Estimation of charge distribution on a bulky solid dielectric using regularization technique

We have been studying a multi‐point charge measurement method using an electrostatic probe. In this technique, charge densities x must be estimated from the probe outputs b by an inverse calculation based on an equation A x = b . The matrix A is obtained by applying a numerical field calculation technique. When the matrix A is in ill‐condition, the solution often makes no sense, including extremely large errors. Therefore, we apply the regularized least squares method (RLS) with a penalty term to perform the inverse calculation stably for the ill‐conditioned matrix. The penalty term imposes some constraints on the solutions. In this paper, first, we have analyzed the accuracy of the charge distribution estimated by the inverse calculation. Although the perturbation bound of the solution errors has already been proposed for the least squares method, it has not yet been given for the RLS. We have derived the equations that express the perturbation bound of the solution errors in applying the RLS to evaluate the estimation accuracy. Second, we have applied the above equations to an experimental result for a cylindrical dielectric solid, and estimated the charge distribution represented by 10,140 unknowns. We have utilized an iteration technique and the symmetric configuration of the measured arrangement so as to reduce the amount of operations and memory capacity required for the inverse calculation. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(2): 1–13, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20412     

Analytical method for evaluating surface charge distribution on adielectric from capacitive probe measurement-application to a cone-typespacer in ±500 kV DC-GIS

The measurement of surface charging on a spacer in a ±500-kV HVDC gas-insulated switchgear (GIS) is performed by a capacitive probe set inside the gas tank. The various factors that cause measurement errors are examined using a simple model. An analytical method to correct the measurement errors and transform the probe output into the charge distribution on the surface of the spacer is developed. The method is an extension of a numerical method for 3-D surface charge calculation. It is shown that the charge distributions from the probe measurement agree fairly well with dust figures     

Influences of probe geometry and experimental errors on spatial resolution of surface charge measurement with electrostatic probe

When an electrostatic probe is used for surface charge measurement on an insulating plate with constant thickness or a long insulating pipe, the configuration of the measuring system is regarded as shift-invariant and the relation between the surface charge density and the probe output can be treated in the spatial frequency domain through Fourier analysis. In the inverse calculation from the probe output to the charge distribution, a Wiener-filter technique is effectively used to suppress the excessive amplification of the noise. Influences of the probe geometry and experimental errors on the spatial resolution of the total measuring system, including the restoration process with the Wiener filter, are quantitatively discussed through the analysis of transfer characteristics in the spatial frequency domain.     

基于彩色CCD测量火焰温度场的算法误差分析

电荷耦合器件(charge coupled device,CCD)成像技术在火焰温度场测量中有广泛的应用,讨论基于CCD测量火焰温度场的反演计算误差。彩色CCD的三基色波段响应输出往往被简化为3个单色波长输出,并通过黑体实验或具体的保障3个基色波长假设在非灰性介质测量中的准确性。因此,以具有特定发射率表现的火焰诊断温度场测量为例,通过数值模拟计算,定量分析计算温度和发射率参数的相对误差分布规律。结果表明,发射率参数的计算相对误差要远远大于温度的相对误差。结论有利于采用CCD成像技术进行火焰温度场测量的计算准确性的改善。     

热脉冲法数据处理的反问题求解研究

应用热脉冲法测量聚合物薄膜电介质内空间电荷分布的数据分析过程涉及第一类Fredholm积分方程,过往先求解电场分布后微分的传统做法,会使反问题求解的不适定性带来的误差进一步放大。该文提出一种用于热脉冲法数据分析中反问题求解的直接计算空间电荷分布方法。结合一维热传导方程,推导得到了能够直接求解获取空间电荷分布的热响应电流方程。以Tikhonov正则化与尺度变换法2种数值求解算法为例,研究了不同信噪比对热脉冲法测量方法中直接计算电荷分布结果的影响,并讨论了2种数值算法直接进行空间电荷分布计算的优缺点。仿真结果表明,应用2种数值方法对含有一定噪声的数据处理时,直接计算空间电荷分布的方式相较于传统对电场分布微分的方式而言,能够很好地克服第一类Fredholm积分方程的不适定性,使解分布曲线中的振荡减少,且对仿真电流信号的噪声敏感程度更低,能更好地契合预设分布曲线,提高了空间电荷计算结果的准确性。     

Semi‐analytical non‐charge‐sheet and non‐depletion MOS model,for inversion charge calculation

A new computationally implemented semi‐analytic mathematical model is presented to obtain a more accurate estimation of the inversion charge in a MOS structure than standard models. The values of the error of the inversion charge obtained are compared with the assumed ‘exact’ numerical calculated values. These errors are appreciably smaller than the estimation coming from the classical charge‐sheet and depletion approximations. Also the calculation time to obtain the inversion charge is shown to be significantly lower than the numerical one. Because of its accuracy and its relatively low computational speed, the proposed model is a good alternative methodology for the calculation of the inversion charge of MOSFET transistors as a function of their physical features and gate bias voltage. In this sense it should be very useful to be implemented by computer‐aided design integrated circuit simulation software. Copyright © 2013 John Wiley & Sons, Ltd.     

基于数字图像处理技术的绝缘子表面电荷测量标度问题的研究

如何实现对绝缘子表面电荷分布进行准确的测量,是高压绝缘领域一个重要的课题。针对这一问题,采用了一种基于数字图像处理的标度方法;在采用静电容探头法测量厚度一定的绝缘子表面电荷时可近似把整个测量系统按平移不平系统进行处理;通过作二维傅里叶变换,把传统的表面电荷测量标度过程转化到频域中完成。同时,为了提高标度的精度,结合数字图像处理中维纳滤波复原技术抑制测量中噪声项的影响。文中给出的算例表明,基于频域的标度方法可以大大地缩短标度计算耗时,并且在一定程度上改善了标度计算的精度。     

A Rapid Semi-Analytic Method for Solving Laplace's Equation

A relatively new semi-analytic method for solving Laplace's equation has been studied in detail and compared with various long-established techniques, which are also briefly reviewed. The method involves dividing the boundary of a region into N segments, each of which has an unknown surface charge. The surface charge on each segment is assumed to be constant or to be represented by a low-degree polynomial. In the latter case, charge and even derivative continuity at the segment boundaries can be imposed. The potential produced by each segment is expressed analytically and satisfaction of the boundary conditions determines the unknown charges. The latter calculation requires the solution of N linear simultaneous equations. The resulting charge pattern enables one to evaluate the potential and/or electric field at any point with no further difference approximations. This procedure compares favorably both in computation speed and accuracy with other numerical and semi-analytic techniques, viz., net, Monte Carlo, and collocation methods.     

Principle of surface charge measurement for thick insulatingspecimens

We discuss the method for measuring surface charge density accumulated on the surface of a solid dielectric (insulating specimen) such as a supporting spacer in gas and vacuum insulated equipment. For such thick specimens, the probe response does not correspond to the charge density directly below the probe, so the measurement necessitates multipoint data together with the aid of numerical field calculations. The probe gives either induced charge or floating potential in response to the surface charge. We compare various previously proposed techniques and give a reasonable procedure for analyzing the data     

High resolution measurements of surface charge densities on insulator surfaces

The uses and limitations of the electrostatic probe for the measurement of charge densities on insulating surfaces are discussed. A development of the technique is described in which two important limitations have together been overcome: (i) The effects on the probe signal of charges on all points of the surface have been taken into account by means of a matrix inversion procedure; (ii) A robotic control system has been developed which enables the probe to follow and scan a wide range of axi-symmetric insulator profiles. The degree of resolution achieved enables the probe system to display and measure charge densities in individual streamer channels of a corona discharge on a polytetrafluoroethylene (PTFE) surface. An example is given and comparison made with a dust figure of the same event.     

几种概率电压稳定分析方法计算误差的对比分析

对电力系统进行电压稳定研究时,为了考虑负荷的随机变化和大规模风电并网引入的发电机出力变化,多种概率电压稳定分析方法先后被提出。分析比较了概率直接法、两点估计法和随机响应面法三种概率电压稳定分析方法的计算误差和计算效率。首先对各种计算方法的原理和步骤进行研究,并找出了可能影响计算误差的因素:负荷随机变量的标准差、风电场风速相关性和负荷随机变量的分布形式。然后在39节点算例系统上进行仿真计算。以蒙特卡洛方法的结果作为参考,比较了各种方法的计算误差和计算效率。分析了负荷随机变量标准差、风电场风速相关性和负荷随机变量分布形式不同,对各种方法计算误差的影响。计算结果表明,随机响应面法计算误差最小,而概率直接法用时最少。     

基于蒙特卡罗法的数字化电能表计量误差评估*

为了准确地评估数字化电能表的计量误差,对影响量误差和综合误差间的关系进行研究。由于数字化电能表计量模型的复杂性,无法直接给出综合误差的解析结果,为此,采用蒙特卡罗法,通过仿真计算和统计特性分析,得到了数字化电能表综合误差及影响量误差的分布特征,并验证了它们之间的函数关系。分析结论可为数字化电能表影响量误差限值的确定及等级划分提供参考。     

Measurement of surface charge on opposite sides of a planar insulator using an electrostatic probe

A digital image processing technique using the Fourier transformation in the spatial domain and the Wiener filter has been developed. This method is applied to the measurement of the accumulated charge on the opposite sides of a planar insulator using an electrostatic probe. In the spatial frequency domain, the relational equations between the probe outputs and charge distribution are given by the first order simultaneous equations of two unknowns. In the course of the estimation of the charge distribution from the probe outputs, the Wiener filter is used to reduce the influence of the experimental noise. The spatial resolution of this method is also quantitatively discussed from an analysis in the spatial frequency domain. Using this technique, the distribution of the surface charge density on both surfaces of an insulating plate is measured immediately after the occurrence of a surface discharge. When the probe scans both sides of the plate, the charge distribution is estimated with a spatial resolution of 1.6 mm. In the case that the probe scans from only one side of the plate, the two-layered charge distribution is estimated with a limited resolution.     

Effect of the variation of the charge distribution along multi-overhead transmission lines’ conductors on the calculation method of ground surface electric field

This paper presents a new methodology to calculate the ground surface electric field, produced by overhead transmission lines (OHTLs), taking into account the effect of the variation of the charge distributions along the conductors of multi-overhead transmission lines. In this paper, the effects of the conductors sag, the presence of the tower, replacing the sub-conductors of each phase with an equivalent conductor, the presence of the ground wires, and the presence of another overhead transmission line (OHTL) circuit on the electric charge distribution along the OHTL conductors and hence on the calculation of the ground surface electric fields are extensively studied. The suggested technique is verified by comparing its results with a measurement by the other. The suggested technique is based on both the Charge Simulation Method (CSM) and the Image Method (IM).     

基于最优未来时间步求解非稳态导热反问题

应用顺序函数法(sequential function specificationmethod,SFSM)研究利用未来时刻的温度测量信息反演非稳态导热系统表面热流问题。分析表面热流反演过程中未来时间步的优化问题,依据残差原理建立最优未来时间步的估算方法,并讨论了温度测量误差和测点位置对未来时间步的优化结果及表面热流反演结果的影响。数值试验结果表明,采用该文方法能够在综合考虑温度测量误差水平和温度测点位置等相关因素的基础上,恰当地选择未来时间步数,从而有效地改善表面热流的反演效果。     

Measurement of streamer charge distribution on an insulator in SF6 Gas

The charge density produced by streamers on an insulator surface in SF₆ has been investigated by using a probe method with a high-speed temporal resolution. Concentric circular probes, which also act as a plane electrode, are used in this probe method. Probe signals are observed oscilloscopically and converted into the charge densities through a numerical calculation. This method reveals the charge distribution before a disturbance caused by the “back discharge.” The charge density thus obtained ranges from several nC/cm² up to about 60 nC/cm². The density depends on the pressure, voltage height and the position of the streamer. The electric field on the insulator is analyzed numerically taking into account the surface charge. The internal electric field of the streamer is found to be 40 ～ 50 kV/cm · atm when the streamer ceases its propagation. However, it partly exceeds the critical one (89 kV/cm · atm) during the propagation.     

基于瞬态热传导反问题反演材料随温度变化的导热系数

基于瞬态热传导反问题,给出反演材料随温度变化的导热系数的一种新方法。在正问题中,采用有限元方法获得测点的温度值。在反问题中,将反演参数作为优化变量,将测点温度计算值与测量值之间的残差作为优化目标函数,通过极小化目标函数进行数值求解。将复变量求导法引入瞬态热传导反问题,计算灵敏度矩阵的各系数。通过几个算例说明了算法的有效性与精度,并研究了测量误差对反演结果的影响。结果表明,给出的反问题求解方法可同时反演多个参数,可以反演具有函数形式的导热系数,亦可不必事先知道导热系数随温度变化的函数形式、反演指定温度处的导热系数。当测量数据准确时,可得到高精度的反演结果;当测量数据存在一定误差时,仍然可以得到较满意的反演结果,说明该文方法具有较好的鲁棒性。     

Pockels效应表面电荷测量中电荷反演算法的研究

Poekels效应表面电荷测量技术以其特有的技术优势逐步用于表面放电和等离子体的研究,然而如何准确获取表面电荷分布仍然是一个重要的研究课题.对Pockels效应表面电荷测量技术中的表面电荷反演算法进行研究,采用二维傅里叶变换将测量信号和表面电荷的复杂关系转换到频域中进行计算,并采用维纳滤波算法进行信号处理.计算结果和传统算法的计算结果进行了对比,结果表明,改进算法在数值计算过程中考虑材料厚度、介电特性及不同位置电荷影响等因素,计算方法更为合理.该方法可用于不同材料表面电荷的测量计算.另外,算法中维纳滤波器是计算算法中关键的组成部分,对降低系统噪声,提高数值计算的稳定性能够起到很重要的作用.     

光学厚度对大型炉膛三维温度场重建的影响分析

由于工业炉膛的大尺寸以及炉内介质的消光作用，从火焰图像中重建炉膛内三维温度场时，光学厚度是一个重要的影响因素。文中通过建立的辐射成像模型，根据CCD摄像机得到的火焰温度图像，用Tikhonov正则化方法重建炉膛三维温度分布。针对一台10m′10m′20m的大型炉膛，给出了不同的光学厚度下三维温度场的重建误差，并考虑测量误差、介质辐射参数分布、壁面辐射对炉内温度场重建的影响。结果表明：当光学厚度在1~15范围之内，炉内三维温度场的重建结果较好。     

Numerical modeling of inhaled charged aerosol deposition in human airways

A new numerical modeling of inhaled charge aerosol has been developed based on a modified Weibel's model. Both the velocity profiles (slug and parabolic flows) and the particle distributions (uniform and parabolic distributions) have been considered. Inhaled particles are modeled as a dilute dispersed phase flow in which the particle motion is controlled by fluid force and external forces acting on particles. This numerical study extends the previous numerical studies by considering both space- and image-charge forces. Because of the complex computation of interacting forces due to space-charge effect, the particle-mesh (PM) method is selected to calculate these forces. In the PM technique, the charges of all particles are assigned to the space-charge field mesh, for calculating charge density. The Poisson's equation of the electrostatic potential is then solved, and the electrostatic force acting on individual particle is interpolated. It is assumed that there is no effect of humidity on charged particles. The results show that many significant factors also affect the deposition, such as the volume of particle cloud, the velocity profile and the particle distribution. This study allows a better understanding of electrostatic mechanism of aerosol transport and deposition in human airways.