GATE EE 2024 Set 1 — Question 46
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Power Systems → Fault Analysis → Symmetrical Components
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Question
For a two-phase network, the phase voltages and are to be expressed in terms of sequence voltages and as . The possible option(s) for matrix is/are
Correct answer
(A) bmatrix 1 & 1 \ 1 & -1 bmatrix; (D) bmatrix -1 & 1 \ 1 & 1 bmatrix
Solution
For a valid sequence transformation in a two-phase system, the transformation matrix must be non-singular (determinant ).
- For (A): . This is the standard symmetrical component transformation for a 2-phase system.
- For (B): . Singular matrix, not a valid transformation.
- For (C): . While non-singular, it is not a standard sequence transformation.
- For (D): . This is a valid variation of the standard transformation (equivalent to a row swap and sign change).
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