EEE 471/591: Power System Analysis [Face-to-Face]

Homework #3

Problem 1 (20 Points)

A single-phase 100-kVA, 2400/240 volt, 60-Hz distribution transformer is used as a step-down transformer. The load, which is connected to the 240-volt secondary winding, absorbs 60 kVA at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power supplied to the primary winding.

Problem 2 (20 Points)

For a conceptual (lossless) single-phase phase-shifting transformer, the primary voltage leads the secondary voltage by 30°. A load connected to the secondary winding absorbs 110 kVA at an 0.8 power factor leading and at a voltage E2 = 277∠0° volts. Determine (a) the primary voltage, (b) primary and secondary currents, (c) load impedance referred to the primary winding, and (d) complex power supplied to the primary winding.

Problem 3 (20 Points)

Three zones of a single-phase circuit are identified in Figure 1. The zones are connected by transformers T1 and T2, whose ratings are shown. Using base values of 20 kVA and 115 volts in zone 3, (a) determine the per-unit impedances, (b) the per-unit source voltage, (c) draw the per-unit circuit, (d) calculate the load current both in per-unit and in Amperes. Transformer winding resistances and shunt admittances are neglected.

Figure 1. Circuit for Problem 3.

Problem 4 (20 Points)

A balanced Y-connected voltage source with  Eag   = 277∠0°  volts is applied to a balanced Y-load in  parallel with a balanced  Δ-load where  Zy   = 20 + j10 oℎm  and  ZΔ  = 30 − j15 oℎm.  The Y load is solidly grounded. Using base values of sbase1φ  = 10KVA  (single-phase power base) and  VbaseLN = 277 volts (line-to-neutral voltage base), calculate the source current  Ia in per unit and in amperes.

Problem 5 (20 Points)

Consider the single-line diagram of the power system shown in Figure 2. Equipment ratings are:

Generator 1:                                                          1000 MVA, 18 kV, X ′′ = 0.2 pu

Generator 2:                                                           1000 MVA, 18 kV, X ′′ = 0.2 pu

Synchronous motor 3:                                              1500 MVA, 20 kV, X ′′ = 0.2 pu

Three-phase Δ-Y transformers T1, T2, T3, and T4:      1000 MVA, 500 kV/20 kV (Y/Δ), X = 0.1 pu

Three-phase Y-Y transformer T5:                               1500 MVA, 500 kV/20 kV (Y/Δ), X = 0.1 pu

Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 1000 MVA and 500 kV for the 50-ohm line. Determine the per-unit reactances for all the generators, motors, transformers, and transmission lines.

Figure 2. Circuit for Problem 5