GATE 2017 EE – Question 30
A three-phase, 50 Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30 $\Omega$ per phase. The load angle is 30°. The power delivered to the motor in kW is ________. (Give the answer up to one decimal place.)
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Correct answer: 835 to 842
Explanation
The phase voltage is $\frac{6600}{\sqrt{3}} = 3810.5$ V. At unity power factor the current is in phase with the terminal voltage, so the voltage drop across the reactance is at 90° to it, and $\tan\delta = \frac{X_s I}{V}$. So $I = \frac{3810.5 \times \tan 30°}{30} = 73.33$ A. The power drawn is $3 \times 3810.5 \times 73.33 = 838.3$ kW.