Capacitance of a Three Phase Line with Unsymmetrical Spacing

Capacitance of a Three Phase Line with Unsymmetrical Spacing

May-05, 06, 11, 16, Dec.-05, 10, 14, 15, 16, 17

The calculation of capacitance in case of conductors in three phase system which are not equally spaced is difficult. If the line is untransposed the capacitances of each phase to neutral is not same.

In case of transposed line the average capacitance of each line to neutral over a complete transposition cycle is same as the average capacitance to neutral of any other phase. Each conductor occupies the same position of every other conductor after equal distance. The effect of unsymmetry between the lines is small and calculations are carried out by considering transposition of lines.

The Fig. 1.30.1 shows three phase line with unsymmetrical spacing. The radius of each conductor is r.

When phase 'a' is in position 1, 'b' in position 2 and 'c' is in position 3.

When phase 'a' is in position 2, 'b' in position 3 and 'c' in position 1,

When phase 'a' is in position 3, 'b' in position 1 and 'c' in position 2

Average voltage between conductors 'a' and 'b' is given by

Example 1.30.1 A 220 kV, 50 Hz, 200 km long three phase line has its conductors on the comers of a triangle with sides 6 m, 6 m and 12 m. The conductor radius is 1.81 cm. Find the capacitance per phase per km, capacitive reactance per phase, charging current and total charging Mega volt-amperes.

Solution : Radius of conductor = 1.81 cm = 0.0181 m

Review Questions

1. Derive an expression for capacitance per km line to neutral of a 3 phase overhead transmission line with unsymmtrical spacing of conductors assuming transposition.

AU : May-05, 16, Marks 10, Dec.-05, 17, Marks 2, | May-06, Marks 16, May-11, Dec.-14, 15, Marks 12

2. Determine the capacitance and charging current per km when the transmission line as shown in Fig. 1.30.3 is operating at 132 kV. The conductor diameter is 20 m.

[Ans.: 9.37 nF/km, 0.2244 A/km]