A Gray-Box Fitting Method of Grid-Connected Inverters Impedance for the Analysis of Harmonic Degradation
Wu Binyuan1, Li Jianwen1, Li Yonggang1, Wang Yue1, Sun Wei2
1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Baoding 071000 China; 2. Baoding Power Supply Subsidiary Company of State Grid Hebei Electric Power Supply Co. Ltd Baoding 071000 China
Abstract：As a large number of distributed generation systems are connected to the grid through inverters, complex interactions between grid-connected inverters and weak-grids are formed, and the problem of harmonic degradation is prominent. One of the key points of harmonic degradation analysis is to establish the impedance model of the grid-connected inverter. The detailed internal information is needed in white-box impedance modeling, and the results of black-box impedance modeling are meaningless. Both methods have defects in practical engineering application. Therefore, setting the result of white-box as the goal and taking the method of black-box as the solution way, this paper presents that the impedance of the grid-connected inverters in gray-box is fitted by rational function approximation. First of all, the discrete impedance data are obtained by dual-mode disturbance, and then the matrix pencil method is used to extract the initial parameters and reduce the time of iterative calculation. An improved vector fitting is proposed. Then a hardware in the loop real-time simulation platform is built based on RT-Lab, and the effectiveness and advantages of this method are verified by comparative experiments. Finally, the analysis of harmonic degradation is carried out based on the results of impedance fitting to verify the practicability of the proposed method.
吴滨源, 李建文, 李永刚, 王月, 孙伟. 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, Wang Yue, Sun Wei. A Gray-Box Fitting Method of Grid-Connected Inverters Impedance for the Analysis of Harmonic Degradation. Transactions of China Electrotechnical Society, 2022, 37(4): 942-953.
[1] Liu Pengcheng, Wang Zheng, Wei Sanmin, et al.Recent developments of modulation and control for high-power current-source-converters fed electric machine systems[J]. CES Transactions on Electrical Machines and Systems, 2020, 4(3): 215-226. [2] 胡鹏, 艾欣, 肖仕武, 等. 静止无功发生器序阻抗建模及对次同步振荡影响因素的分析[J]. 电工技术学报, 2020, 35(17): 3703-3713. Hu Peng, Ai Xin, Xiao Shiwu, et al.Sequence impedance of static var generator and analysis of influencing factors on subsynchronous oscillation[J]. Transactions of China Electrotechnical Society, 2020, 35(17): 3703-3713. [3] 谢志为, 陈燕东, 伍文华, 等. 弱电网下多逆变器并网系统的全局高频振荡抑制方法[J]. 电工技术学报, 2020, 35(4): 885-895. Xie Zhiwei, Chen Yandong, Wu Wenhua, et al.A global high-frequency oscillation suppression method for multi-Inverter grid-connected system in weak grid[J]. Transactions of China Electrotechnical Society, 2020, 35(4): 885-895. [4] 赵强松, 陈莎莎, 周晓宇, 等. 用于并网逆变器谐波抑制的重复-比例复合控制器分析与设计[J]. 电工技术学报, 2019, 34(24): 5189-5198. Zhao Qiangsong, Chen Shasha, Zhou Xiaoyu, et al.Analysis and design of combination controller based on repetitive control and proportional control for harmonics suppression of grid-tied inverters[J]. Transactions of China Electrotechnical Society, 2019, 34(24): 5189-5198. [5] 汪颖, 罗代军, 肖先勇, 等. 多逆变器并网下的超高次谐振特性分析[J]. 电力系统自动化, 2020, 44(1): 192-199. Wang Ying, Luo Daijun, Xiao Xianyong, et al.Analysis on supraharmonic resonance characteristics with integration of multiple inverters[J]. Automation of Electric Power Systems, 2020, 44(1): 192-199. [6] 陈新, 王赟程, 龚春英, 等. 采用阻抗分析方法的并网逆变器稳定性研究综述[J]. 中国电机工程学报, 2018, 38(7): 2082-2094, 2223. Chen Xin, Wang Yuncheng, Gong Chunying, et al.Overview of stability research for grid-connected inverters based on impedance analysis methed[J]. Proceedings of the CSEE, 2018, 38(7): 2082-2094, 2223. [7] 刘津鸣, 陈燕东, 伍文华, 等. 孤岛微电网序阻抗建模与高频振荡抑制[J]. 电工技术学报, 2020, 35(7): 1538-1552. Liu Jinming, Chen Yandong, Wu Wenhua, et al.Sequence impedance modeling and high-frequency oscillation suppression method for island microgrid[J]. Transactions of China Electrotechnical Society, 2020, 35(7): 1538-1552. [8] 钟佩军, 孙建军, 司学振, 等. 基于电压扰动源的并网逆变器输出阻抗测量方法[J]. 电工技术学报, 2019, 34(22): 4739-4750. Zhong Peijun, Sun Jianjun, Si Xuezhen, et al.Measurement method of inverter output impedance based on voltage disturbance source[J]. Transactions of China Electrotechnical Society, 2019, 34(22): 4739-4750. [9] Roinila T, Messo T.Online grid-impedance mea- surement using ternary-sequence injection[J]. IEEE Transactions on Industry Applications, 2018, 54(5): 5097-5103. [10] Belkhayat M.Stability criteria for ac power systems with regulated loads[D]. West Lafayette: Purdue University, 1997. [11] 严干贵, 段双明, 叶德武, 等. 基于输出阻抗的三相LCL型光伏逆变器稳定性分析[J]. 太阳能学报, 2018, 39(2): 558-566. Yan Gangui, Duan Shuangming, Ye Dewu, et al.Stability analysis of three-phase LCL-type photo- voltaic inverter based on the output impedance[J]. Acta Energiae Solaris Sinica, 2018, 39(2): 558-566. [12] 杨苓, 陈燕东, 周乐明, 等. 弱电网下锁相环对三相LCL型并网逆变器小扰动建模影响及稳定性分析[J]. 中国电机工程学报, 2018, 38(13): 3792-3804. Yang Ling, Chen Yandong, Zhou Leming, et al.Effect of phase locked loop on the small-signal perturbation modeling and stability analysis for three-phase LCL-type grid-connected inverter in weak grid[J]. Proceedings of the CSEE, 2018, 38(13): 3792-3804. [13] 李建文, 阮筱菲, 李永刚, 等. 弱电网下多并网逆变器谐振失稳研究综述[J]. 现代电力, 2020, 37(2): 187-196. Li Jianwen, Ruan Xiaofei, Li Yonggang, et al.An overview on resonance instability of multiple grid-connected inverters in weak grid[J]. Modern Electric Power, 2020, 37(2): 187-196. [14] Sun Jian.Small-signal methods for AC distributed power systems-a review[J]. IEEE Transactions on Power Electronics, 2009, 24(11): 2545-2554. [15] 年珩, 杨洪雨. 不平衡运行工况下并网逆变器的阻抗建模及稳定性分析[J]. 电力系统自动化, 2016, 40(10): 76-83. Nian Heng, Yang Hongyu.Impedance modeling and stability analysis of grid-connected inverters under unbalanced operation conditions[J]. Automation of Electric Power System, 2016, 40(10): 76-83. [16] 王赟程, 陈新, 陈杰, 等. 基于谐波线性化的三相LCL型并网逆变器正负序阻抗建模分析[J]. 中国电机工程学报, 2016, 36(21): 5890-5898, 6033. Wang Yuncheng, Chen Xin, Chen Jie, et al.Analysis of positive-sequence and negative-sequence impe- dance modeling of three-phase LCL-type grid- connected inverters based on harmonic lineari- zation[J]. Proceedings of the CSEE, 2016, 36(21): 5890-5898, 6033. [17] 李奕欣, 赵书强, 马燕峰, 等. 三相LCL型并网逆变器的阻抗建模及特性分析[J]. 电力自动化设备, 2019, 39(7): 107-113. Li Yixin, Zhao Shuqiang, Ma Yanfeng, et al.Impedance modeling and characteristic analysis of three-phase LCL-type grid-connected inverters[J]. Electric Power Automation Equipment, 2019, 39(7): 107-113. [18] Liu Junliang, Du Xiong, Shi Ying, et al.Impedance measurement of three-phase inverter in the stationary frame using frequency response analyzer[J]. IEEE Transactions on Power Electronics, 2020, 35(9): 9390-9401. [19] Wang Xiongfei, Blaabjerg F.Harmonic stability in power electronic-based power systems: concept, modeling, and analysis[J]. IEEE Transactions on Power Electronics, 2020, 10(3): 2858-2870. [20] Zhou Weihua, Torres R, Wang Yanbo, et al.A gray-box hierarchical oscillatory instability source identification method of multiple-inverter-fed power systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 9(3): 3095-3113. [21] 李建文, 吴滨源, 李永刚, 等. 分析谐波劣化机理的逆变器灰箱宽频域矩阵模型及求解方法[J]. 电力系统自动化, 2020, 44(18): 155-164. Li Jianwen, Wu Binyuan, Li Yonggang, et al.Gray-box wide frequency domain matrix model of inverter for harmonic degradation mechanism analysis and its solution method[J]. Automation of Electric Power Systems, 2020, 44(18): 155-164. [22] 张重远, 韩启隆. 考虑层间效应的复磁导率铁芯频变模型[J]. 高电压技术, 2019, 45(7): 2292-2298. Zhang Chongyuan, Han Qilong.Frequency-depended modeling for the core of power transformer based on complex permeability considering interlaminar effects[J]. High Voltage Engineering, 2019, 45(7): 2292-2298. [23] 戴宇峰, 鲁军勇, 张晓, 等. 脉冲功率同轴电缆瞬态阻抗特性研究[J]. 高电压技术, 2019, 45(6): 1915-1920. Dai Yufeng, Lu Junyong, Zhang Xiao, et al.Research on transient impedance characteristic of coaxial cable for pulse power[J]. High Voltage Engineering, 2019, 45(6): 1915-1920. [24] 刘威, 刘杰, 吴小丹, 等. 风电场阻抗模型的现场测试[J]. 中国电机工程学报, 2020, 40(增刊1): 91-97. Liu Wei, Liu Jie, Wu Xiaodan, et al.Identifying impedance models of wind farms with field tests[J]. Proceedings of the CSEE, 2020, 40(S1): 91-97. [25] 党杰, 李勇, 徐友平, 等. 基于WAMS和奇异熵矩阵束方法的电网低频振荡仿真分析[J]. 电力系统自动化, 2010, 34(15): 14-18. Dang Jie, Li Yong, Xu Youping, et al.Power grid low frequency oscillation simulation analysis based on WAMS and singular entropy matrix pencil method[J]. Automation of Electric Power System, 2010, 34(15): 14-18. [26] 王印晨, 杨少兵, 宋可荐, 等. 基于滑模结构无源控制的车网耦合系统低频振荡抑制方法[J]. 电工技术学报, 2020, 35(3): 553-563. Wang Yingchen, Yang Shaobing, Song Kejian, et al.An approach based on SMS to suppress low- frequency oscillation in the EMUs and traction network coupling system using PBC[J]. Transactions of China Electrotechnical Society, 2020, 35(3): 553-563. [27] 赵普志, 李之洪, 徐交国, 等. 基于KL散度的电容器谐振研究[J]. 电气技术, 2020, 21(3): 27-30. Zhao Puzhi, Li Zhihong, Xu Jiaoguo.Study on capacitor resonance based on KL dispersion[J]. Electrical Engineering, 2020, 21(3): 27-30. [28] 张学广, 夏丹妮, 陈文佳, 等. 三相并网变流器弱电网下频率耦合抑制控制方法[J]. 电工技术学报, 2019, 34(21): 4559-4571. Zhang Xueguang, Xia Danni, Chen Wenjia, et al.Frequency coupling suppression control method for three-phase grid-connected converter under weak grid[J]. Transactions of China Electrotechnical Society, 2019, 34(21): 4559-4571. [29] 谢志为, 陈燕东, 伍文华, 等. 双模式扰动下新能源发电装备的宽频带序阻抗在线精确测量方法[J]. 中国电机工程学报, 2020, 40(9): 2903-2914. Xie Zhiwei, Chen Yandong, Wu Wenhua, et al.A wide-bandwidth sequence-impedance online precise measurement method for renewable energy generation equipment with dual-mode disturbance[J]. Pro- ceedings of the CSEE, 2020, 40(9): 2903-2914. [30] Gustavsen B, Semlyeen A.Rational approximation of frequency domain responses by vector fitting[J]. IEEE Transactions on Power Delivery, 1999, 14(3): 1052-1061. [31] Gustavsen B.Improving the pole relocating properties of vector fitting[J]. IEEE Transactions on Power Delivery, 2006, 21(3): 1587-1592. [32] 涂春鸣, 李庆, 郭祺, 等. 具备电压质量调节能力的串并联一体化多功能变流器[J]. 电工技术学报, 2020, 35(23): 4852-4863. Tu Chunming, Li Qing, Guo Qi, et al.Research on series-parallel integrated multifunctional converter with voltage quality adjustment[J]. Transactions of China Electrotechnical Society, 2020, 35(23): 4852-4863. [33] 张占俊, 李建文, 董耀, 等. 弱电网下多逆变器并网谐振失稳分析方法[J]. 电气技术, 2020, 21(10): 21-28. Zhang Zhanjun, Li Jianwen, Dong Yao, et al.Method of resonance instability analysis of multiple grid- connected inverters in weak grid[J]. Electrical Engineering, 2020, 21(10): 21-28.
2022, Vol. 37 
