(a) A 3-phase, 50 Hz, 220 kV overhead transmission line is 300 km long. Per km inductance and capacitance of the line per phase are 1 mH and 0.01 uF, respectively. Assuming the line to be lossless, find the propagation constant per km, characteristic impedance, velocity of propagation of current and voltage waves along the line, and the wavelength of those waves.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter5: Transmission Lines: Steady-state Operation
Section: Chapter Questions
Problem 5.31P: A 500-kV, 300-km, 6()-Hz, three-phase overhead transmission line, assumed to be lossless, has a...
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(a) A 3-phase, 50 Hz, 220 kV overhead transmission line is 300 km long. Per km
inductance and capacitance of the line per phase are 1 mH and 0.01 µF, respectively.
Assuming the line to be lossless, find the propagation constant per km, characteristic
impedance, velocity of propagation of current and voltage waves along the line, and
the wavelength of those waves.
(b) A 15 kV, 1500 rpm, 3-phase, round rotor synchronous generator has a synchronous
reactance of 10 N per phase. With the rated voltage at its terminals, the machine is
operating at unity power factor with a load angle, 8 = 8max/3, where &max is the
maximum possible load angle of the generator. What is the internal line to line emf
of the generator?
(c) Solve the following equations by Newton-Raphson method. Take an initial guess of
x1 = 1.5 and x2 = 3.5.
xỉ + x1x2 = 10
X2 + 3x1x = 57
Transcribed Image Text:(a) A 3-phase, 50 Hz, 220 kV overhead transmission line is 300 km long. Per km inductance and capacitance of the line per phase are 1 mH and 0.01 µF, respectively. Assuming the line to be lossless, find the propagation constant per km, characteristic impedance, velocity of propagation of current and voltage waves along the line, and the wavelength of those waves. (b) A 15 kV, 1500 rpm, 3-phase, round rotor synchronous generator has a synchronous reactance of 10 N per phase. With the rated voltage at its terminals, the machine is operating at unity power factor with a load angle, 8 = 8max/3, where &max is the maximum possible load angle of the generator. What is the internal line to line emf of the generator? (c) Solve the following equations by Newton-Raphson method. Take an initial guess of x1 = 1.5 and x2 = 3.5. xỉ + x1x2 = 10 X2 + 3x1x = 57
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