A 40 MVA, 11 KV, 3-phase, 50 Hz, 4-pole turbo alternator has an inertia constant of 15 sec. An input of 20 MW developed 15 MW of output power Then the acceleration is

VA rating (S) = 40 MVA

voltage (V) = 11 kV

Frequency (f) = 50 Hz

Number of poles (P) = 4

Inertia constant (H) = 15 sec

Input power (P_in) = 20 MW

output power (P_out) = 15 MW

Acceleration power P_a = P_in - P_out = 5 MW

\({P_a} = M\frac{{{d^2}\delta }}{{d{t^2}}} = M\alpha\)

\(\Rightarrow {P_a} = \left( {\frac{{SH}}{{180f}}} \right)\alpha\)

\(\Rightarrow \alpha = \frac{{5 \times {{10}^6} \times 180 \times 50}}{{40 \times {{10}^6} \times 15}}\)