Series compensation devices are widely used in power systems. The wind farms grid-connected system composed of large-scale direct permanent magnet synchronous generator with series compensation has the risk of small interference instability in the sub-synchronous oscillation category. Most of the existing literatures are aimed at doubly-fed wind farms. There are few studies on the PMSGs grid-connected wind farm system through series compensation lines, and most of them are based on simulation analysis, lacking in-depth research on the mechanism and analysis of the relationship between various parameters. At the same time, the stability analysis methods of wind farm grid-connected system generally include impedance analysis and mode analysis. However, the system impedance obtained by impedance analysis method is a sufficient but not necessary condition for system stability, which leads to its limitations. Mode analysis method needs to establish a refined model of electromagnetic transient level of power system. When the model scale is too large, there are some problems such as difficult calculation and longtime consumption.
Aiming at the research of the above literatures and existing problems, this paper puts forward a simplified model method and corresponding stability criterion based on different time scales for the stability analysis of PMSG grid-connected wind farm with series compensation lines. Firstly, a full-order model of the system for small signal analysis is established, which can be used to clarify the dominant mode of the system. Then, according to the different time scales studied, each part of the grid-connected system is reasonably simplified and the simplified characteristic equation is solved. Then the analytical stability criteria at different time scales are obtained by using Routh-Hurwitz criterion, and the mechanism explanation of the stability of the system at different time scales is given. Finally, the boundary of the stability criterion is visualized by using the analysis method of feasible region, and the accuracy of the stability criterion is verified by nonlinear simulation.
According to the simulation results, when studying the oscillation on the time scale of AC current, the oscillation frequency of the dominant mode of the system is around 38Hz, and this mode is a phase-locked loop mode, which is unstable with the increase of the equivalent reactance Xc of the series compensation device. Through the analysis of feasible region, the critical stable value of Xc decreases with the increase of xL and increases with the increase of Kp. When studying the oscillation on the time scale of DC voltage, the oscillation frequency of the dominant mode of the system is around 2Hz, and this mode is the outer loop mode of the grid-side converter, which is unstable with the decrease of the equivalent reactance Xc. Through the analysis of feasible region, the critical stable value of Xc increases with the increase of xL and decreases with the increase of Kpdc.
In summary, this paper has the following conclusions: (1) According to the different frequency ranges, this paper simplifies the grid-connected system and lists the simplified characteristic equation. (2) When the grid-connected system oscillates in the time scale of DC voltage, the instability risk of the system decrease with the increase of Xc. However, when the system oscillates in the time scale of AC current, the instability risk of the system increase with the increase of Xc. (3) When the time scale of analysis is different, different parameters have different effects on the critical stability value of Xc.
[1] 马伟明. 关于电工学科前沿技术发展的若干思考[J]. 电工技术学报, 2021, 36(22): 4627-4636.
Ma Weiming.Thoughts on the development of frontier technology in electrical engineering[J]. Transactions of China Electrotechnical Society, 2021, 36(22): 4627-4636.
[3] 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.
[4] 韩应生, 孙海顺, 秦世耀, 等. 电压源型双馈风电并网系统小扰动低频稳定性分析[J]. 电工技术学报, 2023, 38(5): 1312-1324, 1374.
Han Yingsheng, Sun Haishun, Qin Shiyao, et al.Low-frequency stability analysis of voltage-sourced doubly-fed wind power grid-connected system under small disturbance[J]. Transactions of China Electrotechnical Society, 2023, 38(5): 1312-1324, 1374.
[5] 颜湘武, 常文斐, 崔森, 等. 基于线性自抗扰控制的静止无功补偿器抑制弱交流风电系统次同步振荡策略[J]. 电工技术学报, 2022, 37(11): 2825-2836.
Yan Xiangwu, Chang Wenfei, Cui Sen, et al.Sub-synchronous oscillation suppression strategy of weak AC wind power system with static var compensator based on linear active disturbance rejection control[J]. Transactions of China Electrotechnical Society, 2022, 37(11): 2825-2836.
[6] 刘其辉, 洪晨威, 逄思敏, 等. 基于弹性系数的双馈风电机组控制参数对次同步振荡作用分析及调整方法[J]. 电工技术学报, 2022, 37(14): 3528-3541.
Liu Qihui, Hong Chenwei, Pang Simin, et al.Analysis and adjustment method of doubly-fed fan control parameters on subsynchronous oscillation based on impedance elastic sensitivity[J]. Transactions of China Electrotechnical Society, 2022, 37(14): 3528-3541.
[7] 刘其辉, 逄思敏, 吴林林, 等. 大规模风电汇集系统电压不平衡机理、因素及影响规律[J]. 电工技术学报, 2022, 37(21): 5435-5450.
Liu Qihui, Pang Simin, Wu Linlin, et al.The mechanism, factors and influence rules of voltage imbalance in wind power integration areas[J]. Transactions of China Electrotechnical Society, 2022, 37(21): 5435-5450.
[8] 薛峰, 吴家龙, 崔晓丹, 等. 基于阻抗辨识的沽源地区风电并网系统次同步振荡控制策略[J]. 电力系统自动化, 2023, 47(5): 200-207.
Xue Feng, Wu Jialong, Cui Xiaodan, et al.Sub-synchronous oscillation control strategy based on impedance identification for wind power grid-connected system in Guyuan area of China[J]. Automation of Electric Power Systems, 2023, 47(5): 200-207.
[9] Song Yipeng, Blaabjerg F.Overview of DFIG-based wind power system resonances under weak networks[J]. IEEE Transactions on Power Electronics, 2017, 32(6): 4370-4394.
[10] Liu Huakun, Xie Xiaorong, Zhang Chuanyu, et al.Quantitative SSR analysis of series-compensated DFIG-based wind farms using aggregated RLC circuit model[J]. IEEE Transactions on Power Systems, 2017, 32(1): 474-483.
[11] Xie Xiaorong, Zhang Xu, Liu Huakun, et al.Characteristic analysis of subsynchronous resonance in practical wind farms connected to series-compensated transmissions[J]. IEEE Transactions on Energy Conversion, 2017, 32(3): 1117-1126.
[12] Zhao Shuqiang, Wang Nan, Li Ren, et al.Sub-synchronous control interaction between direct-drive PMSG-based wind farms and compensated grids[J]. International Journal of Electrical Power & Energy Systems, 2019, 109(7): 609-617.
[13] Xu Yangkun, Zhang Miao, Fan Lingling, et al.Small-signal stability analysis of type-4 wind in series-compensated networks[J]. IEEE Transactions on Energy Conversion, 2020, 35(1): 529-538.
[14] Beza M, Bongiorno M.On the risk for subsynchronous control interaction in type 4 based wind farms[J]. IEEE Transactions on Sustainable Energy, 2019, 10(3): 1410-1418.
[15] 王俊茜, 贾祺, 刘侃, 等. 混合风电场接入含固定串补系统的次同步振荡特性分析[J]. 可再生能源, 2022, 40(5): 651-659.
Wang Junxi, Jia Qi, Liu Kan, et al.Analysis of subsynchronous oscillation characteristics of hybrid-based wind farm connected with fixed series compensation system[J]. Renewable Energy Resources, 2022, 40(5): 651-659.
[16] Liu Huakun, Xie Xiaorong, He Jingbo, et al.Subsynchronous interaction between direct-drive PMSG based wind farms and weak AC networks[J]. IEEE Transactions on Power Systems, 2017, 32(6): 4708-4720.
[17] 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.
[18] Du Wenjuan, Wang Yang, Wang H F.Strong sub-synchronous control interactions caused by open-loop modal resonance between the DFIG and series-compensated power system[J]. International Journal of Electrical Power & Energy Systems, 2018, 102: 52-59.
[19] 袁小明, 程时杰, 胡家兵. 电力电子化电力系统多尺度电压功角动态稳定问题[J]. 中国电机工程学报, 2016, 36(19): 5145-5154, 5395.
Yuan Xiaoming, Cheng Shijie, Hu Jiabing.Multi-time scale voltage and power angle dynamics in power electronics dominated large power systems[J]. Proceedings of the CSEE, 2016, 36(19): 5145-5154, 5395.
[20] Li Yin, Fan Lingling, Miao Zhixin.Wind in weak grids: low-frequency oscillations, subsynchronous oscillations, and torsional interactions[J]. IEEE Transactions on Power Systems, 2020, 35(1): 109-118.
[21] Zhao Mingquan, Yuan Xiaoming, Hu Jiabing, et al.Voltage dynamics of current control time-scale in a VSC-connected weak grid[J]. IEEE Transactions on Power Systems, 2016, 31(4): 2925-2937.
[22] 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.
[23] 刘佳宁. 高比例风光并网系统稳定机理与功率振荡分析[D]. 杭州: 浙江大学, 2022.
[24] Du Wenjuan, Dong Wenkai, Wang Haifeng, et al.Dynamic aggregation of same wind turbine generators in parallel connection for studying oscillation stability of a wind farm[J]. IEEE Transactions on Power Systems, 2019, 34(6): 4694-4705.
[25] Du Wenjuan, Ren Bixing, Wang Haifeng, et al.Comparison of methods to examine sub-synchronous oscillations caused by grid-connected wind turbine generators[J]. IEEE Transactions on Power Systems, 2019, 34(6): 4931-4943.
