GATE 2019 EE – Question 59
A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 $\mu$F/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, then the receiving end line voltage in kV (round off to two decimal places) will be ________.
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Correct answer: 418
Explanation
For the loss-less open-circuited line, $V_r=\frac{V_s}{\cos\beta l}$ (the Ferranti effect). Here $L=0.3$ H and $C=3\ \mu$F in total, so $\beta l=\omega\sqrt{LC}=314.16\sqrt{0.3\times3\times10^{-6}}=0.298$ rad. So $V_r=\frac{400}{\cos0.298}=\frac{400}{0.956}=418$ kV.