Impedance Modeling and Sub/Super Synchronous Oscillation Stability Analysis of Modular Multilevel Converter under Virtual Synchronous Generator Control
Gao Benfeng1, Shen Yusi1, Song Ruihua2, Yang Daye2, Zhang Jianpo1, Li Gang1
1. Hebei Key Laboratory of Distributed Energy Storage and Micro-Grid North China Electric Power University Baoding 071003 China; 2. China Electric Power Research Institute Beijing 100192 China
Abstract：Virtual synchronous generator (VSG) control has been widely used in new power systems. Its research mainly focuseson new energy, and the problems of sub/supersynchronous oscillation and grid-connected stability in the VSC-HVDC still need to be clarified. Limitations exist in the research on the impedance modeling of grid-forming modular multilevel converter (MMC) and the sub/supersynchronous stability problem. The characteristics of the sub/supersynchronous oscillation mechanism in real projects of grid-forming MMC cannot be characterized, and the oscillation suppression method is also immature. Therefore, it is essential to conduct sequence impedance modeling, grid-connected system stability analysis and control optimization for grid-forming MMC. This paper adopts the harmonic linearization method to establish the sequence impedance model of grid-constructed MMC and verifies the accuracy of the analytical model by frequency scanning. Secondly, the impedance characteristics and grid-connected stability are compared with the traditional grid-following MMC. Then, the control optimization design scheme based on virtual impedance is adopted to optimize the impedance characteristics of the grid-forming MMC and improve the stability of the grid-connected system. Finally, the effects of active control, reactive control, voltage outer loop, and current inner loop parameters on the impedance characteristics of grid-forming MMC areexplored. Results show that grid-forming MMC has better stability in weak grids. However, there is a risk of sub/supersynchronous oscillation in strong grids, and virtual impedance control can increase the equivalent output impedance of the converter, thereby enhancing the stability of the MMC grid-connected system. At the same time, the reactive power droop and voltage outer loop link play a decisive role in the impedance characteristics of the grid-forming MMC. Appropriately increasing the reactive power droop coefficient and the voltage outer loop integration coefficient is conducive to reducing the negative impedance damping interval and improving the stability of the grid-connected system. The following conclusions can be drawn. (1) In the network construction MMC sequence impedance modeling, the small signal of the reference phase angle generated by VSG control has little influence on the impedance characteristics of the system. Thus, the influence of VSG control can be ignored in the impedance modeling process. (2) Compared with traditional control methods, the impedance of the grid-forming MMC is inductive in the sub/supersynchronous frequency band, which is not easy to resonate with the inductive power grid. The impedance characteristics of MMC can be improved using the grid-forming control, and the grid stability of the MMC grid-connected system can be enhanced. (3) Although the grid-forming MMC has good stability under weak power grids, oscillation is risky under strong grids. The virtual impedance control can enhance the stability of the grid-connected MMC system.
[1] 国家发展改革委, 国家能源局. 关于印发“十四五”可再生能源发展规划的通知[EB]. 2021. National Development and Reform Commission, National Energy Administration. Notice on the issuance of the 14th Five-Year renewable energy development plan[EB]. 2021. [2] 孟沛彧, 向往, 潘尔生, 等. 分址建设直流输电系统拓扑方案与运行特性研究[J]. 电工技术学报, 2022, 37(19): 4808-4822. Meng Peiyu, Xiang Wang, Pan Ersheng, et al.Research on topology and operation characteristics of HVDC transmission system based on site-division construction[J]. Transactions of China Electrotech- nical Society, 2022, 37(19): 4808-4822. [3] 汤广福, 庞辉, 贺之渊. 先进交直流输电技术在中国的发展与应用[J]. 中国电机工程学报, 2016, 36(7): 1760-1771. Tang Guangfu, Pang Hui, He Zhiyuan.R & D and application of advanced power transmission tech- nology in China[J]. Proceedings of the CSEE, 2016, 36(7): 1760-1771. [4] Wang Xiongfei, Taul M G, Wu Heng, et al.Grid- synchronization stability of converter-based resources- an overview[J]. IEEE Open Journal of Industry Applications, 2020, 1: 115-134. [5] 汤广福, 罗湘, 魏晓光. 多端直流输电与直流电网技术[J]. 中国电机工程学报, 2013, 33(10): 8-17, 前插2. Tang Guangfu, Luo Xiang, Wei Xiaoguang. Multi- terminal HVDC and DC-grid technology[J]. Pro- ceedings of the CSEE, 2013, 33(10): 8-17, 前插2. [6] 饶宏. 南方电网大功率电力电子技术的研究和应用[J]. 南方电网技术, 2013, 7(1): 1-5. Rao Hong.Research and application of the high- power electronic technology in China southern power grid[J]. Southern Power System Technology, 2013, 7(1): 1-5. [7] Khazaei J, Beza M, Bongiorno M.Impedance analysis of modular multi-level converters connected to weak AC grids[J]. IEEE Transactions on Power Systems, 2018, 33(4): 4015-4025. [8] 谢小荣, 贺静波, 毛航银, 等. “双高”电力系统稳定性的新问题及分类探讨[J]. 中国电机工程学报, 2021, 41(2): 461-474. Xie Xiaorong, He Jingbo, Mao Hangyin, et al.New issues and classification of power system stability with high shares of renewables and power elec- tronics[J]. Proceedings of the CSEE, 2021, 41(2): 461-474. [9] 徐菘, 杨博, 刘浩, 等. 一种提高虚拟同步机电流质量的电压-电流级联闭环控制方案[J]. 电工技术学报, 2024, 39(6): 1871-1885. Xu Song, Yang Bo, Liu Hao, et al.A cascaded harmonic voltage and current closed-loop control method to improve the current quality of virtual synchronous generators[J]. Transactions of China Electrotechnical Society, 2024, 39(6): 1871-1885. [10] 潘子迅, 杨晓峰, 赵锐, 等. 不平衡电网下虚拟同步机的多模式协调策略[J]. 电工技术学报, 2023, 38(16): 4274-4285. Pan Zixun, Yang Xiaofeng, Zhao Rui, et al.Multi- mode coordination control of virtual synchronous generator under unbalanced power grid[J]. Transa- ctions of China Electrotechnical Society, 2023, 38(16): 4274-4285. [11] 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): 2339-2358. 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): 2339-2358. [12] 包广清, 谭宏涛, 丁坤, 等. 基于虚拟同步机的光伏并网系统控制研究[J]. 电气工程学报, 2018, 13(12): 19-23. Bao Guangqing, Tan Hongtao, Ding Kun, et al.Research on grid-connected photovoltaic system control based on virtual synchronous generator[J]. Journal of Electrical Engineering, 2018, 13(12): 19-23. [13] 章艳, 高晗, 张萌. 不同虚拟同步机控制下双馈风机系统频率响应差异研究[J]. 电工技术学报, 2020, 35(13): 2889-2900. Zhang Yan, Gao Han, Zhang Meng.Research on frequency response difference of doubly-fed indu- ction generator system controlled by different virtual synchronous generator controls[J]. Transactions of China Electrotechnical Society, 2020, 35(13): 2889-2900. [14] 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 impe- dance[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4130-4146. [15] 刘芳. 基于虚拟同步机的微网逆变器控制策略研究[D]. 合肥: 合肥工业大学, 2015. Liu Fang.Research on control strategy of microgrid inverter based on virtual synchronous machine[D]. Hefei: Hefei University of Technology, 2015. [16] 马秀达, 卢宇, 田杰, 等. 柔性直流输电系统的构网型控制关键技术与挑战[J]. 电力系统自动化, 2023, 47(3): 1-11. Ma Xiuda, Lu Yu, Tian Jie, et al.Key technologies and challenges of grid-forming control for flexible DC transmission system[J]. Automation of Electric Power Systems, 2023, 47(3): 1-11. [17] 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. 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. [18] 黄勇, 马秀达, 张进, 等. 构网型柔性直流系统阻尼环节控制策略优化研究[J]. 电网技术, 2024, 48(2): 889-896. Huang Yong, Ma Xiuda, Zhang Jin, et al.Opti- mization of damping control strategy for grid-forming VSC-HVDC[J]. Power System Technology, 2024, 48(2): 889-896. [19] 薛翼程, 张哲任, 徐政, 等. 构网型变流器对交流系统低频振荡的影响分析与阻尼控制[J]. 电力系统自动化, 2023, 47(16): 103-113. Xue Yicheng, Zhang Zheren, Xu Zheng, et al.Impact analysis and damping control of grid-forming con- verter for low-frequency oscillation of AC system[J]. Automation of Electric Power Systems, 2023, 47(16): 103-113. [20] 吕敬, 蔡旭. 基于谐波线性化的模块化多电平换流器阻抗建模[J]. 电力系统自动化, 2017, 41(4): 136-142. Lü Jing, Cai Xu.Harmonic linearization based impe- dance modeling of modular multilevel converters[J]. Automation of Electric Power Systems, 2017, 41(4): 136-142. [21] Zhang Bo, Du Xiong, Du Chengmao, et al.Stability modeling of a three-terminal MMC-HVDC trans- mission system[J]. IEEE Transactions on Power Delivery, 2022, 37(3): 1754-1763. [22] 于彦雪, 关万琳, 陈晓光, 等. 基于序阻抗的虚拟同步机同步频率谐振现象[J]. 电工技术学报, 2022, 37(10): 2584-2595. Yu Yanxue, Guan Wanlin, Chen Xiaoguang, et al.Synchronous frequency resonance in virtual syn- chronous generator based on sequence-impedance[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2584-2595. [23] Sun Jian, Liu Hanchao.Sequence impedance mode- ling of modular multilevel converters[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2017, 5(4): 1427-1443. [24] 孙杰, 尹太元, 王跃, 等. 采用VSG策略的MMC阻抗建模及并网稳定性分析[J]. 电源学报, 2021, 19(6): 30-41. Sun Jie, Yin Taiyuan, Wang Yue, et al.Impedance modeling and grid-connected stability analysis of MMC under VSG control strategy[J]. Journal of Power Supply, 2021, 19(6): 30-41. [25] Rosso R, Wang Xiongfei, Liserre M, et al.Grid- forming converters: control approaches, grid- synchronization, and future trends-a review[J]. IEEE Open Journal of Industry Applications, 2021, 2: 93-109. [26] 杜程茂, 杜雄, 邹小明, 等. 考虑频率耦合效应的并网模块化多电平变流器阻抗建模及稳定性分析[J]. 中国电机工程学报, 2020, 40(9): 2866-2876. Du Chengmao, Du Xiong, Zou Xiaoming, et al.Impedance modeling and stability analysis of grid- connected modular multilevel converter considering frequency coupling effect[J]. Proceedings of the CSEE, 2020, 40(9): 2866-2876. [27] Li Yitong, Gu Yunjie, Zhu Yue, 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. [28] Wu Heng, Wang Xiongfei.Dynamic impact of zero- sequence circulating current on modular multilevel converters: complex-valued AC impedance modeling and analysis[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(2): 1947-1963.
2025, Vol. 40 
