GATE EE 2025 Set 1 — Question 49
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Power Systems → Power System Stability → Equal Area Criterion
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Question
In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at very close to circuit breaker 1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?
Correct answer
(B) Fig. (ii)
Solution
1.Pre-fault condition: The generator is supplying power at an initial rotor angle . The electrical power output is .
2.Fault condition: A bolted LLLG fault occurs at the generator terminals ( is very close to CB1). This causes the terminal voltage to drop to zero, resulting in . The rotor accelerates due to the power mismatch . The accelerating area is the area under the line from to the clearing angle .
3.Post-fault condition: The fault is cleared, and the line is restored. The electrical power output returns to . Since at this stage, the rotor decelerates. The decelerating area is the area between the curve and the line from to the maximum angle .
4.Conclusion: Fig. (ii) correctly represents these areas, where is the rectangular area under (since during fault) and is the area above under the sinusoidal power-angle curve.
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