Temperatures in Electric Power Cables Under Variable Loading

Considerable need has been felt for accurate methods of soluttion of the problem of temperature rise under variable loading in order that the maximum use may be made of the large investment in power cables. In this paper a rigorous solution of the problem of temperature rise from sheath surface to conductor is attempted, making use of Bessel functions. The heat flow cycle is resolved into harmonics, and each harmonic solved separately for temperature at the conductor. The various harmonics of temperature are then combined in their proper phase relation to obtain the temperature cycle. For purposes of assigning emergency ratings a solution is arrived at for suddenly applied steady loads, making use of the Fourier integral. The problem is solved rigorously for single-conductor cables and three-conductor cables of shielded (type ``H'') construction. Modifications of the constants of the cables are described which will allow the theory to be applied to cables of standard belted construction with reasonable accuracy. The probable errors involved in the assumptions necessary in the solution are discussed. It is believed that knowing the temperature of the air at the sheath surface, the temperature of the conductor can be calculated within 4 or 5 per cent of the correct value if the constants of the cable are known within this accuracy. The method can also be applied to solution of the temperature rise of the sheath surface provided the constants of the duct bank are known with sufficient accuracy.