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GATE 2018 EE – Question 39

Power Systems · Per-unit quantities, Bus admittance matrix, Gauss-Seidel and Newton-Raphson load flow methods · 2 marks · Multiple choice

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$, and line reactive power loss ($Q_{loss}$) respectively are

Diagram for GATE 2018 EE question 39
  1. 5.00, 12.68, 2.68
  2. 6.34, 10.00, 1.34
  3. 6.34, 11.34, 2.68
  4. 5.00, 11.34, 1.34

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Show answer and explanation

Correct answer: (C) 6.34, 11.34, 2.68

Explanation

Bus 1 has $20$ pu generation and $15$ pu load, so $P_{12}=5=\frac{\sin\delta}{0.1}$ and $\delta=30^\circ$. The reactive flows are $Q_{12}=\frac{1-\cos30^\circ}{0.1}=1.34$ at each end, going out of each bus into the line. Then $Q_{G1}=5+1.34=6.34$, $Q_{G2}=10+1.34=11.34$ and $Q_{loss}=2\times1.34=2.68$.