Impedance Modeling and Analysis of Subsynchronous Oscillation Influencing Factors for Grid Connected System of Matching Control Direct-Drive Wind Turbine
Gao Benfeng1, Wang Qiuwen1, Wang Yaohan2, Sun Dawei2, Wang Xiao2, Wu Linlin2, Liu Hui2, Ran Huijuan1
1. Hebei Key Laboratory of Distributed Energy Storage and Micro-grid North China Electric Power University Baoding 071003 China; 2. State Grid Wind-photovoltaic-energy Storage Hybrid Power Generation Technology Laboratory North China Electric Power Research Institute Co. Ltd Beijing 100045 China
Abstract：When the new energy units, mainly wind power and photovoltaic, are connected to the AC grid on a large scale through power electronic converters, the power system is prone to form a weak AC grid environment, which brings severe challenges to the stable operation of traditional grid-following new energy units. In recent years, scholars at home and abroad have proposed various grid-forming control strategies based on virtual synchronous generator control, sagging control, and matching control, enabling inverters to have suitable voltage and frequency support capabilities. Matching control only measures the DC voltage to realize the autonomous synchronization function and has a fast response speed, receiving widespread attention. However, research on grid-forming new energy units based on matching control focuses on supporting capacity and inertia response characteristics of AC grid, and the impedance characteristics and related influencing factors still need to be studied. This paper first establishes the positive and negative sequence impedance model of matching-control-type direct drive wind turbines (DDWT) using the harmonic linearization method. The impedance analytical model is verified by combining the impedance sweep method. The stability of the matching-control-type DDWT system when connected to AC grids of different intensities is analyzed based on the equivalent RLC stability criterion. Furthermore, the dominant parameters affecting the impedance characteristics of matching-control-type DDWT are analyzed using impedance sensitivity, and a parameter optimization scheme is determined to improve system stability. Finally, the theoretical analysis is verified through PSCAD/EMTDC electromagnetic transient simulation. It can be concluded that the positive sequence impedance model of matching-control-type DDWT is inductive in the low-frequency range and has a negative damping range in the sub-synchronous frequency range, but the phase is within -90°. The negative sequence impedance model exhibits capacitive behavior in the low-frequency range, then becomes inductive, and the phase of the capacitive frequency range is within -90°. Therefore, matching-control-type DDWT makes it challenging to form negative damping oscillation circuits with inductive AC grids. The stability analysis results based on the RLC stability criterion indicate that matching-control-type DDWT has suitable stability in weak AC grids but has a risk of oscillation in strong AC grids. Furthermore, the impedance sensitivity of each control parameter is calculated, and the dominant parameter that affects the impedance characteristics is determined based on the magnitude of the impedance sensitivity amplitude. According to the impedance’s real-imaginary frequency characteristic curve, a parameter adjustment method is obtained to improve the grid stability of matching-control-type DDWT in strong power grids. The proportional coefficient of the reactive outer loop, the proportional coefficient of the current inner loop, and the virtual impedance of the grid side converter mainly affect the impedance characteristics. Properly reducing the reactive outer loop’s proportional coefficient and increasing the current inner loop’s proportional coefficient or virtual impedance can improve the stability of the matching-control-type DDWT grid-connected system.
高本锋, 王秋文, 王耀函, 孙大卫, 王潇, 吴林林, 刘辉, 冉慧娟. 匹配控制型直驱风机并网系统阻抗建模及次同步振荡影响因素分析[J]. 电工技术学报, 2025, 40(14): 4614-4628.
Gao Benfeng, Wang Qiuwen, Wang Yaohan, Sun Dawei, Wang Xiao, Wu Linlin, Liu Hui, Ran Huijuan. Impedance Modeling and Analysis of Subsynchronous Oscillation Influencing Factors for Grid Connected System of Matching Control Direct-Drive Wind Turbine. Transactions of China Electrotechnical Society, 2025, 40(14): 4614-4628.
[1] 周孝信, 陈树勇, 鲁宗相, 等. 能源转型中我国新一代电力系统的技术特征[J]. 中国电机工程学报, 2018, 38(7): 1893-1904, 2205. Zhou Xiaoxin, Chen Shuyong, Lu Zongxiang, et al.Technology features of the new generation power system in China[J]. Proceedings of the CSEE, 2018, 38(7): 1893-1904, 2205. [2] 桑顺, 高宁, 蔡旭, 等. 功率-电压控制型并网逆变器及其弱电网适应性研究[J]. 中国电机工程学报, 2017, 37(8): 2339-2351. Sang Shun, Gao Ning, Cai Xu, et al.A power-voltage controlled grid-connected inverter and its adaptability research under weak grid conditions[J]. Proceedings of the CSEE, 2017, 37(8): 2339-2351. [3] 肖湘宁, 罗超, 廖坤玉. 新能源电力系统次同步振荡问题研究综述[J]. 电工技术学报, 2017, 32(6): 85-97. Xiao Xiangning, Luo Chao, Liao Kunyu.Review of the research on subsynchronous oscillation issues in electric power system with renewable energy sources[J]. Transactions of China Electrotechnical Society, 2017, 32(6): 85-97. [4] 董文凯, 杜文娟, 王海风. 弱连接条件下锁相环动态主导的并网直驱风电场小干扰稳定性研究[J]. 电工技术学报, 2021, 36(3): 609-622. Dong Wenkai, Du Wenjuan, Wang Haifeng.Small- signal stability of a grid-connected PMSG wind farm dominated by dynamics of PLLs under weak grid connection[J]. Transactions of China Electrotechnical Society, 2021, 36(3): 609-622. [5] 许诘翊, 刘威, 刘树, 等. 电力系统变流器构网控制技术的现状与发展趋势[J]. 电网技术, 2022, 46(9): 3586-3595. Xu Jieyi, Liu Wei, Liu Shu, et al.Current state and development trends of power system converter grid-forming control technology[J]. Power System Technology, 2022, 46(9): 3586-3595. [6] 桑顺, 徐婷, 齐琛, 等. 惯性同步构网型变换器定量感知电网频率的机理及抗干扰控制策略[J]. 电网技术, 2023, 47(4): 1395-1408. Sang Shun, Xu Ting, Qi Chen, et al.Mechanism of quantitatively sensing grid frequency and anti- disturbance control strategy for the grid-forming converter[J]. Power System Technology, 2023, 47(4): 1395-1408. [7] Arghir C, Dörfler F.The electronic realization of synchronous machines: model matching, angle tracking, and energy shaping techniques[J]. IEEE Transactions on Power Electronics, 2020, 35(4): 4398-4410. [8] 秦世耀, 齐琛, 李少林, 等. 电压源型构网风电机组研究现状及展望[J]. 中国电机工程学报, 2023, 43(4): 1314-1334. Qin Shiyao, Qi Chen, Li Shaolin, et al.Review of the voltage-source grid forming wind turbine[J]. Pro- ceedings of the CSEE, 2023, 43(4): 1314-1334. [9] 人民网-湖北频道. 国网湖北电力首次实现国内无储能支撑新能源电压源机组运行[EB/OL]. (2022- 03-14)[2024-06-16].http://hb.people.com.cn/n2/2022/0314/c194063-35173448.html. [10] 詹长江, 吴恒, 王雄飞, 等. 构网型变流器稳定性研究综述[J]. 中国电机工程学报, 2023, 43(6): 2339-2359. Zhan Changjiang, Wu Heng, Wang Xiongfei, et al.An overview of stability studies of grid-forming voltage source converters[J]. Proceedings of the CSEE, 2023, 43(6): 2339-2359. [11] 邢华栋, 张叔禹, 尹柏清, 等. 风电并网系统次同步振荡稳定性分析与控制方法研究综述[J]. 电测与仪表, 2020, 57(24): 13-21. Xing Huadong, Zhang Shuyu, Yin Baiqing, et al.Review of sub-synchronous oscillation stability analysis and control method for grid-connected wind power system[J]. Electrical Measurement & Instru- mentation, 2020, 57(24): 13-21. [12] 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 Systems, 2016, 40(10): 76-83. [13] 高本锋, 邓鹏程, 孙大卫, 等. 基于匹配控制的构网型直驱风电场次同步振荡机理与特性研究[J]. 电工技术学报, 2024, 39(9): 2755-2770. Gao Benfeng, Deng Pengcheng, Sun Dawei, et al.Mechanism and characteristics of subsynchronous oscillation of grid-forming direct-drive wind farm based on matching control[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2755-2770. [14] 桑顺, 张琛, 蔡旭, 等. 全功率变换风电机组的电压源控制(一): 控制架构与弱电网运行稳定性分析[J]. 中国电机工程学报, 2021, 41(16): 5604-5616. Sang Shun, Zhang Chen, Cai Xu, et al.Voltage source control of wind turbines with full-scale converters (part Ⅰ): control architecture and stability analysis under weak grid conditions[J]. Proceedings of the CSEE, 2021, 41(16): 5604-5616. [15] 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 method[J]. Proceedings of the CSEE, 2018, 38(7): 2082-2094, 2223. [16] 伍文华, 周乐明, 陈燕东, 等. 序阻抗视角下虚拟同步发电机与传统并网逆变器的稳定性对比分析[J]. 中国电机工程学报, 2019, 39(5): 1411-1421. Wu Wenhua, Zhou Leming, Chen Yandong, et al.Stability comparison and analysis between the virtual synchronous generator and the traditional grid- connected inverter in the view of sequence impe- dance[J]. Proceedings of the CSEE, 2019, 39(5): 1411-1421. [17] Sun Jian.Impedance-based stability criterion for grid-connected inverters[J]. IEEE Transactions on Power Electronics, 2011, 26(11): 3075-3078. [18] Cespedes M, Sun Jian.Impedance modeling and analysis of grid-connected voltage-source con- verters[J]. IEEE Transactions on Power Electronics, 2014, 29(3): 1254-1261. [19] 王利超, 于永军, 张明远, 等. 直驱风电机组阻抗建模及次同步振荡影响因素分析[J]. 电力工程技术, 2020, 39(1): 170-177. Wang Lichao, Yu Yongjun, Zhang Mingyuan, et al.Impedance model and analysis of subsynchronous oscillation influence factors for grid-connected full-converter wind turbines[J]. Electric Power Engineering Technology, 2020, 39(1): 170-177. [20] 桑顺, 张琛, 蔡旭, 等. 计及内、外部交互模态的电压源型风电场-电网稳定性量化分析[J]. 高电压技术, 2022, 48(7): 2840-2853. Sang Shun, Zhang Chen, Cai Xu, et al.Quantitative analysis of the voltage-source-type wind farm-weak grid’s stability considering the internal and external interaction modes[J]. High Voltage Engineering, 2022, 48(7): 2840-2853. [21] 胡宇飞, 田震, 查晓明, 等. 构网型与跟网型变流器主导孤岛微网阻抗稳定性分析及提升策略[J]. 电力系统自动化, 2022, 46(24): 121-131. Hu Yufei, Tian Zhen, Zha Xiaoming, et al.Impedance stability analysis and promotion strategy of islanded microgrid dominated by grid-connected and grid- following converters[J]. Automation of Electric Power Systems, 2022, 46(24): 121-131. [22] 伍文华, 陈燕东, 周乐明, 等. 虚拟同步发电机接入弱电网的序阻抗建模与稳定性分析[J]. 中国电机工程学报, 2019, 39(6): 1560-1571, 1853. Wu Wenhua, Chen Yandong, Zhou Leming, et al.Sequence impedance modeling and stability analysis for virtual synchronous generator connected to the weak grid[J]. Proceedings of the CSEE, 2019, 39(6): 1560-1571, 1853. [23] 杨伊茜, 陈杰, 万雨朦, 等. 电网电压前馈控制VSG的阻抗建模与并网稳定性分析[J]. 电力工程技术, 2021, 40(6): 52-61. Yang Yiqian, Chen Jie, Wan Yumeng, et al.The impedance modelling and stability analysis of VSG with grid voltage feedforward control[J]. Electric Power Engineering Technology, 2021, 40(6): 52-61. [24] 谢小荣, 刘华坤. 风电并网系统次/超同步振荡的分析与控制[M]. 北京: 科学出版社, 2022. Xie xiaorong, Liu Huakun. Analysis and control of sub/ultra synchronous oscillations in wind power grid connected systems[M]. Beijing: Science Press, 2022. [25] Zhang Chen, Cai Xu, Rygg A, et al.Sequence domain SISO equivalent models of a grid-tied voltage source converter system for small-signal stability analysis[J]. IEEE Transactions on Energy Conversion, 2018, 33(2): 741-749. [26] 杜燕, 赵韩广, 杨向真, 等. 考虑频率耦合效应的虚拟同步发电机序阻抗建模[J]. 电源学报, 2020, 18(6): 42-49. Du Yan, Zhao Hanguang, Yang Xiangzhen, et al.Sequence impedance modeling of virtual synchronous generator considering frequency coupling effect[J]. Journal of Power Supply, 2020, 18(6): 42-49. [27] 曾锋, 李崇涛, 舒进, 等. 基于阻抗法的稳定性判据论证及其适用性分析[J]. 电力系统自动化, 2021, 45(8): 146-154. Zeng Feng, Li Chongtao, Shu Jin, et al.Demon- stration of stability criterion based on impedance method and analysis on its applicability[J]. Auto- mation of Electric Power Systems, 2021, 45(8): 146-154. [28] 张海华, 李中烜, 沈鑫, 等. 基于序阻抗模型的直驱风机并网系统RLC稳定判据研究[J]. 湖北电力, 2019, 43(6): 78-85. Zhang Haihua, Li Zhongxuan, Shen Xin, et al.Research on RLC stability criterion of sequence- impedance-model-based direct driven wind-turbine generator grid-connected system[J]. Hubei Electric Power, 2019, 43(6): 78-85. [29] 孙焜, 姚伟, 文劲宇. 双馈风电场经柔直并网系统次同步振荡机理及特性分析[J]. 中国电机工程学报, 2018, 38(22): 6520-6533. Sun Kun, Yao Wei, Wen Jinyu.Mechanism and characteristics analysis of subsynchronous oscillation caused by DFIG-based wind farm integrated into grid through VSC-HVDC system[J]. Proceedings of the CSEE, 2018, 38(22): 6520-6533. [30] 张明远, 肖仕武, 田恬, 等. 基于阻抗灵敏度的直驱风电场并网次同步振荡影响因素及参数调整分析[J]. 电网技术, 2018, 42(9): 2768-2777. Zhang Mingyuan, Xiao Shiwu, Tian Tian, et al.Analysis of SSO influencing factors and parameter adjustment for grid-connected full-converter wind farm based on impedance sensitivity[J]. Power System Technology, 2018, 42(9): 2768-2777.
2025, Vol. 40 
