Influence of the two-dimensional skin- and proximity-effect on electromagnetic field in the conductors systems carrying nonsinusoidal current

Contents The paper present the influence of the skin- and proximity-effect on Joule power losses in the conducto systems placed in a homogeneous medium and carry opposite periodic nonsinusoidal currents. Theoretical calculation and numerical computation hav been carried out by means of the Bubnov-Galerkin method using numerical calculations following the finite elements method, for the conducting region and separation of variables for the air region. On the basis of numerical computation, graphs of the relative power losses for anarbitrary current with a waveform periodically variable in time, an for different skin- and proximity-effect parameters are plotted.

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Einfluß des zweidimensionalen Skin- und Proximity-Effektes auf das elektromagnetische Feld eines Leiter-systems mit nichtsinusoidalen Strömen (In Englisch)

übersicht Der Beitrag stellt den Einfluß der Skin- und Proximity-Effekte auf die Jouleschen Verluste eines Leiter-systems dar. Das System, das sich in einem homogenen Raum befindet, wird von entgegengesetzten, nichtsinusoidalen, periodischen Strömen durchflossen. — Die theoretischen Betrachtungen und die numerischen Berechnungen wurden in Anlehnung an die Bubnov-Galerkin-Methode (in ihrer numerischen Version der Methode der finiten Elemente für Bereiche des Leiters) in Verbindung mit der Methode der Variablentrennung für den Luftraum durchgeführt. — Auf der Grundlage der numerischen Berechnung wurden Diagramme der relativen Verluste für einen willkürlich ausgewählten Strom mit zeitlich periodischem Verlauf und für verschiedene Parameter des Skin- und Proximity-Effektes gezeichnet.

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Symbols A vector potential (complex r.m.s. value) - A z-component ofA (complex r.m.s. value) - B magnetic induction vector (complex r.m.s. value) - d distance between two successive points of the boundary - E electric field intensity vector (complex r.m.s. value) - e single element - H magnetic field intensity vector (complex r.m.s. value) - i, j, k vertices numbers of the considered finite element - I current (r.m.s. value) - I _o direct component of current - imaginary unit - k harmonic numbers - KR skin-effect parameter - L number of discretization points of the region - M number of discretization points on the boundary - N number of the sum terms in the series expression - N _p finite element shape function - P complex Poynting vector - P Joule power losses - R radius of the conductors - S boundary of region - T period - WR proximity-effect parameter - ^c value of the coordinate on the boundary of the conductor - ^l basis function - magnetic permeability - angular frequency - ¹ basis angular frequency - conductivity - conducting region - ^e finite element region - 3.141593...... - ² scalar Laplacian - finite element area - x, y, z rectangular coordinates - , ,z bipolar coordinates - respect to the region boundary     

Stability against tilt of a glass sheet submerged in molten metal with electromagnetic force

In one of the glass sheet tempering processes in which a glass sheet is submerged in molten metal with electromagnetic force by a linear induction motor (LIM), it is necessary to keep the glass sheet vertical in the center of the molten metal tank, because a glass sheet warps unless both sides are uniformly cooled. This paper describes the concept of the center of the buoyancy force on a glass sheet in molten metal, introduced in order to discuss its stability against tilt. If the center of the buoyancy force of a glass sheet is higher than its center of gravity, it is stable against tilt. Numerical simulation of electromagnetic fluid flow is performed to evaluate the center of the buoyancy force. The stability conditions are the following (where τ is the pole pitch of the LIM): (1) The shortest length of a glass sheet is 2τ/3 shorter than that of the LIM. (2) The lowest limit of the center of gravity of a glass sheet is τ/3 higher than the center of the LIM. © 1999 Scripta Technica, Electr Eng Jpn, 126 (3): 64–72, 1999     

电磁耦合式无线供电在金属轴环境中的涡流损耗分析

针对无线供电技术在工程运用中、工作环境中通常存在电磁耦合系统初、次级线圈被金属轴穿过的情况,在金属轴中存在较为严重的涡流效应,对电磁耦合式无线供电系统进行传输模型建立,通过求解麦克斯韦方程组,推导出涡流损耗的解析表达式,并将电磁耦合模型与金属介质中的涡流损耗模型结合来分析系统工作中的涡流损耗特性。通过Maxwell电磁场仿真软件分析涡流特性来验证理论分析结果,并结合最终实验说明铁氧体磁屏蔽材料对于该环境中的涡流损耗的抑制效果。     

Numerical electromagnetic analysis on current distribution in building directly hit by lightning

Lightning current distribution in a directly hit building is studied by using a simple equivalent circuit and an electromagnetic model. The Numerical Electromagnetics Code (NEC‐4) is employed for numerical electromagnetic analysis. The error in the shunt ratio of lightning current entering wiring, which is calculated using the electromagnetic model, is estimated to be less than 4%. The shunt ratios for lightning current entering the wiring on the top floor and the first floor are largest. Although they are larger for a higher building, they are almost constant if the building struck has more than five floors. They are smaller when there are more vertical conductors, or the length of the wiring is longer. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(1): 9–16, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20449     

Eddy current analysis of thin metal container in induction heating by line integral equations

In recent years, induction‐heating cookers have spread rapidly. It is desirable to commercialize flexible and disposable food containers that are suitable for induction heating. In order to develop a good‐quality food container for moderate heating, the eddy currents induced in a thin metal plate must be accurately analyzed. The integral equation method is widely used for solving induction‐heating problems. If the plate thickness approaches zero, the surface integral equations on the upper and lower plate surfaces tend to become the same and the equations become ill‐conditioned. In this paper, we first derive line integral equations from the boundary integral equations under the assumption that the electromagnetic fields in the metal are attenuated more rapidly than those along the metal surface. Next, to test the validity of the line integral equations, we solve for the eddy current induced in a thin metal container in induction heating and obtain the power density imparted to the container and the impedance characteristics of the heating coil. We then compare the computed results with those obtained by the FEM. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 168(2): 20–27, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20813     

Loss calculation of induction motors considering harmonic electromagnetic field in stator and rotor

A method of loss calculation for induction motors is proposed. The combined 3D–2D time‐stepping finite element analysis is carried out to obtain the copper loss and the time variation of the magnetic field in the motor. The iron loss is calculated approximately considering the time variation of the magnetic field direction and the minor hysteresis loops caused by the time‐harmonic fields using practical computer resources. The proposed method is applied to four types of induction motors, which are the solid rotor induction motors with/without slot and the cage induction motors with/without skew. The measured and the calculated total losses and the iron losses agree well in all cases. The differences of the loss distributions of each motor are also compared and investigated. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(2): 63–73, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10305     

Computation of the electromagnetic field distribution inside enclosures with apertures using 3-D FEM

Knowledge of the electromagnetic field distribution inside electronic enclosures due to incident fields is of interest to EMC design engineers. In this paper, a three-dimensional formulation of the finite element method was developed to solve the electromagnetic field distribution inside metal enclosures with apertures. The formulation was developed using a three-component vector magnetic potential and a scalar electric potential. The displacement current as well as the conduction current term was included. The region of interest was discretized using eight-node isoparametric hexahedrons and the potential functions were defined using linear first-order basis functions. The penetration of a steady-state electromagnetic field through an aperture into a simple cavity was analysed with the 3-D FEM program.     

Magnetic field analysis of a squirrel cage induction motor considering rotor skew and higher harmonics in the secondary current

This paper describes a method to analyze harmonic magnetic fields of squirrel cage induction motors considering rotor skew and higher harmonics in the secondary current. The proposed method is based on a two‐dimensional finite element method. The rotor skew structure is expressed by multiple 2D finite element mesh models, produced in suitable axial positions, and the magnetic field in each mesh model is calculated by the revised secondary current taking into account the skew effect. The secondary currents, magnetic flux densities, and electromotive forces are calculated by the proposed method. Then the differences between a skewed rotor and a nonskewed rotor are discussed. From the comparison between the calculated and the experimental results, the proposed method is shown to be appropriate and useful for quantitative estimation of harmonic components of induction motors. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 98–109, 1999     

电磁感应浮力演示装置实验及分析

通过交流电电磁感应浮力演示装置实验推导出电磁感应浮力与交变电流之间的定性关系,运用电磁感应定律及涡流效应从电磁学角度对实验现象进行理论上的分析,探索浮力规律,提出了优化电磁感应浮力的设想。     

Categorization of induction machines in current signature analysis

The so-called specific harmonic-balance model of induction machines is introduced. It allows the classification of squirrel-cage induction machines into three categories. The categorization also preserves its practical utility for machines that do not strictly fulfill the assumptions for the validity of the equations of the specific harmonic-balance model. Categories as well as slot harmonic frequencies are used to study the spectrum of the stator currents by the simultaneous presence of the static and dynamic eccentricity and by the pulsating torque component superimposed on the constant loading component.     

高性能低谐波绕组感应电动机电磁性能的数值分析

针对普通感应电动机采用低谐波绕组后电磁场分析难度将会提高的问题,利用数值计算的方法,给出了适合低谐波绕组电机电磁性能的数值求解方法.以一台普通感应电动机为例,利用低谐波绕组理论,对定子绕组的线规和形式进行调整,设计具有高起动转矩的低谐波电机.通过对低谐波电机电磁性能的数值计算结果与实验结果的比较,验证了所推导的方法的准确性,提高了所设计的低谐波电机的起动性能.将低谐波电机与普通同型式的感应电动机的气隙磁场和转子齿部磁场进行比较,分析两种电机中磁密谐波成分的含量,结果表明低谐波绕组电机的各次谐波磁密大大降低.     

基于谐波分析法的高速变频电机铁耗计算方法

提出了一种计算非正弦供电时的高速变频电机铁耗的简单而有效的方法。该方法以谐波分析法为基础，能够综合考虑电源谐波、电机铁芯饱和以及集肤效应的影响，具有较高的精度。与有限元法计算结果的比较表明，该方法具有较高的精度。     

Multipole analysis of the electromagnetic field in a spherical anechoic chamber

Contents The vector spherical multipole technique is applied to calculate the electromagnetic field within a spherical domain bounded by a perfectly conducting shell and interiorly covered by an arbitrary number of absorbing layers. The structure serves as a cononical model for an anechoic chamber. By analogy to the definition of the shielding effectiveness for a closed spherical shield a normalized chamber effectiveness is introduced, which characterizes the empty chamber performance. To make available an appropriate test source for the numerical evaluation in Part II, the multipole amplitudes of an arbitrarily polarized and located electromagnetic elementary source (Hertz dipole and Fitzgerald dipole; Huygens source) are deduced.

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Multipolanalyse des elektromagnetischen Feldes in einer sphärischen Absorberkammer

Übersicht Unter Verwendung der vektoriellen sphärischen Multipoltechnik wird das Feld im Innenraum einer ideal leitenden Kugelschale berechnet, welche mit einer beliebigen Anzahl absorbierender Schichten ausgekleidet ist. Die Anordnung dient als ein kanonisches Modell für eine Absorberkammer. In Analogie zur Definition der Schirmdämpfung eines Kugelschirms wird eine normierte Kammerdämpfung eingeführt, welche die Absorber- und Geometrieparameter einer leeren Absorberkammer charakterisiert. Um geeignete Testquellen für die numerische Auswertung im Teil II bereitzustellen, werden die Multipolamplituden einer beliebig polarisierten und lokalisierten elektromagnetischen Elementarquelle (Hertzscher und Fitzgeraldscher Dipol; Huygens-Quelle) abgeleitet.

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This work was supported in part by the Deustche Forschungsgememschaft (DFG).     

接地网电流分布的测量与分析

由于在实际接地网中测量接地网电流是不可能的，因此，提出了一种实验室接地模拟的方法来分析实际接地网的电流分布，即在实验水池中，用电量隔离传感器测量接地网的电流分布，测出不同接地网——单根垂直接地体、十字形接地网、水平接地网、复合接地网的电流分布，所得的实验结果为研究接地网中的电位分布及接地网的设计提供较准确的科学数据。     

Numerical electromagnetic field analysis on lightning surgeresponse of tower with shield wire

Lightning surge characteristics of a transmission line comprising a tower, a shield wire and phase conductors are studied with the help of NEC-2. A tower struck by a lightning stroke behaves as an antenna until a traveling wave makes several roundtrips in the tower. During this interval, the tower footing impedance appears to be higher than the footing resistance, and the coupling coefficient between a shield wire and a phase conductor is much lower than that in the TEM mode. These affect the estimation of insulator voltages of transmission towers subject to lightning currents having short rise times. On the basis of these findings, the parameters in the multistory tower model, which has been used widely in EMTP multi-conductor analyzes, are newly proposed