Question Details

The valid positive, negative and zero sequence impedance (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

Options

A

0.15, 0.15 and 0.35

B

0.2, 0.2 and 0.2

C

1.1, 0.15 and 0.08

D

0.1, 0.3 and 0.1

Correct Answer :

0.15, 0.15 and 0.35

Solution :

The correct option is 0.15, 0.15 and 0.35.

To understand why this is the correct choice, let us analyze the sequence impedances of a fully transposed three-phase transmission line:

1. Positive Sequence Impedance (Z1) and Negative Sequence Impedance (Z2):
A transmission line is a static bilateral component. The phase sequence of the applied balanced voltages does not affect the physical symmetry of the line conductors. Since the line is fully transposed, the mutual coupling between the phases is balanced, making the positive-sequence impedance equal to the negative-sequence impedance.
Therefore, we have:
Z1 = Z2
This immediately eliminates options where the first and second values are not identical.

2. Zero Sequence Impedance (Z0):
The zero-sequence currents flow through all three phases in the same direction and must return through the ground or neutral wire. Because the ground return path has a much higher resistivity and a larger effective loop area compared to the path between conductors, the ground return path introduces significant additional resistance and loop inductance. Consequently, the zero-sequence impedance is substantially larger than the positive (or negative) sequence impedance.
Typically, for overhead transmission lines, Z0 is about 2 to 3.5 times Z1:

Z0 > Z1 = Z2

Let us evaluate the given choices based on these rules:
- 0.15, 0.15 and 0.35: Here, Z1 = Z2 = 0.15 p.u. and Z0 = 0.35 p.u. (which is greater than Z1). This satisfies all physical constraints.
- 0.2, 0.2 and 0.2: Here, Z0 = Z1, which is incorrect because the ground return path impedance is neglected.
- 1.1, 0.15 and 0.08: Here, Z1 ≠ Z2, and Z0 is smaller than Z1, which is physically incorrect.
- 0.1, 0.3 and 0.1: Here, Z1 ≠ Z2, which is incorrect for a transposed transmission line.

Thus, the only valid set of positive, negative, and zero sequence impedances is 0.15, 0.15 and 0.35.

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