弱电网下电网阻抗与PLL耦合效应对并网MMC系统稳定性的影响分析

doi:10.19595/j.cnki.1000-6753.tces.240180

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (3547 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract Modular multilevel converters (MMCs) are one of the most promising solutions for integrating renewable energy sources from remote areas into the AC grid. However, the high impedance of long-distance transmission lines causes challenges to the stability of grid-connected MMC systems under a weak grid. Although the interaction of two-level voltage source converters with weak grids and their stability issues have been intensively studied recently, these results are not applicable to grid-connected MMC systems because of the internal dynamic characteristics of MMC. In addition, there are significant coupling effects between these internal dynamics and the AC-side and DC-side output variables. Therefore, the stability of grid-connected MMC systems under a weak grid, especially the ambiguity of the system interaction mechanism and the small-signal stability, still needs further in-depth research. This paper proposes a small-signal transfer function model to describe the interaction between grid impedance, phase-locked loop (PLL), fundamental frequency current control (FFCC), and circulating current suppression control. The instability mechanism of grid-connected MMC systems caused by the coupling effect of grid impedance and PLL under a weak grid is revealed.
First, for the circuit topology and average value model of the grid-connected MMC system, this paper uses the vector representation method of common- and differential-mode signals to construct the basic circuit equations. Then, through coordinate transformation, a linearizable time-varying model of MMC in a synchronous rotating dq coordinate system is established, and the small-signal transfer function model of the grid-connected MMC system is derived. It is found that under the weak grid, the coupling effect between grid impedance and PLL is the key factor affecting the stability of grid-connected MMC systems, and its mechanism is mainly analyzed through the system equivalent loop gain. Then, this paper proposes an analysis method combined with the transfer function zero-pole analysis and the frequency domain characteristics. The results show that the coupling effect of grid impedance and PLL introduces a right half-plane pole in the system equivalent loop gain, thereby destroying the system stability. This potential instability problem can be alleviated by increasing the gain of FFCC. A loop compensation scheme is designed to eliminate the coupling effect between grid impedance and PLL and solve the right half-plane pole problem, thereby improving the stability of grid-connected MMC systems.
The following conclusions can be drawn. (1) Under a weak grid, the coupling effect of grid impedance and PLL introduces right half-plane poles in equivalent loop gain, which is the main reason for the instability of the grid-connected MMC system. (2) Increasing the gain of FFC can alleviate the instability caused by the coupling effect of grid impedance and PLL. An effective loop compensation scheme must be designed to eliminate this potential instability problem. (3) The stability analysis method combining the zero-pole analysis of equivalent loop gain with the frequency domain characteristics can effectively solve the subsystem’s stability problem and overcome the limitations of the traditional impedance stability analysis method.

Key words： Weak grid modular multilevel converter (MMC) grid impedance phase locked loop (PLL) coupling effect stability

Received: 26 January 2024

PACS:

TM46

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Wu Xiangyang
	He Lili
	Li Yang
	Shuai Zhikang

Cite this article:

Wu Xiangyang,He Lili,Li Yang等. Analysis of the Influence of Grid Impedance and PLL Coupling Effect on the Stability of Grid-Connected MMC Systems under Weak Grid[J]. Transactions of China Electrotechnical Society, 2025, 40(4): 1236-1253.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.240180 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I4/1236

[1] 鲁晓军, 林卫星, 向往, 等. 基于模块化多电平换流器的直流电网小信号建模[J]. 中国电机工程学报, 2018, 38(4): 1143-1156, 1292.
Lu Xiaojun, Lin Weixing, Xiang Wang, et al.Small signal modeling of MMC-based DC grid[J]. Proceedings of the CSEE, 2018, 38(4): 1143-1156, 1292.
[2] 易灵芝, 黄晓辉, 黄守道, 等. 基于最近电平逼近调制的模块化多电平变换器中高压变频调速系统运行控制[J]. 电工技术学报, 2020, 35(6): 1303-1315.
Yi Lingzhi, Huang Xiaohui, Huang Shoudao, et al.A medium-voltage motor drive with modular multilevel converter based on nearest level modulation[J]. Transactions of China Electrotechnical Society, 2020, 35(6): 1303-1315.
[3] 武鸿, 王跃, 薛英林, 等. 适用多功率的最近电平调制下MMC子模块开路故障诊断策略[J]. 电工技术学报, 2024, 39(1): 233-245, 302.
Wu Hong, Wang Yue, Xue Yinglin, et al.A diagnosis strategy for open-circuit submodule faults in MMCs under nearst level modulation suitable for different powers[J]. Transactions of China Electrotechnical Society, 2024, 39(1): 233-245, 302.
[4] 赵崇滨, 姜齐荣, 冯海全, 等. 基于MMC的背靠背异步联网系统宽频带频率耦合阻抗模型及小信号稳定性分析[J]. 中国电机工程学报, 2023, 43(10): 3691-3704.
Zhao Chongbin, Jiang Qirong, Feng Haiquan, et al.Frequency-coupling impedance model and smallsignal stability analysis of the MMC-based backto-back asynchronous grid interconnection system[J]. Proceedings of the CSEE, 2023, 43(10): 3691-3704.
[5] 刘计龙, 陈鹏, 肖飞, 等. 面向舰船综合电力系统的10kV/2MW模块化多电平双向直流变换器控制策略[J]. 电工技术学报, 2023, 38(4): 983-997.
Liu Jilong, Chen Peng, Xiao Fei, et al.Control strategy of 10 kV/2 MW modular multilevel bidirectional DC-DC converter for vessel integrated power system[J]. Transactions of China Electrotechnical Society, 2023, 38(4): 983-997.
[6] 吴丽丽, 茆美琴, 施永. 含主动限流控制的MMCHVDC电网直流短路故障电流解析计算[J]. 电工技术学报, 2024, 39(3): 785-797.
Wu Lili, Mao Meiqin, Shi Yong.Analytical calculation of DC short-circuit fault current in MMCHVDC power grid with active current limiting control[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 785-797.
[7] 张国驹, 裴玮, 杨鹏, 等. 中压配电网柔性互联设备的电路拓扑与控制技术综述[J]. 电力系统自动化, 2023, 47(6): 18-29.
Zhang Guoju, Pei Wei, Yang Peng, et al.Review on circuit topology and control technology of flexible interconnection devices for medium-voltage distribution network[J]. Automation of Electric Power Systems, 2023, 47(6): 18-29.
[8] 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.
[9] 李光辉, 王伟胜, 刘纯, 等. 直驱风电场接入弱电网宽频带振荡机理与抑制方法(一): 宽频带阻抗特性与振荡机理分析[J]. 中国电机工程学报, 2019, 39(22): 6547-6562.
Li Guanghui, Wang Weisheng, Liu Chun, et al.Mechanism analysis and suppression method of wideband oscillation of PMSG wind farms connected to weak grid (part Ⅰ): analysis of wideband impedance characteristics and oscillation mechanism[J]. Proceedings of the CSEE, 2019, 39(22): 6547-6562.
[10] Gu Tianming, Wang Puyu, Liu Dingyuan, et al.Modeling and small-signal stability analysis of doubly-fed induction generator integrated system[J]. Global Energy Interconnection, 2023, 6(4): 438-449.
[11] Harnefors L, Bongiorno M, Lundberg S.Inputadmittance calculation and shaping for controlled voltage-source converters[J]. IEEE Transactions on Industrial Electronics, 2007, 54(6): 3323-3334.
[12] Wen Bo, 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.
[13] Huang Linbin, Xin Huanhai, Li Zhiyi, et al.Gridsynchronization stability analysis and loop shaping for PLL-based power converters with different reactive power control[J]. IEEE Transactions on Smart Grid, 2020, 11(1): 501-516.
[14] 吴广禄, 周孝信, 王姗姗, 等. 柔性直流输电接入弱交流电网时锁相环和电流内环交互作用机理解析研究[J]. 中国电机工程学报, 2018, 38(9): 2622-2633, 2830.
Wu Guanglu, Zhou Xiaoxin, Wang Shanshan, et al.Analytical research on the mechanism of the interaction between PLL and inner current loop when VSC-HVDC connected to weak grid[J]. Proceedings of the CSEE, 2018, 38(9): 2622-2633, 2830.
[15] Lü Jing, Zhang Xin, Cai Xu, et al.Harmonic statespace based small-signal impedance modeling of a modular multilevel converter with consideration of internal harmonic dynamics[J]. IEEE Transactions on Power Electronics, 2019, 34(3): 2134-2148.
[16] 李探, Aniruddha MGole, 赵成勇. 考虑内部动态特性的模块化多电平换流器小信号模型[J]. 中国电机工程学报, 2016, 36(11): 2890-2899.
Li Tan, Gole Aniruddha M, Zhao Chengyong.Smallsignal model of the modular multilevel converter considering the internal dynamics[J]. Proceedings of the CSEE, 2016, 36(11): 2890-2899.
[17] 涂春鸣, 邹凯星, 高家元, 等. 基于不对称正负反馈效应的PQ功率控制并网逆变器稳定性分析[J]. 电工技术学报, 2023, 38(2): 496-509.
Tu Chunming, Zou Kaixing, Gao Jiayuan, et al.Stability analysis of grid-connected inverter under PQ power control based on asymmetric positive-negativefeedback effects[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 496-509.
[18] Xu Zigao, Li Binbin, Li Shengyuan, et al.MMC admittance model simplification based on signal-flow graph[J]. IEEE Transactions on Power Electronics, 2022, 37(5): 5547-5561.
[19] 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 circulation equalization strategy of modular multilevel converter in unbalanced power grid[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 541-553.
[20] Sakinci Ö C, Beerten J.Generalized dynamic phasor modeling of the MMC for small-signal stability analysis[J]. IEEE Transactions on Power Delivery, 2019, 34(3): 991-1000.
[21] 宗皓翔, 吕敬, 张琛, 等. MMC多维阻抗模型及其在风场-柔直交互稳定分析中的应用[J]. 中国电机工程学报, 2021, 41(14): 4941-4953.
Zong Haoxiang, Lü Jing, Zhang Chen, et al.MIMO impedance model of MMC and its application in the wind farm-HVDC interaction stability analysis[J]. Proceedings of the CSEE, 2021, 41(14): 4941-4953.
[22] Zhu Shu, Qin Liang, Liu Kaipei, et al.Impedance modeling of modular multilevel converter in D-Q and modified sequence domains[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2022, 10(4): 4361-4382.
[23] 吕敬, 蔡旭, 张占奎, 等. 海上风电场经MMCHVDC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): 3771-3781.
Lü Jing, 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): 3771-3781.
[24] 王燕宁, 郭春义, 王烨. 控制系统对两端MMCHVDC系统小信号稳定性的影响[J]. 电工电能新技术, 2019, 38(10): 20-31.
Wang Yanning, Guo Chunyi, Wang Ye.Impact of control system on small-signal stability of twoterminal MMC-HVDC system[J]. Advanced Technology of Electrical Engineering and Energy, 2019, 38(10): 20-31.
[25] Wang Xiongfei, Blaabjerg F.Harmonic stability in power electronic-based power systems: concept, modeling, and analysis[J]. IEEE Transactions on Smart Grid, 2019, 10(3): 2858-2870.
[26] Gong Hong, Wang Xiongfei, Harnefors L.Rethinking current controller design for PLL-synchronized VSCs in weak grids[J]. IEEE Transactions on Power Electronics, 2022, 37(2): 1369-1381.
[27] 吴广禄, 王姗姗, 周孝信, 等. VSC接入弱电网时外环有功控制稳定性解析[J]. 中国电机工程学报, 2019, 39(21): 6169-6183.
Wu Guanglu, Wang Shanshan, Zhou Xiaoxin, et al.Analytical analysis on the active power control stability of the weak grids-connected VSC[J]. Proceedings of the CSEE, 2019, 39(21): 6169-6183.
[28] Leng Minrui, Zhou Guohua, Li Haoze, et al.Impedance-based stability evaluation for multibus DC microgrid without constraints on subsystems[J]. IEEE Transactions on Power Electronics, 2022, 37(1): 932-943.
[29] Samanes J, Urtasun A, Barrios E L, et al.Control design and stability analysis of power converters: the MIMO generalized Bode criterion[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2020, 8(2): 1880-1893.
[30] Chen Feifan, Zhao Liang, Harnefors L, et al.Enhanced Q-axis voltage-integral damping control for fast PLL-synchronized inverters in weak grids[J]. IEEE Transactions on Power Electronics, 2024, 39(1): 424-435.
[31] Harnefors L, Kukkola J, Routimo M, et al.A universal controller for grid-connected voltage-source converters[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(5): 5761-5770.