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Electromagnetic problems The electromagnetic theory has been fully developed into a mathematical equation system by Maxwell in which he succeeded to explain all physical phenomena. One could ask why after 200 years it is still impossible to accurately solve these equations. The explanation is given by the fact that a solution in a closed form is impossible due to the presence of anisotropic, non‐linear materials with a difficult geometrical shape. Until the sixties, emphasis in clectromagnetism was on finding extremely difficult test functions, offering a solution for a limited category of problems. Examples are the rotating field theory in electrical machines and the wave equations in high voltage line transients.

Finite element discretizations of low‐frequency, time‐harmonic magnetic problems lead to sparse, complex symmetric systems of linear equations. The question arises which Krylov subspace methods are appropriate to solve such systems. The quasi minimal residual method combines a constant amount of work and storage per iteration step with a smooth convergence history. These advantages are obtained by building a quasi minimal residual approach on top of a Lanczos process to construct the search space. Solving the complex systems by transforming them to equivalent real ones of double dimension has to be avoided as such real systems have spectra that are less favourable for the convergence of Krylov‐based methods. Numerical experiments are performed on electromagnetic engineering problems to compare the quasi minimal residual method to the bi‐conjugate gradient method and the generalized minimal residual method.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

To retain small models, electrostatic and electrokinetic finite element formulations are linked with several field‐circuit couplings and floating potential constraints. The approaches enable convenient simulations of a condenser bushing and a dielectric heating device.

Calculating the stator end-winding leakage inductance, taking into account the rotor, is difficult due to the irregular shape of the end-winding. The end-winding leakage may distribute at the end of the active part and the fringing flux of the air gap. The fringing flux belongs to the main flux but goes into the end-winding region. Then, not all the magnetic flux occurring in the end region is the end-winding leakage flux. The purpose of this paper was to find a method to accurately separate the leakage from the total flux, taking into account the rotor.

In this paper, two methods based on energy calculation are presented. Both methods require the assumption that the machine is symmetrical. The first method depends on the total leakage inductance and the machine’s active region length. The second method is based on the energy stored in the end region of the machine. In this case, removing the energy produced by the fringing flux of the air gap is necessary. The model should have a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap.

The method presented in the paper does not require rotor removal. The values of the end-winding leakage inductance computed based on the proposed method were compared with values computed using the method with the removed rotor. The computations show that the proposed method is closest to the results from the method presented in the literature. Results obtained in the first method present that rotor influence on the value of end-winding leakage inductance exists. The model of the stator end-winding described in the paper is general. Therefore, the proposed methods are suitable for calculating the end-winding leakage inductance of other electric machines.

The method presented in the paper considers the rotor in end-winding leakage inductance calculation. It is not necessary to remove the rotor as in the similar method presented in the literature. The authors elaborated a parametric model with a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. The authors also elaborated their 3D model of the machine winding for calculations in Opera 3D.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Presents the use of a 3D eddy current FE procedure for the analysis and design of two different induction machine structures: a radial and an axial machine. In the first case, attention is devoted to the simulation of locked rotor conditions and a linear 3D time harmonic eddy current FE analysis has been employed. The obtained results have been compared to 2D analysis and experimental data. The axial flux machine is analyzed under fixed speed conditions and a 3D time‐stepping and velocity eddy current problems are solved to evaluate machine performances. Different design configurations are analyzed in order to define the best solution.

To propose an air‐gap element for electrical machine simulation which accounts for static and dynamic rotor eccentricity.

The air‐gap element technique is extended to account for a non‐centered rotor. The consistency, stability and convergence of the discretisation error are studied. A specialized efficient solution technique combining the conjugate gradient algorithm with fast Fourier transforms is developed.

The eccentric air‐gap technique offers better discretisation properties than the classical techniques based on remeshing. Thanks to the specialized solver, the computation times remain comparable.

The introduction of eccentricity in the air‐gap element used for finite element electrical machine simulation is a new development.

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.

A magnetic brake with a solid iron cylinder rotating at high speeds is considered. The rotor iron is both conductive and permeable. The magnetisation curve is non‐linear. Special attention is paid to the correct integration of the angular velocity term. A Newton‐Raphson scheme dealing with the non‐linear material characteristics is applied. The numerical oscillations appearing in the finite element model at high velocities are overcome by an adaptive mesh refinement technique combined with the artificial diffusion upwind technique. End effects due to the finite length of the rotor are incorporated by an electric circuit coupling. Simulations are performed to study the influence of the saturation of the moving rotor upon the speed‐torque characteristic of the magnetic brake. It is remarkable that in the case of this solid rotor magnetic brake, the saturation of the rotor iron has a beneficial influence on the device performance.