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GATE 2023 EE – Question 28

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

The bus admittance ($Y_{bus}$) matrix of a 3-bus power system is given below.

$$Y_{bus}=\begin{bmatrix}-j15&j10&j5\\j10&-j13.5&j4\\j5&j4&-j8\end{bmatrix}$$

Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

  1. Line charging capacitor of finite value is present in all three lines
  2. Line charging capacitor of finite value is present in line 2-3 only
  3. Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 1 only
  4. Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 3 only

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Show answer and explanation

Correct answer: (A) Line charging capacitor of finite value is present in all three lines

Explanation

Each row sum of $Y_{bus}$ gives the total shunt susceptance at that bus (half line charging plus any shunt element): bus 1: $-15+10+5=0$; bus 2: $+0.5$; bus 3: $+1$. Bus 1 has zero net shunt, so no line connected to bus 1 (lines 1-2 and 1-3) can have finite charging. That makes "charging in all three lines" impossible.