Chapter 1: Modelling Power System Components

Inductance of a Single-phase Line

Consider two solid round conductors with radii of r1 and r2 as shown in Fig. 1.5. One conductor is the return circuit for the other. This implies that if the current in conductor 1 is I then the current in conductor 2 is -I . First let us consider conductor 1. The current flowing in the conductor will set up flux lines. However, the flux beyond a distance D + r2 from the center of the conductor links a net current of zero and therefore does not contribute to the flux linkage of the circuit. Also at a distance less than D - r2 from the center of conductor 1 the current flowing through this conductor links the flux. Moreover since D >> r2 we can make the following approximations

Fig. 1.5 A single-phase line with two conductors.

Therefore from (1.12) and (1.17) we can specify the inductance of conductor 1 due to internal and external flux as




We can rearrange L1 given in (1.18) as follows

Substituting r1¢ = r1 e-1/4 in the above expression we get




The radius r1¢ can be assumed to be that of a fictitious conductor that has no internal flux but with the same inductance as that of a conductor with radius r1 .

In a similar way the inductance due current in the conductor 2 is given by




Therefore the inductance of the complete circuit is






If we assume r1¢ = r2¢ = r¢ , then the total inductance becomes




where r¢ = re-1/4.