Balancing bundle-conductor transmission-line constants without transpositions

Transpositions, although considered necessary to balance the constants of an h.v. overhead transmission line, are costly and sometimes troublesome in operation; hence the desirability of balancing the line constants without transpositions. Possibilities of separately balancing inductances, earth capacitances and mutual capacitances between phases are considered, by adjusting the equivalent radii of the various phases. As the necessary variations in equivalent radii are considerable, only bundle conductors can be utilised, with suitable subconductor spacings. Simple relations are established for the ratio of subconductor spacings of the central and outer phases of a single-circuit line with symmetric horizontal phase configuration, for inductive and earth-capacitive balancing, first without considering the effect of earth wires. The effect of earth wires is to introduce a multiplying factor. These results show that simultaneous balancing of the constants is not possible for the horizontal arrangement. Balancing of mutual capacitances, though possible, may not be practicable. The Donau-type double-circuit transmission line with one earth wire, as used in the West German 380kV transmission system, is analysed in detail, but the equations are very involved. Simultaneous balancing of inductances and earth capacitances is theoretically possible, by suitably situated earth wires and corresponding subconductor spacings. The suitability of this method has to be judged in each case individually, after working out the details as outlined in the paper. Other methods of balancing some of the constants, in conjunction with this method, may be required for complete balancing.