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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.

Eddy currents are inevitable in magnetic resonance imaging (MRI) systems. These currents are mainly induced by gradient fields. This study aims to propose a fast analytical method to calculate eddy currents induced by frequently switching gradient fields in a traditional C-shape MRI system.

Fourier decomposition and magnetic vector potentials were used to calculate the eddy currents. Calculations with the proposed analytical method revealed the spatial distribution and temporal evolution of eddy currents.

Calculation and Maxwell simulation results were consistent. The agreement between calculation and simulation results indicates that increasingly sophisticated structures could be developed. The calculated results could guide the design of improved gradient coils.

Eddy currents induced by gradient current are decomposed into currents induced by each time-harmonic component, and then adding them together to obtain complete contribution of the eddy current. The analytical method was used to characterize the properties of symmetric and asymmetric eddy currents induced by gradient coils in MRI systems. The analytical method can be used to improve the gradient shield during the design of the gradient coil in the MRI system.

The temperature drop, especially in the edge of rolled steel in the hot rolling cooling has a catastrophic effect on the steel quality. The purpose of this paper is to study the coupled eddy current-temperature field of a C-type edge induction heater to provide references for engineering applications and designs.

Three-dimensional finite element analysis (FEA) model of a C-type edge induction heater is developed. Especially, a numerical methodology to couple the eddy current and temperature fields is proposed for coupled eddy current and temperature problems involving movement components. FEA software ANSYS is used to solve the coupled eddy current and temperature fields. The heat loss from the eddy current fields is abstracted and processed, and taken as internal heat source in the analysis of the temperature field. The temperature distribution of the rolling steel is obtained.

The numerical results can predict exactly the temperature rise of the rolled steel by means of the edge induction heating system.

The proposed numerical methodology for coupling eddy current and temperature fields can be applied to engineering coupled eddy current and temperature problems involving movement components. Also, the developed model and method can be used in the analysis and design of the edge induction heating system.

A numerical methodology to couple eddy current and temperature field for solving multi-physics field problems involving movement components is proposed and implemented in available commercial software. A three-dimensional model of the C-type edge induction heat heater is developed. Finite element method is employed to study the coupled eddy current-thermal problem. A method to deal with the movement of the strip steel is proposed. The proposed methodology can be applied to other coupled eddy current-temperature field problem with moving components.

This study aims to calculate eddy current losses in permanent magnets of BLDC machine in the generator mode of operation with no‐load.

Stator slot openings and special design of the stator poles cause changes in the magnetic flux density changes in permanent magnets. The stator windings are not connected to an outer source and no currents flow in them. The induced eddy currents in permanent magnets are dependent solely on the stator geometry. Analytical approach to calculate the eddy current density distribution in permanent magnets is based on known distribution of magnetic flux density in the air‐gap of BLDC. The magnetic flux density distribution is obtained from magneto‐static finite element model of BLDC. For verification of analytical approach the eddy current density distribution in permanent magnets is also calculated by magneto‐transient finite element model of BLDC.

The eddy current losses in PM obtained with the FEM indicate additional heating of the BLDC machine at high rotational speeds even when it operates at no load. When some special stator designs (the side of the air gap) are needed, the losses in PMs and their heating increase.

To get more precise results, the proposed analytical method for eddy current losses calculation in PM should be further analyzed. More geometric parameters of the BLDC design should be introduced to analytical formulations, especially those which affect variations in reluctance.

When some special stator designs (the side of the air gap) are needed, the losses in PMs should be observed. This is particularly recommended at higher rotation velocities. Any kind of magnetic flux density change induces eddy currents and together with them also power losses. These losses give rise to additional heating of PM. With this, the temperature‐dependent working characteristic of PM (second quadrant of the B‐H curve) moves toward the coordinate origin point. The overall machine performance is reduced. The presented work gives the view about happenings in permanent magnets regarding induced eddy current losses. It is a useful tool for fast estimation and reduction of eddy current losses in PM due to stator geometry.

The value of the paper is the closed view about happenings in permanent magnets regarding induced eddy currents and the calculation of eddy current losses in rotor permanent magnets of BLDC due to stator design. The originality is in the analytical approach to calculate the eddy current losses based only on known magneto‐static flux density distribution in air‐gap of BLDC.

Reducing eddy current losses in magnets of electrical machines can be obtained by means of several techniques. The magnet segmentation is the most popular one. It imposes the least restrictions on machine performances. This paper investigates the effectiveness of the magnet circumferential segmentation technique to reduce these undesirable losses. The full and partial magnet segmentation are both studied for a frequency range from few Hz to a dozen of kHz. To increase the efficiency of these techniques to reduce losses for any working frequency, an optimization strategy based on coupling of finite elements analysis and genetic algorithm is applied. The purpose of this paper is to define the parameters of the total and partial segmentation that can ensure the best reduction of eddy current losses.

First, a model to analyze eddy current losses is presented. Second, the effectiveness of full and partial magnet circumferential segmentation to reduce eddy loss is studied for a range of frequencies from few Hz to a dozen of kHz. To achieve these purposes a 2-D finite element model is developed under MATLAB environment. In a third step of the work, an optimization process is applied to adjust the segmentation design parameters for best reduction of eddy current losses in case of surface mounted permanent magnets synchronous machine.

In case of the skin effect operating, both full and partial magnet segmentations can lead to eddy current losses increases. Such deviations of magnet segmentation techniques can be avoided by an appropriate choice of their design parameters.

Few works are dedicated to investigate partial magnet segmentation for eddy current losses reduction. This paper studied the effectiveness and behaviour of partial segmentation for different frequency ranges. To avoid eventual anomalies related to the skin effect an optimization process based on the association of the finite elements analysis to genetic algorithm method is adopted.

It is important to investigate large‐scale numerical analyses of electromagnetic fields in design processes of electromagnetic machines. Thus, faster solvers for eddy current analyses are necessary. Parallel computation methods for linear solvers in electromagnetic field analyses have been investigated. These methods have gained importance due to the diffusion of PC clusters and multi‐core CPUs in recent years.

This paper discuses linear solvers for the finite element method in eddy current analyses on parallel computers. The preconditioned conjugate gradient method with overlapping domain decomposition is treated. Some techniques treated to improve the convergence was investigated.

The numerical results show that the overlapping effect results in good convergence in eddy current analyses.

The preconditioned conjugate gradient method with overlapping domain decomposition has been treated. The numerical results show that the overlapping method works more efficiently for eddy current analyses. Moreover, this method enables large‐scale analyses on popular computers such as PC clusters.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

In the laminated core of transformer, motor, etc. each electrical steel sheet is usually insulated in order to reduce the eddy current loss. Raw steel sheets without insulation are sometimes used in a small core of electrical machines and electronic equipments, because the cost of iron core can be reduced if cheap steel sheets without insulation are used in the core. The purpose of the paper is to show how the contact resistance between sheets of laminated core affects the interlaminar eddy current and to show the criterion for judgment of the necessity of insulation.

The eddy current losses of core made of SPCC (cold rolled steel sheets) of different widths with and without insulation under various conditions are analyzed by using the finite element method (FEM) considering the contact resistance. The equivalent circuit for such a laminated core without insulation is shown. The experimental investigation is also carried out.

A criterion for the judgment of insulation is examined. It is shown that the increase of eddy current is affected by the ratio (this corresponds to the criterion) of the resistance of steel and the contact resistance.

The paper clarifies a criterion for the necessity of insulation between sheets of laminated core. It is shown that a similar tendency to the measured value of eddy current loss can be obtained by utilizing the modeling method of laminated core.

The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM) technique with an extraction based on the Gauss‐Newton algorithm with Tikhonov regularization is applied.

The aim is to have a computationally fast recognition procedure of defects since the monitoring results in a large amount of data points that need to be analyzed by 3D eddy current model. According to the SM optimization, the finite element method (FEM) is used as a fine model, while the model based on an integral method such as the volume integral method (VIM) serves as a coarse model. This approach, being an example of a two‐level optimization method, allows shifting the optimization load from a time consuming and accurate model to the less precise but faster coarse surrogate.

The application of this method enables shortening of the evaluation time that is required to provide the proper parameter estimation of surface defects.

In this work only the specific kinds of surface defects were considered. Therefore, the reconstruction of arbitrary shapes of defects when using real measurement data from ECT system can be treated in further research.

The paper investigated the eddy current inverse problem. According to aggressive space mapping method, a suitable coarse model is needed. In this case, for the purpose of 3D defect reconstruction, the reduced VIM approach was applied. From a practical view point, the authors demonstrated that the two‐level inversion procedures allow saving of up to 50 percent CPU time in comparison with the optimization by means of regularized Gauss‐Newton algorithm in the same FE model.

The purpose of this paper is to present a methodology for calculating eddy current losses in the core of a single-phase power voltage transformer, which, unlike a standard power transformer, has an open-type core (I-type core). In those apparatus, reduction of core losses is achieved by using a multipart open-type core that is created by merging a larger number of leaner cores.

3D FEM approach for calculation of eddy current losses in open-type cores based on a weak AλA formulation is presented. Method in which redundant degrees of freedom are eliminated is shown. This enables faster convergence of the simulation. The results are benchmarked using simulations with standard AVA formulation.

Results using weak AλA formulation with elimination of redundant degrees of freedom are in agreement with both simulation using only weak AλA formulation and with simulation based on AVA formulation.

The presented methodology is valid in linear cases, whereas the nonlinear case will be part of future work.

Presented procedure can be used for the optimization when designing the open-type core of apparatus like power voltage transformers.

The presented method is specifically adapted for calculating eddy currents in the open-type core. The method is based on a weak formulation for the magnetic vector potential A and the current vector potential λ, incorporating numerical homogenization and a straightforward elimination of redundant degrees of freedom, resulting in faster convergence of the simulation.