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The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.

A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

The purpose of this paper is an accurate computation of eddy currents in laminated media with minimal computer resources.

Modeling each laminate of the laminated core of electrical devices requires prohibitively many finite elements (FEs). To overcome this restriction a higher order multi-scale FE method with the magnetic vector potential

has been developed to cope with 3D problems considering edge effects.

The multi-scale FE approach facilitates an accurate simulation of the eddy current losses with minimal computer resources. Numerical simulations demonstrate a remarkable accuracy and low computational costs. The effect of regularization on the results is shown.

The eddy current losses are of great interest in the design of electrical devices with laminated cores.

The multi-scale FE approach takes also into account of the edge effects in 3D.

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.