For the power system in Problem 3.41, the synchronous motor absorbs \(1500 \mathrm{MW}\) at 0.8 power factor leading with the bus 3 voltage at \(18 \mathrm{kV}\). Determine the bus 1 and bus 2 voltages in \(\mathrm{kV}\). Assume that generators 1 and 2 deliver equal real powers and equal reactive powers. Also assume a balanced three-phase system with positive-sequence sources.

Problem 3.41

Consider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings are

Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 100 MVA and \(500 \mathrm{kV}\) for the 50 -ohm line. Determine the per-unit reactances.

Generator 1: Generator 2: Synchronous motor 3: Three-phase A-Y transformers T, T, T3, T4: Three-phase Y-Y transformer T5: 1000 MVA, 18 kV, X"= 0.2 per unit 1000 MVA, 18 kV, X" = 0.2 p.u. 1500 MVA, 20 kV, X"= 0.2 p.u. 1000 MVA, 500 kV Y/20 kV A, X = 0.1 p.u. 1500 MVA, 500 kV Y/20 kV Y, X = 0.1 p.u.