Question

A fully transposed transmission line has

• A. Zero sequence impedance larger than the positive sequence impedance
• B. Zero sequence impedance smaller than the positive sequence impedance
• C. Zero sequence impedance equal to positive sequence impedance
• D. Positive sequence impedance is larger than the negative sequence impedance

Hint:

For static, passive transmission components like lines and cables, remember that $Z_1 = Z_2$ always holds true, while $Z_0$ is significantly larger due to the high-impedance ground return path.

Answer 1

The Correct Option is A

Concept: Symmetrical component analysis assigns unique sequence network impedances ($Z_1$ for positive, $Z_2$ for negative, and $Z_0$ for zero sequence) to transmission lines. For a fully transposed transmission line, magnetic and electric field imbalances are neutralized across phases, which simplifies the parameters: * Positive sequence impedance ($Z_1$) and Negative sequence impedance ($Z_2$) are equal ($Z_1 = Z_2$). * Zero sequence currents flow in phase through all three conductors and must return through either the ground or ground wires. This shared return path increases the magnetic loop area and ground resistance, making the zero sequence impedance ($Z_0$) significantly larger than the positive sequence impedance ($Z_1$).

Step 1: Understand the physical composition of zero sequence paths.
Positive and negative sequence currents sum to zero at any given node, so they do not require a neutral ground return path. Their loop paths are confined within the phase conductors. In contrast, zero sequence currents ($I_0$) are equal in magnitude and are in phase: \[ I_a0 = I_b0 = I_c0 \] The total current returning through the ground is $3I_0$.

Step 2: Analyze the mathematical effect on impedance.
Because all three lines carry currents in the same direction simultaneously, strong mutual coupling occurs between the lines. This mutual inductance ($X_m$) adds constructively to the self-inductance ($X_s$). The zero-sequence impedance can be written as: \[ Z_0 = Z_s + 2Z_m \] While the positive sequence impedance is: \[ Z_1 = Z_s - Z_m \] Since the mutual terms add to $Z_0$ and subtract from $Z_1$, the zero-sequence impedance is much larger than the positive sequence impedance ($Z_0 > Z_1$). Typically, $Z_0$ is 2 to 3.5 times larger than $Z_1$ for overhead lines. Thus, Option (A) is the correct statement.