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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.

High-voltage overhead lines produce low-frequency electromagnetic fields around them. These fields are easy to compute wherever the line route is straight, as opposed to places where its direction is changed. The purpose of this paper is to perform a numerical analysis of an electromagnetic field occurring along a high-voltage overhead line at the places of the changed direction and to compare the results with the exposure limits for low-frequency electromagnetic fields in order to assess their effects on living organisms.

The computation was conducted in the MATLAB SW by means of a combination of integral and differential methods in a three-dimensional (3D) arrangement, taking into account the location and shape of the tower. Special procedures within the MATLAB software had to be coded.

Within the research, the following electromagnetic field quantities were computed: the distribution of electric field strength, magnetic flux density, Poynting vector, electric potential and surface charge density. The results obtained indicate the influence of both the line route changing its direction and the deviation tower location on the electromagnetic field around the tower.

In order to shorten the computation time, it was necessary to achieve a minimum number of degrees of freedom by adjusting the real shape of both the cross-section of the deviation tower beam and the conductors. In some further research, attempts could be made to further optimize the results by using the real shapes of the cross-section of the deviation tower beam and the conductors. Furthermore, it could be beneficial to shorten the set distance between two adjacent nodes in order to obtain a finer mesh while still achieving an optimal ratio between the number of nodes and the computation time.

The Czech Regulation no. 1/2008 Coll., concerning protection of health against non-ionized radiation, stipulates 100 μT to be the maximum safe value of magnetic flux density in case of an uninterrupted exposure and frequency of 50 Hz. The investigated area did not exhibit values exceeding this limit. The same was true for the maximum permissible level of electric field strength being specified at 5,000 V/m.

Similar problems are often solved by means of FEM in 2D arrangements. However, when applying this method for conductors passing through a large 3D area, it is difficult to model an optimal 3D mesh within the conductors and the tower beams. This research shows that the application of integral methods reduces the complexity of the generated mesh. Unlike FEM, requiring the generation of a 3D mesh, the integral method only requires a surface mesh on the conductors and tower beams, thus significantly reducing the number of degrees of freedom. FEM only remains necessary for areas adjacent to the tower beams and conductors.

Integral equation methods are very often used for high‐voltage field computation. This paper describes an adaptive Gaussian quadrature method for solving potential and field related integrals. Based on computer‐aided design, the high‐voltage configuration is modelled using bi‐cubic spline functions for the description of the boundary surfaces. This problem definition requires a numerical solution of the governing integral equations. Standard Gauss‐Legendre quadrature is improved by an adaptive approach. The describing surfaces are sub‐divided under distance‐dependant aspects. Hence, different rules of Gaussian quadrature are examined and compared to analytically obtained results. The solution is used to compute the potential and field strength on the electrode or insulator contour. The accuracy and the speed‐up of the new method is demonstrated by several calculations.

The application of the fast multipole method reduces the computational costs and the memory requirements of the boundary element method from O(N²) to approximately O(N). In this paper we present that the computational costs can be strongly shortened, when the multipole method is not only used for the solution of the system of linear equations but also for the field computation in arbitrary points.

The paper presents quasi 3D magnetic field computation for anisotropic layer structure of transformer core, but this computation method can be also applied to other magnetically non‐homogeneous structures. To compute magnetic flux density vectors in the layers of the structure the authors applied a new method based on the assumption that different distribution of the magnetic flux in particular layers results from the tendency to reach the minimum of the magnetic field energy.

The electromagnetic fields have a great influence on the behaviour of all the living systems. The as low as reasonably achievable (ALARA) principle imposes, in case of long exposures to low (i.e. power systems) or high frequency (i.e. microwave systems or cell phones) fields, some limitations to the radiated fields by the industrial equipment. On the other hand, some benefits can be taken from the effects of the electromagnetic fields on the living being: the hyperthermal technique is well known for the treatment of the cancer. Either we want to be protected from the fields, or we want to take benefit of the positive effects of these fields, all the effects thermal as well as genetic have to be well known. Like in any industrial application, the electromagnetic field computation allows a better knowledge of the phenomena, and an optimised design. Hence, there is a very important challenge for the techniques of computation of electromagnetic fields. The major difficulties that appear are: (1) related to the material properties – the “material” (the human body) has very unusual properties (magnetic permeability, electric permittivity, electric conductivity), these properties are not well known and depend on the activity of the person, and this material is an active material at the cell scale; (2) related to the coupling phenomena – the problem is actually a coupled problem: the thermal effect is one of the major effects and it is affected by the blood circulation; (3) related to the geometry – the geometry is complex and one has to take into account the environment. The problems that we have to face with are – the identification of the properties of the “material”, the coupled problem solution and the representation of the simulated phenomena.

In the electromagnetic field simulation of modern servo drives, the computation of higher time and space harmonics is essential to consider appearing torque pulsations, radial forces and ripple torques. The purpose of this paper is to propose a method to cover the effect of saturation on the armature flux density within conformal mapping (CM) by an finite element (FE) re‐parameterization.

Field computation by CM techniques is a time‐effective method to compute the radial and tangential field components, but it generally neglects the effect of saturation.

This paper presents a method to re‐parameterize the CM approach by single FE computations so as to consider saturation in the model over a wide operation range of the electrical drive.

The proposed method is applied to a surface permanent magnet synchronous machine, and compared to numerical results obtained by finite element analysis (FEA).

The paper shows that an accuracy similar to that of FE simulations can be obtained with still the low‐computation time that is the characteristic of analytical models.

To provide a general method for coupled simulation of electrical machines and circuits, using finite element analysis and a circuit/system simulator.

The electrical machine is modelled by dynamic inductance and electromotive force (EMF), which are determined by finite element analysis and updated in time‐stepping procedure. Calculation of these parameters is based on current perturbations that are applied on linearized field equations after determining the operating point by nonlinear analysis.

Based on the case studies, the presented method can be utilized in coupled field‐circuit simulation and the results correlate with those obtained by other known methods. The results were also validated according to experimental data.

Calculation of the EMF and the presented implementation for SIMULINK have some limitations regarding the accuracy and stability of the numerical integration. In the future, the numerical methods could be still improved and the implementations could be extended to other simulators.

Since the presented methodology is of a general type, the research provides means to include field‐circuit coupling into a variety of different simulation software.

Definitions of the circuit parameters differ from the conventional ones, as a result of which the parameter extraction can be performed in computation‐effective way. The benefits of the research are met widely, since the general‐purpose methodology is not limited to any single software.

In this paper, a parallel preconditioning technique based on the additive variant of overlapping domain decomposition is described and implemented to solve magnetostatic field problems. This technique involves covering the domain with a number of overlapping subdomains. The pre‐conditioner results from adding together approximate inversions on the subdomains, Theoretical estimates for the rate of convergence for the resulting algorithm are available and are based on the properties of underlying differential equations. Numerical experiments are given to demonstrate the effectiveness of this algorithm.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.