The figure is a per-phase phase-shifting transformer between buses 1 and 2, with complex ratio α having nonzero real and imaginary parts. $Y_{bus}$ and $Z_{bus}$ are each 2×2 bus matrices. Which is true?
Correct answer: (D) Both matrices are unsymmetric.
Explanation
A complex tap makes the two mutual admittance terms proportional to $-1/\alpha$ and $-1/\alpha^*$, respectively. They differ for a nonreal tap, so the bus admittance matrix is not symmetric.
For an invertible matrix, a symmetric inverse would imply a symmetric original matrix. Thus a defined bus impedance matrix is also unsymmetric. This gives the official answer **D**.
**Source qualification:** taken alone with no bus reference/shunt connections, the drawn single branch has a singular two-node admittance matrix. Zbus requires an appropriate reference/network embedding; the keyed comparison assumes that it is defined.
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