# GATE Papers >> EEE >> 2017 >> Question No 55

Question No. 55

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 circuit 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 values of  $P_{max}$, in pu is ________ . (Give the answer up to three decimal places.)

##### Answer : 1.21 to 1.23

Solution of Question No 55 of GATE 2017 EEE Paper

With one transmission line removal, the effective rectance increases so Pmax decreases, the power angle by equal area criterion

$\int\limits_{{\mathrm\delta}_0}^{{\mathrm\delta}_1}$ (1 – Pmax sin $\delta$)d$\delta$ = $\int\limits_{{\mathrm\delta}_1}^{{\mathrm\delta}_2}$ (Pmax sin$\delta$ – 1) d$\delta$

$\begin{array}{l}\left({\mathrm\delta}_1-{\mathrm\delta}_0\right)-{\mathrm P}_\max\left({\mathrm{cosδ}}_0-{\mathrm{cosδ}}_1\right)={\mathrm P}_\max({\mathrm{cosδ}}_1-{\mathrm{cosδ}}_2)-\left({\mathrm\delta}_2-{\mathrm\delta}_1\right)\\\left({\mathrm\delta}_2-{\mathrm\delta}_0\right)={\mathrm P}_\max\left({\mathrm{cosδ}}_0-{\mathrm{cosδ}}_2\right)\\{\mathrm P}_\max=\frac{{\mathrm\delta}_2-{\mathrm\delta}_0}{\left({\mathrm{cosδ}}_0-{\mathrm{cosδ}}_2\right)}\\{\mathrm\delta}_0=\sin^{-1}\frac1{1.5}=0.72972\\{\mathrm P}_\max=\frac{\left(1.221-0.72972\right)}{\cos\left(0.7297\right)-\cos\left(1.221\right)}=1.22\mathrm{pu}\end{array}$

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