Integral equation methods for the calculation of the current distributions of power cables in the high frequency band

The high-frequency characteristics of power cables are very important in many application situations, especially the current distributions of power cables in the high frequency band. This paper mainly presents two important integral equation methods, volume integral equation (VIE) and surface integral equation (SIE), which can be applied to arbitrary shape of cross section of cables. This paper also gives a detailed study of the analytical method for the calculation of the current distribution over circular cross section as well as the partial diffusion equation (PDE)-series method for the calculation of current distribution over rectangular cross section. The current distribution shows strong singularity when the frequency is high enough that the skin depth is smaller than the cable's dimension size. An accurate volume integral equation is presented without approximation by using the Hankel function as the integral kernel. At very low frequencies, it reduces to the widely-used quasi-static VIE. The quasi-static VIE is not accurate enough for the calculation of current distribution. Detailed discussion is given for the different current distributions calculated from different methods.