Medium-Frequency Stability Analysis and Unified Magnitude-Phase Regulation Method For MMC-HVDC Systems
Lu Jiaqi, Chen Xin, Teng Zhiyuan, Zhang Donghui
Jiangsu Key Laboratory of New Energy Generation and Power Conversion College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211106 China
Modular Multilevel Converter-High Voltage Direct Current (MMC-HVDC) systems have been widely applied in large-scale wind power integration and renewable energy transmission. However, due to the multi-time-scale characteristics inherent in the control architecture, the coupling between the current control loop and digital control delay may cause the MMC to exhibit negative-damping behavior in the medium-frequency range (hundreds of hertz). Under such conditions, the impedance interaction between the MMC and the wind-farm-side system may weaken the stability margin and give rise to a potential medium-frequency oscillation risk. Existing oscillation mitigation strategies mainly focus on single-dimensional optimization of either the impedance magnitude or phase characteristics. Moreover, parameter tuning in these methods often relies on empirical adjustment, lacks explicit design criteria, and is difficult to apply consistently in engineering practice while ensuring suppression performance. Therefore, it is necessary to conduct a systematic analysis of medium-frequency instability from an impedance-mechanism perspective and to develop impedance-reshaping methods with clear regulation objectives and quantitative parameter-setting procedures.
In this study, a wind-power-integrated MMC-HVDC transmission system is considered as the research object. First, impedance models of the sending-end MMC and the grid-side converter of a direct-drive wind turbine are established based on a multi-harmonic linearization approach, and the model accuracy is validated through frequency-sweep analysis. On this basis, a simplified MMC impedance model suitable for medium-frequency studies is constructed. An impedance-sensitivity index is further introduced to quantitatively evaluate the influence of different parameters on the medium-frequency impedance characteristics. The analysis indicates that the current control loop and digital control delay of the sending-end MMC are the dominant factors leading to the formation of negative damping in the medium-frequency band. The combined influence of these two factors causes the MMC impedance to exhibit inductive negative-damping characteristics within several hundred hertz, which leads to a potential risk of medium-frequency oscillation during interaction with the wind-farm-side system.
Building upon the above mechanism analysis, an impedance-reshaping strategy with coordinated amplitude-phase regulation capability is proposed. In this strategy, an amplitude-phase coordinated controller is integrated into the MMC current control loop, and an equivalent impedance-regulation function is constructed containing both amplitude-tuning and phase-tuning factors. This function enables coordinated regulation of the impedance magnitude and phase characteristics within the risk-sensitive frequency range. The phase-tuning factor introduces a lead-compensation effect to offset the phase lag induced by control delay, thereby weakening the conditions associated with negative-damping formation. Meanwhile, the amplitude-tuning factor shifts the intersection point of the impedance-magnitude curves away from the original negative-damping region, which contributes to improving the system stability margin. The coordinated action of the two tuning factors enables directional reshaping of the medium-frequency impedance characteristics, and a quantitative parameter-design method corresponding to the proposed strategy is established.
Finally, experimental studies are conducted on an RT-LAB hardware-in-the-loop (HIL) platform. The experiments include reproduction of oscillatory operating conditions, validation of key factors associated with medium-frequency oscillation, and evaluation of the amplitude-phase coordinated controller under multiple operating scenarios. The experimental results verify the correctness of the theoretical analysis and further demonstrate that the proposed strategy realizes coordinated amplitude-phase regulation within the target frequency band while maintaining effective and robust suppression performance across different operating conditions.
[1] 姜云鹏,任洲洋,李秋燕,等.考虑多灵活性资源协调调度的配电网新能源消纳策略[J].电工技术学报,2022,37(07):1820-1835.
Jiang Yunpeng, Ren Zhouyang, Li Qiuyan, et al.An Accommodation Strategy for Renewable Energy in Distribution Network Considering Coordinated Dispatching of Multi-Flexible Resources[J]. Transactions of China Electrotechnical Society, 2022, 37(07): 1820-1835.
[2] 蔡旭,杨仁炘,周剑桥,等.海上风电直流送出与并网技术综述[J].电力系统自动化,2021,45(21):2-22.
CAI Xu, YANG Renxin, ZHOU Jianqiao, et al.Review on offshore wind power integration via DC transmission[J]. Automation of Electric Power Systems, 2021, 45(21): 2-22.
[3] 潘子迅,杨晓峰,赵锐,等.不平衡电网下模块化多电平换流器的直流环流均衡策略[J].电工技术学报, 2024, 39(2):541-553.
Pan Zixun, Yang Xiaofeng, Zhao Rui, et al.DC circulating current balancing control of modular multilevel converter under unbalanced power grid[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 541-553.
[4] BUCHHAGEN C, RAUSCHER C, MENZE A, et al. Bor Win1-First experiences with harmonic interactions in converter dominated grids[C]//International ETG Congress, November 17-18, 2015, Bonn, Germany:1-7.
[5] 杨万开,王兴国,王书扬,等.柔性直流换流器阻抗自适应重塑抑制高频谐振方法[J].电网技术,2022,46(11):4473-4482.
YANG Wankai, WANG Xingguo, WANG Shuyang, et al.High-frequency Resonant Suppression by MMC-HVDC Converter Impedance Adaptive Remodeling[J]. Power System Technology, 2022, 46(11): 4473-4482.
[6] 李奇南,夏勇军,张晓林,等.渝鄂柔性直流输电系统中高频振荡影响因素及抑制策略[J].中国电力,2022,55(07):11-21.
LI Qinan, XIA Yongjun, ZHANG Xiaolin, et al.Key Factors of Medium-High Frequency Oscillation in Chongqing Hubei HVDC System and Suppression Strategies[J]. Electric Power, 2022, 55(07): 11-21.
[7] 高磊,吕敬,蔡旭.如东海上风电柔直送出系统的中频振荡特性分析[J].电网技术,2023,47(09):3495-3509.
GAO Lei, LYU Jing, CAI Xu.Analysis of Mid-frequency Oscillation Characteristics in Rudong MMC-HVDC System for Offshore Wind Farms[J]. Power System Technology, 2023, 47(09): 3495-3509.
[8] 杨志强,王仙荣,邹凯凯,等.海上风电柔直系统中频振荡抑制方法及工程验证[J].电力工程技术,2025,44(05):109-116.
YANG Zhiqiang, WANG Xianrong, ZOU Kaikai, et al.Mid-frequency oscillation suppression methodology for offshore wind power VSC-HVDC system and its engineering validation[J]. Electric Power Engineering Technology, 2025, 44(05): 109-116.
[9] CESPEDES M, SUN J.Impedance modeling and analysis of grid-connected voltage-source converters[J]. IEEE Trans-actions on Power Electronics, 2014, 29(3):1254-1261.
[10] 彭意,郭春义,杜东冶.柔性直流输电的阻抗重塑及中高频振荡抑制方法[J].中国电机工程学报,2022,42(22):8053-8063.
PENG Yi, GUO Chunyi, Du Dongye.Research on Medium and High Frequency Oscillation Suppression Approach Based on Impedance Tuning in Flexible HVDC System[J]. Proceedings of the CSEE, 2022, 42(22):8053-8063.
[11] 刘欣,袁易,王利桐,等.柔性直流输电系统三端口混合参数建模及其稳定性分析[J].电工技术学报,2024,39(16):4968-4984.
Liu Xin, Yuan Yi, Wang Litong, et al. Three-Port Hybrid Parameter Modeling and Stability Analysis of MMC-HVDC System[J]. Transactions of China Electrotechnical Society, 2024, 39(16): 4968-4984.、
[12] 张旭,郝治国,李宇骏,李佳朋,杨松浩,梁天宇,等.基于电气转矩法的VSC-HVDC系统直流电压振荡稳定性评估[J].电网技术,2024,48(10):4306-4316.
ZHANG Xu, HAO Zhiguo, LI Yujun, LI Jiapeng, YANG Songhao, LIANG Tianyu, et al.DC-link Voltage Oscillation Stability Assessment of VSC-HVDC Systems Using Electrical Torque Method[J]. Power System Technology, 2024, 48(10): 4306-4316.
[13] 盛逸标,林涛,陈宝平,等.面向新能源外送系统次/超同步振荡的控制器参数协调优化[J].电工技术学报,2019,34(05):983-993.
Sheng Yibiao, Lin Tao, Chen Baoping, et al.Coordination and Optimization of Controller Parameters for Subsynchronous/Super-Synchronous Oscillation in New Energy Delivery Systems[J]. Transactions of China Electrotechnical Society, 2019, 34(05): 983-993.
[14] 陈明泉,肖世挺,严昌华,等.厦门柔直工程高频谐波保护方案分析与试验[J].电气技术,2023,24(10):79-84.
CHEN Mingquan, XIAO Shiting, YAN Changhua, et al.Analysis and experiment of high frequency harmonic protection scheme in Xiamen flexible HVDC transmission project[J]. Electrical Engineering, 2023, 24(10): 79-84.
[15] 马燕峰,韩珊珊,王子建,等.直驱风电场经柔直外送系统振荡特性及控制环节动态交互作用研究[J/OL].电工技术学报,1-17[2025-11-19].
Ma Yanfeng, Han Shanshan, Wang Zijian, et al.Study on oscillation characteristics and dynamic interaction of control link of a VSC-HVDC connected direct drive wind farm[J/OL]. Transactions of China Electrotechnical Society, 1-17[2025-11-19].
[16] 孙焜,姚伟,周毅,等.基于SISO序阻抗的直驱风场经柔直输电系统中频振荡机理分析及抑制[J].中国电机工程学报,2023,43(02):442-454.
SUN Kun, YAO Wei, ZHOU Yi, et al.Mechanism Analysis and Suppression of Medium-frequency Oscillation Based on the SISO Impedance in a PMSG-based Wind Farm When Connected to a VSC-HVDC[J]. Proceedings of the CSEE. 2023, 43(02): 442-454.
[17] 张东辉,陈新.基于阻抗视角的新能源发电系统宽频振荡抑制技术综述[J].中国电机工程学报,2024,44(24):9672-9691.
ZHANG Donghui, CHEN Xin.Overview of Broadband Oscillation Mitigation of New Energy Generation Power System Based on Impedance Perspective[J]. Proceedings of the CSEE, 2024, 44(24): 9672-9691.
[18] 李奇南,孙宝奎,孙华东,等.柔性直流输电系统中高频振荡研究综述[J].电力自动化设备,2025,45(01):156-171.
LI Qinan, SUN Baokui, SUN Huadong, et al.A review of high-frequency oscillation research in flexible direct current transmission systems[J]. Electric Power Automation Equipment, 2025, 45(01): 156-171.
[19] 李国庆,孙银锋,吴学光.柔性直流输电稳定性分析及控制参数整定[J].电工技术学报,2017,32(06):231-239.
Li Guoqing, Sun Yinfeng, Wu Xueguang.VSC-HVDC Stability Analysis and Control Parameter Setting[J]. Transactions of China Electrotechnical Society, 2017, 32(06): 231-239.
[20] 刘凯,姚骏,汪军,等.基于零序环流控制器的海上风电MMC-HVDC并网系统小干扰稳定分析与优化控[J].中国电机工程学报,2021,41(12):4068-4081.
LIU Kai, YAO Jun, WANG Jun, et al.Small Signal Stability Analysis and Optimization Control of Offshore Wind Power Generation MMC-HVDC Grid-connected System Based on Zero-sequence Circulating Current Controller[J]. Proceedings of the CSEE, 2021, 41(12): 4068-4081.
[21] 张旸,陈新,王昀,等.弱电网下并网逆变器的阻抗相角动态控制方法[J].电工技术学报,2017,32(1):97-106.
ZHANG Yang, CHEN Xin, WANG Yun, et al.Impedance-phased dynamic control method of grid-connected inverters under weak grid condition[J]. Transactions of China Electrotechnical Society, 2017, 32(1): 97-106.
[22] 吴倩,韩笑,叶昊亮,张哲任,徐政.海上风电场经220 kV交流海缆送出系统的无功配置方案[J].电力电容器与无功补偿,2021,42(04):22-30.
WU Qian, HAN Xiao, YE Haoliang, ZHANG Zheren, XU Zheng.Reactive Power Compensation Configuration of Offshore Wind Farm Transmission System with 220 kV AC Submarine Cable[J]. Power Capacitor & Reactive Power Compensation, 2021, 42(04): 22-30.
[23] 薛涛,吕敬,王凯,等.海上全功率风电机组精细化阻抗建模及机网侧耦合分析[J].中国电机工程学报,2022,42(12):4303-4319.
XUE Tao, LYU Jing, WANG Kai, et al.Accurate Impedance Modeling of an Offshore Full-power Wind Turbine System and Analysis of the Coupling Characteristics Between Machine-and Grid-side Systems[J]. Proceedings of the CSEE, 2022, 42(12): 4303-4319.
[24] 徐政,肖晃庆,张哲任.柔性直流输电系统[M].2版.北京:机械工业出版社,2017.
XU Zheng, XIAO Huangqing, ZHANG Zheren.Voltage source converter based HVDC transmission system[M]. 2nd ed. Beijing: China Machine Press, 2017.
[25] 年珩,朱茂玮,徐韵扬,等.双闭环定交流电压控制下MMC换流站阻抗建模及稳定性分析[J].电力系统自动化,2020,44(04):81-90.
NIAN Heng, ZHU Maowei, Xu Yunyang, et al.Impedance Modeling and System Stability Analysis of MMC with Double Closed-loop AC Voltage Control[J]. Automation of Electric Power Systems, 2020, 44(04): 81-90.
[26] 杜步阳,邵德军,朱建行,等.电压源型变流器并网系统多时间尺度间相互作用[J].电工技术学报,2023,38(20):5547-5559.
Du Buyang, Shao Dejun, Zhu Jianhang, et al.The Interaction Between Multiple Timescales of the Grid-Tied Voltage Source Converter[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5547-5559.