Analytical Mathematical Model for the Calculation of Current Density Distribution Over the Cross‐Section of a Multi‐conductor Cable

Abstract
This work presents an analytical model based on Maxwell’s equations for current density and electromagnetic field structure calculations in multi-conductor cables. One example of such cables is a composite fiber-optic overhead ground wire (OPGW). A circular multilayer waveguide model is used to represent approximately this cable. The waveguide consists of four layers: dielectric (silica) in the core, aluminum in the intermediate layer, steel in the outer layer and air. The TMz 0n modes of the waveguide, which have axial symmetry, are analytically analyzed. The numerical results presented here are the dispersion characteristics, the distribution of the electromagnetic fields and the variation of the current density in the cross-section of the waveguide as a function of frequency. This model allows one in particular to investigate the skin effect and the electromagnetic fields inside and outside of the cable.