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GATE 2021 EE – Question 45

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

A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the $Y_{Bus}$ matrix correspond to Bus 1, 2 and 3, respectively, then $Y_{Bus}$ of the network is

Diagram for GATE 2021 EE question 45
  1. Matrix (A)
  2. Matrix (B)
  3. Matrix (C)
  4. Matrix (D)

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Correct answer: (C) Matrix (C)

Explanation

Ideal voltage sources at each bus behave as short circuits to ground in the Y-bus, so each bus sees the line admittances and its own connection to the reference. Building the matrix from the elements of the figure gives diagonal entries of $-\frac34j$ and off-diagonal entries of $\frac14j$ in every row, which is matrix (C).