# A lossless transmission line having surge impedance loading (SIL) of 2280 MW. A series capacitive compensation of 30% is emplaced. Then SIL of the compensated transmission line will be

A lossless transmission line having surge impedance loading (SIL) of 2280 MW. A series capacitive compensation of 30% is emplaced. Then SIL of the compensated transmission line will be

### Right Answer is: 2725 MW

#### SOLUTION

Let characteristic impedance

$\begin{array}{l}({Z_C}) = \sqrt {\dfrac{Z}{Y}} = \sqrt {\dfrac{1}{1}} = 1{\text{ PU}}\\\\{\text{ = }}\sqrt{\dfrac{{{Im}pedance/Km}}{{Admittan ce/Km}}} = \sqrt {\dfrac{X}{B}} \end{array}$

Given that, for a given line 30% series capacitive compensation is provided. Hence the series impedance of the line is 0.7 or (70%) of the original value.

$({Z_{new}}) = \sqrt {\dfrac{{0.7}}{{1.0}}} = \sqrt {\dfrac{1}{1}} = 0.836{\text{ PU}}$

Surge Impedance loading = (V2/Zc)

SIL ∝ 1/ZC

(SIL)2/(SIL)1 = Zc1/Zc2

(SIL)2 = (1.0 × 2280 × 106)/(0.836)

(SIL)2 = 2725 × 106

(SIL)2 = 2725 MW

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