GATE EE 2026 Set 1 — Question 41
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Power Systems → Per-Unit System & Load Flow → Y-Bus Formation
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Question
A three-phase two-winding transformer has a voltage transformation ratio , where is the primary side voltage in p.u., and is the secondary side voltage in p.u. and represent the currents injected into the primary and secondary sides of the transformer, respectively. The admittance corresponding to the leakage impedance of the transformer referred to the secondary is p.u. Neglect the magnetizing branch.
The bus representation of this transformer is:
Correct answer
(D) bmatrix I_P \ I_S bmatrix = bmatrix yₜ & -(yₜ)/(0.866 - j0.5) \ -(yₜ)/(0.866 + j0.5) & yₜ bmatrix bmatrix V_P \ V_S bmatrix
Solution
For a phase-shifting transformer with a complex turns ratio and series admittance referred to the secondary side, the -bus matrix is given by:Given , we find its magnitude and conjugate:Substituting these into the matrix:This matches Option D.
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