MSFEM and MOR to Minimize the Computational Costs of Nonlinear Eddy-Current Problems in Laminated Iron Cores

Abstract

The multiscale finite-element method (MSFEM) reduces the computational costs for the simulation of eddy currents (ECs) in laminated iron cores compared with the standard finite-element method (SFEM) essentially. Nevertheless, the complexity of the resulting problem is still too large to solve it conveniently. The idea is to additionally exploit model order reduction (MOR). Snapshots (SNSs) for a reduced basis are cheaply calculated by the MSFEM. Numerical simulations of a small transformer show exceptional performance. This is well demonstrated by the overall EC losses and by the distribution of the magnetic-flux density, both with respect to those obtained by the MSFEM.

Nonlinear Multi-Scale Model Order Reduction of Eddy-Current Problems

“…Additionally, the parametric CLN obtained with the 2 nd order homogenization using µ d , achieves slightly better accuracy. This is consistent with (12) where the operating point is approximated by µ and the small perturbations are modeled with µ d .…”

“…where µ d = d|B|/d|H| is the differential permeability. In contrast to [2], on (12) the permeability is considered frozen along the lamination thickness, which makes it less accurate, but computationally cheap and interoperable with the CLN.…”

“…Sato and Igarashi [8], considered the magnetic saturation by imposing the nonlinearity on the first inductor L 1 , only. In [9], the nonlinearity was extended to all the circuit elements similar to (12) except that all of the magnetic modes are interpolated with µ or µ d only.…”

“…To handle the saturable laminated core, a nonlinear version of multiscale MOR is required [12]. However, the nonlinearized homogenization method has always been a big challenge and is a fortiori so when applied to the multi-scale MOR.…”

MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

“…MOR is frequently used to facilitate the simulation of electrical machines, see for example [1]. A simple MOR method has been presented in [8] in the context of time stepping for nonlinear 3D problems and a method based on a mixed formulation [9], which can be easily implemented in an existing code for the mixed formulation and standard FEM.…”