PE EE08 - POWER SYSTEM

69. In a 13.8 kV, 10 MVA base three phase system a phase to phase fault occurs. If the thevin's equivalent impedance of the system is 2.63%, what is the magnitude of the fault current? a. 13,800 A b. 15,900 A c. 27,600 A d. 7,970 A

A

70. The sequence components of phase a current are: lao = 0 la1 = 90 + j5.78 A la2 = 10 - j5.78 A Determine the phase C current. a. 91.61<131° A b. 100<0° A c. 100<120° A d. 91.61<251° A

A

8. In a 13.8 kV, 10 MVA base three phase system a phase to phase fault occurs. If the Thevin's equivalent impedance of the system is 2.63%, what is the magnitude of the fault current? a. 13,800 A b. 15,900 A c. 27,600 A d. 7,970 A

A

27. A transformer of 500 kVA is at full-load and p.f. of 0.60 lagging. A parallel capacitor bank is added improving the pf to 0.90 lagging. How many KVARS do these capacitors? a. 215.8 b. 254.7 c. 187.6 d. 222.6

B

4. The reactance of a generator designated X" is given as 0.25 per unit based on the generators nameplate rating of 18 KV, 500 MVA. The base for calculations is 20 KV, 100 MVA. Find X" on the new base. a. 0.0617 pu b. 0.0405 pu c. 0.0081 pu d. 0.0450 pu

B

42. A 3-phase 4-wire system has the following unbalanced loads: Z1 = 10 + j5 Ω, Z2 = 8 + j4Ω and Z3 = 20 + j0Ω. The line to neutral voltage of the system is 120 volts. What is the reading of the wattmeter in watts in Z3. a. 900 b. 720 c. 1000 d. 1050

B

53. A 3-phase, 13 kv distribution line delivers 8 MVA of load. The per-phase impedance of line is 0.01 + j0.05 p.u. referred to a 13 kV, 8 MVA base. What is the voltage drop across the line in volts? a. 650 + j130 b. 130 + j650 c. 130 - j650 d. 650 - j130

B

57. The reactance of a generator designated X" is given as 0.25 per unit based on the generators nameplate rating of 18 KV, 500 MVA. The base for calculations is 20 KV, 100 MVA. Find X" on the new base. a. 0.0617 pu b. 0.0405 pu c. 0.0081 pu d. 0.0450 pu

B

59. At a 115 kV substation the PT ratio is 1000 and the CT ratio is 1200/5. The potential going into the wattmeter is 115 volts. What is the MW indicated when the wattmeter reads 800 watts? a. 150 MW b. 192 MW c. 15 MW d. 19.2 MW

B

62. The per unit reactance of a synchronous generator are Xd = 1.1, Xd' = 0.24, and Xd" = 0.15. The generator is operating without load at 5 percent above rated voltage when a three-phase short circuit occurs at its terminals. If the generator is rated at 500 MVA and 20 kV, determine the sub transient current in kiloamperes. a. 100 b. 101 c. 102 d. 103

B

73. A 5 MVA, 13.8 kV/480V, 5% impedance transformer is tapped at 13.8 kV line where the Thevenin's equivalent impedance is 0.5 ohm. Determine the fault current at the primary for 3-phase fault at the secondary. a. 2334 A b. 3314 A c. 3144 A d. 3341 A

B

76. A 3 phase system having a line voltage of 173.2 V is supplying a balanced, wye-connected load of 7.07 + j7.07 ohms/phase, what is the current in phase a in amperes? a. 5.77 - j10 b. 7.07 - j7.07 c. 5 - j5 d. 10 - j10

B

79. A balanced 3 phase, 3 wire system has a delta connected load with R = 50 ohms, L = 0.56 H and C = 5 μF in series in each phase. Using positive phase sequence with Van = 390∠30° V and ω = 500 rad/sec, find the current in line a in amperes. a. -8.925 + j1.156 b. -1.156 + j8.925 c. 8.925 + j1.156 d. 1.156 + j8.925

B

80. A balanced delta connected load having impedance of 8 + j4 ohms/phase is connected in parallel with a balanced wye-connected load having impedance of 2 - j1 ohms/phase. The two loads are supplied by a balanced 3 phase source through a feeder having impedance of 0.2 + j0 ohm/conductor. The voltage at the load is 120 V line to line. Find the total power loss in the feeder in watts. a. 1240 b. 1420 c. 1450 d. 1670

B

81. A 3 phase, 4157 V abc system supplies a delta connected load with impedance of 38.4 + j28.8 ohms/phase. Taking Vab as the reference vector, find the current in line a in amperes. a. 137.93 + j58.92 b. 58.92 + j137.93 c. 137.93 - j58.92 d. 58.92 - j137.93

B

84. Two generators G1 and G2 are rated 15 MVA, Z equals 0.10, 11 kV and 10 MVA, Z equals 0.10, 11 kV respectively. The generators are connected to a transformer of 15 MVA, 11 per 66 kV and 6 percent impedance. Calculate the fault current in per unit when the three-phase fault occurs on the high voltage side of the transformer. a. 12.5 b. 8.33 c. 16.9 d. 14.2

B

11. A generator of 50 MVA, 4 kV, Xd'' = 25% and transformer of 50 MVA, 4.2 kV delta/115 kV wye grounded, operating on 3.8 kV tap were XT'' = 10% are to be connected into a single equivalent reactance. What is the single equivalent reactance on a 100 MVA, 110 kV base? a. j0.6093 pu b. j0.6667 pu c. j0.8241 pu d. j0.8663 pu

C

13. Power in a balanced 3-phase system is produced by two wattmeter method and it is found that the ratio of the two wattmeter readings is 2 is to 1. What is the power factor of the system? a. 0.9 b. 0.82 c. 0.866 d. 0.707

C

16. A balanced delta connected load of ( 4 + j3) Ω per phase is connected to a three-phase, 230 V supply. Find the total kVA. a. 19.04 kVA b. 37.01 kVA c. 31.74 kVA d. 25.39 kVA

C

61. The line currents in amperes in phases a, b and c respectively are 500 +j150, 100-j600 and -300+ j600. Determine the zero sequence component of phase a current. a. -100 - j50 amps b.-100 + j50 amps c. 100 - j50 amps d. 100 + j50 amps

D

50. For the following phase current Ia = 34.64, Ib = -10 - j17.32, Ic = -10 + j17.32. What is the positive sequence for phase c? a. 12.44 - j21.55 b. 12.44 + j21.55 c. -12.44 + j21.55 d. -12.44 - j21.55

c

14. A 220 V, 3 -phase , 4 wire abc system supplies unbalanced wye-connected resistances of Ra = 10 ohms, Rb = 15 ohms, and Rc = 20 ohms. Determine the total power of the system. a. 3495 W b. 3385 W c. 3560 W d. 3895 W

A

15. In an electric system the available short circuit MVA is 600 MVA. What is the Thevenin's equivalent reactance at 34.5 kV? a. 1.984 Ω b. 1.587 Ω c. 2.561 Ω d. 0.046 Ω

A

18. A load of 10,000 kVA, 80% lagging is connected to a 13,200-volt line. How much capacitive reactive power is needed to correct the power factor to 97% lagging? a. 3995 kVAR b. 3138 kVAR c. 5156 kVAR d. 2547 kVAR

A

21. Two synchronous motors having subtransient reactance of 0.80 and 0.25 per unit, respectively, on a base of 480v, 2000 kVA are connected to a bus. This motor bus is used by a line having a reactance of 0.024 ohm to a bus of a power system. At the power system bus the short-circuit MVA of the power system are 9.6 MVA for a nominal voltage of 480 v. When the voltage at the motor bus is 440 v, neglect load current, find the initial symmetrical rms current in a three-phase fault at the motor bus. a. 16869 A b. 17222 A c. 17485 A d. 16761 A

A

24. A 4157 v rms, three-phase supply is applied to balanced delta-connected three-phase load consisting of three identical impedances of 38.4 + j28.8 ohms. Taking the phase to neutral voltage Van as reference, what is the phasor current for phase A amperes? a. 120 - j90 b. 120 + j90 c. 90 - j120 d. 90 + j120

A

29. One conductor of a three-phase line is open. The current flowing to the Δ-connected load through line a is 20 A. With the current in line a as reference and assuming that line c is open, what is the negative sequence current of phase a? a. 10 + j5.78 b. 10 - j5.78 c. j11.55 d. -10 + j5.78

A

31. A 3-phase balanced system working at 0.9 pf lagging has a line loss of 3600 KW. If pf is reduced to 0.6, the line loss would become __ KW. a. 8100 b. 1600 c. 5400 d. 4800

A

33. A 230-V single phase meter has a constant load current of 4A passing through the meter for five hours at a unity power factor. If the meter disc makes 1104 revolutions during this period, the meter constant in revolutions per KWHR is, a. 240 b. 120 c. 480 d. 360

A

38. The line currents in a three-phase four-wire system are Ia = (300 + j400) A, Ib = (200 + j200) A and Ic = (-400 - j200) A. Determine the positive sequence component of Ia. a. 276 < 25.6°A b. 276 < 145.6°A c. 276 < 265.6°A d. 0

A

39. A balanced wye-connected load consisting of Zy = ( 3 + j4) Ω/phase and a balanced delta-connected load having Z = (9 + j12) Ω/phase are connected to a 220 V three phase source. On a per-phase basis, calculate the line current Ia. a. 50.8 < 53.13°A b. 50.8 < 173.13°A c. 5.08 < 173.13°A d. 5.08 < 53.13°A

A

40. A system is consists of three equal resistors connected in delta and is fed from a balanced 3-phase supply. By how much power is reduced if one of the resistors is disconnected? a. 33% b. 67% c. 50% d. 25%

A

43. The total power consumed by a balanced 3ϕ load is 3000 watts at 80% power factor. Two wattmeters WA and WB are connected to the line. What is the reading of WA? a. 2150 watts b. 200 watts c. 1500 watts d. 2500 watts

A

45. A three-phase transformer rated for 33 kV/6.6 kV is connected Y-Δ and the protecting current transformer on the low side have a ratio of 400/5. What is the ratio of the current transformer on the high voltage side? a. 80: 2.89 b. 80: 5 c. 46.19: 5 d. 46.19: 2.89

A

48. A balanced 3 phase 4,157v rms source supplies a balanced 3 delta-connected load of 38.4 + j28.8 Ω. Find the current in Line A with Van as reference. a. 120 - j90 A b. 120 + j90 A c. -120 + j90 A d. -120 - j90 A

A

55. The synchronous reactance per phase of a 30, wye-connected 6600v synchronous motor is 20Ω. For a certain load, the input is 915 kW at normal voltage and the induced line emf is 8942 v. Neglecting resistance, what is the motor line current? a. 97 A b. 80 A c. 87 A d. 90 A

A

64. In a balanced three-phase wye-wye system the load impedance is 20 + j12Ω. The source has an abc phase sequence and Va'n' = 120 with an angle of 0° v rms. If the load voltage is Van = 110 with an angle of -0.2° v rms, determine the magnitude of the line current if the load is suddenly short circuited. a. 56.6 A b. 58.6 A c. 60.6 A d. 62.6 A

A

65. In a balanced wye-delta system, two wattmeters are connected to measure the total power. If the wattmeter readings are PA = 1,200 w and PB = 480 w and the line voltage is 208 V rms, find the delta load impedance. a. 61.72 with an angle of 36.59° b. 61.72 with an angle of - 36.59° c. 20.57 with an angle of 36.59° d. 20.57 with an angle of -36.59°

A

68. A 3-phase balanced system working at 0.9 p.f. lagging has a line loss of 3,600 kW. If p.f. is reduced to 0.6, the line loss would become ___kW. a. 8,100 b. 1,600 c. 5,400 d. 4,800

A

17. The following are the symmetrical components of phase B current: positive sequence component = 10 cis 45° negative sequence component = 20 cis (-30°) zero sequence component = 0.5 + j0.9 Determine the positive sequence component of phase A, a. 20 cis (-195°) b. 10 cis 195° c. 10 cis (-195°) d. 10 cis (-30°)

C

19. A balanced delta connected load draws 100 A line current from a balanced 3 phase supply. Determine the zero sequence components of the currents. a. -50 - j86.6 b. 50 - j86.6 c. 0 d. 86.6 + j50

C

2. For a single line to ground fault the zero sequence current is given by j3.0 pu. The current carried by the neutral during the fault is, a. j l pu b. j 3 pu c. j 9 pu d. j 6 pu

C

20. The per unit reactances of a synchronous generator are Xd = 1.1, Xd = 0.24, Xd = 0.15. The generator is operating without load at 5 percent above rated voltage when a three-phase short circuit occurs at its terminals. What is the per unit subtransient fault current? a. 6.35 p.u. b. 0.95 p.u. c. 7 p.u. d. 4.735 p.u.

C

22. A synchronous generator and motor are rated 30 MVA 13.2 KV, and both have subtransient reactances of 20%. The line connecting them has a reactance of 12% on the base of the machine ratings. The motor is drawing 20,000 KW at 80% power factor leading and a terminal voltage of 12.8 KV when a symmetrical three-phase fault occurs at the motor terminals. Find the three-phase fault current at the motor terminals. a. 10,600 A b. 10,150 A c. 10,350 A d. 10,800 A

C

28. A 200v, three-phase source is connected to two equal impedances of 7.07 + j7.07 ohms in parallel and with both connected in wye configuration. What is the current per phase of the combination? a. -16.26 - j16.26 A b. 16.26 + j 16.26 A c. 16.26 - j16.26 A d. -16.26 + 16.26 A

C

30. If 25 ohms and 125 amperes are the base impedance and base current, respectively for given system, what is the base KVA? a. 781.25 b. 39.1 c. 390.625 d. 78.12

C

34. Three unbalanced 3ϕ line voltages are given as follows: VA = 10 cis 30° VB = 30 cis (-60°) VC = 15 cis 145° What is the negative sequence component of the line voltage VC? a. 8.24 cis (-156.2°) b. 8.24 cis (-36.2°) c. 8.24 cis (-276.2°) d. 0

C

35. Two purely resistive loads are connected to a 240 V three-phase, 3 wire balanced supply. One of 4 KW is connected across lines A and B and the other of 6 KW is connected across line B and C. The current in line B is, a. 14.67 A b. 8.33 A c. 36.3 A d. 41.67 A

C

46. The positive, negative and zero sequence reactance of 20 MVA, 132 kV synchronous generator are 0.3 pu, 0.2 pu and 0.1 pu, respectively. The generator is solidly grounded is not loaded. A line to ground fault occurs on phase a. Neglecting all the resistances, determine the fault current. a. -j 1.67 pu b. -j 2.89 pu c. -j 5 pu d. -j 3.34 pu

C

47. A positive sequence, balanced delta-connected source supplies a balanced delta connected load. If the impedance per phase of the load is 18 + j12 and Ia = 22.5 ∟ 35° A, find VAB, a. 486.7 ∟ 68.69° v b. 486.7 ∟ 38.69° v c. 281.2 ∟ 98.69° v d. 281.2 ∟ 68.69° v

C

49. Three generators connected in a single bus. Given the data below: MVA KV Xd'' Gen A 50 18.8 20% Gen B 20 13.2 24% Gen C 80 13.8 12% Find the total reactance at the bus when the base is 100 MVA and 13.8 KV. a. j 0.1125 pu b. j0.10 pu c. j0.0992 pu d. j0.56 pu

C

51. A circuit has load impedance Z = 50 + j80 ohms. Determine the parallel impedance required to correct the power factor to unity. a. 32 μF b. 36 μF c. 24 μF d. 28 μF

C

52. A balanced three-phase, three-wire system supplies two balance wye connected loads. The first draws 6 KW at 0.80 lagging power factor while the other requires KW at a power factor of 83.3% leading. If the current in each line is 10 A rms, what is the supply voltage in KV rms? a. 2.190 b. 1.969 c. 1.833 d. 1.855

C

56. The phase b line voltage and the phase a line current of a balanced three phase system are V = 220 sin (ωt+21°C) and I = 10 sin (ωt - 30°) respectively. What is the power of the system? a. 1905 W b. 5716 W c. 3300 W d. 3810 W

C

6. The phase b line voltage and the phase a line current of a balanced three phase system are V = 220 sin (ωt+21°C) and I = 10 sin (ωt - 30°) respectively. What is the power of the system? a. 1905 W b. 5716 W c. 3300 W d. 3810 W

C

60. For a single line to ground fault the zero sequence current is given by j3.0 pu. The current carried by the neutral during the fault is, a. j l pu b. j 3 pu c. j 9 pu d. j 6 pu

C

63. The current from neutral to ground connection is 12 A. what is the zero sequence component in phases? a. 12 A b. 36 A c. 4A d. 3 A

C

74. A 3-phase, 10 MVA, 11kV 60 Hz generator with solidly earthed neutral has a positive negative and zero sequence reactance of 0.2, 0.3 and 0.1 respectively. Determine the sub-transient fault current during single line to ground fault. a. 6224 A b. 6224 A c. 2624 A d. 2264 A

C

77. A 3 phase, wye-connected load is supplied from a 3 phase abc system with Vab = 1500∠30°. What is the phase voltage Van in volts? a. 433 + j750 b. 750 + j433 c. 866 + j0 d. 0 + j866

C

78. A balanced delta connected load draws 30 A phase current from a balanced 3 phase supply. An open circuit fault occurs in one of the lines. Find the line current in amperes. a. 10 b. 15 c. 45 d. 50

C

82. A 3 phase, 4157 V abc system supplies a wye-connected load with impedance of 38.4 + j28.8 ohms/phase. Taking Vab as the reference vector, find the current in line a in amperes. a. 19.64 + j45.98 b. 45.98 + j19.64 c. 19.64 - j45.98 d. 45.98 - j19.64

C

1. The positive, negative zero-sequence reactance of a 20 MVA, 13.2 kV synchronous generators are 0.3 pu, 0.2 pu, and 0.1 pu, respectively. The generator is solidly grounded and is not loaded. If a line to line fault occurs at the terminals of the generator, calculate the fault current. a. 4,750 A b. 4,374 A c. 3,690 A d. 3,030 A

D

10. A 150 MVA, 13.8 kV, Y-connected 3 ϕ, 60 Hz alternator is operating at rated voltage and at no-load when a three-phase fault occurs at its terminals. If the subtransient reactance of the alternator is j 02 p.u., calculate the current at the instant the fault occurs. a. 10,460 A b. 18,117 A c. 6040 A d. 31,380 A

D

12. A 150-MVA, 13.8-KV, Y-connected, 3φ, 60-HZ alternator is operating at rated voltage and at no-load when a threephase faults occurs at its terminals. If the sub transient reactance of the alternators is j0.2 pu, calculate the current the instant the fault occurs. a. 10870 amps b. 6276 amps c. 32611 amps d. 31380 amps

D

23. A three phase, wye connected system with 240-volts per phase is connected to three loads: 10 ohms, 18.79 + j6.84 ohms, 9.83 - j6.88 ohms to phases A, B, C respectively. Find the current in phase C. a. 1.74 + j19.92 A b. -1.74 + j19.92 A c. -1.74 - j19.92 A d. 1.74 - j19.92 A

D

25. In two-wattmeter method of power measurement, the reading of the two wattmeters were 6717 watts and 2658 watts, respectively. Find the power factor. a. 0.90 b. 0.70 c. 0.60 d. 0.80

D

26. A balanced delta connected load of 15 + j18 ohms per phase is connected at the end of a three-phase line. The line impedance is 1 + j2 ohms per phase. a. -7.2 - j9.6 A b. 7.2 + j9.6 A c. -7.2 + j9.6 A d. 7.2 - j9.6 A

D

3. The per unit value of a 2 ohm resistor at 100 MVA base and 10 KV base voltage is, a. 4 pu b. 0.5 pu c. 0.2 pu d. 2 pu

D

32. A 500- KVA, 113,200/240 V, three-phase transformer with an impedance of 4.2% is connected to an infinite bus and without load. If a three-phase fault occurs at the secondary terminals, the fault current in amperes is, a. 26,040 b. 26,840 c. 24,680 d. 28,640

D

36. The apparent power input to a balanced wye-connected load is 30 KVA, and a corresponding true power is 15 KW at 50 A. The phase voltage is, a. 346.4 V b. 400 v c. 230 V d. 200 V

D

37. The load on a three-phase wye connected 220-V system consists of three 6-Ω resistance connected in wye and in parallel with three 9-Ω resistances connected in delta. The magnitude of the line current is, a. 36.66 A b. 24.44 A c. 42.34 A d. 63.50 A

D

41. A 350 KW, 2300 v, three-phase resistive load is measured with two small wattmeters. Two 100/5 A current transformers and two 2300/115 v potential transformers make this possible. Calculate the reading on each wattmeter, a. 874 w & 874 w b. 218 w & 218 w c. 1311 w & 1311 w d. 437 w & 437 w

D

44. A circuit with a resistance of 10Ω supplied with 120 v 60 Hz source. What is the phase angle between the voltage and the current? a. 45° b. 15° c. 30° d. 0°

D

5. The line currents in amperes in phases a, b and c respectively are 500 +j150, 100-j600 and -300+ j600. Determine the zero-sequence component of phase a current. a. -100 - j50 amps b.-100 + j50 amps c. 100 - j50 amps d. 100 + j50 amps

D

54. At a certain point of the system network the positive, negative and zero sequence impedances are 0.25 pu, 0.25 pu, 0.3 pu respectively. The base MVA is 100. The level at that point is 34.5 KV. Determine the zero sequence current for a one line to ground fault. a. 6275 A b. 7516 A c. 8132 A d. 2091 A

D

58. A 150-MVA, 13.8-KV, Y-connected, 3φ, 60-HZ alternator is operating at rated voltage and at no-load when a three phase faults occurs at its terminals. If the sub transient reactance of the alternators is j0.2 pu, calculate the current the instant the fault occurs. a. 10870 amps b. 6276 amps c. 32611 amps d. 31,380 amps

D

66. The positive, negative zero-sequence reactance of a 20 MVA, 13.2 kV synchronous generators are 0.3 pu, 0.2 pu, and 0.1 pu, respectively. The generator is solidly grounded and is not loaded. If a line to line fault occurs at the terminals of the generator, calculate the fault current. a. 4,750 A b. 4,374 A c. 3,690 A d. 3,030 A

D

67. Consider a system with sequence impedances of Z1 = j0.2577 pu , Z2 = j0.2085 pu and Z0 = j0.14p, determine the fault current la1 for a single line to ground fault at A. a. -j2.13 pu b. -j1 pu c. -j3.67 pu d. -j1.65 pu

D

7. Two-wattmeter method is applied to a 3-phase motor running at full-load. Two wattmeters indicate 85.5 kW and 34.7 kW, respectively. What is the operating power of the motor? a. 87.5% b. 89.49% c. 80.69% d. 94.76%

D

71. A 3-phase, 3-wire feeder supplies an industrial plant with the following data: Line voltages: Vab = 230 < 0°V, Vbc = 230 < 240° V Line currents: la = 110 < -36.87° A, Ic = 125 < 53.13° A What is the average power factor of the plant? a. 0.89 lagging b. 0.89 leading c. 0.93 leading d. 0.93 lagging

D

72. Two-wattmeter method is applied to a 3-phase motor running at full-load. Two wattmeters indicate 85.5 kW and 34.7 kW, respectively. What is the operating power of the motor? a. 87.5% b. 89.49% c. 80.69% d. 94.76%

D

75. A 3 phase system supplies two, 3 phase loads connected in parallel as follows: Load 1, 80 KW and 60 leading KVAR and load 2, 180 KW and 160 lagging KVAR. Find the total line current in amperes. a. 121 b. 136 c. 118 d. 129

D

83. An ABC sequence set of voltages feeds a balanced three-phase, wye-wye system. The line and the load impedances are 1 + j1Ω and 10 + j10Ω ohms, respectively. If the load voltage on phase A is Van = 110 v rms with 30 degrees angle, determine the line voltage of the input for phases A and C. a. -j210.0 v rms b. 105 + j60.5 v rms c. -105 + j60.6 rms d. -210.0 v rms

D

85. Consider a system with sequence impedances of Z(+) = j0.2577 pu, Z (-) = j0.2085 pu and Z (0) = j0.14 pu, determine the fault current at phase A for single line to ground fault at A. a. -j6.4 pu b. -j3 pu c. -j11 pu d. -j5 pu

D

9. Consider a system with sequence impedances of Z1 = j0.2577 pu , Z2 = j0.2085 pu and Z0 = j0.14p, determine the fault current la1 for a single line to ground fault at A. a. -j2.13 pu b. -j1 pu c.-j3.67 pu d. -j1.65 pu

D