Abstract：When multiple EMUs are simultaneously in a light-load starting condition within the traction network, it can lead to low-frequency oscillations in the traction network voltage. In severe cases, this may trigger traction locking, which poses a risk to the operational safety of high-speed trains. To address the issue of low-frequency oscillation, this study proposes a method based on virtual impedance for its suppression. First, the impedance model of the EMUs-traction network coupling system is derived, and its stability is analyzed using the impedance ratio stability criterion and the Bode diagram. Second, based on the stability criterion, virtual impedance is incorporated into the EMU control strategy to correct the impedance characteristics of the load subsystem, thereby proposing a low-frequency oscillation suppression method. Third, an adaptive control method for virtual impedance is designed to handle the complex and dynamic working conditions, enabling the system to adjust the virtual impedance parameters and enhance the effectiveness of the suppression method. Finally, the proposed control strategy is compared with the traditional approach through a low-power experimental platform, validating the effectiveness of the suppression method. The results of the system stability analysis indicate that the logarithmic amplitude-frequency characteristic curve of the system impedance ratio is significantly lower than 0 dB when only one unit (m=1) is connected to the traction network, and the absolute value of the system impedance ratio |Tsn(s)| is much less than 1, suggesting system stability. As the value of m increases, the amplitude-frequency characteristic curve approaches 0 dB, resulting in a decline in system stability. When m=6, the amplitude-frequency characteristic curve crosses 0 dB at 7.032 Hz, and the phase angle at the crossover frequency (fc) is 182°. The absolute value of the phase angle exceeds 180°, and the system impedance ratio |Tsn(s)| does not meet the condition of being significantly less than 1, indicating an unstable state. Simulation results with the virtual impedance control strategy indicate that when six EMUs are connected to the traction network at the same time, when the virtual impedance Rp values are 10 Ω, 5 Ω, 2 Ω and 1 Ω respectively, the system voltage and current reach a steady state at 1.6 s, 1 s, 0.3 s, and 0.2 s, respectively. The suppression effect improves as the virtual impedance decreases. The simulation results with the adaptive virtual impedance control strategy show that when six EMUs are connected to the traction network, the system reaches a steady state in approximately 0.5 s. The voltage regulation time for the DC side of the EMUs is 0.46 s, with an overshoot of 37.71% and a post-stabilization voltage fluctuation of 58 V. Subsequently, one EMU with adaptive virtual impedance control is added every 2 seconds, resulting in a total of 11 EMUs. The system remains stable, and the virtual impedance value is reduced to 4.61. The comparative experimental results indicate that, after transitioning from the traditional control strategy to the adaptive virtual impedance control strategy, the system can rapidly recover from a low-frequency oscillation at approximately 7 Hz. Furthermore, the AC-side voltage stabilizes at 20 V, while the DC-side voltage remains stable at 40 V. Based on the analysis, the following conclusions can be drawn: (1) A higher impedance ratio between the two sides of the EMUs-traction network coupling system results in decreased system stability. When the impedance ratio does not meet the stability criterion, system instability is induced, leading to low-frequency oscillations. (2) The incorporation of parallel virtual impedance in the control strategy for the EMU's four-quadrant converter can correct the impedance characteristics of the load subsystem, enhance system stability, and suppress low-frequency oscillation. (3) The adaptive virtual impedance control method can autonomously adjust the virtual impedance value based on the intensity of voltage oscillations on the network side of the EMU, thereby suppressing low-frequency oscillations under varying load conditions, improving the adaptability of the control strategy, and ensuring the stable operation of the EMUs-traction network coupling system across different operating conditions.
逯华, 王喜莲, 周锦晗, 何婷婷. 基于虚拟阻抗的车网耦合系统低频振荡抑制[J]. 电工技术学报, 2025, 40(11): 3381-3394.
Lu Hua, Wang Xilian, Zhou Jinhan, He Tingting. Low-Frequency Oscillation Suppression of EMUs-Traction Network Coupling System Based on Virtual Impedance. Transactions of China Electrotechnical Society, 2025, 40(11): 3381-3394.
[1] 孟昭斐, 胡海涛, 周毅. 电力机车运行工况对车网系统低频振荡的影响规律研究[J]. 电气工程学报, 2022, 17(2): 131-141. Meng Zhaofei, Hu Haitao, Zhou Yi.Study on the influence law of electric vehicle on low frequency oscillation of vehicle-network system under operating condition[J]. Journal of Electrical Engineering, 2022, 17(2): 131-141. [2] Hu Haitao, Tao Haidong, Blaabjerg F, et al.Train-network interactions and stability evaluation in high-speed railways-part Ⅰ: phenomena and modeling[J]. IEEE Transactions on Power Electronics, 2018, 33(6): 4627-4642. [3] Hu Haitao, Tao Haidong, Wang Xiongfei, et al.Train-network interactions and stability evaluation in high-speed railways: part Ⅱ: influential factors and verifications[J]. IEEE Transactions on Power Electronics, 2018, 33(6): 4643-4659. [4] Hu Haitao, Zhou Yi, Li Xin, et al.Low-frequency oscillation in electric railway depot: a comprehensive review[J]. IEEE Transactions on Power Electronics, 2021, 36(1): 295-314. [5] 付莉, 张桂南, 高仕斌. 高速铁路车网耦合系统网压振荡模态分析与对策[J]. 电力系统保护与控制, 2016, 44(1): 24-32. Fu Li, Zhang Guinan, Gao Shibin.Modal analysis and countermeasures on voltage low frequency oscillation of high-speed railway traction network and EMU coupling system[J]. Power System Protection and Control, 2016, 44(1): 24-32. [6] 周毅, 胡海涛, 雷科, 等. 电气化铁路低频等幅振荡机理分析[J]. 中国电机工程学报, 2021, 41(9): 3024-3037. Zhou Yi, Hu Haitao, Lei Ke, et al.Mechanism analysis of the sustained low-frequency oscillation in the electric railway system[J]. Proceedings of the CSEE, 2021, 41(9): 3024-3037. [7] 孔睿, 吕晓琴, 王晓茹, 等. 列车混运的车网系统低频振荡建模与分析[J]. 中国电机工程学报, 2023, 43(10): 3768-3781. Kong Rui, Lü Xiaoqin, Wang Xiaoru, et al.Modeling and analysis of low frequency oscillation in train-network system under mixed operation of trains[J]. Proceedings of the CSEE, 2023, 43(10): 3768-3781. [8] 胡颖新, 宁志毫, 兰征, 等. 基于滑模控制的牵引网低频振荡抑制方法[J]. 电气工程学报, 2022, 17(1): 129-136. Hu Yingxin, Ning Zhihao, Lan Zheng, et al.Low frequency oscillation suppression method of traction network based on sliding mode control[J]. Journal of Electrical Engineering, 2022, 17(1): 129-136. [9] 唐圣德, 胡海涛, 肖冬华, 等. 基于阻抗测量信息的电气化铁路“多车共网” 系统稳定性分析[J]. 电工技术学报, 2024, 39(19): 6039-6053. Tang Shengde, Hu Haitao, Xiao Donghua, et al.Stability analysis of electrified railway multiple train-network system based on impedance measurement information[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 6039-6053. [10] Liu Zhigang, Hu Xinxuan, Liao Yicheng.Vehicle-grid system stability analysis based on norm criterion and suppression of low-frequency oscillation with MMC-STATCOM[J]. IEEE Transactions on Transportation Electrification, 2018, 4(3): 757-766. [11] Wu Siqi, Liu Zhigang.Low-frequency stability analysis of vehicle-grid system with active power filter based on dq-frame impedance[J]. IEEE Transactions on Power Electronics, 2021, 36(8): 9027-9040. [12] 张桂南, 刘志刚, 向川, 等. 高铁车网耦合系统电压低频振荡现象机理研究[J]. 电网技术, 2015, 39(7): 1956-1962. Zhang Guinan, Liu Zhigang, Xiang Chuan, et al.Mechanism on voltage low frequency oscillation of high-speed railway traction network and EMU coupling system[J]. Power System Technology, 2015, 39(7): 1956-1962. [13] 姚书龙, 刘志刚, 张桂南, 等. 基于自抗扰控制的牵引网网压低频振荡抑制方法[J]. 电网技术, 2016, 40(1): 207-213. Yao Shulong, Liu Zhigang, Zhang Guinan, et al.A novel approach based on ADRC to traction network voltage low frequency oscillation suppression research[J]. Power System Technology, 2016, 40(1): 207-213. [14] Zhang Guinan, Liu Zhigang, Yao Shulong, et al.Suppression of low-frequency oscillation in traction network of high-speed railway based on auto-disturbance rejection control[J]. IEEE Transactions on Transportation Electrification, 2016, 2(2): 244-255. [15] 许加柱, 程慧婕, 黄文, 等. 自适应自抗扰比例积分控制下的高速铁路车网耦合系统低频振荡抑制方法[J]. 中国电机工程学报, 2018, 38(14): 4035-4045, 4309. Xu Jiazhu, Cheng Huijie, Huang Wen, et al.A novel approach based on self-adaptive auto disturbance rejection proportional integral controller to suppress low frequency oscillation of high speed railway electric multiple units-traction network coupling system[J]. Proceedings of the CSEE, 2018, 38(14): 4035-4045, 4309. [16] 喻文倩, 刘志刚, 张友刚, 等. 一种改进的高铁牵引变流器反馈线性化控制策略[J]. 电工技术学报, 2023, 38(8): 2136-2147. Yu Wenqian, Liu Zhigang, Zhang Yougang, et al.An improved feedback linearization control strategy for high-speed railway traction converters[J]. Transactions of China Electrotechnical Society, 2023, 38(8): 2136-2147. [17] 王颖杰, 邢涛, 焦岚轶, 等. 基于模糊PI控制的牵引网低频振荡抑制方法[J]. 铁道学报, 2021, 43(3): 62-69. Wang Yingjie, Xing Tao, Jiao Lanyi, et al.Low-frequency oscillation suppression method for traction network based on fuzzy PI control[J]. Journal of the China Railway Society, 2021, 43(3): 62-69. [18] 刘沁怡, 黄伟煌, 郭铸, 等. 基于自适应虚拟阻抗的多并联构网型变流器无功功率分配策略[J]. 电力系统自动化, 2024, 48(15): 122-130. Liu Qinyi, Huang Weihuang, Guo Zhu, et al.Reactive power sharing strategy for multiple parallel grid-forming converters based on adaptive virtual impedance[J]. Automation of Electric Power Systems, 2024, 48(15): 122-130. [19] 谢飞, 许建平, 郭夏, 等. 基于虚拟阻抗的三相Buck整流器输入不平衡控制策略[J]. 电工技术学报, 2024, 39(14): 4456-4466. Xie Fei, Xu Jianping, Guo Xia, et al.A control strategy based on virtual impedance for three-phase buck rectifier under unbalanced phase-voltages[J]. Transactions of China Electrotechnical Society, 2024, 39(14): 4456-4466. [20] 高磊, 吕敬, 马骏超, 等. 基于电路等效的并网逆变器失稳分析与稳定控制[J]. 电工技术学报, 2024, 39(8): 2325-2341. Gao Lei, Lü Jing, Ma Junchao, et al.Instability analysis and stability control of grid-connected inverter based on impedance circuit equivalent[J]. Transactions of China Electrotechnical Society, 2024, 39(8): 2325-2341. [21] Guan Yuanpeng, Xie Yunxiang, Wang Yu, et al.An active damping strategy for input impedance of bidirectional dual active bridge DC-DC converter: modeling, shaping, design, and experiment[J]. IEEE Transactions on Industrial Electronics, 2021, 68(2): 1263-1274. [22] He Jinwei, Li Yun wei. Generalized closed-loop control schemes with embedded virtual impedances for voltage source converters with LC or LCL filters[J]. IEEE Transactions on Power Electronics, 2012, 27(4): 1850-1861. [23] Bao Chenlei, Ruan Xinbo, Wang Xuehua, et al.Step-by-step controller design for LCL-type grid-connected inverter with capacitor-current-feedback active-damping[J]. IEEE Transactions on Power Electronics, 2014, 29(3): 1239-1253. [24] Pan Donghua, Ruan Xinbo, Bao Chenlei, et al.Capacitor-current-feedback active damping with reduced computation delay for improving robustness of LCL-type grid-connected inverter[J]. IEEE Tran-sactions on Power Electronics, 2014, 29(7): 3414-3427. [25] He Yuying, Wang Xuehua, Ruan Xinbo, et al.Capacitor-current proportional-integral positive feedback active damping for LCL-type grid-connected inverter to achieve high robustness against grid impedance variation[J]. IEEE Transactions on Power Electronics, 2019, 34(12): 12423-12436. [26] Shuai Zhikang, Cheng Huijie, Xu Jiazhu, et al.A Notch filter-based active damping control method for low-frequency oscillation suppression in train-network interaction systems[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2019, 7(4): 2417-2427. [27] Brenna M, Foiadelli F, Zaninelli D.New stability analysis for tuning PI controller of power converters in railway application[J]. IEEE Transactions on Industrial Electronics, 2011, 58(2): 533-543. [28] 王晴, 刘增, 韩鹏程, 等. 基于变流器输出阻抗的直流微电网下垂并联系统振荡机理与稳定边界分析[J]. 电工技术学报, 2023, 38(8): 2148-2161. Wang Qing, Liu Zeng, Han Pengcheng, et al.Analysis of oscillation mechanism and stability boundary of droop-controlled parallel converters based on output impedances of individual converters in DC microgrids[J]. Transactions of China Electrotechnical Society, 2023, 38(8): 2148-2161. [29] 冯晓云. 电力牵引交流传动及其控制系统[M]. 北京: 高等教育出版社, 2009.
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