Question

Assignment 4 An 11 kV, 50-Hz, Y-connected synchronous generator has a synchronous reactance of Xs-0.5Ω and armature resistance, Ra-005Ω. The terminal voltage in all working conditions is assumed constant and equal to the rated voltage. The generator is delivering a load current of 2000A at 0.8 PF leading a. Draw the per-phase equivalent circuit of the generator. b. Calculate the induced EMF, EA. c. Calculate the real and reactive power delivered at the generator terminals. d. Sketch the phasor diagram for voltages and current.

Answer 1

(a) Load Voltage/phase V_L_ph = 11000/squareroot 3 = 6350.853V Load current/phase I_L_ph = 2000A (b) E_A = squareroot (V_L_ph cos phi + I_L_ph R_a)^2 + (V_L_ph sin phi - I_L_ph times s)^2 cos phi = 0.8 phi = cos^-1 (0.8) = 36.87 degrees sin phi = sin(36.87 degrees) = 0.6 E_A = squareroot ((6350.853 times 0.8) + (2000 times 0.05))^2 + (6350.853 times 0.6) - (2000 times 0.5))^2 E_A = squareroot (5180.6824)^2 + (2810.518)^2 E_A = 5893.933V/phase \r\n (c) Real power �P� = V_L_ph I_L_ph cos phi = 6350.853 times 2000 times 0.8 = 10.1613 MW/phase Reactive power �Q� = V_L_ph I_L_ph sin phi = 6350.853 times 2000 times 0.6 = 7.621 MVAr/phase (d) E_A^bar = V_L_ph^bar + I_L_ph Z_s = (6350.853 angle 0 degrees) + (2000 angle -36.87) (0.05 + j0.5) E_A^bar = 5893.931 angle 8.390 degrees Load delta = 8.390 degrees