Calculation of Resistances and Inductances in Multi-Conductor Systems Including Solid and Litz Wires Using the 2-D Boundary Element Method

Abstract

Multi-conductor systems can be modeled as multi-port networks made of lumped parameters. In the general case, the computation of such parameters requires the knowledge of the electric and magnetic fields. During the last decades, the finite-element method (FEM) has been widely used to compute the field quantities. Due to the large number of degrees of freedom involved, the application of FEM is prohibitive in cases including a large number of conductors and when a frequency scan is required, which requires a mesh adapted to the frequencies of interest. In this article, the boundary element method (BEM) is instead explored. The BEM formulations of the 2-D magnetic-harmonic problems in multi-conductor systems made of solid and Litz wires are presented in this article. The proximity effects in the Litz wires are considered by means of a complex permeability. The voltages and currents are included in the mathematical formulation of the problem, from which the frequency-dependent resistances and inductances per unit length (p.u.l.) can be directly found. The approach proposed is fast, easy to use, and requires no post-processing steps.