Abstract :
An experimental inverstigation of the copper losses in large cables when carrying alternating current at power frequencies has been carried out at the National Physical Laboratory. Measurements were made with single-phase current on two parallel cables, of equal length and section, forming lead and return. Six pairs of cables of four different cross-sectional enamelled, so that the current was compelled to follow the strand. The strands of the remaining two pairs of cables were unisulated, so that the current was free to flow from strand to strand. The sections of the cables tested ranged between 0.7 sq. in. and 1.9 sq. in., and the range of frequency covered was 25 to 100 cycles per second. The measurements showed that the effective resistance (copper losses/current2) of the cables with enamelled strands was independent of the distance between the lead and return cables, and that its value could be estimated with an error not exceeding 1 per cent from the formula for skin effect for an isolated conductor of circular cross-section, which has been developed by Clerk Maxwell, Lord Kelvin, and others. The measurements made on the cables with bare strands showed that the effective resistance of conducators within the range tested was 1 or 2 per cent higher than that of the same sized cable with enamelled strands at the same frequency, and when the distance between lead and return cables was large. This small increase was due to the spiralling of the strands. Its magnitude is dependent on the lay ratio and on the degree of contact between strands, but it is so small, in even the worst case, as to be negligible for practical purposes. As the distance between the cables was decreaased the effective resistance was observed to increase. This effect is usually known as the proximity effect, and the formulae for its evaluation in the case of solid conductors of circular cross-section have been developed by Mie, Nicholson, Carson, Butterworth, and others. These formulae, how-ev- er, cannot be applied to the calculation of proximity effect in cables since the proximity eddy currents flow from strand to strand, and the resistances of these paths are not amenable to exact calcualation, and are certainly different from the resistances involved in the solid conductor. The degree of contact between strands is probably a very important factor, and measurements on a number of cables would be required in order to establish what consistency could be expected. The effective resistance of the largest cables with bare strands tested (1.9 sq. in.) varied from 110 per cent of the direct-current resistance at a frequency of 25 cycles per second to 132 per cent at 50 cycles per second, and 175 per cent at 100 cycles per second, when the lead and return conductors were far apart. When the lead and return conductors were close to each other the effective resistance was found to be 117 per cent of the direct-current resistance at 25 cycles per second, 155 per cent at 50 cycles per second, and 239 per cent at 100 cycles per second.
