and Systems, Vol. PAS-80, p. 299, June 1961.



[3] Tinney, W. H., and Hart, C. E., "Power Flow Solution by Newton's Method", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-86, No. 11, November 1967



[4] Stott, B., and Alsac, O., "Fast Decoupled Load Flow", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-93, No. 3, May 1974

Related Topics 

Simple Power Flow Example



AC Power Transmission



Newton-Raphson Power Flow



Ill-Conditioning

Categories: Fundamentals | Modelling/Analysis

IP Rating (Redirected from Ingress Protection) Contents [hide] 

1 Introduction



2 Summary of IP Ratings



3 Examples



4 Important Points from IEC 60529

Introduction IP Rating refers to the International Protection or Ingress Protection of electrical enclosures, against the intrusion of solid objects, water, dust and accidental to live parts, as defined by IEC 60529. The rating comprises the letters "IP" followed by two numbers (and an optional letter), where the numbers and letters refer to conformity to levels of protection. The Wikipedia article gives a fairly detailed of IP ratings. Therefore this page is only intended to be a summary of the ratings and more importantly, highlight some key points from IEC 60529 that are commonly overlooked. Summary of IP Ratings Leve

First Number (Protected

l

against solids of size:)

0

No protection against and ingress of objects

Second Number (Proection against water)

Not protected

>50 mm - Any large surface of the 1

body, such as the back of a hand,

Dripping water - Dripping water (vertically falling

but no protection against deliberate

drops) shall have no harmful effect.

with a body part

2

>12.5 mm - Fingers or similar

Dripping water when tilted up to 15° - Vertically

dripping water shall have no harmful effect when objects

the enclosure is tilted at an angle up to 15° from its normal position.

Spraying water - Water falling as a spray at any 3

>2.5 mm - Tools, thick wires, etc.

angle up to 60° from the vertical shall have no harmful effect.

Splashing water - Water splashing against the 4

>1 mm - Most wires, screws, etc.

enclosure from any direction shall have no harmful effect.

Dust protected - Ingress of dust is not entirely prevented, but it must 5

not enter in sufficient quantity to interfere with the satisfactory operation of the equipment;

Water jets - Water projected by a nozzle (6.3mm) against enclosure from any direction shall have no harmful effects.

complete protection against

6

Dust tight - No ingress of dust; complete protection against

Powerful water jets - Water projected in powerful jets (12.5mm nozzle) against the enclosure from any direction shall have no harmful effects.

Immersion up to 1 m - Ingress of water in harmful quantity shall not be possible when the 7

N/A

enclosure is immersed in water under defined conditions of pressure and time (up to 1 m of submersion).

Immersion beyond 1 m - The equipment is suitable for continuous immersion in water under conditions which shall be specified by the 8

N/A

manufacturer. Normally, this will mean that the equipment is hermetically sealed. However, with certain types of equipment, it can mean that water can enter but only in such a manner that produces no harmful effects.

Examples

An IP54 enclosure is dust protected (1st number = 5) and protected against splashing wayer (2nd number = 4). An IP66/67 enclosure is dual protected, both for immersion up to 1m and powerful water jets. Note that it is not always true that an enclosure with a single rating such as IP68 is suitable for use in lower IP environments, such as IP66 (for more details, see the next section below). Important Points from IEC 60529 Section 6 of IEC 60529 makes an important point about backward compliance of IP ratings for water protection, as per the extract below: "Up to and including second characteristic numeral 6, the designation implies compliance with the requirements for all lower characteristic numerals. However, the tests establishing compliance with any one of the lower degrees of protection need not necessarily be carried out provided that these tests obviously would be met if applied. An enclosure designated with second characteristic numeral 7 or 8 only is considered unsuitable for exposure to water jets (designated by second characteristic numeral 5 or 6) and need not comply with requirements for numeral 5 or 6 unless it is dual coded." Category: Fundamentals Load Redundancy Load redundancy is the duplication of load equipment so that an alternative can be used in case one fails or needs to be maintained. Redundancy is common in industrial plants where loads such as pumps, fans, compressors, etc need to operate continuously. In order for there to be minimal plant downtime, these loads are replicated to ensure some redundancy. Most commonly, the use of duty and standby equipment ("A" and "B" loads) is used. In a scenario where the A/B loads are 100% redundant, the equipment can be referred to as "2 x 100%", meaning that there are 2 equipment items capable of delivering 100% output each. Other examples of redundant (and semi-redundant) configurations: 

2 x 50% - 2 equipment items capable of delivering 50% output each. If one fails, then output is reduced to 50%.



3 x 50% - 3 equipment items capable of delivering 50% output each. In this case, there is always one equipment item out of service / on standby



3 x 33% - 3 equipment items capable of delivering 33% output each. If one fails, then output is reduced to 66%.

Category: Fundamentals Load factor The load factor represents the operating / duty point of a load and is defined as the ratio of the absorbed power to the rated power, i.e.

Where

is the load factor (pu) is the absorbed power of the load (kW) is the rated power of the load (kW)

Newton-Raphson Power Flow The Newton-Raphson algorithm is the most commonly used iterative method to solve the power flow problem. Contents [hide] 

1 Derivation of the Newton-Raphson Method using Taylor Series



2 Multi-dimensional Newton-Raphson Method



3 Application to the Power Flow Problem o

3.1 Basic Algorithm

o

3.2 Jacobian Matrix

o

3.3 Ill-conditioning

o

3.4 Numerical Techniques to Improve Computation Time

o

3.5 Techniques to Improve Convergence

o

3.6 Characteristics of the Newton-Raphson Algorithm



4 References



5 Related Topics

Derivation of the Newton-Raphson Method using Taylor Series A nonlinear function that is differentiable can be approximated by a polynomial using a Taylor series. Let f(x) be a function of a single variable x. It is approximated about a point x0 using a Taylor series as follows:

... Equ. (1) The function f(x) is said to be linearly approximated when only the first two are retained and if we include the second derivatives, then it said to be a quadratic approximation.

Figure 1. Comparison of the original and linear approximated function Example 1: Determine the linear approximation of the following function at a given point using a Taylor series. Plot the original function and its linear approximation over the interval

and compare the result. ,

The function and its derivative at a given point are as follows:

The linear Taylor series approximation is:

In Figure 1, the original and linear approximation of the function is plotted. It can be seen that the approximation is good near x0, however, as we move away from the approximation point, the original function and linear approximation begin to diverge. The approximation result can be improved by adding higher order derivative . Try formulating the quadratic approximation equation and compare it with the original function. In the above example, we have learned how to approximate the non-linear equation and calculate the value of a function at a given point. Similarly, linear approximations of a Taylor series can be used for calculating the solution of the non-linear equation and determine the value of x at a given f(x). In Equation 1, if we neglect the second and higher differential order term then the equation can be written as:

... Equ. (2) We have seen from Example 1 that the linear approximation function provides the result near to the actual result only if the value of x is near x0, similarly, the solution x cannot be estimated correctly if the initial guess x0 is very far from the actual solution. Therefore, in order to estimate the result close to the actual solution, after estimating the value x based on initial guess x0, the function is again linearized around a point x and the solution is estimated again. This process is repeated until the difference between current estimation and previously estimated value is lower than a predefined tolerance. This method of iteration is called Newton-Raphson method and Equation 3 is commonly known as Newton-Raphson equation.

... Equ. (3) Here, k = 0, 1, 2… is a number of the current iteration. Example 2: Determine the value x at which f(x) = 103 using Newton-Raphson method. Use the same function defined in Example 1 with initial guess of x0 = -1. The function and its first derivative are as follows:

Thus, the Newton-Raphson equation becomes:

Starting from k = 0, we can estimate the solution x for k+1 until the error term

.

The values of the first 8 iterations are as follows:

It is noticeable that the solution has converged after iteration k = 5 to the value x = -5.00 and the difference between the solution of two iteration onward is lower than the tolerance. The solution can be verified by calculating the function value at x = -5.00. Generally, non-linear equations have more than one solution but the Newton-Raphson method provides only one solution that is close to the starting point. In order to get the other solution, the initial value must be changed to different value. In the same example, if we change the initial value to x0 = 1.00, the solution will converge in the same number of iteration but in opposite direction and provide second solution i.e. x = 5.0. The Newton-Raphson method converges quickly when the starting point is close to the solution. However, in some circumstances, the method is known to diverge or provide no information that the solution exists. In the example above, if f(x) = 0, then the Newton-Raphson method will not converge. Traditionally, the Newton-Raphson equation is formulated to find the root of a function, i.e. solving for x when

. Hence the Newton-Raphson iteration in Equation (3) reduces to:

... Equ. (4) Multi-dimensional Newton-Raphson Method In the derivation above, the Newton-Raphson method is used to find the root of a single equation

. In order to simultaneously solve the roots for a set of n equations

, the

Newton-Raphson iteration in Equation (4) can be extended to the following matrix form:

... Equ. (5) where

is an n x 1 vector of roots to the set of functions

is the n x n Jacobian matrix Application to the Power Flow Problem When applied to the power flow problem, the Newton-Raphson algorithm is used to solve for a vector of bus voltage magnitudes and angles, i.e.

Things to note: (1) The voltage and angle at the swing bus is specified (i.e. known a priori) and is therefore not part of the solution vector

.

(2) Bus voltage magnitudes at PV buses are specified and therefore not part of

. Only the

bus voltage magnitudes of PQ buses are included. (3)

includes all PQ and PV buses.

Therefore, the vector

where

is an m x 1 vector with:

is the number of PQ buses is the number of PV buses

Note that buses in the network must be ordered such that the PQ buses are first, followed by the PV buses. Basic Algorithm The basic Newton-Raphson iteration is as follows:

where

is the vector of bus voltage angles at the k-th iteration is the vector of bus voltage magnitudes at the k-th iteration is the vector of mismatches between the specified and

calculated bus active power injections (with calculated injections computed using bus voltage magnitudes and angles at the k-th iteration) is the vector of mismatches between the specified and calculated bus reactive power injections (with calculated injections computed using bus voltage magnitudes and angles at the k-th iteration) Jacobian Matrix By convention, the Jacobian matrix is set up as a partitioned matrix of the form:

Where each term is a sub-matrix of the form (using

as an example):

In rectangular form, the in the sub-matrices are real numbers calculated by the following expressions:

(i) Sub-matrix

(ii) Sub-matrix

:

:

(iii) Sub-matrix

:

(iv) Sub-matrix

:

Ill-conditioning The power flow problem is said to be ill-conditioned if the Jacobian matrix is ill-conditioned. This is because in the Newton-Raphson algorithm, each iteration has the following linear form:

where

is the power flow Jacobian matrix

is the bus voltage (magnitude and angle) correction vector

is the active and reactive power mismatch vector Therefore, if the Jacobian matrix is ill-conditioned, the solution to the power flow iteration can become wildly unstable or divergent. The most common characteristics that lead to ill-conditioned power flow problems are as follows: 

Heavily loaded power system (i.e. voltage stability problem where system has reached nose point of PV curve)



Lines with high R/X ratios



Large system with many radial lines



Poor selection of the slack bus (e.g. in a weakly ed part of the network)

Numerical Techniques to Improve Computation Time Each iteration of the Newton-Raphson algorithm requires basic matrix operations to be performed, i.e. matrix arithmetic, multiplication and inversion. For large networks, the use of efficient numerical techniques can significantly improve computation times: 

Sparsity techniques: in most practical networks, the bus ittance matrix is sparse, and the Jacobian matrix has the same level of sparsity. The use of sparse matrix techniques reduces the memory storage requirements of an from

entries to

ittance matrix

, where b is the number of branches in the network.

Suppose a network has on average 2 branches for every bus, then the storage requirements for such a network is is

entries. If the network had 200 buses, then the storage requirements for the full matrix and

for the sparse matrix.

Efficient methods for solving linear equations involving sparse matrix also exist, which can also help to improve computational times. 

LU Decomposition: sometimes called triangular factorisation or LU factorisation, LU decomposition is an efficient technique for inverting the Jacobian matrix by factoring the Jacobian matrix into lower (L) and upper (U) triangular matrices and then solving the equations via forward/backward substitutions. This technique reduces the number of full

matrix multiplication operations when compared to conventional matrix inversion techniques. 

Optimal ordering: the rows of the Jacobian matrix can be ordered so as to minimise the number of non-zero entries in the upper triangular matrix during LU decomposition. The ordering only needs to be done once and is generally set up so that the rows with the least number of branches are worked on first during the triangular factorisation process.



Less frequent update of the Jacobian matrix: in the default formulation, the power flow Jacobian matrix is calculated at every iteration. However, as the algorithm gets close to the solution, the Jacobian matrix does not change significantly and computation time can be saved by only updating the Jacobian matrix less frequently, e.g. every second or third iteration.

Techniques to Improve Convergence The Newton-Raphson algorithm has the tendency to converge (or diverge) to an incorrect solution within several iterations, depending on such factors as the level of ill-conditioning, quality of the initial estimates, etc. Some techniques for improving convergence are listed below: 

Damping factors: the step length of each iteration can be controlled by a damping factor



, which limits the the size of

and

at the iteration, i.e.

Use of previous solutions: by default, a "flat start" estimate is used for the initial bus voltages (i.e. 1 + j0 pu). This may be far from the actual solution and may cause the Newton-Raphson algorithm to diverge. In network augmentations and what-if scenarios, a successful solution often already exists for a base network and convergence difficulties arise for the expanded system. In such cases, the previously solved bus voltages could be used as initial estimates in lieu of a flat start.



Use of DC load flow solution: the DC load flow is a direct linear method (i.e. noniterative) for estimating active power flows in a network by making several assumptions (e.g. all voltage magnitudes are 1pu). Since the DC load flow always solves as long as the Ybus matrix is invertible, then the solution can be used as initial estimates for the voltage angles in the Newton-Raphson algorithm.

Characteristics of the Newton-Raphson Algorithm The Newton-Raphson algorithm is without doubt the most widely used method for solving power flows because of some key favourable characteristics: 

Convergence properties and accuracy: the Newton-Raphson algorithm exhibits quadratic convergence, leading to highly accurate solutions for most practical systems within 5 iterations.



Speed: the numerical techniques (sparsity, optimal ordering, LU factorisation, etc) have made the Newton-Raphson algorithm computationally efficient and competitive against other algorithms even for large systems.



Reliability: the algorithm is very reliable and able to solve even heavily loaded systems operating at close to voltage collapse.



Flexibility: the basic algorithm can be readily extended to cater for tap-changing transformers, FACTS and other reactive devices, DC systems, phase shifting transformers, etc.

References 

[1] Tinney, W. H., and Hart, C. E., "Power Flow Solution by Newton's Method", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-86, No. 11, 1967

Related Topics 

Power Flow



Simple Power Flow Example



AC Power Transmission



Ill-Conditioning

Categories: Fundamentals | Modelling/Analysis

Resonance (Redirected from Parallel Resonance) Contents [hide] 



1 Classical Derivations o

1.1 Series Resonance

o

1.2 Parallel Resonance

2 Resonance in Practical Circuits o

2.1 Series Resonance

o

2.2 Parallel Resonance

Classical Derivations Series Resonance

Figure 1. Classical series resonance circuit The classical circuit to demonstrate series resonance is the RLC circuit shown in the figure right, which shows a voltage source connected to R, L and C impedances in series. Given a fixed ac voltage source U operating at angular frequency ω, the current in the circuit is given by the following:

The current is at a maximum when the impedance is at a minimum. So given constant R, L and C, the minimum impedance occurs when:

or

This angular frequency is called the resonant frequency of the circuit. At this frequency, the current in the series circuit is at a maximum and this is referred to as a point of series resonance. The significance of this in practice is when harmonic voltages at the resonant frequency cause high levels of current distortion. Parallel Resonance

Figure 2. Classical parallel resonance circuit The classical circuit to demonstrate series resonance is the RLC circuit shown in the figure right, which shows a current source connected to R, L and C impedances in parallel. Given a fixed ac current source I operating at angular frequency ω, the voltage across the impedances is given by the following:

The voltage is at a maximum when the impedance is also at a maximum. So given constant R, L and C, the maximum impedance occurs when:

or

Notice that the resonant frequency is the same as that in the series resonance case. At this resonant frequency, the voltage in the parallel circuit is at a maximum and this is referred to as a point of parallel resonance. The significance of this in practice is when harmonic currents at the resonant frequency cause high levels of voltage distortion. Resonance in Practical Circuits Series Resonance

Here a distorted voltage at the input of the transformer can cause high harmonic current distortion (Ih) at the resonant frequency of the RLC circuit. Parallel Resonance

In this more common scenario, a harmonic current source (Ih) can cause high harmonic voltage distortion on the busbar at the resonant frequency of the RLC circuit. The harmonic current source could be any non-linear load, e.g. power electronics interfaces such as converters, switchmode power supplies, etc. Categories: Fundamentals | Harmonics

Per-unit System Contents [hide] 

1 Introduction



2 Why bother?



3 Calculation of Base Values



4 Calculation of Per-unit Impedances



5 Application Examples o

5.1 System Analysis

o

5.2 Transformers

o

5.3 Induction Machines

Introduction The per-unit system is a method of expressing quantities in an electrical system (e.g. voltage, current, impedance, etc) as a proportion of pre-defined base quantities. By definition, the perunit value of a quantity is the ratio of the original quantity to its base value (which results in a dimensionless "per-unit" or "pu" value):

Where

is the per-unit quantity (dimensionless or just "pu")

is quantity in normal units is the base value of the quantity in normal units For example, suppose the base value of current is 100A, then a current of 50A has a per-unit value of 50/100 = 0.5 pu. Why bother? The per-unit system was originally developed to simplify laborious hand calculations and while it is now not always necessary (due to the widespread use of computers), the per-unit system does still offer some distinct advantages over standard SI values: 

The relative magnitudes of all similar network quantities (e.g. voltages throughout the system) can be directly compared



Constant such as

can be eliminated, and therefore avoids confusion

between quantities (e.g. line-line vs line-neutral) 

Per-unit impedance values of equipment are normally found over a small range of values irrespective of the absolute size. On the other hand, ohmic values may have significant variation and are often proportional to nominal rating. Therefore, typical values can be used as a reasonable first approximation where detailed / accurate information is not known.



Per-unit impedances of transformers are the same whether referred to either side of the transformer (primary or secondary) and are independent of winding connections (for polyphase transformers), voltage level and phase shifts



Impedances are often quoted in of per-unit values by manufacturers (on a base of rated kVA or kW and voltage)



Multiplying per-unit quantities results in more per-unit quantities (and requires no conversion of units)



Manual calculations are often simplified using per-unit values (for all of the reasons above)

Calculation of Base Values Not all system quantities are independent from each other (e.g. apparent power is related to voltage and current, S = VI), so base values are both selected and calculated. Normally, the rated (apparent) power and nominal voltage are arbitrarily selected as base quantities: 

Base power (



Base voltage (

) = nominal apparent power of the equipment (or system) ) = nominal voltage of the equipment (or system)

The other base quantities can then be derived by calculation from these two base quantities:

Base current (

)

(Note that for three-phase systems and where the base voltage is expressed as a line-to-line

voltage, then

)

Base impedance (

)

(Note that for three-phase systems, and

, where

are the line-to-neutral and line-to-line base voltages respectively.

Base flux linkage (

)

Calculation of Per-unit Impedances Per-unit impedances are calculated by dividing the ohmic impedance by the base impedance:

Per-unit resistance and reactance values can be calculated by dividing by the base impedance (which also works in series and parallel combinations of impedances), i.e.

Application Examples

System Analysis The analysis of an electrical network can be simplified by using the per-unit system. Firstly, a system-wide base MVA is chosen and base voltages are selected for different parts of the system such that they correspond to the turns ratios of the transformers in the system. Choosing such voltages ensures that the per-unit impedance of the transformer is the same on both the primary and secondary sides and therefore the entire system can be combined using a single set of perunit impedances. Next, all impedances in the network must be converted to the base values. Often, the per-unit impedance of system components are expressed on another base (e.g. transformer impedances are typically expressed on the rated kVA base and rated voltage). Therefore, we would need to perform a change of base operation:

Where

and

and

are the old and new base voltages (V) are the old and new base powers (VA)

Transformers The transformer (leakage) impedance is normally expressed as a per-unit or percent quantity on the transformer kVA base and rated voltage. The impedance is calculated by computing the impedance voltage from a standard short-circuit test measurement - with the windings connected for the rated voltage (e.g. delta, wye, etc), a variable voltage is applied to one winding with the other winding short circuited. The impedance voltage is the value of the applied voltage required to circulate the rated current in the winding (that is not short circuited). The per-unit impedance of the transformer is found by converting the impedance voltage to a perunit quantity.

Where

is the impedance voltage (V) is the transformer rated (base) voltage (V)

An advantage of the per-unit impedance is that it is the same whether it is referred to the primary or secondary side of the transformer and is independent of winding connection (e.g. delta, wye, etc) and phase shifts. Induction Machines It is often more convenient to express induction motor equivalent circuit parameters in per-unit since they are invariant of winding connection. First, select the power and voltage base values as the nominal kVA rating and the rated voltage of the induction motor. The motor full load current is therefore the current base. The other per-unit quantities can be calculated as follows: 

Rated active power (pu):



Rated reactive power (pu):



Rated mechanical power (pu):



Rated torque (pu):

Category: Fundamentals

Phase Conversion Contents [hide] 

1 Introduction



2 1-phase VS 3-phase



3 Phase Conversion o

3.1 Power Electronics

o

3.2 Manual Modification

Introduction

Figure 1. 1-phase vs 3-phase sytem Single (1-phase) or multi (3-phase) phase voltage systems are the most common voltage systems used in the power network. In of power consumption single phase system is used for low voltage application, where the supplied devices are smaller loads; such in commercial or domestical usage, small industry or utility workshops etc. Typically, single phase devices are the most common devices found in our household (floor lamp, microwave oven, coffee machine, fan, PC...). Multi phase system is used for all voltage levels (typically multi phase refers to the 3phase). In high voltage (from 30 kV) it is used for transmission of electric power, in medium voltage (up to 30 kV) for transmission and as a supply to the powerful 3-phase AC motors and in low voltage (up to 1 kV) as a supply to the 3-phase AC motors or heaters. 1-phase VS 3-phase Electricity is either connected at 230 or 240 V (1-phase, which s for the majority of domestic situations), or 400 and 415 V (3-phase). The latter is better suited to providing for powerful appliances and fixed plant, and is more commonly used by industrial and larger commercial s. 1-phase comes to the home with two wires: active and neutral. The neutral wire is connected to earth (water pipe, earth stake, etc.) at the switchboard.

3-phase has four wires: three actives (called phases) and one neutral. The neutral wire is earthed at the switchboard. The common appliancies are: 

Big electric motors (usually more than 2 kW) need 3-phase power. This includes large workshop equipment.



Large domestic installations sometimes have 3-phase because it distributes the total load in a way that ensures that the current in each phase is lower.

Example: Imagine the total electrical load is 24 kW (that's a lot for a domestic installation). For a normal, 1-phase power supply at 240 V, the maximum current would be 100 A. Derived from the Ohm's law: the current in amperes multiplied by voltage in volts gives power in watts (Power = Voltage x Current). If a 3-phase supply is available, then the 24 kW are divided by 3, meaning that 8 kW is being used per phase. Now the current per phase is also down to a third of what it would be with a single phase supply (about 30 A per phase, rather than 100 A). Putting that in perspective, then 100 W lighting fixtures represent 1 kW of power, which equates to a bit under 40 A. Typically, connection fees for 3-phase are higher, and there are fixed annual charges as well for 3-phase so don’t contemplate it for a new home unless you really need it. Rural connections and SWER Depending on your locality you may be connected to a SWER line. These are used in many country areas. Single wire, earth return (SWER) delivers single phase power. It’s an economical way of distributing power, because only one transmission line (active) is needed. There is no neutral - instead the earth is employed as the ‘return’ conductor. If three-phase motors have to be used, a 1-phase to 3-phase power converter has to be installed by the electricity consumer. Phase Conversion Power Electronics A phase converter is a device that produces 3-phase electrical power from a 1-phase source, thus allowing the operation of 3-phase equipment at a site that only has 1-phase electrical service. Phase converters are the economical option, however power quality is often compromised with poor voltage balancing and for most equipment loads, an oversized converter must be specified to enable motor start-up. These inefficiencies lead to increased energy consumption and eventually may cause damage to the 3-phase equipment, especially digital or electronic machinery. Manual Modification In the case of simple thermal loads which are supplied by the 3-phase system, then the conversion to 1-phase can be made by changing the wiring system inside installation. This applies to the older 3-phase heaters, ovens or water boilers. In newer versions of those devices usually we can find some of the power electronics, which needs to be powered by the line voltage i.e. 400 Volts. Before proceeding further few things should be kept in mind :

1) Device power could be tripple lowered (i.e. 18 kW will become 6 kW), 2) 1-phase must sustain 3-phase load (i.e. 18 kW , which is 78 A load for 231 V), 3) Cable installations could be endangered (overloaded), 4) Protection device could be damaged (if not resized accordingly), 5) Device efficency could be lowered (i.e. tripple time to reach operating point), 6) If power electronics is stored inside those devices, better to avoid phase conversion, due to the certain damages. Also, it is possible to adjust total resistance of the load, by rewiring resistors into parallel or series connection, to get lower or higher values. Parallel conection will provide lower resistance values. The simpliest is to use one phase, then the total resistance Rt is the phase resistance:

If only two phases will be used then the total resistance is calculated as:

In case of all three phases:

Series conection will provide higher resistance values, since total resistance is the sum of all involved resistances. Categories: Fundamentals | Power Electronics

Referring Impedances In a system with multiple voltage levels, it is sometimes necessary convert impedances from one voltage to another, i.e. so that they can be used in a single equivalent circuit. Note that the whole process of referring impedances can be avoided by using the per-unit system. Referring Impedances in General Generally, one can refer an impedance Z1 at some voltage V1 to another voltage V2 by the following calculation:

Where

is the impedance at voltage V1 (Ω)

is the impedance at voltage V2 (Ω) Referring Impedances across Transformers

The winding ratio of a transformer can be calculated as follows:

Where

is the transformer winding ratio

is the transformer nominal secondary voltage at the principal tap (Vac) is the transformer nominal primary voltage (Vac) is the specified tap setting (%) Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV) side of the transformer by the following relation:

Where

is the impedance referred to the primary (HV) side (Ω) is the impedance at the secondary (LV) side (Ω)

is the transformer winding ratio (pu) Conversely, by re-arranging the equation above, impedances can be referred to the LV side:

Category: Fundamentals

Simple Power Flow Example Consider the simple model shown in Figure 1, where a large stiff network supplies a constant power load

through an impedance

:

Figure 1. Simple power flow model (note that all quantities are in per-unit)

Suppose the load power

is known and we want to calculate the load bus voltage

.

Unfortunately, this cannot be computed in a straightforward manner because the load is of constant power and thus the load current and impedance are voltage dependent, i.e. the load

draws more current as voltage decreases. As a result, the load bus voltage is non-linearly related to the load itself. Derivation of the Load Bus Voltage Note that in this derivation, all quantities are in per-unit. Recall that the load complex power can be calculated from the voltage and current phasors as follows:

Suppose that we represent both the load power

and impedance

in polar coordinates, i.e.

Then the power equation can be re-written as:

Conjugating the in brackets and simplifying, we get:

Applying Euler's law, we get:

Separating the real and imaginary of the above equation:

Squaring both equations and summing them together, we get:

Simplifying and re-arranging the equation above, we can get the following homogenous equation:

This equation can be solved for the load bus voltage

using the quadratic formula:

... Equ. (1) Where and Worked Example Suppose that the source bus has a nominal voltage of 33kV and a short circuit level of 800MVA at X/R ratio of 10. What is the voltage at the load bus if it is supplying a constant 50MW load at 0.8pf (lagging)? The source impedance is:

Converted to per-unit values (on a 100MVA base):

For an X/R ratio of 10, the source impedance is therefore: (angle in radians) The 50MW load converted to per unit is (by convention, a load with lagging power factor has a negative reactive power): (angle in radians) Plugging the parameters

,

,

and

into

Equation (1), we get the load bus voltage:

Intuition for General Power Flow Solutions We saw in this simple example that the power flow problem for constant power loads is nonlinear (i.e. quadratic) and cannot be solved with linear techniques. This intuition can be extended to more general power flow problems. While a closed form solution was found for this simple case, the general power flow problem is typically solved using iterative numerical methods, for example a Newton-Raphson algorithm. Categories: Fundamentals | Modelling/Analysis

Symmetrical Components Symmetrical components is a mathematical method for representing an unbalanced set of phasors into three decoupled (independent) sets of phasors - two balanced sets and a third set

with identical phasors. The method was originally developed in 1918 by Charles LeGeyt Fortescue and simplifies the analysis of unbalanced polyphase systems (e.g. commonly used for three-phase voltage, current and impedance phasors). Contents [hide] 

1 Basic Transformation



2 Visual Depiction



3 Shorthand Notation



4 Voltage, Current and Impedances o

4.1 Voltage and Current

o

4.2 Impedance



5 Balanced Impedances



6 References



7 Related Topics

Basic Transformation An arbitrary set of n phasors has 2n degrees of freedom, i.e. for each phasor, there is a magnitude and independent phase angle. Fortescue proposed a transformation that would also have 2n degrees of freedom, but have the advantage of symmetry. We will restrict ourselves to sets of 3 phasors, which is the most useful for modern electrical engineering. Given a set of three arbitrary phasors, say voltage phasors, we can express these as follows:

Where

,

and

are the set of arbitrary voltage phasors (balanced or otherwise)

,

and

are the set of zero sequence voltage phasors

,

and

are the set of positive sequence voltage phasors

,

and

are the set of negative sequence voltage phasors

We have essentially broken down each original phasor into a linear combination of three phasors. But wait, aren't we now making this more complicated? If we left it as is, then that would certainly be true. After all, we initially had 6 degrees of freedom (i.e. 2 for each of the three phasors) and now we have 18.

But we let's impose some constraints on the new sets of phasors: 

Firstly, let's say that the positive sequence phasors are balanced and perfecty symmetrical. This means that we can describe the set of three phasors using only a single reference phasor (an arbitrary choice, but we'll choose phasor a). Therefore:

where 

is the 120o rotation operator (

)

Secondly, we impose a similar constraint on the negative sequence phasors. They must be balanced and perfectly symmetrical, but they have the oppositve phase sequence to the positive sequence phasors, i.e. the peaks of the phasors occur in the opposite order (acb instead of abc). Mathematically,



Lastly for the zero sequence phasors, we impose the constraint that they shall all be identical, i.e:

Each of these three constraints removes 4 degrees of freedom and in the end, we can describe everything with just 3 phasors and 6 degrees of freedom (the same as the initial set of phasors). However, we have the advantage that the new phasors are balanced and symmetrical (or are identical in the case of the zero sequence phasors). In matrix notation, we can write the set of equations as follows:

Where

,

and

are the set of arbitrary voltage phasors (balanced or otherwise)

is the zero-sequence voltage component is the positive-sequence voltage component is the negative-sequence voltage component is the 120o rotation operator (

)

The inverse of the above gives the transformation equation:

Visual Depiction

Suppose we had a set of three unbalanced voltage waveforms as follows:

The phasor plot of the original phasors and the symmetrical component decomposition is shown below:

The time-domain waveforms of the positive, negative and zero sequence phasors is shown below:

The time-domain plots above nicely illustrate the difference between positive and negative sequences. Look at the positive and negative sequence plots. In the positive sequence plot, the waveform peaks appear in the following order: Va (red), Vb (blue), Vc (green). In the negative sequence plot, the peaks are in a different order: Va (red), Vc (green), Vb (blue). Steven Blair at the University of Strathclyde has a good interactive tool for visualising symmetrical components. Shorthand Notation To reduce the amount of writing, it may be preferable to refer to the original unbalanced phasors and their symmetrical components via the following shorthand notation. The original unbalanced phasors are denoted

:

The transformed symmetrical component phasors are denoted

The transformation matrices are denoted:

:

Therefore in matrix form, the symmetrical component transformations are as follows:

Voltage, Current and Impedances The transformation of an unbalanced three-phase network into its symmetrical components have the following relationships regarding voltage, current and impedance. Voltage and Current Voltage and current phasors are resolved into symmetrical components by the basic transform described above, i.e.

Impedance Impedance is not resolved into symmetrical components in such a straightforward manner since voltage, current and impedance are related by Ohm's law. Therefore, we want an expression for the symmetrical components of impedance such that Ohm's law is satisfied:

To do this, we work backward from the original unbalanced phasors, and then apply the transforms:

This is now in the form as the first equation above and therefore we can conclude that:

Note that the impedance

is a symmetric 3 x 3 matrix that consists of self-impedances on

the diagonal and mutual impedances (between phases) on the off-diagonals:

Restating Ohnm's law in of symmetrical components, we get:

From the equation above, we can see that there is cross-coupling between the symmetrical components of the network quantities. For example, the zero sequence voltage

is equal to

the weighted sum of the positive, negative and zero sequence currents:

Balanced Impedances A special case occurs in systems with balanced impedances, i.e. where the impedance matrices

are of the form:

In such balanced systems, the transformed impedance matrix

is a diagonal matrix of the

form:

Because all of the off-diagonals are zero, the corresponding positive, negative and zero sequence voltages and currents are independent from each other, i.e. they are completely de-coupled and have no cross-, and therefore can be treated as three de-coupled equations:

In summary, we can say that in a balanced system, the symmetrical components of netwrok quantities form a de-coupled system of equations. The de-coupled system of equations are then typically used to form sequence networks. This result forms the basis of most analyses that use symmetrical components. For example, in unbalanced fault analysis, we first assume that the system is balanced before the fault. By doing this, we can construct the sequence networks as completely de-coupled systems. The unbalance

is introduced at the fault location (e.g. a phase-to-earth fault) and the previously de-coupled sequence networks are connected together to yield the unbalanced system. References [1] Charles L. Fortescue, "Method of Symmetrical Co-Ordinates Applied to the Solution of



Polyphase Networks". Presented at the 34th annual convention of the AIEE (American Institute of Electrical Engineers) in Atlantic City, N.J. on 28 July 1918. Related Topics Sequence Networks



Category: Fundamentals

Anatomy of a Short Circuit (Redirected from Short Circuit) A short circuit is an electrical fault where a conductive path (usually of low impedance) is formed between two or more conductive parts of an electrical system (e.g. phase-phase, phase-earth, phase-neutral, etc). This article looks at the nature of short circuits and tries to break down and explain the constituent parts of fault currents. Note that the "short circuit" and "fault" are often used interchangeably. In most networks, a short circuit is similar to the closing transient of an RL circuit, where the R and L components are the impedances of the source(s). The transient characteristics of short circuit currents vary depending on whether they are near or far from synchronous generators. The sections below describe the two general types of short circuits: Near-to-Generator Short Circuit A fault close to a synchronous generator has the following maximum short circuit current isc(t):

Where

is the phase-to-neutral rms voltage at the generator terminals (V)

is the generator direct-axis subtransient reactance (Ω) is the generator direct-axis transient reactance (Ω) is the generator synchronous reactance (Ω) is the generator subtransient time constant (s) is the generator transient time constant (s) is the aperiodic time constant (s) From the above equation, it can be seen that the short circuit current can be broken up into an aperiodic current (dc component of the short circuit):

And a series of three damped sinusoidal waveforms corresponding to the following distinct stages:

(1) Subtransient component:

This period typically lasts 10 to 20ms from the start of the fault. The subtransient reactance is due to the flux casued by the stator currents crossing the air gap and reaching the rotor surface or amortisseur / damper windings.

(2) Transient component:

This period typically lasts 100 to 400ms after the subtransient period. The transient reactance occurs when all the damping currents in the rotor surface or amortisseur / damper windings have decayed, but while the damping currents in the field winding are still in action.

(3) Steady-state component: The steady-state occurs after the transient period when all the damping currents in the field windings have decayed, and essentially remains until the fault is cleared.

Putting these all together, we get the familiar near-to-generator short circuit waveform:

Far-from-Generator Short Circuit In short circuits occurring far from synchronous generators, we can ignore the effects of the generator subtransient behaviour. It can be shown through transient circuit analysis that the maximum far-from-generator short circuit is as follows:

Where

is the rms voltage of the circuit (V)

is the fault impedance (Ω)

is the R/X ratio at the point of fault (pu) We can see that there are two components:

(1) A decaying aperiodic component:

(2) A steady state component:

Putting these together, we get the total far-from-generator fault current:

During the transient period, the peak transient current is typically 1.5 to 2.5 times higher than the peak steady state current. Droop Control Droop control is a control strategy commonly applied to generators for primary frequency control (and occasionally voltaqe control) to allow parallel generator operation (e.g. load sharing). Contents [hide] 

1 Background



2 Droop Control Setpoints



3 Limitations of Droop Control



4 Related Articles

Background Recall that the active and reactive power transmitted across a lossless line are:

Since the power angle approximations

is typically small, we can simplify this further by using the and

:

From the above, we can see that active power has a large influence on the power angle and reactive power has a large influence on the voltage difference. Restated, by controlling active and reactive power, we can also control the power angle and voltage. We also know from the swing equation that frequency is related to the power angle, so by controlling active power, we can therefore control frequency. This forms the basis of frequency and voltage droop control where active and reactive power are adjusted according to linear characteristics, based on the following control equations:

Where

is the system frequency

is the base frequency is the frequency droop control setting is the active power of the unit is the base active power of the unit is the voltage at the measurement location is the base voltage is the reactive power of the unit is the base reactive power of the unit is the voltage droop control setting These two equations are plotted in the characteristics below:

Frequency droop characteristic

Voltage droop characteristic

The frequency droop characteristic above can be interpreted as follows: when frequency falls from f0 to f, the power output of the generating unit is allowed to increase from P0to P. A falling frequency indicates an increase in loading and a requirement for more active power. Multiple parallel units with the same droop characteristic can respond to the fall in frequency by increasing their active power outputs simultaneously. The increase in active power output will counteract the reduction in frequency and the units will settle at active power outputs and frequency at a steady-state point on the droop characteristic. The droop characteristic therefore allows multiple units to share load without the units fighting each other to control the load (called "hunting"). The same logic above can be applied to the voltage droop characteristic. Droop Control Setpoints Droop settings are normally quoted in % droop. The setting indicates the percentage amount the measured quantity must change to cause a 100% change in the controlled quantity. For example, a 5% frequency droop setting means that for a 5% change in frequency, the unit's power output changes by 100%. This means that if the frequency falls by 1%, the unit with a 5% droop setting will increase its power output by 20%. The short video below shows some examples of frequency (speed) droop: Limitations of Droop Control Frequency droop control is useful for allowing multiple generating units to automatically change their power outputs based on dynamically changing loads. However, consider what happens when there is a significant contingency such as the loss of a large generating unit. If the system remains stable, all the other units would pick up the slack, but the droop characteristic allows the frequency to settle at a steady-state value below its nominal value (for example, 49.7Hz or 59.7hz). Other controllers are therefore necessary to bring the frequency back to its nominal value (i.e. 50Hz or 60hz), which are called secondary and tertiary frequency controllers. Related Articles

Synchronous Machine Models

This page describes the most common synchronous machine models used in stability studies. Contents [hide] 

1 Nomenclature



2 6th Order (Sauer-Pai) Model



3 6th Order (Anderson-Fouad) Model



4 4th Order (Two-Axis) Model



5 2nd Order (Classical) Model

Nomenclature The standard machine parameters are defined as follows: 

is the armature resistance (pu)



is the armature reactance (pu)



is the d-axis synchronous reactance (pu)



is the q-axis synchronous reactance (pu)



is the d-axis transient reactance (pu)



is the q-axis transient reactance (pu)



is the d-axis subtransient reactance (pu)



is the q-axis subtransient reactance (pu)



is the d-axis transient open loop time constant (s)



is the q-axis transient open loop time constant (s)



is the d-axis subtransient open loop time constant (s)



is the q-axis subtransient open loop time constant (s)



is the machine inertia constant (MWs/MVA)



is an additional damping constant (pu)

Note that per-unit values are usually expressed on the machine's MVA base. 6th Order (Sauer-Pai) Model 6th order synchronous machine model based on the book:

Sauer, P.W., Pai, M. A., "Power System Dynamics and Stability", Stipes Publishing, 2006 Stator magnetic equations:

where

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

6th Order (Anderson-Fouad) Model 6th order synchronous machine model based on the book: Anderson, P. M., Fouad, A. A., "Power System Control and Stability", Wiley-IEEE Press, New York, 2002 Stator magnetic equations:

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

4th Order (Two-Axis) Model Stator magnetic equations:

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

2nd Order (Classical) Model

Stator equations:

Equations of motion:

Initialisation:

Categories: Modelling/Analysis | Generators

DC Motors Contents [hide] 



1 DC Motor Application Considerations o

1.1 Electromagnetic Interference (EI)

o

1.2 Motor Service Life

2 Reference

DC Motor Application Considerations Audible Noise: Audible noise is a concern in some types of motor applications. In many medical applications like infusion pumps or prosthetic devices, the patient can be very sensitive to the noise disturbance. Good design practice requires that the noise be limited as much as possible. In large machines, the combination of hundreds of DC motors and gears operating simultaneously can be very loud and distracting to the employees who have to work in close proximity to the machine

Quality Components: Probably the best method of insuring low audible noise in motors is to specify quality components. Motors using cheap or poorly fitted bearings are more likely to be noisy. Poorly designed or loose fitting brush sets can contribute to audibly noisy commutation. Manufacturers of inexpensive, high volume motors cannot reasonably be expected to concern themselves with quiet operation beyond some minimum standard, and the use of such motors in applications where quiet operation is important should be considered carefully. The designer must consider whether low cost takes precedence over quiet operation in the priorities of the customer. Bearing Choice: The use of ball bearings without preload is a potential source of audible noise. Where the specific application permits, ball bearings should be preloaded. This means that the balls will not be able to move axially in the race and cause the minute intermittent rattling that can sometime be associated with unpreloaded ball bearings. Smaller ball bearings can be sensitive to heavy shaft loads. They are easily damaged during press fitting added components and by short radial or axial overloads. Care should be taken not to exceed the shaft loading ranges specified in the datasheets. A damaged ball bearing can be a significant source of audible noise and can effect motor life. Sintered sleeve bearings are a very good choice when limiting audible noise if the application does not require the motor to endure significant continuous or intermittent changes in the shaft loading characteristics. The shaft of the motor actually rides on a thermodynamic film of lubrication and the reduced friction can limit audible noise. If the bearing is overloaded radially, however, this film breaks down and the shaft will grind the bearing down causing audible noise and reducing the operational lifetime of the motor. Vibration: Rotor vibration can be a significant source of audible noise. Vibration and noise increases with speed. Even a slight imbalance in the rotor can cause major vibrations at speeds of 10,000 rpm. Brush Options: Copper-graphite type brushes tend to be both audibly and electrically noisier than precious metal systems. Graphite based brushes are capable of withstanding considerably higher current densities, however, and they are often required in an application for that reason. Where a choice is available for a specific application and audible noise is important, precious metal brushes are the better choice. Electromagnetic Interference (EI) DC motors are a source of electrical as well as audible noise. EMI (electro-magnetic interference) can be radiated by motor terminals and lead wires and may cause problems with other components in the vicinity of the motor. It is also possible for spikes to be coupled onto data lines or output lines from encoders. The result can be false data or encoder information. There are a number of methods that can be used to minimize EMI in motor applications. Like many other considerations in DC motor applications, each has its advantages and disadvantages and must be evaluated within the context of the application. Motor Commutation: The most common source of EMI problems is the commutation of motors. At each commutation point, when the brush breaks with a commutator segment, the energy stored in the motor winding as a magnetic field causes an arc or voltage spike between the brush and the commutator segment. This occurs not only during normal commutation but

also in situations where the brushes "bounce" on the rotating commutator. Coreless DC motors are typically less electrically noisy than iron core DC motors because of the lower armature inductance which in turn reduces the level of the arc energy. This arcing can be further mitigated with the addition of a capacitor ring, which serves to dissipate the energy through a capacitor and resistor series back into the motor coil. Quality Components: The importance of using quality components in any motor design is of a crucial importance. As was the case with audible noise, the use of cheap, poorly constructed motors adds to the electrical noise problem. "Open case" motors do not effectively block EMI radiated from the coil windings. Poorly fitted brush holders and inadequate brush tension contribute to radiated EMI as well. Coreless motors: Coreless DC motors have much lower armature inductance than iron-core motors of comparable size. Since armature inductance is the primary cause of EMI problems, minimizing it through selection of coreless motors is recommended where EMI is a critical factor. Lead Wires and Shielding: Motor lead wires should be placed as close together as possible so that EMI radiated from the two leads can cancel each other. This canceling effect can be improved by using so-called "twisted pairs" where the positive and negative lead wires are twisted together. Motor leads should be physically separated from data lines or encoder outputs to reduce the possibility of coupling motor noise onto them. This means that when using shielded pigtails, the lines should be shielded separately from the motor leads. If noise is still causing problems with the encoder signals than it may be time to consider using a differential encoder to eliminate the effect of interference on the encoder. PWM switching noise is another source of EMI problems. Most commonly, PWM switching results in radiated noise from motor lead wires. Shielding and lead wire placement can also help mitigate the effect of PWM generated EMI. ive components: EMI problems can often be significantly reduced by the simple act of installing a capacitor across the motor terminals. In some types of applications, this method may not be suitable since a resonant circuit is created which can cause "ringing" problems near resonant frequencies. In these instances, an RC snubber network across the motor terminals may be more effective. Component values are not critical for motors driven with DC, but care must be taken in selecting components for PWM driven systems. Motor Service Life Operating Point: In most applications, the torque and speed demands placed upon a DC motor determine its overall operational lifetime. As the torque requirements on the motor increase, the current through the armature increases proportionally, thus increasing the current density at the brush-commutator interface. High current densities promote electro-erosion of brush and commutator materials, a limiting factor in motor service life. In addition, high rotational speeds shorten motor service life by accelerating mechanical wear. Although each application has its own specific requirements to be addressed, it is usually advisable to operate a DC motor with precious metal brushes and commutator continuously at no more than 1/3 of its rated stall torque. Motors with graphite on copper commutation systems should be run continuously at no more than 1/2 of the motor's rated stall torque. These

recommendations attempt to maximize motor service life. Some applications may not require the maximum lifetime that the motor has to offer. Rotor Inductance: One of the factors limiting brush and commutator life is the inductance of the motor armature. During commutation, when current flows through a particular coil winding there is storage of energy in the form of a magnetic field. When the motor commutates and the current flow is switched to another winding, the magnetic field collapses and the resulting discharge of energy causes an arc between the commutator and brush. This arcing accelerates electro-erosion and decreases motor life. One could, theoretically, reduce the armature inductance of the motor windings by decreasing the number of turns in each armature segment. This lowers the torque constant of the motor, however, which increases the motor current for a given torque and, therefore, increases the current density at the brush-commutator interface. This is not recommended. To reduce the affect of inductance and arcing on motor lifetime a capacitor ring is being mounted to the commutator. The ring provides the equivalent effect of each winding connected in parallel with a small capacitor and resistor. The collapse of the magnetic field during commutation then serves to charge the capacitor rather than creating an arc between brush and commutator. The stored energy is released and dissipated back into the next coil phase in the commutation sequence. This technique, while slightly increasing the electrical time constant of the motor, dramatically increases motor service life. Drive Profiles: Operating conditions other than torque and speed also affect service life. The application may require frequent starting and stopping or reversals of direction. Both situations result in periods of high current density and a resulting shortening of service life. A similar effect is seen in applications where pulse width modulated (PWM) drives are used. If the PWM frequency is too low, the motor is constantly accelerating and decelerating with an accompanying increase in current density. As a general rule, PWM frequencies of 20 kHz or higher are recommended for ironless core motors. Environmental Considerations: Environmental conditions can have a profound effect on motor service life. One good example is the rapid drying and wear of graphite-based brushes in a vacuum or very dry environment. Very warm and dry conditions also hasten the breakdown of bearing and commutator lubricants. The ambient temperature has a cumulative effect on the motor's operational temperature and can lower performance by limiting the operational temperature range of the motor. External cooling by , air or forced air can produce significant gains in motor performance. At the opposite extreme, very cold conditions increase the viscosity of lubricants and cause the motor to run at a higher current. Shaft Loading: Shock loads and vibration contribute to the tendency of the brushes to "bounce" on the commutator, thus causing arcing and accelerated electro-erosion. Shock loads and vibration also accelerate bearing wear. Excessive axial or radial shaft loads decrease the life of bearings, sometimes significantly. In continuous duty applications with low radial shaft loads, sintered bearings are the inexpensive choice. For increased radial loads, ceramic bearings are available. Ball bearings are typically specified when the application calls for higher radial and axial shaft loads.

Reference

MICROMO - rotary and linear custom motion solutions Related topics: Category: Motors 

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Motor Driven Load Contents [hide] 

1 Load Characteristics o

1.1 Constant Torque Loads

o

1.2 Variable Torque Loads

o

1.3 Constant Power Loads

o

1.4 Constant Torque / Power

o

1.5 High Starting Torque - Constant Torque

Load Characteristics Constant Torque Loads In this load characteristic, the torque is constant across the entire speed range. The power is therefore directly proportional to the speed and therefore, reducing the speed will also reduce the power required in a linear fashion. e.g. screw compressors and conveyors

Variable Torque Loads

Also called quadratic torque loads, the torque of the load is proportional to the square of the speed. The load power is therefore proportional to the cube of the speed. e.g. centrifugal pumps, fans and blowers

Constant Power Loads In this load characteristic, the power output of the load is constant across the entire speed range, and therefore torque requirements are high at low speeds. e.g. Centre driven winders and machine tool spindles

Constant Torque / Power

This load characteristic is a combination of constant torque in one speed range and constant power in another. e.g. paper making machines

High Starting Torque - Constant Torque This load characteristic has high torque at starting and low speeds, followed by constant torque at higher speeds. e.g. extruders and positive displacement pumps

Category: Motors

LV Motor Data (IEC) The following typical low voltage motor characteristics can be used as a quick reference data set when specific information is not available. The data is based on Toshiba TEFC, heavy duty, high efficiency general purpose motors operating at 50Hz.

Full Load

No

Current (A) Loa

k W

0. 3 7

0. 3 7

0. 3 7

0. 5 5

0. 5 5

0. 5 5

R P M

d

Fra

Cur

me Siz e

ren At

At

At

41

40

38

5V

0V

0V

28

D7

70

1M

14

D7

1.

1.

1.

05

1

2

2

2

93

D8

1.

1.

1.

5

0

4

5

6

28

D7

1.

1.

1.

05

1

3

4

4

14

D8

1.

1.

1.

10

0

3

4

4

93

D8

1.

1.

1.

5

0

9

9

9

1

1

0. 95

t at 415 V (A)

Loc ked Rot

Torque (%

Efficiency

F/L)

(%)

Cur ren t (% F/L )

Loc ked Rot or

P ul l U p

580

300

9 0

3 0.9

458

395

6 0

3 0.8

411

370

5 2

1 0.7

392

260

4 9

3 0.8

600

330

0 2

3 1.6

Factor (pu)

or

2 0.7

Power

474

345

2 0

Br ea

Fu

Fu

k

ll

75 50 ll

-d

Lo

%

ow

ad

%

Lo

Rot

dB

or

(A

GD

)

(kg. at

75 50 m2) % %

1m

ad

n

34

72

70

64

0.

0.

0.

0.00

5

.7

.3

.6

75

65

52

2

67

60

0.

0.

0.

0.00

.6

.6

65

56

44

4

38 5

70

36

65

62

55

0.

0.

0.

0.01

9

.7

.6

.4

59

49

39

6

31

70

70

66

0.

0.

0.

0.00

4

.1

.1

.4

87

82

73

2

34

74

73

69

0.

0.

0.

5

.4

.7

.3

79

71

58

33

72

69

63

0.

0.

0.

0

.1

.7

.5

58

48

37

54

46

48

54

0.01 48

TBA

50

0.

28

D8

1.

1.

1.

40

0

8

8

8

14

D8

1.

1.

1.

00

0

8

8

9

93

D9

2

2

5

0S

70

10

2.

2.

2.

0

0L

2

3

4

1.

28

D8

2.

2.

2.

1

30

0

3

4

5

1.

14

D9

2.

2.

2.

1

25

0S

5

6

6

1.

94

D9

3

3

1

0

0L

1.

70

D1

3.

3.

3.

1

5

00L

4

5

7

1.

28

D9

2.

5

50

0S

9

1.

14

D9

3.

3.

3.

5

20

0L

3

4

5

7 5

0. 7 5

0. 7 5

0. 7 5

2.

3 1.1

771

414

7

1.1

543

295

0

1

490

248

3.

2 2 8

2

360

200

1 6 4

1

739

366

2 9 2

1.4

620

301

2 4 5

2.1

540

298

2 7

2

3

2 8

1

3.

8

6

2.4

440

230

2 0 5

0.9

759

312

2 1

2

5

1.7

636

310

3 0 3

44

76

75

69

0.

0.

0.

0.00

0

.5

.3

.3

8

71

59

7

31

74

74

70

0.

0.

0.

0.01

0

.5

.4

.6

8

72

59

1

78

75

0.

0.

0.

0.02

.4

.5

69

6

48

2

72

68

0.

0.

0.

0.02

.7

.7

67

58

47

8

74

0.

0.

0.

0.00

.4

87

82

71

8

25

78

8

22

73

0

78

37

78

0

.1

31

81

81

79

0.

0.

0.

0.01

0

.4

.9

.7

77

7

57

9

30

78

78

75

0.

0.

0.

0.02

8

.9

.7

.3

66

57

44

8

23

74

73

0.

0.

0.

0.03

0

.6

.4

62

53

42

4

30

84

84

82

0.

0.

0.

0.01

5

.1

.8

.9

9

87

79

4

34

81

82

80

0.

0.

0.

0.02

0

.7

.3

.4

79

72

59

2

69

64

48

49

47

64

50

48

51

65

50

1.

94

D1

3.

3.

3.

5

0

00L

6

6

7

1.

69

4.

4.

4.

5

0

5

7

9

2.

28

D9

4.

4.

2

10

0L

2

5

2.

14

D1

4.

4.

4.

2

15

00L

5

6

8

2.

94

5.

5.

5.

2

0

2

4

6

2.

71

5.

5.

5.

2

0

4

6

9

3

3

3

3

D1 12 M

D1 12 M

D1 32 S

4

D1

5.

5.

90

00L

6

8

14

D1

6.

6.

6.

20

00L

3

4

6

7

7

0

71 0

D1 32 S

D1 32 M

2.1

583

295

7 0

1 2.6

420

240

7 0

2 1.1

775

345

6 6

2 2.3

656

288

4 6

2 3.5

654

315

8 0

2 4.1

520

200

0 0

1

28

96

2

6

1.8

786

225

7 2

7. 2

7.

7.

7.

2

5

9

3 3.4

762

390

7 0

2 4.6

529

220

1 2

2 5

510

260

5 0

31

81

82

0

.9

.3

23

74

0

.3

31 2

85

0.

0.

0.

0.05

73

65

52

2

70

0.

0.

0.

0.07

.1

62

53

42

6

86

86

0.

0.

0.

0.01

.9

.8

91

89

81

6

74

80

29

82

83

81

0.

0.

0.

0.04

7

.8

.6

.9

82

75

63

1

33

81

81

78

0.

0.

0.

0

.6

.6

.6

71

62

5

25

79

79

75

0.

0.

0.

0.13

0

.8

.3

.8

73

65

52

2

30

85

86

85

0.

0.

0.

0.04

5

.8

.9

.9

9

88

8

5

39

85

85

83

0.

0.

0.

0.05

4

.1

.5

.8

79

72

59

9

27

82

81

78

0.

0.

0.

0.12

5

.2

.7

.9

73

64

52

3

80

77

0.

0.

0.

0.20

.7

.7

74

66

53

7

32 0

81

51

53

64

53

0.07 55

57

68

52

53

58

4

4

4

4

28 90

14 20

96 0

70 5

5.

28

5

80

5.

14

5

40

5.

96

5

5

5.

71

5

0

7.

29

5

10

7.

14

5

45

D1 12 M

D1 12 M

D1 32 M

D1 60 M

7.

6

8

7.

8.

8.

8

1

5

8.

9.

9.

8

1

5

9. 6

D1 32

11

S

D1 32

11

S

D1 32 M

D1 60 M

D1 32 S

D1 32 M

1

7.

11 .5

10

11 .5

11 .5

12

8

10 .5

5

2 3.7

769

310

5 2

2 5.3

591

245

2 5

1 5.4

480

180

9 5

4.6

582

220

8 0

2 12

5

600

254

3 0

12 .5

2 5.7

678

240

1 5

1

.9

.4

14

14

15

.2

.7

.5

15

240

1 12

12

.5

763

2

11

14

2.7

13

6.9

500

170

9 0

15 .5

1 5.6

697

226

8 5

2 6

648

296

6 9

35

85

86

85

0.

0.

0.

0.05

0

.9

.5

.2

89

86

77

1

34

85

86

85

0.

0.

0.

0.07

5

.5

.3

.3

83

77

65

2

29

84

84

82

0.

0.

0.

0.14

0

.7

.7

.6

75

67

54

8

82

81

79

0.

0.

0.

0.37

71

66

59

2

83

0.

0.

0.

0.06

.2

8

75

66

4

28 0

27

86

3

.4

26

86

86

84

0.

0.

0.

0.12

8

.1

.3

.6

82

77

67

9

25

87

87

0.

0.

0.

0.25

2

.2

.8

77

7

59

5

26

84

84

82

0.

0.

0.

0

.1

.4

.5

79

73

61

30

87

87

85

0.

0.

0.

0.08

5

.6

.4

.2

84

8

7

7

31

87

87

85

0.

0.

0.

0.17

8

.2

.3

.1

84

8

7

9

86

87

68

56

54

57

74

61

53

0.57 60

74

61

D1

7.

96

5

0

7.

71

D1

16

16

17

5

5

60L

.1

.7

.6

1

29

1

25

1

14

1

60

1

96

D1

1

5

60L

1

72

D1

1

0

80L

1

29

5

20

1

14

D1

27

5

55

60L

.5

1

97

D1

5

5

80L

1

73

D2

5

0

00L

60

17

17

M

D1 60

20

M

20 .5

17 .5

2 9.3

565

255

0

1 10

550

180

2 21

7.6

725

250

0 0

2 21

22

23

9.5

714

295

M

4 0

2 24

24

25

15

600

327

3 2

24

D1 60

9 5

D1 60

4

27

M

24

26

.9

.2

27

28

.5

.5

28

29 .5

2 17

520

230

1 0

2 5.7

715

255

0 8

2 11.1 727

295

2 5

1 29

30

31

21.1 638

216

7 5

30

31

32

.4

.8

1 18.9 530

195

8 0

30

86

0.

0.

0.

0.57

5

.1

74

67

54

5

28

81

0.

0.

0.

.7

.1

79

73

62

89

88

86

0.

0.

0.

0.16

5

.1

.9

.8

86

82

73

7

33

88

87

85

0.

0.

0.

0.34

0

.4

.9

.7

83

78

67

6

33

88

88

86

0.

0.

0.

6

.6

.4

.4

71

62

5

87

87

85

0.

0.

0.

75

7

62

31

89

89

87

0.

0.

0.

0.21

8

.4

.3

.6

88

85

78

5

31

89

89

0.

0.

0.

0.48

5

.5

.6

86

81

72

5

26

88

88

88

0.

0.

0.

5

.5

.9

.1

82

77

67

24

89

89

88

0.

0.

0.

0

.4

.8

.4

78

74

62

86

84

83

83

0

.9

30

28 0

88

0.9

64

61

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References For details on specific motors, EuroDEEM, the European Database of Efficient Electric Motors, is an excellent resource. Category: Motors

Motor Performance Induction motors typically run at highest efficiency and power factor at full-load. However when motors are run at lower load factors, there is generally a corresponding decline in performance. This drop in performance tends to vary non-linearly (with respect to the load factor), with larger drops in performance at low load factors (0% to 40%). For example, the figure below shows the performance test data of a 155kW, 2000V, 50Hz induction motor at load factors from 0% to 100%:

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Motor Parameter Estimation from Steady-State Models Estimation of an induction motor's equivalent circuit parameters from steady-state models and manufacturer performance data is the most common approach for offline power system studies, e.g. dynamic motor starting, transient stability, etc [5].

Contents [hide] 

1 Parameter Estimation Problem



2 Problem Formulation Ignoring Core Losses



o

2.1 Single Cage Model (Ignoring Core Losses)

o

2.2 Double Cage Model (Ignoring Core Losses)

3 Problem Formulation Considering Core Losses o

3.1 Single Cage Model (With Core Losses)

o

3.2 Double Cage Model (With Core Losses)



4 Parameter Estimation Algorithms



5 Software



6 References



7 Related Topics

Parameter Estimation Problem The characteristics of an induction motor are normally provided by manufacturers in the form of a standard set of performance parameters, with the following parameters being the most common: 

Nominal voltage,

(V)



Nominal frequency,



Rated asynchronous speed,



Rated (stator) current,



Rated mechanical power,



Rated torque,



Full load power factor,



Full load efficiency,



Breakdown torque,



Locked rotor torque,



Locked rotor current,

(Hz) (rpm) (A) (kW)

(Nm) (pu) (pu) (normalised) (normalised) (pu)

We know that a set of equivalent circuit parameters can yield specific torque-speed and currentspeed curves. So given a set of performance parameters that contain features on the torquespeed and current-speed curves (e.g. breakdown torque, locked-rotor current, etc), is it possible to determine the corresponding equivalent circuit parameters that yield these features? This is the crux of the parameter estimation problem and can be posed as follows - "How can the motor performance parameters be converted into equivalent circuit parameters?". While all of the performance parameters in the above set can be used in an estimation procedure, there are actually only six indpendent magnitudes that can be formed from them:

,

,

,

,

and

[1]. These independent magnitudes will thus form

the basis of the problem formulation, where the independent magnitudes calculated from the equivalent circuit are matched with the performance parameters supplied by the manufacturer. The basic double cage model is used to illustrate how these six independent magnitudes can be calculated from the equivalent circuit model. Stator and rotor currents at slip "s" can be readily calculated from the equivalent circuit. Quantities for per-unit active power

, reactive power

and power factor

can be calculated as follows:

Nominal speed

where

and full load slip

is calculated as follows:

is the number of motor poles

is the nominal frequency (Hz) is the asynchronous speed at full load (rpm) Calculating the slip at maximum torque

(Under the condition that the second derivative

is found by solving the equation:

)

at slip "s"

In the double cage model, the solution to this equation is not trivial and it is more convenient to use an estimate, e.g. based on an interval search between s=0 and s=0.5. Problem Formulation Ignoring Core Losses Single Cage Model (Ignoring Core Losses) In the single cage model, the locked rotor torque

and locked rotor current

are not used

because the single cage model does not have enough degrees of freedom to capture both the starting and breakdown torque characteristics without introducing significant errors [1]. As a result, it is more commonplace to only consider the breakdown torque

in the single cage

model and simply ignore the torque and current characteristics at locked rotor. For wound-rotor motors, this yields sufficiently accurate results (i.e. in of the resulting torque-speed curve). However, a single-cage model is unable to accurately model the torque-speed characteristics of squirrel cage motors, especially those with deep bars. Without taking into core losses, the full load motor efficiency

also cannot be used.

Therefore, there are only three independent parameters that can be used in the problem formulation:

,

and

.

These independent parameters can be used to formulate the parameter estimation in of a non-linear least squares problem, with a set of non-linear equations of the form

where

:

are the equivalent circuit

parameters of the single cage model Double Cage Model (Ignoring Core Losses) In the double cage model, the locked rotor torque

and locked rotor current

are included

as independent parameters. As in the single cage model, the full load motor efficiency cannot be used without taking into core losses. Therefore, there are five independent parameters and the following non-linear least squares problem:

where

are the

equivalent circuit parameters of the double cage model Problem Formulation Considering Core Losses Without taking into the core (and mechanical) losses, the motor full load efficiency cannot be used as an independent parameter in the problem formulation. This is because efficiency is calculated based on the ratio of output mechanical power to input electrical power. If the heat losses through the core and rotor frictional losses are not taken into , then the equivalent circuit is not suitable to accurately estimate motor efficiency. It follows that attempting to use the motor full load efficiency in the estimation of the equivalent circuit without a core loss component would cause errors in the parameter estimates (e.g. the stator resistance would be overestimated). When core losses are included in the model, then the motor full load efficiency

can also be

used as an independent parameter. The problem formulations are restated below for the single cage and double cage models with core losses taken into . Single Cage Model (With Core Losses) The non-linear least squares problem for the single cage model with core losses is as follows:

where

are the equivalent circuit

parameters of the single cage model (with core losses) Double Cage Model (With Core Losses) The non-linear least squares problem for the double cage model with core losses is as follows:

where equivalent circuit parameters of the double cage model (with core losses) Parameter Estimation Algorithms

are the

The most common algorithms used to solve the non-linear least squares problems for motor parameter estimation are as follows: 

Newton-Raphson Algorithm



Levenberg-Marquardt Algorithm



Genetic Algorithm (or equivalent evolutionary method)

Software Many commercial software packages for power systems analysis such as ETAP and DIgSILENT PowerFactory contain integrated routines for estimating motor parameters from manufacturer data. The commercial packages typically use some variant of the Newton-Raphson algorithm. Moto is a free standalone tool for estimating induction motor parameters based on commonly available manufacturer data (i.e. breakdown torque, locked rotor torque, full load power factor, etc). The program s a number of estimation algorithms including Newton-Raphson, Levenberg-Marquardt and genetic algorithms. References 

[1] Pedra, J., “Estimation of typical squirrel-cage induction motor parameters for dynamic performance simulation”, IEEE Proceedings on Generation, Transmission and Distribution, Vol. 153, No. 2, 2006



[2] Filho, E., Lima, A., and Jacobina, C., “Parameter Estimation for Induction Machines via Non-Linear Least Squares Method”, Conference proceedings of IECON, 1991



[3] Rogers, G., Shirmohammadi, D., “Induction Machine Modelling for Electromagnetic Transient Program”, IEEE Transactions on Energy Conversion, Vol. EC-2, No. 4, 1987



[4] Waters, S. S., Willoughby, R. D., "Modeling Induction Motors for System Studies", IEEE Transactions on Industry Applications, Vol 1A-19, No. 5, 1983



[5] Lindenmeyer, D., Dommel, H. W., Moshref, A., and Kundur, P., "An induction motor parameter estimation method", Electrical Power and Energy Systems, Vol. 23, 2001

Related Topics 

Induction Motor Model

Categories: Motors | Modelling/Analysis

Induction Motor Torque The torque developed in an induction machine can be calculated from the motor model / equivalent circuit because the torque developed is proportional to the square of rotor current, i.e.

Where

is the torque developed in the motor (N-m)

is the number of motor poles is the number of stator phases is the nominal frequency (Hz) is the equivalent rotor resistance (Ω) is the motor slip (pu) is the rotor current (A) Contents [hide] 



1 Calculating Per-Unit Torque from the Equivalent Circuit o

1.1 Single Cage Model

o

1.2 Double Cage Model

2 Torque-Speed Curves

Calculating Per-Unit Torque from the Equivalent Circuit By using per unit values, the constant can be eliminated and the equation above reduces to:

Where in this equation, all quantities are in per-unit. Using this relationship, we can simply analyse the equivalent circuit of an induction motor and solve for the rotor current. For simplicity, all of the analyses below will be performed using per unit values. Note also that complex impedances (or ittances) obey the rules of complex arithmetic. Single Cage Model

Single cage model equivalent circuit

The equivalent circuit for the single cage model is shown in the figure to the right. Recasting the impedances as ittances:

Applying Kirchhoff's law at node

The per-unit stator current

The per-unit rotor current

:

:

:

The per-unit torque developed is:

Double Cage Model

Double cage model equivalent circuit The equivalent circuit for the double cage model is shown in the figure to the right. Recasting the impedances as ittances:

Applying Kirchhoff's law at node

The per-unit stator current

The per-unit rotor currents

:

:

and

The per-unit torque developed is:

Torque-Speed Curves

:

Torque-speed curve implied by an equivalent circuit Based on the torque equations developed in the previous section for the single cage and double cage motor models, torque-speed curves can be constructed from the equivalent circuit by calculating the torque at each point on the full range of motor speeds (i.e. from standtill to synchronous speed). Category: Motors Induction Motor Model Contents [hide] 

1 Single Cage Model



2 Double Cage Model



3 Core Losses



4 Parameter Mismatch with Measured Data



5 Parameter Estimation



6 References



7 Related Topics

Single Cage Model

Figure 1. Single cage model equivalent circuit The single cage model has the following parameters: 

= motor terminal voltage



= stator resistance



= stator leakage reactance



= magnetising reactance



= rotor resistance



= rotor reactance

It has been shown (for example, in [1]) that the single cage model is not able to capture both the starting characteristics and the breakdown torque characteristics of a cage induction motor. Therefore for motor startup simulations, the double cage model is recommended. Double Cage Model

Figure 2. Double cage model equivalent circuit The double cage model has the following parameters: 

= motor terminal voltage



= stator resistance



= stator leakage reactance



= magnetising reactance



= inner cage rotor resistance



= inner cage rotor reactance



= outer cage rotor resistance



= outer cage rotor reactance

Core Losses You will notice that in the models above, the shunt magnetising branch is represented as a magnetising reactance only (Xm). In a practical motor, there will also be eddy currents in the core laminations that manifest themselves as heat losses. These so called core (or iron) losses can be modelled as a shunt resistance as per the standard transformer model. Parameter Mismatch with Measured Data Manufacturers sometimes provide the electrical parameters for the motor equivalent circuit (usually the single cage model) on their data sheets, based on measured test data (e.g. using the standard tests in IEEE Std 112). However, if one were to compute the motor torque-speed curve using these parameters, significant differences will often be found between the torquespeed curve implied by the equivalent circuit and the torque-speed curve from the manufacturer’s performance data (e.g. breakdown torque, locked rotor torque, etc) [2]. The reason for this is that the equivalent circuit model is a simplification of reality. For modelling purposes, we would like an equivalent circuit with constant parameters that is reasonably accurate (when compared to the performance data) over the full range of slip values. However, this simplified model doesn't take into consideration a number of factors present in practical motors, for example: 

The equivalent circuit parameters are not constant, and actually vary with frequency (slip). The manufacturer will sometimes provide measured electrical parameter data at various slip values and they will no doubt be different. For example, rotor resistance is frequency (slip) dependent, caused by eddy currents in deep and shaped rotor bars. Likewise, leakage inductances vary due to eddy currents and saturation of the leakage flux path [3]



The parameters also vary with temperature and saturation of the teeth and core [4]



Stator resistance is normally measured with a dc resistance test (e.g. IEEE Std 112), but the ac resistance may be different in practice and is also temperature dependent



Saturation of the leakage path of stator and rotor magnetic fields during DOL starting reduces the leakage reactances at locked rotor conditions. However the locked-rotor test is done at reduced voltages to simulate full load currents. Therefore the test doesn’t actually simulate the high currents on starting and thus tends to overestimate the rotor and stator leakage reactances.



The skin effect reduces rotor leakage inductance



The effect of space and time mmf harmonics



For deep bar or double cage machines, classical no-load and locked rotor tests result in rotor resistances that are often too high

As mentioned above, we want an equivalent circuit with constant parameters that is reasonably accurate over the full range of slip values from 0 to 1pu. Sometimes such an equivalent circuit doesn’t actually exist, and in such cases we have to decide which parts to sacrifice (e.g. if only the starting characteristics are important in the study, then it may be acceptable for the full-load characteristics to be less accurate). Parameter Estimation The equivalent circuit parameters of an induction motor can be estimated by various classes of parameter estimation methods, depending on what type of data sets are available and the applications of the model. The estimation methods generally fall into one of five classes [5]: Class

Description

Data Required

Applications

1. Parameter

Accurate

Details on motor

manufacture of

calculation from

electromagnetic field

construction, e.g.

induction motors to

motor

based calculation of

geometrical and

meet certain

construction data

motor parameters

material data

performance

Design and

requirements

2. Parameter estimation based on steady-state motor models

3. Frequencydomain parameter estimation

Iterative estimation algorithms based on steady-state network data and motor manufacturer data

Motor performance data from manufacturer, e.g.

Desktop (offline)

nameplate details,

power system studies

torque-slip curves, current-slip curves

Parameter estimation

Offline power system

based on stand-still

studies when SSFR

frequency response (SSFR) test

test results are SSFR test results

available (more

measurements and

accurate than

resulting transfer

estimation based on

function

steady-state models)

4. Time-domain

Time-domain motor test

Motor test and

Simplified models

parameter

measurements are used

measurement setup

based on real test

estimation

to tune model

data

parameters

Simplified model 5. Real-time

sstimation based on

parameter

real-time measurements

estimation

of actual motor

Online tuning of Motor sensors and

induction motor drive

measurement devices

controllers (e.g.

operation

variable speed drives)

References 

[1] Pedra, J., “Estimation of typical squirrel-cage induction motor parameters for dynamic performance simulation”, IEEE Proceedings on Generation, Transmission and Distribution, Vol. 153, No. 2, 2006



[2] Filho, E., Lima, A., and Jacobina, C., “Parameter Estimation for Induction Machines via Non-Linear Least Squares Method”, Conference proceedings of IECON, 1991



[3] Rogers, G., Shirmohammadi, D., “Induction Machine Modelling for Electromagnetic Transient Program”, IEEE Transactions on Energy Conversion, Vol. EC-2, No. 4, 1987



[4] Waters, S. S., Willoughby, R. D., "Modeling Induction Motors for System Studies", IEEE Transactions on Industry Applications, Vol 1A-19, No. 5, 1983



[5] Lindenmeyer, D., Dommel, H. W., Moshref, A., and Kundur, P., "An induction motor parameter estimation method", Electrical Power and Energy Systems, Vol. 23, 2001

Related Topics 

Motor Parameter Estimation from Steady-State Models

Categories: Motors | Modelling/Analysis Category:Transformers Introduction A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field through the secondary winding. This varying magnetic field induces a varying electromotive force (EMF), or "voltage", in the secondary winding. This effect is called inductive coupling.

2 Winding Transformer Models Contents [hide]



1 Positive Sequence Model



2 Zero Sequence Models o

2.1 Effects of Core Construction



3 References



4 Related Topics

Positive Sequence Model

Figure 1. Positive sequence two-winding transformer equivalent circuit The standard positive sequence model for a two-winding transformer has the following per-unit parameters: 

= primary side terminal voltage (pu)



= secondary side terminal voltage (pu)



= primary winding resistance (pu)



= primary winding leakage reactance (pu)



= secondary winding resistance (pu)



= secondary winding leakage reactance (pu)



= magnetising reactance (pu)



= eddy current / core losses (pu)



= primary current (pu)



= secondary current (pu)



= magnetising current (pu)

Zero Sequence Models The zero sequence model of a transformer depends on the winding and neutral earthing arrangements. The figure below presents simplified zero sequence models (ignoring the magnetising branch and with all leakage impedances lumped together) for the most common types of two-winding transformer connections. Note that all impedances are in per unit values.

Figure 2. Zero-sequence transformer models for common connections

Figure 3. Zero sequence current flows in a delta-wye transformer A key insight about transformer zero sequence connections stems from one of the fundamental tenets of transformers: a current will only flow in one winding if there is a corresponding current in the other winding (ignoring magnetising currents). This is important to understand why zero sequence current can flow in a delta-wye transformer with the star point earthed. Clearly on the wye winding, zero sequence current can flow to earth through the star point, but zero sequence current must also be able to circulate in the delta windings. This also explains why no zero sequence current can flow in wye-wye transformers (with only one star point earthed). A zero sequence current would need to induce a current in the unearthed wye winding, but there is nowhere for the current to go. Thus it is shown as disconnected in the zero sequence equivalent circuit. Effects of Core Construction The simplified zero sequence models in the previous section ignored the magnetising branch. For shell type and 5-limb core type transformers, this is a reasonable assumption since the zero sequence magnetising reactance is large and similar to that of the positive (and negative) sequence magnetising reactance. However, care must be taken for the zero-sequence modelling of 3-limb core type transformers. The shape of the core is such that during unbalanced operation (i.e. presence of zero-sequence currents), the flux is forced to take a path outside of the transformer core (low reluctance) and through the air, tank, oil and transformer frame (high reluctance). As magnetising reactance is inversely proportional to reluctance, the high reluctance path causes the magnetising reactance in 3-limb core type transformers to be significantly lower than in 5-limb core type or shell type transformers. This is particularly relevant for wye connected windings, especially Yyn (or YNy) connections with only one star point earthed. We mentioned previously that zero sequence currents cannot flow in this configuration. But for 3-limb core type transformers, the alternative flux path through the

tank, oil and frame allows for sufficient zero-sequence current to be induced and circulate around the tank and frame. In this way, the tank and frame acts like an internal delta winding. References 

[1] Blackburn, J., "Symmetrical Components for Power Systems Engineering", CRC Press, 1993



[2] Tleis, N., "Power Systems Modelling and Fault Analysis - Theory and Practice", Newnes, 2008

Related Topics 

Transformer Impedance

Categories: Transformers | Modelling/Analysis

Current transformer

Figure 1. A Current Transformer in a 150kV line

Figure 2. The simplified equivalent diagram of aCurrent Transformer Current Transformers or CT's are Instrument Transformers that convert a generally high primary current Ip to a k-times lower secondary current Is that can be connected to standard measuring or protection devices. The primary and secondary windings are galvanically separated and can be on a different potential level. The transformation ratio k of a current transformer is the number of secondary turns Ns to the number of primary turns Np and is equal to the primary current Ipover the secondary current Is.

Contents [hide] 

1 Standards for current transformers o

1.1 According IEC

o

1.2 Other standard organisations



2 Functioning of a Current Transformer



3 General property's of a Current Transformer o

3.1 The Primary current Ip

o

3.2 The Secondary current Is

o

3.3 Dual or Multi-Ratio CT's

o

3.4 Ratio k



o

3.5 RCT The internal copper resistance

o

3.6 Accuracy

o

3.7 Load, Rated load and Burden

4 The use and specification of Current Transformers o

4.1 Protection CT's

o

4.2 Measurement CT's

Standards for current transformers According IEC At the moment TC38 of the IEC is busy converting all the instrument transformers from the 60044-family to the new 61869 family with a general part and specific parts. 

IEC 60044-1 Consolidated Edition 1.2 (incl. am1+am2) (2003-02) TC/SC 38 Instrument transformers - Part 1: Current

transformers 

IEC 60044-3 Edition 2.0 (2002-12) TC/SC 38 Instrument transformers - Part 3: Combined transformers



IEC 60044-6 Edition 1.0 (1992-03) TC/SC 38 Instrument transformers - Part 6: Requirements for protective current

transformers for transient performance 

IEC 60044-8 Edition 1.0 (2002-07) TC/SC 38 Instrument transformers - Part 8: Electronic current transformers



IEC 61869-1 Edition 1.0 (2007-10) TC/SC 38 Instrument transformers - Part 1: General requirements

Other standard organisations 

IEEE Std C57.13-1993: IEEE Standard requirements for Instrument transformers



Canada CAN3-C13-M83: Instrument transformers



Australia AS 1675 Current transformers - Measurement and protection



British Standard BS3938 Specifications for Current Transformers (Withdrawn and replaced by IEC 60044-1)

Functioning of a Current Transformer

Figure 3. The functioning principle of a current transformer Just like a normal voltage transformer, a CT has a primary winding, a secondary winding and a magnetic core. In the window-type and bushing-type CT's, the primary winding is reduced to one wire ing trough the round or square shaped core, ing for 1 turn. The primary current Ip will produce a magnetic field with induction B round the conductor. The magnetic induction B is amplified by the core material with very high magnetic permeability µ and will produce a primary flux that will magnetise the core with cross section A and induces a secondary voltage V s in the secondary winding with N turns.

At the same time, a N times smaller voltage, opposed to the primary current will be induced in the primary wire creating a small extra resistance in the primary circuit. The induced secondary voltage will drive the secondary current Is that will flow for the mayor part trough the connected load Rb and for a small part (the error current) Ie trough the internal resistance and induction. The internal resistance and induction represent the part of the current that is used to magnetise the core (Inductive part) and to heat-up the core material as iron-losses. Actually the magnetising current is taken from the primary side but that will only make the calculation model more difficult and does not form any additional value. The secondary current I s will also produce a secondary flux, opposite to the primary flux. The resulting flux in the CT core is a very small magnetising flux so that the core does not saturate at normal operation currents. The secondary current Is will be N times smaller than the primary current Ip.

The error current Ie exists for the major part of a purely inductive part; the magnetising current Im that can be seen on the magnetising curve of the CT and a small resistive part Ig that represent the iron losses. The magnetising current Im is proportional to the field strength H

The copper losses are represented in the series resistor RCT General property's of a Current Transformer The Primary current Ip According to IEC 60044-1, the primary current I_p is standadise of the decadic series 1 - 1,25 1,5 - 2 - 2,5 - 3 - 4 - 5 - 6 - 7,5. When selecting a CT; the primary current of the CT must be at least the maximum current of the line in which the CT will operate. When the current is bigger than the rated primary current of the CT, the windings will overheat, age faster and finally the insulation will fail. According ANSI, the primary currents are fixed values; for single Ratio CT's Ip = 10; 15; 25; 40; 50; 75; 100; 200; 300; 400; 600; 800; 1200; 1500; 2000; 3000; 4000; 5000; 6000; 8000; 12000A. The Secondary current Is According IEC the secondary current can be 0.5, 1 , 2 or 5A. According ANSI the secondary current is allways 5A. Dual or Multi-Ratio CT's Dual ratio CT's exist in all standards but only according the ANSI standard, the ratio's are standardised. Note the for multi ratio CT's, many primary currents are mentionned and only one secondary current but in reality there is only one primary connection and 5 secondary terminals that allow 10 different ratings. Ratio k As already mentionned, the most important property of the current transformer is the ratio k that is both the ratio of secundary turns to primary turns and the ratio of primary current to secondary current. Note the often the primary is only one turn and practically it's just the conductor ing trough the core. Since a small amount of energy is necessary to magnetising the core and to produce heat as iron loss in the core, the secondary output Ampere-turns is a bit less than the primary Ampere-turns. The difference in current is the error current or magnetising current. In case of very critical CT's, ratio-turn-correction is applied; remove some secondary turns so that the ratio is a bit higher and the output is thus a bit higher at rated current. Of course this can only be applied when the CT meets all accuracy requirements after ratio-turn correction. RCT The internal copper resistance RCT is often called the secondary DC resistance at 75°C. It's value depends on the length en cross section of the secondary winding wire Pouillet's law. So RCT also depends on the core dimensions; bigger core cross section implies a longer wire length per turn. The smaller R CT; the more the current transformer approaches the ideal current source. Accuracy

Figure 4. The current vectors Ip and k.Is and the error current vector Ic

Figure 5. The current error of a measuring class CT; here class 0.5 and class 1 are represented The accuracy of a CT is given by it's "class". The division into accuracy classes depends on the type of CT; we mainly distinguish measuring class CT's and Protection class CT's who are defined quite differently. We will discuss accuracy for both types further. Of course they both have a primary current I_p, a secondary current I_s and a ratio k. From these 3 parameters we can define some important property's related to accuracy. 

The primary current vector Ip.



The secondary current vector Is that is here represented k times larger to be able to compare them and to have an idea of the error current. In case the error would be 0, both vectors I_p and k.I_s would be identical.



The total error vector (composite error) can be seen as the composition of: 

an amplitude error (ratio error), expressed in % and



an angle error, expressed in radians or seconds.

Note that for protection CT's, the angle error is disregarded and only the total composite error is given in %. When examining the equivalent diagram, one would easily conclude that the error

current can only be the magnetising current of the CT. Indeed, normally the magnetising current is very low but at the saturation point of the core, 50% increase in magnetising current produces only 10% extra secondary voltage so at saturation the error current rises quickly. Therefore, the property's accuracy and saturation of the core are closely linked. Hense the error vector is allways a reducion in secondary output current; negative error. Positive error is only possible by ratio-turn correction. Load, Rated load and Burden A Voltage transformer is unloaded when the secondary terminals are open; it behaves like a normal voltage source. A current transformer is just the opposite and is unloaded with the secondary terminals short-circuited. Stonger even, when the secondary terminals of a CT are open, there is no secondary flux to oppose the primary flux and the core goes to positive saturation on the positive current-sine and to negative saturation on the negative current sine. The induced seconday voltage is proportional to - N.dφ / dt and from -Vsat to +Vsat is a huge voltage. One might also conclude that the current transformen is raising the voltage in trying to drive the secondary current trough the open terminals. The insulation of the CT is not calculated for this situation and it will distroy the CT secondary winding and may cause fire at the terminals & high voltage injury. The nominal load of a CT is the rated resistive burden R B; expressed in VA. The correct resistance can be calculated with below formula

Example: A 50VA CT with rated secondary current of 5A is designed for a connected load of 50VA/5² = 2 Ohm. Measuring transformers are tested at rated load and at 1/4 of the rated load so this CT should be loaded within these limits to be sure the accuracy is within specification. The use and specification of Current Transformers Current transformers are used to measure high currents; higher than 5A. So the most important parameter in defining a CT is indeed the Ratio that gives us the Magnetude of primary current and the secondary current. But for the following specifications of the current transformer, the purpose of the CT is needed since measuring CT's and Protection CT's require different specifications. Indeed, there will be two mayor groups of Current Transformers: 

Protection current transformers



Measurement current transformers

Regarding specification, different standards have different ways in specifying CT's but it all comes down to specifying core property's (saturation point or knee-point) and secondary wire property's (RCT) although it may look a totally different. Protection CT's

Figure 6. The ratio of a protection CT as a function of the current Protection CT's: 

are meant to protect an elektrical installation in case of overcurrent or short circuit and their operating current range is above nominal current In or more specific from In to ALF times In. It is important for the good functionning of the protection relays that the CT's are NOT saturated at ALF times rated current. Where ALF is the ratio of the expected maximum fault current over the rated current. It is thus important that the core material has a high saturation induction.



their accuracy is not very high but most important is that the accuracy in fault conditions is high enough. This can only be the case when the core is not saturated in case of a fault current. Therefore their accuracy is best described with an Accuracy Limit and an Accuracy Limit Factor (ALF).E.g. a 5P20 CT has an Accuracy limit of 5% at 20 times rated current (Accuracy Limit Factor). The accuracy of this CT at rated current is 1%.



They will be connected to one or more protection relays



according the application, they can be defined in a few ways: 

The standard IEC protection class CT's are of class "P" that only takes the AC behaviour into in IEC 60044-1



Class PX CT's are defined by the position of the knee-point (saturation point or knee-point voltage and magnetising current) and the secondary wire resistance RCT.



Class PR CT's are defined like the PX CT's but they have a low remanence; less than 10%. Note that remanence in CT's can be 60-80% that may cause quick saturation in case of a fault-current DC offset in the remanent direction. A class PX CT can't have that problem.



CT's for transient response class "TP" are defined by their connected load R B, time constant TS and their overcurrent figure KSSC. These linearised CT's have air-gaps in the core to obtain extreme high saturation voltage and current.

Figure 7. The error limits of a protection CT per IEC 60044-1

Ex. A 5P10 CT at 10 times rated current has a maximum error of 5% and only 1% at nominal current. A 10P15 CT at 15 times rated current has a maximum error of 10% and 3% at nominal current. Measurement CT's

Figure 8. The ratio of a measurement CT as a function of the current 

Are aimed to measure accurately within their normal operating range of 0 to I n. Therefore, the core material must have a high permeability (µ-metal) so that the magnetising current is low.



Measurement CT's are often being used for billing of electrical power consumption and their accuracy is determinent for a lot of money.



For the protection of the measuring instruments in case of a fault current, it is favorable that for currents far above rated current In, the core is saturated and the output lowers so that the fault-current trough the meter is only a part of the expected current trough the meter. This is expressed by the Instrument Security Factor SF. Of course, the dilemma is that the CT must be accurate at In (and 1,2 x In) but at f.i. 5 times rated current ( FS 5) the CT may be saturated for at least 10%.



The accuracy of a measurement CT is given by it's accuracy class that corresponds to the error% at rated current and at 1.2 times rated current In. The standard accuracy classes according IEC are class 0.2, 0.5, 1, 3 en 5. For classes 3 and 5, no angle error is specified. The classes 0.2S and 0.5S have their accuracy shifted toward the lower currents. This means that they have 5 measuring points instead of 4 (or 2 for class 3 & 5).

Figure 9. The error for measurment CT's according IEC 60044-1



The accuracy of the CT must be within these limits at the given currents and with rated load and at 1/4 of the rated load. A measurement CT that is not loaded is therefore not necessary accurate! Ratio turn correction may have been applied to get the CT ratings witthin spec and then not loading gives a higher error.

Categories: Transformers | Protection

Dry-Type Transformer Testing Contents [hide] 

1 Introduction



2 Testing



o

2.1 Insulation Resistance Tests

o

2.2 Dielectric Loss Angle Measurement Tests

o

2.3 Partial Discharge Tests

o

2.4 Frequency Response Analysis

o

2.5 Acoustic Emission Tests

o

2.6 Thermographic Surveys

3 References

Introduction The primary concern with all transformers (and also the key indicator of life expectancy) is the condition of the insulation system. For dry type transformers, the insulation system consists of the cast resin winding and core insulation and the termination system insulation (e.g. bushings). The structural strength and insulating properties of materials used for these insulation systems degrade over time through normal ageing. They can also degrade prematurely as a result of overheating and mechanical and electrical stresses (e.g. faults, overvoltages, inrush currents, etc). The initial breakdown of insulation around the windings can result in inter-turn faults, especially on the high voltage windings where the electric field strength is high enough to ionise air gaps and cause corona activity. Inter-turn faults are short circuits between coil turns on a single winding. Further degradation of the insulation could see inter-turn faults develop into more serious faults such as inter-winding and earth faults.

Testing The most frequent mode of failure for dry type transformers is insulation breakdown resulting in inter-turn faults which leads to more severe faults such as phase to phase winding or earth faults. The insulation condition of component parts of the transformer (i.e. windings, core, bushings, etc) can be determined by a suite of tests. Dissolved gas analysis is the most commonly used method for determining winding insulation condition in oil-type transformers, but is not possible for dry-type transformers. The following tests are discussed further: 

Insulation resistance / polarisation index tests



Dielectric loss angle measurement tests



Partial discharge tests



Frequency response analysis



Acoustic emission tests (in conjunction with partial discharge tests)



Thermographic surveys

Insulation Resistance Tests Insulation resistance, measured by application of an impressed DC voltage (i.e. Megger), gives a general indication of the insulation condition between the phase windings and earth. The

measurements are typically taken over time (i.e. 1 minute intervals over 10 minutes) to generate a curve, called the Dielectric Absorption curve. The Polarisation Index is the steepness of the curve at a given temperature and is defined as per the following equation [1]:

Where R10 = megohms insulation resistance at 10 minutes R1 = megohms insulation resistance at 1 minute The Polarisation Index indicates the relative dryness and level of moisture ingress into the insulation. Dielectric Loss Angle Measurement Tests Dielectric loss angle tests, also called dissipation factor, power factor or tan delta tests, determine the insulation dielectric power loss by measurement of the power angle between an applied AC voltage and the resultant current. In the ideal insulator, the power angle would be 90°C as it is purely capacitive and non-conducting. However in real insulators, there is some leakage current and resistive losses through the dielectric. Relative increases in dielectric power losses are indicative of insulation deterioration and may further accelerate degradation due to increased heating. Note that dielectric power loss does not translate to dielectric strength, though there are often common causes for increases in power loss and decreases in dielectric strength.

The cosine of the power angle (θ) is called the power factor. The complement of θ is denoted δ as shown in the diagram above. The power factor can be practically approximated by taking the tangent of δ (hence the name tan delta). This approximation is called the dissipation factor and is roughly equal to the power factor between values of 0 and 0.08, which covers the majority of tests. The dissipation factor is essentially the ratio between the resistive and capacitive components of the insulation and can be measured directly (via a capacitance bridge circuit). The lower the

quality of the insulation condition, the more resistive it will appear and the more power loss will be dissipated through it (in the form of heat). The increase in the dissipation factor values as the test voltage is increased is called the "tip-up". The technical literature on this subject has noted that this test is useful for detecting moisture ingress in the bushings and windings. About 90% of bushing failures may be attributed to moisture ingress evidenced by an increasing power factor from dielectric loss angle testing on a scheduled basis. Partial Discharge Tests Partial discharges are localised incipient electrical discharges that only partially bridge the insulation between conductors. Partial discharges can occur in any location where the local electrical field strength is sufficient to breakdown that portion of the dielectric material (whether it be deteriorated insulation or air). In dry-type transformers they can occur within air-filled voids where the solid insulation has degraded. Partial discharge testing can detect the presence and location of partial discharge activity in a transformer. Partial discharges in transformers are typically measured by applying a pre-specified voltage to the transformer windings and measuring induced charges via a coupling device (e.g. coupling capacitors). AS 60076.11 and AS 60270 set out the requirements, procedure, equipment and acceptance levels for partial discharge testing [3] [4]. It should be noted that the partial discharge tests specified in AS 60076.11 are intended as routine tests for new transformers. This involves applying a “pre-stress” voltage of 1.8 times rated voltage to the windings. This may be excessive for transformers already in service for over 20 years. Analysis of the partial discharge measurements gathered (i.e. pulse waveforms, magnitude, duration and intervals between pulses) can be used as a guide regarding the condition of the insulation. The results can be trended to chart the rate of insulation degradation between consecutive tests. Frequency Response Analysis Frequency response analysis is a diagnostic testing technique that measures the impedance of the transformer windings over a wide range of frequencies. The measurements are compared with a reference set and the differences are highlighted. The differences may indicate mechanical damage to the windings (e.g. winding displacement or loose winding) and electrical faults (e.g. interturn faults). Frequency response analysis can be achieved by either injecting a low voltage impulse into the winding (i.e. impulse response method) or by making a frequency sweep using a sinusoidal signal (i.e. swept frequency method). For frequency response analysis to be useful, a baseline reference set of measurements need to be determined and periodic tests need to be conducted to compare the differences. Refer to research by S. Tenbohlen et al at the University of Stuttgart [5]. Acoustic Emission Tests

Partial discharges in transformers can also be detected and localised via acoustic emission testing. Acoustic emission testing is based on the acoustic detection of the partial discharge pulses and conversion to an electrical signal. Sensors are coupled to the surface of the transformer and during operation of the transformer, the output of the sensors are fed into an electronic module. The signals are filtered to remove noise and processed to determine the presence and location of any partial discharges in the transformer. Thermographic Surveys Infrared thermography is commonly used in preventative maintenance to detect hotspots, especially at ts and terminations. IR Thermography cameras measure surface temperatures and the resulting thermal image can be used to identify overheating at the transformer terminations. For thermographic surveys to be conducted, thermographic windows need to be installed looking at the terminations and windings. References 1. Facilities Instruction, Standards and Techniques Volume 3-1, “Testing Solid Insulation of Electrical Equipment”, U.S Department of the Interior, Reclamation Branch, December 1991 2. Facilities Instruction, Standards and Techniques Volume 3-31, “Transformer Diagnostics”, U.S Department of the Interior, Reclamation Branch, June 2003 3. AS 60076.11, “Power transformers Part 11: Dry-type transformers”, 2006 4. AS 60270, “High-voltage test techniques – Partial discharge measurements”, 2001 5. Research at University of Stuttgart (including Tenbohlen's papers) Categories: Transformers | Electrical Testing

Transformer Impedance Contents [hide] 

1 Positive Sequence Impedance o

o

1.1 Two Winding Transformer 

1.1.1 Impedance Measurement



1.1.2 Copper Losses



1.1.3 Calculation of R1 and X1



1.1.4 Application in Transformer Models

1.2 Winding Connections



2 Zero Sequence Impedance o



2.1 Two Winding Transformer 

2.1.1 Impedance Measurement



2.1.2 Calculation of R0 and X0

3 References

Positive Sequence Impedance The transformer positive sequence impedance is also called the short circuit impedance (because it is measured from a short circuit test) or the impedance voltage (because a voltage is measured from the short circuit test - more details below). Two Winding Transformer Impedance Measurement

Positive sequence impedance test circuit for three-phase 2-winding transformer The positive sequence impedance is measured from a standard short circuit test (see figure right). In this test, one set of windings is shorted (typically the LV windings) and a three-phase voltage source is applied to the other set of windings. The voltage is steadily increased until the rated phase current is measured. The voltage at this point is called the impedance voltage. When the impedance voltage is expressed as aper-unit value (on the transformer rated line-to-line voltage), the impedance voltage is equivalent to the per-unit impedance, i.e.

where

is the measured impedance voltage (V)

is the rated transformer line-to-line voltage / base voltage (V) is the rated transformer current (A) is the positive sequence impedance (Ω)

is the transformer base impedance (Ω) is the positive sequence impedance (pu) The impedance voltage is also often expressed as a percentage (Z%). Copper Losses Full load copper (or iron) losses are measured in the same test as the impedance voltage by taking the power reading (from the wattmeter in the test circuit). The copper losses represent the I2R losses from the full load current in the phase windings, as well as stray losses due to induced eddy currents from leakage fluxes in the windings, core clamps, tank and other magnetic pathways. Calculation of R1 and X1 The resistive and reactive components of the positive sequence transformer impedance can be estimated from the two short circuit test measurements - 1) impedance voltage, and 2) full load copper losses. The expressions below calculate the resistance and reactance in per-unit quanitities.

Where

is the positive sequence resistance (pu) is the positive sequence reactance (pu) is the positive sequence impedance (pu)

are the full load copper losses (W) is the transformer rated power (kVA) Application in Transformer Models The positive sequence impedance measured and calculated above is most often applied in the standard positive sequence two-winding transformer model as representing the transformer leakage impedance. This representation assumes that the parallel magnetising and core loss branch in the T-circuit is a negligible part of the measured positive sequence impedance (note that the magnetising reactance and core losses are estimated separately in no-load (open circuit) tests). You will notice that the standard positive sequence transformer model has leakage impedances on both the primary and secondar sides of the transformer. However in our measurements, we only calculate a single impedance. It is common practice to distribute the impedance across both sides (for example, 50%-50% if no other information is available). Winding Connections

It is worth noting that the transformer impedance voltage (expressed in percent or per-unit) is independent of the winding connection. This is because each winding is tested separately and normally quoted as a per-unit (or percent) impedance voltage based on the transformer's rated line-to-line voltage (see IEEE Std C57.12.90). If the winding connections are changed, then the line-to-line voltage would also have to change. But since it is a per-unit (or percent) value, the impedance voltage would remain the same. Zero Sequence Impedance Two Winding Transformer Impedance Measurement

Zero sequence impedance test circuit for three-phase 2-winding transformer (with accessible neutral) In the zero sequence test, a single-phase voltage source is applied between the three phase terminals (connected together) and an externally available neutral terminal (see the test circuit in the figure right). Like in the positive sequence test, the voltage is steadily increased until the rated current is measured.

where

is the measured zero sequence impedance voltage (V)

is the rated transformer line-to-line voltage / base voltage (V) is the rated transformer current (A) is the zero sequence impedance (Ω) is the transformer base impedance (Ω) is the zero sequence impedance (pu) Note that the measured impedance voltage is actually equivalent to a third of Z0. This is because the three phase windings are connected together and the current flowing through each individual winding is a third of the measured rated current.

Tleis [2] also suggests that for earthed star-star (YNyn) transformers with a three-limbed core construction, zero sequence flux can circulate around a path through the core, tank, insulating oil and air. Therefore this magnetic path acts like a "virtual" delta winding, and the zero sequence impedance can be lower than the standard measured value. Tleis suggests treating these transformers like three-winding transformers and performing at least three test measurements. Calculation of R0 and X0 Occasionally the zero sequence copper losses (Pc,0) are also measured as part of the zero sequence test. When this is the case, calculations similar to that of the positive sequence impedance can be applied:

Where

is the zero sequence resistance (pu) is the zero sequence reactance (pu) is the zero sequence impedance (pu)

are the zero sequence copper losses (W) is the transformer rated power (kVA) However, when the zero sequence copper losses are not known, it is common to use the same X/R ratio as in the positive sequence, i.e.

Where

is the positive sequence X/R ratio

References 

[1] IEEE Std C57.12.90, "IEEE Standard Test Code for Liquid-Immersed Distribution, Power and Regulating Transformers", 2010



[2] Tleis, N., "Power Systems Modelling and Fault Analysis - Theory and Practice", Newnes, 2008

Category: Transformers

Transformer Impedance Correction Factor IEC 60909 uses a simplifying assumption where the pre-fault voltage at the fault location is not calculated (e.g. by a load flow), but rather an equivalent voltage source is used (assumed to be the nominal voltage multiplied by some voltage factor c). Furthermore, the pre-fault load current is not known (i.e. not calculated) and transformers can operate at a wide range of off-nominal tap settings. Therefore, the simplified IEC calculations did not correspond to the calculations based on the more accurate superposition method. An impedance correction factor was thus introduced to improve the accuracy of the calculated fault currents. In the older versions of IEC 60909 (pre-2001), there was no explicit impedance correction factor for transformers, instead just a suggestion that considerations need to be made. IEC found this unsatisfactory and introduced the correction factor in the 2001 edition. The correction factor was essentially defined empirically through a statistical analysis of a few hundred transformers. Most of this is described in some detail in IEC 60909-1. Transformer Inrush Transformer (magnetising) inrush currents are caused by sudden step-changes in the transformer magnetising voltage and can be divided into three general types: 

Energisation inrush - occurs when a transformer is switched on from a de-energised state



Recovery inrush - occurs when voltage is restored to the transformer after a brief voltage dip or interruption



Sympathetic inrush - occurs when a transformer is switched on and is connected in parallel to an already energised transformer. The abrupt voltage drop caused by energising the first transformer can cause inrush currents (in the opposite direction) in the already energised transformer.

Transformer energisation is considered to cause the highest inrush currents and will be the focus of this article. When energised, an initial magnetising inrush current flows into the transformer. Typically, the inrush current lasts in the order of 0.1s and has the following magnitude: 

For transformers up to 2500kVA: 8x nominal current



For transformers greater than 2500kVA: 10x nominal current

Transformer inrush currents are predominantly due to saturation of the transformer core and can be modelled as an RL switching transient with a saturable inductance L. Contents [hide] 

1 Technical Background o

1.1 Effects of Switching Angle

o

1.2 Effects of Residual Flux

o

1.3 Transient Flux in Practical Transformers



o

1.4 Non-Linear Relationship between Flux and Current

o

1.5 Summary

2 References

Technical Background

Figure 1. Simple model for transformer inrush Consider the application of a sinusoidal voltage to a transformer that is modelled very simply as a coil of N turns. By Faraday's law, we get:

Where

is the voltage amplitude (V)

is an arbitrary switching angle (radians) is the number of turns in the transformer coil is the transformer magnetising flux To solve this differential equation for flux given some initial (residual) flux the Laplace transform of it:

Solving for

:

Simplifying further:

, we take

Taking the inverse Laplace transform, we finally get:

(1) While this is a gross simplification of reality, the equation above can give us some intuition about the nature of the transformer flux during a transient switching on (energisation) event. Effects of Switching Angle From equation (1) above, it can be shown that the switching angle results in a dc offset of the flux waveform. The figure below shows the effects of the switching angle on the flux waveform at three angles (relative to the ac supply voltage): 1) a positive zero crossing (θ = 0), 2) a voltage peak (

) and 3) a negative zero crossing (θ = π).

Figure 2. The effects of switching angle on flux

Here it can be seen that switching at a positive zero crossing shifts the flux waveform up to a peak flux of 2pu (and vice versa for a negative zero crossing, i.e. peak flux down to -2pu). There

is no dc offset when switching at a voltage peak. Any other switching angle will result in a dc offset in between the zero crossing waveforms. Effects of Residual Flux It can be readily seen from transient flux waveform in equation (1) that the residual flux causes a dc offset in the flux waveform, i.e. a positive residual flux offsets the waveform up and vice versa for a negative residual flux. Therefore, depending on the switching angle, a residual flux can actually be beneficial to keeping inrush currents low. For example, if the switching angle was a negative zero crossing (e.g. θ = π, this would offset the flux waveform down. But a positive residual flux would have the opposite effect by offsetting the flux waveform up. On the other hand, the residual flux can reinforce the dc offset caused by the switching angle and can result in peak flux values (absolute) well over 2pu. Transient Flux in Practical Transformers In our idealised model above, the transient flux waveform on switching has constant dc offsets depending on the switching angle and residual flux. However in a practical transformer, the effect of leakage impedances (i.e. winding resistances and leakage reactances) will lead to an exponentially decaying dc offset component (like in theswitching of RL circuits), with the rate of decay depending on the time constant

.

The figure below presents a more realistic transient flux waveform on switching, displaying a decaying dc component:

Figure 3. Example of transient flux waveform in practical transformers

Non-Linear Relationship between Flux and Current

Figure 4. Flux-current hysteresis loop

We saw above that during transient conditions, the magnetising flux can rise up over 2pu (depending on the switching angle and residual flux). The other key factor that leads to high inrush currents is the non-linear relationship between flux and current. The transformer core exhibits saturation characteristics like the hysteresis loop in the figure shown on the right. Here it can be seen that at 1 pu flux, the core is already saturating and the slope of the curve begins to approache a horizontal line. Therefore, if the flux is increased further above 1 pu flux, the current drawn can be several orders of magnitude higher. Summary Putting all the pieces together, the general intuition explaining transformer energisation inrush can be put as follows: 1) On the sudden application of a voltage to the transformer (i.e. circuit breaker is closed), a transient flux waveform is generated that, depending on the switching angle and residual flux, can reach a peak of over two times nominal flux. 2) The relationship between flux and current is highly non-linear. At higher than nominal flux, the core will begin to saturate and the related magnetising currents can get very high. This is equivalent to saying that as the core saturates, the magnetising reactance decreases significantly. References 

[1] Greenwood, A., "Electrical Transients in Power Systems", Wiley, 1991

Categories: EMT | Modelling/Analysis | Transformers

Transformer Impedance (Redirected from Transformer Short Circuit Test) Contents [hide] 

1 Positive Sequence Impedance o

o 

1.1 Two Winding Transformer 

1.1.1 Impedance Measurement



1.1.2 Copper Losses



1.1.3 Calculation of R1 and X1



1.1.4 Application in Transformer Models

1.2 Winding Connections

2 Zero Sequence Impedance o

2.1 Two Winding Transformer





2.1.1 Impedance Measurement



2.1.2 Calculation of R0 and X0

3 References

Positive Sequence Impedance The transformer positive sequence impedance is also called the short circuit impedance (because it is measured from a short circuit test) or the impedance voltage (because a voltage is measured from the short circuit test - more details below). Two Winding Transformer Impedance Measurement

Positive sequence impedance test circuit for three-phase 2-winding transformer The positive sequence impedance is measured from a standard short circuit test (see figure right). In this test, one set of windings is shorted (typically the LV windings) and a three-phase voltage source is applied to the other set of windings. The voltage is steadily increased until the rated phase current is measured. The voltage at this point is called the impedance voltage. When the impedance voltage is expressed as aper-unit value (on the transformer rated line-to-line voltage), the impedance voltage is equivalent to the per-unit impedance, i.e.

where

is the measured impedance voltage (V)

is the rated transformer line-to-line voltage / base voltage (V) is the rated transformer current (A) is the positive sequence impedance (Ω) is the transformer base impedance (Ω)

is the positive sequence impedance (pu) The impedance voltage is also often expressed as a percentage (Z%). Copper Losses Full load copper (or iron) losses are measured in the same test as the impedance voltage by taking the power reading (from the wattmeter in the test circuit). The copper losses represent the I2R losses from the full load current in the phase windings, as well as stray losses due to induced eddy currents from leakage fluxes in the windings, core clamps, tank and other magnetic pathways. Calculation of R1 and X1 The resistive and reactive components of the positive sequence transformer impedance can be estimated from the two short circuit test measurements - 1) impedance voltage, and 2) full load copper losses. The expressions below calculate the resistance and reactance in per-unit quanitities.

Where

is the positive sequence resistance (pu) is the positive sequence reactance (pu) is the positive sequence impedance (pu)

are the full load copper losses (W) is the transformer rated power (kVA) Application in Transformer Models The positive sequence impedance measured and calculated above is most often applied in the standard positive sequence two-winding transformer model as representing the transformer leakage impedance. This representation assumes that the parallel magnetising and core loss branch in the T-circuit is a negligible part of the measured positive sequence impedance (note that the magnetising reactance and core losses are estimated separately in no-load (open circuit) tests). You will notice that the standard positive sequence transformer model has leakage impedances on both the primary and secondar sides of the transformer. However in our measurements, we only calculate a single impedance. It is common practice to distribute the impedance across both sides (for example, 50%-50% if no other information is available). Winding Connections It is worth noting that the transformer impedance voltage (expressed in percent or per-unit) is independent of the winding connection. This is because each winding is tested separately and

normally quoted as a per-unit (or percent) impedance voltage based on the transformer's rated line-to-line voltage (see IEEE Std C57.12.90). If the winding connections are changed, then the line-to-line voltage would also have to change. But since it is a per-unit (or percent) value, the impedance voltage would remain the same. Zero Sequence Impedance Two Winding Transformer Impedance Measurement

Zero sequence impedance test circuit for three-phase 2-winding transformer (with accessible neutral) In the zero sequence test, a single-phase voltage source is applied between the three phase terminals (connected together) and an externally available neutral terminal (see the test circuit in the figure right). Like in the positive sequence test, the voltage is steadily increased until the rated current is measured.

where

is the measured zero sequence impedance voltage (V)

is the rated transformer line-to-line voltage / base voltage (V) is the rated transformer current (A) is the zero sequence impedance (Ω) is the transformer base impedance (Ω) is the zero sequence impedance (pu) Note that the measured impedance voltage is actually equivalent to a third of Z0. This is because the three phase windings are connected together and the current flowing through each individual winding is a third of the measured rated current. Tleis [2] also suggests that for earthed star-star (YNyn) transformers with a three-limbed core construction, zero sequence flux can circulate around a path through the core, tank, insulating oil and air. Therefore this magnetic path acts like a "virtual" delta winding, and the zero sequence

impedance can be lower than the standard measured value. Tleis suggests treating these transformers like three-winding transformers and performing at least three test measurements. Calculation of R0 and X0 Occasionally the zero sequence copper losses (Pc,0) are also measured as part of the zero sequence test. When this is the case, calculations similar to that of the positive sequence impedance can be applied:

Where

is the zero sequence resistance (pu) is the zero sequence reactance (pu) is the zero sequence impedance (pu)

are the zero sequence copper losses (W) is the transformer rated power (kVA) However, when the zero sequence copper losses are not known, it is common to use the same X/R ratio as in the positive sequence, i.e.

Where

is the positive sequence X/R ratio

References 

[1] IEEE Std C57.12.90, "IEEE Standard Test Code for Liquid-Immersed Distribution, Power and Regulating Transformers", 2010



[2] Tleis, N., "Power Systems Modelling and Fault Analysis - Theory and Practice", Newnes, 2008

Category: Transformers According to the ANSI/IEEE 946 Contents

[hide] 

1 Introduction



2 Voltage Considerations



3 Available Short-Circuit Current



4 Calculation Approach



5 Partial Fault Currents



o

5.1 Short-Circuit Current from Batteries

o

5.2 Short-Circuit Current from DC Motors/Generators

o

5.3 Short-Circuit Currents from Chargers

6 References

Introduction Scope of the IEEE 946-1992: This recommended practice provides guidance for the design of the DC auxiliary power systems for nuclear and non-nuclear power generating stations. The components of the DC auxiliary power system addressed by this recommended practice include lead-acid storage batteries, static battery chargers and distribution equipment. Guidance for selecting the quantity and types of equipment, the equipment ratings, interconnections, instrumentation, control and protection is also provided.

Figure 1. 125 VDC system key diagram This recommended practice is intended for nuclear and large fossil-fueled generating stations. Each recommendation may or may not be appropriate for other generating facilities; e.g.,

combustion turbines, hydro, wind turbines, etc. The AC power supply (to the chargers), the loads served by the DC systems, except as they influence the DC system design, and engine starting (cranking) battery systems are beyond the scope of this recommended practice. For more informations please refer to the standard itself IEEE 946-1992. Voltage Considerations The nominal voltages of 250, 125, 48, and 24 are generally utilized in station DC auxiliary power systems. The type, rating, cost, availability, and location of the connected equipment should be used to determine which nominal system voltage is appropriate for a specific application. 250 VDC systems are typically used to power motors for emergency pumps, large valve operators, and large inverters. 125 VDC systems are typically used for control power for nest relay logic circuits andthe closing and tripping of switchgear circuit breakers. 48 VDC or 24 VDC systems are typically used for specialized instrumentation.

Figure 2. Recommended voltage range of 125 V and 250 V DC (nominal) rated components (for designs in which the battery is equalized while connected to the load) Available Short-Circuit Current For the purpose of determining the maximum available short-circuit current (e.g., the required interrupting capacity for feeder breakers/fuses and withstand capability of the distribution buses

and disconnecting devices), the total short-circuit current is the sum of that delivered by the battery, charger, and motors (as applicable). When a more accurate value of maximum available short-circuit current is required, the analysis should for interconnecting cable resistance. Calculation Approach As defined in "Industrial power systems data book" [2], there are two calculation ways to acquire the fault current: 

1. Approximation Method: All the network is converted into the equivalent impedance (Req, Leq are used for the time constant) and the system voltage is being used for the fault current calculation:



2. Superposition Method: The fault current is calculated for each source individually, while other, not observed sources, are being shorted out (with their internal resistances). The voltage for each partial current is the rated voltage of the source. The total current is the sum of the partial currents. This approach shall be described in following articles.

Partial Fault Currents Short-Circuit Current from Batteries The current that a battery will deliver on short-circuit depends on the total resistance of the short-circuit path. A conservative approach in determining the short-circuit current that the battery will deliver at 25°C is to assume that the maximum available short-circuit current is 10 times the 1 minute ampere rating (to 1.75 V per cell). For more than 25°C the short-circuit current for the specific application should be calculated or actual test data should be obtained from the battery manufacturer. The battery nominal voltage should be used when calculating the maximum short-circuit current. Tests have shown that an increase in electrolyte temperature (above 25°C) or elevated battery terminal voltage (above nominal voltage) will have no appreciable effect on the magnitude of short-circuit current delivered by a battery. The internal battery resistance is calculated using:

Where EB is the battery rated voltage and I8hrs is the 8-hour battery capacity. The maximum (or peak) short-circuit current is:

RBBr is the sum of the battery internal resistance RB and the line resistance RBr up to the fault location. The initial maximum rate of rise of the current at t=0 s is as follows:

The time constant is calculated as:

The sustained short-circuit current is calculated using:

And the fault current from the battery for the time t:

Short-Circuit Current from DC Motors/Generators

Figure 3. Typical short-circuit characteristic of DC motor/generator DC motors, if operating, will contribute to the total fault current. The maximum current that a DC motor will deliver to a short-circuit at its terminals is limited by the effective transient armature resistance (r'd) of the motor. For DC motors of the type, speed, voltage, and size typically used in generating stations, rd is in the range of 0.1 to 0.15 per unit. Thus, the maximum fault current for a short-circuit at the motor terminals will typically range from 7 to 10 times the motor’s rated

armature current. Therefore, it is conservative to estimate the maximum current that a motor will contribute to a fault as 10 times the motor’s rated full load current. When a more accurate value is required, the short-circuit contribution should be calculated, using specific r d data for the specific motor, or actual test data should be obtained from the motor manufacturer. For additional accuracy, the calculation should for the resistance of the cables between the motor and the fault. A complete expression for the short-circuit current is:

Where: ia per-unit current, e0 is the internal emf prior short-circuit (p.u.), rd steady-state effective resistance of machine (p.u.), r'd transient effective resistance of machine (p.u.). The frequency is 60 Hz. Typically, for motors e0=0,97 p.u., and for generators e0=1,03 p.u. The machine electrical parameter are to be calculated in case when no additional data is known for observed machine. Normally, it is more practical to use the real machine data given by the manufacturer. The machine inductance is derived from the following equation:

Where P is the pole number, nn nominal speed, UM nominal voltage and IM nominal current. Cx depends on the machine type: Cx=0,4 is for motors without pole face windings, Cx=0,1 is for motors with pole face windings, Cx=0,6 is for generators without pole face windings, and Cx=0,2 is for generators with pole face windings. The base resistance of the machine is derived from:

Then the transient resistance in Ohms is derived from:

The peak short-circuit current in Amps:

Or in p.u.:

The initial rate of rise of the current is:

The first 2/3-time constant of rise is:

And the second 1/3-time constant of rise is:

The total time constant is:

The armature circuit decrement factor is:

The field circuit decrement factor is:

Short-Circuit Currents from Chargers The maximum current that a charger will deliver into a short-circuit, coincident with the maximum battery short-circuit current, is determined by the charger current-limit circuit. The current-limit setting is adjustable in most chargers and may vary from manufacturer to manufacturer. Thus, the maximum current that a charger will deliver on short circuit will not typically exceed 150% of the charger ampere rating.

Figure 4. Peak fault current factor as a function of system constants

The initial sustained short-circuit current (or quasi steady-state current) is given by:

The factor K2 is taken from the diagram of sustained fault current factor versus rectifier terminal voltage, zCis the commutating impedance per unit and IR is the rated rectifier current. The commutating impedance includes AC side impedance with transformer (R C and XC).If the commutating impedance is in per-unit value then it should be converted.

Figure 5. Sustained fault current vs rectifier terminal voltage Conversion of zC (p.u.) to ZC (Ohms): 

Case of double-way rectifier, equation is:



Case of double-wye rectifier:

The current Ida is used to determine equivalent rectifier resistance and inductance on the DC side, which are then given by:

Where Eda is the assumed voltage at the rectifier terminals during the fault and equals e0 (p.u.) x System Voltage (Volts). If the fault current is calculated using the superposition method, then the following relations are used:

When:

Then:

When:

Then:

The sustained value of the fault current is:

The rectifier terminal voltage is:

The rate of rise fault current is:

The peak current is given as:

Where the factor K1 is taken from the diagram and is in function of K3 and K4, which are calculated as follows, for the full-wave bridge connected rectifier:

Note: The value Eda = edaED should be within 10% of the calculated value Edc, the rectifier terminal voltage under sustained short-circuit current. The iterative process is repeated until the desired tolerance is achieved. 

K1 - peak fault current factor



K2 - sustained fault current factor



K3 - reactance constant (used to determine K1)



K4 - resistance constant (used to determine K1)



Index "RBr" refers to the combined resistance of the rectifier and the branch up to the fault location

References 1. IEEE 946-1992: IEEE Recommended Practice for the Design of DC Auxiliary Power Systems for Generating Stations For more informations please refer to the standard itselfIEEE 946-1992. 2. Industrial power systems data book, General Electric, 1956 At the Iowa Digital Library General Electric Industrial Power Systems Data Book. Related topics: Short Circuit Calculation according to the IEC 61660 Categories: Calculations | Protection According to the IEC 61660 Contents [hide] 

1 Introduction



2 Calculating the Total Short-Circuit Current



3 Partial Fault Currents



o

3.1 Fault Current from Batteries

o

3.2 Fault Current from Capacitors

o

3.3 Fault Current from Rectifiers

o

3.4 Fault Current from DC Machines

o

3.5 Correction Factors

4 References

Introduction

Figure 1. Equivalent circuit diagram for calculating the partial short-circuit currents The scope of IEC 61660 is to describe a method for calculating short-circuit currents in DC auxiliary systems in power plants and substations. Such systems can be equipped with the following equipment, acting as short-circuit current sources: 

rectifiers in three-phase AC bridge connection for 50 Hz;



stationary lead-acid batteries;



smoothing capacitors;



DC motors with independent excitation.

NOTE – Rectifiers in three-phase AC bridge connection for 60 Hz are under consideration. The data of other equipment may be given by the manufacturer. This standard is only concerned with rectifiers in three-phase AC bridge connection. It is not concerned with other types of rectifiers.

The purpose of the standard is to provide a generally applicable method of calculation which produces results of sufficient accuracy on the conservative side. Special methods, adjusted to particular circumstances, may be used if they give at least the same precision. Short-circuit currents, resistances and inductances may also be ascertained from system tests or measurements on model systems. In existing DC systems the necessary values can be ascertained from measurements taken at the assumed short-circuit location. The load current is not taken into consideration when calculating the short-circuit current. It is necessary to distinguish between two different values of short-circuit current: 

the maximum short-circuit current which determines the rating of the electrical equipment;



the minimum short-circuit current which can be taken as the basis for fuse and protection ratings and settings.

For more information please refer to the standard itself IEC 61660-1. Calculating the Total Short-Circuit Current Each DC source during the fault shall contribute to the total short-circuit current. The superposition principle is being applied. When one source is observed then the other ones are being disconnected and ignored. The potential DC sources are battery, rectifier, capacitor and machine. The partial short-circuit currents are calculated for each of those sources as follows: 

for 0

t

tp:

Where tp is the time to peak of the partial current and τ1 is the rise time constant for the partial current source. 

for tp

t

Tk:

Where Tk is the fault duration time and τ2 the decay time constant for the partial current source. And the total short-circuit current is the sum as follows:

for 0

t

Tk. And nDC is the number of the DC sources contributing the fault current, j is the

observed DC source. Partial Fault Currents

Fault Current from Batteries

Figure 2. Time to peak and rise time constant (Figure 10. IEC 61660:1997) The peak short-circuit current is calculated as:

The quasi steady-state short-circuit current is calculated as follows:

The decay component is calculated as:

The rise-time constant (τ1B) and time-to-peak of short-circuit currents of batteries is taken from the diagram (Figure 10. in IEC 61660:1997). The time constant of the battery T B is assumed to be 30 ms. The decay-time constant (τ2B) is assumed to 100 ms. RBBr is the sum of the battery internal resistance and the line (path) resistance up to the fault location (RBBr=0,9RB+RBr). LBBr is the sum of the battery internal inductance and the line (path) inductance up to the fault location. 

Rise-time current , for 0 ≤ t ≤ tpB:



Decay-time current, for tpB ≤ t ≤ Tk:

And the total current from the battery is:

Fault Current from Capacitors

Figure 3. Factor k1C to determine rise-time constant (Figure 14. IEC 61660:1997)

Figure 4. Factor k2C to determine decay-time constant (Figure 15. IEC 61660:1997) The peak short-circuit current is calculated using:

Where EC is the voltage of the capacitor terminal before the fault, and RCBr is the sum of capacitor and branch resistance, up to the fault location. The factor κC depends on the eigen-frequency ω0 and the decay coefficient δ, as follows:

LCBr is the inductance of the capacitor and common branch up to the fault location. 

a) If δ > ω0:



b) If δ < ω0:



c) If δ = ω0:

Where the time-to-peak is tpC. And the rise-time constant is:

And the decay-time constant is:

And coefficients k1C and k2C are taken from the diagrams/tables (defined in Figure 14. IEC 61660). The quasi steady-state current of the capacitor is considered to be 0. 

Rise-time current , for 0 ≤ t ≤ tpC:



Decay-time current, for tpC ≤ t ≤ Tk:

And the total current from the battery is:

Fault Current from Rectifiers The quasi steady-state short-circuit current IkD of a rectifier in three-phase AC bridge connection is:

Where Un is the nominal system voltage on AC side of rectifier, ZN is the network impedance AC side, UnTLV and UnTHV are transformer rated voltages of low and high voltage side, respectively. The factor λD is calculated using:

The peak short-circuit current is calculated using:

And the factor κD and

is calculated using:

The time-to-peak is calculated for all values κD ≥1,05 as follows:



for

it is



for

it is

The rise-time constant for rectifiers is: 

For κD >= 1.05 :



For κD < 1.05 :

The suitable approximation is given as:

The decay-time constant is calculated using:

(ms)

(ms)

Fault Current from DC Machines The quasi steady-state short-circuit current is calculated using:

Where LF is the field inductance and LOF is the unsaturated field inductance at no-load. This equation is valid only if the motor speed remains constant during the duration of the short-circuit fault. Otherwise IkM = 0.

Figure 5. Factor κM for determining the peak shortcircuit current ipM (Figure 17. IEC 61660:1997)

Figure 6. Factors for determining tpM, τ1M for nominal and decreasing speed (Figure 18. IEC 61660:1997)

The armature time constant is calculated as:

The time constant of the field circuit is calculated as:

And the mechanical time constant is calculated as:

Figure 7. tpM for decresing speed (Figure 19. IEC 61660:1997)

The eigen frequency is calculated as:

The decay coefficient is calculated from:

The peak short-circuit current:

The factors k1M, k2M, k3M and k4M are taken from the diagrams (Figure 18, 20, 21 in IEC 61660). The factor κM is taken from the diagram (Figure 17 in IEC 61660).

Figure 8. Factor k3M for determining the risetime constant t1M for decreasing speed (Figure 20. IEC 61660:1997) The time-to-peak in case when τMec≥10τF:

Figure 9. Factor k4M for determining the decaytime constant t2M for decreasing speed (Figure 21. IEC 61660:1997)



And the rise-time constant:



The decay-time constant:

τ2M = τF when n=nn=const. τ2M = (k4M)(τMec)(LOF/LF) when n→0 In case when τMec<10τF then the time-to-peak is taken from the diagram/table (Figure 19. IEC 61660).

The rise-time constant and the decay-time constant τ1M and τ2M are calculated using:



Rise-time current , for 0 ≤ t ≤ tpM:

Where tp is the time to peak of the partial current and τ1 is the rise time constant for the observed voltage source. 

Decay-time current, for tpM ≤ t ≤ Tk:



And the total current from the DC machine is:

Correction Factors

Corrected resistance for the each source Due to the fact that all non-observed sources at the time are neglected along with their branches it is suggested to use correction factors, which are supposed to improve total results. Each calculated correction factor is multiplied with the partial fault current of the each source, as follows:

Where Ij is the initial partial fault current and σj is the correction factor, both for the source "j".

Y refers to the branch (Br). References IEC 61660: Short-circuit currents in d.c. auxiliary installations in power plants and substations Part 1: Calculation of short-circuit currents. For more information please refer to the standard itself IEC 61660-1. Related topics: 

Short Circuit Calculation



according to the ANSI/IEEE 946

Categories: Calculations | Protection

Arc Fault

Contents [hide] 

1 Arc Flash History



2 Arc Flash Definitions



3 Arc Flash Mitigation in Switchgear



4 Arc Flash PPE



5 Arc Flash Calculation according to the IEEE Std. 1584-2002 o

5.1 Determining the arc current

o

5.2 Determine the incident energy

o

5.3 Determine the flash boundary

o

5.4 Other calculation approaches for the incident energy



6 NPFA-70E-2004 Application



7 Methods for reducing arc flash hazards o

7.1 Arc Flash Detection Principles

o

7.2 Responses to Arc Flash Faults



8 Arc Flash Calculator



9 References

Arc Flash History First official publication on the arc flash hazard was published by Ralph Lee published in "The Other Electrical Hazard, Electric Arc Blast Burns", 1982. In this paper the thermal event associated with an electric arc and its effects on the human body was analysed and described. Value of the 1.2 cal/cm2 was defined as the "curable burn level" (defined as the lower limit for a 3rd degree burn) that is still used today, also some calculations to determine the curable burn distance for an electric arc in air. In 1987 Ralph Lee published another paper, "Pressures Developed from Arcs", where the sound and pressure effects of an arc in air were described. Included in this paper were charts to determine the pressure wave forces at various distances based on the fault duties at the location. Two more papers were published that further defined the energies in arcing faults. The first was the paper "Testing Update on Protective Clothing and Equipment for Electric Arc Exposure", 1997, by Bingham, Doughty, and Neal. In that paper the authors used empirical test data to determine the incident energy at various distances from a low voltage arcing fault. They were the first to express the directional effect of an arc within an enclosure. In 2000, Doughty, Floyd, and Neal published "Predicting Incident Energy to Better Manage the Electric Arc Hazard on 600 V Power Distribution Systems", which defined incident energy based on fault duty, working distance and clearing time for arcs in air or in an enclosure.

This work was used in the NFPA-70E Standard for Electrical Safety Requirements for Employee Workplaces, 2000 Edition, for use in developing safe work practices with regard to arc flash hazards, but was limited to low voltage applications. It also represented the basis for further research that resulted in the publication of the IEEE Std. 1584-2002, "IEEE Guide for Performing Arc-Flash Hazard Calculations". Arc Flash Definitions An arc fault is an electrical discharge between two or more conductors, where the insulating atmosphere (air or gas) has been broken down by the electric field between the conductors. Whenever there is an arc fault, the gases and vapours that make up the atmosphere between the conductors become ionised. The magnitude of an arc fault is highly variable. The instantaneous arc fault current may be high, approaching the bolted short circuit current, or reasonably low, comparable to the load current. An arc will continue until it becomes unstable and extinguishes itself or until it is interrupted by a protection device (i.e. fuse or circuit breaker).

Figure 1. Arc fault explosion on a 480 V switchboard with 23 kA upstream fault capacity Arc faults are characterised by extreme temperatures that can cause severe burns depending on the distance of the operator to the arc. Neal et al [1] in Table IV determined that a 600 V, 40 kA arc fault with a duration of 0.5 s has enough energy to cause second-degree burns at a distance of 77 inches (1.96 m).

Additionally, arc faults tend to melt terminals that can potentially shower the immediate vicinity with molten metal. The extreme temperatures produced by an arc fault can also lead to fires, causing major damage to equipment.

Figure 2. Damage caused by arc faults Annex C of IEEE Std 1584 [2] outlines case histories of real life arc fault incidents. The majority of incidents occurred during energisation and switching operations or live electrical installation work. The potential causes of arc faults include contamination / pollution ingress, equipment failure, rodents / vermin and accidental with tools.

Common definitions: Incident Energy Exposure:the amount of thermal incident energy to which the worker's face and chest could be exposed at working distance during an electrical arc event. Incident energy is measured in joules per centimeter squared (J/cm2) or calories per centimeter squared (cal/cm2). Flash Protection Boundary: the flash protection boundary is an approach limit at a distance from exposed live parts or enclosed live parts if operation, manipulation, or testing of equipment creates a potential flash hazard, within which a person could receive a second degree burn if an electrical arc flash were to occur. Incident Energy at Flash Protection Boundary: the arc flash protection boundary (FPB) distance for the specific incident energy, usually provided from the manufactures for the corresponding personal protection equipment (PPE). Hazard Risk Category: this is the minimum level of the personal protective equipment (PPE) in cal/cm2, as evaluated in the IEEE Standard 1584, with the intent to protect the worker from the thermal effects of the arc flash at 45 cm or 18 inches from the source of the arc. Grounding Type: according to the IEEE 1584 procedure two grounding classes are applied: a) ungrounded, which included ungrounded, high-resistance grounding and low-resistance grounding, and b) solidly grounded. Gap between Conductors: equipment bus gap in mm. Gaps of 3 to 40 mm were used for low voltage testing to simulate gaps between conductors in low voltage equipment and cables. Gaps 13, 104 and 152 mm. were used in 5 and 15 kV equipment testings. For cases where gap is outside the range of the standard empirically derived model, the theoretically derived Lee method can be applied. Working Distance: typical working distance is the sum of the distance between the worker standing in front of the equipment, and from the front of the equipment to the potential arc source inside the equipment. Arc-fash protection is always based on the incident energy level on the person's face and body at the working distance, not the incident energy on the hands or arms. The degree of injury in a burn depends on the percentage of a person's skin that is burned. The head and body are a large percentage of total skin surface area and injury to these areas is much more life threatening than burns on the extremities (see Fig.3).

Figure 3. Arc flash zones For the Figure 3. following definitions can be applied: Flash Protection Boundary: An approach limit at a distance from exposed live parts within which a person could receive a second degree burn if an electric arc flash were to occur. Appropriate flash-flame protection equipment must be utilized for persons entering the flash protection region. Limited Approach Boundary: An approach limit at distance from an exposed live part within which a shock hazard exists. A person crossing the limited approach boundary and entering the limited region must be qualified to perform the job/task. Restricted Approach Boundary: An approach limit at a distance from an exposed live part within which there is an increase risk of shock, due to electrical arc over combined with inadvertent movement, for personnel working in close proximity to the live part. The person crossing the restricted approach boundary and entering the restricted space must have a documented work plan approved by authorized management, use PPE that is appropriate for the working being performed and is rated for voltage and energy level involved. Prohibited Approach Boundary: An approach limit at a distance from and exposed live part within which work is considered the same as making with the live part. The person entering the prohibited space must have specified training to work on energized conductors or live parts. Any tools used in the prohibited space must be rated for direct at the voltage and energy level involved. Arc Flash Mitigation in Switchgear

Annex ZC6 of AS 3439.1 [3] provides guidelines for the minimisation, detection and containment of internal arc faults in switchgear. These are summarised below: 

Insulation of live conductors (in addition to clearances in air)



Arrangement of busbars and functional units in separate vented compartments, for more rapid extinguishing of the arc and to contain an arc fault in a single compartment



Use of protection devices to limit magnitude and duration of arcing current



Use of devices sensitive to energy radiated from an arc to initiate protection and interrupt arcing current



Use of earth current detection devices for interruption of arc faults to earth



Combinations of the above

It should be noted that uncontained arc faults can spread to other parts of the switchboard and develop into larger faults (e.g. functional unit arc fault spreading to busbars). Arc Flash PPE

Figure 4. Typical arc flash suit As a general guideline, Neal et al [1] recommends the following personal protection equipment to safeguard against arc faults: 

Clothing consisting of outer layer(s) of loose fitting flame-resistant fabric without openings and inner layers of non-meltable fibres



Switchman’s hood or faceshield with 0.08 inch thick polycarbonate viewing window



Heavy duty flame-resistant work gloves



Heavy duty work boots

Annex C of IEEE Std 1584 [2] illustrates a case study (No. 42) of a 2.3 kV switching operation that ultimately ended in an arc fault. The operator was wearing a full arc flash suit, safety glasses and fire resistant shirt and pants. The PPE prevented any burn injuries from the arc flash. Other case studies where the operators were not wearing appropriate PPE resulted in severe burns or death. Arc flash PPE is normally rated to an Arc Thermal Performance exposure Value (ATPV), which specifies the maximum incident arc fault energy that can protect the wearer (measured in calories per cm2). By way of example, the results of an arc flash hazard calculation based on IEEE Std 1584 follows to determine the appropriate ATPV rating of PPE. The prospective fault current used was 25 kA. A fault clearing time of 0.5 s was chosen, which is suitably onerous for a worst-case incident. The calculation concluded that to protect against injury from an arc fault of this magnitude, PPE with an ATPV rating of over 50 cal/cm2). is required. The ATPV rating is typically quoted on commonly available arc flash PPE. Typical arc fault PPE is available from vendors such as Oberon. Arc Flash Calculation according to the IEEE Std. 1584-2002 IEEE Std 1584-2002 contains calculation methods developed through testing by several sources to determine boundary distances for unprotected personnel and the incident energy at the working distance for qualified personnel working on energized equipment. The incident energy level can be used to determine the proper PPE required for personnel. The equations developed in the IEEE standard assess the arc flash hazard based on the available (bolted) fault current, voltage, clearing time, equipment type, grounding, and working distance. The working voltage is also used to determine other variables. The equations have other variables that for grounding, equipment type, and construction. This method can also determine the impact of certain current limiting low voltage fuses as well as certain types of low voltage breakers. It is an improvement over the previous work in that the calculations can be applied over a large range of voltages. The many variables of this method make it the preferred choice for Arc-Flash evaluations, but at the same time requires either a complex spreadsheet or computer program to be used efficiently. Determining the arc current For applications under 1 kV:

For applications above 1 kV:

And getting the value from the log10:

where: Ia - the arc fault current (kA), K - for the open configurations (-0.153), for the closed/boxed configurations (-0.097), If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage, dG - the gap between conductors (mm). The second arc current (I2a) is equal to 85% of the first current, or:

Determine the incident energy When the arc current is known the incident energy could be calculated. But first the incident energy normalized for the time and distance is calculated:

Now the incident energy can be calculated as follows, for the systems where the voltage does not exceed 15 kV:

And for the location where the voltage exceeds 15 kV the Lee method is used:

Where: En - the incident energy normalized for time and distance (cal/cm 2), K1 - for the open configurations (-0.792), for the closed/boxed configurations (-0.555), K2 - for the ungrounded or high resistance grounded systems (0), for grounded systems (0.113), dG - the gap between conductors (mm), E - the incident energy (cal/cm2), Cf - the voltage factor (1.0 for Usys > 1 kV, 1.5 for Usys <= 1 kV), t - the arc duration time (s), D - the distance from the possible arc location to the person (mm), x - the distance factor (check table below), If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage. The arc duration time is the clearing time for the source-side protecting device that clears the fault first. System voltage (kV)

Equipment type

Typical gap between conductors (mm)

Distance factor, x

Open air

10-40

2.0

Switchgear

32

1.473

MCC and s

25

1.641

Cable

13

2.0

Open air

10-40

2.0

Switchgear

13 - 102

0.973

Cable

13

2.0

Open air

10-40

2.0

Switchgear

153

0.973

Cable

13

2.0

0.208 - 1.0

> 1.0 - 5.0

> 5.0 - 15.0

Determine the flash boundary The flash boundary is the distance from an arcing fault where the incident energy is equal to 1.2 cal/cm2. For the IEEE Std. 1584 empirically derived model equation is:

For the Lee method:

Where: DB - the distance of the boundary from arcing point (mm), En - the incident energy (cal/cm2) normalized for time and distance, Cf - the voltage factor (1.0 for Usys > 1 kV, 1.5 for Usys <= 1 kV), t - the arc duration time (s), EB - the incident energy in cal/cm2 at the boundary distance, x - the distance factor (check table above),

If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage. Other calculation approaches for the incident energy In 2000, Doughty, Floyd, and Neal published "Predicting Incident Energy to Better Manage the Electric Arc Hazard on 600 V Power Distribution Systems", which defined incident energy based on fault duty, working distance and clearing time for arcs in air or in an enclosure. For open installations:

And for closed/boxed installations:

Where: EMA - incident energy for an arc in open air (cal/cm2), EMB - incident energy for an arc in a box (size 50 cm or 20 inches maximum)(cal/cm 2), DA,DB - distance from the arc, If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), tA - the arc duration time (s). NPFA-70E-2004 Application In April 2004., the NFPA released an update to NFPA-70E that adopted the IEEE Std. 1584-2002 methods for determining the incident energy. The standard was renamed to NFPA 70E Standard for Employee Safety in the Workplace 2004 Edition. It is different from IEEE Std. 1584 with regard to arc flash in that it is used to determine the appropriate PPE based on the incident energy calculated. PPE is rated by the Arc Thermal Performance Value (ATPV) with units in cal/cm2. The required PPE is determined by comparing the calculated incident energy to the ratings for specific combinations of PPE. An example is given in NPFA 70E as follows in table below: Hazard/Risk Category

0

Typical Protective Clothing Systems

Non-melting, flammable materials (natural or treated materials with at least 4.5 z/yd2)

Required Minimum Arc Rating of PPE (cal/cm2)

N/A (1.2)

1

FR pants and FR shirt, or FR coverall

4

2

Cotton Underwear, plus FR shirt and FR pants

8

3

Cotton Underwear, plus FR shirt and FR pants

25

and FR coverall

4

Cotton Underwear, plus FR shirt and FR pants and multiple layer flash suit

40

Where FR refers to the flame resistant or flame retardant.

Figure 5. Typical arc flash warning label This example should NOT be used for final calculations. For actual applications, the calculated incident energy must be compared to specific PPE combinations used at the facility being evaluated. The exception to this is the upper limit of 40 cal/cm2. While PPE is available in ATPV values of 100 cal/cm2 or more, values above 40 are considered prohibited due to the sound, pressure and concussive forces present. Above this level these forces are more significant than the thermal values. Methods for reducing arc flash hazards Reducing the Arcing Current: certain protective devices are current limiting in design. By limiting the current available for a fault there is a corresponding reduction in the incident energy for clearing times that are short in duration (1-3 cycles). Fault duties at these devices must be in the current limiting range for them to be effective (typically at least 10-15 times the device rating). Increasing the Working Distance: since the incident energy is proportional to the square of the distance (in open air), increasing the working distance will significantly reduce the incident energy. Working distance can be increased by using remote racking devices, remote operating devices, and extension tools (i.e. hotsticks). Reducing the Clearing Time: traditional methods to reduce clearing times include: lowered device settings (permanently or temporarily), bus differential protection, and zone selective interlocking (typically low voltage only). It should be noted that the calculations assume that the protective devices are set in accordance with the study, and that the devices operate properly. Arc Flash Detection Principles

An arc flash fault typically results in an enormous and nearly instantaneous increase in light intensity in the vicinity of the fault. Light intensity levels often rise to several thousand times normal ambient lighting levels. For this reason most, if not all, arc flash detecting relays rely on optical sensor(s) to detect this rapid increase in light intensity. For security reasons, the optical sensing logic is typically further supervised by instantaneous over-current elements (ANSI device 50) operating as a fault detector. Arc flash detection relays are capable of issuing a trip signal in as little as 2.5 ms after initiation of the arcing fault. Arc flash relaying compliments existing conventional relaying. The arc flash detection relay requires a rapid increase in light intensity to operate and is designed with the single purpose of detecting very dangerous explosive-like conditions resulting from an arc flash fault. It operates independently and does not need to be coordinated with existing relaying schemes. Responses to Arc Flash Faults Once the arc flash fault has been detected, there are at least two design options. One option involves directly tripping the upstream bus breaker(s). Since the arc flash detection time is so short, overall clearing time is essentially reduced to the operating time of the upstream breaker. A second option involves creating an intentional three-phase bus fault by energizing a high-speed grounding switch. This approach shunts the arcing energy through the high-speed grounding switch and both faults are then cleared by conventional upstream bus protection. Because the grounding switch typically closes faster than the upstream breaker opens, this approach will result in lower incident energy levels than the first approach. However, it also introduces a second three-phase bolted fault on the system and it requires that a separate high-speed grounding switch be installed and operational. Assuming there is space available for the addition of the grounding switch, there is a significantly higher cost of implementation involved compared to the first approach, and so may not be a practical alternative, especially for existing switchgear lineups. Arc Flash Calculator Also, we have provided a free arc flash calculator for android based smartphones Arc Flash Calculator References 1. Neal, T., Bingham, A., Doughty, R.L, “Protective Clothing for Electric Arc Exposure”, IEEE, July / Aug 1997 2. IEEE Std 1584, “Arc Flash Hazard Calculations”, 2002 3. AS 3439.1, “Low-voltage switchgear and control gear assemblies – Part 1: Type-tested and partially type tested assemblies”, 2002 4. "Arc flash hazard analysis and mitigation", 2004, Christopher Inshaw, Robert A. Wilson 5. Arc advisor data Category: Protection

Arc Fault

(Redirected from Arc Flash) Contents [hide] 

1 Arc Flash History



2 Arc Flash Definitions



3 Arc Flash Mitigation in Switchgear



4 Arc Flash PPE



5 Arc Flash Calculation according to the IEEE Std. 1584-2002 o

5.1 Determining the arc current

o

5.2 Determine the incident energy

o

5.3 Determine the flash boundary

o

5.4 Other calculation approaches for the incident energy



6 NPFA-70E-2004 Application



7 Methods for reducing arc flash hazards o

7.1 Arc Flash Detection Principles

o

7.2 Responses to Arc Flash Faults



8 Arc Flash Calculator



9 References

Arc Flash History First official publication on the arc flash hazard was published by Ralph Lee published in "The Other Electrical Hazard, Electric Arc Blast Burns", 1982. In this paper the thermal event associated with an electric arc and its effects on the human body was analysed and described. Value of the 1.2 cal/cm2 was defined as the "curable burn level" (defined as the lower limit for a 3rd degree burn) that is still used today, also some calculations to determine the curable burn distance for an electric arc in air. In 1987 Ralph Lee published another paper, "Pressures Developed from Arcs", where the sound and pressure effects of an arc in air were described. Included in this paper were charts to determine the pressure wave forces at various distances based on the fault duties at the location. Two more papers were published that further defined the energies in arcing faults. The first was the paper "Testing Update on Protective Clothing and Equipment for Electric Arc Exposure", 1997, by Bingham, Doughty, and Neal. In that paper the authors used empirical test data to determine the incident energy at various distances from a low voltage arcing fault. They were the first to express the directional effect of an arc within an enclosure. In 2000, Doughty, Floyd, and Neal published "Predicting Incident Energy to Better Manage the Electric Arc Hazard on 600 V Power

Distribution Systems", which defined incident energy based on fault duty, working distance and clearing time for arcs in air or in an enclosure. This work was used in the NFPA-70E Standard for Electrical Safety Requirements for Employee Workplaces, 2000 Edition, for use in developing safe work practices with regard to arc flash hazards, but was limited to low voltage applications. It also represented the basis for further research that resulted in the publication of the IEEE Std. 1584-2002, "IEEE Guide for Performing Arc-Flash Hazard Calculations". Arc Flash Definitions An arc fault is an electrical discharge between two or more conductors, where the insulating atmosphere (air or gas) has been broken down by the electric field between the conductors. Whenever there is an arc fault, the gases and vapours that make up the atmosphere between the conductors become ionised. The magnitude of an arc fault is highly variable. The instantaneous arc fault current may be high, approaching the bolted short circuit current, or reasonably low, comparable to the load current. An arc will continue until it becomes unstable and extinguishes itself or until it is interrupted by a protection device (i.e. fuse or circuit breaker).

Figure 1. Arc fault explosion on a 480 V switchboard with 23 kA upstream fault capacity Arc faults are characterised by extreme temperatures that can cause severe burns depending on the distance of the operator to the arc. Neal et al [1] in Table IV determined that a 600 V, 40 kA

arc fault with a duration of 0.5 s has enough energy to cause second-degree burns at a distance of 77 inches (1.96 m). Additionally, arc faults tend to melt terminals that can potentially shower the immediate vicinity with molten metal. The extreme temperatures produced by an arc fault can also lead to fires, causing major damage to equipment.

Figure 2. Damage caused by arc faults Annex C of IEEE Std 1584 [2] outlines case histories of real life arc fault incidents. The majority of incidents occurred during energisation and switching operations or live electrical installation

work. The potential causes of arc faults include contamination / pollution ingress, equipment failure, rodents / vermin and accidental with tools. Common definitions: Incident Energy Exposure:the amount of thermal incident energy to which the worker's face and chest could be exposed at working distance during an electrical arc event. Incident energy is measured in joules per centimeter squared (J/cm2) or calories per centimeter squared (cal/cm2). Flash Protection Boundary: the flash protection boundary is an approach limit at a distance from exposed live parts or enclosed live parts if operation, manipulation, or testing of equipment creates a potential flash hazard, within which a person could receive a second degree burn if an electrical arc flash were to occur. Incident Energy at Flash Protection Boundary: the arc flash protection boundary (FPB) distance for the specific incident energy, usually provided from the manufactures for the corresponding personal protection equipment (PPE). Hazard Risk Category: this is the minimum level of the personal protective equipment (PPE) in cal/cm2, as evaluated in the IEEE Standard 1584, with the intent to protect the worker from the thermal effects of the arc flash at 45 cm or 18 inches from the source of the arc. Grounding Type: according to the IEEE 1584 procedure two grounding classes are applied: a) ungrounded, which included ungrounded, high-resistance grounding and low-resistance grounding, and b) solidly grounded. Gap between Conductors: equipment bus gap in mm. Gaps of 3 to 40 mm were used for low voltage testing to simulate gaps between conductors in low voltage equipment and cables. Gaps 13, 104 and 152 mm. were used in 5 and 15 kV equipment testings. For cases where gap is outside the range of the standard empirically derived model, the theoretically derived Lee method can be applied. Working Distance: typical working distance is the sum of the distance between the worker standing in front of the equipment, and from the front of the equipment to the potential arc source inside the equipment. Arc-fash protection is always based on the incident energy level on the person's face and body at the working distance, not the incident energy on the hands or arms. The degree of injury in a burn depends on the percentage of a person's skin that is burned. The head and body are a large percentage of total skin surface area and injury to these areas is much more life threatening than burns on the extremities (see Fig.3).

Figure 3. Arc flash zones For the Figure 3. following definitions can be applied: Flash Protection Boundary: An approach limit at a distance from exposed live parts within which a person could receive a second degree burn if an electric arc flash were to occur. Appropriate flash-flame protection equipment must be utilized for persons entering the flash protection region. Limited Approach Boundary: An approach limit at distance from an exposed live part within which a shock hazard exists. A person crossing the limited approach boundary and entering the limited region must be qualified to perform the job/task. Restricted Approach Boundary: An approach limit at a distance from an exposed live part within which there is an increase risk of shock, due to electrical arc over combined with inadvertent movement, for personnel working in close proximity to the live part. The person crossing the restricted approach boundary and entering the restricted space must have a documented work plan approved by authorized management, use PPE that is appropriate for the working being performed and is rated for voltage and energy level involved. Prohibited Approach Boundary: An approach limit at a distance from and exposed live part within which work is considered the same as making with the live part. The person entering the prohibited space must have specified training to work on energized conductors or live parts. Any tools used in the prohibited space must be rated for direct at the voltage and energy level involved. Arc Flash Mitigation in Switchgear

Annex ZC6 of AS 3439.1 [3] provides guidelines for the minimisation, detection and containment of internal arc faults in switchgear. These are summarised below: 

Insulation of live conductors (in addition to clearances in air)



Arrangement of busbars and functional units in separate vented compartments, for more rapid extinguishing of the arc and to contain an arc fault in a single compartment



Use of protection devices to limit magnitude and duration of arcing current



Use of devices sensitive to energy radiated from an arc to initiate protection and interrupt arcing current



Use of earth current detection devices for interruption of arc faults to earth



Combinations of the above

It should be noted that uncontained arc faults can spread to other parts of the switchboard and develop into larger faults (e.g. functional unit arc fault spreading to busbars). Arc Flash PPE

Figure 4. Typical arc flash suit As a general guideline, Neal et al [1] recommends the following personal protection equipment to safeguard against arc faults: 

Clothing consisting of outer layer(s) of loose fitting flame-resistant fabric without openings and inner layers of non-meltable fibres



Switchman’s hood or faceshield with 0.08 inch thick polycarbonate viewing window



Heavy duty flame-resistant work gloves



Heavy duty work boots

Annex C of IEEE Std 1584 [2] illustrates a case study (No. 42) of a 2.3 kV switching operation that ultimately ended in an arc fault. The operator was wearing a full arc flash suit, safety glasses and fire resistant shirt and pants. The PPE prevented any burn injuries from the arc flash. Other case studies where the operators were not wearing appropriate PPE resulted in severe burns or death. Arc flash PPE is normally rated to an Arc Thermal Performance exposure Value (ATPV), which specifies the maximum incident arc fault energy that can protect the wearer (measured in calories per cm2). By way of example, the results of an arc flash hazard calculation based on IEEE Std 1584 follows to determine the appropriate ATPV rating of PPE. The prospective fault current used was 25 kA. A fault clearing time of 0.5 s was chosen, which is suitably onerous for a worst-case incident. The calculation concluded that to protect against injury from an arc fault of this magnitude, PPE with an ATPV rating of over 50 cal/cm2). is required. The ATPV rating is typically quoted on commonly available arc flash PPE. Typical arc fault PPE is available from vendors such as Oberon. Arc Flash Calculation according to the IEEE Std. 1584-2002 IEEE Std 1584-2002 contains calculation methods developed through testing by several sources to determine boundary distances for unprotected personnel and the incident energy at the working distance for qualified personnel working on energized equipment. The incident energy level can be used to determine the proper PPE required for personnel. The equations developed in the IEEE standard assess the arc flash hazard based on the available (bolted) fault current, voltage, clearing time, equipment type, grounding, and working distance. The working voltage is also used to determine other variables. The equations have other variables that for grounding, equipment type, and construction. This method can also determine the impact of certain current limiting low voltage fuses as well as certain types of low voltage breakers. It is an improvement over the previous work in that the calculations can be applied over a large range of voltages. The many variables of this method make it the preferred choice for Arc-Flash evaluations, but at the same time requires either a complex spreadsheet or computer program to be used efficiently. Determining the arc current For applications under 1 kV:

For applications above 1 kV:

And getting the value from the log10:

where: Ia - the arc fault current (kA), K - for the open configurations (-0.153), for the closed/boxed configurations (-0.097), If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage, dG - the gap between conductors (mm). The second arc current (I2a) is equal to 85% of the first current, or:

Determine the incident energy When the arc current is known the incident energy could be calculated. But first the incident energy normalized for the time and distance is calculated:

Now the incident energy can be calculated as follows, for the systems where the voltage does not exceed 15 kV:

And for the location where the voltage exceeds 15 kV the Lee method is used:

Where: En - the incident energy normalized for time and distance (cal/cm 2), K1 - for the open configurations (-0.792), for the closed/boxed configurations (-0.555), K2 - for the ungrounded or high resistance grounded systems (0), for grounded systems (0.113), dG - the gap between conductors (mm), E - the incident energy (cal/cm2), Cf - the voltage factor (1.0 for Usys > 1 kV, 1.5 for Usys <= 1 kV), t - the arc duration time (s), D - the distance from the possible arc location to the person (mm), x - the distance factor (check table below), If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage. The arc duration time is the clearing time for the source-side protecting device that clears the fault first. System voltage (kV)

Equipment type

Typical gap between conductors (mm)

Distance factor, x

Open air

10-40

2.0

Switchgear

32

1.473

MCC and s

25

1.641

Cable

13

2.0

Open air

10-40

2.0

Switchgear

13 - 102

0.973

Cable

13

2.0

Open air

10-40

2.0

Switchgear

153

0.973

Cable

13

2.0

0.208 - 1.0

> 1.0 - 5.0

> 5.0 - 15.0

Determine the flash boundary The flash boundary is the distance from an arcing fault where the incident energy is equal to 1.2 cal/cm2. For the IEEE Std. 1584 empirically derived model equation is:

For the Lee method:

Where: DB - the distance of the boundary from arcing point (mm), En - the incident energy (cal/cm2) normalized for time and distance, Cf - the voltage factor (1.0 for Usys > 1 kV, 1.5 for Usys <= 1 kV), t - the arc duration time (s), EB - the incident energy in cal/cm2 at the boundary distance, x - the distance factor (check table above),

If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), Usys - the system voltage. Other calculation approaches for the incident energy In 2000, Doughty, Floyd, and Neal published "Predicting Incident Energy to Better Manage the Electric Arc Hazard on 600 V Power Distribution Systems", which defined incident energy based on fault duty, working distance and clearing time for arcs in air or in an enclosure. For open installations:

And for closed/boxed installations:

Where: EMA - incident energy for an arc in open air (cal/cm2), EMB - incident energy for an arc in a box (size 50 cm or 20 inches maximum)(cal/cm 2), DA,DB - distance from the arc, If - is the bolted fault current for three-phase faults (symmetrical RMS)(kA), tA - the arc duration time (s). NPFA-70E-2004 Application In April 2004., the NFPA released an update to NFPA-70E that adopted the IEEE Std. 1584-2002 methods for determining the incident energy. The standard was renamed to NFPA 70E Standard for Employee Safety in the Workplace 2004 Edition. It is different from IEEE Std. 1584 with regard to arc flash in that it is used to determine the appropriate PPE based on the incident energy calculated. PPE is rated by the Arc Thermal Performance Value (ATPV) with units in cal/cm2. The required PPE is determined by comparing the calculated incident energy to the ratings for specific combinations of PPE. An example is given in NPFA 70E as follows in table below: Hazard/Risk Category

0

Typical Protective Clothing Systems

Non-melting, flammable materials (natural or treated materials with at least 4.5 z/yd2)

Required Minimum Arc Rating of PPE (cal/cm2)

N/A (1.2)

1

FR pants and FR shirt, or FR coverall

4

2

Cotton Underwear, plus FR shirt and FR pants

8

3

Cotton Underwear, plus FR shirt and FR pants

25

and FR coverall

4

Cotton Underwear, plus FR shirt and FR pants and multiple layer flash suit

40

Where FR refers to the flame resistant or flame retardant.

Figure 5. Typical arc flash warning label This example should NOT be used for final calculations. For actual applications, the calculated incident energy must be compared to specific PPE combinations used at the facility being evaluated. The exception to this is the upper limit of 40 cal/cm2. While PPE is available in ATPV values of 100 cal/cm2 or more, values above 40 are considered prohibited due to the sound, pressure and concussive forces present. Above this level these forces are more significant than the thermal values. Methods for reducing arc flash hazards Reducing the Arcing Current: certain protective devices are current limiting in design. By limiting the current available for a fault there is a corresponding reduction in the incident energy for clearing times that are short in duration (1-3 cycles). Fault duties at these devices must be in the current limiting range for them to be effective (typically at least 10-15 times the device rating). Increasing the Working Distance: since the incident energy is proportional to the square of the distance (in open air), increasing the working distance will significantly reduce the incident energy. Working distance can be increased by using remote racking devices, remote operating devices, and extension tools (i.e. hotsticks). Reducing the Clearing Time: traditional methods to reduce clearing times include: lowered device settings (permanently or temporarily), bus differential protection, and zone selective interlocking (typically low voltage only). It should be noted that the calculations assume that the protective devices are set in accordance with the study, and that the devices operate properly. Arc Flash Detection Principles

An arc flash fault typically results in an enormous and nearly instantaneous increase in light intensity in the vicinity of the fault. Light intensity levels often rise to several thousand times normal ambient lighting levels. For this reason most, if not all, arc flash detecting relays rely on optical sensor(s) to detect this rapid increase in light intensity. For security reasons, the optical sensing logic is typically further supervised by instantaneous over-current elements (ANSI device 50) operating as a fault detector. Arc flash detection relays are capable of issuing a trip signal in as little as 2.5 ms after initiation of the arcing fault. Arc flash relaying compliments existing conventional relaying. The arc flash detection relay requires a rapid increase in light intensity to operate and is designed with the single purpose of detecting very dangerous explosive-like conditions resulting from an arc flash fault. It operates independently and does not need to be coordinated with existing relaying schemes. Responses to Arc Flash Faults Once the arc flash fault has been detected, there are at least two design options. One option involves directly tripping the upstream bus breaker(s). Since the arc flash detection time is so short, overall clearing time is essentially reduced to the operating time of the upstream breaker. A second option involves creating an intentional three-phase bus fault by energizing a high-speed grounding switch. This approach shunts the arcing energy through the high-speed grounding switch and both faults are then cleared by conventional upstream bus protection. Because the grounding switch typically closes faster than the upstream breaker opens, this approach will result in lower incident energy levels than the first approach. However, it also introduces a second three-phase bolted fault on the system and it requires that a separate high-speed grounding switch be installed and operational. Assuming there is space available for the addition of the grounding switch, there is a significantly higher cost of implementation involved compared to the first approach, and so may not be a practical alternative, especially for existing switchgear lineups. Arc Flash Calculator Also, we have provided a free arc flash calculator for android based smartphones Arc Flash Calculator References 1. Neal, T., Bingham, A., Doughty, R.L, “Protective Clothing for Electric Arc Exposure”, IEEE, July / Aug 1997 2. IEEE Std 1584, “Arc Flash Hazard Calculations”, 2002 3. AS 3439.1, “Low-voltage switchgear and control gear assemblies – Part 1: Type-tested and partially type tested assemblies”, 2002 4. "Arc flash hazard analysis and mitigation", 2004, Christopher Inshaw, Robert A. Wilson 5. Arc advisor data Category: Protection

Circuit Breaker Ratings

Contents [hide] 





1 High Voltage Circuit Breakers o

1.1 Ir (Rated normal current)

o

1.2 Ik (Rated short-time withstand current)

o

1.3 Ip (Rated peak withstand current)

o

1.4 Isc (Rated short-circuit breaking current)

o

1.5 Imc (Rated short-circuit making current)

o

1.6 TRV (Transient recovery voltage)

2 Low Voltage Circuit Breakers o

2.1 In (Rated current)

o

2.2 Icm (Rated short-circuit making current)

o

2.3 Icu (Rated ultimate short-circuit current)

o

2.4 Ics (Rated service short-circuit current)

o

2.5 Icw (Rated short time withstand current)

3 Other Ratings o

3.1 Ith (Thermal short-circuit current)

High Voltage Circuit Breakers Based on IEC 62271-100 (HV circuit breakers) and IEC 62271-1 (HV switchgear): Ir (Rated normal current) The rated continuous / uninterrupted current that the circuit breaker can carry. Ik (Rated short-time withstand current) The rms value of the current which must be carried by the circuit breaker in the closed position during a specified short time under prescribed use and behaviour. The specified time is called the rated "duration of short circuit" or tk, and has a standard value of 1s. Other recommended values are 0.5s, 2s and 3s. The rated short-time withstand current is equal to the rated shortcircuit breaking current (Isc). Ip (Rated peak withstand current) The peak current associated with the rated short-time withstand current, and is defined according to the dc time constant (where a time constant of 45ms covers the majority of cases and corresponds to a rated peak withstand current of 2.5 x Ik for 50Hz and below or 2.6 x Ik for 60Hz systems). The rated peak withstand current is equal to the rated short-circuit making current (Imc).

Isc (Rated short-circuit breaking current) The highest short-circuit current that the circuit breaker shall be capable of breaking under the conditions of use and behaviour prescribed in IEC 62271-100. It is characterised by two values: 

AC component - the rms value that is a standard current selected from the R10 series of numbers



DC time constant - the time constant that results in a percentage of the dc component of the short-circuit at separation. A standard value of 45ms covers the majority of all cases. Special time constants can also be used depending on voltage (e.g. 120ms for <52kV, 60ms for <420kV and 75ms for >550kV)

Imc (Rated short-circuit making current) The short-circuit current that the circuit breaker can withstand as it is closing where the act of closing initiates the fault. TRV (Transient recovery voltage) The reference voltage which constitutes the limit of the prospective transient recovery voltage of circuits which the circuit breaker shall be capable of withstanding under short circuit conditions. Low Voltage Circuit Breakers Based on IEC 60947-2 (LV switchgear and controlgear - Part 2: Circuit breakers): In (Rated current) The rated continuous / uninterrupted current that the circuit breaker can carry. Icm (Rated short-circuit making current) The short-circuit current that the circuit breaker can withstand as it is closing where the act of closing initiates the fault. Icu (Rated ultimate short-circuit current) The maximum symmetrical short-circuit current the circuit breaker can interrupt. Ics (Rated service short-circuit current) The breaking capacity such that the circuit breaker is tested to carry its current continuously. The test sequence verifies that the breaker can be returned to service. Ics is the maximum current the breaker can interrupt multiple times and be returned to service without being damaged and is expressed as a % of Icu. Icw (Rated short time withstand current) This is the steady state symmetrical fault current the breaker has to be able to carry for a duration of 0.05s to 3s without exceeding its thermal integrity. Other Ratings Ith (Thermal short-circuit current)

Ith is the joule integral and thermal equivalent short-circuit current and is a measure of the energy generated in the resistive element of the system by the short-circuit current (see IEC 60909-0 Clause 4.8). Categories: Switchgear | Protection

Circuit breakers Contents [hide] 

1 Circuit breakers



2 Air circuit breakers (ACB)



o

2.1 Plain break

o

2.2 Air-blast break

o

2.3 Miniature circuit breakers

3 Oil circuit brakers (OCB) o

3.1 Bulk oil circuit breakers (BOCB)

o

3.2 Minimum oil circuit brakers (MOCB)



4 Vacuum circuit brakers (VCB)



5 Sulfur-hexafluoride (SF6) circuit breakers



o

5.1 Gas properties

o

5.2 Breaker properties

o

5.3 Gas Insulated Substation (GIS)

6 Trivia

Circuit breakers

IEC Circuit Breaker Symbol Electrical circuit breaker is a switching device which can be operated both manually and automatically for controlling and protection of any electrical power system. As the modern power system deals with huge currents, the spacial attention should be given during deg of circuit breaker to safe interruption of arc produced during the opening/closing operation of circuit breaker. According to their arc quenching (rapid cooling) media the circuit breaker can be divided as: 

1) Air circuit breaker



2) Oil circuit breaker



3) Vacuum circuit breaker



4) SF6 circuit breaker

According to their services the circuit breaker can be divided as: 

1) Outdoor circuit breaker



2) Indoor circuit breaker

According to the operating mechanism of circuit breaker they can be divided as: 

1) Spring operated circuit breaker



2) Pneumatic circuit breaker



3) Hydraulic circuit breaker

According to the voltage level of installation types of circuit breaker are referred as: 

1) High voltage circuit breaker (> 72 kV)



2) Medium voltage circuit breaker (1-72 kV)



3) Low voltage circuit breaker (< 1 kV)

Circuit breaker ratings according to the IEC 62271-100, IEC 62271-1 and IEC 60947-2 are explained on this page "Circuit Breaker Ratings". Short summary for breakers: 

Plain-break air breakers are used in low voltage and medium voltage up to 15 kV



For low and medium voltages fuses can be also used, but the main disadvantage is that they must be replaced after fault clearing



In medium voltage systems minimum oil, SF6 and vacuum breakers are also being used



For high voltages minimum oil, SF6 and blast-air breakers are used, but always with multiple interrupters in series



The maximum voltage per interrupter is 100 kV for air-blast and SF6 breakers, 170 kV for minimum oil breakers

Air circuit breakers (ACB) The circuit breaker which operates in air at atmospheric pressure. The working principle of this breaker is rather different from those in any other types of circuit breakers. The main aim of all kind of circuit breaker is to prevent the reestablishment of arcing after current zero by creating a situation where the gap will withstand the system recovery voltage. The air circuit breaker does the same but in different manner. For interrupting arc it creates an arc voltage in excess of the supply voltage. Arc voltage is defined as the minimum voltage required maintaining the arc. This circuit breaker increases the arc voltage by mainly three different ways: 

It may increase the arc voltage by cooling the arc plasma. As the temperature of arc plasma is decreased, the mobility of the particle in arc plasma is reduced; hence more voltage gradient is required to maintain the arc.



It may increase the arc voltage by lengthening the arc path. As the length of arc path is increased, the resistance of the path is increased, and hence to maintain the same arc current more voltage is required to be applied across the arc path. That means arc voltage is increased.



Splitting up the arc into a number of series arcs also increases the arc voltage.

There are mainly two types of ACB available. 

1) Plain air circuit breaker



2) Air-blast circuit breaker

Figure 1.a) ABB Low voltage air breaker, 600V/400A

Figure 1.b) WEG Low voltage air breaker, 400V/6300A

Plain break Air-break circuit breakers extinguish the arc by simply stretching it until the dielectric strength of the gap is larger than the voltage across the gap. The longer arc has a larger cooling surface and higher resistance, which decreases the current flow and the amount of heat created. To stretch the arc, horn gap shaped s are used. Due to a natural convection, the arc moves upwards. To further increase the length, the arc is stretched by forcing it into an arc chute made of metal barriers or insulating material. The metal barriers chop the arc into many smaller arcs. Used from 120 V up to 15 kV.

Fi

ra

Figure 2.b) Air breaker Figure 2.a) Air breaker - plain break Air-blast break In the air-blast breaker the arc is not stretched. To extinguish the arc, a blast of compressed air is directed into the arc path to cool the ionized gas and remove it from the gap between the s. The s are held closed by a spring. A blast of air into the interrupting head forces the s to open. The s will close as soon as the air flow stops. The compressed air can be blown into the arc perpendicular to it (cross blast), or along its axis (axial blast). All modern breakers use the axial blast. The air blast circuit breakers are built up to the highest used voltages (765 kV) by connecting several interrupter heads in series.

Figure 3.a) Axial air-blast

Figure 3.b) Axial air-blast

breaker

breaker

Miniature circuit breakers For miniature circuit breakers (or MCB) used in households refer to the Small air breakers for low voltage domestic circuits. Oil circuit brakers (OCB) Mineral oil has better insulating property than air. The oil is used to insulate between the phases and between the phases and the ground, and to extinguish the arc. When electric arc is drawn under oil, the arc vaporizes the oil and creates a large bubble of hydrogen that surrounds the arc. The oil surrounding the bubble conducts the heat away from the arc and thus also contributes to deionization and extinction of the arc. Disadvantage of the oil circuit breakers is the flammability of the oil, and the maintenance necessary (i.e. changing and purifying the oil). The oil circuit breaker is the one of the oldest type of circuit breakers. Bulk oil circuit breakers (BOCB) Bulk oil circuit breaker (or BOCB) is a such type of the circuit breakers where oil is used as arc quenching media as well as insulating media between current carrying s and earthed parts of the breaker. The oil used here is same as transformer insulating oil. These types of breakers are designed in all voltage ranges from 1 kV up to 330 kV.

Figure 4.a) 66 kV Oil Circuit Breaker Figure 4.b) Bulk oil circui Modern arc-controlled oil breakers have an arc control device surrounding the breaker s to improve extinction of arc. In cross blast interrupters, the arc is drawn in front of several lateral vents. The gas formed by the arc causes high pressure inside the arc control device. The arc is forced to bow into the lateral vents in the pot, which increases the length of the arc and shortens the interruption time. The axial blast interrupters use similar principle. Oil breakers are design for both three-phase and single-phase circuit brakers. At voltages higher than 115 kV, separate tanks for each phase are used. The practical limit for the bulk oil breakers is 275 kV. Minimum oil circuit brakers (MOCB) In minimum oil breakers the oil is used only for extinguishing of the arc. The arc control devices are the same as for the bulk-oil breakers. However, unlike bulk oil circuit breakers, these designs place the interrupting units in insulating chambers at live potential. To improve breaker performance, oil is injected into the arc. The interrupter containers of the minimum oil breakers are made of insulating material and are insulated from the ground. This is usually referred to as live tank construction. For high voltages (above 132 kV), the interrupters are arranged in series. It is essential to ensure that each interrupter carries its share of the duty. Care must be taken that all breaks occur simultaneously, and that the restriking voltage is divided equally across the breaks during the interrupting process. The features of deg MOCB is to reduce requirement of oil, and hence these breaker are called minimum oil circuit breaker. These designs are available in voltages ranging from 1 kV to 765 kV using the multi-break technique.

Figure 5. 36 kV MOCB a) Typical design, b) Cross-section of the Vacuum circuit brakers (VCB) Vacuum circuit breakers are used mostly for low and medium voltages. Vacuum interrupters are developed for up to 36 kV and can be connected in series for higher voltages. The interrupting chambers are made of porcelain and sealed. They cannot be open for maintenance, but life is expected to be about 20 years, provided that the vacuum is maintained. Because of the high dielectric strength of vacuum, the interrupters are small. The gap between the s is about 1 cm for 15 kV interrupters, 2 mm for 3 kV interrupters.

Figure 6.a) Vacuum interrupter

Figure 6.b)

circuit brea Service life of the VCB is much longer than other types of circuit breakers. There is no chance of fire hazard as oil circuit breaker. It is much environment friendly than SF6 circuit breaker. Sulfur-hexafluoride (SF6) circuit breakers Gas properties

Figure 7. SF6 gas molecule Sulfur-hexafluoride (SF6) is an excellent gaseous dielectric for high voltage power applications. SF6 is a colorless non-toxic gas, with good thermal conductivity and density approximately five times that of air (6.14 kg/m3.). It does not react with materials commonly used in high voltage circuit breakers. It has been used extensively in high voltage circuit breakers and other switchgear employed by the power industry. Applications for SF6 include gas insulated transmission lines and gas insulated power distribution substations. The combined electrical, physical, chemical and thermal properties offer many advantages when used in power switchgear. Some of the outstanding properties of SF6 which make its use in power applications desirable are: 

high dielectric strength



unique arc-quenching ability



excellent thermal stability



good thermal conductivity

The SF6 gas is identified as a greenhouse gas, safety regulation are being introduced in many countries in order to prevent its release into atmosphere. Breaker properties The principle of operation is similar to the air blast breakers, except that SF6 is not discharged in the atmosphere. A closed-circuit, sealed construction is used. There are mainly three types of SF6 CB depending upon the voltage level of application: 

1) Single interrupter SF6 CB applied for up to 245 kV (220 kV) system



2) Two interrupter SF6 CB applied for up to 420 kV (400 kV) system



3) Four interrupter SF6 CB applied for up to 800 kV (715 kV) system

During the opening operation the gas contained inside a part of the breaker is compressed by a moving cylinder that s the s or by a piston. This forces the SF6 through the interrupting nozzle. When the s separate, an arc is established. If the current is not very

high, it is extinguished at the first zero crossing by the pushing the SF6 through the arc by the piston. If the short circuit current is high, the arc extinction may not occur at the first zero crossing, but the gas pressure will increase sufficiently to blow the arc out. By connecting several interrupting heads in series, SF6 breakers can be constructed for voltages of up to 765 kV.

Figure 8.a) SF6 CB scheme

Gas Insulated Substation (GIS) In GIS the high-voltage conductors, circuit breaker interrupters, switches, current transformers, voltage transformers and lightning arresters are encapsulated in SF6 gas inside grounded metal enclosures. Locations where gas insulated substation is preferred: Large cities and towns Under ground stations Highly polluted and saline environment Indoor GIS occupies very little space Substations and power stations located Off shore Mountains and valley regions Gas insulated substation has gas monitoring system. Gas inside each compartment should have a pressure of about 3 kg/cm2.The gas density in each compartment is monitored. If the pressure drops slightly, the gas is automatically trapped up. With further gas leakage, the low pressure alarm is sounded or automatic tripping or lock-out occurs. Trivia Category: Protection

Earth Fault Protection Contents [hide] 



1 Recommended Settings o

1.1 Solidly Earthed Systems

o

1.2 Impedance Earthed Systems

o

1.3 Unearthed Systems

2 References

Recommended Settings Solidly Earthed Systems From Alstom Network Protection and Automation Guide (2011) Section 9.16 [3]: "Typical [earth fault relay] settings are 30-40% of nominal full-load current or minimum earth fault current for the circuit being protected." Therefore, a pickup setting of 30% - 40% of In is suggested, where In is: 

For transformer feeders: In = full load current of transformer



For cable feeders: In = cable rated current



For motor feeders: In = full load current of motor

Fielding [5] suggests higher sensitivity to earth faults, with pickup settings of 20% of In. Ultimately, the decision depends on the trade-off between high sensitivity to earth faults and the probability of spurious and nuisance tripping. Impedance Earthed Systems In an impedance earthed system, earth faults are limited to a maximum value by some impedance. An earth fault pickup setting of 10% - 20% of the maximum earth fault current is recommended, to be selected in conjunction with the following minimum pickup settings suggested in [4] to avoid spurious tripping: 

For CTs in residual connection: >12% of the nominal CT primary current



For core balance CTs: >1A for 0.1s

Unearthed Systems In an unearthed system, core balance CTs are necessary to have the sensitivity to detect earth fault currents (because earth fault currents are purely capacitive). The minmum threshold for core balance CTs should be >1A for >0.1s as suggested by [4] to avoid spurious tripping. References 

[1] IEEE Std 242, “IEEE Recommended Practice for Protection and Coordination – Industrial and Commercial Power Systems (Buff book)”, 2001



[2] IEEE Std 142, “ IEEE Recommended Practice for Grounding of Industrial and Commercial Power systems (Green book)”, 2007



[3] Alstom Grid, “ Network Protection and Automation Guide”, May 2011



[4] Preve, C., “Protection of Electrical Networks”, 2006, ISTE Ltd, London



[5] Fielding, G., “Protection of MV Industrial Networks”, 1997, IEE Colloquium, London

Category: Protection Electrical Fuse Contents [hide] 

1 Main definition by IEC



2 General information



3 Construction



4 Characteristic parameters o

4.1 Rated current IN

o

4.2 The I2t value

o

4.3 Breaking capacity

o

4.4 Rated voltage

o

4.5 Voltage drop

o

4.6 Temperature derating



5 Markings



6 Fuse standards





o

6.1 IEC 60269 fuses

o

6.2 UL 248 fuses (North America)

7 Fuse Types o

7.1 Low voltage fuses

o

7.2 High voltage fuses

o

7.3 Resettable fuses

o

7.4 Thermal fuses

8 Trivia

Main definition by IEC

Fuse symbol by IEC A device that by the fusing (melting) of one or more of its specially designed and proportioned components, opens the circuit in which it is inserted by breaking the current when this exceeds a given value for a sufficient time. The fuse comprises all the parts that form the complete device. General information In electronics and electrical engineering, a fuse is a type of low resistance resistor that acts as a "sacrificial" device to provide overcurrent protection, of either the load or source circuit. Its essential component is a metal wire or strip that melts when too much current flows, which interrupts the circuit in which it is connected. Short circuit, overloading, mismatched loads or device failure are the prime reasons for excessive current. A fuse interrupts excessive current (blows) so that further damage by overheating or fire is prevented. Wiring regulations often define a maximum fuse current rating for particular circuits. Overcurrent protection devices are essential in electrical systems to limit threats to human life and property damage. Fuses are selected to allow age of normal current plus a marginal percentage and to allow excessive current only for short periods. Slow blow fuses are designed to allow higher currents for a modest amount of time longer, and such considerations are and were commonly necessary when electronics devices or systems had electronic tube tech or a large number of incandescent lights were being powered such as in a large hall, theater or stadium. Tubes and incandescent lights each have reduced current needs as they heat up to operating temperatures for their internal resistance grows as they are heated— the same physics principle causes the fuse material to melt, disconnecting the circuit from power.

Construction

Simplified fuse scheme A fuse consists of a metal strip or wire fuse element, of small cross-section compared to the circuit conductors, mounted between a pair of electrical terminals, and (usually) enclosed by a non-combustible housing. The fuse is arranged in series to carry all the current ing through the protected circuit. The resistance of the element generates heat due to the current flow. The size and construction of the element is determined so that the heat produced for a normal current does not cause the element to attain a high temperature. If too high current flows, the element rises to a higher temperature and either directly melts, or else melts a soldered t within the fuse, opening the circuit. The fuse element is made of zinc, copper, silver, aluminum, or alloys to provide stable and predictable characteristics. The fuse ideally would carry its rated current indefinitely, and melt quickly on a small excess. The element must not be damaged by minor harmless surges of current, and must not oxidize or change its behavior after possibly years of service. The fuse elements may be shaped to increase heating effect. In large fuses, current may be divided between multiple strips of metal. A dual-element fuse may contain a metal strip that melts instantly on a short-circuit, and also contain a low-melting solder t that responds to long-term overload of low values compared to a short-circuit. Fuse elements may be ed by steel or nichrome wires, so that no strain is placed on the element, but a spring may be included to increase the speed of parting of the element fragments. The fuse element may be surrounded by air, or by materials intended to speed the quenching of the arc. Silica sand or non-conducting liquids may be used.

Dimensions Fuses can be built with different sized enclosures to prevent interchange of different ratings or types of fuse. For example, bottle style fuses distinguish between ratings with different cap diameters. Automotive glass fuses were made in different lengths, to prevent high-rated fuses being installed in a circuit intended for a lower rating. Special features Glass cartridge and plug fuses allow direct inspection of the fusible element. Other fuses have other indication methods including: 

Indicating pin or striker pin — extends out of the fuse cap when the element is blown.



Indicating disc — a coloured disc (flush mounted in the end cap of the fuse) falls out when the element is blown.



Element window — a small window built into the fuse body to provide visual indication of a blown element.



External trip indicator — similar function to striker pin, but can be externally attached (using clips) to a compatible fuse.

Some fuses allow a special purpose micro switch or relay unit to be fixed to the fuse body. When the fuse element blows, the indicating pin extends to activate the micro switch or relay, which, in turn, triggers an event. Some fuses for medium-voltage applications use two separate barrels and two fuse elements in parallel. Characteristic parameters Rated current IN A maximum current that the fuse can continuously conduct without interrupting the circuit. The speed at which a fuse blows depends on how much current flows through it and the material of which the fuse is made. The operating time is not a fixed interval, but decreases as the current increases. Fuses have different characteristics of operating time compared to current, characterized as fast-blow, slow-blow, or time-delay, according to time required to respond to an overcurrent condition. A standard fuse may require twice its rated current to open in one second, a fast-blow fuse may require twice its rated current to blow in 0.1 seconds, and a slow-blow fuse may require twice its rated current for tens of seconds to blow. Fuse selection depends on the load's characteristics. Semiconductor devices may use a fast or ultrafast fuse as semiconductor devices heat rapidly when excess current flows. The fastest blowing fuses are designed for the most sensitive electrical equipment, where even a short exposure to an overload current could be very damaging. Normal fast-blow fuses are the most general purpose fuses. The time delay fuse (also known as anti-surge, or slow-blow) are designed to allow a current which is above the rated value of the fuse to flow for a short period

of time without the fuse blowing. These types of fuse are used on equipment such as motors, which can draw larger than normal currents for up to several seconds while coming up to speed. Time-Current Characteristics Of Fuses

Time-Current characteristic A 100 ampere fuse does not open instantly at 101 amperes, nor even at 200 amperes. The fuse opening time is dependent on the type of fuse and magnitude of the overcurrent. In fact, this delay may be desirable. An overload current condition may only be temporary in nature, and the current may subside to normal current conditions in short order. For example, a typical harmless current overload is encountered whenever most motors are started. The built-in fuse time delay permits the motor to start without unnecessarily blowing fuses. Two broad fuse characteristic types are (1) dual-element, time-delay fuses and (2) non-time delay fuses. Each type has attributes suitable for specific applications. The dual-element, timedelay fuses are widely used in general purpose applications, motor circuits, transformers, and other circuits. The non-time delay current-limiting fuses are used where fast response with little or no overload delay is desired. A typical application of these is for protecting circuit breakers for possible large short-circuit current levels. The graph shows the difference between the melting curves of a typical 100 ampere dualelement time delay fuse and a non-time delay fuse. If we look at a comparison at 500 amperes, the dual-element fuse melts in about 10 seconds and the non-time delay fuse melts in .2 seconds. This is a time ratio of 50 to one. At a current of 200 amperes (twice the nominal rating) the time ratio is about 9 to one. The I2t value

The amount of energy spent by the fuse element to clear the electrical fault. This term is normally used in short circuit conditions and the values are used to perform co-ordination studies in electrical networks. I2t parameters are provided by charts in manufacturer data sheets for each fuse family. For coordination of fuse operation with upstream or downstream devices, both melting I2t and clearing I2t are specified. The melting I2t, is proportional to the amount of energy required to begin melting the fuse element. The clearing I2t is proportional to the total energy let through by the fuse when clearing a fault. The energy is mainly dependent on current and time for fuses as well as the available fault level and system voltage. Since the I 2t rating of the fuse is proportional to the energy it lets through, it is a measure of the thermal damage and magnetic forces that will be produced by a fault. General formulation should be: I2t value of surge current < I2t value of fuse < Maximum allowable fault current I2t Breaking capacity The breaking capacity is the maximum current that can safely be interrupted by the fuse. Generally, this should be higher than the prospective short circuit current. Miniature fuses may have an interrupting rating only 10 times their rated current. Some fuses are designated High Rupture Capacity (HRC) and are usually filled with sand or a similar material. Fuses for small, low-voltage, usually residential, wiring systems are commonly rated, in North American practice, to interrupt 10,000 amperes. Fuses for larger power systems must have higher interrupting ratings, with some low-voltage current-limiting high interrupting fuses rated for 300,000 amperes. Fuses for high-voltage equipment, up to 115,000 volts, are rated by the total apparent power (megavolt-amperes, MVA) of the fault level on the circuit. Rated voltage Voltage rating of the fuse must be greater than or equal to what would become the open circuit voltage. For example, a glass tube fuse rated at 32 volts would not reliably interrupt current from a voltage source of 120 or 230 V. If a 32 V fuse attempts to interrupt the 120 or 230 V source, an arc may result. Plasma inside that glass tube fuse may continue to conduct current until current eventually so diminishes that plasma reverts to an insulating gas. Rated voltage should be larger than the maximum voltage source it would have to disconnect. Rated voltage remains same for any one fuse, even when similar fuses are connected in series. Connecting fuses in series does not increase the rated voltage of the combination (nor of any one fuse). Medium-voltage fuses rated for a few thousand volts are never used on low voltage circuits, because of their cost and because they cannot properly clear the circuit when operating at very low voltages. Voltage drop A voltage drop across the fuse is usually provided by its manufacturer. Resistance may change when a fuse becomes hot due to energy dissipation while conducting higher currents. This resulting voltage drop should be taken into , particularly when using a fuse in low-voltage applications. Voltage drop often is not significant in more traditional wire type fuses, but can be significant in other technologies such as resettable fuse (PPTC) type fuses. Temperature derating

Ambient temperature will change a fuse's operational parameters. A fuse rated for 1 A at 25 °C may conduct up to 10% or 20% more current at −40 °C and may open at 80% of its rated value at 100 °C. Operating values will vary with each fuse family and are provided in manufacturer data sheets.

Fuse derating characteristic Markings

Typical domestic fuse, gL/gG, 500V, 16A, SIEMENS Most fuses are marked on the body or end caps with markings that indicate their ratings. Surface-mount technology "chip type" fuses feature few or no markings, making identification very difficult. Similar appearing fuses may have significantly different properties, identified by their markings. Fuse markings will generally convey the following information, either explicitly as text, or else implicit with the approval agency marking for a particular type: 

Current rating of the fuse.



Voltage rating of the fuse.



Time-current characteristic; i.e. fuse speed.



Product certification or approvals by national and international standards agencies.



Manufacturing/part number/series.



Breaking capacity.

Fuse standards IEC 60269 fuses The International Electrotechnical Commission publishes standard 60269 for low-voltage power fuses. The standard is in four volumes, which describe general requirements, fuses for industrial and commercial applications, fuses for residential applications, and fuses to protect semiconductor devices. The IEC standard unifies several national standards, thereby improving the interchangeability of fuses in international trade. All fuses of different technologies tested to meet IEC standards will have similar time-current characteristics, which simplifies design and maintenance. UL 248 fuses (North America) In the United States and Canada, low-voltage fuses to 1 kV AC rating are made in accordance with Underwriters Laboratories standard UL 248 or the harmonized Canadian Standards Association standard C22.2 No. 248. This standard applies to fuses rated 1 kV or less, AC or DC, and with breaking capacity up to 200 kA. These fuses are intended for installations following Canadian Electrical Code, Part I (CEC), or the National Electrical Code, NFPA 70 (NEC). IEC and UL nomenclature varies slightly. IEC standards refer to a "fuse" as the assembly of a fuse link and fuse holder. In North American standards, the fuse is the replaceable portion of the assembly, and a fuse link would be a bare metal element for installation in a fuse. Fuse Types Low voltage fuses In this category all fuses up to 1.5 kV can be included. But the most typical voltage levels for low voltage fuses are 500 V, 690 V and 750 V. LV HRC fuses are used for installation systems in non-residential, commercial and industrial buildings, as well as in the switchboards of power supply companies. They therefore protect essential building parts and installations. LV HRC fuse links are available in the following operational classes: 

gG (previously gL) for cable and line protection



aM for the short-circuit protection of switching devices in motor circuits



gR or aR for the protection of power semiconductors



gS operational class combines cable and line protection with semiconductor protection.

Various low voltage fuses

Motor fuse, aM, 690V, 500A

Various cylindrical low voltage

Various gG fuses for 500V

fuses High voltage fuses All fuses used on power systems from 1.5 kV up to 138 kV are categorized as high voltage fuses. High voltage fuses are used to protect instrument transformers used for electricity metering, or for small power transformers where the expense of a circuit breaker is not warranted. For example, in distribution systems, a power fuse may be used to protect a transformer serving 1–3 houses. A circuit breaker at 115 kV may cost up to five times as much as a set of power fuses, so the resulting saving can be tens of thousands of dollars. Pole-mounted distribution transformers are nearly always protected by a fusible cutout, which can have the fuse element replaced using live-line maintenance tools. Large power fuses use fusible elements made of silver, copper or tin to provide stable and predictable performance. High voltage expulsion fuses surround the fusible link with gas-evolving substances, such as boric acid. When the fuse blows, heat from the arc causes the boric acid to evolve large volumes of gases. The associated high pressure (often greater than 100 atmospheres) and cooling gases rapidly quench the resulting arc. The hot gases are then explosively expelled out of the end(s) of the fuse. Such fuses can only be used outdoors. Various high voltage fuses

High voltage fuses, 115 kV Medium voltage fuse for transformer protection, 24 kV, 200 A

Medium voltage fuse, 24 kV

High voltage high power fuses are standalone protective switching devices used to 138 kV. They are used in power supply networks and for distribution uses. The most frequent application is in transformer circuits, with further uses in motor circuits and capacitor banks. These type of fuses may have an impact pin to operate a switch mechanism, so that all three phases are interrupted if any one fuse blows. High-power fuse means that these fuses can interrupt several kiloamperes. Some manufacturers have tested their fuses for up to 63 kA cut-off current. Resettable fuses So-called self-resetting fuses use a thermoplastic conductive element known as a Polymeric Positive Temperature Coefficient (or PPTC) thermistor that impedes the circuit during an overcurrent condition (by increasing device resistance). The PPTC thermistor is self-resetting in that when current is removed, the device will cool and revert back to low resistance. These devices are often used in aerospace/nuclear applications where replacement is difficult, or on a computer motherboard so that a shorted mouse or keyboard does not cause motherboard damage.

PTC Resettable fuse, 30V Thermal fuses A thermal fuse is often found in consumer equipment such as coffee makers or hair dryers or transformers powering small consumer electronics devices. They contain a fusible, temperaturesensitive alloy which holds a spring mechanism normally closed. When the surrounding temperature gets too high, the alloy melts and allows the spring mechanism to break the circuit. The device can be used to prevent a fire in a hair dryer for example, by cutting off the power supply to the heater elements when the air flow is interrupted (e.g., the blower motor stops or the air intake becomes accidentally blocked). Thermal fuses are a 'one shot', nonresettable device which must be replaced once they have been activated (blown).

Thermal fuse, 120V, 15A Trivia Category: Protection Electrical Fuse (Redirected from Fuse) Contents [hide] 

1 Main definition by IEC



2 General information



3 Construction



4 Characteristic parameters o

4.1 Rated current IN

o

4.2 The I2t value

o

4.3 Breaking capacity

o

4.4 Rated voltage

o

4.5 Voltage drop

o

4.6 Temperature derating



5 Markings



6 Fuse standards



o

6.1 IEC 60269 fuses

o

6.2 UL 248 fuses (North America)

7 Fuse Types



o

7.1 Low voltage fuses

o

7.2 High voltage fuses

o

7.3 Resettable fuses

o

7.4 Thermal fuses

8 Trivia

Main definition by IEC

Fuse symbol by IEC A device that by the fusing (melting) of one or more of its specially designed and proportioned components, opens the circuit in which it is inserted by breaking the current when this exceeds a given value for a sufficient time. The fuse comprises all the parts that form the complete device. General information In electronics and electrical engineering, a fuse is a type of low resistance resistor that acts as a "sacrificial" device to provide overcurrent protection, of either the load or source circuit. Its essential component is a metal wire or strip that melts when too much current flows, which interrupts the circuit in which it is connected. Short circuit, overloading, mismatched loads or device failure are the prime reasons for excessive current. A fuse interrupts excessive current (blows) so that further damage by overheating or fire is prevented. Wiring regulations often define a maximum fuse current rating for particular circuits. Overcurrent protection devices are essential in electrical systems to limit threats to human life and property damage. Fuses are selected to allow age of normal current plus a marginal percentage and to allow excessive current only for short periods. Slow blow fuses are designed to allow higher currents for a modest amount of time longer, and such considerations are and were commonly necessary when electronics devices or systems had electronic tube tech or a large number of incandescent lights were being powered such as in a large hall, theater or stadium. Tubes and incandescent lights each have reduced current needs as they heat up to operating temperatures for their internal resistance grows as they are heated— the same physics principle causes the fuse material to melt, disconnecting the circuit from power.

Construction

Simplified fuse scheme A fuse consists of a metal strip or wire fuse element, of small cross-section compared to the circuit conductors, mounted between a pair of electrical terminals, and (usually) enclosed by a non-combustible housing. The fuse is arranged in series to carry all the current ing through the protected circuit. The resistance of the element generates heat due to the current flow. The size and construction of the element is determined so that the heat produced for a normal current does not cause the element to attain a high temperature. If too high current flows, the element rises to a higher temperature and either directly melts, or else melts a soldered t within the fuse, opening the circuit. The fuse element is made of zinc, copper, silver, aluminum, or alloys to provide stable and predictable characteristics. The fuse ideally would carry its rated current indefinitely, and melt quickly on a small excess. The element must not be damaged by minor harmless surges of current, and must not oxidize or change its behavior after possibly years of service. The fuse elements may be shaped to increase heating effect. In large fuses, current may be divided between multiple strips of metal. A dual-element fuse may contain a metal strip that melts instantly on a short-circuit, and also contain a low-melting solder t that responds to long-term overload of low values compared to a short-circuit. Fuse elements may be ed by steel or nichrome wires, so that no strain is placed on the element, but a spring may be included to increase the speed of parting of the element fragments. The fuse element may be surrounded by air, or by materials intended to speed the quenching of the arc. Silica sand or non-conducting liquids may be used.

Dimensions Fuses can be built with different sized enclosures to prevent interchange of different ratings or types of fuse. For example, bottle style fuses distinguish between ratings with different cap diameters. Automotive glass fuses were made in different lengths, to prevent high-rated fuses being installed in a circuit intended for a lower rating. Special features Glass cartridge and plug fuses allow direct inspection of the fusible element. Other fuses have other indication methods including: 

Indicating pin or striker pin — extends out of the fuse cap when the element is blown.



Indicating disc — a coloured disc (flush mounted in the end cap of the fuse) falls out when the element is blown.



Element window — a small window built into the fuse body to provide visual indication of a blown element.



External trip indicator — similar function to striker pin, but can be externally attached (using clips) to a compatible fuse.

Some fuses allow a special purpose micro switch or relay unit to be fixed to the fuse body. When the fuse element blows, the indicating pin extends to activate the micro switch or relay, which, in turn, triggers an event. Some fuses for medium-voltage applications use two separate barrels and two fuse elements in parallel. Characteristic parameters Rated current IN A maximum current that the fuse can continuously conduct without interrupting the circuit. The speed at which a fuse blows depends on how much current flows through it and the material of which the fuse is made. The operating time is not a fixed interval, but decreases as the current increases. Fuses have different characteristics of operating time compared to current, characterized as fast-blow, slow-blow, or time-delay, according to time required to respond to an overcurrent condition. A standard fuse may require twice its rated current to open in one second, a fast-blow fuse may require twice its rated current to blow in 0.1 seconds, and a slow-blow fuse may require twice its rated current for tens of seconds to blow. Fuse selection depends on the load's characteristics. Semiconductor devices may use a fast or ultrafast fuse as semiconductor devices heat rapidly when excess current flows. The fastest blowing fuses are designed for the most sensitive electrical equipment, where even a short exposure to an overload current could be very damaging. Normal fast-blow fuses are the most general purpose fuses. The time delay fuse (also known as anti-surge, or slow-blow) are designed to allow a current which is above the rated value of the fuse to flow for a short period

of time without the fuse blowing. These types of fuse are used on equipment such as motors, which can draw larger than normal currents for up to several seconds while coming up to speed. Time-Current Characteristics Of Fuses

Time-Current characteristic A 100 ampere fuse does not open instantly at 101 amperes, nor even at 200 amperes. The fuse opening time is dependent on the type of fuse and magnitude of the overcurrent. In fact, this delay may be desirable. An overload current condition may only be temporary in nature, and the current may subside to normal current conditions in short order. For example, a typical harmless current overload is encountered whenever most motors are started. The built-in fuse time delay permits the motor to start without unnecessarily blowing fuses. Two broad fuse characteristic types are (1) dual-element, time-delay fuses and (2) non-time delay fuses. Each type has attributes suitable for specific applications. The dual-element, timedelay fuses are widely used in general purpose applications, motor circuits, transformers, and other circuits. The non-time delay current-limiting fuses are used where fast response with little or no overload delay is desired. A typical application of these is for protecting circuit breakers for possible large short-circuit current levels. The graph shows the difference between the melting curves of a typical 100 ampere dualelement time delay fuse and a non-time delay fuse. If we look at a comparison at 500 amperes, the dual-element fuse melts in about 10 seconds and the non-time delay fuse melts in .2 seconds. This is a time ratio of 50 to one. At a current of 200 amperes (twice the nominal rating) the time ratio is about 9 to one. The I2t value

The amount of energy spent by the fuse element to clear the electrical fault. This term is normally used in short circuit conditions and the values are used to perform co-ordination studies in electrical networks. I2t parameters are provided by charts in manufacturer data sheets for each fuse family. For coordination of fuse operation with upstream or downstream devices, both melting I2t and clearing I2t are specified. The melting I2t, is proportional to the amount of energy required to begin melting the fuse element. The clearing I2t is proportional to the total energy let through by the fuse when clearing a fault. The energy is mainly dependent on current and time for fuses as well as the available fault level and system voltage. Since the I 2t rating of the fuse is proportional to the energy it lets through, it is a measure of the thermal damage and magnetic forces that will be produced by a fault. General formulation should be: I2t value of surge current < I2t value of fuse < Maximum allowable fault current I2t Breaking capacity The breaking capacity is the maximum current that can safely be interrupted by the fuse. Generally, this should be higher than the prospective short circuit current. Miniature fuses may have an interrupting rating only 10 times their rated current. Some fuses are designated High Rupture Capacity (HRC) and are usually filled with sand or a similar material. Fuses for small, low-voltage, usually residential, wiring systems are commonly rated, in North American practice, to interrupt 10,000 amperes. Fuses for larger power systems must have higher interrupting ratings, with some low-voltage current-limiting high interrupting fuses rated for 300,000 amperes. Fuses for high-voltage equipment, up to 115,000 volts, are rated by the total apparent power (megavolt-amperes, MVA) of the fault level on the circuit. Rated voltage Voltage rating of the fuse must be greater than or equal to what would become the open circuit voltage. For example, a glass tube fuse rated at 32 volts would not reliably interrupt current from a voltage source of 120 or 230 V. If a 32 V fuse attempts to interrupt the 120 or 230 V source, an arc may result. Plasma inside that glass tube fuse may continue to conduct current until current eventually so diminishes that plasma reverts to an insulating gas. Rated voltage should be larger than the maximum voltage source it would have to disconnect. Rated voltage remains same for any one fuse, even when similar fuses are connected in series. Connecting fuses in series does not increase the rated voltage of the combination (nor of any one fuse). Medium-voltage fuses rated for a few thousand volts are never used on low voltage circuits, because of their cost and because they cannot properly clear the circuit when operating at very low voltages. Voltage drop A voltage drop across the fuse is usually provided by its manufacturer. Resistance may change when a fuse becomes hot due to energy dissipation while conducting higher currents. This resulting voltage drop should be taken into , particularly when using a fuse in low-voltage applications. Voltage drop often is not significant in more traditional wire type fuses, but can be significant in other technologies such as resettable fuse (PPTC) type fuses. Temperature derating

Ambient temperature will change a fuse's operational parameters. A fuse rated for 1 A at 25 °C may conduct up to 10% or 20% more current at −40 °C and may open at 80% of its rated value at 100 °C. Operating values will vary with each fuse family and are provided in manufacturer data sheets.

Fuse derating characteristic Markings

Typical domestic fuse, gL/gG, 500V, 16A, SIEMENS Most fuses are marked on the body or end caps with markings that indicate their ratings. Surface-mount technology "chip type" fuses feature few or no markings, making identification very difficult. Similar appearing fuses may have significantly different properties, identified by their markings. Fuse markings will generally convey the following information, either explicitly as text, or else implicit with the approval agency marking for a particular type: 

Current rating of the fuse.



Voltage rating of the fuse.



Time-current characteristic; i.e. fuse speed.



Product certification or approvals by national and international standards agencies.



Manufacturing/part number/series.



Breaking capacity.

Fuse standards IEC 60269 fuses The International Electrotechnical Commission publishes standard 60269 for low-voltage power fuses. The standard is in four volumes, which describe general requirements, fuses for industrial and commercial applications, fuses for residential applications, and fuses to protect semiconductor devices. The IEC standard unifies several national standards, thereby improving the interchangeability of fuses in international trade. All fuses of different technologies tested to meet IEC standards will have similar time-current characteristics, which simplifies design and maintenance. UL 248 fuses (North America) In the United States and Canada, low-voltage fuses to 1 kV AC rating are made in accordance with Underwriters Laboratories standard UL 248 or the harmonized Canadian Standards Association standard C22.2 No. 248. This standard applies to fuses rated 1 kV or less, AC or DC, and with breaking capacity up to 200 kA. These fuses are intended for installations following Canadian Electrical Code, Part I (CEC), or the National Electrical Code, NFPA 70 (NEC). IEC and UL nomenclature varies slightly. IEC standards refer to a "fuse" as the assembly of a fuse link and fuse holder. In North American standards, the fuse is the replaceable portion of the assembly, and a fuse link would be a bare metal element for installation in a fuse. Fuse Types Low voltage fuses In this category all fuses up to 1.5 kV can be included. But the most typical voltage levels for low voltage fuses are 500 V, 690 V and 750 V. LV HRC fuses are used for installation systems in non-residential, commercial and industrial buildings, as well as in the switchboards of power supply companies. They therefore protect essential building parts and installations. LV HRC fuse links are available in the following operational classes: 

gG (previously gL) for cable and line protection



aM for the short-circuit protection of switching devices in motor circuits



gR or aR for the protection of power semiconductors



gS operational class combines cable and line protection with semiconductor protection.

Various low voltage fuses

Motor fuse, aM, 690V, 500A

Various cylindrical low voltage

Various gG fuses for 500V

fuses High voltage fuses All fuses used on power systems from 1.5 kV up to 138 kV are categorized as high voltage fuses. High voltage fuses are used to protect instrument transformers used for electricity metering, or for small power transformers where the expense of a circuit breaker is not warranted. For example, in distribution systems, a power fuse may be used to protect a transformer serving 1–3 houses. A circuit breaker at 115 kV may cost up to five times as much as a set of power fuses, so the resulting saving can be tens of thousands of dollars. Pole-mounted distribution transformers are nearly always protected by a fusible cutout, which can have the fuse element replaced using live-line maintenance tools. Large power fuses use fusible elements made of silver, copper or tin to provide stable and predictable performance. High voltage expulsion fuses surround the fusible link with gas-evolving substances, such as boric acid. When the fuse blows, heat from the arc causes the boric acid to evolve large volumes of gases. The associated high pressure (often greater than 100 atmospheres) and cooling gases rapidly quench the resulting arc. The hot gases are then explosively expelled out of the end(s) of the fuse. Such fuses can only be used outdoors. Various high voltage fuses

High voltage fuses, 115 kV Medium voltage fuse for transformer protection, 24 kV, 200 A

Medium voltage fuse, 24 kV

High voltage high power fuses are standalone protective switching devices used to 138 kV. They are used in power supply networks and for distribution uses. The most frequent application is in transformer circuits, with further uses in motor circuits and capacitor banks. These type of fuses may have an impact pin to operate a switch mechanism, so that all three phases are interrupted if any one fuse blows. High-power fuse means that these fuses can interrupt several kiloamperes. Some manufacturers have tested their fuses for up to 63 kA cut-off current. Resettable fuses So-called self-resetting fuses use a thermoplastic conductive element known as a Polymeric Positive Temperature Coefficient (or PPTC) thermistor that impedes the circuit during an overcurrent condition (by increasing device resistance). The PPTC thermistor is self-resetting in that when current is removed, the device will cool and revert back to low resistance. These devices are often used in aerospace/nuclear applications where replacement is difficult, or on a computer motherboard so that a shorted mouse or keyboard does not cause motherboard damage.

PTC Resettable fuse, 30V Thermal fuses A thermal fuse is often found in consumer equipment such as coffee makers or hair dryers or transformers powering small consumer electronics devices. They contain a fusible, temperaturesensitive alloy which holds a spring mechanism normally closed. When the surrounding temperature gets too high, the alloy melts and allows the spring mechanism to break the circuit. The device can be used to prevent a fire in a hair dryer for example, by cutting off the power supply to the heater elements when the air flow is interrupted (e.g., the blower motor stops or the air intake becomes accidentally blocked). Thermal fuses are a 'one shot', nonresettable device which must be replaced once they have been activated (blown).

Thermal fuse, 120V, 15A Trivia Category: Protection IS Limiter Contents [hide] 

1 Introduction



2 Application



3 Parameter Settings



o

3.1 Trigger Level

o

3.2 di/dt

4 References

Introduction

Figure 1. Typical IS limiter design (image courtesy of [1])

IS limiters are fault current limiting devices that use chemical charges and current-limiting fuses to interrupt the fault current within the first quarter to half cycle (i.e. before the first peak). In a typical IS limiter design, the device is composed of two current paths connected together in parallel – one path is an element rated for the full load current (which can have high continuous current ratings, e.g. 3000A), and the other path provides the current limiting function via a current-limiting fuse (which typically has a continuous current rating of <300A at 15kV). In the event of a fault, the device operates by physically destroying the continuous current path using one or more chemical charges triggered by an electronic sensing and control unit. The fault current is thus forced through the current-limiting fuse.

Figure 2. IS limiter block diagram (courtesy of [1]) Application IS limiters are used for fault reduction in a system, typically to limit the fault current to within the rated capacity of downstream equipment. This is usually necessary due to system overexpansion or undersizing of equipment fault ratings. By using IS limiters, expensive upgrades or replacement of equipment can potentially be avoided. A natural question to ask is why current-limiting fuses can't just be used in lieu of IS limiters? The answer is that they can - but within limits. Current-limiting fuses typically have continuous current ratings <300A [1], so if the application calls for currents lower than that, then currentlimiting fuses by themselves are fine. However in many applications, the fault current needs to

be limited on a busbar with higher continuous load currents. This is where IS limiters or other types of fault current limiting devices need to be used. IS limiters are often installed at bus-ties / couplers to limit the fault contribution from one or more bus sections. This can allow the interconnection of systems that would normally have prospective short circuit currents exceeding fault ratings. IS limiters can also be installed at bus incomers to limit the upstream fault contribution. Parameter Settings IS limiters typically operate using a combination of two parameters: 

Trigger level



di/dt

Trigger Level The trigger level is the current magnitude at which the fault current limiter will initiate the transfer to the current limiting path (i.e. by activating the chemical charge). The trigger level is typically defined as the "the maximum short-circuit contribution permitted by a major power source, so that the total overall fault current superimposed from all short-circuit contributions will not exceed the momentary and interrupting ratings of the switchgear" [2]. The trigger level is set using trial and error, typically based on an initial trial value of the difference between the switchgear instantaneous rating and the peak instantaneous fault current. When selecting the trigger level, other considerations such as transformer inrush currents, overcurrent protection coordination and breaker operating margins should also be examined. di/dt The di/dt parameter is a value describing the minimum fault current rate of change (in kA/s) at which the transfer will be initiated. This is used to avoid nuisance tripping for asymmetrical faults that may have high peak values (above the trigger level), but rms values within the ratings of the switchgear. The transfer to the current limiting path will only be initiated if the fault current exceeds both the trigger level and di/dt limit. The di/dt limit can be approximated as follows [2]:

Where

is the system angular frequency (radians/s)

is the peak symmetrical short circuit current (A) References [1] Chao, T., "Electronically Controlled Current Limiting Fuses", 1995, Proceedings of 1995 IEEE Annual Pulp and Paper Industry Technology Conference, Vancouver, Canada [2] Wu, Al., and Yin,Y., "Fault-Current Limiter Applications in Medium- And High-Voltage Power Distribution Systems", 1998, IEEE Transactions on Industry Applications, Vol. 34, No. 1 Category: Protection

Overcurrent Protection Contents [hide] 



1 Recommended Settings o

1.1 Transformer Protection

o

1.2 Motor Protection

o

1.3 Branch / Feeder Protection

o

1.4 Generator Protection

2 References

Recommended Settings Transformer Protection Normally the transformers are protected by overcurrent protection devices at the primary (HV) and secondary (LV) winding. The primary winding overcurrent protection is typically set with three steps: 

The first step (I>) is adjusted to between 1.0 and 1.3 times the nominal current of the transformer with an inverse curve. A pickup of >1.25 times the nominal current is suggested by [6].



The second step (I>>) operates as back-up protection for short circuits at the secondary side of the transformer and is adjusted to 80% – 90% of the minimum possible short circuit at the low voltage terminal. This step is usually a definite time curve and is time selective with the protection at the secondary side.



The third step (I>>>) operates in instantaneous time and is adjusted to 110% - 120% of the maximum possible short circuit at the secondary side of the transformer. If the relay has only two steps, the second step will be adjusted according to I>>>.

The secondary winding overcurrent protection is typically set with two steps: 

The first step (I>) is adjusted to between 1.0 and 1.3 times the nominal current of the transformer if possible with an IDMT extremely inverse curve. A pickup of >1.25 times the nominal current is suggested by [6].



The second step (I>>) is used for short circuit protection and it is usually a definite time curve. The current setting of I>> is at maximum 80-90% of the minimum possible short circuit current and it has to be time selective with the downstream protection devices.

Protection devices should also consider transformer inrush currents. Overcurrent relays should not trip during energisation and inrush. An assumption of 20 times the nominal full load current for 10ms can be used to approximate inrush currents when no other data is available. Motor Protection

Thermal overload [49]: The current setting has been adjusted where possible between 1.0 and 1.1 times the motor nominal current. The nominal current of the motor has been taken from the load lists supplied by Petrobel staff. The time setting has been selected in order that the protection curve lay over the starting current at the maximum starting time of the motor but lower than the maximum permissible operation limit under warm condition. Short circuit and locked rotor protection [51, 51LR]: The setting for locked rotor protection has been selected between 1.0 and 1.1 times the motor starting current. The short circuit protection has been adjusted at maximum 80-90% of the minimum short circuit current at motor terminals but at least 1.5 times the starting current of the motor. The short circuit protection of almost all motors is done by fuses. Nevertheless in this study the setting for the short circuit protection has been calculated for all relays with this protection function available. For all motors where the or is not able to disconnect short circuit currents the undelayable short circuit protection has to be put out of service. The size of the recommended fuse has been selected in order that the nominal current of the fuse is higher than 130% of the nominal current of the motor and that the fuse curve is higher than 120% of the starting current of the motor. Branch / Feeder Protection Branches and feeders can be set with overcurrent protection devices of two steps. The first step will be usually adjusted to 120% of the nominal current of the branch. The second step has to be current and time selective with the downstream protection devices. Generator Protection The setting for the overload protection is suggested to be between 100% and 120% of the nominal current of the generators. The short circuit protection may be selected to 80% of the current contribution of each generator to the minimum short circuit current. References 

[1] IEEE Std 242, “IEEE Recommended Practice for Protection and Coordination – Industrial and Commercial Power Systems (Buff book)”, 2001



[2] IEEE Std 142, “ IEEE Recommended Practice for Grounding of Industrial and Commercial Power systems (Green book)”, 2007



[3] Alstom Grid, “ Network Protection and Automation Guide”, May 2011



[4] Preve, C., “Protection of Electrical Networks”, 2006, ISTE Ltd, London



[5] Fielding, G., “Protection of MV Industrial Networks”, 1997, IEE Colloquium, London



[6] Gers, J. M., and Holmes, E. J., “Protection of Electricity Distribution Networks”, 2nd Edition, Institution of Electrical Engineers, London, 2004

Category: Protection Protection Devices 

12 – Overspeed Device



14 – Underspeed Device



21 – Distance Relay



25 – Synchronizing or Synchronism-Check Device



27 – Undervoltage Relay



32 – Directional Power Relay



37 – Undercurrent or Underpower Relay



38 – Bearing Protective Device



40 – Field (over/under excitation) Relay



46 – Reverse-phase or Phase-Balance Current Relay



47 – Phase-Sequence or Phase-Balance Voltage Relay



48 – Incomplete Sequence Relay



49 – Machine or Transformer, Thermal Relay



50 – Instantaneous Overcurrent Relay



50N – Instantaneous Overcurrent Relay (Earth Fault)



51 – AC Inverse Time Overcurrent Relay



51N – AC Inverse Time Overcurrent Relay (Earth Fault)



53 – Exciter or DC Generator Relay



55 – Power Factor Relay



56 – Field Application Relay



58 – Rectification Failure Relay



59 – Overvoltage Relay



60 – Voltage or Current Balance Relay



64 - Ground Detector Relay



67 – AC Directional Overcurrent Relay



68 – Blocking or "Out-of-Step" Relay



76 – DC Overcurrent Relay



79 – AC Reclosing Relay



81 – Frequency Relay



82 – DC Reclosing Relay



83 – Automatic Selective Control or Transfer Relay



85 – Communications,Carrier or Pilot-Wire Relay



86 – Lockout Relay



87 – Differential Protective Relay



91 – Voltage Directional Relay



92 – Voltage and Power Directional Relay



94 – Tripping or Trip-Free Relay

For the entire list of ANSI device numbers, refer to this Wikipedia page.

Relays Contents [hide] 

1 Introduction o

1.1 Overcurrent relays 

1.1.1 Overcurrent relays - instantaneous



1.1.2 Overcurrent relays – inverse time



1.1.3 Overcurrent relays – induction disk

o

1.2 Recommended settings for overcurrent protection

o

1.3 Small air breakers for low voltage domestic circuits

o

1.4 Differential (unit) protection

o

1.5 Distance relays

o



1.5.1 Impedance relays



1.5.2 ittance relays



1.5.3 Reactance relays

1.6 Trivia

Introduction The relays is the element that senses an abnormal condition in the circuit and commands the operation of the breaker. They can be classified in a number of ways: 

According to the quantity sensed: current, voltage, active power, reactive power, impedance relays



According to the tripping: instantaneous trip, delayed trip, inverse timecurrent response



According to the operating principle: electromagnetic relays, induction relays, thermal relays, static or digital relays

More general classification distinguish two types of relays: 

1. Electromechanical relays



2. Digital relays

Currently, electromechanical relay in all its forms is being replaced by static, digital and numerical relays, each change bringing with it reductions and size and improvements in functionality. In most types (except digital relays) the relays s are closed by a moving part which senses a force proportional to the current (or other sensed quantity) in the circuit. A restraining force produced by a spring or other means sets the threshold above which the relay operates. In a protection relay, the term "static" refers to the absence of moving parts to create the relay characteristic. Compared to static relays, digital relays introduced A/D conversion of all measured analogue quantities and use a microprocessor to implement protection algorithm. The distinction between digital and numerical relays rests on points of fine technical detail, and is rearly found in areas other than protection. They can be viewed as natural developments of digital relays as a result of advances in technology.

Relay timing mechanisms: a) Instantaneous, b) Inverse time, c) Timed Overcurrent relays IEC definition states that overcurrent relay is a measuring relay which operates when the value of the current exceeds the setting (operating value) of the relay. There are generally 3 types of these relays: instantaneous, inverse and induction. Relays are adaptable to transmission lines, buses, feeder circuits, transformers and motors. Overcurrent relays - instantaneous Overcurrent relays are electromagnetic relays. They are based on electrodynamic force produced on a moving part by the current flowing through a coil. Instantaneous relays operate without intentional time delay. They are used for faults close to the source when the fault current is very high. The operating time is approximately 10 ms. The construction of instantaneous relays is usually moving armature, plunger, or induction disk. An important characteristic of an instantaneous relay is a drop-out ratio. drop-out ratio = (drop-out current) / (pick-up current) Drop-out ratio is usually less than 1.

Instantaneous overcurrent relay

Instantaneous overcurrent protection

MCTI instantaneous overcurrent relay

Overcurrent relays – inverse time Time overcurrent relays operate with a time delay, which is adjustable. For given setting, the actual time delay depends on the current through the relay coil. Higher current will cause a faster operation of the relay. The minimum relay operation current (pick-up current) is also adjustable. The most commonly used overcurrent relay has both the instantaneous response for very large currents and the inverse time response for lower currents. Time overcurrent relays come in five different versions that are defined by the steepness of the time-overcurrent characteristic: 

definite time



moderately inverse



inverse



very inverse



extremely inverse

Inverse time overcurrent relay characteristics, different delay settings

Time overcurrent relay characteristics, all versions

Inverse time overcurrent relay

Overcurrent relays – induction disk The inverse time response can be provided by an induction disk unit. In the induction disk unit, a metal disk is mounted on a shaft that can freely rotate. The current coils are fixed and create magnetic field that induces eddy currents in the metal disk. The magnetic field of the eddy currents interacts with the magnetic field of the stationary coils and produce torque on the disk. The disk and its shaft rotate and bring the moving towards the fixed into a closed position. The motion of the shaft is opposed by a spring that returns the disk and the moving into the open position when the current drops below a preset value. The time to close the depends on the travel distance which is set by a time dial. The pick-up current is adjustable by selecting current taps on the current coil. The relays are normally available with three ranges of current taps: 0.5 to 2.0 A, 1.5 to 6.0 A, and 4 to 16 A. The time dial has usually positions marked from 0 to 10, where for 0 setting the is permanently closed.

Induction disk overcurrent relay Induction disk type relay Recommended settings for overcurrent protection More on recommended settings for overcurrent devices: Overcurrent Protection Small air breakers for low voltage domestic circuits Circuit breakers that are used at the distribution board in houses are called MCBs (minature circuit breakers). The distribution board is also called the consumer unit. Thermal The load current is ed through a small heater, the temperature of which depends upon the current it carries. The heater will warm up a bimetal strip. When excessive current flows the bimetal strip will warp to trip the latch mechanism. Some delay occurs owing to the transfer of heat produced by the load current to the bimetal strip. Thermal trips are suitable only for small overloads of long duration. Excessive heat caused by heavy overload can buckle and distort the bimetal strip. Magnetic The principle used in this type is the magnetic force of attraction set up by the magnetic field of a coil carrying the load current. At normal currents the magnetic field is not strong enough to attract the latch. Overload currents will increase the force of attraction and operate the latch to trip the main s. Inside a 10 amp thermal-magnetic circuit breaker. These circuit breakers are standard in modern domestic and commercial electrical distribution boards.

Simple MCB

Cross-section of the thermal-magnetic circuit breaker

Thermal-magnetic circuit Typical magnetic circuit breaker

breaker (1Ph + N) 2A250VAC

Number description: 1. Actuator lever - used to manually trip and reset the circuit breaker. Also indicates the status of the circuit breaker (On/Off/tripped). 2. Actuator mechanism - forces the s together or apart. 3. s - Allow current to flow when touching and break the flow of current when moved apart. 4. Terminals 5. Bimetallic strip 6. Calibration screw - allows to adjust the trip current of the device after assembly. 7. Solenoid 8. Arc divider / extinguisher Differential (unit) protection Differential protection is a very reliable method of protecting generators, transformers, buses, and transmission lines from the effects of internal faults. In normal operating conditions, the current through the CTs is the same so the relay sees no differential current. This is also the case

for external faults. Differential protection can be used for protecting generators from faults to ground. Differential protection of busbars in substations uses one CT for each incoming line. All incoming currents are added up and compared to the sum of all outgoing currents.

Microproce General schematics of the differential relay Differential (unit) protection for transformers In applying the principles of differential protection to transformers, a variety of considerations have to be taken into . These include: a) correction for possible phase shift across the transformer windings (phase correction) b) the effects of the variety of earthing and winding arrangements (filtering of zero sequence currents) c) correction for possible unbalance of signals from current transformers on either side of the windings (ratio correction) d) the effect of magnetising inrush during initial energisation e) the possible occurrence of overfluxing The primary and secondary currents have different magnitudes and phases, so the magnitude and the phase shift must be balanced by appropriate ratio of the CTs. If the transformer is Y-Δ, the currents also have 30° phase shift. The phase shift is corrected by connecting the CTs on the Δ side in Y, and on the Y side in Δ.

relay

Differential protection in transformers When used on the overhead lines, the differential protection has the practical length limitation of 40 km for problems with the pilot wire (wire used to transfer state data of the protected line, i.e. to send information if the fault has occured). Distance relays The impedance of a transmission line is proportional to its length, for distance measurement it is appropriate to use a relay capable of measuring the impedance of a line up to a predetermined point (the reach point). Such a relay is described as a distance relay and is designed to operate only for faults occurring between the relay location and the selected reach point, thus giving discrimination for faults that may occur in different line sections. The basic principle of distance protection involves the division of the voltage at the relaying point by the measured current. The apparent impedance so calculated is compared with the reach point impedance. If the measured impedance is less than the reach point impedance, it is assumed that a fault exists on the line between the relay and the reach point. The reach point of a relay is the point along the line impedance locus (set of points) that is intersected by the boundary characteristic of the relay. Since this is dependent on the ratio of voltage and current and the phase angle between them, it may be plotted on an R/X diagram. The loci of power system impedances as seen by the relay during faults, power swings and load variations may be plotted on the same diagram and in this manner the performance of the relay in the presence of system faults and disturbances may be studied.

General setting of the distance protec

As the power systems become more complex and the fault current varies with changes in generation and system configuration, directional overcurrent relays become difficult to apply and to set for all contingencies, whereas the distance relay setting is constant for a wide variety of changes external to the protected line. Following topics give the main overview over the different distance relay types: Impedance relays Impedance relays are used whenever overcurrent relays do not provide adequate protection. They function even if the short circuit current is relatively low. The speed of operation is independent of current magnitude. The relay consists of a balanced beam. At each end of the balanced beam is a coil that exerts a force on the beam at that end. One coil is connected to a current transformer, the other coil to a potential transformer. Under normal conditions, the of the relay is kept open. During a fault, the voltage drops, and the current rises. The torque due to the current coil overpowers the torque due to the voltage coil, and the relay closes its . The impedance relay has a circular characteristic centered at the origin of the R-X diagram. It is nondirectional and is used primarily as a fault detector. ittance relays The ittance relay is the most commonly used distance relay. It is the tripping relay in pilot schemes and as the back-up relay in step distance schemes. Its characteristic es through the

origin of the R-X diagram and is therefore directional. In the electromechanical design it is circular, and in the solid state design, it can be shaped to correspond to the transmission line impedance. Reactance relays The reactance relay is a straight-line characteristic that responds only to the reactance (X L) of the protected line. It is nondirectional and is used to supplement the ittance relay as a tripping relay to make the overall protection independent of resistance. It is particularly useful on short lines where the fault arc resistance is the same order of magnitude as the line length. Trivia MCB short overview:

Category: Protection Zones of protection To limit the extent of the power system that is disconnected when a fault occurs, protection is arranged in zones. Ideally, the zones of protection should overlap, so that no part of the power system is left unprotected. For practical physical and economic reasons, this ideal is not always achieved, accommodation for current transformers being in some cases available only on one side of the circuit breakers. This leaves a section between the current transformers and the circuit breaker A that is not completely protected against faults. In Figure 2 b) a fault at F would cause the busbar protection to operate and open the circuit breaker but the fault may continue to be fed through the feeder. The feeder protection, if of the unit type, would not operate, since the fault is outside its zone. This problem is dealt with by intertripping or some form of zone extension, to ensure that the remote end of the feeder is tripped also. The point of connection of the protection with the power system usually defines the zone and corresponds to the location of the current transformers. Unit type protection will result in the boundary being a clearly defined closed loop. Figure 3 illustrates a typical arrangement of overlapping zones. Alternatively, the zone may be unrestricted; the start will be defined but the extent (or ‘reach’) will depend on measurement of the system quantities and will therefore be subject to variation, owing to changes in system conditions and measurement errors.

Figure 3 Overlapping zones of protection systems

Figure 2 CT locations Figure 1 Division of power system into protection zones Selectivity When a fault occurs, the protection scheme is required to trip only those circuit breakers whose operation is required to isolate the fault. This property of selective tripping is also called 'discrimination' and is achieved by two general methods: 

1. Time Grading

Protection systems in successive zones are arranged to operate in times that are graded through the sequence of equipments so that upon the occurrence of a fault, although a number of protection equipments respond, only those relevant to the faulty zone complete the tripping

function. The others make incomplete operations and then reset. The speed of response will often depend on the severity of the fault, and will generally be slower than for a unit system. 

2. Unit Systems

It is possible to design protection systems that respond only to fault conditions occurring within a clearly defined zone. This type of protection system is known as 'unit protection'. Certain types of unit protection are known by specific names, e.g. restricted earth fault and differential protection. Unit protection can be applied throughout a power system and, since it does not involve time grading, is relatively fast in operation. The speed of response is substantially independent of fault severity. Unit protection usually involves comparison of quantities at the boundaries of the protected zone as defined by the locations of the current transformers. This comparison may be achieved by direct hard-wired connections or may be achieved via a communications link. However certain protection systems derive their 'restricted' property from the configuration of the power system and may be classed as unit protection, e.g. earth fault protection applied to the high voltage delta winding of a power transformer. Whichever method is used, it must be kept in mind that selectivity is not merely a matter of relay design. It also depends on the correct coordination of current transformers and relays with a suitable choice of relay settings, taking into the possible range of such variables as fault currents, maximum load current, system impedances and other related factors, where appropriate. Category: Protection Resistance Test The resistance test (commonly known as the Ductor test) measures the resistance of electrical connections such as ts, terminations, connectors, etc. These can be connections between any two conductors, for instance busbar sections or cable connections. The test measures the resistance at the micro- or milli-ohm level and is used primarily to that electrical connections are made properly, and can detect the following problems: 

Loose connections



Adequate tension on bolted ts



Eroded surfaces



Contaminated or corroded s

This is particularly important for s that carry large amounts of current (e.g. switchgear busbars) as higher resistance leads to higher losses and lower current carrying capacity. Test Equipment resistance tests are normally performed using a micro/milli-ohmmeter or low resistance ohmmeter. "Ductor" was the name originally given to the low resistance ohmmeter manufactured by the Megger company, which became an industry standard. Test Criteria The criteria for evaluating the resistance of electrical connections largely depends on the type of connection (e.g. bolted, soldered, clamped, welded, etc), the metallic surface area, the pressure, etc. These will differ by equipment and manufacturer and there is no

code or standard that mandates minimum resistances. As such, manufacturer recommendations need to be consulted. For example, manufacturers sometimes quote a maximum resistance of 10 micro-ohms for large bolted busbar ts. International Standards 

ASTM B539-02 (R2008), "Standard Test Method for Measuring Resistance of Electrical Connections (Static s)"

Category: Electrical Testing Category:Electrical Testing Contents [hide] 

1 Introduction



2 Types of Tests



3 Tests for Specific Equipment



4 Standards

Introduction Types of Tests Electrical tests for assessing insulation systems: 

Insulation resistance test (Megger)



Dielectric absorption test (Time-resistance)



High voltage tests with DC voltages



High voltage tests with AC voltages



High voltage tests with impulse voltages



Dielectric loss angle test



Partial discharge test

Chemical tests for oil-paper insulation systems: 

Dissolved gas analysis



Oil sample tests

Other tests: 

resistance test (Ductor)



Thermographic imaging surveys



Frequency response analysis



Load Bank Testing

Tests for Specific Equipment 

Transformer impedance (short-circuit) tests - short-circuit tests for positive and zero sequence impedance of transformers



Dry-type transformer testing

Standards 

ANSI/NETA ATS, "Standard for Acceptance Testing Specifications for Electrical Power Equipment and Systems", 2009

Pages in category "Electrical Testing" The following 9 pages are in this category, out of 9 total. DGA Testing Contents [hide] 

1 Introduction



2 Interpretation of Results



3 Types of Faults



4 References

Introduction Dissolved Gas Analysis (DGA) is a test used to assess paper-oil insulation systems, and the most commonly used technique for oil-insulated power transformers. Over time (and due to electrical stresses and thermal decomposition), the cellulose paper and insulating (mineral) oil in paper-oil insulation systems break down and forms gases which are dissolved in the oil. In DGA testing, a sample of oil is collected and analysed for the types, volumes, concentrations and formation rates of dissolved gases. This can provide important information on the condition of the insulation system, as well as the nature of the electrical disturbances that the system has been subjected to. Gas decomposition typically involves chemical reactions that break up the carbon and hydrogen bonds of the hydrocarbon chains in both the cellulose and oil. The following gases are most commonly formed and are considered the most significant in the context of DGA testing: 

From insulating oil: hydrogen (H2), methane (CH4), acetylene (C2H2), ethylene (C2H4) and ethane (C2H6)



From cellulose: hydrogen (H2), methane (CH4, carbon monoxide (CO) and carbon dioxide (CO2)

Interpretation of Results ANSI/IEEE Std C57.104 [1] provides guidance on concentration limits of the key gases:

Interpretati

Dissolved gas concentration limit (ppm)

on

Carbo Hydroge

Methan

Acetylen

n (H2)

e (CH4)

e (C2H2)

Ethylen

Ethan

Carbon

n

e

e

monoxid

dioxid

(C2H4)

(C2H6) e (CO)

e

TDC G (*)

(CO2)

100

120

101 -

121 -

700

400

701 -

401 -

1800

1000

1

50

2-9

51 - 100

10 - 35

65

350

2500

720

Satisfactory

66 -

351 -

2500 -

721 -

Fault may be

100

570

4000

1920

present

101 -

101 -

571 -

4001 -

200

150

1400

10000

1921 4630

Fault probably present

Continued >1800

>1000

>35

>200

>150

>1400

>1000

>463

operation

0

0

could result in failure

(*) TDCG = Total dissolved combustible gas Types of Faults The relative proportions of gas types can suggest the type of fault that has occurred in the transformer to form the particular gases, as shown in the figure below (courtesy of IEEE C57.104 [1]):

References 

[1] ANSI/IEEE C57.104, IEEE Guide for the Interpretation of Gases Generated in OilImmersed Transformers, 2008



[2] IEC 60599, Mineral oil-impregnated electrical equipment in service - Guide to the interpretation of dissolved and free gases analysis, 1999

Category: Electrical Testing DLA Testing Dielectric loss angle tests, also called dissipation factor, power factor or tan delta tests, determine the insulation dielectric power loss by measuring the power angle between an applied AC voltage and the resultant current. In the ideal insulator / dielectric, the power angle would be 90°C as it is purely capacitive and non-conducting. However in real insulators, there is some leakage current and resistive losses through the dielectric. Relative increases in dielectric power losses are indicative of insulation deterioration and may further accelerate degradation due to increased heating. Note that dielectric power loss does not translate to dielectric strength, though there are often common causes for increases in power loss and decreases in dielectric strength. Contents [hide]



1 Relationship between Power Factor and Dissipation Factor



2 Measurement o

2.1 Schering Bridge

o

2.2 Transformer Ratio-Arm Bridge



3 Interpretation of Results



4 References

Relationship between Power Factor and Dissipation Factor

The cosine of the power angle (θ) is called the power factor. The complement of θ is called the loss angle and is denoted by δ in the diagram above. The power factor can also be approximated by taking the tangent of δ (hence the name tan delta). This approximation is called the dissipation factor (or loss tangent) and is roughly equal to the power factor between values of 0 and 0.08 pu, which covers the majority of tests (in insulating oils of good condition, the dissipation factor / power factor is in the order 0.005). Therefore, dissipation factor and power factor can be considered interchangeable. The exact relationship between dissipation factor (DF) and power factor (PF) is as follows [2]:

The dissipation factor is essentially the ratio between the resistive and capacitive components of the insulation and can be measured directly (e.g. with a capacitance bridge circuit - more on this later). The lower the quality of the insulation condition, the more resistive it will appear and the more power loss will be dissipated through it (in the form of heat), and thus the dissipation factor will be higher. The increase in the dissipation factor values as the test voltage is increased is called the "tip-up" (dissipation factor or power factor tip-up). Measurement Schering Bridge

Schering capacitance bridge circuit As mentioned earlier, the dissipation factor can be measured directly using a Schering capacitance bridge circuit (named after Harald Schering). The basic circuit is shown in the figure right where Cx is the unknown capacitance under test. Like other bridge circuits (such as the Wheatstone bridge), the circuit is tuned until the current through the middle of the bridge is zero and the circuit is balanced. For a capacitanceCn with low losses, the unknown capacitance and dissipation factor can be calculated as follows:

The Schering bridge is typically accurate for measuring dissipation factors down to 0.001 (i.e. good for liquid insulating materials). For other solid insulating materials such as XLPE and polypropylene that have dissipation factors <0.001, the Schering bridge may not be able to provide the accuracy without careful screening and good earthing. Transformer Ratio-Arm Bridge TBA Interpretation of Results

Dissipation factor or power factor is either expressed as a decimal per-unit value (e.g. 0.005) or as a percentage (e.g. 0.5%). TBA The technical literature on this subject has noted that this test is useful for detecting moisture ingress in bushings and windings. About 90% of bushing failures may be attributed to moisture ingress evidenced by an increasing power factor from dielectric loss angle testing on a scheduled basis. References 

[1] ANSI/NETA ATS, "Standard for Acceptance Testing Specifications for Electrical Power Equipment and Systems", 2009



[2] ASTM D924, "Standard Test Method for Dissipation Factor (or Power Factor) and Relative Permittivity (Dielectric Constant) of Electrical Insulating Liquids", 2008



[3] ASTM D150, "Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation", 2011

Category: Electrical Testing Insulation Resistance Test The insulation resistance (IR) test (also commonly known as a Megger) is a spot insulation test which uses an applied DC voltage (typically either 250Vdc, 500Vdc or 1,000Vdc for low voltage equipment <600V and 2,500Vdc and 5,000Vdc for high voltage equipment) to measure insulation resistance in either kΩ, MΩ or GΩ. The measured resistance is intended to indicate the condition of the insulation or dieletric between two conductive parts, where the higher the resistance, the better the condition of the insulation. Ideally, the insulation resistance would be infinite, but as no insulators are perfect, leakage currents through the dielectric will ensure that a finite (though high) resistance value is measured. Because IR testers are portable, the IR test is often used in the field as the final check of equipment insulation and also to confirm the reliability of the circuit and that there are no leakage currents from unintended faults in the wiring (e.g. a shorted connection would be obvious from the test results). One of the advantages of the IR test is its non-destructive nature. DC voltages do not cause harmful and/or cumulative effects on insulation materials and provided the voltage is below the breakdown voltage of the insulation, does not deteriorate the insulation. IR test voltages are all well within the safe test voltage for most (if not all) insulation materials. Contents [hide] 

1 Test Equipment



2 Test Procedure



3 Interpretation of Test Results



4 Factors Affecting Test Results o

4.1 Temperature

o

4.2 Humidity



5 Related Tests



6 References

Test Equipment

IR test set (courtesy ofMegger) The Megger company were the original manufacturers of IR test equipment over 100 years ago and have become synonymous with insulation resistance testing. Most modern IR testers are digital, portable / handheld units and some have multi-functional capabilities (e.g. built-in continuity testing). Test Procedure Firstly ensure that the equipment to be tested and the work area is safe, e.g. equipment is deenergised and disconnected, all the relevant work permits have been approved and all locks / tags in place. Next, discharge capacitances on the equipment (especially for HV equipment) with static discharge sticks or an IR tester with automatic discharging capabilities. The leads on the IR tester can then be connected to the conductive parts of the equipment. For example, for a three-core and earth cable, the IR test would be applied between cores (Core 1 to Core 2, Core 1 to Core 3 and Core 2 to Core 3) and between each core and earth. Similarly for three-phase motors, circuit breakrs, switch-disconnectors, etc the IR test can be applied at the equipment terminals (and earth connection). Note that when applying an IR test to earth, it is good practice to connect the positive pole of the IR tester to earth in order to avoid any polarisation effects on the earth. Once connected, the IR tester is energised for a typical test duration of 1 minute. The IR test measurements are recorded after 1 minute. When the IR test is finished, discharge capacitances again for a period of 4-5 times the test duration.

Interpretation of Test Results The minimum values for IR tests vary depending on the type of equipment and the nominal voltage. They also vary according to international standards. Some standards will define the minimum IR test values for the general electrical installations. For example, for low voltage installations in the IEC world, IEC 60364-6 [1] Table 6A gives the minimum IR values and also suggests test voltage, i.e. Nominal Circuit Voltage (Vac)

Test Voltage (Vdc)

Insulation Resistance (MΩ)

Extra low voltage

250

0.5

Up to 500V

500

1.0

Above 500V

1,000

1.0

In the ANSI/NEC world, the standard ANSI/NETA ATS-2009 [2] provides test procedures and acceptance levels for most types of electrical equipment. Table 100.1 provides representative acceptance values for IR test measurements, which should be used in the absence of any other guidance (from the manufacturer or other standards): Nominal Equipment Voltage

Min Test Voltage

Min Insulation Resistance

(Vac)

(Vdc)

(MΩ)

250

500

25

600

1,000

100

1,000

1,000

100

2,500

1,000

500

5,000

2,500

1,000

8,000

2,500

2,000

15,000

2,500

5,000

25,000

5,000

20,000

34,500 and above

15,000

100,000

NFPA 70B [3] also provides some guidance on insulation resistance testing for different types of equipment. Factors Affecting Test Results There are two main factors that will affect IR test results: Temperature Electrical resistance has an inverse exponential relationship with temperature, i.e. as temperature increases, resistance will decrease and vice versa. Since the minimum acceptable IR test values are based on a fixed reference temperature (usually 20 oC), the measured IR test values must be corrected to the reference temperature in order to make sense of them. As a rule of thumb, the resistance halves for every 10oC increase in temperature (and vice versa). So if the measured IR test value was 2MΩ at 20oC, then it would be 1MΩ at 30oC or 4MΩ at 10oC. ANSI/NETA ATS-2009 Table 100.14 provides correction factors for IR test measurements taken at temperatures other than 20oC or 40oC, which were in turn based on the correction factors in the freely available Megger book "A stitch in time..." [4]. Humidity The presence (or lack) of moisture can also affect the IR test measurements, the higher the moisture content in the air, the lower the IR test reading. If possible, IR tests should not be carried out in very humid atmospheres (below the dew point). While there are no standard correction factors or guidance for humid conditions, it is good practice to record the relative humidity of each IR test so that they can be used for baseline comparisons in future tests. For example, having past data on the IR test values for dry and humid days will give you a foundation for evaluating future test values. Related Tests For equipment maintenance, the Dielectric Absorption Test is normally performed in conjunction with the IR test using the same testing equipment. The results are either in the form of a Dielectric Absorption Ratio (DAR) or a Polarisation Index (PI). Refer to the Dielectric Absorption Test article for more details. References 

1. IEC 60364-6, "Low voltage electrical installations - Part 6: Verification", 2006



2. ANSI/NETA ATS, "Standard for Acceptance Testing Specifications for Electrical Power Equipment and Systems", 2013



3. NFPA 70B, "Recommended Practice for Electrical Equipment Maintenance", 2013



4. Megger, "A stitch in time - The Complete Guide to Electrical Insulation Testing", a free book which is an excellent resource on IR testing

Category: Electrical Testing Load Bank Testing The purpose of a load bank test is to simulate real-world scenarios that can be used to confirm proper functionality. Load banks are provided to simulate electrical load, as it is important to test various electrical apparatus in its installed location. While the equipment under test (EUT) may have been tested at the factory, the installation variables (Eg. altitude, ambient temperature, air intake, fuel, exhaust, cooling systems and contractor/sub-contractor workmanship quality) can be significantly affected by the installation. The proper use of a load bank can be used to effectively test the operating capability of the complete system, as delivered from the manufacturer. A load bank is a device which develops an electrical load, applies the load to an electrical power source and converts or dissipates the resultant power output of the source. The purpose of a load bank is to accurately mimic the operational or “real” load that a power source will see in actual application. However, unlike the “real” load, which is likely to be dispersed, unpredictable and random in value, a load bank provides a contained, organized and fully controllable load. Consequently, a load bank can be further defined as a self-contained, unitized, systematic device that includes load elements with control and accessory devices required for operation. Whereas the “real” load is served by the power source and uses the energy output of the source for some productive purpose, the load bank serves the power source, using its energy output to test, or protect the power source. Contents [hide] 

1 Applications



2 Load bank types o

2.1 Resistive load bank

o

2.2 Reactive load banks

o 



2.2.1 Inductive load banks



2.2.2 Capacitive load banks

2.3 Resistive/Reactive load banks

3 Alternative load banks o

3.1 Electronic load banks

o

3.2 Water-Cooled load banks



o

3.3 Medium-Voltage load banks

o

3.4 Server Simulating load banks

o

3.5 Non-linear load banks

o

3.6 400Hz load banks

o

3.7 Regenerative load banks

o

3.8 Resonant load banks

4 Load Bank Manufacturers

Applications Load banks are used in a variety of applications, including: 

Factory testing of turbines and engine diesel generator sets



Reduction of wet stacking problems

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Periodic exercising of stand-by engine generator sets



Battery and UPS system testing



Ground power testing



Load optimization in prime power applications



Removal of carbon build-up on piston rings



Load rejection test

Load bank types The three most common types of load banks are resistive, inductive, and capacitive. Both inductive and capacitive loads create what is known as reactance in an AC circuit. Reactance is a circuit element's opposition to an alternating current, caused by the build up of electric or magnetic fields in the element due to the current and is the "imaginary" component of impedance, or the resistance to AC signals at a certain frequency. Capacitive reactance is equal to 1/(2⋅π⋅f⋅C), and inductive reactance is equal to 2⋅π⋅f⋅L. The unit of reactance is the ohm. Inductive reactance resists the change to current, causing the circuit current to lag voltage. Capacitive reactance resists the change to voltage, causing the circuit current to lead voltage. Resistive load bank A resistive load bank, the most common type, provides equivalent loading for both generators and prime movers. That is, for each kilowatt (or horsepower) of load applied to the generator by the load bank, an equal amount of load is applied to the prime mover by the generator. A resistive load bank, therefore, removes energy from the complete system: load bank from generator—generator from prime mover—prime mover from fuel. Additional energy is removed as a consequence of resistive load bank operation: waste heat from coolant, exhaust and generator losses and energy consumed by accessory devices. A resistive load bank impacts upon all aspects of a generating system.

The load of a resistive load bank is created by the conversion of electrical energy to heat via high-power resistors such as grid resistors. This heat must be dissipated from the load bank, either by air or by water, by forced means or convection. In a testing system, a resistive load simulates real-life resistive loads, such as incandescent lighting and heating loads as well as the resistive or unity power factor component of magnetic (motors, transformers) loads. The most common type uses wire resistance, usually with fan cooling, and this type is often portable and moved from generator to generator for test purposes. Sometimes a load of this type is built into a building, but this is unusual. Rarely a salt water rheostat is used. It can be readily improvised, which makes it useful in remote locations. Reactive load banks Inductive load banks An inductive load includes inductive (lagging power factor) loads. An inductive load consists of an iron-core reactive element which, when used in conjunction with a resistive load bank, creates a lagging power factor load. Typically, the inductive load will be rated at a numeric value 75% that of the corresponding resistive load such that when applied together a resultant 0.8 power factor load is provided. That is to say, for each 100 kW of resistive load, 75 kVAr of inductive load is provided. Other ratios are possible to obtain other power factor ratings. An inductive load is used to simulate a real-life mixed commercial loads consisting of lighting, heating, motors, transformers, etc. With a resistive-inductive load bank, full power system testing is possible, because the provided impedance supplies currents out of phase with voltage and allows for performance evaluation of generators, voltage regulators, load tap changers, conductors, switchgear and other equipment. Capacitive load banks An capacitive load includes capacitive (leading power factor) loads. A capacitive load bank or capacitor bank is similar to an inductive load bank in rating and purpose, except leading power factor loads are created, so reactive power is supplied from these loads to the system, hence improves the power factor. These loads simulate certain electronic or non-linear loads typical of telecommunications, computer or UPS industries. Resistive/Reactive load banks These are a combination of primarily resistive and inductive load elements suitable for performing power factor testing. Resistive/reactive combination load banks are used to test the engine generator set at its rated power factor and in the majority of cases this will be 0.8 power factor. The reactive component of the load will have a current that “lags” the voltage. The resulting power is described in two , the KW, or real power and the KVA or apparent power. Since the current lags the voltage in the reactive load the total power is not the direct sum of the two but their vector sum. That vector is the phase angle difference between the voltage and the

current. The combination of resistive and reactive current in the load will allow for the full nameplate KVA rating of the generator windings to be tested. Even though the generator set is producing more KVA it is actually not producing more KW. The “real” power or horsepower required from the engine is essentially the same. Alternative load banks Electronic load banks An electronic load bank tends to be a fully programmable, air- or water-cooled design used to simulate a solid state load and to provide constant power and current loading on circuits for precision testing. These units tend to be somewhat rare, but are great for testing labs to perform constant power, voltage and current load tests. Water-Cooled load banks Often times, situations require customers to test power supplies, namely generators and UPS systems, in locations that are not conducive to normal forced – air cooled load banks, either due to environment or physical constraints. For example, a UPS system that is underground, located in a parking garage or located on top of a rooftop. In these situations, very long runs of cable sometimes more then 300'+ may be used, but due increased resistance and subsequent voltage – drop, may pose and add to the existing challenge. In addition to the above scenario, water – cooled load banks can be used to provide heated water to simulate water – based server and or chillers So this leaves us with an open – loop, water – cycle load cell, whereby chilled water is supplied to a device with heating elements. An easy way to envision this is to think of it as an expensive hot – water heater. Medium-Voltage load banks The notion of using medium – voltage load bank for portable testing purpose, came about from thinking outside the box. The extra logistics costs for transporting, craning into position and connecting the low – voltage cable, became rather tedious. A medium – voltage load bank is just like any other load bank in that it contains resistors, reactors or capacitors. However, the voltage ratings are greater than 600 VAC and below 69,000 VAC. Medium – voltage load banks are often used for commissioning power plants, maritime electrical systems, standby generator systems and substations, essentially the same as low – voltage load banks, the only difference being the voltage. The alternate method of testing without medium voltage load banks is to use low – voltage load banks with step down transformers used to serve the low voltage load banks. Typically it is always advantageous to test with medium – voltage load banks versus just using low – voltage load banks, as the added logistics and procurement costs for low – voltage load banks are far more expensive.

Server Simulating load banks These are typically rack – mountable and used to simulate true hot – aisle/cold – aisle containment systems, heat and air flow. These simulate physical servers as installed at a data – center by way of heat – discharge, electrical – resistance and air – flow. The resultant heat output of the load banks are of a benefit in that they are used to load computer room air – conditioners, whilst creating an electrical load to the primary and standby systems in the data center. Non-linear load banks A load is considered non – linear if its impedance changes with the applied voltage. The changing impedance means that the current drawn by the non – linear load will not be sinusoidal even when it is connected to a sinusoidal voltage. These non – sinusoidal currents contain harmonic currents that interact with the impedance of the power distribution system to create voltage distortion that can affect both the distribution system equipment and the loads connected to it. In the past, non – linear loads were primarily found in heavy industrial applications such as arc furnaces, large variable frequency drives (VFD), heavy rectifiers for electrolytic refining, etc. The harmonics they generated were typically localized and often addressed by knowledgeable experts. Times have changed and harmonic problems are now common in not only industrial applications but in commercial buildings as well. This is due primarily to new power conversion technologies, such as the Switch – mode Power Supply (SMPS), which can be found in virtually every power electronic and power conversion device. Namely wind – farms are notorious for this and require special considerations due tot eh extra harmonic content. 400Hz load banks These are normally used on aircraft and ship based systems that require commissioning or testing before being placed in service. 400 Hz systems are used where weight is important because the magnetic cores can be smaller/lighter. This applies to transformers as well since a lower inductance (smaller core/number of turns) can be used than required by lower frequencies. It is worthy to note that resistors rated for 60Hz can operate at the higher value of 400Hz without a problem, but inductors and capacitors cannot. Regenerative load banks Reverse power/regenerative power protection of generator by sensing power direction, magnitude and automatic addition to act as a power sink. These are seen primarily used to capture and dissipate regenerative power from large motors and are found in the following settings: 

Cranes and rigs



Mining



Cable laying vessels



Elevators

Resonant load banks Resonant loads are becoming increasingly prevalent due to solar inverter anti – islanding testing and commissioning per IEEE on photovoltaic systems. These are comprised of an exact balance of resistive, capacitive and inductive loads in a 1:1:1, or 1:2.5:2.5 ratios so as to provide a specific quality – factor. Many solar inverters are designed to be connected to a utility grid, and will not operate when they do not detect the presence of the grid. They contain special circuitry to precisely match the voltage and frequency of the grid. Traditional utility electric power systems were designed to a one way power flow from the point of generation through a transmission system to distribution level loads. These systems were not originally intended to accommodate the back – feed of power from distributed generation systems at the distribution level. Islanding refers to the condition in which a distributed generator continues to power a location even though electrical grid power when the electric utility is no longer present. Islanding can be dangerous to utility workers, who may not realize that a circuit is still powered, and it may prevent automatic re – connection of devices. For that reason, distributed generators must detect islanding and immediately stop producing power; this is referred to as anti – islanding. Load Bank Manufacturers Here is a brief listing of commonly known load bank manufacturers: 

Avtron



Loadtec



Cannon



Hawthorne



Crestchic UK



Northbridge



Froment



Simplex

Note: This listing is by no way complete or absolute. Category: Electrical Testing

Partial Discharge A partial discharge, as defined by IEC 60270, is a "localised electrical discharges that only partially bridges the insulation between conductors and which can or cannot occur adjacent to conductors". In other words, it is a partial breakdown in the insulation between two active conductors. Partial discharges can occur in any location where the local electrical field strength is sufficient to breakdown that portion of the dielectric material (whether it be a deteriorated piece of insulation

or an air cavity). The discharges generally appear as pulses with a typical duration of less than 1us. While very short in duration, the energy present in the discharge can interact with the surrounding dielectric material resulting in further insulation degradation and eventually if left unchecked, insulation failure. Partial Discharge Testing Partial discharge testing can detect the presence and location of partial discharge activity in electrical equipment. Suppose a piece of electrical equipment has a small air cavity in its insulation due to prolonged degradation and the cavity is subject to partial discharge. We want to test for partial discharge and so we connect a set of coupling capacitors in parallel to measure the charges caused by the partial discharge.

Partial discharge equivalent circuit with test circuit The figure right shows a simplified equivalent circuit combined with a typical test circuit (as suggested in IEC 60270). The circuit elements are as follows: 

Vn is the voltage source



Ci is the capacitance of the insulation system



is the capacitance of an air cavity in the insulation due to degradation



Ci' is the capacitance of the rest of the insulation around the air cavity



Ck is the capacitance of the coupling capacitor



M is the measuring system hooked up in series

At some inception volage, the electromagnetic field is strong enough to bridge the air cavity in the insulation and a partial discharge occurs. After the breakdown of the air gap, the rest of the insulation around the cavity (Ci) now sees the full voltage Vn and therefore the charge across Ci' increases. This extra charge must be provided by all of the parallel capacitances around it (e.g. in this model Ci and Ck) or the voltage source (though it is usually too slow to react). So in a typical situation, the capacitances Ci and Ck discharge a short pulse into Ci' to provide the extra charge. However doing so reduces the voltage across all the capacitances and the voltage source Vn reacts by charging all of the capacitances in the system (including the air cavity) back to the normal voltage Vn.

Partial discharge testing is done by directly measuring the short pulse discharged into Ci' by the coupling capacitor Ck. In the equivalent circuit, the measuring system is represented by a single box M, but in practice, this includes the coupling device, connecting cables, measuring device, etc. Now it's clear that any pulse measured by the measuring system is not the actual partial discharge, but an apparent charge caused by the real partial discharge (i.e. because the coupling capacitor Ck has to help provide the extra charge for Ci'). It's not possible to directly measure the partial discharge, but the apparent charges can be used to infer the level of partial discharge activity in the insulation system. Test Circuit Calibration Because only the apparent charges can be measured, it is important that the test circuit is properly calibrated. During calibration, a pulse of known magnitude is delivered into the system to simulate a partial discharge. The measuring system is then monitored to ensure that the test pulses are captured. The calibration process is done so that pulses with magnitudes of interest (i.e. that will damage the system) are reliably captured. A scaling factor can also be inferred based on the calibration tests. References 

[1] IEC 60270 (2000) "High Voltage Test Techniques - Partial Discharge Measurements"



[2] IEEE 400 (2001) "IEEE Guide for Field Testing and Evaluation of the Insulation of Shielded Power Cable Systems"



[3] IEEE 1434 (2000) "IEEE Trial-Use Guide to the Measurement of Partial Discharges in Rotating Machinery"

Category: Electrical Testing