GATE 2016 EE – Question 61
A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 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 D 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 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is ________.
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Correct answer: 1.41 to 1.47
Explanation
The inductance per conductor is proportional to $\ln\frac{\text{GMD}}{r'}$, where $r' = 0.7788 r = 0.007788$ m. For the single-phase line, $\ln\frac{1}{0.007788} = 4.855$. For the transposed three-phase line the GMD is $(1 \times D \times D)^{1/3} = D^{2/3}$. We need $\ln\frac{D^{2/3}}{r'} = 1.05 \times 4.855 = 5.098$, so $\frac{2}{3}\ln D = 5.098 - 4.855 = 0.243$. Then $\ln D = 0.364$ and $D = 1.44$ m.