Capacitance of a Three-Phase Transposed Line

Consider the three-phase transposed line shown in Fig. 1.14. In this the charges on conductors of phases a, b and c are q_a, q_band q_c espectively. Since the system is assumed to be balanced we have

(1.68)

Fig. 1.14 Charge on a three-phase transposed line.

Using superposition, the voltage V_ab for the first, second and third sections of the transposition are given respectively as

V	(1.69)
V	(1.70)
V	(1.71)

Then the average value of the voltage is

V

(1.72)

This implies

V

(1.73)

The GMD of the conductors is given in (1.42). We can therefore write

V

(1.74)

Similarly the voltage V_ac is given as

(1.75)

Adding (1.74) and (1.75) and using (1.68) we get

(1.76)

For a set of balanced three-phase voltages

Therefore we can write

V

(1.78)

Combining (1.76) and (1.77) we get

V

(1.78)

Therefore the capacitance to neutral is given by

F/m

(1.79)

For bundles conductor 

where