ECE470 POWER SYSTEMS I Homework Set 1 1. Using 250 MVA and 500 kV as base values, express 525 kV, 125 MVA, 216.5 A, and 50 Ω in per-unit. 2. The per-unit impedance of an electric load is 1.2. The base power is 250 MVA, and the base voltage is 115 kV. a) Find the per-unit impedance of the load if 750 MVA and 230 kV are selected as base values. b) Find the ohmic value of the impedance. 3. A 500 MVA, 23 kV ac generator has a synchronous reactance of 1.5 per unit. It is connected to a circuit for which the specified bases are 200 MVA, 230 kV. Find: a) The per-unit value of the generator synchronous reactance on the specified bases. b) The ohmic value of the synchronous reactance. 4. A single-phase source is connected to an electrical load. The load draws a 0.5 pu current at 1.05 pu voltage while taking a real power of 0.5 pu at a lagging power factor. Choose a base voltage of 7.2 kV and a base current of 125 A. Calculate the following: a) Real power in kW. b) Reactive power in kVAR. c) Power factor. d) The ohmic values of the resistance and the reactance of the load (assume series).5. The single-line diagram of a 3φ power system is shown below. The system data, on equipment rating bases are: Generator 1: 20 MVA, 13.8 kV, Xs"= 0.2 pu Generator 2: 30 MVA, 18 kV, Xs"= 0.2 pu Generator 3: 30 MVA, 20 kV, Xs"= 0.2 pu Transformer T1: 25 MVA, 13.8/220 kV, X = 10% Transformer T2: (3x1φ) 10 MVA, 18/127 kV, X = 10 % Transformer T3: 35 MVA, 22/220 kV, X = 10 % Line L1 80 Ω, 220 kV Line L2 100 Ω, 220 kV Using 50 MVA, 13.8 kV base in the circuit of generator 1, draw the impedance diagram with all reactances marked in pu. 6. The single-line diagram of a 3φ power system is shown below. The system data, on equipment rating bases are: G1 18 kV 20 MVA X = 0.2 G2 18 kV 20 MVA X = 0.2 G3 13.8 kV 30 MVA X = 0.2 3φ Y – Y Trans. 20/138 kV 20 MVA X = 10% 3φ Y – ∆ Trans. 13.8/138 kV 15 MVA X = 10% L1-2 138 kV X = 40 Ω L1-3 138 kV X = 20 Ω L2-3 138 kV X = 20 Ω Draw the impedance diagram using 50 MVA, 138 kV base in the zone of each