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
For a phase-shifting transformer with a complex turns ratio , the relationship between currents and voltages at the two buses is non-reciprocal. The admittance matrix for such a transformer is given by:where . Since is a complex number with non-zero imaginary parts, , which implies . Therefore, is unsymmetric. Since , the inverse of an unsymmetric matrix is also unsymmetric. Thus, both and are unsymmetric.
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