The electric field near bundle conductors

The electric field surrounding bundle conductors can be determined by replacing each conductor of the bundle by one of negligible radius displaced slightly from the centre of the original conductor. This is based on the fact that equipotential surfaces near such a thin conductor are nearly cylindrical, so that an actual conductor may be so placed as to take up the position of one of the equipotentials. The accuracy of the method depends on the ratio, D/d, between the diameter of the bundle circle and that of each conductor; the greater the ratio, the more accurate is the method. With the ratios usually found in high-voltage transmission lines, the deviation of the equipotential surface from a true cylinder is small, and it can be arranged that the deviation is zero at the point of maximum surface gradient. Maximum deviation from the surface of a cylinder occurs somewhere between points of maximum and minimum gradients. For example, with a bundle of two conductors and D/d = 10, this maximum deviation does not exceed 0.5%; with D/d = 20 it is about 0.1%. The analysis deals with single-phase lines with a bundle of 2, 3 or 4 conductors, but it can be extended to cover any number of conductors in a bundle. For 3-phase lines the resultant field can be found by the principle of superposition when the fields due to the two other phases are taken into consideration. In the latter case, the electric charge per metre of each phase is to be determined with all the three phases and their images involved. Formulae giving the potential gradient at any point on a conductor surface are developed and compared with those given by Cahen. The method is checked by experimental field mapping using a circular double-layer electrolytic tank.