Home › Previous year questions › GATE 2016 EE (EE2) › Question 50GATE 2016 EE (EE2) – Question 50 Power Systems · Basic concepts of electrical power generation, AC and DC transmission concepts, Models and performance of transmission lines and cables · 2 marks · Numerical answer
A no-load lossless three-phase 50 Hz line has sending and receiving line voltages 400 kV and 420 kV. Traveling-wave velocity equals light speed. Find its length in km.
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Show answer and explanation Correct answer: 294.0 to 298.0
Explanation For a lossless line with receiving current zero, Vs=Vr cos(βl). Thus cos(βl)=400/420=20/21.
Use β=2πf/c and take the physically usual shortest positive line length. Then $l=c\cos^{-1}(20/21)/(2\pi50)$.
With c=300000 km/s this gives **295.88 km**, within 294–298 km. The receiving voltage exceeds sending voltage due to the no-load Ferranti effect.
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