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GATE 2020 EE – Question 57

Power Systems · Series and shunt compensation, Electric field distribution and insulators, Distribution systems · 2 marks · Numerical answer

Bus 1 with voltage magnitude $V_1=1.1$ pu is sending reactive power $Q_{12}$ towards bus 2 with voltage magnitude $V_2=1$ pu through a lossless transmission line of reactance $X$. Keeping the voltage at bus 2 fixed at 1 pu, magnitude of voltage at bus 1 is changed, so that the reactive power $Q_{12}$ sent from bus 1 is increased by 20%. Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude, $V_1$, in pu (rounded off to 2 decimal places), at bus 1 is ________.

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Correct answer: 1.11 to 1.13

Explanation

With no real power flow the angle is zero, so $Q_{12}=\frac{V_1(V_1-V_2)}{X}$. Initially $Q_{12}=\frac{1.1\times0.1}{X}=\frac{0.11}{X}$. The new value is $1.2\times0.11/X$, so $V_1(V_1-1)=0.132$, i.e. $V_1^2-V_1-0.132=0$, giving $V_1=\frac{1+\sqrt{1.528}}{2}=1.118$ pu.