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GATE 2026 EE – Question 18

Power Systems · Per-unit quantities, Bus admittance matrix, Gauss-Seidel and Newton-Raphson load flow methods · 1 mark · Multiple choice

Consider a power system with $N$ buses, of which $P$ are generator buses and the remaining $Q$ are load buses (where there is no generation).

Assume that there are no reactive power-limit violations at the generator buses.

What is the size of the Jacobian matrix in the Newton-Raphson load flow method?

  1. $2N\times2N$
  2. $(2N-1-P)\times(2N-1-P)$
  3. $(2N-Q)\times(2N-Q)$
  4. $(P+Q)\times(P+Q)$

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Show answer and explanation

Correct answer: (B) $(2N-1-P)\times(2N-1-P)$

Explanation

The $P$ generator buses include the slack bus, so $N=P+Q$. The unknowns are the voltage angles at all buses except the slack ($N-1$) and the voltage magnitudes at the load buses ($Q$). The Jacobian is $(N-1+Q)\times(N-1+Q)$. Since $Q=N-P$, this is $(2N-1-P)\times(2N-1-P)$.