Inductance of Transmission Line with Unsymmetrical Spacing

Inductance of Transmission Line with Unsymmetrical Spacing

Consider the same three conductors a, b, c having radius r but unsymmetrically spaced as shown in the Fig. 1.18.1.

Flux linkage of conductor a is given by,

From the above expressions it can be seen that the individual phase inductance of a line which is unsymmetrically spaced is a complex number. The imaginary part in the expression for inductance represents exchange of energy between phases.

Review Questions

1. Derive expression for the inductance of a 3 phase line with conductors untransposed. What is the significance of imaginary term in the expression for inductance ? Hence derive the expressions for inductance for a completely transposed line.

2. Derive an expression for the inductance of a 3 ϕ overhead transmission lines with unsymmetrical spacing. Also explain the concept of transposition of conductors.