SHORT TRANSMISSION LINES B. 13.67% D. 17.

52%
(Practice Problems)
11. A 60-Hz short transmission line having R = 0.62 ohm
1. A 60-Hz short transmission line having R = 0.62 ohms per phase and L = 93.24 mH per phase, supplies a 3-
per phase and L = 93.24 mH per phase, supplies a three- phase, wye-connected 100 MW load of 0.90 lagging power
phase wye-connected 100 MW load at 0.90 lagging power factor at 215 kV line to line voltage. Calculate the sending
factor at 215 kV line-to-line voltage. Determine the end voltage per phase.
voltage regulation of the line. A. 129 kV C. 122 kV
A. 3.93% C. 3.69% B. 136 kV D. 132 kV
B. 4.08% D. 4.72%
12. A load is represented by a parallel combination of a
2. A short transmission line is 20 km long. The line has a resistor R and a capacitor of reactance X ohms
per phase series impedance of 0.13 + j0.45 ohm per km. respectively. The load is fed from a single-phase supply
The line delivers 75 MVA, 0.80 lagging power factor at 66 through a line impedance of 8.4 + j11.2 ohms. The rms
kV. Determine the sending end voltage between lines. voltage at the load terminal is 1200 V and the load is
A. 73.29 kV C. 74.77 kV taking 30 kVA at 0.80 power factor leading. Determine the
B. 75.22 kV D. 72.64 kV supply voltage.
A. 1280 V C. 1270 V
3. A certain station has 36 kV, 3-phase, is to supply 12 B. 1260 V D. 1250 V
MW load at 30 kV and 0.80 power factor lagging over a 3-
phase transmission line. Find the resistance of the line if 13. A balanced delta-connected load with impedance
the length of the transmission line is 4 km and the Z = 25.98 + j15 ohms per phase is connected to a three-
efficiency is 90%. phase, three-wire 250 V system by conductors having an
A. 5.33 ohms C. 4.45 ohms impedance of Z = 0.4 + j0.3 ohm per conductor. Solve the
B. 6.31 ohms D. 3.56 ohms line to line voltage at the load.
A. 239 V C. 208 V
4. A 3-phase, 60-Hz transmission line is required to B. 138 V D. 228 V
deliver
20 MW at 66 kV at a distance of 30 miles. The load power 14. A balanced delta load consisting of pure resistances of
factor is 85% lagging. Each line conductor has a 15 ohms per phase is in parallel with a balanced wye-load
resistance per mile of 0.326 ohm and a reactance per mile having phase impedances of 8 + j6 ohms. Identical
of 0.742 ohm. Find the efficiency of transmission. impedances of 2 + j5 ohms are in each of the three lines
A. 97.22% C. 95.32% connecting the combined loads to a 110-V three-phase
B. 94.14% D. 96.24% supply. Find the current drawn from the supply.
A. 10.52 A C. 9.62 A
5. A 10 km long, single-phase short transmission line has B. 8.05 A D. 11.18 A
0.50cis(60o) ohm per km impedance. The line supplies a
316.8 kW load at 0.80 power factor lagging. What is the 15. A balanced delta-connected load of (15 + j18) ohms
voltage regulation if the receiving end voltage is 3.3 kV? per phase is connected at the end of a three-phase line.
A. 20.52% C. 18.14% The line impedance is (1 + j2) ohms per phase. The line is
B. 16.94% D. 12.86% supplied from a three-phase source with a line-to-line
voltage of 207.85 V. Solve for the line current.
*6. At 85% lagging power factor, 20 MW is to be delivered A. 16 A C. 12 A
at 69 kV, 60-Hz over a 30-mile 3-phase transmission line. B. 14 A D. 18 A
Resistance of the conductor is 0.326 ohm per mile while
reactance is 0.742 ohm per mile. Assume negligible 16. A balanced delta-connected load consisting of a pure
charging capacitance. Determine the source end voltage resistance of 18 ohms per phase is in parallel with a
per phase. purely resistive balanced wye-connected load of 12 ohms
A. 38.43 kV C. 43.87 kV per phase. The combination is connected to a 3-phase
B. 34.50 kV D. 35.41 kV balanced supply of 346.41 V (line to line) via a 3-phase
line having an inductive reactance of j3 ohms per phase.
7. A 230 kV transmission line has an impedance of Determine the total complex power drawn from the
(1.045 + j4.89) ohms. The sending end power is 100 MW supply.
at 230 kV and 85% power factor. What is the line loss? A. 19.2 – j14.4, KVA C. 24.2 + 12.8, kVA
A. 1.21 MW C. 962 kW B. 19.2 + 14.4, KVA D. 24.2 – j12.8, kVA
B. 728 kW D. 272 kW
17. Three wye-connected impedance of (3 + j5) ohms per
8. A 3-phase transmission line is 40 km long. The phase are connected across a balanced 3-phase source of
resistance per phase is 0.15 ohm per km and the 100 V per phase through a line impedance of (1 + j1)
inductance per phase is 1.3263 mH per km. The shunt ohm. Determine the magnitude of the line current.
capacitance is negligible. Find the voltage regulation when A. 16.31 A C. 13.86 A
the line is supplying a three-phase load of 381 MVA at B. 12.45 A D. 17.15 A
0.80 power factor lagging at 220 kV.
A. 10.81% C. 12.43% 18. A load of 12 MVA, 0.80 power factor lagging, 22 kV is
B. 11.54% D. 13.64% served by a transmission line which has a line resistance
of
3 ohms and a line reactance of 10 ohms. Solve for the
9. A 3-phase wye-connected, 20-MW load of power factor sending end voltage.
0.866 lagging is to be supplied by a transmission line at A. 24.34 kV C. 26.79 kV
138 kV. It is desired that the line losses must not to B. 23.63 kV D. 25.09 kV
exceed 5% of the load. If the per phase resistance of the
line is 19. A three-phase, 3-wire short transmission line having
0.70 ohm/km, what is the maximum length of the line? an impedance of 3.6 + j16 ohms per wire is used to
A. 55 km C. 60 km supply an inductive load of 100 A at 0.707 power factor
B. 58 km D. 51 km and a capacitive load of 50 A at 0.50 power factor. The
receiving end voltage is 4160 volts per phase. Find the
10. A three-phase short transmission line is 20 km long. percent regulation.
The line has a per phase series impedance of 0.135 + A. 25.46% C. 20.33%
j0.475 ohm per km. Determine the voltage regulation B. 26.34% D. 23.71%
when the line delivers 75 MVA at 0.866 lagging power
factor at 64 kV. 20. A short transmission line is 20 km long. The line has a
A. 11.75% C. 15.97% per-phase series impedance of 0.13 + j0.45 ohm per km.
The line delivers 75 MVA, 0.80 power factor at 66 kV.
Determine the efficiency of transmission.
A. 97.12% C. 94.68%
B. 96.24% D. 95.35%

21. A three-phase transmission line has a resistance of

1 ohm and an inductive reactance of 3 ohms. It is 31. The per phase impedance of a short transmission line
supplying power to a balanced 20 MW load at unity power is 0.3 + j0.4 ohm. The sending end line to line voltage is
factor. Determine the sending end voltage of the line. 3300 V and the load at the receiving end is 300 kW per
Assume the line has an efficiency of 92%. phase at 0.80 power factor lagging. Calculate the
A. 14.06 kV C. 16.96 kV receiving end voltage per phase.
B. 15.20 kV D. 17.88 kV A. 1910 V C. 1828 V
B. 1722 V D. 1805 V
22. A three-phase, 3-wire transmission line has an
impedance per wire of 3 + j7 ohms, the receiving end load 32. A three-phase, 3-wire short transmission line has an
is 1950 kW, 0.65 power factor lagging with the line impedance of 5 + j12 ohms per wire and transmit power
voltage of 13,200 V. Solve for the efficiency of the line. to a 3-phase load drawing 1000 kW at 13,120 V line to
A. 92.64% C. 95.21% line, 0.80 power factor lagging. Determine the voltage
B. 90.24% D. 93.05% regulation of the line.
A. 6.78% C. 8.23%
23. A three-phase, 15 hp, 440-V motor operating at full- B. 7.72% D. 9.11%
load, 90% efficiency and 80% power factor lagging is
supplied from the bus. If the impedance of each of the 33. A 3-phase line has a reactance of 4.32 ohms and a
three lines connecting the motor to the bus is (0.3 + j1.0) resistance of 4.15 ohms. The load at the receiving end is
ohms, find the line-to-line voltage at the bus which 3800 kW at 75% power factor lagging and the voltage at
supplies 440 V at the motor. the sending end is 36 kV. Determine the voltage at the
A. 470 V C. 460 V receiving end.
B. 475 V D. 465 V A. 34.24 kV C. 33.86 kV
B. 35.14 kV D. 32.45 kV
24. A short transmission line is 20 km long. The line has a
per-phase series impedance of 0.13 + j0.45 ohm per km. 34. A 3-phase transmission line has a line impedance of
The line delivers 75 MVA, 0.80 lagging power factor at 66 10 + j40 ohms. It delivers power to a three-phase load
kV. Determine the sending end apparent power. rated 5.5 MW, 44 kV, 0.80 power factor lagging.
A. 78.12 MVA C. 81.92 MVA Determine the efficiency of the line under the given load.
B. 84.97 MVA D. 79.89 MVA A. 93.43% C. 96.43%
B. 94.12% D. 95.75%
25. A 15 km long 3-phase, 50-Hz overhead short line
delivers 5 MW at 11 kV at a power factor of 0.80 lagging. 35. A balanced 3-phase, 3-wire, 60 Hz transmission line is
Line loss is 12% of the power delivered. Line inductance is use to transmit power to a 450 kVA, 6600-volt, inductive
1.1 mH per km per phase. Calculate the voltage load at 0.80 power factor. The line has a resistance of 3.5
regulation. ohms and reactance of 10.5 ohms per wire. Find the
A. 22.48% C. 24.71% sending end power factor.
B. 30.62% D. 31.23% A. 0.834 lag C. 0.811 lag
B. 0.749 lag D. 0.763 lag
26. A short transmission line is 20 km long. The line has
a per-phase series impedance of 0.13 + j0.45 ohm per 36. A short transmission line serves at its end an induction
km. The line delivers 75 MVA, 0.80 lagging power factor at motor rated 500 hp, 0.88 power factor lagging, 0.90
66 kV. Determine the voltage regulation. efficiency, at 2.44 kV line to neutral. If the transmission
A. 10.10% C. 13.97% line has a resistance of 1.5 ohms and a reactance of 2.4
B. 13.28% D. 11.05% ohms per phase, solve for the voltage regulation of the
line.
27. The per phase impedance of a short transmission line A. 5.63% C. 8.25%
is 0.3 + j0.4 ohm. The sending end line to line voltage is B. 9.22% D. 6.77%
3300 V and the load at the receiving end is 300 kW per
phase at 0.80 power factor lagging. Calculate the line 37. A short 3-phase, 3-wire transmission line has an
current. impedance of 2 + j5 ohms per wire. At the receiving end,
A. 207.75 A C. 214.83 A a balanced 3-phase load and capacitor bank draw 3000
B. 210.12 A D. 217.48 A kVA, 0.71 power factor lagging and 600 kVAR respectively
at 800 volts per phase to neutral. Determine the power
28. A short line has a resistance of 4 ohms and a loss of the transmission line.
reactance of 12 ohms per wire and transmit power to a A. 81.32 kW C. 69.57 kW
concentrated load of 1000 kVA, 13,200 volts, 3-phase, 60 B. 90.74 kW D. 71.09 kW
Hz, 0.80 power factor inductive load. Find its efficiency.
A. 93.30% C. 96.95% 38. A short 3-phase, 3-wire, transmission line has a
B. 95.75% D. 97.21% receiving end voltage of 4,160 volts phase to neutral and
serving a balanced 3-phase load of 998,400 volt-amperes
29. A 3-km, 3-phase transmission line is supplying power at 0.82 power factor lagging. At the sending end, the
to a 10 MW, 31 kV balanced load at 90% power factor voltage is 4,600 volts phase to neutral and the power
lagging. If the sending end voltage of the line is 33 kV and factor is 0.77 lagging. What is the series impedance?
the operating efficiency of the line is 96%, determine the A. 1.335 + j9.62 Ω C. 2.420 + j5.99 Ω
series resistance of the line in ohms. B. 1.635 + j6.92 Ω D. 1.735 + j6.75 Ω
A. 2.15 ohms C. 3.12 ohms
B. 2.65 ohms D. 3.24 ohms 39. A three-phase, 3-wire transmission line which has an
impedance per wire of 3 + j7 ohms. The receiving end
30. A three-phase transmission line has conductors having load is 1,950 kW at 0.65 power factor lagging with a line
a resistance of 0.892 ohm per km. This line delivers power voltage of 13,800 volts. What kVAR of bank of capacitors
to a load drawing 20 MW at 80% power factor and 132 kV. to be placed at the input end of the line to increase the
If line loss is known to be 8% of the load delivered, power factor at that end to 0.80 lagging?
determine the length of the line. A. 817.5 C. 1,042
A. 55 km C. 50 km B. 4,180 D. 975.5
B. 60 km D. 45 km