# At no-load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively.

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At no-load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is ____________.

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For a long transmission line receiving end voltage is higher than sending end voltage, this indicated Ferranti effect

Vs = A VR (at the lightly loaded condition)

Where

Vs is the sending end voltage

VR is the receiving end voltage

Also from the ABCD parameters, the approximate value of A is

$A=1+\frac{YZ}{2}=1-\frac{\omega^{2}l^{2}}{2V^{2}}$
$A = \frac{{{V_S}}}{{{V_R}}} = \frac{{400 \times {{10}^3}}}{{420 \times {{10}^3}}} = 0.95$

$A=0.95=1 - \frac{{{\omega ^2}{l^2}}}{{2{V^2}}}$

$⇒ 1 - \frac{{{{\left( {2\pi \times 50} \right)}^2}{l^2}}}{{2 \times {{\left( {C} \right)}^2}}} = 0.95$

⇒ l = 294.8 km

Therefore the length of the transmission line will be 294.8km