Capacitance of Three Phase Overhead Line:

In a Capacitance of Three Phase Overhead Line, the capacitance of each conductor is considered instead of capacitance from conductor to conductor. Here, again two cases arise viz., symmetrical spacing and unsym­metrical spacing.

Capacitance of Three Phase Overhead Line

1.Symmetrical Spacing:

Fig. 9.24 shows the three con­ductors A, B and C of the 3-phase overhead transmission line having charges QA, QB and QC per metre length respectively. Let the conductors be equidistant (d metres) from each other. We shall find the capacitance from line conductor to neutral in this symmetrically spaced line. Referring to Fig. 9.24, overall potential difference between conductor A and infinite neutral plane is given by

Capacitance of Three Phase Overhead Line

Assuming Balanced supply, we have

Capacitance of Three Phase Overhead Line

Capacitance of Three Phase Overhead Line

Capacitance of conductor A w.r.t neutral,

Capacitance of Three Phase Overhead Line

Note that this equation is identical to capacitance to neutral for two-wire line. Derived in a similar manner, the expressions for capacitance are the same for conductors B and C.

2.Unsymmetrical Spacing:

Fig. 9.25 shows a 3-phase transposed line having unsymmetrical spacing. Let us assume balanced conditions i.e. QA + QB + QC = 0.

Capacitance of Three Phase Overhead Line

Considering all the three sections of the transposed line for phase A,

Potential of 1st position,

Capacitance of Three Phase Overhead Line

Potential of 2nd position,

Capacitance of Three Phase Overhead Line

Potential of 3rd position,

Capacitance of Three Phase Overhead Line

Average voltage on condutor A is

Capacitance of Three Phase Overhead Line

Capacitance of Three Phase Overhead Line

Capacitance from conductor to neutral is

Capacitance of Three Phase Overhead Line

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