Capacitance of a Three Phase Line Equilateral Spacing

Capacitance of a Three Phase Line Equilateral Spacing:

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

Capacitance of a Three Phase Line Equilateral Spacing

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

 

Capacitance of a Three Phase Line Equilateral Spacing

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

 

Capacitance of a Three Phase Line Equilateral Spacing

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

 

Capacitance of a Three Phase Line Equilateral Spacing

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

Capacitance of a Three Phase Line Equilateral Spacing

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

 

Capacitance of a Three Phase Line Equilateral Spacing

The capacitance of line to neutral immediately follows as

Capacitance of a Three Phase Line Equilateral SpacingFor air medium (kr = 1),

Capacitance of a Three Phase Line Equilateral Spacing

 

The line charging current of phase a is

Ia (line charging) = jωCnVan

Capacitance of a Three Phase Line Equilateral Spacing

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