1. A 20,000 kVA, 110/13.8 kV, Y-D three phase transformer has a series impedance of 0.02 + j0.08 pu. Find the per-unit impedance of this transformer in a power system with a base apparent power of 500 MVA and a base voltage on the high side of 120 kV.
2. Two 4.16 kV three-phase synchronous motors are connected to the same bus. The motor ratings are:
Motor 1: 5,000 hp, 0.8 PF lagging, 95% efficiency, R = 3%, XS= 90%
Motor 2: 3,000 hp, 1.0 PF, 95% efficiency, R = 3%, XS= 90%
Calculate the per-unit impedances of these motors to a base of 20 MVA, 4.16 kV. (Note: To calculate these values, you will first have to determine the rated apparent power of each motor considering its rated output power, efficiency, and power factor.)