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To compare the numerical solutions in primal and dual meshes of magnetostatic problems solved with the finite integration technique.

The development of the whole set of magnetostatic discrete formulations is proposed. Four formulations are computed: two in terms of fields and two in terms of potentials. Moreover, each computation is carried out on the primal and dual mesh. Two applications are presented and the results are analysed and discussed.

The whole set of magnetostatic formulations gives only two solutions. The solutions do not depend of the formulation, but they depend of the choice of the field discretisation in primal or dual mesh.

The computation is carried out on the dual mesh.

This paper presents a model based on the 2D finite element method (FEM) which can be used to study a self‐excited induction generator in unbalanced modes. In the proposed model, we take into account the magnetic non linearity of the iron by introducing a B(H) curve which is identified experimentally from magnetic materials. On the other hand, effects such as end windings and the short circuit ring are also taken into account using analytical expressions. The coupling between electrical circuit and FE equations is introduced. After validating the model in steady and transient modes, we will discuss the choice of the different capacitances and give simulated results of a specific unbalanced case.

Aims to determine the magnetic parameters at no‐load of a variable reluctance machine excited by DC and AC currents.

Presents the linear analytical model used to determine the electro‐magnetic variables of a stator current excited reluctance machine. The 2D FEM approach is also introduced. Then the prototype designed in the laboratory is presented and its magnetic characteristics determined. The results are calculated using both models and compared with the experimental values.

According to the different results, apart from the atypical E(I_e) characteristic, for both excitation models, the doubly slotted machine excited by current in the stator can be modelled in a manner similar to that of a smooth rotor synchronous machine with an electromagnetic gear box.

This paper has succeeded in determining the magnetic parameters at no‐load of a variable reluctance machine excited by DC and AC currents.

The purpose of this paper is to propose some a posteriori residual error estimators (REEs)to evaluate the accuracy of the finite element method for quasi-static electromagnetic problems with mixed boundary conditions. Both classical magnetodynamic A-ϕ and T-Ω formulations in harmonic case are analysed. As an example of application the estimated error maps of an electromagnetic system are studied. At last, a remeshing process is done according to the estimated error maps.

The paper proposes to analyze the efficiency of numerical REEs in the case of magnetodynamic harmonic formulations. The deal is to determine the areas where it is necessary to improve the mesh. Moreover the error estimators are applied for structures with mixed boundary conditions.

The studied application shows the possibilities of the residual error estimators in the case of electromagnetic structures. The comparison of the remeshed show the improvement of the obtained solution when the authors compare with a reference one.

The paper provides some interesting results in the case of magnetodynamic harmonic formulations in terms of potentials. Both classical formulations are studied.

The paper provides some informations to develop the proposed formulations in the software using finite element method.

The paper deals with the possibility to improve the determination of the meshes in the analysis of electromagnetic structure with the finite element method. The proposed method can be a good solution to obtain an optimal mesh for a given numerical error.

The paper proposes some elements of solution for the numerical analysis of electromagnetic structures. More particularly the results can be used to determine the good meshes of the finite element method.

Electromagnetic actuators, with very specific features for industrial processes, are needed much more for an increase in reliability and dynamic. To reach the wanted features, the actuator has to be designed and its performance has to be quantified with good accuracy and reasonable computation time. The purpose of this paper is to present the design and the study of a permanent magnet linear actuator.

The first design of the permanent magnet linear actuator has been introduced from electromechanical considerations. Then, both models utilized to study the actuator are presented: the permeance network model (PNM) and the 3D finite element model. These models are used to quantify the performance of the prototype. Owing to its speed, the influence of geometric parameters on the performances are studied by the PNM. Then, both models are used to perform calculations on global variables. A prototype of the designed actuator has been built up and the results obtained by both models are compared with the measurements.

The developed model has been used to study the behaviour of the designed actuator. Using the 3D‐FEM, the local phenomena have been highlighted as the magnetic flux density and the induced current. Then, global variables as the no load fluxes and the forces at load have been determined. The results obtained by both models have been compared together and show a good agreement. They are also very close to the measurements achieved on the prototype constructed.

This paper shows that it is possible to use a PNM model to design a permanent magnet linear actuator with a relative good accuracy. The PNM developed does not permit one to calculate the cogging forces and does not take into account the induced currents but it gives accurate results when the interest is focused only on the magnetostatic load operating. The comparison with the results given by 3D‐FEM and to the measurements shows a good agreement.

In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation.

The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency).

This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation.

In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

Proposes to compare two models ‐ finite element method and “magnetic” equivalent scheme ‐ for numerical modelling of electromagnetic systems. Both these approaches coupled with electric circuit equations take into account saturation effects. Uses a machine of 5.5kW as a model to show the validity of these approaches. Compares the results obtained from numerical calculation with experimental ones.

Electrical machines with nonlinear magnetic circuits are usually modelled by coupling magnetic and electric equations using software for magnetic field investigation. These hybrid methods are practically effective only for steady states, due to their time‐consuming calculations. The separation of both sets of equations will be possible if the unique relationships between linked fluxes and all armature currents become determined. It needs, of course, the neglect of the eddy‐currents in the machine rotor. Generally, they are defined as the partial derivatives of coenergy:

The purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.

In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.

The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.

The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.

In the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.

The proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.

The novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.