Electromagnetic Field Computation Research Articles

Parameters for calculation of three-dimensional electromagnetic field by asymptotic expansion method

The paper deals with an approximate analytical solution of a three-dimensional problem of the theory of electromagnetic field, which is based on the use of asymptotic expansion under the condition of a strong skin-effect for a field produced by a closed current-carrying loop located near a conducting half-space. It is noted that each member of an asymptotic series is determined with an error, the value of which depends on the value of a small parameter and increases with increasing the index of series member resulting in limited number of its members. It is identified that when using the method of asymptotic expansion, the number of members of a series can be limited by the relatively small number, which is determined by the specified limits of the allowable accuracy of calculation (relative error). The authors determine the optimal number of asymptotic series members, and indicate that calculation accuracy depends on the value of a small parameter, and for a specific conducting material it depends on the field frequency and the minimum distance from external field sources to a conducting body.

Electric Motor for Brakes – Optimal Design

<div class="section abstract"><div class="htmlview paragraph">A multi-objective optimal design of a brushless DC electric motor for a brake system application is presented. Fifteen design variables are considered for the definition of the stator and rotor geometry, pole pieces and permanent magnets included. Target performance indices (peak torque, efficiency, rotor mass and inertia) are defined together with design constraints that refer to components stress levels and temperature thresholds, not to be surpassed after heavy duty cycles. The mathematical models used for optimization refer to electromagnetic field and related currents computation, to thermo-fluid dynamic simulation, to local stress and vibration assessment. An Artificial Neural Network model, trained with an iterative procedure, is employed for global approximation purposes. This allows to reduce the number of simulation runs needed to find the optimal configurations. Some of the Pareto-optimal solutions resulting from the optimal design process are analysed. They show high improvements of the performance indices with respect to a reference solution.</div></div>

K-domain method for the fast calculation of electromagnetic fields propagating in graded-index media.

A conceptually straightforward method for the fast calculation of electromagnetic fields propagating in graded-index media is presented. More specifically, in this method, we convert Maxwell's curl equations into the spatial-frequency domain to obtain an ordinary differential equation (ODE), and subsequently solve the ODE with the 4th-order Runge-Kutta method. Compared to the traditional beam propagation methods, this method deals with vectorial fields accurately, without physical approximations, like the scalar field approximation or the paraxial approximation; numerically, this method takes advantage of the fast Fourier transform and the convolution theorem to achieve an efficient calculation.

HST calculation of a 10 kV oil‐immersed transformer with 3D coupled‐field method

Transformer winding hot-spot temperature (HST) is one of the important factors affecting transformer oil–paper insulation deterioration. This study presents a three-dimensional coupled electromagnetic-fluid-thermal analysis method for HST calculation in a 10 kV oil-immersed distribution transformer, the influence of the transformer internal metal structure parts on the HST of the winding is considered in the simulation. Combining electromagnetic-field calculation with no-load test and load test of the transformer provides a more accurate method to determine internal losses of the transformer. Taking those power losses as heat sources, the transformer fluid-thermal field analysis is conducted with the finite volume method. The variation of physical parameters of transformer oil with temperature is considered in the simulation. On the basis of the equivalent thermal resistance theory, the equivalent thermal conductivities of transformer windings are obtained. The simulation results deduced from the proposed method agree well with the experimental ones, which are obtained with fibre optic temperature sensors during the transformer temperature rise test, the maximum temperature difference is <3°C. The results validated the validity and accuracy of the proposed transformer HST calculation method.

Analysis of Electromechanical Processes in Asynchronous Machines during Tests by the Loading-Back Method with Energy Recovery in the Network

The article discusses the interrelated electromechanical processes in asynchronous machines when testing by the loading-back method with energy recovery in the network. We analyze a system of two asynchronous machines connected by a common shaft, in which one machine operates as an engine with the voltage supply of increased frequency from the frequency converter and the external machine operates as a network generator. Electromechanical processes in machines have an influence on each other. We have carried out the simulation of electromechanical processes in the motors with allowance for several factors—namely, different degrees of saturation of magnetic cores, torque equalization, and the change in parameters of the windings when changing the operating mode with a nonsinusoidal voltage supply to the asynchronous motor from the frequency converter. A modeling technique with mutual matching of the electromagnetic field models of machines through the relationship of torques on the shaft, based on system minimization of the electromagnetic energy functionals has been presented. The results of simultaneous numerical calculations of interrelated electromagnetic fields in machines and electromechanical processes have been presented. The calculations of electromechanical processes and the characteristics of an asynchronous motor–generator system with a common shaft, mutual load and energy recovery in the network have been performed. The results of experimental studies of a two-machine unit are presented, confirming the theoretical results. It is established that the application of the calculation technique with direct computing the interrelated electromagnetic fields in the engine and generator with allowance for the electromagnetic torque on the shaft provides an error of no more than 7% compared with the experiment.

Выбор конструкции электрического ветрогенератора мегаваттного диапазона мощности

The paper deals with an analysis of possible designs of megawatt power range wind generators for wind turbines of mainland and offshore wind farms of low-speed and gearless drive. Synchronous generators with both radial and tangential magnetization of permanent magnets with classical distributed and concentrated windings are considered. Electromagnetic calculations were carried out for generators with rated speeds of 150 rpm and 12 rpm with a maximum power of 8000 kW at a linear voltage of 6300 V. The possibility of using electromagnetic calculation data for analysis was confirmed by numerical calculation of the two-dimensional electromagnetic field by finite element method using the ELCUT software. It is found that tangential magnetization increases the machine operating ratio for both types of windings. At tangential magnetization it is necessary to give preference to the choice of the concentrated winding at which generators with rated speeds of 150 rpm and 12 rpm will have higher efficiency, smaller masses of active materials and the smallest mass of magnets.

Theoretical study on lowering loss of skin effect suppressed multi-layer transmission line with positive/negative (Cu/NiFe) permeability materials for high data-rate and low delay-time I/O interface board

This paper proposes a new application of skin effect suppression technology for long wiring on high-speed &amp; low-delay I/O board. This proposal will overcome the difficulty of further reducing the transmission losses on the I/O board with vert &amp;gt;vert 50 Gb/s data rate. In previous research, it was demonstrated that suppression of the skin effect by electroplated conductor/magnetic multi-layer, and estimated that the degree of transmission loss decrease at 16 GHz would be 5 %. A major challenge in this paper is to propose an electromagnetic field calculation theory for rectangular multi-layer transmission line, verify it under the same conditions, clarify a lower loss structure by changing thickness of each layer. Also it is expanded to low loss design technology. Cu and NiFe were selected as metal conductor material and negative permeability magnetic material, respectively. The Cu and NiFe films are alternately stacked to form the multi-layer. The top and bottom surface layers are Cu layers. The loss suppression was compared under the following conditions. 1) Total number of layers was 33 and total thickness was 12.67 μm by a constant ratio, Cu: tN = 0.51μm and NiFe: tF = 0.25μm. 2) Optimal stacking determined by changing the thickness of each layer. Compared to conventional thickness by a constant ratio 1), in our proposal 2), we estimated that the loss would dropped to 92% in optimal thickness. By offsetting the phase change of current density, a lower loss structure could be determined. Compared with Cu conductor, the top and bottom surface current densities become low, and depth center current density becomes slightly high for the multi-layer, showing the skin effect is suppressed.

Mutual inductance calculation of the one-primary multiple-secondary coil system

It is of great significance to accurately calculate the mutual inductance of one-primary multiple-secondary coil system (OPMSC) in order to improve energy transmission efficiency, measurement accuracy of magnetic sensor, etc. In this paper, a method based on time harmonic field to calculate such mutual inductance is proposed. Both the high frequency alternating current model and the time-harmonic electromagnetic field calculation method are used to ensure engineering practicability of the method. The current of each coil and the relative position between coils are considered in the proposed method. Moreover, according to the full derivation of a new analytical method. the extremum phenomenon of mutual inductance is described. And this method is verified by both finite element simulations and experiments, which proves that the method is effective for optimizing the relative position of the multiple coils when mutual influence among all the coils is taken into account.

Global model of a radio-frequency ion thruster based on a holistic treatment of electron and ion density profiles

We present a global model of a radio-frequency ion thruster. The model takes into account radial and axial density distributions for electrons and ions of the plasma inside the ionization vessel. These spatial distributions are based on analytical equations and heuristic assumptions and are used self-consistently in all conservation equations. They are considered in the 3D computation of electromagnetic fields and used to calculate the induced power generated by the coil current. We also consider the spatial ionization and excitation inside the plasma volume in the context of energy and charge conservation. Furthermore, the model includes effects of local charge and power losses on the walls. The extraction grid system is modeled in detail describing each extraction channel separately. The spatial dependence of the electron and ion density profile also leads to a radially varying ion beam current and ion focus across the grid system. Therefore, the parameters of each beamlet differ and need to be described individually by the 3D ion extraction code. An extension of the extraction code also simulates the neutral gas transmission coefficient of the aperture system. This approach enables us to determine the neutral gas density inside the ionization vessel as well as the neutral gas losses. The peripheral electric losses in the coil, the RF cables and the radio-frequency generator are derived by a circuit model.

CALCULATION OF ELECTROMAGNETIC FIELDS IN INHOMOGENEOUS MEDIA FOR SELECTION OF PROTECTIVE COATINGS

The aim of the work is to develop a method for high-frequency EMFs calculation in terms of the modified vector potential and to use it for choice of the parameters of the layered absorbing coatings that provide effective absorption of radio wave radiation. Methodology. A method for calculation of electromagnetic fields in inhomogeneous media is described. It is performed in terms of the modified magnetic potential at presented a plane electromagnetic wave as an incident and reflected one. To reduce the computational domain size, additional uniaxially perfectly matched layers ensuring fast and non-reflective attenuation of electromagnetic field (EMF) strengths are used at its boundaries. It is supposed that electrical parameters of such layers have not only resistive, but also magnetic losses. Results. Modification of the known methods for dividing the wave into the incident and reflected, as well as introducing uniaxially perfectly matched layers at the domain boundaries and formulation of the problem in terms of the modified vector potential, provide a possibility to solve the problem of the electromagnetic wave incidence onto heterogeneous media at reduced memory and counting time compared to the formulation tasks through the EMF strengths. Practical value. The described method was used to select parameters of radio-absorbing coatings, application of which on conductive bodies reduces the reflections from them of the incident electromagnetic waves. This provides a possibility to choose the electrical parameters of layered coatings with active losses, as well as magnetic losses, which provide a decrease of the reflected waves amplitude by an order of magnitude or more. Originality. For the first time, the problem of calculating the incidence of an electromagnetic wave on an inhomogeneous medium with active electrical and magnetic losses was formulated in terms of the modified vector potential. The parameters of a multilayer lossy coating, which ensures decrease of the reflected EMF wave strengths by an order of magnitude or more are determined.

A new approach to vector scattering: the 3s boundary source method.

This paper describes a novel Boundary Source Method (BSM) applied to the vector calculation of electromagnetic fields from a surface defined by the interface between homogenous, isotropic media. In this way, the reflected and transmitted fields are represented as an expansion of the electric fields generated by a basis of orthogonal electric and magnetic dipole sources that are tangential to, and evenly distributed over the surface of interest. The dipole moments required to generate these fields are then calculated according to the extinction theorem of Ewald and Oseen applied at control points situated at either side of the boundary. It is shown that the sources are essentially vector-equivalent Huygens' wavelets applied at discrete points at the boundary and special attention is given to their placement and the corresponding placement of control points according to the Nyquist sampling criteria. The central result of this paper is that the extinction theorem should be applied at control points situated at a distance d = 3s (where s is the separation of the sources) and consequently we refer to the method as 3sBSM. The method is applied to reflection at a plane dielectric surface and a spherical dielectric sphere and good agreement is demonstrated in comparison with the Fresnel equations and Mie series expansion respectively (even at resonance). We conclude that 3sBSM provides an accurate solution to electromagnetic scattering from a bandlimited surface and efficiently avoids the singular surface integrals and special basis functions proposed by others.

Design of DEMO PF Coils Based on Cable-in-Conduit Conductor

The poloidal field (PF) coils are designed based on the requirements defined by the EUROfusion 2015 DEMO baseline. The conductors are forced flow, NbTi cable-in-conduit. The design addresses the dimensioning of the winding pack, the electromagnetic field calculation and mechanical load. The cross sections of the cable, i.e., superconductor, copper and helium are allocated to fulfill the design criteria for the temperature margin and pressure drop in the operation. The conductors have rectangular cross section and are layer wound, multiple-in-hand, to minimize the hydraulic length (1 single turn can be as long as 100 m). The orientation of the wide side parallel to the main field component minimizes the ac loss. The larger radius compared to international thermonuclear experimental reactor (ITER) PF coils calls for larger electromagnetic load and hence much larger cross section for the structural support, which must be added on top of the conductor conduit to avoid unmanageable thick conduit walls. For PF1 and PF6 coils, a design option with Nb3Sn conductor may need to be considered due to the effective magnetic field in excess of 6.2 T.

Optimal Design of 1200 kV UHV AC Transmission Lines in India using Newly Developed Standalone MATLAB GUI

Owing to tremendous growth in requirement of electrical power in the country, technological advancement in transmission systems is essential for transmission of bulk amount of power over long distances. Deciding value of corridor width for transmission lines are greatly influenced by magnitudes of electric and magnetic fields along its length. The precise evaluation of the electromagnetic fields and effects of corona like Radio Interference and Audible Noise generated by overhead transmission lines are thus of greater interest. This paper presents implementation of a novel GUI based technique to compute the fields generated by power transmission lines using three dimensional techniques. Actual case of Ultra High Voltage AC (UHVAC) line is considered for study. Transmission lines are analyzed by using newly developed software that facilitates computation and plotting of electromagnetic fields and corona effects in 3D coordinates. MATLAB is used as platform for development of GUI based software to analyze the fields along the entire length of transmission lines under study. It uses concept of charge simulation method (CSM) along with most fundamental Maxwell’s potential coefficient theory and 3D integration techniques.

Influence of Electric Shield Materials on Temperature Distribution in the End Region of a Large Water–Hydrogen–Hydrogen-Cooled Turbogenerator

To investigate the influence of different electric shield materials on the temperature distribution in the turbogenerator end region, a 330-MW water–hydrogen–hydrogen-cooled turbogenerator is considered in this paper. Mathematical and physical models of the three-dimensional (3-D) transient electromagnetic field in the turbogenerator end region are established. The magnetic density distribution and the losses of end parts are obtained with different electric shield materials. The loss values obtained from the 3-D transient electromagnetic field calculations with different electric shield materials are applied to the end parts as heat sources. Pressure and fluid velocity values from flow network calculations are applied to the end region as boundary conditions for the fluid and thermal coupling analysis. In addition, a 3-D fluid and thermal coupling model of the turbogenerator end region is established. The distributions of the surface heat transfer coefficient on the inner and outer surfaces of the electric shield are determined with different electric shield materials. Temperature distributions of the stator-end copper winding, finger plate, clamping plate, and electric shield in the turbogenerator end region are investigated with different electric shield materials. The calculated temperature results for the electric shield are compared with measured values, and the calculated results agree well with the measured values.

Efficient numerical simulation of eddy current pulsed thermography NDT signals based on FEM-BEM method and energy equivalent principle

The numerical simulation of eddy current pulsed thermography (ECPT) signals can be divided into two parts, the computation of electromagnetic field and the simulation of thermal field. It is difficult to obtain accurate ECPT signal efficiently due to the high excitation frequency and the short heating stage. In this study, due to the linear characteristic of the electromagnetic field numerical simulation, the eddy current field has been obtained rapidly through the superposition of eddy current response signals of harmonic excitation current based on the FEM-BEM method. The heat source of temperature field has been obtained by the equivalence of eddy current filed based on energy equivalent principle. The temperature signals of ECPT are computed using the time step iteration algorithm. The proposed method is proved to be accurate and significantly efficient through numerical validation and ECPT experiments. Finally, the quantitative analysis of the temperature decay in SUS 304 plate shows that, at the skin depth of eddy current, the temperature difference decays to 90.22% of the plate surface, while the eddy current decays to 1/e.

Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations

For an accurate description of electromagneto–thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame to the current placement of the matter and the Lagrangean frame to a reference placement. We present a rigorous and thermodynamically consistent derivation of governing equations for fully coupled electromagneto–thermomechanical systems properly handling finite deformations. A clear separation of the different frames is necessary. There are various attempts to formulate electromagnetism in the Lagrangean frame, or even to compute all fields in the current placement. Both formulations are challenging and heavily discussed in the literature. In this work, we propose another solution scheme that exploits the capabilities of advanced computational tools. Instead of amending the formulation, we can solve thermomechanics in the Lagrangean frame and electromagnetism in the Eulerian frame and manage the interaction between the fields. The approach is similar to its analog in fluid structure interaction, but more challenging because the field equations in electromagnetism must also be solved within the solid body while following their own different set of transformation rules. We additionally present a mesh-morphing algorithm necessary to accommodate finite deformations to solve the electromagnetic fields outside of the material body. We illustrate the use of the new formulation by developing an open-source implementation using the FEniCS package and applying this implementation to several engineering problems in electromagnetic structure interaction undergoing large deformations.

3-D FDTD Computation of Electromagnetic Fields Associated With Lightning Strikes to a Tower Climbed on a Trapezoidal Mountain

In this paper, we are interested in the study of electromagnetic (EM) field waveforms generated by a lightning strike to a tower located on a trapezoidal mountain. The latter has a height of 500 m and a steepness angle of slope of 45°. The EM field components are calculated at six points and in three directions from the tower. Among these six points, four of them are placed on a flat ground and located at close distances from the mountain bottom while the other two points are located on the mountain at close distances from the tower. Also, because of the three-dimensional (3-D) geometry of the problem being treated, the computation is performed in three dimensions by using the finite-difference time-domain (FDTD) method. In this computation, the lightning channel is represented by the transmission line model extended to include a tall strike object. To evaluate the influence of the presence of mountain on the EM field waveforms, a comparison between the results obtained in the presence and absence of the mountain has been done. On the other hand, the ground conductivity effect on the EM field components has been also studied. At the end of this study, we show that the trapezoidal mountain shadowing effect causes a reduction of the vertical electric field calculated on a flat ground at close distances from the mountain bottom, while the field is enhanced on the top of the mountain. The same conclusion is drawn for the azimuthal magnetic field. Furthermore, the initial peaks of the vertical electric field and the azimuthal magnetic field, above the ground, have been attenuated because of the finite conductivity of ground. The horizontal electric fields above the ground are characterized by oscillations due to the presence of tower and mountain. The underground horizontal electric field and azimuthal magnetic field have the same waveforms as those obtained above the ground but with smaller magnitudes. Thus, the underground vertical electric is initially bipolar and then essentially zero. Finally, the 3-D-FDTD developed program was validated (see the Appendix).

A Novel Gauged Potential Formulation for 3-D Electromagnetic Field Analysis Including Both Inductive and Capacitive Effects

In this paper, a novel potential formulation for low-frequency (LF) applications taking into account both inductive and capacitive effects but without considering wave propagation is proposed. Both time-domain and frequency-domain formulations are presented. The resultant fully discrete finite-element matrix is made symmetric by incorporating a gauge condition and also rewriting the current continuity equation. To improve numerical accuracy and computational efficiency, high-order mixed edge elements and nodal elements are adopted to approximate the vector and scalar unknown variables together with high-order time-stepping schemes. Several numerical examples are solved to validate and showcase the accuracy of the proposed methods. The proposed formulations are stable in use for LF electromagnetic field computations by considering inductive and capacitive effects simultaneously, such as finding the resonant frequencies of wireless power transfer devices.

Influence of different underexcited operations on thermal field in the turbogenerator end region with magnetic shield structure

The losses and temperatures of end parts will increase obviously in the turbogenerator end region under underexcited operation. In order to study the influence of different underexcited operations on temperature of end parts in the turbogenerator end region with magnetic shield structure, a turbogenerator is considered as an example in this paper. Three-dimensional transient electromagnetic field of turbogenerator end region is given. The magnetic density distribution of clamping plate and magnetic shield is researched. The losses of end parts and stator end cores from three-dimensional transient electromagnetic field calculation are applied to end region as heat sources under different underexcited operations. Pressure value of fan outlet and velocity values of different inlets from flow network calculations are applied to end region as boundary conditions in the 3-D fluid and thermal coupling analysis model. Further, fluid field and thermal field are calculated under different underexcited operations. The distribution laws of fluid velocity and fluid temperature in the turbogenerator end region are determined. The temperature distribution laws of the stator-end copper windings, press finger, clamping plate, screen plate, magnetic shield, and stator end cores are studied under different underexcited operations. The accuracy of numerical calculation is validated by measured values.

GPU-Accelerated Computation of Time-Evolving Electromagnetic Backscattering Field From Large Dynamic Sea Surfaces

An efficient facet-based composite scattering model (FBCSM) is developed for calculating the time-evolving electromagnetic (EM) scattering field (TESF) to study the normalized radar cross section and Doppler spectrum characteristics from dynamic sea surfaces. The dynamic sea surface comprises two-scale profiles: small-scale capillary ripples modulated by large-scale gravity waves, which are modeled by millions of small facets. In microwave bands, two scattering mechanisms, quasi-specular scattering with respect to gravity waves and Bragg scattering with respect to ripples, are taken into account in the FBCSM for computation of the time-evolving EM scattering field under diverse polarizations. However, it may be very time-consuming and difficult to calculate the TESF due to the high resolution and dynamic complexity of the large dynamic sea surface. In this paper, the NVIDIA Tesla K80 graphics processing unit (GPU) with the compute unified device architecture is utilized to improve the computational performance of the TESF. The whole GPU-based TESF computation includes the optimal use of temporary variables, shared memory, constant memory and register, fast-math compiler options, asynchronous data transfer, and the most suitable block size and number of registers. By utilizing the proposed five improvement strategies, a significant speedup of $1200 \times $ can be achieved for computation of TESF from large dynamic sea surfaces for microwave bands compared with the single-threaded C program executed on the Intel(R) Core(TM) i5-3450 CPU.