GATE EE 2017 Set 2 — Question 15
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Power Systems → Per-Unit System & Load Flow → Y-Bus Formation
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Question
The figure shows the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where is a complex number with non-zero real and imaginary parts.
For the given circuit, and are bus admittance matrix and bus impedance matrix, respectively, each of size . Which one of the following statements is true?
Correct answer
(D) Both Y_(bus) and Z_(bus) are unsymmetric
Solution
Let , let be the voltage on the primary (bus-1 side) of the ideal transformer, and let be the currents injected into the network at buses 1 and 2.Ideal transformer : , and since it is lossless, the complex power entering the primary leaves the secondary:Series impedance:HenceBecause has a non-zero imaginary part, , so : is unsymmetric.. If were symmetric, then would also be symmetric, since . So is unsymmetric too. (As drawn, with no shunt element to ground, this has zero determinant; the symmetry conclusion is for the usual case where shunt elements make it invertible, and adding shunt admittances to the diagonal does not change .)Answer: (D) Both and are unsymmetric
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