Ebook: Advanced Computer Techniques in Applied Electromagnetics

This book contains papers presented at the International Symposium on Electromagnetic Fields in Electrical Engineering ISEF'07 which was held in Prague, the Czech Republic on September 13–15 2007. ISEF conferences have been organized since 1985 as a common initiative of Polish and European researchers who deal with electromagnetic field applied to electrical engineering. Until the present the conferences have been held every two years either in Poland or in one of European academic centres renowned for electromagnetic research. Technical University of Prague and the Chech Academy of Sciences make Prague be such a centre. Additionally, Prague is well-known in the world for its beauty and charm and it is called “Golden Prague”. The city of Prague is one of the six most frequently visited cities in Europe. Indeed, it is indisputable that Prague can attract every has the opportunity to visit it.

The long, more then 20-year-old, tradition of ISEF meetings is that they try to tangle quite a vast area of computational and applied electromagnetics. Moreover, ISEF symposia aim at joining theory and practice, thus the majority of papers are deeply rooted in engineering problems and simultaneously present high theoretical level. Bearing this tradition, we attempt to touch the core of electromagnetic phenomena.

After the selection process 237 papers were accepted for the presentation at the Symposium and almost all of them were presented at the conference, both orally and in the poster sessions. The papers have been divided into the following groups:

• Micro and Special Devices

• Electromagnetic Engineering

• Computational Electromagnetics

• Coupled Problems and Special Applications

• Measurement Monitoring and Testing Techniques

• Bioelectromagnetics

• Magnetic Material Modelling

The papers which were presented at the symposium had been reviewed and assessed by the sessions' chairmen and the Editorial Board assembled for the post-conference issue of ISEF'07. All the papers accepted for further publication were divided into three groups: 1) of more computational aspect, 2) of information technology aspect and 3) of more applicable nature. The latter ones are published in this volume while the first ones went to COMPEL journal (COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 27, No. 3/2008) and the second group to Springer Verlag (series on Studies in Computational Intelligence, vol. 119, 2008).

The papers selected for this volume have been grouped in three chapters and seven sub-chapters. The division introduces some order in the pile of papers and the titles of chapters mirror the content of the papers to some extent. Names of chapters and subchapters are as follows:

Chapter A Fundamental Problems and Methods

 Fundamental Problems

 Methods

Chapter B Computer Methods in Applied Electromagnetism

 Computational Methods

 Numerical Modelling of Devices

Chapter C Applications

 Electrical Machines and Transformers

 Actuators and Special Devices

 Special Applications

The papers gathered in Chapter A are mainly devoted to physics of electromagnetic materials and mathematical approaches to electromagnetic problems. In the first sub-chapter papers concern physical phenomena, like magnetostriction, vibrations, anisotropy, occuring in the various electromagnetic materials from ferromagnetics to dielectromagnetics. And the second sub-chapter consists of papers concerning methods of analysis of electromagnetic phenomena in their methodological aspects.

Chapter B contains papers dealing with numerical (or computer) analysis of electromagnetic devices and phenomena. The first sub-chapter shows how mathematical methods are realised numerically, i.e. how to make real calculation, based on numbers. And the papers gathered in the second sub-chapter deal with numerical modelling of some groups of devices.

Chapter C, in turn, reveals the world of engineering problems, showing how theoretical and methodological considerations can be transferred to real engineering problems. Indeed, the chapter gives the image of real applied electromagnetics. The first sub-chapter is devoted to the very classical electrical devices, namely transformers and electrical machines. In spite of avery long tradition of numerical analysis of electromagnetic phenomena in such devices, the papers bring some new ideas and approaches. The second sub-chapter shows newer applications like sensors and actuators, and thus the area of engineering called mechatronics. Special approaches are needed inthe analysis of these devices as their size and operation features are quite different fromthe previous ones. And the last sub-chapter gathers a few papers dealing with very special applications based, for example, on superconductivity or ferroresonance. Needless to add that the electromagnetic analysis in such cases requires again new techniques and methods.

The division of the papers is far from clear distinction of the papers' topics and content. It is a very rough distinction which gives prospective readers some suggestion on how to find a paper of their personal interest.

Summarising this introductory remarks we, the Editors of the book, would like to express our hope that the book you have in your hands will help the world-wide electromagnetic community, both academic and engineering, in better understanding electromagnetism itself and its application to technical problems.

At the end of these remarks let us be allowed to express our thanks to our colleagues who have contributed to the book by submitting their papers or/and by peer-reviewing the papers at the conference as well as in the publishing process. We also convey our thanks to IOS Press Publisher for their effective collaboration in giving this very attractive shape of the book and its promoting. Let us also express our strong belief that ISEF conference will maintain strong links with IOS Press in the future.

Ivo Dolezel, Chairman of the Organising Committee

Andrzej Krawczyk, Scientific Secretary

Sławomir Wiak, Chairman of the ISEF Symposium

On the grounds the author's early works the analytical formulae for unit active power (losses) and reactive power in magnetic lamination were presented. The elliptical hysteresis approach of magnetic loops was assumed.

In particular, these powers have been refereed to magnetization frequency. The universal functions F₁, F₂ for the case of magnetic flux forcing and F₃, F₄ for magnetic strength application on the booth side of lamination have been deduced in the work.

Study of electromagnetic field in the neighbourhood of the metallic corners is an aim of the present paper. Concave and convex corners are considered.

This paper deals with the numerical computation of eddy currents and the forces they cause. These effects are of special interest when considering pulsed magnetic forming, which is a technique to form thin metal sheets or pipes. A high transient current in a coil near to the work piece excites eddy currents and the associated Lorentz forces press the work piece into a die.

The paper deals with non-destructive (NDT) microwave measurement of defects in metal samples exploiting the waveguide features at the defect depth evaluation. In this article some results concerning their evaluations regarding to microwave access are shown. More measurements were performed to evaluate the geometry of defects in metal samples. Apart from established methods two new unusual microwave connections are presented and the results with their use at defects examination are given and compared with the previous results. Their advantages are discussed and some proposals for their utilizations are given.

This paper refers to electromagnetic field propagation around high-current circuits. The effects of its influence on conducting bodies that are seals and casings of electric devices are discussed. These barriers which are the constructional parts are made of ferromagnetic materials – good absorbers of energy transformed into heat in their structures. Intensity of absorbance depends on the distance between the barrier and source of radiant energy. Limitation of diffusing energy by absorbing it requires a high accuracy quantitative analysis to assure a high value of absorption coefficient and optimal power density of heat sources. The analysis results of basic geometries are shown.

Development of technology and notably development of new generation magnetic materials caused substitution of cast magnets with magnets manufactured in the process of powder metallurgy. Development in magnetic materials is observed not only hard magnetic materials, but also soft magnetic materials. Particular intensive development can be observed in powder materials, which more and more often substitute traditional materials, e.g. electrical steel. The main factor deciding about application of soft magnetic elements is its magnetic properties. In many applications mechanic properties are equally important as magnetic parameters. Physical properties of materials change with the change in temperature. The main goal of research is to know changes of mechanical properties of dielectromagnetics with changes of temperature.

Non grain-oriented electrical steel has an inherent anisotropy, which is normally neglected in the calculation of electrical machines. Moreover, the magnetic anisotropy is usually measured in small material samples. Due to the cutting effect, the magnetic anisotropy in the machine is not the same as in the sample. In this paper, the magnetic anisotropy is considered as a global problem. A method to measure it is presented and its influence on the electromagnetic and acoustic behavior is considered through the example of an induction motor.

Recently, it is examined with many papers about magnetostriction of electrical steel sheet and magnetostriction of transformer model. In this paper, deformation and vibration of electrical steel sheet by magnetostriction was analyzed and measured. There results were compared and examined. As results, it was reported that natural mode was provoked to force of magnetostriction.

Rapid design is one of the main imperatives of modern manufacturing, followed from principles of mechatronics [1], and is handy tool of regular optimization of structure. In this work it is presented such rapid design method for specific class of power transformers with sandwich windings. To accelerate the design process an expert system and rapid interactive procedure was applied. At such approach the more scientific and design experience is located into the Knowledge Base of the Expert System, the more, rapid, easier and cheaper is a regular design and optimization of a machine. Thanks to analytical preparation, approximation and linearization coefficients the programming and calculation is discharged from cumbersome iteration and other formal disturbances. Hybrid analytically-reluctance Network Method three-dimensional RNM–3D [2] has proved here as one of the best for rapid design of such complex structures like modern transformers with extreme electromagnetic filed concentration, its crushing forces, eddy current loss and overheating hazard.

Description of method of calculation of electromagnetic field induced by sinusoidal alternating current (or direct current) flowing in the infinitely long cylinder with convex intersection is aim of this paper. Potential of simple layer and Newtonian potential are applied. Adequate integral equations were introduced for calculation of integrands in these potentials. In the event of alternating current impedance boundary condition is considered.

In this work the inverse problem solution with iterative Gauss-Newton algorithm and Truncated Singular Value Decomposition (TSVD) is shown. For the goal function a norm l2 was chosen. To solve the inverse problem, which consists of the identification of conductivity distribution in a 3D model, the multi-frequency sensitivity analysis has been applied. The correctness of sensitivity calculation has been proved utilizing three different methods, namely Tellegen's method of adjoint model, differentiation of stiffness and mass matrix, as well as sensitivity approximation by means of difference quotient. Regarding the effectiveness of those methods, the first one is preferred because of shortest computational time.

Torque and e.m.f. of an induction motor can be derived from the air-gap flux density. The paper shows a new method for computing the flux density distribution of constant air-gap width machines, neglecting magnetic saturation, by making use of very efficient techniques widely used in the field of discrete signals processing: the Fast Fourier Transform (FFT) and the Discrete Circular Convolution. The mutual inductances between the phases of the machine are obtained with a single, very simple formula, in terms of the machine's windings distribution and the geometric dimensions, which is solved with the FFT. As the method can handle arbitrary winding conductor distributions, it is highly suitable to the analysis of the magnetic field and electromagnetic torque in machines with stator or rotor faults, such as inter-turn short circuits or broken bars.

Inductive ovens heat with eddy currents due to a low frequency electromagnetic field. Within a first approximative approach, the effects of thermal conduction and thermal radiation are taken into account. Therefore, a finite element method for calculating the thermal conduction is coupled to a boundary element method for calculating the resulting thermal radiation. For the presented application, a steel tube surrounded by an axisymmetric coil is chosen and the normalized thermal radiation distribution resulting from the thermal conductive transfer and the eddy current density is examined.

The paper presents a model of electrodynamic computation (current density, power loss, temperatures) of three-phase heavy current busways with the use of integral equation method. The computation makes allowance of coupling between the electromagnetic and thermal fields. Results of calculation are shown and compared with the measurement trials performed with physical objects.

There is a great multitude of different approaches to compute magnetic forces, each of them giving different results. Therefore, in this paper three popular force computation methods are investigated for nonlinear magnetostatic problems with the integral equation method. Computed results are compared with measurements from two setups. First, the recently presented TEAM Workshop Problem No. 33.a is used since it allows for verification of force densities. Second, the computed total magnetic force acting on a body is verified with the TEAM Workshop Problem No. 20.

In this paper a numerical model and simulation of non-linear field – circuit system dynamics is presented. The system includes electromagnet coupled with two RC circuits. The RC circuit performs a current rise acceleration and improves the electromagnet dynamics. In proposed system a value of capacitance C impact on electromagnet dynamics is numerically determined.

Metal enclosed generator busbars are applied in electric power plants for the transmission of electric power from generator to transformer. The losses in conductors and enclosures due to rated current are the basis for the calculation of steady state temperature-rises. On the other hand, the maximum force on the conductor due to short-circuit current is an important parameter in determination of mechanical stresses in the conductors and supports. In this paper, using a program based on finite element method (FEM), power losses and short-circuit forces are calculated in arrangement of isolated-phase generator busbar.

Eddy current losses in rotor permanent magnets (PM) of synchronous machines are calculated for sinusoidal stator currents and for PWM inverter supply. Three calculation methods are compared in the FE environment: a) time-stepping method, b) quasi-static method, c) semi-analytical post-processing. These 2D methods are with end effect coefficients, and they consider the time variation of currents and of the rotor position. Whereas method a) includes the variation of flux-density over the magnet cross section and the reaction field of the eddy currents, method b) is neglecting the reaction field. Method c) in several variants features either neglecting of the eddy current reaction field or an averaging of the flux density along the magnet width or height. Neglecting the reaction field is possible for materials with low conductivity and low permeability like rare-earth magnets for low to medium frequencies up to several kHz. The quasi-static methods need less computation time, but depend on the machine geometry like stator MMF wave length, slot pitch, segmented vs. massive magnets and small or big magnet height. The comparison of methods a), b), c) is given for two different stator geometries of permanent magnet synchronous machines with open vs. semi-closed slots and surface-mounted vs. buried magnets.

In this paper, the effects of the stepwise skew on the torque waveform of an interior permanent magnet motor are analyzed by using the 3-D finite element method. The usefulness of the stepwise skew is confirmed through the calculated torque waveforms and measured ones.

In the paper, circuit and field-circuit analyses of high-speed small size inductionmotors are presented. The circuit analysis is possible only for the first harmonic of the supply voltage. For the real shape of the voltage which has many higher harmonics accurate field – circuit analysis is necessary, but this method is very time consuming. The circuit and field-circuit analyses were done for 2-D structure of the motor and for all values of applied frequencies. The results of calculation of magnetizing current are compared with the measurement.

The method presented in this paper allows computing the equivalent characteristic of anisotropic steel sheets used to stack the magnetic circuits. The reluctivity of the anisotropic sheets is a function of the flux density B and the angle between the flux density vector and the rolling direction. This paper focuses particularly the problem of modeling different kinds of overlaps and apparent air-gaps is solved by the homogenization technique which is based on the assumption that, in the layer structure, the magnetic field energy tends to achieve its minimum. The presented method has been verified by comparing the computational results with the measurements of real sets. The paper presents the analysis of magnetic properties of overlaps taking into account the magnetic characteristics of the steel.