A mathematical model of a two-dimensional electrostatic problem for the cross section of an electric cable is considered. The unknown quantities in the model are the distributed electric potential outside the conductors and a constant potential at the boundary of each conductor. The known quantities are the distributed electric charge in the insulation and the total charge of each conductor. To solve a boundary value problem with equipotential unknown conditions at the boundaries of the conductors, the article examines a method that reduces this problem to a set of ordinary boundary value problems with Dirichlet conditions. The unique solvability of the boundary value electrostatic problem is demonstrated, and a detailed algorithm for its solution is presented. A computational module based on the Galerkin finite element method with quadratic elements is adapted for the numerical modeling of a spatially charged electric cable. The method is suitable for calculating multi-core cables with any number of cores and arbitrary geometry. Results demonstrating the operability of the numerical method for solving boundary value problems of electrostatics with equipotential boundary conditions on the conductors are presented. The technique can be used to model electrical interference in spatially charged multi-core cables.
Zhukov et al. (Wed,) studied this question.