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.

I. Introduction

Litz wires are widely used in many application fields of power electronics as they strongly mitigate the skin and proximity effects, thus reducing the ac losses. Currently there is an increasing interest on litz wires due to their wide use in the emerging technology known as wireless power transfer (WPT) and based on inductive coupling [1], [2]. In this technology, the conductors used for the coils are often made by litz wires and the coils are generally in air. Thus, the magnetic field in WPT applications is lower than that of traditional inductors with magnetic core, but the frequency is higher than powerline frequency (e.g., 50/60 Hz). Typical operating frequencies in WPT applications using litz wire coils range from tens of kilohertz to a few megahertz.