GATE EE 2015 Set 2 — Question 26
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Power Systems → Power System Stability → Steady-State & Transient Stability
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Question
The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude are constant. If one line is tripped at time by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle shows the transient correctly?
Correct answer
(A) [figure]
Solution
1.Initial State: The generator delivers power , where is the equivalent reactance of the two parallel lines. In steady state, .
2.Disturbance: At , one line is tripped. The equivalent reactance increases to .
3.Immediate Effect: The electrical power output drops below the constant mechanical input . This creates an accelerating power .
4.Transient Response: Due to the accelerating power, the rotor angle begins to increase. The new steady-state angle must satisfy . Since , it follows that .
5.Stability: The system is stated to undergo a stable transient, meaning will oscillate around the new equilibrium point and eventually settle there due to damping.
6.Conclusion: Waveform (A) is the only one showing increasing from and oscillating around a higher value.
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