Non-salient power angle relation for salient machines

The statement is true. The power-angle equation of a non-salient (cylindrical-rotor) machine is

$$P = \frac{3EV}{X_s}\sin\delta$$

It assumes a uniform air gap, so the same reactance $X_s$ acts on the armature mmf in every direction.

Why it fails for salient-pole machines

1. A salient-pole rotor has a non-uniform air gap: small under the pole (direct axis, d-axis) and large between poles (quadrature axis, q-axis).
2. Reluctance along the d-axis is low, so $X_d$ is large; along the q-axis reluctance is high, so $X_q$ is smaller ($X_d > X_q$). A single $X_s$ cannot represent the machine.
3. The armature current must be split into $I_d$ and $I_q$ (two-reaction theory), and the power becomes

$$P = \frac{3EV}{X_d}\sin\delta + \frac{3V^2}{2}\left(\frac{1}{X_q} - \frac{1}{X_d}\right)\sin2\delta$$

4. The second term is the reluctance power; it exists even with zero excitation ($E = 0$), because the rotor tends to align with the stator field along its minimum-reluctance path. A cylindrical rotor has no such term ($X_d = X_q$).

Effect on the curve

 P
 |        resultant (salient)
 |      .-"-.
 |    .'  .--'-.  excitation term
 |  .'  .'      '.
 |.' .-'-.        '.  reluctance term (sin 2d)
 +--------'----------'----> delta
 0     45   70  90     180

• Maximum power occurs at $\delta < 90^\circ$ (typically 60°–75°), not at 90°.
• $P_{max}$ is larger than for a cylindrical machine with the same $E$ and $X_d$; the curve is steeper at small $\delta$ (higher synchronising power).

Hence the cylindrical-rotor formula would give a wrong $P_{max}$ and wrong stability limit for salient-pole machines.