Wattmeter 4a4t2k

PERTEMUAN 13

PENGUKURAN DAYA

Introduction • Power may be defined as the rate at which energy is transformed oe made available • In almost all cases the power in a d.c. circuit is best measured by separately measuring quantities, V and I and by computing P=VI • In case of a.c. circuits the instantaneous power varies continuously as the current and voltage go through a cycle of values • The fact that the power factor is involved in the expression for the power means that a wattmeter must be used instead of merely an ammeter and voltmeter.

Wattmeter • A wattmeter is essentially an inherent combination of an ammeter and a voltmeter and, therefore , consists of two coils known as current coil and pressure coil. • Wattmeter connection:

Wattmeter Errors

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Error due to inductance of pressure coil True power 

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cos   Re ading of wattmeter cos  cos   

Error due to pressure coil capacitance sin  sin   cot 

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Error due to Eddy currents : soild metal parts are removed as far away from the current coil as possible

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Error due to power loss in pressure coil or current coil There are two method of connecting wattmeters in the circuit for measurement of power, as shown in figure below (a) and (b). Fig (a) : Wattmeter reading  W  I r

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Fig (b) :

2

c

Wattmeter reading  W 

V2 R  rp

Measurement of Power in Single Phase A.C. Circuit

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3-voltmeter method P

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V32  V12  V22 2R

V32  V12  V22 cos  2V1V2

Disadvantages : (i) Even small errors in measurement of voltages may cause serious errors in the value of power, (ii) Supply voltage higher than normal voltage is required

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3-Ammeter method



R P  I 32  I 12  I 22 2

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

cos 

I 32  I 12  I 22 2I 1 I 2

The disadvantages of measurement of power by 3 voltmeters are overcome in this method

Measurement of power in conjuction with instrument transformers • This method is used when the currents and voltages of the circuits to be measured are high • Figure below shows a measurement of power with wattmeter in conjunction with instrument transformers in single phase A.C. circuits

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Vector diagram for inductive load       

K

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cos  cos  cos       

Vector diagram for capasitive load      

K

cos  cos  cos       

Measurement of Power in 3-Phase Circuit •

Measurement of power in 3phase, 4-wire circuits-----------

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P=W1+W2+W3

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Measurement of power in 3phase, 3-wire circuits-------------

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P=W1+W2+W3

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3-wattmeter method of measuring 3-phase power of delta connected P=W1+W2+W3

1-wattmeter method of measuring balanced 3-phase power (a) star connected, (b) delta connected P=3W

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2-wattmeter method of measuring 3-phase 3-wire power : – (a) star connected, – P=W1+W2

– (b) delta connected – P=W1+W2

Determination of P.F. from Wattmeter Reading •

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If load is balanced, then p.f. of the load can be determined from the wattmeter readings Vector diagram for balanced star connected inductive load ----- cos  cos tan 1

3 W1  W2  W1  W2

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The watt-ratio Curve ----------

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p.f. can be determined from reading of two wattmeters