Numerical Simulation of Charged Multicore Electrical Cable

To simulate the electrical properties of spatially charged multicore cable, various numerical methods based on Maxwell’s equations are applicable, although such approaches are resource intensive. In the proposed approach, a reasonable transition is made from the 3D Maxwell equations to the 1D telegraphic equations, which describe time evolution of voltage and current pulses in a spatially charged cable. In a such way the 3D problem is reduced to solving 1D telegraph equations along the cable and a series of 2D electrostatic problems in a set of the cable cross-sections. The result is an effective two-stage splitting scheme: the parameters obtained from the solution of 2D problems, provide time integration of the telegraph equations. Solving the stated 2D electrostatic problems presents considerable mathematical difficulties. It is necessary to find the distributed potential outside the conductors and the surface potential at the boundary of each conductor, provided that the charge of each conductor is known. To solve this problem, we propose an original method that reduce each complicated 2D electrostatic problem to a set of simplest Dirichlet boundary value problems. This method is suitable for multicore cables with any number of conductors of arbitrary shape. The Galerkin finite element method with quadratic elements is implemented to calculate 2D electrostatic problems in a software package designed to calculate spatially charged electrical cables. Numerical tests are presented that demonstrate the efficiency of the method.