The GATE Grind

GATE 2018 EE – Question 38

Power Systems · Symmetrical components, Symmetrical and unsymmetrical fault analysis · 2 marks · Multiple choice

The positive, negative and zero sequence impedances of a three phase generator are $Z_1$, $Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$, the fault current is $I_{f1}=kI_f$, where $I_f$ is the fault current with zero fault impedance. The relation between $Z_f$ and $k$ is

  1. $Z_f=\dfrac{(Z_1+Z_2)(1-k)}{k}$
  2. $Z_f=\dfrac{(Z_1+Z_2)(1+k)}{k}$
  3. $Z_f=\dfrac{(Z_1+Z_2)k}{1-k}$
  4. $Z_f=\dfrac{(Z_1+Z_2)k}{1+k}$

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Correct answer: (A) $Z_f=\dfrac{(Z_1+Z_2)(1-k)}{k}$

Explanation

For a line-to-line fault the fault current is proportional to $\frac{1}{Z_1+Z_2+Z_f}$, and for $Z_f=0$ it is proportional to $\frac{1}{Z_1+Z_2}$. So $k=\frac{Z_1+Z_2}{Z_1+Z_2+Z_f}$, which gives $Z_f=\frac{(Z_1+Z_2)(1-k)}{k}$.