Inductance of Three Phase Lines With Equilateral and Symmetrical Spacing

 Consider a three phase line consisting of three phase conductors a, b and c as shown in the Fig. 1. These three conductors are equally spaced at the corners of an equilateral triangle having radius r.

Fig. 1

     
The flux linkages of conductor a are given by,

        If the currents are assumed to be balanced than 

                          I_a+ I_b + I_c = 0

       .^..                I_a = - ( I_b + I_c )

       or               ( I_b + I_c) = - I_a

       The above equation becomes,

       The inductance of conductor a is given by

       because of symmetry, conductors b and c will have same inductance as that of conductor a. Each phase consists of only one conductor. So the above equation gives inductance per phase of the three phase lines. For stranded conductor we write D_s whereas for single conductor it is replaced by r'.