## Description

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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