Polyphase Circuits 2f2h22

This Free Quality Manual is Found Only at PO\VERLINE

PO"'ERLINE E·MAil: [email protected]

POWERLINE REVIEW CENTER 1:

I! ,,

MEZZANINE FLOOR, DONA AMPARO BUILDING CORNER ESPANA & G. M. TOLENTINO STREETS SAMPALOC, MANILA TEL NOS. 735-73-02 & 733-2:1.-1..8

CEERS- POWERLINE REVIEW CENTER TEL. NOS. (032)26:1-2244 & (032)261-8452

=~=------

1

POWERLINE ENGINEERING REVIEW CENTER, INC. AC CIRCUITS- 2 (THREE PHASE CIRCUITS)

I- BALANCED 3q> CIRCUITS :

°

The magnitude of the line currents are the same and they have 120 phase difference.

( 1) WYE (STAR) Connected System : One-line equivalent circuit :

Tt I

I

I

Vr_ I

I I

·---> .... rL

vLt---'

I

I

VL.

(One phase of- oolcmc.e.rl W~e- crmnerAed iq~-fem)

IL=-I¢

~ k---------~~~--------~ Relationships : IL =I

= [L

(2) DELTA (MESH) Con11ected System:

~

l

1

IL

VL:.Vtf, I

VL-=-vq,.(\..-----;;-~IIJ--~.....-4_....__,..._... I I

..Jv:. ¥41

IL

J_~'------~--------------~ Relations/zips :

IL

I,

!-=-·

"fj

NOTE : To analyzed Delta-connected system using one-line equivalent circuits, It is first transformed Into an equivalent >rye-connected load making used of:

rI i'

1

I j

l

ll 1

1 Zy =-Zil. 3

2

VOLTAGE TRIANGLES:

Positive phase sequence : {ref. VAs) Negative phase sequence : (ref. VAs) AB-BC-CA, A··B-C, AN-BN-CN AB-CA-BC, A-C-B, AN-Cl\'-BN Note: l.fthe phase sequence Is. not given, you can give the positive phase sequence. Alternators are designed to operate with positive sequence voltage.

BALANCED 3tpPOWER Equations: PT R¢ kW where: c o s B = - = - = Sr Z¢ kVA Qy X,p kVAR . smB=-=-=·-ST Z¢ kVA B = angle...between ...V¢ & I¢

I.

One~wattmeter Method-

POWER MEASUREMENT in a 3pSvstenz ; used to measure total" balanced" 3

c.) Potcllfiall.ead-sh(fr Method d.) Current 7/·ansformer Method .

Note: for further discussion, pls. refer to Electrical Circuits by: Charles S. Siskind 2nd. Ed.(p.494-498) 2. Two-wattmeter Method- used to measure power drawn py a 3

Diagram of Connection as Shown:

·-:r----r

~o-----~~

~--~-----o

--~~-,~3~~~·~Yab

v'CAn

I._ WMR 1 =VLI L cos(30~ .. WMR 2 = VLIL

e)

co~30° +B) Pr = WMR 1 +WMR 2 = total real power of the balance;J3

Where : f\

a = p,f. angle of the balanced 3

.

I·· i

!

3

Note : If WMR 1+ WMR2 is negative, you. can carry the negative sign. '· Consider the Following : I. If p.f. = 1.0, both Wattmeters reads positive W 1 =W2 2. If p.f. > 0.50 , both readings are positive PT = w! + w2 3. If p.f ~ 0.50 ,only .one wattmeter gives reading, other will not read

PT= w,

-

4. If p.f. < 0.50, only one wattmeter will read positive and other will give reversed reading (i.e. negative)

II- UNBALANCED lq> CIRCUITS : The line currents will not be equal nor will they have 120 a phase difference as was the r::ase of with balanced loads. (b.) For unbalanced 3q> system: Consider the first Wattmeter's current coil in line a ,and potential coil between lines a and c. While the second Wattmeter's current coil in line band rotential coil between lines band c. The Wattmeter readings will be:

3.

VoJ

It 0 - - ..,__........... - - e - ... - - - _o 11 WMR,

=V"',I" cos(}, ]~:"

BLONI>EL 'S THEOREM : States that the minimum number of wattmeters required to measure power in a polyphase System is "ONE- LESS" than the number of wires in the system.

4 SYMMETRICAL COMPONENTS : ( FORTESCUE'S THEOREM ) Any unbalanced 3tp system of vectors can be resolved into three (3) balanced sy:.tem of vectors Namely: (ll.) A balanced set of 3 vectors having the same phase sequence as the original unbalanced system of vectors. This balanced system of 3

"Negatlvs Seque11ceSystem". (3.) A set of three (3) l

"Zero Sequellce or Uuipltase System". For Positive Sequence components :

For Negative Sequence components :

Va

vb2

Val

Vol

v.2

Vaz.

2

Vb1=a Val Vet

vb2 =a v.2

=a Val

Vb1

For Zero Sequence components:

!l;vw

Vc1. Where: a= 1 I 120

° =- 0.5 + j 0 866

a 2 == 1 I 240 ° =- 0.5 - j 0.866

Vw =Van

Identity:

I +a +·a 2 = 0

·NOTE : Symmetrical components do not have separate existence, they are only mathematical components which does not exist at all.

HARMONICS in different 3m systems: In 3

The following pnints are importattt in harmonic analysis for 3 fP systems : All trifle-n harmonics i.e. 3'd.,9m., l5 1h•••• etc. are in phase. .

(i) (ii) (iii) (iv)

(v)

(vi)

lI l

!

The 71 .,131h.,&l91h. Harmonics have positve phase rotation of A-B-C. The sm.,ll th., &l7 1h. Harmonics have negative phase rotation of A-C-B. For Star-connected system ,the line voltages will be the difference between the successive phase voltages and hence will contain No 3"1• harmonic , bcca•.1se being identical in each phase, thus it will cancel out. For Delta-connected system ,the resultant emf acting around the closed loop would be the sum of the phase cmfs. It is zero in the case of fundamcntal,5'".,7'"., 11 11'.,1 '7'1'.,etc. but for 3rd.,91h.,l5 1h.,etc,the resultant emf is 3 times the phase value acting in the loop. For 3

I I

I ' !

POWERLINE REVIEW CENTER Inc. The Ultimate E.E. Review Ceuter

POLYPHASE CIRCUITS REVIEW QUESTIONS 1. In a two-phase 2400 volts motor, phase current is 800 amperes, efficiency is 90% and power factor is 85%. What is the hp of 2-phase motor? A. 2372 C. 2784 B. 2844 D. 1288 2. A balanced three phase wye connected source has using''positive phase'' {.AP>c,) sequence, Vca = 398 Vrms with 90 degrees angle. Determine Vbn. ~.-230+jOV C.115-j199V B. -115-j199V D. -j230V 3. A balanced three phase wye connected source has using''negative phase c~tcs) sequence, Van = 220 V rms with 30 degrees angle. Determine Vbc A.-190.5 + j330 V C. -190.5- j330 V B. - 330 + j190.5 V D. - j381 V 11

4. The three phase rural distribution system has a phase-to-neutral voltage is 40,000 volts, what is the line to line voltage? A. 20,000 volts C. 40,000 volts B. 34,500 volts D. 69,000 volts

5. The rated line current of a delta connected motor is 18 amperes, calculate the rated current of each winding. A 11.4 A B. 6A

C. 18 A D. 10.4A

A three phase, balanced delta connected resistive load draws 30 ampere phase current from balance three phase supply. An open circuit fault occurs in one of the lines. Determine the line current. A 45A c. 90A B. 60A D. 100A Three 3.33 ohms resistance are connected in wye across 220 V, 3-phase supply. What is its equivalent delta connected resistance? A 2.22 Q C. 6.7 Q B. 200 D. 10Q eThree capacitors, each having a capacitance of 75 uF are connected in star to a 400V, 3<1>, 50Hz supply. Calculate the delta equivalent capacitance so that when they are connected in the same supply, the line current will remain the same. A. 150 J..LF C. 225 J..LF ~· 25 J..LF D. 75 JiF

j

l l l

9. Three identical resistance connected in wye carry a line current of 20 Amp. If the--- · same resistances are connected in delta across the same supply, what is the line current? ' A. 10 A C. 30A §.._ 60A D. 90A 10. The secondary of a transformer bank is wye-grounded, it has a balance voltage and the balanced toad. The voltage to ground is 132V and its line current is 40A. What is kva of the load? C. 27.4 A. 9.1 D. 15.84 8.19.2

11.A generator supplies 3-phase power to a balanced load. The voltage is 230 Volts, the current is 18 Amperes and the power factor is 85%. What is the power? A.. 3.6 kW Q.. 6.1 kW B. 1.6 kW D. 1.4 kW 12. Find the total power in a d~Jta connected load with 6+j8 ohms per phase and supplied from a 220V, 3-phase source. C. 8367w A. 8712 w -_,,, D. 8617w B. 8376W 13. A balanced delta connected load of 4 - j3 ohms/phase is fed by a 380 V, 3-phas~/ system. Find the reactive power. · "-/ A. 52 kVARS C. 69 kVARS 29 kVARS D. 87 kVARS

R

14. The phase b line voltage and the phase a line current of a balanced 3-phase system· are : V = 220 sin ( w t + 21 0°} Volts and I = 10 sin ( m t- 30°) Amp respectively. What is the power of the system ? A. 1905 Watts C. 5716 Watts §. 3300 Watts D. 3810 Watts 15.A wye-connected balanced load takes 100 WNA from a 34.5 KV system, What is the ioad impedance? A. 11.9 ohms C. 71.4 ohms B. 23.8 ohms D. 8.36 ohms 16.A balanced three-phase wye-connected load of 150 kW takes a leading current of 100 A, when the line is 2400 V, 60 Hz. What is the capacitance per phase? A. 21 mF C. 20.5 J.t-F -~8. 21 J.LF D. 205 J.tF

-

17.A delta connected load of 9+j12 ohms per phase is supplied by a 3-phase balance source of 230 volt rms through a line with an impedance of 0.06+j 0.12 Ohm. Find phase voltage at the load. A. 288 volt C. 132 volt ~- 224 volt D. 228 volt

18.1n a balanced three-phase system, the wye-connected impedances connected are 10 ohms with 30 degrees angle. lfVbc is equal to 416 Vwith 240 degrees angle, determine len. Assume the phase sequence is abc. A. 12 + j20.8 A C. 12- j20.8 A B. 20.8- j12 A D. 20.8 + j12 A 19.A delta connected load with 50 ohm resistance, 209 mH inductance and 50 microfarad capacitance in series per phase is supplied at angular frequency of 500 rad/sec. With Vcn=390L 30° as reference, what is the phase Cline current? A. 13.37 +j5.42 Amp C. 13.27-j5.42 Amp B. 4.42+j1.81 Amp D. 4.42-j1.81 Amp

20. The load on a 230 volt three phase generator consist of (a) three groups of incandescent lamps, each group containing twenty 100 watt lamps and (b) a 9 hp motor operating at 82 percent P.F. at 87 percent efficiency . Find the total load current in amperes? A 37 C. 45 B. 25 D. 30 21.A 3-phase 480 volts supply delivers power to a wye-connected load with impedance per phase of 10+j5 and a wye connected pure resistive load of 15+j0. What is the average power of one phase? A. 11.2 kw C. 12 kw B. 3.3 kw D. 33.8 kw 22.A balanced 3-phase source supplies three loads. Load 1 is 15 kva at 75% pf lagging, Load 2 is 10 kw at 90% pf lagging and load 3 is unknown. If the generator delivers 35.52 kva at 80% p.f. lagging, what is the unknown load? A 8.37kva at 76.4% pf lagging C. 8.37kva at 76.4% pf lagging B. 9.3kva at 89.4% pf lagging D. 9.7kva at 73.8% pf lagging 23.A balanced 3-phase, 3 wire system supplies two balance wye-connected loads. The first draws 6 kw at 0.8 pf lagging while the other requires 12 k.w ay 0.833 pf leading. If the current in each line is 8 A Find the supply voltage in kv. A 1.544 C. 2.291 B. 1.682 D. 1.323 24. A 120 volts per phase, 3-phase wye connected source delivers power to the following delta connected load. Phase 1: 40+j0 ohms, Phase 2: 20 cis (-60°)ohms, phase 3: 15 cis45° ohms. Find the current at line 1. (Use1-3-2 sequence) A. 18.5+j 3.57 C. -15.2 +jO B. -2.9-j3.57 D. -2.6+j 0.8

25. A circuit consisting of three resistors rated: 10 ohms, 15 ohms and 20 ohms are connected in DELTA. What would be the resistances of. the equivalent WYE connected load ? A. 0.30, 0.23 & 0.15 ohm ~ 3.33, 4.44 & 6.67 ohms B. 3.00, 4.00 & 5.00 ohms D. 5.77, 8.66 & 11.55 ohms

- - - - - - - - - - - - - - - - - - - - -

26. Three impedance, -j10, j10, and 10 ohms are WYE connected. Determine the impedance of an equivalent DELTA. A. 12.5,j12.5,-12.5 ohms C. j8.5, j12.5, 8 ohms ~ 10,j10, -j10 ohms D. 5, j5, --j5 ohms 27.A balanced 3-phase, 3 wire, 240 V, 60Hz, ABC source supplies power to a star connected resistance 10 n, 15 n and 20 n. What is the current through 15 ohms resistance ? A. 11.23 Amp C. 15.93Amp B. 9.77 Amp D. 8.05 Amp

II ,,ill' :~ :~

28. The load of a wye-connected transformer are: Ia = 10 cis (-30°) lb = 12 cis 215° lc = 15 cis 82° What is the neutral current? A. 1.04 cis 72.8° C. 0.92 cis 62.5° B. · 2.21 cis (-30°) p. 3.11 cis 72.8° 29. The 3-phase, 4-wire source voltage of Van =230 sin(rot+30deg.) volts supply loads with the following line currents: lc 3.4 sin(rot+120deg.) Ia 4.7 sin(rot +30 deg.) lb;:: 6.8 sin(rot-60deg) Determine the total power.

=

=

A. 3113 watts

C. 2786 watts D. 2733 watts

B. 2768 watts

30.A balance three phase resistive load is supplied. by 230 volts 60Hz and draws a current of 90A. If two wattmeter is used, what will be the reading of each wattmeter. A 20.7 kw C. 25.7 kw B. 35.9 kw D. 17.93 kw 31. The power input to 440 Volt, 3-phase motor is measured by two wattmeter method, the readings are 460 W and 780 W. What i~ the input current! A. 1.78 A C. 1.63 A 8. 0.94 A D. 2.82 A 32.A three phase balanced load id connected across 220 volts three phasesource. A wattmeter reads 600 watts when its current coil is connected in line a ani potential coil across line a and b. Next, the voltage coil is connected betveen lines b and c, but the current coil remains at line a. The wattmeter again eads 600 watts. Calculate the load power factor. A. 0.8 C. 0.806 B. 0.866 D. 0.5 33.An unbalanced wye connected loads on a 3 phase four wire system consht of Z1 10 + j5, Z2 8 + j4 and Z3 20 + jO. The wye connected generator·· su~plying the unbalanced load is balanced voltage to neutral of 120 volts. What ~s the wattmeter reading at Z1 , watts?

=

=

=

A. 720 B.3312

C. 1440 D. 1152

34.A 132 KV line, three phase system delivers 70.7 MVA of a balanced delta load of power factor 70. 7%. Determine the reactance necessary to attain unity power factor. A. 1092 ohms C. 1142 ohms B. 965 ohms D. 1045 ohms 35.A balanced Y-connectedload of 30+j10 ohms per phase is connected to a 3phase 208 volts 60 Hz supply. Determine the value of each capacitor in f.J F which will yield to unity power factor. A. 88.4 C. 26.5 B. 8.84 D. 2.65 36.1t is required to increase: the- power factor of a 750 kw three phase balance load from 70% lagging to 90 %lagging. The line voltage is 6,900 volts, 60Hz. Specify the capacitor required to, increase the power factor of this wye connected load in micro-farad per phase_ A. 20.45 C. 22.39 B. 18.58 D. 17.22 37.A 3-phase 150 hp, 480 \tolfs synchronous motor with rated efficiency of 90% is operating at rated loadL It is in parallel with 3-phase balanced load of 400 kW at 0.75 p.f. lagging. In order to improve to p.f. to 0.95 lagging, the excitation of the motor was increased. Calculate the operating power factor of the motor. A 0.65 C. 0.57 8. 0.38 D. 0.82 38. Given the following sets: of per unit symmetrical component of phase a currents, determine the phase B current lao=1.0 cis 75 aeg, tat= 1;0 cis 15 deg., la2= 1.0 cis(-45deg) A 0.259 + j0.966 p.u~ C. 1.932 + j0.518 p.u. B. 0.516 + j1.931 p.u. D. 1.414 + j1.414 p.u. 39. The line currents in a delta connected load are Ia= 5 cis Odeg. Ib=7.07 cis 225deg and Ic = 5 cis 90 deg .. Calculate the positive sequence components of current for phase a.

A. 7.94L224°

8. 5.57 L-15°

B. 0 D. 8.35L-25° 40.A three phase, unbalance delta load draws 100 ampere of line current from balance three phase supply. An open circuit fault occurs in one of the lines. Determine the negative sequence components of the currents in the unfaulted lines. A 50- j28.86 C. 50+ j28.86 8.0 D. 33.3+j0

Sept.1010

Supplementary Problems 1.

In a balanced 2-phase voltage system, the phase voltages are 120 volts, what is the line to line voltage? A. 120 volts C. 240 volts §.. 170 volts D. 60 volts

2.

In a balanced 3-phase voltage generator, the different phase voltages are__ degrees apart. A. 120 C. 60 8. 240 D. 30

3. In a 13,800 volts 3-phase delta system, what is the phase voltage? A. 4,600 volts Q. 13,800 volts 8. 6,900 volts

D. 8,000 volts

4.

The secondary of a 3-phase transformer bank is cqnnected delta, the line to line voltage is 480V, the midpoint of the winding between terminal A & 8 is grounded. What is the voltage across terminal C & the ground? A. 240 volts s; 720 volts 8. 277 volts D. 416 volts

5.

Three identical capacitance, each of 150 f.LF are connected in delta. The value of capacitance in each phase of the equivalent star connected load would be ...... . A. 50f.LF C. 150f.LF ~ 450f.LF D. 100f.LF

6.

Three equal resistors are connected in delta across 240 Volts, 3-phase lines. To what value should the line voltage be changed to obtain the same power with the resistors wye connected ? A. 240V C. 720V B. 139 V 0,.-416 V

7.

A balanced delta connected load of 4 + j3 ohms per phase is connected to a 3-phase 230 V supply. What is the line current? 6,. BOA C. 23A B. 46A D. 33A

8.

Three heater units each taking 1500 watts are connected delta to a 120 volt three phase line. Two wattmeters Wa and We are used to measure the power supply. What is the resistance of each unit in ohms. A 7.5. C. 9.6 B. 5.4 D. 8.6

9.

A balanced delta connected load draws 10 Amp line current and 3 kW at 220V. The reactance of each phase of the load in ohms is...... . A. 30 C. 38.1 B. 23.5 D. 20

-

--

10. Three ider.ilcal impedance are connected in delta to a 3-phase supply of 400 Volts. The line current is 34.65 Amp and the total power taken from the supply is 14.4 kW. What is the impedance in each phase ? A 12 + j16n c. 16 + i12 n B. 20+jOQ D. + i20

o

n

11. A 25 kva delta connected balance load is supplied from 230 volts, 3-phase source. What is the impedance? A 3.5 ohms c. 10.6 ohms 8. 2.3 ohms D. 6.3 ohms

I ,f I ! /

I

12. Three 100 ohm resistors are connected in wye across 480 Volts, 3-phase source. If one of the resistor is open, What is the power absorbed by the remaining resistors ? ~ 1,152 W . C. 768 W B. 1,536 W D. 2,304 W 13. The phase b voltage and the phase a current of a balanced three-phase system are : V = 220 sin ((I) t + 210°) Volts and 1 10 sin ((I) t + 60°) Amp respectively. What is the power of the system? A. 0 c. 1905 B. 3300 D. 6600

=

14. In an unbalanced wye system, the phase voltages are: Vna = 132 cis 0° Vnb = 130 cis235° Vnc = 133 cis 111' What is the line to line voltage Vcb? A. 227 cis (-15.2°) B. 218 cis 37.2°

C. 225.44 cis (-93.6°) D. 232.4 cis 27.3°

15. A three phase source of 230-V supplies the following three phase loads. 20 KW at 90% power factor leading 50 KW at 80% power factor lagging 10 KW at unity power factor What is the total kva and current? A. 85.7 & 225 A B. 94.7& 182.8 A

C. 84.7 & 212.6 A D. 84.7 & 92.88 A

16. A 3-phase AC generator is supplying power to a balanced load of 3,200 kW at 2.3 kV and 0.80 p.f. lag'g. What is the current drawn by the load? A. 1004 A C. 803 A B. 580 A D. 1391 A 17. Three identical impedances of 15 cis 60° ohms are connected in star to a 3-phase, 3 wire, 240 V system. The lines between the supply and the load have impedance of 2 + j1 ohms. Find magnitude of the line vottage at the load. A. 220V C. 240V B. 185 V D. 213 V

in parallel with a balanced delta connected foad having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Find the total volt-amperes

18. A three phase motor takes 10 KVA at 0.6 power factor from a source of 230 V. It is

i

A. 12.8 B. 17.9

C. 7.9 D. 15.3

;j

19. Three star-connected impedances 2 1 = 20 + j37.7 ohms per phase are connected in parallel with three delta-connected impedances 2 2 =30- j159.3 ohms per phase. The line voltage is 398 V. Find the line current.

A. 3.36 A B. 7.26 A

•..·

C. 5.8 A D. 4.24 A

20. The phase A line voltage and the phase C line current of a balanced three-phase system are : V = 220 sin ( m t- 30°) Volts and I = 10 sin ((I) t + 90°) Amp respectively. What is the impedance of the system?

l l

A 19.1-,j11

C. 19.1 +j11

B. 33- j19.1

D. 33+j19.1

--~~~~-~----------------------------------

21. A balanced 3-phase, 3 wire, 240 V, 60Hz source supplies power to a star connected load ZA = 10 + jOO., Ze = 10 + j10 Q and Zc= 10 + jO 0.. What is the line current 19 ? A 11.53 Amp C. 15.93 Amp B. 10.02 Amp D. 16.97 Amp 22. Three unequal single-phase induction motor are connected between lines and the neutral of balanced 3-phase, 350-V circuit. The line to neutral voltage are each 202 volts. The first load takes 20 kw at 0.82 power factor, the second takes 28 kw at 0. 75 power factor and the third takes 36 kw at 0.8 power factor. What is the current in the neutral conductor? A 105.5 A C. 85.6 A B. 125.4 A D. 133.4 A 23. The primary of 34.5 KV/13.8 KV, 50 MVA transformer is wye-grounded. The three primary currents are: Ia 720 cis - 30°, lb 695 cis 209° lc = 710 cis 88° Determine the neutral current? A 42.39 cis 17.34° C. 30.2 cis 20.51° B. 57.81 cis {-15.21°) D. 14.13 cis(- 12.31°)

= =

24. An unbalanced wye - connected system Vna 132 cis 0° Vnb=130 cis 235° Vnc=133 cis 11rc What is the total power in Watts? A 2820 B. 4325

=

il I

=

Ia 10 cis (-32°) lb =13 cis {212°) lc =14 cis 86°

C. 4271 D. 3650

25. The power input to a 100 hp, 480 Volt, 85% efficiency and 75% power factor 3-phase motor at full load is measured by two wattmeter connected at lines A & C. What are the readings in kw? A 66.23 & 21.55 C. 87.76 & 11.7 B. 69.5 & 18.26 D. 67.89 & 30.4 26. The ratio of the wattmeter readings in the 3-phase inductive system is 5:3 when power is measured by these two wattmeter. What is the power factor of the load ? A 0.92 C. 0.80

B. 0.50

D. 0.866

27. A 7.5 hp wound-rotor, 3-phase induction motor draws a line current of 18.4 Amp at 230 V line when operating at rated output and efficiency of 88%. Applying artificial neutral-Method of measuring 3-phase power using only one wattmeter, What is the wattmeter reading ? A 3179W C. 2119W B. 2126 D. 1590 W 28. What will be the rating of a phase advancing plant in kVA if it improves the power factor from 0,8 lagging to 0.95 lagging? The consumer load is 500 kW and the current taken by phase advancer lead the supply voltage at a power factor of 0.25. A. 150 kVA C. 175 kVA B. 200 kVA D. 250 kVA 29. A 4,160 V, 3-phase, 3 wire ABC source supplies power to an industrial load that draws the following line currents : Ia 110 cis (-36.87~ Amp, lb 166.5 cis (-168.2°} Amp. Using two wattmeter method, what is the total power drawn by the load? A 882.5 kW C. 1,281 kW B. 828.5 kW D. 97.5 kW

=

=

30. A three phase induction motor takes 3000 W at 80 percent power factor. Two wattmeters are used to measure the power, Wa and We . What is the reading of Wa? A 2000 C. 2150 B. 3000 D. 2500

31. A three phase system delivers 50 MVA of a balanced delta load of power factor 78%. Determine the size of capacitor bank necessary to raise the power factor to 90%. A 17.3 MVAR C. 11.4 MVAR B. 13.5 MVAR .Q. 12.4 MVAR 32. In a 3-phase 4-wire system, the§line voltage is 4160 volts. What is the line to neutral voltage? A 1390 volts "' .k. 2400 volts 8 2080 volts D. 4160 volts 33. The line currents of unbalance delta connected load are: la=50 cis 0 degree, lb=40 cis 240 degrees, Determine the phase B zero sequence component. A zero C.16+j7.25 B. 45-j.2.9 D: 5-j2.9

34. A three phase unbalanced current are:

=

=

Ia 10 cis (-30°), lb 0, What is the phase b positive sequence current?

lc

lc=45.8 cis 130.9 degrees.

=10 cis 150°

c.

A 8.66

5.77 D. 8.66 cis 120°

B. 5.77 cis 240°

35. The sequence components of three phase current are: I zero = 0 I positive 90 + j5. 78 amp. I negative = 10-j 5. 78 amp. Determine phase C current? A. 100 cis 120° C. 73.22 cis 118° B. 82 cis 122° D. 91.65cis 131°

=

36. The sequence component of phase 2 currents are: lo= 0 lpos=11.55 Determine the phase A current. A 22.3 cis 15 deg. §.. 20 cis 150 deg.

I neg.=11.55 cis (-60deg)

C. 73.22 cis 1l8 deg. D. 91.65 cis 131 deg.

37. Thirty (30) units of 200 watts, 250 volts incandescent bulbs are connected in balanced delta across a 3-phase 230 volts source. What would be the current in each line? C. 22.1 A A. 12.8 A

B. 7.36A 38. The three phase unbalance currents are : lb = 0, Ia = 10 cis {-30°) Amp. Find the negative sequence current of phase b. A 8.66 cis 30° B. 5. 77 cis ( - 60°}

D. 30A

lc =10 cis 150° Amp

c. -5.77 D. 5. ??cis 60° s.-

39. Three identical resistors are connected in delta across balance, 3-phase source. If one of the resistor is open, A Power will ~me double B. Power is reduce by 33%

C. Power will become three times D. Power will increase by 67%

40. A 170 kV, 3-phase electric source delivers 200 MVA to a balanced load which has a power factor of 90 % lagging. What is the line current ? A 257 A C. 402 A B. 502A D. 679A

41. The metering of a 3·phase inductive load indicated the following values: 4000 kw, 34.5 KV, 80% power factor. What is the kva? . A. 3000 c. 5000 B. 4000 D. 7000 42. A balance 3-phase load takes 20 amperes at 230 volts line to line. The phase A line current lags the line voltage Vba by 50 degrees. What is the power factor of the load in percent? A. 86.6 c. 94 B. 64.3

D. 76.6

43. In a balanced three phase, 208 volts circuit, the line current is 100 amperes. The power is measured by two wattmeter method, one reads 18 kw and the other is 9 kw. What is the power factor of the load? A. 0.8 C. 0.866 B. 0.5 D. 0.95 ~

44. The phase b voltage and the phase b current of a balance 3-phase system are: V = 220 sin(rot+210°) and 1=10 sin (oot-180°). What is the power of the system? A. 5716 watts C. 1905 watts B. 3810 watts D. 3300 watts 45. The wye connected three phase ABC voltage source has Vc= 115 v rms with -240 degrees angle. Find the line to line voltage Vbc. c. -172.5-j99 A. 0- j199 B. 0 + j 199 D. 172.5-j99 46. A delta connected load has a per phase impedance of 29.8757 -j 25.0687 It is supplied with a wye connected balance source through a 3-phase line with 4 ohm resistance. The voltage

sequence is given by Va=277 cis-30deg Vb=277 cis -150deg Vc=277 cis 90deg. What is the line A current?

c.

A 17·j0.267 B. 17+j0.267

6.5+j0. 75 D. 6.5-jO. 75

47. What is 1+A+A2 in rectangular form?

A. 0.5 +j0.866 B. -0.5-j0.866

C. O+j1.732

D. 0

48. A three phase unbalanced current are: Ia = 10 cis (-30}, lb = 0, What is the phase b positive sequence current? A 8.66 B. 5.77cis240

lc = 10 cis 150°

c.

5.77

D. 8.66cis 120

49. A delta connected transformer has the following line current: lb=40 cis 240 degrees, lc=45.8 cis 130.9 degrees. la=50 cis 0 degree, Determine the phase A negative sequence component A.15+j6.21 C.16+j7.25 B. 8-j4.22 D. 5-:i2.9 50. The line currents of unbalance delta connected load are: la=50 cis 0 degree, lb=40 cis 240 degrees, lc=45.8 cis 130.9 degrees. Determine the phase 8 zero sequence component. A. zero C.16+j7.25 B. 45·j.2.9 D. 5-j2.9 PRACTICE Makes Perfect ! !!

~--~~~~--·

---

-~---

·----~-