Numerical Modeling of Litz Wires Based on Discrete Transpositions of Strands and 2-D Finite Element Analysis

A new numerical method is proposed to model the electric behavior of a single bundle litz wire with a large number of strands. The method is first based on a two-dimensional (2-D) finite element analysis (FEA) to evaluate the series impedance matrix of a multistrand cable with parallel strands. Then, a mathematical algorithm for a discrete transposition of all strands is applied to simulate the bunching and twisting of the strands. The new procedure is very efficient and accurate, as demonstrated by the excellent agreement of the numerical results with those obtained by experiments or with 3-D FEA. The error in terms of ac-to-dc resistance ratio is less than 10% in the tested configurations. Furthermore, the computational cost of the proposed method is very low and comparable with a simple 2-D FEA.