基于混合Lanczos-Tikhonov算法的绝缘子表面电荷反演计算  

Inversion Algorithm for Surface Charge on Insulator Based on Hybrid Lanczos-Tikhonov Algorithm

作　　者：毛诗壹 潘成 罗毅[1] 邱宇杰 唐炬[1] Mao Shiyi;Pan Cheng;Luo Yi;Qiu Yujie;Tang Ju(School of Electrical Engineering and Automation Wuhan University,Wuhan 430072 China)

机构地区：[1]武汉大学电气与自动化学院,武汉430072

出　　处：《电工技术学报》2023年第7期1921-1934,共14页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金联合基金资助项目(U2066215)。

摘　　要：表面电荷反演计算是表面电荷密度分布测量的重要环节。该文针对盆式或锥形绝缘子这类平移变化系统,引入迭代正则化方法,提出了基于Lanczos双对角化与Tikhonov正则化算法混合方法的表面电荷反演算法。通过Lanczos双对角化将电位-电荷之间的矩阵运算投影至维数更小的子空间后,应用Tikhonov正则化求解子空间投影最小二乘问题,大大减小了矩阵的计算量;同时引入自适应加权广义交叉验证(A-WGCV)方法选择正则化参数;结合仿真算例讨论了该算法的实现过程以及计算精度,并与视在电荷法及维纳滤波法进行了对比;最后,通过粉尘图法验证了该算法的准确性和可靠性,并结合粉尘图像和算法反演两种方法获取了针电极下不同电压等级下的电荷分布。With the improvement of the level of DC transmission and the expansion of the application range,the surface charge accumulation of insulators in DC transmission system has been widely concerned by scholars.In order to suppress the charge accumulation on insulator surface under DC electric field and improve the insulation performance of DC GIS/GIL,accurate measurement of the charge density distribution is a very important step.The inverse calculation of surface charge on insulators is an important step for surface charge density distribution measurement,too.In this paper,based on hybrid Lanczos-Tikhonov method,an inversion algorithm is proposed for“shift-invariant system”.Firstly,the iterative regularization method is introduced,and in each iteration,after projecting the potential-charge transfer matrix to a low-dimensional subspace through Lanczos bidiagonalization,Tikhonov regularization is applied to solve the least squares problem of projection in subspace.At the same time,an adaptive weighted generalized cross validation(A-WGCV)method is introduced to adaptively select the optimal regularization parameter in each iteration.After the iterative calculation is finished according to the iterative stopping condition,the solution of the last iteration is transformed to obtain the complete result of the surface charge density distribution of the insulator.In order to analyze the calculation accuracy of hybrid Lanczos-Tikhonov algorithm,a simulation example is used to simulate the complete calculation process in real measurement.Firstly,the charge density was preset by COMSOL,and the corresponding surface potential distribution was calculated.After the data with different degrees of Gaussian noise are superimposed on the potential distribution data,Lanczos-Tikhonov hybrid algorithm,Wiener filtering method and apparent charge method are used to carry out inversion calculation for this example respectively.The calculation time and inversion image of the three methods are compared in this paper.In addition,the SNR a

关 键 词：高压直流电气设备 表面电荷密度分布 表面电荷反演 自适应加权广义交叉验证 (A-WGCV) Lanczos-Tikhonov混合方法 

分 类 号：TM85[电气工程—高电压与绝缘技术]