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A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto‐hydro‐dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

A finite‐element formulation is developed to analyze nonlinear electromagnetic devices in steady‐state conditions under specified alternating terminal voltages. The circuit equations are used to express current densities in terms of the unknown vector potential, so that only one nonlinear field equation must be solved. The mathematical formulation and the finite‐element and Fourier approximations are developed and the numerical algorithm used to solve the resulting block system is discussed. Finally, an application of the method to analyze an electromagnet with shading coils is presented.

This paper deals with the magnetic vector and scalar potential formulation for two‐dimensional (2D) finite element (FE) calculations including a vector hysteresis model, namely a vectorized Jiles‐Atherton model. The particular case of a current‐free FE model with imposed fluxes and magnetomotive forces is studied. The non‐linear equations are solved by means of the Newton‐Raphson method, which leads to the use of the differential reluctivity and permeability tensor. The proposed method is applied to a simple 2D model exhibiting rotational flux, viz the T‐joint of a three‐phase transformer.

This paper aims to propose a new design for high-power compact solid-state transformers (SSTs) made with grain-oriented electrical steel (GOES) wound cores that benefit from the natural reduction of iron losses at high temperatures.

An experimental approach, coupled with numerical and analytical investigations, is widely used for proving the validity of the proposed concept.

With cores much hotter than coils, the new design of medium frequency transformers can be used for building compact SSTs that rated powers and common-mode insulation voltages much higher than existing ones with similar efficiencies.

The thermal design must provide a large difference between core and coil temperatures in a reasonable volume.

The increasing number of intermittent renewable sources place electric grid stability at risk. Smart nodes, made of SSTs, improve the global grid stability because they are able to provide real-time control of energy fluxes at critical points. In railway applications, high-power SST cells can be distributed along the train providing a larger volume for passengers.

The increasing part of electricity in a flexible grid requires performant and high-power SSTs made with components that have an environmental footprint as low as possible.

This paper proves that the design of high-power transformers with GOES wound cores much hotter than coils is possible. It proposes also a thermal equivalent circuit that helps the design.

This paper deals with the incorporation of a vector hysteresis model in 2D finite‐element (FE) magnetic field calculations. A previously proposed vector extension of the well‐known scalar Jiles‐Atherton model is considered. The vectorised hysteresis model is shown to have the same advantages as the scalar one: a limited number of parameters (which have the same value in both models) and ease of implementation. The classical magnetic vector potential FE formulation is adopted. Particular attention is paid to the resolution of the nonlinear equations by means of the Newton‐Raphson method. It is shown that the application of the latter method naturally leads to the use of the differential reluctivity tensor, i.e. the derivative of the magnetic field vector with respect to the magnetic induction vector. This second rank tensor can be straightforwardly calculated for the considered hysteresis model. By way of example, the vector Jiles‐Atherton is applied to two simple 2D FE models exhibiting rotational flux. The excellent convergence of the Newton‐Raphson method is demonstrated.

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 influence of overlap joints in transformer cores on the local flux and eddy current distribution and on overall transformer characteristics is studied by means of two‐dimensional finite element (2D FE) models. A simplified 2D FE model of a single overlap joint is used for estimating the resulting increased magnetomotive force and increased eddy current losses. Both effects can be accounted for in a 2D FE model of the complete transformer by locally adopting modified material characteristics (viz. BH‐curve and electrical conductivity) in the cross‐section of the core. This novel method is demonstrated and validated by applying it to a three phase transformer. The calculated no‐load currents and losses are compared to the measured ones.

The implementation of a vector Preisach model for the modelling of anisotropic hysteretic soft magnetic materials is outlined. Some comparisons with measurements on alternate and rotational magnetic field excitations are shown. The hysteresis model is inserted inside a two‐dimensional finite element solver formulated in terms of magnetic vector potential and nonlinear solution is handled by means of the fixed point method with H‐scheme. Results obtained on a two‐dimensional geometry are described and discussed.

The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical field analysis. The hysteresis model must be fast and well applicable in electromagnetic field simulations.

Iron parts of electrical machines are made of non-oriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of different electrical equipment.

The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of TEAM Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure.

The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed-point method with stable scheme has been realized to take frequency dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations.

This paper presents the development of a procedure for the determination of the local magnetic loss distribution in transformer cores. An efficient identification method of the parameters of the Jiles‐Atherton model is first described. This method uses nonlinear optimization techniques and several experimental loops with different magnitudes, or measurements obtained with a low frequency supply signal, for a precise determination of the hysteresis model parameters. It is validated by the identification of two different kinds of magnetic materials: a standard laminated material made of 1008 steel and a soft magnetic composite Atomet‐EM1. The implementation of the hysteresis Jiles‐Atherton model in a 2D field calculation tool is detailed. The field calculation procedure is illustrated by two application examples involving single phase tranformers with cores made of the soft magnetic composite Atomet‐EM1.