Electric field calculation in composite dielectrics by a curved triangular surface charge method

This paper describes a triangular surface charge method (TSCM) called (3,1)‐TSCM, which uses curved surface elements for calculating electric fields in composite dielectrics. The boundary element utilizes a cubic shape function with nine degrees of freedom and a linear function for representing the charge density on its surface. Conventional SCMs, including the (3,1)‐TSCM, show a very large relative error in the composite dielectrics where the permittivity is much higher in one medium than in the other. A modified method called the β method can suppress such relative errors, which expresses electric fields by surface charges without subtraction causing large relative errors. We have applied the β method to the (3,1)‐TSCM and calculated electric fields for a spherical dielectric under a uniform field. The calculated results show that the (3,1)‐TSCM improves the accuracy of the electric field by more than one order compared with the method using flat surface elements with constant charge density on each element. Furthermore, the β method completely suppresses the divergence of relative errors even when the ratio of the permittivity of two media reaches 10¹⁰. © 2001 Scripta Technica, Electr Eng Jpn, 136(1): 1–8, 2001     

An effective modelling method to analyze the electric field aroundtransmission lines and substations using a generalized finite linecharge

For the rather complicated and time-consuming three-dimensional electric field calculation in the vicinity of transmission lines and substations, this paper proposes an effective numerical calculation method based on the charge simulation method (CSM). In order to better represent nonuniform charge distribution on an electrode, it is subdivided into small segments with linear charge density. Each segment with linear charge density can be easily represented by a generalized finite line type of charge whose expressions for potential and electric field were analytically derived and which was named “finite slant line charge” in this paper. As for the arrangement of small segments of a subdivided electrode, it has been found that the unequally spaced arrangement method is superior to the equally spaced one. In order to arrange segments fast and effectively, effective formulas were derived from multiple regression analysis of many simulations. The proposed method is applied to the electric field calculation around the transmission lines with significant change in direction and substation busbars     

Optimization on the internal insulation system of gas‐insulated bushing for 1100‐kV GIS based on multiobjective optimization method

In this paper, we first study the voltage and electric field distribution characteristics under the basic lightning impulse level (BIL) of 2400 kV by finite element method (FEM) calculation which are affected by the internal shielding structure of the gas‐insulated bushing for the 1100‐kV gas‐insulated substation (GIS). On this basis, four parameters of the shielding structure are determined to be the decision variables in the optimization process. Four electric field objective functions and four potential objective functions are also proposed. Using a multiobjective optimization method, we then construct an evaluation function with the eight objective functions mentioned above, which are used to evaluate the electric field and potential distribution synthetically. Furthermore, a combination of FEM and the evolution strategy is used to construct the stochastic optimization objective function with the multiobjective evaluation function. The electric field and potential distribution of the gas‐insulated bushing are greatly improved after optimization, and the electric field strength at key spots is effectively reduced. The insulation system of gas‐insulated bushing for 1100‐kV GIS designed by this method has passed type tests and worked well nearly 3 years. So, this optimization provides a constructive method and useful basis for the design of gas‐insulated bushings for 1100‐kV GIS and other electrical equipment. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Electric field optimization of the power cable joint by using evolutionary calculation method

This paper examines electric field optimizations at the joint of power cables by using evolution strategy [(1+1)‐ES, (µ+λ)‐ES] and genetic algorithm which are so‐ called evolutionary calculation methods. The object of the paper is to minimize the electric field strength on the inner curved electrode under the constraint that the electric field strength along the interface between the two different insulators should be below the permissible value. The surface charge method that provides accurate solutions on the boundaries for the multilayer substances with a relatively small number of elements is employed for the calculation of the electric field distribution. Three evolutionary calculation methods are employed for the optimization method. Because these methods employ mutation and rearrangement (cross‐over) processes, the shape design can be performed widely and locally. As a result, each method can reduce the electric field strength on the inner curved electrode while the electric field strength along the interface was kept below the permissible value. The search results of each optimization method were compared and (µ+λ)‐ES was found to have the best performance of the three methods. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 150(4): 44–53, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10287     

Numerical modelling of equilibrium charge separation in poled devices

We describe an efficient numerical procedure for the equilibrium solution of the internal electric field distribution resulting from poling of photo‐refractive materials. This technique has been developed to model the equilibrium state in poled bulk devices requiring bulk charge neutrality to facilitate the modelling of blocking boundaries for a high externally applied voltage (bias) in the kV range for a small number of points. This technique is an improvement on existing conventional numerical techniques employed for modelling semiconductor devices that are intended for low bias. This method can also accommodate the modelling of planar insulators and organic optical materials. We develop an algorithm incorporating the existing Newton–Raphson method for solving Kukhtarev's equations that enforces conservation of charge within the modelled system. We apply this technique to model one‐dimensional charge separation in ultraviolet (UV) excited poling of glass and, report numerical equilibrium electric field distribution for a 2 kV bias. The convergence behaviour of the algorithm is investigated and compared against the Newton–Raphson method. Copyright © 2001 John Wiley & Sons, Ltd.     

用虚拟材料参数法计算含有电位悬浮导体的电场分布

讨论了利用虚拟电导率和虚拟介电常数求解含有电位悬浮导体的电准静态场和静电场的电场分布方法 ,通过分析实例 ,找到了这两种方法的有效应用范围 ,该方法突出的优点在于对于悬浮导体的数目没有限制 ,程序编制简单 ,稍加修改即可用于三维场的计算。应用此方法对算例进行计算得到的计算结果与导电纸实测结果相吻合 ,从而验证了该方法的正确性。该方法便于工程技术人员实际操作 ,程序的可复用性较强 ,为以后解决类似工程问题提供了依据。     

Breakdown characteristics of gas‐insulated switchgear for nonstandard lightning impulse waveforms under nonuniform electric field

To improve the insulation specification of gas‐insulated switchgear (GIS), it is necessary to recognize the insulation characteristics of SF₆ gas during actual surges (called nonstandard lightning impulse waveforms) occurring at field substations. The authors observed the insulation characteristics of SF₆ gas gap under various types of nonstandard lightning impulse waveforms and compared them quantitatively with those obtained with standard lightning impulse waveforms. The experimental results were used to derive an evaluation method for real surges, which was applied to typical surges for various UHV and 500‐kV systems. In the preceding study, therefore, only the case of a quasi‐uniform electric field (with a typical range of field utilization factors in the bus of a GIS) was investigated. In the present investigation, the insulation characteristics of an SF₆ gas gap for a nonuniform electric field were observed experimentally and an evaluation method for converting nonstandard lightning impulse waveforms equivalently to the standard lightning impulse waveform was investigated. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(1): 11–18, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21144     

线性规划技术在电场综合中的应用

本文描述了一种电场综合的新方法。本方法在电荷模拟法计算电场的基础上,应用线性规划技术确定高压装置屏蔽电极的电位,以达到所要求的电场分布。方法简单,并有现成程序可用。     

电力金具数值模拟分析中单元划分的影响

介绍通过有限元分析方法模拟机械部件在运行状态下的应力数值,用此方法模拟金具工作状态时应力分布,有助于金具失效分析工作.列举了两个金具的失效实例,讨论了平面单元和实体单元运用于金具有限元分析的选择标准.     

Analysis of electric field induced by ELF magnetic field utilizing fast‐multipole surface‐charge simulation method for voxel data

This paper presents a fast‐multipole surface‐charge‐simulation method for calculating three‐dimensional Laplacian fields in voxel models. This method treats a surface of a voxel that has different inside and outside conductivities as a surface element of the indirect BEM (boundary element method). The main features of the proposed method are as follows. (1) An O(D²) performance in the memory capacity and operation cost is provided by applying the diagonal form fast multipole method (FMM), when the number of voxels is about D³. (2) The boundary matching is imposed by the continuity of the total flux passing through each element, which guarantees the solution globally satisfying Gauss's law; therefore the solution is globally stabilized. This method is successfully applied to calculate the electric field induced by an applied homogeneous ELF (extremely low frequency) magnetic field in a human head model that has 1 mm ×1 mm 1 mm voxel size. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 165(4): 1–10, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20529     

外加电压及绝缘温差对XLPE直流电缆电场分布的影响

为了明确交联聚乙烯绝缘直流电缆电场随外加电压和绝缘温差的分布规律,基于有限元仿真分析方法,对±500 kV交联聚乙烯绝缘直流海缆进行了不同外加电压和绝缘温差下的电场分布研究,并与拉普拉斯场强计算方法进行对比.结果表明,通过拉普拉斯场强计算方法得到的直流电缆绝缘场强呈稳定分布,而有限元仿真情况下可见随着绝缘温差升高直流电...     

Optical measurement of electric field vector distribution in a liquid insulator using simultaneous three‐direction optical measurement system

We have already reported on reconstructions of the symmetrical and nonsymmetrical electric field vector distribution using the Kerr electrooptic effect and our unique reconstruction method, a modified computed tomography technique. This reconstruction technique gives an electric field map, that is, the strength and the direction of the electric field vector, on any plane. For the reconstruction of one field vector distribution, it was necessary to measure the light intensity twice while changing the optical axis of optical wedges. Moreover, the intensity measurement must be carried out at many points around the electrode system. Therefore, considerable time was required to measure the electric field distribution. We therefore developed a simultaneous three‐direction optical measurement system with three optical systems combined with the two‐beam method. Using the new measurement system, we measured the electric field distribution on planes in a sphere‐to‐sphere electrode system. It took about 0.1 second to measure the light intensity data for the reconstruction. © 2002 Scripta Technica, Electr Eng Jpn, 139(1): 9–15, 2002; DOI 10.1002/eej.1141     

The surface charging effects in three‐dimensional simulation of the profiles of plasma‐etched nanostructures

Particles and fields represent two major modeling paradigms in pure and applied science at all. Particles typically exist in a spatial domain and they may interact with other particles or with field quantities defined on that domain. A field, on the other hand, defines a set of values on a region of space. In this paper, a methodology and some of the results for three‐dimensional (3D) simulations that includes both field and particle abstractions are presented. In our studies, charging damage to a semiconductor structure during plasma etching is simulated by using 3D level set profile evolution simulator. The surface potential profiles and electric field for the entire feature were generated by solving the Laplace equation using finite elements method. Calculations were performed in the case of simplified model of Ar⁺/CF₄ non‐equilibrium plasma etching of SiO₂. Copyright © 2010 John Wiley & Sons, Ltd.     

Generation mechanism of electrochemical migration in printed wiring board insulation

In order to study the generation mechanism of electrochemical migration in a printed wiring board, paper/phenol‐resin composites with and without an adhesive layer, epoxy resin, and a laminate of epoxy resin and a paper/phenol‐resin composite were aged at 85 °C and 85% relative humidity (RH) with and without application of a DC voltage, and the space charge distributions in the samples were observed by the pulsed electroacoustic method. In the case of the composite with the adhesive layer, a large amount of negative charge is induced at the interface between the composite and the adhesive layer on the anode. It was found that such formation of space charge enhances the electric field intensity at the anode. The reason for this is because the conductivity is much lower in the adhesive layer than in the composite. Electrochemical migration does not occur when the same electric field is applied to the composite without the adhesive layer, whereas it does occur if the adhesive layer was replaced by epoxy resin with a similar conductivity to the adhesive layer. These results clearly indicate that electrochemical migration generates because the electric field at the anode surface is enhanced due to the low conductivity of the adhesive layer. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Evaluation method of computational error for electric field analysis by a surface charge method

In this paper, an evaluation method of computational error for the electric field analysis by a surface charge method is proposed. In the method, an approximate equation of the smoothness of the electric field distribution is used to evaluate the computational error. In two‐dimensional and axisymmetric problems, the approximate equation of the smoothness is expressed by the second derivative form of the surface charge density with respect to the distance along the surface. Furthermore, the smoothness is expanded to three‐dimensional problems and a general form of the equation for the smoothness is obtained. The applicability of the proposed method is verified by computation results of a two‐sphere model and a hyperboloid model. © 1998 Scripta Technica, Electr Eng Jpn, 126(1): 7–14, 1999     

绞线花纹导线表面电场强度计算与分析

为了准确计算输电绞线花纹多股绞线表面电场强度的大小,建立了二维电场模型,采用有限元法与镜像法相结合的方法计算带有花纹的输电线表面场强,并与光滑导线模型的场强进行比较,还分析了绞线花纹对导线表面最大场强的影响。考虑输电线表面花纹后计算出的表面最大场强与将导线视为光滑圆柱体的计算结果相差>20%。在导线选型时,应充分考虑绞线花纹对导线表面最大场强的影响。     

The modified multilevel compressed block decomposition algorithms for analyzing the scattering of objects in half space

The convergence rate of iterative methods can vary in an unpredictable way. It is related to the matrix condition number, which is notoriously bad for the electric field integral equation in the large‐scale electromagnetic problems. Therefore, an efficient direct solution—a multilevel compressed block decomposition (MLCBD) algorithm based on the adaptive cross‐approximation algorithm—is applied to overcome this problem; it is very efficient for the monostatic problems. Simulation results of the objects up and below ground in half space demonstrate that the proposed MLCBD method is efficient for analyzing electromagnetic problems. Copyright © 2013 John Wiley & Sons, Ltd.     

直流电弧炉电弧等离子体射流的数值模拟

数值模拟是研究直流电弧炉中电弧等离子体射流特性的有效方法,它可为理解和优化电弧炉冶炼过程提供参考依据。本文对直流电弧炉冶炼过程建立了电弧等离子体的二维稳态轴对称磁流体力学模型,采用大型商业软件PHOENICS对电弧流场和温度场进行了计算,仿真结果与文献报导的实际测量结果吻合良好。     

有限元电场计算时模型表面网格精细控制方法

大型复杂模型有限元电场求解过程中,所关注设备表面网格的精细化控制往往难度较大。为此,对有限元电场数值计算时网格划分的相关基本原则进行讨论,考虑实体模型的基本几何结构,提出了基于多层外包实体实现设备表面网格精细控制的思想,在此基础上研究了有限元建模方法。以简单三维模型为例,分别介绍了外包实体生成算法、区域划分原则及相关操作流程。以标准模型为例介绍了所提方法的具体应用过程,同时对外包实体的参数设定进行了讨论。将该方法应用于±1100 kV特高压换流站直流阀厅设备表面电场计算中,计算所得模型表面电场过渡平滑,电场强度最大值为13.8 kV/cm。该方法有效实现了模型表面网格的精细控制,对大型复杂有限元模型的高效、精确建模具有一定的指导意义。     

Negative First Return‐Stroke Current Peaks and Impulse Charge Transfer

For the effective and efficient insulation design of a power line, the return‐stroke current waveform parameters are indispensable. Charge transfer is one of the important parameters when damage to equipment on a power line due to the energy of lightning is discussed. The amount of charge transfer associated with a lightning flash or individual strokes can be estimated by using the electric field change obtained with a slow antenna. The authors observed the electric field waveforms in south Kyushu for the purpose of efficient acquisition of return‐stroke current parameters. In this paper, the authors discuss the relation between the negative first return‐stroke current peaks and the impulse charge transfer based on the observed electric field waveforms.