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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.

To review and discuss recently proposed homogenization methods for laminated magnetic cores and multi‐turn windings in FE models of electromagnetic devices.

The frequency‐domain homogenization is based on the adoption of complex and frequency‐dependent material characteristics (e.g. reluctivity) in the homogenized domain. The value of the complex quantity is obtained analytically or by means of a simple 2D FE model. The time‐domain counterpart requires the introduction of additional unknowns and equation.

The homogenization methods allow to take into account the global eddy current effect in the individual laminations and wires, with a reasonable precision and computational cost.

The homogenization methods have been validated numerically, i.e. by comparison with brute‐force FE computations where the eddy current effects are directly and accurately taken into account. Experimental validation should follow.

The analogy between the homogenization of laminated cores and windings has been evidenced.

To study the inclusion of inter‐bar (IB) currents in a multi‐slice finite element (FE) model of induction motors and in particular the effect of the associated skew discretisation. To validate the model experimentally.

Both a classical uniform distribution and a gauss distribution of the slices and the lumped IB resistances are considered. Measurements on a 3 kW induction motor allows one to estimate its IB resistance and to validate the FE model.

A gauss distribution of the slices allows one to use fewer slices and thus reduces the computational cost. The simulation results show that, at full load, skew changes the different loss components significantly, while the IB currents have a minor effect.

The direct measurement of the IB resistance is by no means trivial. In the frame of this paper, it was indirectly determined, namely by means of a short‐circuit test.

The gauss distribution of the slices and the IB resistance; the systematic study of the skew discretisation; the experimental determination of the IB resistance.

An original and easy‐to‐implement method to take into account movement (motion) in the 2D harmonic balance finite element modelling of electrical machines is presented. The global harmonic balance system of algebraic equations is derived by applying the Galerkin approach to both the space and time discretisation. The harmonic basis functions, i.e. a cosine and a sine function for each nonzero frequency and a constant function 1 for the DC component, are used for approximating the periodic time variation as well as for weighing the time domain equations in the fundamental period. In practice, this requires some elementary manipulations of the moving band stiffness matrix. Magnetic saturation and electrical circuit coupling are considered in the analysis as well. As an application example, the noload operation of a permanent‐magnet machine is considered. The voltage and induction waveforms obtained with the proposed harmonic balance method are shown to converge well to those obtained with time stepping.

This paper deals with the modelling of transformer supply in the two‐dimensional (2D) finite element (FE) simulation of rotating electrical machines. Three different transformer models are compared. The reference one is based on two 2D FE models, considering a cross‐section either parallel or perpendicular to the laminations of the magnetic core. The parameters of the two other transformer models, a magnetic equivalent circuit and an electrical equivalent circuit, can be derived from the reference model. Particular attention is paid to some common features of the transformer models, e.g. with regard to the inclusion of iron losses. The three models are used in the 2D FE simulation of the steady‐state load operation and the starting from stand‐still of an induction motor.

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.

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy currents in electrical steel laminations. The magnetic flux through the flux gates of the conducting region is imposed via the boundary terms of the weak formulations, in a natural way thanks to the use of edge finite elements. The two formulations are applied to a simple 1D eddy current problem with analytical solution. As a practical 3D application example, a T‐joint region of an electrical steel lamination is considered.

This paper deals with the two‐dimensional finite element analysis in the frequency domain of saturated electromagnetic devices coupled to electrical circuits comprising nonlinear resistive and inductive components. The resulting system of nonlinear algebraic equations is solved straightforwardly by means of the Newton‐Raphson method. As an application example we consider a three‐phase transformer feeding a nonlinear RL load through a six‐pulse diode rectifier. The harmonic balance results are compared to those obtained with time‐stepping and the computational cost is briefly discussed.

To develop a homogenization technique to directly and efficiently take the eddy current effects in laminated magnetic cores within time domain finite element (FE) analyses.

The technique is developed for being used within a 3D magnetodynamic b‐conform FE formulation, e.g. using a magnetic vector potential. To avoid a fine FE discretization of all the laminations of a magnetic core, this one is considered as a source region that carries predefined current and magnetic flux density distributions describing the eddy currents and skin effect along each lamination thickness. Both these distributions are related and are first approximated with sub‐basis functions. Through the homogenization or averaging of the sub‐basis functions contributions in the FE formulation, the stacked laminations are then converted into continua, thus implicitly considering the eddy current loops produced by parallel magnetic fluxes. The continuum is then approximated with classical FE basis functions and can be defined on a coarser discretization.

The developed method appears attractive for directly and efficiently taking into account within finite element analyses the eddy current effects, i.e. the associated losses and magnetic flux reduction, that are particularly significant for high frequency excitations. The time domain analysis allows the consideration of both non‐linear and transient phenomena.

The averaging of sub‐basis functions contributions, describing fine distributions of fields, in an FE formulation leads to an original way of homogenizing laminated regions. The proposed method is naturally adapted for time domain analyses and in some sense generalizes what can be done more easily in the frequency domain.

Develops a method to take the eddy currents in stacked thin regions, in particular lamination stacks, into account with the finite element method using the 3D magnetic vector potential magnetodynamic formulation. It consists in converting the stacked laminations into continuums with which terms are associated for considering the eddy current loops produced by both parallel and perpendicular fluxes. Non‐zero global currents can be considered in the laminations, in particular for studying the effect of imperfect insulation between their ends. The method is based on an analytical expression of eddy currents and is adapted to a wide frequency range.