# GATE Papers >> EEE >> 2017 >> Question No 115

Question No. 115

The figure shows the power per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where $\alpha$ is a complex number with non-zero real and imaginary parts. For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 × 2. Which one of the following statements is true?

##### Answer : (D) Both Ybus and Zbus are unsymmetric

Solution of Question No 115 of GATE 2017 EEE Paper For the above network

E1 = $\frac{{\mathrm V}_2}{\mathrm\alpha}$

${\mathrm I}_1=\mathrm\alpha\;{\mathrm I}_2$

By KVL

V1 = E1 + I1 Z = $\frac{{\mathrm V}_2}{\mathrm\alpha}+\left(\mathrm\alpha\;\mathrm Z\right){\mathrm I}_2$

In matrix form,

$\begin{bmatrix}\begin{array}{c}{\mathrm V}_1\\{\mathrm I}_1\end{array}\end{bmatrix}\begin{bmatrix}1/\mathrm\alpha&\mathrm{αZ}\\0&\mathrm\alpha\end{bmatrix}\begin{bmatrix}{\mathrm V}_2\\{\mathrm I}_2\end{bmatrix}$

Since A $\neq$ D, the system is asymmetric and hence YBUS and ZBUS will also be asymmetric.

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