GATE EE 2016 Set 1 — Question 61
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Question
A single-phase transmission line has two conductors each of mm radius. These are fixed at a center-to-center distance of m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be more than that of the inductance per conductor of the single-phase system. The distance , in meters, is _______.
Correct answer
1.41 to 1.47
Solution
1.Single-phase line inductance per conductor:
The inductance per conductor is given by:H/m
where m is the distance between conductors and is the self-GMD.
mm m.
m.
2.Three-phase line positive sequence inductance:
For a transposed three-phase line, the inductance per phase is:H/m
The distances between conductors are m, , and .
.
3.Applying the given condition:
m.The value of is approximately meters, which falls within the range .
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