GATE 2017 EE (EE2) – Question 64

Power Systems · System stability concepts, Equal area criterion · 2 marks · Numerical answer

A 3-phase, 2-pole, 50 Hz synchronous generator is rated 250 MVA at 0.8 lagging pf. Its synchronous-speed kinetic energy is 1000 MJ. It initially delivers 60 MW at power angle 10 electrical degrees. The load is removed suddenly; assume constant acceleration for 10 cycles. Find its power angle after 5 cycles in electrical degrees.

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Correct answer: 12.5 to 12.9

Explanation

The inertia constant is H=1000/250=4 s. After removal, accelerating power is 60 MW or 0.24 pu, with unchanged mechanical input.

The swing equation gives electrical acceleration $\ddot\delta=\omega_sP_a/(2H)=2\pi50(0.24)/(8)=3\pi$ rad/s².

Five cycles take 5/50=0.1 s. Initial relative speed is zero, so angle increase is $\tfrac12(3\pi)(0.1)^2=0.015\pi$ rad=2.7°. Therefore the final angle is **12.7°**.

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