GATE 2018 EE – Question 30
The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix}Z_s&Z_m&Z_m\\Z_m&Z_s&Z_m\\Z_m&Z_m&Z_s\end{bmatrix}$. If the positive sequence impedance is $(1+j10)\ \Omega$, and the zero sequence impedance is $(4+j31)\ \Omega$, then the imaginary part of $Z_m$ (in $\Omega$) is ________ (up to 2 decimal places).
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Correct answer: 7
Explanation
$Z_1=Z_s-Z_m=1+j10$ and $Z_0=Z_s+2Z_m=4+j31$. Subtracting, $3Z_m=3+j21$, so $Z_m=1+j7$ and its imaginary part is $7\ \Omega$.