# An 800 kV transmission line has a maximum power transfer capacity of P. When operated at 400 kV with the series reactance unchanged, the new maximum p

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An 800 kV transmission line has a maximum power transfer capacity of P. When operated at 400 kV with the series reactance unchanged, the new maximum power transfer capacity is approximately
1. P
2. 2 P
3. P / 2
4. P / 4

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Correct Answer - Option 4 : P / 4

Concept:

Power transfer capability of the transmission line is the indication of how much power transfers can be increased without compromising system security.

$P\propto \frac{{{V}_{S}}\cdot {{V}_{R}}}{{{X}_{S}}}$

$or~{{P}_{max}}=\frac{V_{S}^{2}}{{{X}_{S}}}$

It can be increased either by increasing voltage or by decreasing the reactance of the line.

Calculation:

It is given that XS = constant

${{P}_{max}}=\frac{V_{S}^{2}}{{{X}_{S}}}~or~P\propto V_{S}^{2}$

At VS = 800 V, Pm1 ∝ (800)2

And at VS = 400 V, Pm2 ∝ (400)2

$\Rightarrow \frac{{{P}_{m1}}}{{{P}_{m2}}}=\frac{{{\left( 800 \right)}^{2}}}{{{\left( 400 \right)}^{2}}}=4$

⇒ P2 = P1 / 4

And power transfer capability at VS = 800 V is P.

⇒ Power transfer capability at VS = 400 V

$\Rightarrow {{P}_{2}}=\frac{P}{4}$