GATE 2025 EE – Question 33
The bus impedance matrix of a 3-bus system (in pu) is
$$Z_{bus}=\begin{bmatrix}j0.059&j0.061&j0.038\\j0.061&j0.093&j0.066\\j0.038&j0.066&j0.110\end{bmatrix}$$
A symmetrical fault (through a fault impedance of $j0.007$ pu) occurs at bus 2. Neglecting pre-fault loading conditions, the voltage at bus 1, during the fault is __________ pu (round off to three decimal places).
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Show answer and explanation
Correct answer: 0.38 to 0.40
Explanation
With no pre-fault loading all bus voltages are 1 pu before the fault. The fault current at bus 2 is $I_f=\dfrac{1}{Z_{22}+Z_f}=\dfrac{1}{j0.093+j0.007}=-j10$ pu. The voltage at bus 1 during the fault is $V_1=1-Z_{12}I_f=1-j0.061\times(-j10)=1-0.61=0.390$ pu.