Chapter 1: Modelling Power System Components

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 qa, qband qc espectively. Since the system is assumed to be balanced we have



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

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







Then the average value of the voltage is




This implies




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




Similarly the voltage Vac is given as




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





For a set of balanced three-phase voltages




Therefore we can write



Combining (1.76) and (1.77) we get




Therefore the capacitance to neutral is given by




For bundles conductor