Question

A 400 kV, 3-$\varphi$, 300 km lossless transmission line operated at 50 Hz. If the surge impedance of line is 400, then sending end current (in ampere) of line at no load is________.

• A. 122.56
• B. 187.60
• C. 324.91
• D. 0

Answer 1

The correct option is B 187.60

Given line is long transmission line

$V_S=V_{R}cos\beta l+j{Z}_C{I}_{R}sin\beta l$

$I_S=\frac{j{V}_R}{Z_C}.sin\beta l+I_{R}cos\beta l$ (Equation of loss-less transmission line)


$\beta =\frac{2\pi }{\lambda }$

$\lambda =\frac{c}{f}$

$c=3\times {10}^{5}km/sec$

$f=50Hz$

$\beta =\frac{2\pi \times 50}{3\times {10}^5}=1.04719\times {10}^{-3}rad/km$

$\beta l=\frac{\pi }{10}={18}^o$

At no load, $I_R=0$

Receiving end line voltage $=V_{RL}$

$V_{RL}=\frac{V_S}{cos\beta l}=\frac{400}{cos18}=420.58kV$

$V_{Rph}=242.82kV$

$|I_S|=\frac{V_R}{Z_C}.sin\beta l=\frac{242.82\times {10}^3}{400}\times sin{18}^{\circ }=187.59Amp$