Question

1. A three-phase, 5 kVA, 208 V, four-pole, 60 Hz, wye-connected synchronous machine has negligible stator winding resistance and a synchronous reactance of 8 Wper phase. It is operated in parallel with a three-phase, 208 V, 60 Hz power supply.

Determine the excitation voltage and the power angle when the machine is delivering rated kVA at 0.8 pf lagging. Draw the phasor diagram

Answer 1

V_L - L = 208 V V_P R = 208/squareroot 3 = 120 V R_S almostequalto 0 x_5 = j 8 ohm X_5 = 5 K V A taken V_P R at reference I. e, V_p R = 120 angle 0 degree (a) excitation voltage, E^vector = ? power factor = cos phi = 0.8_log = phi = 36.86 degree I = 5/squareroot 3 V I = 5000/squareroot 208 I = 13.37 Amp implies I = 13.87 angle - 36.86 degree [because factor is lagging] Applying K V L, E_p R^vector = V^vector + I^vector times (j times 5) E_PR^vector = 120 angle 0 degree + (13.87 angle - 36.86 degree) times (8 angle 90 degree) E_PR^vector = V^vector + I^vector times (j times 5) E_PR^vector = 120 angle 0 degree + (13.87 angle - 36.86 degree) times (8 angle 90 degree) E_PR^vector = 206 angle 25.44 degree volts power angle = angle 25.44 degree (b) If field excitation current uparrow used by

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