High-Order Methods Applied to Nonlinear Magnetostatic Problems

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.

Convergence Analysis of the Fixed-Point Method With the Hybrid Analytical Modeling for 2-D Nonlinear Magnetostatic Problems

“…The figure shows that 0.18% absolute error in the attraction force is achieved with N x =120, N y =60, and N h =50. This shows that FPM used in HAM is able to obtain similar accuracy as state-of-the-art high-order methods [16]. On the other hand, it is also observed that analyzing further than that point causes the system of equation to be illconditioned, which leads to numerical errors in the solution.…”

Time- and Frequency-Domain Steady-State Solutions of Nonlinear Motional Eddy Currents Problems

“…This is not straightforward for the complex-valued operator [38,39], for which the construction of the Jacobian matrix is cumbersome. Instead, for the complex-valued operator, a fixed-point method (FPM) is often preferred [18,37,40].…”

“…To include the effect of the nonlinear constitutive equations, i.e., the nonlinear softmagnetic material B-H characteristics, two methods are usually considered: the fixed-point method (FPM) or the Newton-Raphson method (NRM). A comparison between both nonlinear methods is presented in [18] in the various frameworks of the isogeometric analysis, the finite element method, and the spectral element method. In this paper, the NRM is considered to account for the field dependency of the magnetic permeability ν(x, B), using the Jacobian matrix J.…”

Analysis of Motional Eddy Currents in the Slitted Stator Core of an Axial-Flux Permanent-Magnet Machine

“…However, in this paper, because of the introduction of the source description using complex position-dependent magnetization, the motional eddy currents can be analyzed. The complex-valued problem derived from the harmonic balance is linearized using the fixed-point method described in [11]. The solution in the time-domain is reconstructed from the computed Fourier coefficients.…”