Description
Transmission Line Functions
The accompanying data file shows the frequency dependence of the line parameters
R(ω) and L(ω) for a typical three-phase transmission line 300 km long and 500 kV.
Subscript “zero” refers to Eigenmode 1, where the return conductor is the ground, while
subscript “positive” refers to Eigenmode 2, where the return conductor is a normal
conductor. The capacitance C and the shunt conductance G are assumed to be constant
with frequency. Notice that G is not zero but a small value.
For the given data, evaluate and plot the transmission line propagation functions
for eigenmodes 1 and 2:
1. The characteristic impedance Zc(ω) in magnitude and phase angle
2. The propagation function e
−γ(ω)`
in magnitude and phase angle. Make sure the
angle of this function is a monotonic function, that is, it does not wind up every
2π radians .
3. The attenuation α(ω) is in nepers/km, the phase displacement β(ω) is in radians/km, and the propagation speed a(ω) is in km/s.
4. Comments:
(a) Compare the positive and zero sequence shapes of Zc(ω) and e
−γ(ω)`
.
(b) Why is the velocity of propagation a(ω) not equal to the speed of light for
all frequencies?
(c) Any other relevant comment.
Annexes:
• Data file “Data Assign04.txt”
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