GATE 2015 EE – Question 53
A 50 Hz generating unit has $H$-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle $\delta$ is 5°, when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of $\delta$ in degrees, 0.02 second after the fault is ________.
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Correct answer: 5.7 to 6.1
Explanation
A bolted three-phase fault at the terminals makes the electrical output zero, so the whole 1 pu of mechanical power accelerates the rotor. The swing equation gives $\frac{d^2\delta}{dt^2} = \frac{180 f}{H} P_a = \frac{180 \times 50}{2} \times 1 = 4500$ degrees/s$^2$. After 0.02 s, $\delta = 5 + \frac{1}{2} \times 4500 \times (0.02)^2 = 5 + 0.9 = 5.9°$.