Abstract：With the implementation of the "carbon peaking and carbon neutrality goals", the wind-thermal bundled system has become the main form of wind power transmission in recent years. However, when the doubly-fed wind farm is integrated into power system with series compensated transmission lines, it may have an impact on the subsynchronous resonance (SSR) of the thermal power unit and threaten the safe and stable operation of the system. Therefore, the oscillation problem cannot be ignored. The influence of sub-synchronous control interaction (SSCI) caused by doubly-fed wind farms on SSR of thermal power units is not clear. Firstly, the 'modular' modeling of each component is carried out for the doubly-fed wind farm and the thermal power unit bundled series compensated transmission system. By extending the complex frequency domain model of the thermal power unit to the doubly fed induction generator (DFIG), a complex torque coefficient method with decentralized elimination of variables suitable for the system with doubly-fed wind farm is put forward. Secondly, the complex torque coefficients of the thermal power unit and DFIG in classical example are obtained by using the proposed method. The mechanism of multi-mode SSR caused by the system is explained from the perspective of damping characteristics, and the SSR mechanism is verified by time-domain simulation. Then, the conclusions and methods are further verified by the actual system examples in North China. Finally, the influence of dominant oscillation factors including series compensation degree, SSCI, series compensation transmission line resistance and wind farm grid-connected capacity on SSR is analyzed. The mechanism analysis of SSR generation in the system shows that, after the system is subjected to small disturbances, if the electrical resonance frequency caused by series compensation is close to the SSR modal frequency, the electrical damping of the thermal power unit will show a large negative value, resulting in SSR instability. At the same time, when the system has a weak damping SSR mode, the generated small SSR component will enter the control link of the DFIG through the line. If the DFIG shows a large negative damping in this mode, it will help to increase the subsynchronous component current corresponding to the weak damping mode, and then stimulate each other with the shaft of the thermal power unit, resulting in the aggravation of the SSR component in this mode, thus causing SSR instability. The main conclusions of this paper are as follows: (1) Compared with the traditional complex torque coefficient method, the proposed method can avoid the dimension disaster problem to a certain extent, realize the modularization of each component, and is easy to model and versatile. Compared with the time domain simulation method, it can provide more oscillation information of the system, explain the oscillation mechanism and characteristics, and calculate quickly. It is suitable for multi-machine systems. (2) The inappropriate series compensation degree is the dominant factor causing SSR instability of the system, and different series compensation degrees may lead to different modes of SSR. At the same time, DFIG grid connection may introduce SSCI. If the DFIG presents a large negative damping in a SSR weak damping mode, it will help to increase the subsynchronous component current of the mode, and then stimulate each other with the shaft of the thermal power unit, causing new SSR mode instability. When the two act on different modes, it may lead to multi-mode SSR instability in the system. (3) The series compensation degree has a great influence on the damping characteristics. Within a certain range of series compensation degree, reducing the series compensation degree is beneficial to the stability of SSR. When the resistance of the series compensated transmission line changes, the change trend of different mode damping is different. Selecting a reasonable series compensated transmission line resistance is beneficial to reduce the risk of SSR. With the increase of the capacity of the doubly-fed wind farm, the damping of the thermal power unit increases and the stability of the SSR increases.
马燕峰, 程有深, 赵书强, 赵志冲, 王翌静. 双馈风电场并网引起火电机组多模态次同步谐振机理分析[J]. 电工技术学报, 2025, 40(5): 1395-1410.
Ma Yanfeng, Cheng Youshen, Zhao Shuqiang, Zhao Zhichong, Wang Yijing. Mechanism Analysis of Multi-Mode SSR of Thermal Power Unit Caused by Doubly Fed Wind Farm Integration. Transactions of China Electrotechnical Society, 2025, 40(5): 1395-1410.
[1] 国家能源局. 国家能源局发布2023年全国电力工业统计数据[EB/OL]. 2024-01-26[2023-02-03]. http://www.nea.gov.cn/2024-01/26/c_1310762246.htm. [2] 李明节, 于钊, 许涛, 等. 新能源并网系统引发的复杂振荡问题及其对策研究[J]. 电网技术, 2017, 41(4): 1035-1042. Li Mingjie, Yu Zhao, Xu Tao, et al.Study of complex oscillation caused by renewable energy integration and its solution[J]. Power System Technology, 2017, 41(4): 1035-1042. [3] 谢小荣, 刘华坤, 贺静波, 等. 电力系统新型振荡问题浅析[J]. 中国电机工程学报, 2018, 38(10): 2821-2828, 3133. Xie Xiaorong, Liu Huakun, He Jingbo, et al.On new oscillation issues of power systems[J]. Proceedings of the CSEE, 2018, 38(10): 2821-2828, 3133. [4] Shair J, Xie Xiaorong, Wang Luping, et al.Overview of emerging subsynchronous oscillations in practical wind power systems[J]. Renewable and Sustainable Energy Reviews, 2019, 99: 159-168. [5] 郑泽天, 沈沉, 严鋆, 等. 直驱风电场多电压源型变流器控制耦合引发振荡的机理分析[J]. 电力系统自动化, 2023, 47(17): 14-26. Zheng Zetian, Shen Chen, Yan Jun, et al.Mechanism analysis of oscillations induced by control coupling of voltage source converters in wind farms with direct-driven turbines[J]. Automation of Electric Power Systems, 2023, 47(17): 14-26. [6] 郑少明, 刘一民, 董鹏, 等. 张北工程风电柔直汇集系统次、超同步振荡分析[J]. 全球能源互联网, 2023, 6(6): 608-617. Zheng Shaoming, Liu Yimin, Dong Peng, et al.Analysis of sub/super-synchronous oscillation between wind farm and MMC in Zhangbei Project[J]. Journal of Global Energy Interconnection, 2023, 6(6): 608-617. [7] 吴杨. 风火打捆经串补外送系统次同步振荡分析与抑制[D]. 北京: 华北电力大学, 2019. Wu Yang.Analysis and Suppression of Subsynchronous Oscillation in Wind-Fire Bundling System with Series Compensation[D]. Beijing: North China Electric Power University, 2019. [8] 赵阳. 含双馈风电电力系统次同步振荡机理分析及抑制策略研究[D]. 重庆: 重庆大学, 2021. Zhao Yang.Analysis of sub-synchronous oscillation mechanism and research on suppression strategies of power system with dfig-based wind power generation[D]. Chongqing: Chongqing University, 2021. [9] 赵书强, 李忍, 高本锋, 等. 双馈风电机组经串补并网的振荡模式分析[J]. 高电压技术, 2016, 42(10): 3263-3273. Zhao Shuqiang, Li Ren, Gao Benfeng, et al.Modal analysis of doubly-fed induction generator integrated to compensated grid[J]. High Voltage Engineering, 2016, 42(10): 3263-3273. [10] 杜程茂, 杜雄, 苏婧媛, 等. 定子电流控制的双馈风机导纳建模与次同步振荡风险分析[J]. 电力系统自动化, 2023, 47(13): 159-167. Du Chengmao, Du Xiong, Su Jingyuan, et al.Admittance modeling and subsynchronous oscillation risk analysis of DFIG-based wind turbine with stator current control[J]. Automation of Electric Power Systems, 2023, 47(13): 159-167. [11] 李光辉, 王伟胜, 张兴, 等. 双馈风电场并网次/超同步振荡建模与机理分析(一):考虑功率外环的阻抗建模[J]. 中国电机工程学报, 2022, 42(7): 2438-2449. Li Guanghui, Wang Weisheng, Zhang Xing, et al.Modeling and suppression method of Sub/Super-synchronous oscillation of grid-connected dfig wind farms (part Ⅰ): sequence impedance modeling and analysis of dfig wind turbines considering power loop[J]. Proceedings of the CSEE, 2022, 42(7): 2438-2449. [12] 李光辉, 王伟胜, 张兴, 等. 双馈风电场并网次/超同步振荡建模与机理分析(二):阻抗特性与振荡机理分析[J]. 中国电机工程学报, 2022, 42(10): 3614-3627. Li Guanghui, Wang Weisheng, Zhang Xing, et al.Modeling and mechanism analysis of Sub/Super-synchronous oscillation of grid-connected dfig wind farms (part Ⅱ): analysis of impedance characteristic and oscillation mechanism[J]. Proceedings of the CSEE, 2022, 42(10): 3614-3627. [13] 季一宁, 王海风. 包含串补的并网直驱风电场振荡稳定性及可行域分析[J]. 电工技术学报, 2024, 39(3): 686-698. Ji Yining, Wang Haifeng.Analysis of oscillation stability and feasible region of parameters in grid-connected direct-drive wind farm with series compensation[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 686-698. [14] 吴翔宇, 张晓红, 尚子轩, 等. 基于频域阻抗网络建模分析的交直流微电网振荡问题研究[J]. 电工技术学报, 2024, 39(8): 2294-2310. Wu Xiangyu, Zhang Xiaohong, Shang Zixuan, et al.Research on the oscillation problem of AC-DC microgrids based on frequency domain impedance network modeling and analysis[J]. Transactions of China Electrotechnical Society, 2024, 39(8): 2294-2310. [15] 刘芳, 刘威, 汪浩东, 等. 高比例新能源电力系统振荡机理及其分析方法研究综述[J]. 高电压技术, 2022, 48(1): 95-114. Liu Fang, Liu Wei, Wang Haodong, et al.Review on oscillation mechanism and analysis methods of high proportion renewable energy power system[J]. High Voltage Engineering, 2022, 48(1): 95-114. [16] 高本锋, 邓鹏程, 梁纪峰, 等. 光伏电站与弱交流电网间次同步交互作用路径及阻尼特性分析[J]. 电工技术学报, 2023, 38(24): 6679-6694. Gao Benfeng, Deng Pengcheng, Liang Jifeng, et al.Analysis of path and damping characteristics of subsynchronous interaction between photovoltaic plant and weak AC grid[J]. Transactions of China Electrotechnical Society, 2023, 38(24): 6679-6694. [17] 高本锋, 王义, 范辉, 等. 基于阻尼路径的新能源经LCC-HVDC送出系统次同步交互作用分析方法[J]. 电工技术学报, 2023, 38(20): 5572-5589. Gao Benfeng, Wang Yi, Fan Hui, et al.A sub-synchronous interaction analysis method of renewable energy generations integrated with LCC-HVDC system based on damping path[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5572-5589. [18] 王一珺, 杜文娟, 王海风. 基于改进复转矩系数法的多风电场接入引发多机电力系统次同步振荡机理分析[J]. 中国电机工程学报, 2021, 41(7): 2383-2395. Wang Yijun, Du Wenjuan, Wang Haifeng.Analysis of subsynchronous oscillation in multi-machine power system caused by the integration of multiple wind farms based on improved complex torque coefficient method[J]. Proceedings of the CSEE, 2021, 41(7): 2383-2395. [19] 郭春义, 刘晓颖, 吕乃航, 等. 风火打捆传统直流外送系统中控制环节对轴系-控制交互模式的影响机理研究[J]. 中国电机工程学报, 2024, 44(9): 3463-3476. Guo Chunyi, Lü Xiaoying, Lyu Naihang, et al.Research on the influence mechanism of control loops on shaft-control interactive mode for wind-thermal-bundled power transmission through LCC-HVDC system[J]. Proceedings of the CSEE, 2024, 44(9): 3463-3476. [20] 高本锋, 李忍, 杨大业, 等. 双馈风电机组次同步振荡阻尼特性与抑制策略[J]. 电力自动化设备, 2015, 35(12): 11-20. Gao Benfeng, Li Ren, Yang Daye, et al.Damping characteristics and countermeasure of DFIG sub-synchronous oscillation[J]. Electric Power Automation Equipment, 2015, 35(12): 11-20. [21] Guo Chunlin, Zhou Shuangya, Xu Kun, et al.The study of complex torque coefficient approach based on benchmark[C]//2011 International Conference on Electrical and Control Engineering, Yichang, China, 2011: 1374-1379. [22] 朱鑫要, 孙海顺, 文劲宇, 等. 基于CPCM的复转矩系数法在复杂电力系统SSR问题研究中的应用[J]. 中国电机工程学报, 2013, 33(4): 77-84, 11. Zhu Xinyao, Sun Haishun, Wen Jinyu, et al.Application of complex torque coefficient basing on CPCM to SSR study of complex power system[J]. Proceedings of the CSEE, 2013, 33(4): 77-84, 11. [23] Zhu Xinyao, Sun Haishun, Wen Jinyu, et al.A practical method to construct network state equations in multi-machine system SSR study[J]. Electric Power Systems Research, 2014, 107: 51-58. [24] 王冠青. 电力系统次同步谐振的分析方法和抑制措施研究[D]. 武汉: 华中科技大学, 2013. Wang Guanqing.Research on methods of analysis for subsynchronous resonance of power systems and its countermeatures[D]. Wuhan: Huazhong University of Science and Technology, 2013. [25] 毛俞杰, 孙海顺, 韩应生, 等. 采用STATCOM抑制多机系统次同步振荡的理论与仿真[J]. 电力系统保护与控制, 2022, 50(6): 23-32. Mao Yujie, Sun Haishun, Han Yingsheng, et al.Theory and simulation of STATCOM for damping subsynchronous oscillation of a multi-machine system[J]. Power System Protection and Control, 2022, 50(6): 23-32. [26] 毛俞杰. 火电机组次同步振荡阻尼特性分析及大规模风电场接入对其影响研究[D]. 武汉: 华中科技大学, 2022. Mao Yujie.Analysis on damping characteristics of subsynchronous oscillation of thermal power unit and study on the influence of large-scale wind farms connected to the grid on it[D]. Wuhan: Huazhong University of Science and Technology, 2022. [27] IEEE SSR Working Group. First benchmark model for computer simulation of subsynchronous resonance[J]. IEEE Transactions on Power Apparatus and Systems, 1977, 96(5): 1565-1572. [28] 高本锋, 刘培鑫, 刘王锋, 等. 直驱风电场并网对火电机组次同步谐振影响[J]. 电工技术学报, 2024, 39(11): 3308-3322. Gao Benfeng, Liu Peixin, Liu Wangfeng, et al.Influence of grid connected direct drive wind farm on subsynchronous resonance of thermal power units[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3308-3322. [29] 倪以信, 陈寿孙, 张宝霖. 动态电力系统的理论和分析[M]. 北京: 清华大学出版社, 2002. [30] 程时杰, 曹一家, 江全元. 电力系统次同步振荡的理论与方法[M]. 北京: 科学出版社, 2009. [31] 王毅, 朱晓荣, 赵书强. 风力发电系统的建模与仿真[M]. 北京: 中国水利水电出版社, 2015. [32] Canay I M. A novel approach to the torsional interaction and electrical damping of the synchronous machine. part I: theory[J]. IEEE Power Engineering Review, 1982, PER-2(10): 24. [33] Canay I M. A novel approach to the torsional interaction and electrical damping of the synchronous machine. part I: theory[J]. IEEE Power Engineering Review, 1982, PER-2(10): 24. [34] 高本锋, 刘晋, 李忍, 等. 风电机组的次同步控制相互作用研究综述[J]. 电工技术学报, 2015, 30(16): 154-161. Gao Benfeng, Liu Jin, Li Ren, et al.Studies of sub-synchronous control interaction in wind turbine generators[J]. Transactions of China Electrotechnical Society, 2015, 30(16): 154-161. [35] 王一珺, 杜文娟, 陈晨, 等. 基于复转矩系数法研究并网双馈风电场引发电力系统次同步振荡问题综述[J]. 发电技术, 2018, 39(3): 195-203. Wang Yijun, Du Wenjuan, Chen Chen, et al.A review of investigations on sub-synchronous oscillations in power systems caused by DFIG wind farms based on the complex torque coefficients method[J]. Power Generation Technology, 2018, 39(3): 195-203. [36] 杨博闻, 占颖, 谢小荣, 等. 双馈风电场接入串补输电系统引发次同步谐振的研究模型[J]. 电力系统保护与控制, 2020, 48(8): 120-126. Yang Bowen, Zhan Ying, Xie Xiaorong, et al.A study model for subsynchronous resonance in DFIG based wind farms connected to a series-compensated power system[J]. Power System Protection and Control, 2020, 48(8): 120-126.
2025, Vol. 40 
