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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.

Capacitance of Three Phase Transmission Line with Equilateral Spacing

Using Eq. (3.2) we can write the expressions for Vab and Vac as

Capacitance of Three Phase Transmission Line with Equilateral Spacing

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 qb + qc = – qa, 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

Phasor Diagram of Capacitance of Three Phase Transmission Line with Equilateral Spacing

Substituting for (Vab + Vac) from Eq. (3.12) in Eq. (3.11), we get

Capacitance of Three Phase Transmission Line with Equilateral Spacing

The capacitance of line to neutral immediately follows as

Capacitance of Three Phase Transmission Line with Equilateral Spacing

For air medium (kr = 1),

Capacitance of Three Phase Transmission Line with Equilateral Spacing

The line charging current of phase a is

Capacitance of Three Phase Transmission Line with Equilateral Spacing