Correct Answer - Option 1 : 4271.2 kW

**Concept:**

For Synchronous motor power is given by

\(P = \frac{{E{V_t}}}{{{X_s}}}\sin \delta \)

For maximum power δ = 90° ⇒ sin 90° = 1

\(P_{max} = \frac{{E{V_t}}}{{{X_s}}}\)

E = generated voltage

V_{t} = terminal voltage

X_{s} = synchronous reactance

**Calculation:**

Given that

V_{ph} = 4000 / √3 = 2309.4 V and X_{S} = 4 Ω

\({I_L} = \frac{{1500}}{{√ 3 × 4000 × 1}} = 216.5\;A\)

E_{ph} = √(Vcos ϕ + I_{a}R_{a})^{2} + (Vsin ϕ + I_{a}X_{s})^{2}

Eph = √(2309.4 × 1 + 0)2 + (0 + 216.5 × 4)2

E_{ph} = 2466.5 V

E = √3E_{ph} = 4272 V

\(P_{max} = \frac{{E{V_t}}}{{{X_s}}}\)

\(P_{max} = \frac{{4272 × 4000 }}{{{4}}}=4271.2\;kW\)