郑乐,梁以宁
ZHENG Le,LIANG Yining

• 1:新能源电力系统国家重点实验室(华北电力大学)

摘要(Abstract)：

在众多电力系统振荡分析方法中，阻抗分析法和转矩分析法受到广泛关注。两种方法均从端口角度描述系统特性，因此振荡问题的端口分析方法具有重要研究价值。从端口角度分析，阻抗分析法和转矩分析法分别使用阻抗端口和转矩系数端口描述系统，因此重点对两种端口的研究现状做出综述。首先研究了变流器并网常用的阻抗端口，分析了不同类型阻抗端口的特点，总结阻抗端口在变流器系统稳定性分析中的优点；其次研究同步电机并网常用的转矩系数端口，重点从物理意义上阐释转矩系数端口的特点，指出了其在工程应用上的优越性；最后介绍了两种端口统一性相关理论，指出端口在不同场景下表现出不同的特点，为端口分析方法的选择提供一定参考。
Among the various oscillation analysis methods in power systems, impedance-based and torque-based analysis methods have garnered significant attention. Both approaches describe system characteristics from a portbased perspective, making port-based oscillation analysis methods a valuable research focus. From this perspective, impedance-based and torque-based methods characterize systems using impedance ports and torque coefficient ports, respectively. This paper presents a comprehensive review of the current state of research on these two ports.First, the commonly used impedance port for grid-connected converters is examined, analyzing the characteristics of different types of impedance ports and summarizing their advantages in stability analysis of converter-based systems. Second, the torque coefficient port commonly used for grid-connected synchronous motors is studied, with an emphasis on explaining its physical significance and highlighting its superiority in engineering applications. Lastly, unified theories related to the two ports are introduced, identifying how ports exhibit distinct features in different scenarios, thus offering insights into the selection of port-based analysis methods.

关键词(KeyWords)： 小扰动稳定性分析;端口选择;阻抗分析法;转矩分析法
small-signal stability analysis;port selection;impedance-based analysis method;torque-based analysis method

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金（52307095）

作者(Author): 郑乐,梁以宁
ZHENG Le,LIANG Yining

DOI: 10.19585/j.zjdl.202501001

参考文献(References)：

• [1]张智刚，康重庆.碳中和目标下构建新型电力系统的挑战与展望[J].中国电机工程学报，2022,42(8):2806-2819.ZHANG Zhigang,KANG Chongqing. Challenges and prospects for constructing the new-type power system towards a carbon neutrality future[J]. Proceedings of the CSEE,2022,42(8):2806-2819.
• [2]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)[2024-07-01].http：//www.nea.gov.cn/2024-01/26/c_1310762246.htm.
• [3]李军军，吴政球，谭勋琼，等.风力发电及其技术发展综述[J].电力建设，2011,32(8):64-72.LI Junjun,WU Zhengqiu,TAN Xunqiong,et al. Review of wind power generation and relative technology development[J].Electric Power Construction,2011,32(8):64-72.
• [4]陈炜，艾欣，吴涛，等.光伏并网发电系统对电网的影响研究综述[J].电力自动化设备，2013,33(2):26-32.CHEN Wei,AI Xin,WU Tao,et al. Influence of gridconnected photovoltaic system on power network[J].Electric Power Automation Equipment,2013,33(2):26-32.
• [5]李海盼，年珩，胡彬，等.风电并网系统宽频振荡分析与抑制方法综述[J].新型电力系统，2023(3):237-255.LI Haipan,NIAN Heng,HU Bin,et al.Review of analysis and suppression methods for wide-band oscillation in wind power gridconnected systems[J].New Type Power Systems,2023(3):237-255.
• [6]马宁宁，谢小荣，贺静波，等.高比例新能源和电力电子设备电力系统的宽频振荡研究综述[J].中国电机工程学报，2020,40(15):4720-4732.MA Ningning,XIE Xiaorong,HE Jingbo,et al.Review of wide-band oscillation in renewable and power electronics highly integrated power systems[J]. Proceedings of the CSEE,2020,40(15):4720-4732.
• [7] KUNDUR P.Power system stability and control[M].中国电力出版社，1994:504-534.
• [8] ZHOU J Z,DING H,FAN S T,et al. Impact of shortcircuit ratio and phase-locked-loop parameters on the smallsignal behavior of a VSC-HVDC converter[J]. IEEE Transactions on Power Delivery,2014,29(5):2287-2296.
• [9] HUANG Y H,YUAN X M,HU J B,et al.Modeling of VSC connected to weak grid for stability analysis of DClink voltage control[J].IEEE Journal of Emerging and Selected Topics in Power Electronics,2015,3(4):1193-1204.
• [10] GU Y J,GREEN T C.Power system stability with a high penetration of inverter-based resources[J].Proceedings of the IEEE,2023,111(7):832-853.
• [11] SUN J. Impedance-based stability criterion for gridconnected inverters[J].IEEE Transactions on Power Electronics,2011,26(11):3075-3078.
• [12]王波，卢继平，龚建原，等.含双馈机组转子侧附加控制的风电场次同步振荡抑制方法[J].电网技术，2013,37(9):2580-2584.WANG Bo,LU Jiping,GONG Jianyuan,et al.A method to suppress sub-synchronous oscillation of wind farm composed of doubly fed induction generators with additional rotor side control[J].Power System Technology,2013,37(9):2580-2584.
• [13]王一珺，杜文娟，陈晨，等.基于改进复转矩系数法的风电场并网引发电力系统次同步振荡研究[J].电工技术学报，2020,35(15):3258-3269.WANG Yijun,DU Wenjuan,CHEN Chen,et al.Study on sub-synchronous oscillations of power systems caused by grid-connected wind farms based on the improved complex torque coefficients method[J].Transactions of China Electrotechnical Society,2020,35(15):3258-3269.
• [14]陈新，王赟程，龚春英，等.采用阻抗分析方法的并网变流器稳定性研究综述[J].中国电机工程学报，2018,38(7):2082-2094.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.
• [15] MIDDLEBROOK R. Input filter considerations in design and application of switching regulators[C]//PESC'76,IEEE Power Electronics Specialists,Conference.1976.
• [16] SUN J. Small-signal methods for AC distributed power systems-a review[J].IEEE Transactions on Power Electronics,2009,24(11):2545-2554.
• [17] FANG Q,XING F C,JIANG Z,et al.Equivalence analysis of different sequence impedance modeling methods[C]//2023 IEEE 6th International Electrical and Energy Conference(CIEEC). May 12-14,2023,Hefei,China.IEEE,2023:3800-3805.
• [18] CESPEDES M,SUN J.Impedance modeling and analysis of grid-connected voltage-source converters[J]. IEEE Transactions on Power Electronics,2014,29(3):1254-1261.
• [19]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.WANG Yuncheng,CHEN Xin,CHEN Jie,et al.Analysis of positive-sequence and negative-sequence impedance modeling of three-phase LCL-type grid-connected inverters based on harmonic linearization[J].Proceedings of the CSEE,2016,36(21):5890-5898.
• [20]吕敬，蔡旭，张占奎，等.海上风电场经MMC-HVDC并网的阻抗建模及稳定性分析[J].中国电机工程学报，2016,36(14):3771-3780.LüJing,CAI Xu,ZHANG Zhankui,et al. Impedance modeling and stability analysis of MMC-based HVDC for offshore wind farms[J].Proceedings of the CSEE,2016,36(14):3771-3780.
• [21]杨洪雨.双馈异步发电机系统阻抗建模及稳定性分析[D].杭州：浙江大学，2016.YANG Hongyu. Impedance modeling and stability analysis of doubly-fed asynchronous generator system[D].Hangzhou:Zhejiang University,2016.
• [22]刘欣，郭志博，贾焦心，等.基于序阻抗的虚拟同步发电机并网稳定性分析及虚拟阻抗设计[J].电工技术学报，2023,38(15):4130-4146.LIU Xin,GUO Zhibo,JIA Jiaoxin,et al.Stability analysis and virtual impedance design of virtual synchronous machine based on sequence impedance[J]. Transactions of China Electrotechnical Society,2023,38(15):4130-4146.
• [23] CéSPEDES M,SUN J.Methods for stability analysis of unbalanced three-phase systems[C]//2012 IEEE Energy Conversion Congress and Exposition(ECCE).September15-20,2012,Raleigh,NC,USA.IEEE,2012:3090-3097.
• [24] WEN B,BOROYEVICH D,MATTAVELLI P,et al.Experimental verification of the Generalized Nyquist stability criterion for balanced three-phase ac systems in the presence of constant power loads[C]//2012 IEEE Energy Conversion Congress and Exposition(ECCE).September15-20,2012,Raleigh,NC,USA.IEEE,2012:3926-3933.
• [25]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,2016,40:76-83.
• [26]吴恒，阮新波，杨东升.弱电网条件下锁相环对LCL型并网逆变器稳定性的影响研究及锁相环参数设计[J].中国电机工程学报，2014,34(30):5259-5268.WU Heng,RUAN Xinbo,YANG Dongsheng. Research on the stability caused by phase-locked loop for LCL-type grid-connected inverter in weak grid condition[J].Proceedings of the CSEE,2014,34(30):5259-5268.
• [27] KAZEM BAKHSHIZADEH M, WANG X F,BLAABJERG F,et al.Couplings in phase domain impedance modeling of grid-connected converters[J]. IEEE Transactions on Power Electronics,2016,31(10):6792-6796.
• [28]刘威，谢小荣，黄金魁，等.并网变流器的频率耦合阻抗模型及其稳定性分析[J].电力系统自动化，2019,43(3):138-146.LIU Wei,XIE Xiaorong,HUANG Jinkui,et al.Frequencycoupled impedance model and stability analysis of gridconnected converter[J]. Automation of Electric Power Systems,2019,43(3):138-146.
• [29]年珩，徐韵扬，陈亮，等.并网逆变器频率耦合特性建模及系统稳定性分析[J].中国电机工程学报，2019,39(5):1421-1432.NIAN Heng,XU Yunyang,CHEN Liang,et al. Frequency coupling characteristic modeling of grid-connected inverter and system stability analysis[J]. Proceedings of the CSEE,2019,39(5):1421-1432.
• [30]邹小明，杜雄，王国宁，等.三相并网逆变器频率耦合机理分析及稳定性判定[J].电力系统自动化，2018,42(18):57-63.ZOU Xiaoming,DU Xiong,WANG Guoning,et al.Frequency coupling mechanism analysis and stability judgement for three-phase grid-connected inverter[J].Automation of Electric Power Systems,2018,42(18):57-63.
• [31]武相强，王赟程，陈新，等.考虑频率耦合效应的三相并网逆变器序阻抗模型及其交互稳定性研究[J].中国电机工程学报，2020,40(5):1605-1616.WU Xiangqiang,WANG Yuncheng,CHEN Xin,et al.Sequence impedance model and interaction stability research of three-phase grid-connected inverters with considering coupling effects[J]. Proceedings of the CSEE,2020,40(5):1605-1616.
• [32] BELKHAYAT M. Stability criteria for AC power systems with regulated loads[M].Purdue University,1997.
• [33] WEN B,BOROYEVICH D,BURGOS R,et al.Analysis of D-Q small-signal impedance of grid-tied inverters[J].IEEE Transactions on Power Electronics,2016,31(1):675-687.
• [34] SCHWEIZER M,KOLAR J W. Shifting input filter resonances-An intelligent converter behavior for maintaining system stability[C]//The 2010 International Power Electronics Conference-ECCE ASIA-June 21-24,2010.Sapporo,Japan.IEEE,2010:906-913.
• [35]谢小荣，刘华坤，贺静波，等.直驱风机风电场与交流电网相互作用引发次同步振荡的机理与特性分析[J].中国电机工程学报，2016,36(9):2366-2372.XIE Xiaorong,LIU Huakun,HE Jingbo,et al.Mechanism and characteristics of subsynchronous oscillation caused by the interaction between full-converter wind turbines and AC systems[J].Proceedings of the CSEE,2016,36(9):2366-2372.
• [36]曾志杰，肖华锋，高博，等.并网逆变器小信号建模简化方法与应用[J].中国电机工程学报，2020,40(21):7002-7011.ZENG Zhijie,XIAO Huafeng,GAO Bo,et al.Simplified small-signal modeling method of grid-connected inverters and its applications[J].Proceedings of the CSEE,2020,40(21):7002-7011.
• [37] FRANCIS G,BURGOS R,BOROYEVICH D,et al.An algorithm and implementation system for measuring impedance in the D-Q domain[C]//2011 IEEE Energy Conversion Congress and Exposition.September 17-22,2011.Phoenix,AZ,USA.IEEE,2011:3221-3228.
• [38]吴滨源，李建文，李永刚，等.基于知识和数据联合驱动的并网逆变器多工况阻抗获取方法[J].电力系统自动化，2022,46(6):83-91.WU Binyuan,LI Jianwen,LI Yonggang,et al.Combined data-knowledge-driven impedance acquisition method for grid-connected inverter under multiple operation conditions[J].Automation of Electric Power Systems,2022,46(6):83-91.
• [39]徐德鸿.电力电子系统建模及控制[M].北京：机械工业出版社，2006.
• [40] HARNEFORS L. Modeling of three-phase dynamic systems using complex transfer functions and transfer matrices[J].IEEE Transactions on Industrial Electronics,2007,54(4):2239-2248.
• [41] WANG X F,HARNEFORS L,BLAABJERG F.Unified impedance model of grid-connected voltage-source converters[J]. IEEE Transactions on Power Electronics,2018,33(2):1775-1787.
• [42]苏晨博，刘崇茹，王瑾媛，等.考虑频率耦合特性的DPMSG复数域阻抗建模及其特征分析[J].电力系统自动化，2024,48(10):118-128.SU Chenbo,LIU Chongru,WANG Jinyuan,et al.Impedance modeling of direct-drive permanent magnet synchronous generator in complex field and its feature analysis considering frequency coupling characteristics[J].Automation of Electric Power Systems,2024,48(10):118-128.
• [43] LI Y T,GU Y J,ZHU Y,et al.Impedance circuit model of grid-forming inverter:visualizing control algorithms as circuit elements[J].IEEE Transactions on Power Electronics,2021,36(3):3377-3395.
• [44]辛焕海，李子恒，董炜，等.三相变流器并网系统的广义阻抗及稳定判据[J].中国电机工程学报，2017,37(5):1277-1292.XIN Huanhai,LI Ziheng,DONG Wei,et al.Generalizedimpedance and stability criterion for grid-connected converters[J].Proceedings of the CSEE,2017,37(5):1277-1292.
• [45]赵永光，艾力西尔·亚尔买买提，汤波，等.串补电容对锁相环主导下变流器振荡问题的影响分析[J].电力自动化设备，2024,44(6):102-109.ZHAO Yongguang,YAERMAIMAITI Ailixier,TANG Bo,et al. Analysis of influence of series complement capacitor on converter oscillation dominated by phase locked loop[J].Electric Power Automation Equipment,2024,44(6):102-109.
• [46] GU Y J,LI Y T,ZHU Y,et al.Impedance-based wholesystem modeling for a composite grid via embedding of frame dynamics[J].IEEE Transactions on Power Systems,2021,36(1):336-345.
• [47] ZHU Y,GU Y J,LI Y T,et al.Participation analysis in impedance models:the grey-box approach for power system stability[J]. IEEE Transactions on Power Systems,2022,37(1):343-353.
• [48] ZHU Y,GU Y J,LI Y T,et al. Impedance-based rootcause analysis:comparative study of impedance models and calculation of eigenvalue sensitivity[J].IEEE Transactions on Power Systems,2023,38(2):1642-1654.
• [49]袁小明，程时杰，胡家兵.电力电子化电力系统多尺度电压功角动态稳定问题[J].中国电机工程学报，2016,36(19):5145-5154.YUAN Xiaoming,CHENG Shijie,HU Jiabing.Multi-time scale voltage and power angle dynamics in power electronics dominated large power systems[J].Proceedings of the CSEE,2016,36(19):5145-5154.
• [50] CHEN Q,BU S,CHUNG Y C.Small-signal stability criteria in power electronics-dominated power systems:a comparative review[J].Journal of Modern Power Systems and Clean Energy,2024,12(4):1003-1018.
• [51] MIAO L J,XIN J Z,ZHAO B H.Revisit nyquist-bode stability criteria for power electronic system with nonminimum phase system[C]//2019 IEEE 4th International Future Energy Electronics Conference(IFEEC).November 25-28,2019.Singapore,Singapore.IEEE,2019:1-6.
• [52] CANAY I. A novel approach to the torsional interaction and electrical damping of the synchronous machine part I:theory[J]. IEEE Transactions on Power Apparatus Systems,1982,101(10):3630-3638.
• [53]陈陈，杨煜.几种次同步振荡分析方法和工具的阐述[J].电网技术，1998,22(8):10-13.CHEN Chen,YANG Yu.Discussion of several analytical approaches and tools about subsynchronous resonance[J].Power System Technology,1998,22(8):10-13.
• [54]吕世荣，刘晓鹏，郭强，等.次同步谐振分析中复转矩系数与特征值之间的关系[J].电力系统自动化，1999,23(3):16-18.LYU Shirong,LIU Xiaopeng,GUO Qiang,et al.Relationship between complex torque coefficients and eigenvalues in subsynchronous resonance analysis[J]. Automation of Electric Power Systems,1999,23(3):16-18.
• [55]闵勇，陈磊，姜齐荣.电力系统稳定分析[M].北京：清华大学出版社，2016.
• [56]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].发电与空调，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.
• [57]徐政.复转矩系数法的适用性分析及其时域仿真实现[J].中国电机工程学报，2000,20(6):1-4.XU Zheng.The complex torque coefficient approach’s applicability analysis and its realization by time domain simulation[J].Proceedings of the CSEE,2000,20(6):1-4.
• [58]姜齐荣，陈湘，王天，等.多机系统复转矩系数分析及PSS参数计算[J].电力系统及其自动化学报，2010(1):20-25.JIANG Qirong,CHEN Xiang,WANG Tian,et al.Analysis of complex torque coefficient in multi-machines system and PSS parameters assignment[J]. Proceedings of the CSU-EPSA,2010(1):20-25.
• [59]高本锋.电力系统次同步振荡分析方法与抑制技术研究[D].北京：华北电力大学，2011.GAO Benfeng.Research on analysis method and suppression technology of power system sub-synchronous oscillation[D].Beijing:North China Electric Power University,2011.
• [60]马燕峰，程有深，赵书强，等.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/OL].电工技术学报，1-16[2024-07-01]. https：//doi. org/10.19595/j. cnki. 1000-6753.tces.240366.MA Yanfeng,CHENG Youshen,ZHAO Shuqiang,et al.Mechanism analysis of multi-mode SSR of thermal power unit caused by doubly fed wind farm integration[J/OL].Transactions of China Electrotechnical Society,1-16[2024-07-01]. https：//doi. org/10.19595/j. cnki. 1000-6753.tces.240366.
• [61]周长春，徐政.由直流输电引起的次同步振荡的阻尼特性分析[J].中国电机工程学报，2003,23(10):6-10.ZHOU Changchun,XU Zheng.Damping analysis of subsynchronous oscillation caused by hvdc[J].Proceedings of the CSEE,2003,23(10):6-10.
• [62]徐坤，赵成勇，高本锋.VSC-HVDC的次同步阻尼特性研究[J].电力系统保护与控制，2012,40(2):1-5.XU Kun,ZHAO Chengyong,GAO Benfeng. Study on sub-synchronous damping characteristic of VSC-HVDC[J].Power System Protection and Control,2012,40(2):1-5.
• [63]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.
• [64]董晓亮，谢小荣，韩英铎，等.基于定转子转矩分析法的双馈风机次同步谐振机理研究[J].中国电机工程学报，2015,35(19):4861-4869.DONG Xiaoliang,XIE Xiaorong,HAN Yingduo,et al.Mechanism study of DFIG-related SSR based on separate stator and rotor torque analysis[J]. Proceedings of the CSEE,2015,35(19):4861-4869.
• [65]李长宇，刘博昊，肖仕武，等.基于功率外环附加阻尼控制的柔性直流抑制送端火电机组次同步振荡研究[J].电力科学与技术学报，2024,39(2):20-27.LI Changyu,LIU Bohao,XIAO Shiwu,et al.Research on subsynchronous oscillation suppression strategy of flexible HVDC with thermal power units based on external loop damping control[J].Journal of Electric Power Science and Technology,2024,39(2):20-27.
• [66]王旭斌，杜文娟，王海风.弱连接条件下并网VSC系统稳定性分析研究综述[J].中国电机工程学报，2018,38(6):1593-1604.WANG Xubin,DU Wenjuan,WANG Haifeng. Stability analysis of grid-tied VSC systems under weak connection conditions[J]. Proceedings of the CSEE,2018,38(6):1593-1604.
• [67]宫泽旭，艾力西尔·亚尔买买提，辛焕海，等.新能源电力系统并网设备小扰动稳定分析（一）：机理模型与稳定判据适用性[J].中国电机工程学报，2022,42(12):4405-4418.GONG Zexu,YAERMAIMAITI Ailixier,XIN Huanhai,et al. Small signal stability analysis of equipment in renewable energy power system(partⅠ)：mechanism model and adaptation of stability criterion[J].Proceedings of the CSEE,2022,42(12):4405-4418.
• [68] YUAN H,YUAN X M,HU J B. Modeling of gridconnected VSCs for power system small-signal stability analysis in DC-link voltage control timescale[J]. IEEE Transactions on Power Systems,2017,32(5):3981-3991.
• [69] HU J B,HU Q,WANG B,et al.Small signal instability of PLL-synchronized type-4 wind turbines connected to highimpedance AC grid during LVRT[J].IEEE Transactions on Energy Conversion,2016,31(4):1676-1687.
• [70] WU X F,DU Z C,LI Y J,et al.Stability analysis of gridconnected VSC dominated by PLL using electrical torque method[J]. IEEE Transactions on Energy Conversion,2022,37(3):1864-1874.
• [71] ZHAO B Y,CHEN L,MIN Y,et al.Corrected complex torque coefficient method for synchronization stability analysis of grid-connected VSC[J]. IET Renewable Power Generation,2024,18(3):412-425.
• [72] YU P,TIAN Z,ZHA X M,et al.Impact analysis of fast dynamics on stability of grid-tied inverter based on oscillator model and damping torque analysis[J].IEEE Transactions on Power Systems,2022,37(3):1881-1892.
• [73] QU Z S,PENG J C H,YANG H,et al. Modeling and analysis of inner controls effects on damping and synchronizing torque components in VSG-controlled converter[J].IEEE Transactions on Energy Conversion,2021,36(1):488-499.
• [74] CHEN X T,WU C,WANG Y.An improved virtual impedance method for single-loop controlled grid-forming inverters to suppress low-frequency oscillations[C]//2024IEEE 10th International Power Electronics and Motion Control Conference(IPEMC2024-ECCE Asia).May 17-20,2024,Chengdu,China.IEEE,2024:2395-2400.
• [75] LI Y T,GU Y J,GREEN T C.Mapping of dynamics between mechanical and electrical ports in SG-IBR composite grids[J].IEEE Transactions on Power Systems,2022,37(5):3423-3433.