竺明哲,王宇航,葛乐
ZHU Mingzhe,WANG Yuhang,GE Le

• 1:南京工程学院电力工程学院、沈国荣学院

摘要(Abstract)：

并网逆变器为新能源发电核心装备，而多逆变器并网系统存在潜在的谐振风险。为此，对近年来该领域研究成果进行了梳理并对未来发展趋势进行展望。分析了影响多逆变器谐振的因素，包括电网阻抗、非线性特性、逆变器参数差异等方面。在建模方法层面，重点探讨诺顿等效模型、特征值分析模型以及谐波状态空间模型的建模方法及其优缺点与适用场景。阐述了有源阻尼法、阻抗重塑和有源阻尼器等主动谐振抑制策略。最后，围绕所提及的3个方面，对其未来的发展趋势和核心挑战进行了展望。本文可为多逆变器并网系统谐振问题的研究提供参考，助力高比例可再生能源接入下的电网稳定运行。
Grid-connected inverters are the core equipment of renewable energy generation, while multi-inverter grid-connected systems are subject to potential resonance risks. To address this issue, recent research progress in this field is systematically reviewed, and future development trends are discussed. The factors influencing resonance in multi-inverter systems are analyzed, including grid impedance, system nonlinearities, and parameter mismatches among inverters. From the perspective of modeling methods, Norton equivalent models, eigenvalue-based analysis models, and harmonic state-space models are examined in detail, with emphasis on their respective advantages, limitations, and applicable scenarios. Active resonance suppression strategies, such as active damping methods, impedance reshaping, and active dampers, are then elaborated. Finally, future research directions and key challenges are outlined around the three aforementioned aspects. This review provides a useful reference for research on resonance in multi-inverter grid-connected systems and contributes to the stable operation of power grids with high penetration of renewable energy.

关键词(KeyWords)： 多逆变器系统;谐振稳定性;谐振抑制策略
multi-inverter systems;resonance stability;resonance suppression strategy

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(52477101)

作者(Author): 竺明哲,王宇航,葛乐
ZHU Mingzhe,WANG Yuhang,GE Le

DOI: 10.19585/j.zjdl.202603010

参考文献(References)：

• [1]张兴，李明，郭梓暄，等.新能源并网逆变器控制策略研究综述与展望[J].全球能源互联网，2021,4(5):506-515.ZHANG Xing,LI Ming,GUO Zixuan,et al.Review and perspectives on control strategies for renewable energy grid-connected inverters[J].Journal of Global Energy Interconnection,2021,4(5):506-515.
• [2]别朝红，王则凯，肖遥，等.双碳目标下新型电力系统发展展望[J].新型电力系统，2023,1(2):116-131.BIE Zhaohong,WANG Zekai,XIAO Yao,et al.Outlook on the development of new power system under dualcarbon target[J].New Type Power Systems,2023,1(2):116-131.
• [3]郑嘉龙，杨鸽，陈开宇，等.LCL型多逆变器并网系统谐振研究综述[J].电力系统保护与控制，2022,50(21):177-186.ZHENG Jialong,YANG Ge,CHEN Kaiyu,et al.An overview on resonance for a multiple LCL-type inverter gridconnected system[J].Power System Protection and Control,2022,50(21):177-186.
• [4]辛建波，舒展，赵诗萌，等.双馈-直驱混合风电场次同步振荡影响因素分析[J].电工电能新技术，2019,38(11):24-32.XIN Jianbo,SHU Zhan,ZHAO Shimeng,et al.Research on influencing factors of DFIG-PMSG hybrid wind farm sub-synchronous oscillations[J].Advanced Technology of Electrical Engineering and Energy,2019,38(11):24-32.
• [5]孙东阳，钱梓杰，曹骏，等.基于哈密顿模型的DFIG强迫型次同步振荡自适应抑制策略研究[J].中国电机工程学报，2025,45(8):3132-3147.SUN Dongyang,QIAN Zijie,CAO Jun,et al. Adaptive suppression strategy research of DFIG forced subsynchronous oscillation based on Hamiltonian model[J].Proceedings of the CSEE,2025,45(8):3132-3147.
• [6]郭琦，郭海平，黄立滨.电网电压前馈对柔性直流输电在弱电网下的稳定性影响[J].电力系统自动化，2018,42(14):139-144.GUO Qi,GUO Haiping,HUANG Libin. Effect of grid voltage feedforward on VSC-HVDC stability in weak power grid[J]. Automation of Electric Power Systems,2018,42(14):139-144.
• [7]张东辉，陈新，杨舒婷，等.含静止无功补偿装置的光伏电站高频谐振分析及抑制策略研究[J].中国电机工程学报，2023,43(24):9580-9594.ZHANG Donghui,CHEN Xin,YANG Shuting,et al.Analysis of high-frequency resonance and suppression strategy of photovoltaic power plant with static reactive power compensation device[J].Proceedings of the CSEE,2023,43(24):9580-9594.
• [8]WANG F,DUARTE J L,HENDRIX M A M,et al.Modeling and analysis of grid harmonic distortion impact of aggregated DG inverters[J]. IEEE Transactions on Power Electronics,2011,26(3):786-797.
• [9]曹芸凯，赵涛，朱爱华，等.计及电网和线路阻抗的并联逆变器谐振抑制方法[J].电力科学与技术学报，2022,37(2):188-196.CAO Yunkai,ZHAO Tao,ZHU Aihua,et al.Resonance suppression method for parallel inverters considering the grid and line impedance[J].Journal of Electric Power Science and Technology,2022,37(2):188-196.
• [10]CHEN W,ZHANG Y,TU Y M,et al. Active damping control for LCL filters with inverter-side current feedback only[J].IEEE Transactions on Power Electronics,2022,37(9):10065-10069.
• [11]杨林，曾江，黄仲龙.线性自抗扰技术在LCL逆变器并网电流控制及有源阻尼中的应用[J].电网技术，2019,43(4):1378-1386.YANG Lin,ZENG Jiang,HUANG Zhonglong. Application of linear active disturbance rejection technique in gridconnected current control and active damping of LCL type inverter[J]. Power System Technology,2019,43(4):1378-1386.
• [12]周雪松，郭帅朝，马幼婕，等.基于LADRC和准PR的三相LCL型光伏并网逆变器谐波谐振抑制策略[J].太阳能学报，2023,44(3):465-474.ZHOU Xuesong,GUO Shuaichao,MA Youjie,et al.Harmonic resonance suppression strategy of three-phase lcl photovoltaic grid-connected inverter based on ladrc and quasi pr[J]. Acta Energiae Solaris Sinica,2023,44(3):465-474.
• [13]沈姝衡，方天治，章益凡.高带宽数字控制LCL型并网逆变器及其提高并网系统鲁棒性的谐振抑制技术研究[J].电工技术学报，2022,37(21):5548-5561.SHEN Shuheng,FANG Tianzhi,ZHANG Yifan.A highbandwidth digital-control LCL-type grid-tied inverter and resonance-suppressing technique for improving the robustness of grid-connected system[J]. Transactions of China Electrotechnical Society,2022,37(21):5548-5561.
• [14]吴丽珍，刘腾飞，陈伟，等.弱电网中LLCL型并网逆变器的谐振分析与抑制策略研究[J].太阳能学报，2021,42(3):276-282.WU Lizhen,LIU Tengfei,CHEN Wei,et al.Research on resonance analysis and suppression strategy of gridconnected inverter with llcl filter in weak grid[J].Acta Energiae Solaris Sinica,2021,42(3):276-282.
• [15]LU M H,WANG X F,LOH P C,et al.Resonance interaction of multiparallel grid-connected inverters with LCL filter[J].IEEE Transactions on Power Electronics,2017,32(2):894-899.
• [16]黄亚申，汪海宁，马志保，等.并网逆变器系统的谐振抑制研究综述[J].电源学报，2018,16(4):143-156.HUANG Yashen,WANG Haining,MA Zhibao,et al.Review on researches of resonance suppression for gridconnected inverter system[J]. Journal of Power Supply,2018,16(4):143-156.
• [17]ZHANG Xing,YU Changzhou,LIU Fang,et al. Overview on resonance characteristics and resonance suppression strategy of multi-parallel photovoltaic inverters[J].Chinese Journal of Electrical Engineering,2016,2(1):40-51.
• [18]郑嘉龙，冯黎兵，杨鸽，等.Matlab在LC与LCL两种滤波器对比实验中的应用[J].实验室科学，2019,22(4):31-34.ZHENG Jialong,FENG Libing,YANG Ge,et al.Application of Matlab in comparative experiment between LC and LCL filters[J].Laboratory Science,2019,22(4):31-34.
• [19]HONG L C,SHU W T,WANG J H,et al. Harmonic resonance investigation of a multi-inverter grid-connected system using resonance modal analysis[J].IEEE Transactions on Power Delivery,2019,34(1):63-72.
• [20]孙振奥，杨子龙，王一波，等.光伏并网逆变器集群的谐振原因及其抑制方法[J].中国电机工程学报，2015,35(2):418-425.SUN Zhen’ao,YANG Zilong,WANG Yibo,et al. The cause analysis and suppression method of resonances in clustered grid-connected photovoltaic inverters[J]. Proceedings of the CSEE,2015,35(2):418-425.
• [21]赵曦，杨洪耕.基于二自由度内模控制的LCL并网逆变器控制策略[J].现代电力，2018,35(6):86-91.ZHAO Xi,YANG Honggeng. LCL grid-connected inverter control strategy based on two-degree-of-freedom internal model control[J].Modern Electric Power,2018,35(6):86-91.
• [22]ASIMINOAEI L,TEODORESCU R,BLAABJERG F,et al. A digital controlled PV-inverter with grid impedance estimation for ENS detection[J]. IEEE Transactions on Power Electronics,2005,20(6):1480-1490.
• [23]COBRECES S,BUENO E J,PIZARRO D,et al.Grid impedance monitoring system for distributed power generation electronic interfaces[J].IEEE Transactions on Instrumentation and Measurement,2009,58(9):3112-3121.
• [24]刘桂花，曹小娇，王卫.弱电网下单相光伏并网逆变器锁频环同步方法[J].中国电机工程学报，2015,35(19):5022-5029.LIU Guihua,CAO Xiaojiao,WANG Wei. A frequency locked loop grid synchronization method of single-phase grid-connected PV inverter under weak grid[J].Proceedings of the CSEE,2015,35(19):5022-5029.
• [25]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.
• [26]许德志，汪飞，阮毅，等.多逆变器并网系统输出阻抗建模与谐波交互[J].电机与控制学报，2014,18(2):1-7.XU Dezhi,WANG Fei,RUAN Yi,et al. Output impedance modeling and harmonic interactions of multiple inverters grid-connected system[J].Electric Machines and Control,2014,18(2):1-7.
• [27]许德志，汪飞，毛华龙，等.多并网逆变器与电网的谐波交互建模与分析[J].中国电机工程学报，2013,33(12):64-71.XU Dezhi,WANG Fei,MAO Hualong,et al. Modeling and analysis of harmonic interaction between multiple gridconnected inverters and the utility grid[J].Proceedings of the CSEE,2013,33(12):64-71.
• [28]AGORRETA J L,BORREGA M,L??PEZ J,et al.Modeling and control of$N$-paralleled grid-connected inverters with LCL filter coupled due to grid impedance in PV plants[J].IEEE Transactions on Power Electronics,2011,26(3):770-785.
• [29]杨明，周林，张东霞，等.考虑电网阻抗影响的大型光伏电站并网稳定性分析[J].电工技术学报，2013,28(9):214-223.YANG Ming,ZHOU Lin,ZHANG Dongxia,et al.Stability analysis of large-scale photovoltaic power plants for the effect of grid impedance[J].Transactions of China Electrotechnical Society,2013,28(9):214-223.
• [30]曹芸凯，赵涛，陈静，等.弱电网下并联逆变器谐振模态分析与抑制方法[J].机械与电子，2022,40(6):14-21.CAO Yunkai,ZHAO Tao,CHEN Jing,et al. Resonant mode analysis and suppression method of parallel inverters in weak grid[J].Machinery&Electronics,2022,40(6):14-21.
• [31]陶海军，周犹松，张国澎，等.LCL型并网逆变器并联谐振机理分析及抑制方法[J].上海交通大学学报，2020,54(10):1065-1073.TAO Haijun,ZHOU Yousong,ZHANG Guopeng,et al.Parallel resonance mechanism analysis and suppression method for LCL type grid-connected inverter[J]. Journal of Shanghai Jiao Tong University,2020,54(10):1065-1073.
• [32]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.
• [33]鲍陈磊，阮新波，王学华，等.基于PI调节器和电容电流反馈有源阻尼的LCL型并网逆变器闭环参数设计[J].中国电机工程学报，2012,32(25):133-142.BAO Chenlei,RUAN Xinbo,WANG Xuehua,et al.Design of grid-connected inverters with LCL filter based on PI regulator and capacitor current feedback active damping[J].Proceedings of the CSEE,2012,32(25):133-142.
• [34]HE J W,LI Y W,BOSNJAK D,et al.Investigation and active damping of multiple resonances in a parallelinverter-based microgrid[J].IEEE Transactions on Power Electronics,2013,28(1):234-246.
• [35]聂程，雷万钧，王跃，等.多变流器并联时谐振特性及最优虚拟阻尼方法[J].中国电机工程学报，2017,37(5):1467-1478.NIE Cheng,LEI Wanjun,WANG Yue,et al.Resonance analysis of multi-paralleled converter systems and research on optimal virtual resistor damping methods[J].Proceedings of the CSEE,2017,37(5):1467-1478.
• [36]胡伟，孙建军，马谦，等.多逆变器并网系统谐振特性分析[J].电力自动化设备，2014,34(7):93-98.HU Wei,SUN Jianjun,MA Qian,et al.Resonant characteristics of multi-inverter grid-connection system[J].Electric Power Automation Equipment,2014,34(7):93-98.
• [37]XU W,HUANG Z Y,CUI Y,et al.Harmonic resonance mode analysis[J].IEEE Transactions on Power Delivery,2005,20(2):1182-1190.
• [38]LIU Z F,RONG J,ZHAO G K,et al.Harmonic assessment for wind parks based on sensitivity analysis[J].IEEE Transactions on Sustainable Energy,2017,8(4):1373-1382.
• [39]王乐天，薛嘉辰，张梦琪，等.基于半功率带宽法的改进模态分析法[J].电力科学与技术学报，2023,38(5):129-142.WANG Letian,XUE Jiachen,ZHANG Mengqi,et al.An improved modal analysis method based on half power bandwidth method[J]. Journal of Electric Power Science and Technology,2023,38(5):129-142.
• [40]HONG L C,SHU W T,WANG J H,et al. Harmonic resonance investigation of a multi-inverter grid-connected system using resonance modal analysis[J].IEEE Transactions on Power Delivery,2019,34(1):63-72.
• [41]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.
• [42]戴烨敏，李育坤，林顺富，等.多逆变器并网系统多谐波建模及谐波交互分析[J].电气传动，2022,52(14):25-31.DAI Yemin,LI Yukun,LIN Shunfu,et al. Multiple harmonic modeling and harmonic interaction analysis of multiinverter grid-connected system[J].Electric Drive,2022,52(14):25-31.
• [43]CAI Y X,HE Y J,DU H T,et al.Harmonic state-space modeling and system characteristic analysis of gridconnected inverter parallel-operation system considering asynchronous carriers[J]. IEEE Transactions on Power Electronics,2024,39(7):8645-8666.
• [44]MOTWANI J K,XUE Y S,NAZARI A,et al.Modeling of power electronics systems and PWM modulators in harmonic-state space[J]. IEEE Open Journal of Power Electronics,2022,3:689-704.
• [45]LIN J C,LIU S Q,WANG G.Active disturbance rejection controller design for harmonic suppression in MPC optimal control based on harmonic state space modeling[J].International Journal of Circuit Theory and Applications,2023,51(12):5650-5671.
• [46]郑航，张辉，肖曦，等.微电网中并联逆变器与电网的谐波交互分析[J].电网技术，2016,40(8):2518-2524.ZHENG Hang,ZHANG Hui,XIAO Xi,et al.Analysis of harmonic interaction between multi-paralleled inverters and grid in microgrid[J]. Power System Technology,2016,40(8):2518-2524.
• [47]于航，李鹏，夏曼，等.基于有源阻尼器的并联逆变器集群集中式谐振抑制策略[J].电测与仪表，2017,54(11):71-75.YU Hang,LI Peng,XIA Man,et al.A centre resonance mitigation strategy for clustered grid-connected inverters based on active damper[J].Electrical Measurement&Instrumentation,2017,54(11):71-75.
• [48]王磊，张凌博.多逆变器并网等值建模及谐振抑制优化[J].电力系统保护与控制，2021,49(6):19-29.WANG Lei,ZHANG Lingbo. Equivalent modeling of multi-inverters connected to the grid and optimization of resonance suppression[J]. Power System Protection and Control,2021,49(6):19-29.
• [49]何国锋，徐德鸿.基于有源阻尼的多逆变器并网谐振抑制[J].电机与控制学报，2017,21(10):62-68.HE Guofeng,XU Dehong.Resonance suppression for gridconnected multi-inverter based on active damping method[J].Electric Machines and Control,2017,21(10):62-68.
• [50]匡慧敏，罗安，陈智勇，等.多逆变器并网耦合谐振机理及有源阻尼优化方法[J].电网技术，2016,40(4):1180-1189.KUANG Huimin,LUO An,CHEN Zhiyong,et al. Coupling resonances mechanism of grid-connected multiparallel inverters and its active damping parameter optimal method[J]. Power System Technology,2016,40(4):1180-1189.
• [51]金国彬，谢飞，李国庆，等.弱电网且谐波畸变背景下分布式电源并网系统谐振抑制[J].电力系统保护与控制，2023,51(5):1-10.JIN Guobin,XIE Fei,LI Guoqing,et al.Resonance suppression of a distributed power grid-connected system in a weak grid and with harmonic distortion background[J].Power System Protection and Control,2023,51(5):1-10.
• [52]陈林，徐永海，王天泽，等.弱电网下计及背景谐波的多并网逆变器阻抗重塑谐振抑制方法[J].电力系统保护与控制，2024,52(1):59-72.CHEN Lin,XU Yonghai,WANG Tianze,et al. Resonance suppression method for multiple grid-connected inverters with impedance remodeling with background harmonics in a weak power grid[J].Power System Protection and Control,2024,52(1):59-72.
• [53]PE??A-ALZOLA R,LISERRE M,BLAABJERG F,et al.A self-commissioning Notch filter for active damping in a three-phase LCL-filter-based grid-Tie converter[J].IEEE Transactions on Power Electronics,2014,29(12):6754-6761.
• [54]王毅，高爱杰，胡楠，等.多并网逆变器并联运行的谐振抑制策略[J].南方电网技术，2022,16(5):87-96.WANG Yi,GAO Aijie,HU Nan,et al. Resonance suppression strategy for multi-parallel grid-connected inverters[J]. Southern Power System Technology,2022,16(5):87-96.
• [55]李圣清，王志健，郑剑，等.基于混合阻尼的光伏集群逆变器并网谐振抑制[J].电力电子技术，2021,55(9):81-85.LI Shengqing,WANG Zhijian,ZHENG Jian,et al.Gridconnected resonance suppression of group-series photovoltaic cluster inverters based on hybrid damping[J].Power Electronics,2021,55(9):81-85.
• [56]张计科，王贵发.基于阻抗重塑的多并网逆变器并联系统谐振抑制方法研究[J].电网与清洁能源，2023,39(6):1-7.ZHANG Jike,WANG Guifa. Research on the resonance suppression method of the multiple grid-connected inverter parallel system based on impedance remodeling[J]. Power System and Clean Energy,2023,39(6):1-7.
• [57]王瑞斌，刘佳庆，王庆园，等.弱电网下基于前置低通滤波器的电网电压加权前馈控制策略[J].电力系统及其自动化学报，2025,37(3):93-99.WANG Ruibin,LIU Jiaqing,WANG Qingyuan,et al.Grid voltage weighted feedforward control strategy based on pre-low pass filter under weak grid[J].Proceedings of the CSU-EPSA,2025,37(3):93-99.
• [58]武健，赵家琦，王超，等.多逆变器并网系统谐振特性模态分析与有源阻尼稳定域计算[J].电机与控制学报，2018,22(2):98-107.WU Jian,ZHAO Jiaqi,WANG Chao,et al. Resonant analysis and stable domain calculation in multi-inverter grid-connection system[J].Electric Machines and Control,2018,22(2):98-107.
• [59]WANG X F,BLAABJERG F,LISERRE M,et al.An active damper for stabilizing power-electronics-based AC systems[J]. IEEE Transactions on Power Electronics,2014,29(7):3318-3329.
• [60]JIA L,RUAN X B,ZHAO W X,et al.An adaptive active damper for improving the stability of grid-connected inverters under weak grid[J]. IEEE Transactions on Power Electronics,2018,33(11):9561-9574.
• [61]史明明，姜云龙，史鸿飞，等.集成有源阻尼器功能的并网逆变器虚拟电阻补偿控制方法[J].电力自动化设备，2024,44(4):119-126.SHI Mingming,JIANG Yunlong,SHI Hongfei,et al.Virtual resistance compensation control method for gridconnected inverter integrated with active damper function[J].Electric Power Automation Equipment,2024,44(4):119-126.
• [62]陈来军，黎立丰，郑天文，等.基于自适应滤波的并联逆变器谐振抑制策略[J].电网技术，2020,44(1):200-207.CHEN Laijun,LI Lifeng,ZHENG Tianwen,et al.Resonance suppression strategy for multi-parallel inverters based on adaptive filtering[J].Power System Technology,2020,44(1):200-207.
• [63]黄仁志，全相军，吴在军，等.基于多重谐振控制器的参考值前馈自适应控制[J].电工技术学报，2022,37(16):4212-4224.HUANG Renzhi,QUAN Xiangjun,WU Zaijun,et al. A multiple resonant based on reference feedforward adaptive voltage control of three-phase inverter[J].Transactions of China Electrotechnical Society,2022,37(16):4212-4224.
• [64]刘万超，桑亚维，谢威，等.一种适用于风电送出的新型大功率整流器研究[J].电力电容器与无功补偿，2025,46(4):98-106.LIU Wanchao,SANG Yawei,XIE Wei,et al.Research on a new type of high-power rectifier suitable for wind power transmission[J].Power Capacitor&Reactive Power Compensation,2025,46(4):98-106.
• [65]马为民，李明，薛英林，等.大容量电压源型逆变器在新型电力系统构建中的关键技术和创新展望[J].电力建设，2025,46(10):1-11.MA Weimin,LI Ming,XUE Yinglin,et al.Key technologies and innovation prospects of large-capacity voltagesourced inverter in the construction of new power systems[J].Electric Power Construction,2025,46(10):1-11.
• [66]刘延龙，陈晓光，姚爽爽，等.基于构网型SVG控制优化的双馈风场高频谐振抑制分析[J].电力建设，2024,45(11):125-136.LIU Yanlong,CHEN Xiaoguang,YAO Shuangshuang,et al. Analysis of high-frequency resonance suppression in doubly-fed wind farms based on grid-forming SVG control optimization[J]. Electric Power Construction,2024,45(11):125-136.
• [67]罗军杰，粟时平，倪亮，等.基于改进下垂的多逆变器并联控制策略[J].电力电容器与无功补偿，2024,45(2):169-176.LUO Junjie,SU Shiping,NI Liang,et al.Parallel control strategy of multiple inverters based on improved droop[J].Power Capacitor&Reactive Power Compensation,2024,45(2):169-176.
• [68]程勇，宋世雄，赵建文.基于改进双矢量模型预测控制的逆变器功率均分控制策略[J].电力建设，2024,45(11):137-147.CHENG Yong,SONG Shixiong,ZHAO Jianwen.Inverter power equalization control strategy based on improved dual-vector model predictive control[J]. Electric Power Construction,2024,45(11):137-147.
• [69]ZHANG J H,MEN Y X,DING L Z,et al.Gray-box modeling for distribution systems with inverter-based resources:integrating physics-based and data-driven approaches[J].IEEE Transactions on Industry Applications,2024,60(4):5490-5498.