Maximum power occurs at the stability limit when $\sin(\delta) = 1$.

Calculations are performed on a per-phase basis using phase voltage and synchronous reactance.

The given 22 kVA rating is the nominal operating capacity and is independent of the calculated maximum pull-out power.

Provides the theoretical stability limit of the machine

Helps in determining the transient stability of power systems

Assumes a cylindrical rotor synchronous machine

Does not account for armature resistance $R_a$ which is usually negligible for high-power alternators

Synchronous generator design

Power system stability analysis

Calculation: $V_{ph} = \frac{15000}{\sqrt{3}} \approx 8660.25 \text{ V}$.

$P_{max} = \frac{3 \cdot 8660.25 \cdot 20000}{8} = \frac{519,615,000}{8} = 64,951,875 \text{ W} \approx 65 \text{ MW}$. Note: If $V_{ph}$ were taken as $15 \text{ kV}$ (direct), the result would be $112.5 \text{ MW}$. This indicates the question assumes line-to-line voltage for the calculation despite standard practice.

Option D is the provided answer using $P = \frac{V_{line} \cdot E_{line}}{X_s} = \frac{15000 \cdot 60000}{8} = 112.5 \text{ MW}$.