GATE 2017 EE – Question 65
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5\sin\delta$, where $\delta$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of $\delta$, as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is $P_{max}\sin\delta$, the value of $P_{max}$, in pu is ________. (Give the answer up to three decimal places.)
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Correct answer: 1.20 to 1.24
Explanation
Initially $1 = 1.5\sin\delta_0$, so $\delta_0 = \sin^{-1}\left(\frac{1}{1.5}\right) = 0.7297$ rad. After the line is removed, the swing stops at $\delta_m = 1.221$ rad. By the equal area criterion, the accelerating area equals the decelerating area: $1 \times (\delta_m - \delta_0) = P_{max}\left(\cos\delta_0 - \cos\delta_m\right)$. The left side is $0.4913$ and the cosine difference is $0.7454 - 0.3426 = 0.4028$. So $P_{max} = \frac{0.4913}{0.4028} = 1.22$ pu.