GATE EE 2017 Set 1 — Question 55
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Power Systems → Power System Stability → Equal Area Criterion
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Question
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is , where is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to pu. If one of the transmission line circuits is removed, the maximum value of , as the rotor swings, is radian. If the expression for electrical power with one transmission line circuit removed is , the value of , in pu is ______. (Give the answer up to three decimal places.)
Correct answer
1.2 to 1.24
Solution
1.Initial State:
The system is operating at a stable equilibrium point where mechanical power equals electrical power .pu,
At equilibrium:
rad
2.Post-Fault State:
One circuit is removed. The new electrical power is .The mechanical power remains pu.
3.Equal Area Criterion:
For the maximum swing rad, the accelerating area must equal the decelerating area. This is equivalent to saying the net work done on the rotor is zero at the peak of the swing:4.Calculation:
puRounding to three decimal places, . The official range is to .
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