Comparison between line and surface integral formulations of the hybrid mode‐matching/two‐dimensional finite element method

The hybrid mode‐matching/two‐dimensional‐finite‐element (MM/FEM2D) technique has been proposed for the analysis of discontinuities with waveguides of arbitrary cross section; this technique combines the computational efficiency of modal analysis with the versatility and flexibility of the FEM approach. In this paper, we present in detail a surface‐integrals and a line‐integrals formulation of the hybrid MM/FEM2D technique, in case the ‘Standard Formulation’ is used as FEM2D formulation. Such formulations allow computing analytically both the normalization and the coupling integrals. Furthermore, we compare the accuracy obtained by using the line‐integrals and the corresponding surface‐integrals formulation. To these aims we present several numerical results. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient computation of the surface fields of a horizontal magnetic dipole located at the air‐ground interface

In this paper, the classic problem of determining the fields of a vertically oriented current‐carrying small circular‐loop antenna located near a plane air–earth boundary is revisited. It is well known that the Sommerfeld integrals describing the field components generated by the loop source cannot be exactly evaluated and that their numerical integration is made difficult by the presence of highly oscillatory terms in the integrands. Here, for both source and observation points on the interface, a rigorous method is developed that allows analytical integration of the Sommerfeld integrals, providing fast‐convergent series representations for the surface fields. The obtained formulas permit to overcome all the drawbacks of the previously published approximate solutions to this problem, and to avoid the necessity of using purely numerical approaches when high computational accuracy is required. At the same time, the proposed series representations constitute an analytical benchmark for numerical procedures employed to solve electromagnetic boundary value problems, with applications in antenna design and close‐to‐the‐surface communication. Copyright © 2015 John Wiley & Sons, Ltd.     

A study of the electric-field intensity of conductors of a 500-kV air line

Electrostatic-field intensities have been obtained by mathematical simulations of the electric field of AS conductors of a 500-kV air line (AL) and numerical analysis based on the finite-element method using the Ansoft Maxwell software. The irregularity of the wire surface of an air line and the inhomogeneities of surface of the last cable layer have been taken into account in the study. The latter lead to a local increase in the field intensity, which, in turn, results in a loss of useful power. Phase splitting is used to decrease the electric- field intensity on air lines. Furthermore, the intensity on the individual wire decreases and, as a result, loss of power is reduced with respect to the corona discharge and line inductive reactance. Thus, to decrease loss of power of wires and to prolong the lifetime of wires, it is necessary to determine correctly the cross section of wires and kind of phase splitting. A 2D mathematical model of the AL electrostatic field has been developed that takes into account the inhomogeneity of the shape of the wire surface. The analytical solution of the initial problem has been considered, and the numerical and analytical results for a cylindrical wire surface have been compared. The fields for four cases of an AS conductor with different versions of splitting have been studied. The curves of field intensities near a conductor surface as a function of the cross section and number of wires in the AL phase have been plotted.     

复镜像法在平板导体涡流场计算中的应用

为了根据涡流检测中积分方程法(IEM)的理想裂缝模型,用矢量磁位推导出平板导体涡流场的并矢格林函数,将复镜像法用于涡流场并矢格林函数的计算,用Prony方法对矢量磁位中广义Sommerfeld积分(GSI)的被积函数进行指数逼近,使GSI转化为有限项级数之和,加速了无穷积分的计算,提高了涡流场的求解速度和计算精度。用涡流无损检测中的两组典型数据比较用复镜像法和直接数值积分法计算广义Sommerfeld积分的计算精度和求解速度,结果表明复镜像法在涡流场GSI积分计算中准确且高效。用复镜像法计算平板导体中含有平行裂缝和十字型裂缝的涡流场,其结果与有限元一边界元耦合法的计算结果对比表明求解方法正确和高效。     

海底电缆用阻水型线导体设计方法及试验研究

阻水导体的设计制造是海底电缆领域内的关键课题之一。提出一种等截面梯形型线阻水导体结构的理论设计方法,通用性强,可编程性高,适用于50~3 500 mm²阻水导体的设计和生产制造,可解决阻水型线导体设计和制造困难、尺寸不合理等问题,导体填充系数可达到0.96以上;然后,通过阻水、机械、电气性能试验,验证所述理论设计方法和工艺制造的合理性,导体结构对海缆的整体性能无不良影响,且阻水胶型线导体结构优于阻水带结构;最后,根据理论计算,所述方法设计的中压海缆型线导体外径比紧压圆形导体小3.9%~7.0%,最大可降低1.1%的制造成本。导体截面越大,型线导体结构优化越显著,验证了型线结构海缆的经济性。     

Threshold voltage modeling for dual‐metal quadruple‐gate (DMQG) MOSFETs

In this paper, a three‐dimensional (3D) model of threshold voltage is presented for dual‐metal quadruple‐gate metal‐oxide‐semiconductor field effect transistors. The 3D channel potential is obtained by solving 3D Laplace's equation using an isomorphic polynomial function. Threshold voltage is defined as the gate voltage, at which the integrated charge (Q_inv) at the ‘virtual‐cathode’ reaches to a critical charge Q_th. The potential distribution and the threshold voltage are studied with varying the device parameters like gate metal work functions, channel cross‐section, oxide thickness, and gate length ratio. Further, the drain‐induced barrier lowering has also been analyzed for different gate length ratios. The model results are compared with the numerical simulation results obtained from 3D ATLAS device simulation results. Copyright © 2015 John Wiley & Sons, Ltd.     

有限宽金属平板对工频磁场的屏蔽

为了定量评估金属平板对工频磁场的屏蔽效果,在阐述了理想导磁材料和理想导电材料的磁场屏蔽原理基础上,基于无限宽金属平板屏蔽区域磁场解析式,通过计算域映射,推导了有限宽金属平板屏蔽区域磁场解析式.通过仿真分析了对称三相传输线屏蔽系统,讨论了导线组排列位置、屏蔽材料类型对屏蔽效果的影响.结果表明,采用解析式,可对有限宽金属平板的屏蔽效果进行快速计算,其准确性和计算效率优于现有电磁场分析软件所采用的数值求解方法,可对实际屏蔽系统的设计提供参考.     

梯形Halbach永磁阵列空心直线同步电动机特性的解析计算与优化

提出了一种新型的双边不对称梯形永磁空心直线电动机。首先使用等效磁荷法建立了梯形单块磁体的三维空间磁场解析模型,再由叠加原理得到双边Halbach阵列空心电机的气隙磁密三维模型。在考虑线圈横向端部效应的基础上,推导出电机运行过程中的反电动势与电磁推力的表达式。利用解析模型分析了梯形磁体阵列气隙磁密谐波分布的规律,并对其进行优化;三维有限元仿真结果表明所提解析模型具有较高的准确度,同时采用经过优化的梯形阵列定子,可以达到提高气隙磁密正弦性从而减小推力波动的目的。     

Improving time integration scheme for FEM analysis of MTL problems

This paper presents improved algorithm for electromagnetic transient calculations on multiconductor transmission line (MTL) achieved by improvement of the time integration when forming a local system of equations for a finite element. Improvement of accuracy was obtained by using Heun's method. Previously developed local system of equations of MTL has been obtained using the generalized trapezoidal rule (ϑ -method). The use of the generalized trapezoidal rule for the time integration sometimes causes numerical oscillations or numerical diffusion of numerical solutions. Numerical solutions obtained using Heun's method and using the generalized trapezoidal rule for different values of a time integration parameter are compared with analytical solution. It has been shown that Heun's method yields the results with much higher accuracy comparing to results obtained by generalized trapezoidal rule.     

Analytical Modeling of an Eddy-current Adjustable-speed Coupling System with a Three-segment Halbach Magnet Array

This article presents a two-dimensional analytical model to predict the magnetic field distributions and torque characteristics in an axial-flux eddy-current adjustable-speed coupling system with a three-segment Halbach magnet array. The main contribution of this article is the analytical evaluation of a moving-conductor eddy-current problem based on a three-segment Halbach magnet array by considering the influence of the eddy currents on the magnetic field. Based on the layer model method, the three-dimensional eddy-current problem is linearized to a two-dimensional problem, and the field equations derived from Maxwell's equations in each layer (iron core, magnet, air gap, and conductor) are solved by using the variable separation method and Cramer's rule. The proposed analytical model is validated by the three-dimensional finite-element method in terms of both magnetic field prediction and parameter analysis. Because the analytical methods take less computational time than numerical methods, they are an effective tool for the first step of design optimization.     

Accurate evaluation of the magnetic field strength of largesubstation air-core reactor coils

A circular cylindrical conductor segment is a basic modeling element of substation air-core reactor coils. The analytical expressions for evaluating the stationary and quasi-stationary magnetic field strength of a segment are derived. In the derivation, a surface source model is developed to substitute the given volume current distribution by equivalent surface sources. The magnetic flux density of sample coils is calculated by using the derived equations. The results are compared with those obtained by the finite element method. Good agreement is observed. The derived equations are very useful for solving problems that involve the accurate calculation of the magnetic field distribution around a coil, the magnitude of forces on a coil, the current distribution in the conductors of a coil and the inductive properties of a coil     

Approximate method for calculating the impedances of multiconductors with cross sections of arbitrary shapes

This paper proposes an approximate impedance formula of a conductor with an arbitrary cross section, and also a method of approximating the conductor by an equivalent circular conductor. Thus, a multiconductor system consisting of arbitrary cross section conductors is represented by circular cross section conductors, the impedance of admittance of which are evaluated by the existing impedance and admittance formulas. The calculated results by the proposed method agree satisfactorily with measured results and numerical results by a finite-element method which is, at present, the only way of calculating such impedance, but requires a large computation time and large memory. The proposed method might be very useful in evaluating the impedance and admittance of a multiconductor system consisting of arbitrary cross section conductors.     

Numerical calculation of AC substation grounding systems buried in a vertical multilayered earth model by higher‐order basis function

To study the accuracy of numerical simulations for an AC substation grounding problem embedded in a vertical multilayered earth model, this paper proposes a novel algorithm combining the rapidly convergent one‐dimensional Galerkin's BEM with higher‐order basis functions on the basis of the quasi‐static electric field theory. General analytical formulas for the mutual impedance between any pair of short line conductors are also derived to accelerate the numerical integration. These formulas can work in not only complex space but also real space because of our application of the quasi‐static complex image method, which is different from the contribution of other earlier scientists, whose formula can work just in real space. The algorithm can be used to simulate and analyze any grounding system, including those incorporating a floating grid located anywhere in the earth model. Copyright © 2011 John Wiley & Sons, Ltd.     

Efficient modelling of curved surfaces by planar patches and wire grids for electromagnetic scattering

The scattering of conducting regular polyhedrons of resonant size is studied by means of the electrical field integral equation (EFIE) and the method of moments (MoM). Two models are generated for each polyhedron, a wire grid model and a triangular patch model. Two numerical codes associated with those modelling techniques are used to obtain the radar cross section (RCS) of the polyhedrons. The calculated results are compared with the analytical results of the scattering of a perfectly conducting sphere. Practical criteria relating geometric properties of the sphere and the polyhedrons are investigated for the modelling of curved surfaces by facets in electromagnetic simulations.     

Modelling of lossy curved surfaces in the 3‐D frequency‐domain finite‐difference methods

A conformal first‐order or Leontovic surface‐impedance boundary condition (SIBC) for the modelling of fully three‐dimensional (3‐D) lossy curved surfaces in a Cartesian grid is presented for the frequency‐domain finite‐difference (FD) methods. The impedance boundary condition is applied to auxiliary tangential electric and magnetic field components defined at the curved surface. The auxiliary components are subsequently eliminated from the formulation resulting in a modification of the local permeability value at boundary cells, allowing the curved 3‐D surface to be described in terms of Cartesian grid components. The proposed formulation can be applied to model skin‐effect loss in time‐harmonic driven problems. In addition, the impedance matrix can be used as a post‐processor for the eigenmode solver to calculate the wall loss. The validity of the proposed model is evaluated by investigating the quality factors of cylindrical and spherical cavity resonators. The results are compared with analytic solutions and numerical reference data calculated with the commercial software package CST Microwave Studio™ (MWS). The convergence rate of the results is shown to be of second‐order for smooth curved metal surfaces. The overall accuracy of the approach is comparable to that of CST MWS™. Copyright © 2006 John Wiley & Sons, Ltd.     

罗氏线圈非理想工作情况分析

为了分析罗氏线圈非理想工作情况对测量结果的影响,在假设线圈绕制完全均匀的前提条件下采用了积分算法对非理想工作情况进行分析计算,包括:被测电流导体偏离线圈中心位置、线圈周围存在干扰磁场。计算结果表明:在绕线完全均匀的条件下,上述两种非理想情况对线圈测量结果没有影响。最后分析了被测电流导体与线圈平面不垂直的非理想工作情况的影响。     

AAAC 导线在大跨越输电线路中的应用

AAAC 导线是一种性能优良的导线,它与同截面钢芯铝绞线相比载流量高1 % ,无磁滞和涡流损耗。AAAC - 400 导线的拉重比达11. 67 km ,一般可用于1 000 m左右大跨越线路上,且具有较高的抗疲劳强度。但在大跨越线路设计中,需加强防振,采用组合防振措施。     

Distribution of residual magnetic induction along a solid circular core magnetized in longitudinal constant homogeneous magnetic field

An amalysis of the data obtained experimentally and by numerical computation on the distribution of residual magnetic induction averaged in a cross section along the longitudinal axis of a solid circular core magnetized by a constant homogeneous magnetic field is given. A new calculation formula that takesinto account the dependence of the magnetic material characteristics on the value of the magnetizing field is proposed. The calculation and experimental data are compared for cores with various geometries and magnetic material characteristics. The area of applications for the formula is shown.     

螺旋线圈电磁发射器径向受力仿真与电枢设计

通过数值仿真,根据螺旋线圈电磁发射器(HCEL)驱动线圈的径向磁场分布,提出一种"D"形截面电枢并确定其最佳受力位置.计算表明,相同线度的"D"形电枢比矩形电枢加速度更大,即在炮长(弹丸加速长度)相同的情况下,"D"形电枢比矩形电枢具有更高的出口速度.以"D"形电枢为例,分析了弹丸线圈与驱动线圈上的轴向、径向受力分布....     

梯形永磁体盘式无铁心电机的设计与研究

针对永磁盘式无铁心同步电机的轴向磁场结构,在现有Halbach永磁阵列的基础上,提出一种梯形结构永磁体阵列。详细阐述该电机的结构与优点,利用有限元方法研究了不同梯形结构永磁体阵列对气隙磁密的影响,根据气隙磁场中的谐波含量及空载反电势畸变率选取最优转子结构。该结构在保证与传统结构永磁体材料用量相当的前提下,有效提高气隙磁密的基波,降低谐波含量。由于轴向磁场结构的特殊性,给出该电机的设计规则,如磁极尺寸和导体占空比的确定。计算了电机在负载工况下不同定子电流对交直轴电感的影响,为该类电机的设计提供了一定的参考价值。