GATE 2022 EE – Question 57
A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s$^2$ is ________. (round off to nearest integer)
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Correct answer: 75
Explanation
The accelerating power is $15-10=5$ MW, i.e. $0.25$ pu on the 20 MVA base. The swing equation $\frac{H}{\pi f}\frac{d^2\delta}{dt^2}=P_a$ gives $\frac{d^2\delta}{dt^2}=\frac{\pi\times50\times0.25}{15}=2.618$ electrical rad/s$^2$. For a 4-pole machine the mechanical value is half, $1.309$ rad/s$^2=75$ degrees/s$^2$.