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GATE 2020 EE – Question 39

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

Two buses, $i$ and $j$, are connected with a transmission line of admittance $Y$, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:

Diagram for GATE 2020 EE question 39
  1. Matrix (A)
  2. Matrix (B)
  3. Matrix (C)
  4. Matrix (D)

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Correct answer: (C) Matrix (C)

Explanation

Referring the line to each bus gives the diagonal entries $t_i^2Y$ and $t_j^2Y$ (each end sees the line admittance scaled by the square of its tap ratio), and the off-diagonal entries are $-t_it_jY$. That is matrix (C).