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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.

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 to show how the EStra-Many method works on optimization problems characterized by high-dimensionality of the objective space. Moreover, a comparison with a more classical approach (a constrained bi-objective problem solved by means of NSGA-II) is done.

The six reactances of a compensation network (CN) for a wireless power transfer system (WPTS) are synthesized by means of an automated optimal design. In particular, an evolutionary algorithm EStra-Many coupled with a sorting strategy has been applied to an optimization problem with four objective functions (OFs). To assess the obtained results, a classical genetic algorithm NSGA-II has been run on a bi-objective problem, constrained by two functions, and the solutions have been analyzed and compared with the ones obtained by EStra-Many.

The proposed EStra-Many method identified a solution (CN synthesis) that enhances the WPTS, considering all the four OFs. In particular, to assess the synthesized CN, the Bode diagram of the frequency response and a circuital simulation were evaluated a posteriori; they showed good performance of the CN, with smooth response and without unwanted oscillations when fed by a square wave signal with offset. The EStra-Many method has been able to find a good solution among all the feasible solutions, showing potentiality also for other fields of research, in fact, a solution nondominated with respect to the starting point has been identified. From the methodological viewpoint, the main finding is a new formulation of the many-objective optimization problem based on the concept of degree of conflict, which gives rise to an implementation free from hierarchical weights.

The new approach EStra-Many used in this paper showed to properly find an optimal solution, trading-off multiple objectives. The compensation network so synthesized by the proposed method showed good properties in terms of frequency response and robustness. The proposed method, able to deal effectively with four OFs, could be applied to solve problems with a higher number of OFs in a variety of applications because of its generality.