Inductance of Transmission Line With Unsymmetrical Spacing

Consider the same three conductors a, b, c having radius r but Unsymmetrically speed as shown in the Fig. 1.

Fig. 1

     
Flux linkage of conductor a is given by,

       If all the three currents are assumed to be balanced with I_a as a reference phasor.

       Substituting this in equation for L_a,

       Similarly we have,

       Also we have,

       Which on simplifying gives,

       The inductances of the three phases are respectively as follows,

       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.