In determination of capacitance of transmission lines, the presence of earth is ignored. But it is not true; the presence of earth affects the electric field of a line and so the capacitance. The effect of earth on capacitance can be modelled by the method of images.
The electric field of too long, parallel conductors having charge +q and -q per unit is such that it has a zero potential between the conductors, as depicted in Fig. 4.36. If a conducting sheet of infinite dimensions is placed at the zero potential planes, the electric field is not disturbed. Further, if the conductor carrying charge -q is now removed, the electric field above the conducting sheet stays intact, while that below it disappears.
Using these well known facts in reverse, the presence of ground below a charged conductor can be replaced by a fictitious conductor having equal and opposite charge and located as far below the ground surface as the overhead conductor above it—such a fictitious conductor is the mirror image of the overhead conductor. This method of producing the same electric field as in the presence of earth is called the method of images originally suggested by Lord Kelvin.
Effect of Earth on the Capacitance of a Single Phase Transmission Line:
ADVERTISEMENTS:
Considering the case of a single phase overhead line, assume conductors A’ and B’ as image conductors of conductors A and B respectively, as shown in Fig. 4.37. Let the height of conductors be h metres above the earth and charge of +q coulombs per metre length and -q coulombs per metre length on the conductors A and B respectively.
The equation for the voltage drop VAB as determined by two charged conductors A and B and their images A’ and B’ may be written as follows:
Substituting qA = q’B = + q and q’A = qB = -q we have,
Capacitance between conductors A and B,
The above expression for capacitance reveals that the presence of earth modifies the radius of conductor r to 
The effect of earth on the capacitance of the system is to increase it. However, normally the distance of separation between the conductors is much smaller than the height of the conductor from the ground, therefore, 
and for all practical purposes the effect of earth on line capacitance can be neglected.
Effect of Earth on the Capacitance of a Three Phase Line:
Figure 4.38 shows the conductors of a 3-phase line along with image conductors. The line is assumed to be transposed and in the first part of the transposition cycle conductor A is in position 1, B is in position 2 and C is in position 3. Let the charges on line conductors be qA, qB and qC while those on image conductors be –qA, –qB and –qC respectively, as shown in the figure.
The equation for the three sections of transposition cycle can be written for the voltage drop VAB as determined by three charged conductors and their images. With conductor in position 1, B in position 2 and C in position 3, we have,
Similarly, equations for VAR can be written for the second and third sections of the transposition cycle. If the fairly accurate assumption of constant charge per unit length of the conductor throughout the transmission cycle is made, the average value of three sections of the cycle is given by,
The equation for the average value of the voltage VAC can be determined in the same way. Using VAB + VAC = 3VAN and qA + qB + qC = 0, we ultimately have the following expression for the capacitance to neutral,
A comparison of above equation with Eq. (4.51) reveals that the presence of earth increases the line capacitance by a small amount. However, the effect is very-very small because the heights of conductors are large as compared to the distance between them.
