Showing papers in "Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering in 1995"

Optimum geometry for torque ripple minimization of switched reluctance motors

Abstract: This paper briefly describes an approach to determine the optimum magnetic circuit parameters to minimize low speed torque ripple for switched reluctance (SR) motors. For prediction of the torque ripple, normalized data obtained from field solution and a neural network approach is used. Comparison of experimental results with computations illustrates the accuracy of the method. The optimization method is briefly described and some results are presented.

Summary of results for problem 20 (3‐d static force problem)

Abstract: Thirteen computer codes developed by eleven groups are applied to the benchmark problem 20 (3‐D static force problem) for the TEAM Workshop. The solutions are compared with each other and with experimental results.

On the homogenization of maxwell equations

Abstract: We discuss the following general problem: given a composite, made from at least two different materials with each its own (scalar, and possibly complex‐valued) e and μ, distributed in space in a regular, crystal‐like, pattern, find the equivalent permittivity and permeability (they will, in general, be tensors). This is homogenization. A computation in which such repetitive composites are present can then be done by simply replacing these with their equivalent, homogenized, materials.

SIMULATION OF n+−n−n+ DEVICES BY A HYDRODYNAMIC MODEL: SUBSONIC AND SUPERSONIC FLOWS

Abstract: The effects of viscosity, previously neglected in electronic device stimulations, are studied using a non‐standard hydrodynamic model, following Anile and Pennisi. Results are compared with those of Gardner.

Summary of results for team workshop problem 13 (3‐d nonlinear magnetostatic model)

Abstract: Seven computer codes developed by five groups are applied to the benchmark problem 13 of the TEAM Workshop which consists of steel plates around a coil (a nonlinear magnetostatic problem). The solutions are compared with each other and with experimental results.

Summary of the results for magnetic damping in torsional mode (team problem 16)

Abstract: This paper describes the results for magnetic damping in torsional mode (TEAM problem 16). A total of six solutions are presented and compared with experimental results. The problem is treated as a coupled electromagnetomechanical one. In general numerical predictions agree well with experiment.

Analytical solution for the eddy current problem inside a conducting cylinder using the second order magnetic vector potential

Abstract: The evaluation of eddy currents in cylindrical geometries is examined analytically by using a method, which utilises the second order magnetic vector potential. As an example the three‐dimensional problem of the calculation of eddy currents inside a long conducting cylinder excited by a saddle shaped coil is studied.

End winding leakage calculation of a squirrel-cage induction motor for different load conditions

Abstract: The calculation of the end winding leakage of a squirrel‐cage induction motor using a three‐dimensional finite element method is discussed The end winding inductance is thought to consist of a leakage, describing the flux linked with the end winding only, and a mutual part, describing the flux linked with both end winding and end ring Both leakage and mutual inductance are found to vary for different load conditions

Simulation of an electromagnetic actuator by a coupled magneto‐mechanical modelling

Abstract: This paper presents a model for the simulation of dynamic behaviours of a coupled magneto‐mechanical system The magnetic equation is solved with the help of the finite element method The local magnetic material saturation is considered The moving band technique is used for accounting the movement The magnetic torque of permanent magnet synchronous machine is calculated from the field solution according to virtual work principle and then introduced in the mechanical motion equation to calculate the shaft position The complete differential equation system is solved with an iterative procedure

The near field to far field transformation

Abstract: If a scattering problem is solved by finite element, finite volume or finite difference methods, it is necessary to predict the far field pattern (or radar cross‐section) by using a near field to far field transformation. Usually this is done using the Stratton‐Chu integral relations, which give the far field pattern in terms of a near field surface integral. When volume‐based methods are used this is unnatural, and it may be necessary to employ interpolation procedures to provide the necessary surface data. In this paper an alternative method based on volume integrals is proposed. The main advantage of the new procedure is that it allows the use of discrete quantities that are naturally available from the numerical scheme. However, it is now necessary to perform volume integrals. The error in the new procedure is examined, and a simple numerical example provided.

An analysis of the hydrodynamic semiconductor device model — boundary conditions and simulations

Abstract: A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem Several possible sets of boundary conditions are given to illustrate the proper boundary conditions Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation

‘a posteriori’ error indicator and error estimators for adaptive mesh refinement

Abstract: Two different ‘a posteriori’ error estimation techniques are proposed in this paper. The effectiveness of the error estimates in adaptive mesh refinement for 2D and 3D electrostatic problems are also analyzed with numerical test results. The post‐processing method employs an improved solution to estimate the error, whereas the gradient of field method utilizes the gradient of the field solution for estimating the ‘a posterior’ error. The gradient of field method is computationally inexpensive, since it solves a local problem on a patch of elements. The error estimates are tested by solving a set of self‐adjoint boundary value problems in 2D and 3D using a hierarchical minimal tree based mesh refinement algorithm. The numerical test results and the performance evaluation establish the effectiveness of the proposed error estimates for adaptive mesh refinement.

3d magnetic field distribution of yoke flux in three‐phase transformers without ferromagnetic tanks

Abstract: The 3D calculation of the monophase flux, due to n‐triple harmonics of the windings currents is considered. For small, three‐phase transformers without ferromagnetic tanks the calculation consists in unbounded problem solution. The 3D magnetic field of the yoke flux outside the magnetic core was analysed numerically by means of integral equations method. Our computer program subroutines, written in Fortran 77, have been implemented to a personal computer. The calculated components of the magnetic flux density were compared with the measured ones. The distribution of the different flux parts was calculated and tested by measurements for a three‐phase transformer.

Singular and near‐singular integrals in high‐precision derivative computation

Abstract: Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

The comparison of the methods used for estimation of current transformer metrological properties

Abstract: In the paper, research results on applying field methods in the process determining the parameters of a current transformer equivalent circuit have been published. The metrological characteristics were determined by solving a non‐linear electrical circuit, that is, the equivalent circuit of a current transformer, assuming different values of the forcing current and load. The method gave satisfactory results (the curve 1 in Figure 1) but was found to be time and labour‐consuming. The determination of non‐linear characteristics of RFe and Xµ elements of the equivalent circuit of a current transformer, using field methods, required carrying out a number of calculations of field distributions at the current transformer no‐load state, with different forcing currents and allowing for the magnetization characteristic of the core as well. The total magnetic energy at no‐load state is related to the main flux which permits to determine the Xµ magnetizing reactance, for a given saturation state of the core. On the basis of the calculated distribution of the vector potential, the Bmax magnetic flux density may be calculated in each element of the core and then, the total core losses and the RFe resistance may be calculated using the p = ƒ(Bmax) characteristics of the core sheet loss. Using field methods makes it possible to determine the X2r leakage reactance of the secondary winding, on the basis of the magnetic energy related to the leakage flux of the secondary winding, independently from the shape or localization of the core and the windings as well, while using the analytic method, the formulas used are true only for cylindrical coaxial windings located on the same column of the core. These formulas have been derived with the assumption that the distribution of the flux in the gap between the windings is uniform and that the flux is divided equally between the primary and the secondary windings, which is not true actually. The obtained characteristics of the RFe and the Xµ non‐linear elements, approximated by n‐degree polynomial, and also X2r were used as the input data for solving the non‐linear circuit, in order to determine the error characteristics.

Calculation of the tangential components of the magnetic field strength from vector potentials for 3d

Abstract: Normal components of B and the tangential components of H alike are needed for the force calculation. If the field is calculated numerically, only one of these components is known exactly (in numerical sense), the other one is known only approximately.

Infinite elements for 2D unbounded wave problems

Abstract: A basic difficulty encountered in applying the finite element method to unbounded wave problems is that the domain in which the field is to be computed is unbounded, while finite element models are of finite size. There are several ways to overcome this difficulty. The widely used method is to truncate the finite element model at a finite position and apply suitable boundary conditions there. The relevant boundary conditions must absorb the outgoing wave and have been called absorbing boundary conditions (ABC's).

First steps towards a full integrated cad system for electrical machines

Abstract: An approach for electrical machines design by using a software which links the sizing procedure to the magnetic field computation is presented in this paper. After reviewing the principles of an electrical machine general design, the process of the development and the use of a special link between the dimensions data and the magnetic field computation is described. The whole solution procedure is conducted automatically. Any change on the machine dimensions can be made and the sequence of the CAD tasks can be prepared and run automatically without any user intervention. The whole procedure is applied to a comparative study of different structures of permanent magnets synchronous motors.

Analysis and optimization of planar thick film ni‐ferrite inductor

Abstract: Ni‐ferrite powder average grain size less than 0.9µm was used for the ferrite paste preparation. Ferrite paste was printed on Al2O3 substrate and fired 850°C/10min. After Ni‐ferrite thick film characterization had been done, simple planar inductor geometry, such as square spirals, were printed on it. Measurements were done, using an HP 4194A impedance analyser. The experimental results were summarized and compared with theoretical predictions given by the electromagnetic analysis using the method of current images for the reason of accounting the effect of magnetic substrate. The computer program, developed here, allows determination of the required thickness of the substrate which will produce inductance enhancement of the given permeability of the substrate material. The same results can also be used to determine the permeability of magnetic film or substrate quickly and are directly applicable to the design of the planar inductors.

Modelling ac losses in high‐temperature superconductors as a nonlinear diffusion process

Abstract: Ceramic superconductors experience losses when carrying alternating currents. A first step in an attempt to macroscopically model the loss mechanism is to consider the ac transport current in a ribbon that has a cross‐section of width much greater than thickness. To some extent high‐temperature superconductors behave in a way similar to type II superconductors in which the loss mechanism is described by the critical state model, where the current is assumed to flow with a constant critical density Jc and is independent of the magnetic flux density B and ∂B/∂t. The dominant mechanism is the irreversible motion of fluxoids due to their interaction with the pinning sites, resulting in a form of hysteretic loss that can be represented in macroscopic terms (in a system with only one component of magnetic field) as proportional to ∫HsdBa/T over a complete cycle of period T, where Hs is the surface magnetic field strength and Ba is the space average value of flux density. However, it is found that the high‐temperature materials exhibit strong flux creep effects, and so the critical state model may not provide a sufficient description. To find an alternative formulation it is necessary to consider the flux creep E‐J characteristic of the ceramic material. If a highly nonlinear expression for the resistivity ? can be found, it may be possible to model the flux and current behaviour as a diffusion process.

Quasi 3d magnetic field computation for anisotropic sheet layer structure

Abstract: 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.

Contribution to the transient analysis of induction motors solving the electrodynamic equations by using the finite elements method

Abstract: This paper details how the equations describing the magnetic field inside the motor and the equations of its electric circuit can be integrated in one only system, which can be solved using the Finite Element Method (FEM). When a model of a circuit is used, the solution of the magnetic field equation is the input to calculate the currents of the machine windings. As the magnetic field depends on these currents, it is necessary to follow an iterative process until initial and final currents match. With the technique proposed in this paper, because both magnetic field equations and electric circuit equations are integrated in the system, just in one step, the currents and induced voltages can be obtained with high accuracy and considerable time saving.

Analytical calculation of double‐side planar travelling wave induction heating systems

Abstract: The heating of flat workpieces of different materials and geometrical characteristics (width, thickness) is often required in the metal industry. The temperature requirements depend on the process to which the workpiece should undergo and the mechanical and chemical characteristics which must be obtained by the heat treatment. For certain applications in which the electrical resistivity of the workpiece material is low or the ratio between the width and thickness of the body is high, the classical longitudinal flux induction heating is efficient only if high frequencies are used. A good alternative is the travelling wave induction heating (TWIH) which has a structure similar to the linear induction machines (LIM).

3d eddy currents modelling by using a particular two component technique

Abstract: Several formulations have been developed solving 3D eddy current problems by the Finite element method based on vector quantities. Scalars, involving only one unknown per node of the mesh seem to be, however, more efficient. A particular scalar potential formulation has already been developed which is able to handle 3D magnetostatics,. This technique has been extended for cases involving eddy currents developed at low frequencies, where the skin effect can be neglected.

The role of the knowledge on electromagnetism for electric engineer education

Abstract: Introduction Depending on the way of teaching process organization the theory of electromagnetic field is considered either as a part of theoretical electrical engineering or as an individual subject. The electromagnetic field theory plays a double role in the education of electric engineers: comprehensive or specialized one. However, the electromagnetic field can be treated from the other point of view. It can be lectured with pointing out the calculation methods or phenomena occurring in “pure” electromagnetic field, and on the other hand, with reference to phenomena occurring in coupled fields, where those fields are affecting non‐living or having objects.

Electromagnetic field investigations inside a hollow cylinder

Abstract: The behaviours of the electric and magnetic fields inside a conducting cylinder with a single axial aperture are not as well understood as is commonly believed. The experimental measurements and computer simulations described in this paper comprise a work in progress. The intention of the work is to use the conducting cylinder with a single axial aperture as a standard test object, in order to demonstrate present capabilities in measuring field strengths inside such a test object and to demonstrate the level of agreement attainable with commonly used computer codes. As the following experimental data will show, current free‐field B‐dot sensors cannot be used for measurements inside cavities, as they significantly perturb the fields they are trying to measure. There is indeed a pressing need to develop such nonperturbing sensors for use inside cavities.

Magnetotherapy due to eddy currents induced in neural cells by magnetic stimulation

Abstract: The problem of generating currents of neural cells in human brain has been recently investigated, as it is believed to substitute electroconvulsive therapy (ECT) having the same therapeutic effects but realized in much safer way (painless, non‐invasive and without motor seizure). The magnetic stimulation (transcranial magnetic stimulation — TMS) uses low frequency pulse, from a few cycles per second to a few of tens, magnetic field in order to induce eddy currents in the deeper layer of brain structure.

Calculation of flux distribution in transformer core taking hysteresis into account

Abstract: Calculation of flux distribution in three‐phase three‐limb transformer core has been made using 2D finite element method. The calculation has been performed with and without taking into account lthe hysteresis of magnetic material. Anisotropy of magnetic material has been modelled through the so‐called elliptic permeability model. Comparison of results of calculation and results of measurement has been performed for a scale model of transformer core. An agreement better than 3 per cent has been obtained, for calculated and measured results of third harmonics and of flux distortion factors, when hysteresis has been taken into account. The CPU‐time was 6–10 times longer when hysteresis has been included into calculation.

The 3d analysis of the leakage field in a transformer with disk windings

Abstract: The calculation of the leakage quasi‐stationary magnetic field of a three‐phase transformer with disk‐windings is presented in the paper. A mathematical model of the transformer based on Maxwell's equations has been applied. Computational results of the short‐circuit reactance have been compared with analytical formulas according to Richter's formulas.

Design optimization of an electrostatic micromotor with axial field

Abstract: Historically, the idea of using electrostatic phenomena to produce motion has long stimulated the activity of scientists. Although the power generated by electrostatic motors is modest, the absence of windings and ferromagnetic material makes this kind of device competitive for applications characterized by low levels of torque and reduced volumes. During last years a renewed attention appeared towards electrostatic devices in the microscopic scale; their fabrication has been possible thanks to the technology for Si‐integrated‐circuits. In particular, electrostatic micromotors have an increasing role as position actuators when submillimetric movements are required. Methodologies of numerical simulation applied to microdevices are a helpful tool for the designer, who should fulfil criteria often in mutual clash like electromechanical response and fabrication cost. More generally, procedures of automated optimal design are now available, tackling the design problem as the constrained minimization of an objective function suitably set up.