Capacitance of Three Phase Transmission Line with Equilateral Spacing:

Figure 3.5 shows a Capacitance of Three Phase Transmission Line with Equilateral Spacing composed of three identical conductors of radius r placed in equilateral configuration.

Using Eq. (3.2) we can write the expressions for V_ab and V_ac as

Adding Eqs. (3.8) and (3 9), we get

Since there are no other charges in the vicinity, the sum of charges on the three conductors is zero. Thus q_b + q_c = – q_a, which when substituted in Eq. (3.10) yields

With balanced three-phase voltages applied to the line, it follows from the phasor diagram of Fig. 3.6 that

Substituting for (V_ab + V_ac) from Eq. (3.12) in Eq. (3.11), we get

The capacitance of line to neutral immediately follows as

For air medium (k_r = 1),

The line charging current of phase a is