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 μF/km per phase. T - Electrical Engineering NAT PYQs Based test 12: Power Systems | ExamTest.live

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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 μF/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be ___________.

Correct Answer

414-423

Solution & Step-by-step Explanation

Given that, sending end voltage (V_{S}) = 400 kV length of transmission line (L) = 300 km inductance (L) = 1 mH/km/phase capacitance (c) = 0.01 μF/km/phase We know that, V = \frac{1}{L C} = \frac{1}{1 \times 10 ^{- 3} \times 0.01 \times 10 ^{- 6}} = 3.16 \times 1 0^{5} km / s β = \frac{2 π f L}{V} = \frac{2 π \times 50 \times 300}{3.16 \times 10 ^{5}} = 0.298 A = 1 - \frac{β ^{2}}{2} = 1 - \frac{( 0.298 ) ^{2}}{2} = 0.955 V_{R} = \frac{V _{S}}{A} = \frac{400}{0.955} = 418.85 V

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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 μF/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be ___________.

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