GATE 2022 EE – Question 64

Electrical Machines · Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors · 2 marks · Numerical answer

A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is ________. (round off to nearest integer).

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Correct answer: 245

Explanation

The input power is $10+2=12$ kW $=\sqrt3\times400\times I\times0.8$, so $I=21.65$ A. The phase voltage is $\frac{400}{\sqrt3}=230.9$ V. For a motor $E=V-jX_sI$ with the current leading by $36.87^\circ$: $I=21.65(0.8+j0.6)=17.32+j13.0$, so $E=230.9-j(17.32+j13.0)=243.9-j17.3$ and $|E|=244.6\approx245$ V.