System Voltage Support Strength Evaluation for Renewables HVDC Transmission System Considering Operating Condition
Wang Xiangyu1, Xin Huanhai1, Fu Chuang2, Ma Fuyilong1, Hou Zhixian1
1. College of Electrical Engineering Zhejiang University Hangzhou 310027 China; 2. Electric Power Research Institute China Southern Power Grid Guangzhou 510663 China
Abstract：Large-scale renewable energy transmission via high voltage direct current system (HVDC) has become a typical scenario in modern power system. The evaluation method of voltage support strength (referred to as system strength) based on the generalized short-circuit ratio index can describe the stability margin of renewable energy transmission system via two-level converter HVDC. However, modular multilevel converter high voltage direct current system (MMC-HVDC) is more commonly utilized in power transmission of renewable bases. Compared with the two-level converter HVDC, MMC-HVDC is more complicated in dynamical characteristic because of complex harmonic coupling. Consequently, it remains unclear how to quantify the voltage support capability of the ac grid containing MMC-HVDC, especially when analyzing small-disturbance voltage stability. Furthermore, the operating conditions of renewables are changing in the actual operating system. Operating conditions have a significant impact on the stability of the system, further increasing the difficulty of assessing the system strength. To solve the challenge mentioned above, this paper proposes the system strength assessment method considering operating conditions, focusing on small-disturbance voltage stability. Firstly, the frequency-domain closed-loop transfer function matrix of the renewables MMC-HVDC transmission system (RMTS) is established by linearization of the state equations at the stable operating point. The sensitivity relationship between bus voltage response and small-disturbance current is described by impedance matrix. Based on the transfer function matrix, the closed-loop characteristic equation of RMTS is derived. Secondly, the small-disturbance voltage support capability of MMC-HVDC is analyzed equivalently based on the maximum singular value of its impedance matrix, and an equivalent model of MMC-HVDC is proposed accordingly. This equivalence results in modification to the ac grid admittance matrix. Then, the definition of generalized operational short-circuit ratio (gOSCR) is extended to RMTS considering operating conditions. The relative difference between gOSCR and critical gOSCR is defined as the stability margin of RMTS, as performing the evaluation of the system strength. Finally, the effectiveness of the proposed methods is verified by electromagnetic transient simulation of 4-infeed RMTS in varied operating conditions. The results show that the evaluation results correspond with time-domain simulation waveform. The following conclusion can be drawn: (1) The critical gOSCR reflects the tolerance of renewable energy devices to the ac grid strength supported by MMC-HVDC, which is related to the characteristics of devices. The gOSCR characterizes the voltage support capability of ac grids with MMC-HVDC. By comparing the gOSCR and critical gOSCR, the small-disturbance voltage stability of RMTS can be assessed in a rapid way, avoiding massive work of electromagnetic transient modeling. The proposed method can be applied in both the operational scenario and the planning phase. (2) The variation of power output and bus voltage of renewable energy are reflected in gOSCR. When the output of the renewables increases, the bus voltage of the renewables gradually decreases, leading to reduction in the system stability margin of RMTS and thus a decrease in system stability margin. (3) The gOSCR is also determined by the voltage support dynamic characteristics of MMC-HVDC. When the voltage support dynamic of MMC-HVDC approaches ideal voltage source, the gOSCR increases, resulting in increment of RMTS stability margin.
王祥宇, 辛焕海, 傅闯, 马富艺龙, 侯智贤. 考虑实际工况的新能源经柔性直流送出系统强度评估[J]. 电工技术学报, 2025, 40(15): 4708-4721.
Wang Xiangyu, Xin Huanhai, Fu Chuang, Ma Fuyilong, Hou Zhixian. System Voltage Support Strength Evaluation for Renewables HVDC Transmission System Considering Operating Condition. Transactions of China Electrotechnical Society, 2025, 40(15): 4708-4721.
[1] 杨鹏, 刘锋, 姜齐荣, 等. “双高”电力系统大扰动稳定性: 问题、挑战与展望[J]. 清华大学学报(自然科学版), 2021, 61(5): 403-414. Yang Peng, Liu Feng, Jiang Qirong, et al.Large disturbance stability of “double high” power system: problems, challenges and prospects[J]. Journal of Tsinghua University (Science and Technology), 2021, 61(5): 403-414. [2] Wang Weisheng, Li Guanghui, Guo Jianbo.Large-scale renewable energy transmission by HVDC: challenges and proposals[J]. Engineering, 2022, 19: 252-267. [3] Wang Yifan, Zhao Chengyong, Guo Chunyi, et al.Dynamics and small signal stability analysis of PMSG-based wind farm with an MMC-HVDC system[J]. CSEE Journal of Power and Energy Systems, 2020, 6(1): 226-235. [4] 郭贤珊, 李云丰, 谢欣涛, 等. 直驱风电场经柔直并网诱发的次同步振荡特性[J]. 中国电机工程学报, 2020, 40(4): 1149-1160, 1407. Guo Xianshan, Li Yunfeng, Xie Xintao, et al.Sub-synchronous oscillation characteristics caused by PMSG-based wind plant farm integrated via flexible HVDC system[J]. Proceedings of the CSEE, 2020, 40(4): 1149-1160, 1407. [5] 邵冰冰, 赵峥, 肖琪, 等. 多直驱风机经柔直并网系统相近次同步振荡模式参与因子的弱鲁棒性分析[J]. 电工技术学报, 2023, 38(3): 754-769. Shao Bingbing, Zhao Zheng, Xiao Qi, et al.Weak robustness analysis of close subsynchronous oscillation modes' participation factors in multiple direct-drive wind turbines with the VSC-HVDC system[J]. Transactions of China Electrotechnical Society, 2023, 38(3): 754-769. [6] 王一凡, 赵成勇, 郭春义. 双馈风电场孤岛经模块化多电平换流器直流输电并网系统小信号稳定性分析与振荡抑制方法[J]. 电工技术学报, 2019, 34(10): 2116-2129. Wang Yifan, Zhao Chengyong, Guo Chunyi.Small signal stability and oscillation suppression method for islanded double fed induction generator-based wind farm integrated by modular multilevel converter based HVDC system[J]. Transactions of China Electrotechnical Society, 2019, 34(10): 2116-2129. [7] 李光辉, 王伟胜, 郭剑波, 等. 风电场经MMC-HVDC送出系统宽频带振荡机理与分析方法[J]. 中国电机工程学报, 2019, 39(18): 5281-5297, 5575. Li Guanghui, Wang Weisheng, Guo Jianbo, et al.Broadband oscillation mechanism and analysis for wind farm integration through MMC-HVDC system[J]. Proceedings of the CSEE, 2019, 39(18): 5281-5297, 5575. [8] 辛焕海, 董炜, 袁小明, 等. 电力电子多馈入电力系统的广义短路比[J]. 中国电机工程学报, 2016, 36(22): 6013-6027. Xin Huanhai, Dong Wei, Yuan Xiaoming, et al.Generalized short circuit ratio for multi power electronic based devices infeed to power systems[J]. Proceedings of the CSEE, 2016, 36(22): 6013-6027. [9] 辛焕海, 甘德强, 鞠平. 多馈入电力系统广义短路比: 多样化新能源场景[J]. 中国电机工程学报, 2020, 40(17): 5516-5527. Xin Huanhai, Gan Deqiang, Ju Ping.Generalized short circuit ratio of power systems with multiple power electronic devices: analysis for various renewable power generations[J]. Proceedings of the CSEE, 2020, 40(17): 5516-5527. [10] CIGRE Working Group B4.41. Systems with multiple DC infeed[R]. Paris, France: CIGRE, 2008. [11] 于琳, 孙华东, 赵兵, 等. 新能源并网系统短路比指标分析及临界短路比计算方法[J]. 中国电机工程学报, 2022, 42(3): 919-929. Yu Lin, Sun Huadong, Zhao Bing, et al.Short circuit ratio index analysis and critical short circuit ratio calculation of renewable energy grid-connected system[J]. Proceedings of the CSEE, 2022, 42(3): 919-929. [12] 刘晨曦, 辛焕海. 考虑实际工况的新能源多馈入系统广义运行短路比[J]. 电力系统自动化, 2025, 49(8): 12-20. Liu Chenxi, Xin Huanhai.Generalized operational short circuit ratio of renewable energy multi-infeed systems considering actual operating conditions[J]. Automation of Electric Power Systems, 2025, 49(8): 12-20. [13] 徐政. 新型电力系统背景下电网强度的合理定义及其计算方法[J]. 高电压技术, 2022, 48(10): 3805-3819. Xu Zheng.Reasonable definition and calculation method of power grid strength under the background of new type power systems[J]. High Voltage Engineering, 2022, 48(10): 3805-3819. [14] 马富艺龙, 辛焕海, 刘晨曦, 等. 新能源基地柔性直流送出系统小扰动电压支撑强度评估[J]. 电工技术学报, 2023, 38(21): 5758-5770, 5938. Ma Fuyilong, Xin Huanhai, Liu Chenxi, et al.Small-disturbance system voltage support strength assessment method for renewables VSC-HVDC delivery system[J]. Transactions of China Electrotechnical Society, 2023, 38(21): 5758-5770, 5938. [15] 张志强, 李秋彤, 余浩, 等. 海上直驱风电经柔直并网系统的次/超同步振荡特性分析[J]. 上海交通大学学报, 2022, 56(12): 1572-1583. Zhang Zhiqiang, Li Qiutong, Yu Hao, et al.Analysis of sub/super-synchronous oscillation of direct-drive offshore wind power grid-connected system via VSC-HVDC[J]. Journal of Shanghai Jiao Tong University, 2022, 56(12): 1572-1583. [16] Dong Wei, Xin Huanhai, Wu Di, et al.Small signal stability analysis of multi-infeed power electronic systems based on grid strength assessment[J]. IEEE Transactions on Power Systems, 2019, 34(2): 1393-1403. [17] 李龙源, 付瑞清, 吕晓琴, 等. 接入弱电网的同型机直驱风电场单机等值建模[J]. 电工技术学报, 2023, 38(3): 712-725. Li Longyuan, Fu Ruiqing, Lü Xiaoqin, et al.Single machine equivalent modeling of weak grid connected wind farm with same type PMSGs[J]. Transactions of China Electrotechnical Society, 2023, 38(3): 712-725. [18] 李探, Aniruddha M.Gole, 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 A M, Zhao Chengyong.Small-signal model of the modular multilevel converter considering the internal dynamics[J]. Proceedings of the CSEE, 2016, 36(11): 2890-2899. [19] Wang Zhong, Lü Jing, Rao Yiming, et al.Data-driven impedance identification and stability online assessment of DFIG-based wind farm integration with MMC-HVDC[C]//2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, China, 2023: 4500-4504. [20] 周瑀涵, 辛焕海, 鞠平. 基于广义短路比的多馈入系统强度量化原理与方法: 回顾、探讨与展望[J]. 中国电机工程学报, 2023, 43(10): 3794-3811. Zhou Yuhan, Xin Huanhai, Ju Ping.System strength quantification principle and method of multi-infeed systems based on generalized short-circuit ratio: reviews, discussions and outlooks[J]. Proceedings of the CSEE, 2023, 43(10): 3794-3811. [21] 迟永宁, 江炳蔚, 胡家兵, 等. 构网型变流器: 物理本质与特征[J]. 高电压技术, 2024, 50(2): 590-604. Chi Yongning, Jiang Bingwei, Hu Jiabing, et al.Grid-forming converters: physical mechanism and characteristics[J]. High Voltage Engineering, 2024, 50(2): 590-604. [22] 吕敬, 蔡旭. 提高风场柔直并网系统稳定性的控制器参数优化设计[J]. 中国电机工程学报, 2018, 38(2): 431-443, 674. Lü Jing, Cai Xu.Controller parameters optimization design for enhancing the stability of wind farm with VSC-HVDC system[J]. Proceedings of the CSEE, 2018, 38(2): 431-443, 674. [23] Fang Qiao, Xing Facai, Jiang Zhe, et al.Equivalence analysis of different sequence impedance modeling methods[C]//2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, China, 2023: 3800-3805. [24] 辛焕海, 刘晨曦, 黄林彬, 等. 基于特征子系统的广义短路比导出原理及计算方法[J]. 中国电机工程学报, 2025, 45(7): 2447-2461. Xin Huanhai, Liu Chenxi, Huang Linbin, et al.Derivation principle and calculation method for generalized short-circuit ratio based on eigen-subsystems[J]. Proceedings of the CSEE, 2025, 45(7): 2447-2461.
2025, Vol. 40 
