GATE 2018 EE Q.2: solution and answer

Official answer: BSource: Official answer key, GATE 2018 EE (IIT Guwahati)

1. Power developed by a salient-pole synchronous motor has two components: an excitation (magnet) component and a reluctance component:
   $$P(\delta )=\frac{EV}{X_d}\sin \delta +\frac{V^2}{2}\left(\frac{1}{X_q}-\frac{1}{X_d}\right)\sin 2\delta$$

2. The second term — the reluctance power (and hence reluctance torque) — exists only because of rotor saliency ($X_d\ne X_q$) and is proportional to $\sin 2\delta$, independent of the excitation emf $E$.

3. The magnitude of $\sin 2\delta$ is maximum (equal to 1) when $2\delta =90^{\circ }$, i.e. when $\delta =45^{\circ }$.

4. Therefore the developed reluctance torque attains its maximum value at a load angle of $45^{\circ }$ electrical, independent of the excitation torque component (which instead peaks at $\delta =90^{\circ }$).

5. This corresponds to option (B).