Capacitance of a 3-Phase Line With Unsymmetrical Spacing

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

Fig. 1

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' is in position 1.

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

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

       Similarly average voltage drop between a and c is given by,

       We have, V_ab + V_ac = 3 V_an 

       For balanced circuit (q_a + q_b + q_c ) = 0