GATE 2016 EE – Question 58
A three-phase, 50 Hz salient-pole synchronous motor has a per-phase direct-axis reactance ($X_d$) of 0.8 pu and a per-phase quadrature-axis reactance ($X_q$) of 0.6 pu. Resistance of the machine is negligible. It is drawing full-load current at 0.8 pf (leading). When the terminal voltage is 1 pu, per-phase induced voltage, in pu, is ________.
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Correct answer: 1.58 to 1.62
Explanation
Take $V = 1\angle 0°$ and $I = 1\angle 36.87°$ (0.8 leading). First find $E' = V - jX_q I = 1 - j0.6(0.8 + j0.6) = 1.36 - j0.48$. Its magnitude is 1.442 and its angle is $-19.44°$. The angle between $I$ and $E'$ is $36.87° + 19.44° = 56.31°$, so the direct-axis current is $I_d = 1 \times \sin 56.31° = 0.832$. The induced voltage is $E = |E'| + (X_d - X_q) I_d = 1.442 + 0.2 \times 0.832 = 1.61$ pu.