# In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

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1. 0
2. 45
3. 60
4. 90

Option 2 : 45
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CIL MT Electrical: 2020 Official Paper
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## Detailed Solution

Concept:

In a salient pole synchronous motor, the power flow is given by,

$$P = \frac{{EV}}{{{X_d}}}\sin \delta + \frac{{{V^2}}}{2}\left[ {\frac{1}{{{X_q}}} - \frac{1}{{{X_d}}}} \right]\sin 2\delta$$

The torque equation is given by

$$T = \frac{{60}}{{2\pi {N_S}}}\left[ {\frac{{EV}}{{{X_d}}}\sin \delta + \frac{{{V^2}}}{2}\left[ {\frac{1}{{{X_q}}} - \frac{1}{{{X_d}}}} \right]\sin 2\delta } \right]$$

Here,

$$\frac{{EV}}{{{X_d}}}\sin \delta$$ is electromagnetic torque

$${\rm{and}}\frac{{{V^2}}}{2}\left[ {\frac{1}{{{X_q}}} - \frac{1}{{{X_d}}}} \right]\sin 2\delta = Reluctance\;torque.$$

Explanation:

As we know that Vt = terminal voltage depends on the load.

Xd and Xq depend on the power factor angle which also depends on the load.

So, we cannot change the value of the three-parameter.

The value of sin 2δ always varies in the range +1 to -1.

For the maximum value of TR sin 2δ should be maximum

⇒ sin 2δ = + 1

⇒ 2δ = sin-1 (1) = 90°

⇒ δ = 45°

Torque angle δ is 45° for maximum reluctance torque to be produced in a synchronous motor.
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