Grey Box Model and Optimization for Inductance Calculation of EHV Reactors
Jin Liang1,2, Zhu Dengfeng1,2, Yang Qingxin1,2, Zhang Junjie3, Gong Dexin1,2
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300400 China; 2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300400 China; 3. Baoding Tianwei BaoBian Electric Co. Ltd Baoding 071056 China
Abstract：The error of the existing EHV reactor inductance analysis and empirical calculation formula is greater than 1% of the engineering requirements. When the inductance calculation error is large, the optimization result of the reactor will be poor. Based on the electromagnetic principle, the revised inductance calculation empirical formula is established to reduce the error to about 1%, and the identifiable inductance calculation grey box model based on the prior electromagnetic principle is established. Based on the inductance sample data set obtained by numerical simulation, by introducing the adaptive variation factor and the optimal individual, an improved differential evolution algorithm was established and the parameters of the grey box model were identified, and a high-precision inductance calculation model with an error of 0.1% was obtained. Using the NSGA-II algorithm to optimize the design of the ultra-high voltage reactor, the wire quality and loss of the reactor were reduced by 21.4% and 18.6%, respectively. The experiment proves the correctness of the grey box model of inductance calculation obtained by parameter identification and the effectiveness of the optimization method. The reactor inductance parameter identification method established in this paper provides a new theoretical and practical idea for high-precision inductance calculation.
金亮, 祝登锋, 杨庆新, 张俊杰, 巩德鑫. 超高压电抗器电感计算灰箱模型与优化[J]. 电工技术学报, 2022, 37(23): 6093-6103.
Jin Liang, Zhu Dengfeng, Yang Qingxin, Zhang Junjie, Gong Dexin. Grey Box Model and Optimization for Inductance Calculation of EHV Reactors. Transactions of China Electrotechnical Society, 2022, 37(23): 6093-6103.
[1] 胡鹏飞, 谢诞梅, 熊扬恒. 一种基于白箱模型的人工神经网络参数辨识算法[J]. 中国电机工程学报, 2016, 36(10): 2734-2741. Hu Pengfei, Xie Danmei, Xiong Yangheng.An algorithm of parameter identification for wright-box models based on artificial neuron network[J]. Proceedings of the CSEE, 2016, 36(10): 2734-2741. [2] 姜静雅, 王玮, 唐芬, 等. 基于电网扰动暂态响应分析的虚拟同步机黑箱建模[J]. 电网技术, 2020, 44(11): 4227-4236. Jiang Jingya, Wang Wei, Tang Fen, et al.Black-box modeling of virtual synchronous generator based on transient response analysis under grid disturbances[J]. Power System Technology, 2020, 44(11): 4227-4236. [3] Kristensen N R, Madsen H, Jørgensen S B.Parameter estimation in stochastic grey-box models[J]. Automatica, 2004, 40(2): 225-237. [4] Fawzi T H, Burke P E. The accurate computation of self and mutual inductances of circular coils[J]. IEEE Transactions on Power Apparatus and Systems, 1978, PAS-97(2): 464-468. [5] 郑莉平, 孙强, 刘小河, 等. 干式空心电抗器设计和计算方法[J]. 电工技术学报, 2003, 18(4): 81-84, 93. Zheng Liping, Sun Qiang, Liu Xiaohe, et al.Design and calculation methods of dry-type air reactors[J]. Transactions of China Electrotechnical Society, 2003, 18(4): 81-84, 93. [6] 吴书煜, 马宏忠, 魏旭, 等. 高压电抗器匝间短路三维模型计算与分析[J]. 电力自动化设备, 2019, 39(4): 148-154. Wu Shuyu, Ma Hongzhong, Wei Xu, et al.Calculation and analysis of three-dimensional model for turn-to-turn short circuit of high voltage reactor[J]. Electric Power Automation Equipment, 2019, 39(4): 148-154. [7] 赵小军, 曹越芝, 刘兰荣, 等. 交直流混合激励下变压器用叠片式磁构件杂散损耗问题的数值模拟及实验验证[J]. 电工技术学报, 2021, 36(1): 141-150. Zhao Xiaojun, Cao Yuezhi, Liu Lanrong, et al.Numerical simulation and experimental verification of stray loss of laminated magnetic components for transformers under AC-DC hybrid excitation[J]. Transactions of China Electrotechnical Society, 2021, 36(1): 141-150. [8] Grover F W.Tables for the calculation of the mutual inductance of any two coaxial single-layer coils[J]. Proceedings of the Institute of Radio Engineers, 1933, 21(7): 1039-1049. [9] 机械工程手册编辑委员会电机工程手册编辑委员会. 电机工程手册-二-基础卷[M]. 2版. 北京: 机械工业出版社, 1996. [10] Langford-Smith F.Radiotron designer's handbook[M]. 4th ed. Sydney: the Wireless Press for Amalgamated Wireless Valve Company. Pty. Ltd., 1953. [11] 陈海昕, 邓凯文, 李润泽. 机器学习技术在气动优化中的应用[J]. 航空学报, 2019, 40(1): 52-68. Chen Haixin, Deng Kaiwen, Li Runze.Utilization of machine learning technology in aerodynamic optimization[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1): 52-68. [12] 陈锋, 王嘉玮, 吴梦晗, 等. 基于RBF神经网络的干式空心电抗器涡流损耗计算[J]. 电工技术学报, 2018, 33(11): 2545-2553. Chen Feng, Wang Jiawei, Wu Menghan, et al.Eddy Current loss calculation of dry-type air-core reactor based on radial basis function neural network[J]. Transactions of China Electrotechnical Society, 2018, 33(11): 2545-2553. [13] Yang Hang, Lu Gao, Ji Shengchang, et al.Detection method of turn to turn insulation short circuit fault of dry-type air-core reactor using vibration characteristics based on machine learning[C]//2019 IEEE 8th International Conference on Advanced Power System Automation and Protection, Xi'an, China, 2019: 363-367. [14] Zhou Yuren, He Xiaoyu, Chen Zefeng, et al.A neighborhood regression optimization algorithm for computationally expensive optimization problems[J]. IEEE Transactions on Cybernetics, 2022, 52(5): 3018-3031. [15] 周奇, 杨扬, 宋学官, 等. 变可信度近似模型及其在复杂装备优化设计中的应用研究进展[J]. 机械工程学报, 2020, 56(24): 219-245. Zhou Qi, Yang Yang, Song Xueguan, et al.Survey of multi-fidelity surrogate models and their applications in the design and optimization of engineering equipment[J]. Journal of Mechanical Engineering, 2020, 56(24): 219-245. [16] 虞振洋, 王世山. 基于有限元模型重构的多物理场耦合空心电抗器优化设计[J]. 电工技术学报, 2015, 30(20): 71-78. Yu Zhenyang, Wang Shishan.Optimum design of dry-type air-core reactor based on coupled multi-physics of reconstructed finite element model[J]. Transactions of China Electrotechnical Society, 2015, 30(20): 71-78. [17] 吴滨源, 李建文, 李永刚, 等. 用于谐波劣化分析的并网逆变器阻抗灰箱拟合方法[J]. 电工技术学报, 2022, 37(4): 942-953. Wu Binyuan, Li Jianwen, Li Yonggang, et al.A gray-box fitting method of grid-connected inverters impedance for the analysis of harmonic degradation[J]. Transactions of China Electrotechnical Society, 2022, 37(4): 942-953. [18] Storn R, Price K.Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4): 341-359. [19] 袁发庭. 基于热、磁联合的干式空心电抗器优化设计[D]. 武汉: 华中科技大学, 2018. [20] 陈锋, 巴灿, 徐玉东, 等. 矩形截面导线绕制的干式空心电抗器优化设计方法[J]. 电工技术学报, 2019, 34(24): 5115-5125. Chen Feng, Ba Can, Xu Yudong, et al.Optimum design of dry-type air-core reactor wound with wire of rectangular cross-section[J]. Transactions of China Electrotechnical Society, 2019, 34(24): 5115-5125. [21] 王佳宁, 邹强, 胡嘉汶, 等. 一种中压绝缘大功率中频变压器的优化设计方法[J]. 电工技术学报, 2022, 37(12): 3048-3060. Wang Jianing, Zou Qiang, Hu Jiawen, et al.An optimal design method for medium-voltage insulated high-power medium-frequency transformer[J]. Transactions of China Electrotechnical Society, 2022, 37(12): 3048-3060. [22] 王革鹏, 金文德, 曾向阳, 等. 特高压并联电抗器铁心振动的分析与控制研究[J]. 电工技术学报, 2022, 37(9): 2190-2198. Wang Gepeng, Jin Wende, Zeng Xiangyang, et al.Analysis and control research on core vibration of UHV shunt reactor[J]. Transactions of China Electrotechnical Society, 2022, 37(9): 2190-2198. [23] 张成芬, 赵彦珍, 陈锋, 等. 基于改进NSGA-Ⅱ算法的干式空心电抗器多目标优化设计[J]. 中国电机工程学报, 2010, 30(18): 115-121. Zhang Chengfen, Zhao Yanzhen, Chen Feng, et al.Multi-objective optimum design of dry-type air-core reactor based on improved NSGA-Ⅱ algorithm[J]. Proceedings of the CSEE, 2010, 30(18): 115-121. [24] 谢毓城. 电力变压器手册[M]. 北京: 机械工业出版社, 2003. [25] Deb K, Pratap A, Agarwal S, et al.A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197. [26] 龙腾, 刘建, Wang G G, 等. 基于计算试验设计与代理模型的飞行器近似优化策略探讨[J]. 机械工程学报, 2016, 52(14): 79-105. Long Teng, Liu Jian, Wang G G, et al.Discuss on approximate optimization strategies using design of computer experiments and metamodels for flight vehicle design[J]. Journal of Mechanical Engineering, 2016, 52(14): 79-105.
2022, Vol. 37 
