GATE EE 2018 Set 1 — Question 30
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Power Systems → Fault Analysis → Symmetrical Components
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Question
The series impedance matrix of a short three-phase transmission line in phase coordinates isIf the positive sequence impedance is , and the zero sequence is , then the imaginary part of (in ) is __________ (up to 2 decimal places).
Correct answer
7 to 7
Solution
The relationship between phase impedances (, ) and sequence impedances (, , ) for a balanced transmission line is given by:
We have a system of two linear equations with two unknowns, and :
(i)
(ii) To find , we can subtract equation (i) from equation (ii):
The question asks for the imaginary part of .
.To be complete, we can also find from equation (i):
.
Let's check this with equation (ii):
, which matches the given .The imaginary part of is 7.00.
1.Zero sequence impedance:
2.Positive sequence impedance:
3.Negative sequence impedance:
We are given:We have a system of two linear equations with two unknowns, and :
(i)
(ii) To find , we can subtract equation (i) from equation (ii):
The question asks for the imaginary part of .
.To be complete, we can also find from equation (i):
.
Let's check this with equation (ii):
, which matches the given .The imaginary part of is 7.00.
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