2-D Reduced Model for Eddy Currents Calculation in Litz Wire and Its Application for Switched Reluctance Machine

The strong correlation between the level of eddy current losses and the winding geometry shows the necessity to pay attention to the manner of disposition of coils in machine slots. The conductor type, whether it is solid or stranded, also has a crucial influence. This paper suggests an electromagnetic analysis of complex stranded conductors, such as litz wire (LW) and twisted wire. Each conductor is composed of individual strands that are woven or twisted in the slot throughout the machine length. Combined with several electric circuit relationships that interpret the strands transposition, a 2-D finite-element (FE) model is developed in this paper so that the copper losses in each strand can be calculated individually. A model reduction is also proposed in the case of LWs. This allows the benefit of only one complete FE solution to find fast solutions in the slots' domains when any variation of geometrical data occurrs. It allows adapting non-conforming subdomains' meshes and seeing that it prevents the Newton-Raphson iterations and the moving band technique, the model reduction presents clear interests in repetitive analysis, such as winding optimization processes.

I. Introduction

Copper losses are subdivided into classical ohmic dc losses and additional eddy current losses [1]. The latter exists due to the strong electromagnetic coupling between the current density and the time varying magnetic fields penetrating the copper conductors. Because this interaction between electric and magnetic variables cannot be solved easily, finite-element (FE) methods may be used to give a numerical solution. Litz wires (LWs) and twisted wires (TWs) reduce eddy currents in an effective way because of the strands transposition. Hence, the 3-D FE model is the suitable means to picking up the electromagnetic effects in case of such complex wires. In spite of its precise solution, the 3-D resolution leads to substantial calculation time and requires large storage capacity. These heavy constraints hinder any process of conception and optimization of winding geometries in terms of copper losses. Model order reduction methods can be effective in reducing the computational time [2]; furthermore, perturbation FE methods provide clear advantages in repetitive analysis [3]. This paper proposes a 2-D FE approximate model of LW and TW. It also suggests in the case of LW a model reduction that allows benefiting from only one complete FE (CFE) solution to find fast solutions in the slots domains when any variation of the number of LW strands or of their geometry of distribution occurred.