High-Order Methods Applied to Nonlinear Magnetostatic Problems

Léo Friedrich,Mitrofan Curti,Bart Gysen,Elena Lomonova

doi:10.3390/mca24010019

Abstract

This paper presents a comparison between two high-order modeling methods for solving magnetostatic problems under magnetic saturation, focused on the extraction of machine parameters. Two formulations are compared, the first is based on the Newton-Raphson approach, and the second successively iterates the local remanent magnetization and the incremental reluctivity of the nonlinear soft-magnetic material. The latter approach is more robust than the Newton-Raphson method, and uncovers useful properties for the fast and accurate calculation of incremental inductance. A novel estimate for the incremental inductance relying on a single additional computation is proposed to avoid multiple nonlinear simulations which are traditionally operated with finite difference linearization or spline interpolation techniques. Fast convergence and high accuracy of the presented methods are demonstrated for the force calculation, which demonstrates their applicability for the design and analysis of electromagnetic devices.

Highlights

Electrical machine design often aims at achieving the highest power density, as it leads to weight and cost savings
A faster convergence is achieved resulting in fewer degrees of freedom for the same error compared to low-order methods such as the Finite Elements Method (FEM)
Two different electromagnetic problems are simulated in Spectral Element Method (SEM), Isogeometric Analysis (IGA), and FEM

Summary

Introduction

Electrical machine design often aims at achieving the highest power density, as it leads to weight and cost savings. Motor topologies in current research, such as reluctance [2,3,4] or flux-switching machines [5], entirely rely on these phenomena. It is, of high importance to be able to rigorously calculate global electromagnetic quantities, such as forces and inductances, in presence of nonlinear material characteristics, as well as obtaining accurate local field distribution. Two high-order methods have gained attention namely, the Spectral Element Method (SEM) and Isogeometric Analysis (IGA) [10,11] They are applied to modeling of magnetic devices such as actuators and electrical machines in [12,13,14,15]

Methods

Results

Conclusion