Effect of Earth on Capacitance of Transmission Line

The capacitance of transmission line is affected by the presence of earth. Because of earth, electric field of a line is reduced. If we assume that the earth is a perfect conductor in the form of a horizontal plane of infinite extent, we realize that the electric field of charged conductors above the earth is not the same as it would be if the equipotential surface of earth were not present.

      
The method of images is used while considering this type of problems. For this consider a single phase line having 2 conductors as shown in the Fig. 1.

       A fictitious conductor is placed below each conductor of the same size and shape as the overhead conductor lying directly below the original conductor at a distance equal to twice the distance of the conductor above the plane of ground. If the earth is removed and a charge equal and opposite to that an overhead conductor is assumed on the fictitious conductor, the plane midway between conductor and its image is an equipotential surface and occupies the same position as the equipotential surface of earth. This fictitious conductor is called image conductor having the charge opposite to that of overhead conductor.

Fig. 1

       The voltage V_ab is given as,

       But   q_b = - q_a 

       Comparing above equation with expression for capacitance of single phase line without considering the effect of earth, we can see that earth tries to increase the capacitance of line by small amount. But the effect is negligible if the conductors are high above ground compared to distances between them.