Complex Signal Modeling Method for Harmonic Source Based on Multivariate Gaussian Process Regression and DBSCAN Algorithm
Chu Yulin1,2, Chen Hongkun1,2, Wang Jiaqi1,2, Wu Yanmei1,2, Lei Aoyu3
1. Hubei Engineering and Technology Research Center for AC/DC Intelligent Distribution Network Wuhan University Wuhan 430072 China; 2. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China; 3. China Southern Power Grid Power Dispatching and Control Center Guangzhou 510663 China
Abstract：The data-driven harmonic source modeling method uses amplitude and phase angle data of harmonic electrical signals to train the model, which is essentially an analysis and processing process for complex signals. The design and implementation of traditional data-driven algorithms are mostly carried out in the real number field, and there is a problem of information loss when performing complex signal regression. In addition, the fitting effect of data-driven methods on harmonic source models is closely related to the learning samples. Due to limited data samples in certain scenarios, the current data-driven harmonic source model can only describe the local harmonic emission characteristics of harmonic source equipment under partial operating conditions, making it difficult to achieve global learning and regression. To solve the problem of information loss in traditional data-driven algorithms for complex signal regression, this paper first proposed a multivariate gaussian process regression (MV-GPR) algorithm based on matrix variable Gaussian distribution. The MV-GPR algorithm uses the covariance matrix to characterize the correlation information between the real and imaginary parts of the target complex signal. The posterior distribution calculation and parameter estimation methods of multivariate Gaussian process were derived to achieve uncertainty regression of complex signals. Next, based on the influencing factors of harmonic emission characteristics of various types of harmonic sources, the modeling characteristic variables of complex signal harmonic sources under three-phase unbalance conditions were selected, and the principal component analysis method was used to reduce the dimensionality of the input characteristic variables to ensure the convergence of the algorithm. To solve the problem of poor global learning performance in current data-driven harmonic source modeling methods, this paper proposed a model global improvement method according to the better performance of MV-GPR algorithm in small-scale sample regression. Firstly, the density-based spatial clustering of applications with noise (DBSCAN) algorithm was used to divide historical sample data into sub sample sets representing different operating states of harmonic sources. Then, sub harmonic source models were established based on each sub sample set, and the closest sub model was selected for regression according to the distance between the sample to be regressed and the historical sub sample set, thereby improving the learning and regression effect of the harmonic source model on global samples. Based on simulation data from multiple types of harmonic sources model and actual measurement data from a 500kV substation of Southern Power Grid, the MV-GPR algorithm, modeling feature selection results and model global improvement method proposed in this paper were compared and verified. The following conclusions can be drawn: (1) The MV-GPR algorithm has higher accuracy in complex signal regression than GPR and CLS algorithms, and can achieve high hit rate uncertainty regression with lower conservatism. (2) The selected MV-GPR complex signal harmonic source model input characteristic variables can accurately reflect the harmonic emission characteristics of multiple types of harmonic sources, and the equivalent fitting accuracy is significantly higher in harmonic source equipment group scenarios. (3) The DBSCAN algorithm can effectively divide historical sample sets under different operating states into multiple sub sample sets. The method of using sub sample set to train sub models can effectively improve the regression accuracy of the harmonic source model on global samples, and can significantly reduce the training time of the algorithm.
褚昱麟, 陈红坤, 王嘉琦, 吴艳梅, 雷傲宇. 基于多元高斯过程回归和空间聚类的复信号谐波源建模[J]. 电工技术学报, 2025, 40(23): 7621-7634.
Chu Yulin, Chen Hongkun, Wang Jiaqi, Wu Yanmei, Lei Aoyu. Complex Signal Modeling Method for Harmonic Source Based on Multivariate Gaussian Process Regression and DBSCAN Algorithm. Transactions of China Electrotechnical Society, 2025, 40(23): 7621-7634.
[1] 李戎, 李建文, 李永刚, 等. 结合特征根及模态分析法的逆变器多机并网系统谐波扰动响应分析[J]. 电工技术学报, 2024, 39(14): 4519-4534. Li Rong, Li Jianwen, Li Yonggang, et al.Analysis of harmonic disturbance response of multi-inverter grid-connected system combining characteristic root and modal analysis method[J]. Transactions of China Electrotechnical Society, 2024, 39(14): 4519-4534. [2] 李建闽, 曹远远, 姚文轩, 等. 基于自适应移频滤波的电力系统谐波分析方法[J]. 电工技术学报, 2024, 39(13): 4015-4024. Li Jianmin, Cao Yuanyuan, Yao Wenxuan, et al.Power system harmonic analysis method based on adaptive frequency-shift filtering[J]. Transactions of China Electrotechnical Society, 2024, 39(13): 4015-4024. [3] 国家发展和改革委员会. 电能质量管理办法(暂行)[EB/OL].https://www.gov.cn/gongbao/2024/issue_11226/202403/content_6940055.html. [4] 丁同, 陈红坤, 吴斌, 等. 多谐波源定位及谐波责任量化区分方法综述[J]. 电力自动化设备, 2020, 40(1): 19-30. Ding Tong, Chen Hongkun, Wu Bin, et al.Overview on location and harmonic responsibility quantitative determination methods of multiple harmonic sources[J]. Electric Power Automation Equipment, 2020, 40(1): 19-30. [5] 王杨, 田旭, 赵劲帅, 等. 基于相移原理的LCC-HVDC降维谐波状态空间建模[J]. 电力系统保护与控制, 2023, 51(14): 11-22. Wang Yang, Tian Xu, Zhao Jinshuai, et al.Dimension-reduced harmonic state space modeling of an LCC-HVDC based on the phase shift principle[J]. Power System Protection and Control, 2023, 51(14): 11-22. [6] 邵振国, 黄伟达. 考虑出力不确定性的分布式电源谐波传播计算[J]. 电工技术学报, 2019, 34(增刊2): 674-683. Shao Zhenguo, Huang Weida.A calculation method of harmonic propagation considering the uncertainty of distributed generation[J]. Transactions of China Electrotechnical Society, 2019, 34(S2): 674-683. [7] Fauri M.Harmonic modelling of non-linear load by means of crossed frequency admittance matrix[J]. IEEE Transactions on Power Systems, 1997, 12(4): 1632-1638. [8] Hu Zhe, Han Yang, Zalhaf A S, et al.Harmonic sources modeling and characterization in modern power systems: a comprehensive overview[J]. Electric Power Systems Research, 2023, 218: 109234. [9] 张逸, 孟祥亮, 刘必杰. 谐波源建模现状及新型电力系统下的发展趋势[J]. 电力系统及其自动化学报, 2022, 34(8): 139-149. Zhang Yi, Meng Xiangliang, Liu Bijie.Current situation of harmonic source modeling and development trend under novel power system[J]. Proceedings of the CSU-EPSA, 2022, 34(8): 139-149. [10] 李湘, 陈民铀, 郑永伟, 等. 基于稳健偏最小二乘法的谐波发射水平估计[J]. 电力系统及其自动化学报, 2016, 28(6): 86-90. Li Xiang, Chen Minyou, Zheng Yongwei, et al.Assessing harmonic emission level based on robust partial least squares regression[J]. Proceedings of the CSU-EPSA, 2016, 28(6): 86-90. [11] Moreno M A, Usaola J.A new balanced harmonic load flow including nonlinear loads modeled with RBF networks[J]. IEEE Transactions on Power Delivery, 2004, 19(2): 686-693. [12] 郑连清, 吴萍, 刘小龙. 基于遗传算法的LS-SVM在谐波源建模中的应用[J]. 电力系统保护与控制, 2011, 39(3): 52-56. Zheng Lianqing, Wu Ping, Liu Xiaolong.Application of least squares support vector machine to harmonic sources modeling based on genetic algorithm[J]. Power System Protection and Control, 2011, 39(3): 52-56. [13] 张逸, 刘必杰, 邵振国, 等. 基于高斯过程回归的谐波源不确定性通用模型[J]. 中国电机工程学报, 2022, 42(3): 992-1002. Zhang Yi, Liu Bijie, Shao Zhenguo, et al.General and uncertain harmonic source model based on Gaussian process regression[J]. Proceedings of the CSEE, 2022, 42(3): 992-1002. [14] Xia Yili, Mandic D P.Widely linear adaptive frequency estimation of unbalanced three-phase power systems[J]. IEEE Transactions on Instrumentation and Measurement, 2012, 61(1): 74-83. [15] 张行. 面向非圆复数的自适应估计算法性能分析及其应用研究[D]. 南京: 东南大学, 2021. Zhang Xing.Performance analysis and application research of adaptive estimation algorithm for noncircular complex numbers[D]. Nanjing: Southeast University, 2021. [16] 贾秀芳, 华回春, 曹东升, 等. 基于复线性最小二乘法的谐波责任定量划分[J]. 中国电机工程学报, 2013, 33(4): 149-155, 20. Jia Xiufang, Hua Huichun, Cao Dongsheng, et al.Determining harmonic contributions based on complex least squares method[J]. Proceedings of the CSEE, 2013, 33(4): 149-155, 20. [17] 李亚辉, 孙媛媛, 王庆岩, 等. 基于源荷谐波耦合模型的数据驱动概率谐波潮流计算[J]. 中国电机工程学报, 2024, 44(11): 4323-4335. Li Yahui, Sun Yuanyuan, Wang Qingyan, et al.Data-driven probabilistic harmonic power flow calculation based on source and load harmonic coupling model[J]. Proceedings of the CSEE, 2024, 44(11): 4323-4335. [18] 李峰, 王琦, 胡健雄, 等. 数据与知识联合驱动方法研究进展及其在电力系统中应用展望[J]. 中国电机工程学报, 2021, 41(13): 4377-4390. Li Feng, Wang Qi, Hu Jianxiong, et al.Combined data-driven and knowledge-driven methodology research advances and its applied prospect in power systems[J]. Proceedings of the CSEE, 2021, 41(13): 4377-4390. [19] Thompson G Z, Maitra R, Meeker W Q, et al.Classification with the matrix-variate-t distribution[J]. Journal of Computational and Graphical Statistics, 2020, 29(3): 668-674. [20] Chen Zexun, Wang Bo, Gorban A N.Multivariate Gaussian and Student-t process regression for multi-output prediction[J]. Neural Computing and Applications, 2020, 32(8): 3005-3028. [21] Boloix-Tortosa R, Murillo-Fuentes J J, Payan-Somet F J, et al. Complex Gaussian processes for regression[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(11): 5499-5511. [22] 陈少伟, 卢镇江, 沈渊彬, 等. 基于典型关联分析算法的恒流源型谐波用户识别[J]. 供用电, 2020, 37(11): 34-41. Chen Shaowei, Lu Zhenjiang, Shen Yuanbin, et al.A method of constant current source type harmonic users identification based on typical association analysis[J]. Distribution & Utilization, 2020, 37(11): 34-41. [23] 刘博, 杜正春. 含VSC-HVDC交直流混联电力系统三相谐波潮流统一算法[J]. 中国电机工程学报, 2018, 38(8): 2284-2293, 2538. Liu Bo, Du Zhengchun.Unified Newton’s solution to three-phase harmonic power flow of VSC-HVDC based AC/DC power systems[J]. Proceedings of the CSEE, 2018, 38(8): 2284-2293, 2538. [24] 李亚辉, 孙媛媛, 李可军, 等. 不平衡供电条件下多脉动整流器的谐波特性分析[J]. 电力系统自动化, 2021, 45(23): 152-161. Li Yahui, Sun Yuanyuan, Li Kejun, et al.Harmonic characteristic analysis of multi-pulse rectifier under unbalanced power supply condition[J]. Automation of Electric Power Systems, 2021, 45(23): 152-161. [25] 姜雅男, 于永进, 李长云. 基于改进TOPSIS模型的绝缘纸机-热老化状态评估方法[J]. 电工技术学报, 2022, 37(6): 1572-1582. Jiang Yanan, Yu Yongjin, Li Changyun.Evaluation method of insulation paper deterioration status with mechanical-thermal synergy based on improved TOPSIS model[J]. Transactions of China Electro-technical Society, 2022, 37(6): 1572-1582. [26] 吕俊超, 丁志远, 傅琪雯. 一种海上风电场柔直送出线单端保护方案[J]. 电气技术, 2024, 25(4): 47-51. Lü Junchao, Ding Zhiyuan, Fu Qiwen.A single-end protection scheme for voltage source converter based high voltage DC transmission line of offshore wind farm[J]. Electrical Engineering, 2024, 25(4): 47-51. [27] 陈光宇, 袁文辉, 徐晓春, 等. 基于残差图卷积深度网络的电网无功储备需求快速计算方法[J]. 电工技术学报, 2023, 38(17): 4683-4700. Chen Guangyu, Yuan Wenhui, Xu Xiaochun, et al.Fast calculation method for grid reactive power reserve demand based on residual graph convolutional deep network[J]. Transactions of China Electro-technical Society, 2023, 38(17): 4683-4700. [28] 刘征宇, 郭乐凯, 孟辉, 等. 基于改进DBSCAN的退役动力电池分选方法[J]. 电工技术学报, 2023, 38(11): 3073-3083. Liu Zhengyu, Guo Lekai, Meng Hui, et al.A sorting method of retired power battery based on improved DBSCAN[J]. Transactions of China Electrotechnical Society, 2023, 38(11): 3073-3083. [29] 周国亮, 宋亚奇, 王桂兰, 等. 状态监测大数据存储及聚类划分研究[J]. 电工技术学报, 2013, 28(增刊2): 337-344. Zhou Guoliang, Song Yaqi, Wang Guilan, et al.Research of condition monitoring big data storage and clustering[J]. Transactions of China Electrotechnical Society, 2013, 28(S2): 337-344. [30] 胡畔, 陈红坤, 孙志达, 等. 一种交流电弧炉通用性模型[J]. 电工技术学报, 2016, 31(8): 172-180. Hu Pan, Chen Hongkun, Sun Zhidang, et al.A versatility model of AC electric arc furnace[J]. Transactions of China Electrotechnical Society, 2016, 31(8): 172-180.
2025, Vol. 40 
