Accuracy Analysis of the Method for Locating Internal Discharge Points of Insulating Materials in Laboratory Partial Discharge Experiment Based on Electric Field Inversion
Zhao Li1, Cheng Yangchun1, Yang Ziqi2, Cao Ronghao1, Xu Hanwei1, Zhang Jiaxuan1
1. Beijing Key Laboratory of High Voltage & EMC North China Electric Power University Beijing 102206 China; 2. State Grid Shanghai Pudong Electric Power Supply Company Shanghai 200120 China
Abstract：Solid insulating materials (such as oil impregnated paperboard, cross-linked polyethylene, silicone rubber) are prone to produce partial discharge (PD) under strong electric field for a long time, forming electrical trees and eventually causing electrical breakdown. The study of the growth pattern of electrical tree is crucial for improving the PD resistance of materials, quantifying the severity of defects and predicting the insulation life. However, the existing PD monitoring techniques can only qualitatively determine the presence of defects, but cannot measure the size of electrical tree or predict the service lifetime, resulting in frequent insulation failures; laboratory studies are also limited by the lack of methods to locate the discharge points. To solve this problem, the authors previously proposed a method based on the boundary electric field inversion of the discharge point location, using a one-dimensional electrode array to locate the carbonization trace of paperboard, with an accuracy of 0.35 mm, but the positioning dimension is limited (two-dimensional) and the vertical error is as high as 1 mm. This study proposes a two-dimensional planar boundary electric field measurement system on the basis of the existing technique based on the boundary electric field inversion of the field source charge, and investigates the accuracy of this method for locating the charge points. Firstly, a simplified electrostatic field calculation model was constructed for the multi-layer dielectric scene in partial discharge experiment, and the forward calculation of electrostatic field was realized. Secondly, a spatial searching problem was constructed to invert the position of the partial discharge legacy charge using the matched-point electric field ratio measurements and the forward computational model. Thirdly, the characteristics of the objective function of the optimization problem were analyzed, as well as the accuracy and the ability of the particle swarm algorithm withstand random noise. Besides, the electric field measurement system of matching points distributed on the two-dimensional plane was constructed, and the discharge point location method was established combined with particle swarm optimization algorithm. Finally, the accuracy of this method for field source charge location was determined through high voltage corona discharge experiment and grating ruler. In summary, the following conclusions are drawn: (1) The objective function of the optimization problem constructed by using the ratio of the voltage signals of the measuring electrodes on the two-dimensional plane as the characteristic quantity of the matching point has only a single extreme value within the search range, and there is no obvious local optimal solution; the particle swarm search algorithm can achieve the accurate localization of the field source charge, and the algorithm itself has an error of approximately 1 nm. (2) With the increase of white noise in the measuring signals, the overall error of the field source charge localization is linearly rising. When the noise is less than 3%, the positioning error in each direction is less than 0.05 mm; even if the noise reaches 10%, the overall positioning error average is only 0.2 mm. (3) Through the laboratory discharge experiments and the use of a scale to measure the moving distance of the discharge source, when the tip of the high-voltage electrode is 2 mm away from the surface of the insulating material, and the discharge amount of 1 500~1 800 pC, the average positioning error of the field source charge positioning method is about 0.168 mm in the xOy plane, less than 0.5 mm in z-axis direction is, and about 0.19 mm in three-dimensional space.
赵丽, 程养春, 杨紫淇, 曹荣浩, 许翰伟, 张嘉轩. 基于电场反演的实验室局部放电试验中绝缘材料内部放电点定位方法准确度分析[J]. 电工技术学报, 2026, 41(11): 3855-3867.
Zhao Li, Cheng Yangchun, Yang Ziqi, Cao Ronghao, Xu Hanwei, Zhang Jiaxuan. Accuracy Analysis of the Method for Locating Internal Discharge Points of Insulating Materials in Laboratory Partial Discharge Experiment Based on Electric Field Inversion. Transactions of China Electrotechnical Society, 2026, 41(11): 3855-3867.
[1] 张雯嘉, 王伟, 袁浩, 等. 接枝聚丙烯电缆绝缘材料的电树枝特性及机理[J]. 电工技术学报, 2024, 39(1): 88-98. Zhang Wenjia, Wang Wei, Yuan Hao, et al.Electrical tree characteristics and mechanism of grafted polypropylene cable insulation[J]. Transactions of China Electrotechnical Society, 2024, 39(1): 88-98. [2] 边浩然, 姚成, 董守龙. 基于反幂定律的聚合物电树枝生长数值模拟[J]. 电工技术学报, 2025, 40(11): 3643-3652. Bian Haoran, Yao Cheng, Dong Shoulong.Numerical simulation of polymer electrical tree growth based on inverse power law[J]. Transactions of China Electro-technical Society, 2025, 40(11): 3643-3652. [3] 刘云鹏, 尹子澳, 刘贺晨, 等. 低频电压下XLPE电树枝生长及局部放电特性[J]. 绝缘材料, 2024, 57(4): 66-71. Liu Yunpeng, Yin Ziao, Liu Hechen, et al.Propagation and partial discharge characteristics of electrical tree in XLPE cable insulation under low-frequency AC voltage[J]. Insulating Materials, 2024, 57(4): 66-71. [4] 国家能源局. 油浸式变压器: DL/T 1685—2017[S]. 北京: 中国电力出版社, 2017. [5] 国家电网有限公司. 新型电力系统数字化支撑技术体系白皮书[R]. 北京: 国家电网有限公司, 2022. [6] 盛戈皞, 钱勇, 罗林根, 等. 面向新型电力系统的数字化电力设备关键技术及其发展趋势[J]. 高电压技术, 2023, 49(5): 1765-1778. Sheng Gehao, Qian Yong, Luo Lingen, et al.Key technologies and development trends of digital power equipment for new type power system[J]. High Voltage Engineering, 2023, 49(5): 1765-1778. [7] 刘云鹏, 刘一瑾, 刘刚, 等. 电力变压器智能运维的数字孪生体构想[J]. 中国电机工程学报, 2023, 43(22): 8636-8652. Liu Yunpeng, Liu Yijin, Liu Gang, et al.Digital twin conception of intelligent operation and maintenance of power transformer[J]. Proceedings of the CSEE, 2023, 43(22): 8636-8652. [8] Zhang Yunxiao, Zhou Yuanxiang, Liu Rui, et al.Three-dimensional morphology and spherical growth mechanisms of electrical trees in silicone rubber[J]. Journal of Electrostatics, 2015, 76: 83-88. [9] 周远翔, 张旭, 刘睿, 等. 硅橡胶电树枝通道微观形貌研究[J]. 高电压技术, 2014, 40(1): 9-15. Zhou Yuanxiang, Zhang Xu, Liu Rui, et al.Study on micromorphology of electrical trees in silicon rubber[J]. High Voltage Engineering, 2014, 40(1): 9-15. [10] Schurch R, Ardila-Rey J, Montana J, et al.3D characterization of electrical tree structures[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2019, 26(1): 220-228. [11] Schurch R, Rowland S, Bradley R, et al.Imaging and analysis techniques for electrical trees using X-ray computed tomography[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2014, 21(1): 53-63. [12] Ma Zhenli, Cheng Yangchun, Chen Ming, et al.Study on the influence of gases on white marks and carbonized tracks generated by partial discharge in transformer oil-paper insulation[C]//2013 IEEE International Conference on Solid Dielectrics (ICSD), Bologna, Italy, 2013: 967-970. [13] Okabe S, Ueta G, Wada H, et al.Partial discharge- induced degradation characteristics of oil- impregnated insulating material used in oil-immersed power transformers[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2010, 17(4): 1225-1232. [14] Yi X, Wang Z.Surface tracking on pressboard in natural and synthetic transformer liquids under AC stress[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2013, 20(5): 1625-1634. [15] Sitorus H B H, Beroual A, Setiabudy R, et al. Creeping discharges over pressboard immersed in jatropha curcas methyl ester and mineral oils[C]//2015 IEEE 11th International Conference on the Properties and Applications of Dielectric Materials (ICPADM), Sydney, Australia, 2015: 152-155. [16] Cheng Yangchun, Duan Botao, Tan Xiao, et al.A novel method of measuring length and location of single channel carbonized trees in oil-impregnated pressboard[C]//2016 IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), Toronto, ON, Canada, 2016: 1003-1006. [17] Cheng Yangchun, Duan Botao, Li Feiran.Electrical tree reconstruction method for oil-impregnated pressboards based on the inverse problem for the electrostatic field[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2020, 27(1): 94-102. [18] Cheng Yangchun, Yang Ziqi, Zhao Li, et al.Partial discharge location accuracy in oil-immersed pressboards based on PSO[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2024, 31(5): 2587-2594. [19] 曹荣浩, 程养春, 许翰伟, 等. 局部放电实验中用于放电点定位的边界电场测量误差分析[J]. 高电压技术, 2025, 51(11): 5578-5585. Cao Ronghao, Cheng Yangchun, Xu Hanwei, et al.Error analysis of boundary electric field measurement for charge localization in partial discharge experiments[J]. High Voltage Engineering, 2025, 51(11): 5578-5585. [20] Ariza D, Becerra M, Hollertz R, et al.First mode negative streamers along mineral oil-solid interfaces[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2017, 24(4): 2371-2382. [21] Florkowski M, Florkowska B, Wlodek R.Investigations on post partial discharge charge decay in void using chopped sequence[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2017, 24(6): 3831-3838. [22] 杨紫淇. 实验室浸油纸板局部放电定位方法研究[D]. 北京: 华北电力大学, 2024. Yang Ziqi.Research on partial discharge location method of oil-immersed pressboard in laboratory[D]. Beijing: North China Electric Power University, 2024. [23] Zhang Shuang, Cheng Yangchun, Yu Haibo.Three- dimensional reconstruction of the electric tree in oil-impregnated pressboard based on partial discharge location[C]//2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), Beijing, China, 2020: 1-4. [24] 贠祥, 张鑫, 王超, 等. 基于联合参数辨识的粒子群优化扩展粒子滤波的锂电池荷电状态估计[J]. 电工技术学报, 2024, 39(2): 595-606. Yun Xiang, Zhang Xin, Wang Chao, et al.State of charge estimation of Li-ion battery using particle swarm optimization extended Kalman particle filter based on joint parameter identification[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 595-606. [25] 艾萌萌, 宋兴宇, 刘文辉, 等. 基于多目标粒子群算法考虑饱和情况异步起动永磁同步电机转子设计[J]. 电工技术学报, 2025, 40(12): 3857-3867. Ai Mengmeng, Song Xingyu, Liu Wenhui, et al.Design of multi-objective particle swarm algorithm for line-start permanent magnet synchronous motor considering saturation condition[J]. Transactions of China Electrotechnical Society, 2025, 40(12): 3857-3867. [26] 刘刚, 高成龙, 胡万君, 等. 基于鲸鱼优化算法超参数优化的径向基函数响应面模型的油浸式变压器绕组挡板结构优化[J]. 电工技术学报, 2024, 39(17): 5331-5343. Liu Gang, Gao Chenglong, Hu Wanjun, et al.Optimization of winding block washer structure for oil immersed transformers based on radial basis function response surface model with whale optimization algorithm hyper-parameters optimization[J]. Transactions of China Electrotechnical Society, 2024, 39(17): 5331-5343.
2026, Vol. 41 
