Impedance Modeling and Grid-Connected Stability Analysis of Variable-Speed Pumped Storage Unit with Full-Size Converter
Zhang Qi1, Du Xiong1, Ding Lijie2, Liu Junliang1, Shi Huabo3
1. National Key Laboratory of Power Transmission and Transformation Equipment Technology Chongqing University Chongqing 400044 China; 2. Power Internet of Things Key Laboratory of Sichuan Province Chengdu 610041 China; 3. State Grid Sichuan Electric Power Research Institute Chengdu 610041 China
Abstract：In the existing energy storage system, pumped storage units have the advantages of large capacity, flexible operation, rapid start and stop, etc., and play an important role in the peak frequency regulation of the power system, and pumped storage units and wind power, photovoltaic power generation, etc. with the use of the power system can promote the new energy consumption level. However, the complex frequency domain characteristics presented by the multi-timescale control of the power electronic devices are prone to interacting with the power grid and triggering the oscillation phenomenon. Currently, there are relatively few studies on impedance modeling of the variable-speed pumped storage unit with full-size converter and their stability analysis based on impedance criterion. The impedance modeling of the variable-speed pumped storage unit with full-size converter and its analysis are of great significance for the future stability analysis of large-scale pumped storage units connected to the power grid. Therefore, this paper establishes an impedance model of the variable-speed pumped storage unit with full-size converter taking into account the frequency coupling effect, and analyzes the stability of the grid-connected system of the pumped storage unit based on the impedance model. In the process of establishing the equivalent impedance model of the variable-speed pumped storage unit with full-size converter, the state-space model of the hydraulic turbine and the synchronous motor are firstly established, and the impedance model in the dq coordinate system is obtained on the basis of the model. After that, the impedance models of the machine-side converter and the grid-side converter are established respectively, and finally the equivalent impedance model of the variable-speed pumped storage unit with full-size converter considering the frequency coupling effect is established taking into account the effect of the grid impedance. Further, the correctness of the impedance model of the variable-speed pumped storage unit with full-size converter was verified using the frequency scanning method. Based on the established impedance model, the grid-connected stability of the pumped storage unit under different grid impedance conditions is investigated by using Nyquist stability criterion. And the effects of key turbine and governor parameters as well as common control loop parameters such as phase-locked loop, DC voltage outer loop and current loop parameters of the full-power converter on the impedance characteristics of the unit as well as on the grid-connected stability are also investigated. This study draws the following conclusions: (1) A more accurate equivalent impedance model of the variable-speed pumped storage unit with full-size converter that takes into account the frequency coupling effect is established. (2) As the grid impedance increases, i.e., the grid strength becomes weaker, the stability of the unit deteriorates. (3) Under the same grid strength, the bandwidths of the phase-locked loop and the current loop have a greater impact on the system stability, while the bandwidth of the DC voltage loop has a smaller impact on its stability. In addition, the values of the key parameters of the turbine as well as the governor have no significant effect on the impedance characteristics of the unit and very little effect on the stability of the system.
张琦, 杜雄, 丁理杰, 刘俊良, 史华勃. 全功率变速抽水蓄能机组的阻抗建模及并网稳定性分析[J]. 电工技术学报, 2025, 40(13): 4229-4240.
Zhang Qi, Du Xiong, Ding Lijie, Liu Junliang, Shi Huabo. Impedance Modeling and Grid-Connected Stability Analysis of Variable-Speed Pumped Storage Unit with Full-Size Converter. Transactions of China Electrotechnical Society, 2025, 40(13): 4229-4240.
[1] 孔令国, 王嘉祺, 韩子娇, 等. 基于权重调节模型预测控制的风-光-储-氢耦合系统在线功率调控[J]. 电工技术学报, 2023, 38(15): 4192-4207. Kong Lingguo, Wang Jiaqi, Han Zijiao, et al.On-line power regulation of wind-photovoltaic-storage-hydrogen coupling system based on weight adjustment model predictive control[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4192-4207. [2] 张海波, 胡玉康, 李正荣, 等. 负荷高密度地区中计及灵活性不足风险的储能优化配置[J]. 电网技术, 2023, 47(12): 4926-4940. Zhang Haibo, Hu Yukang, Li Zhengrong, et al.Optimal configuration of energy storage considering the risk of insufficient flexibility in high load density areas[J]. Power System Technology, 2023, 47(12): 4926-4940. [3] 刘畅, 卓建坤, 赵东明, 等. 利用储能系统实现可再生能源微电网灵活安全运行的研究综述[J]. 中国电机工程学报, 2020, 40(1): 1-18, 369. Liu Chang, Zhuo Jiankun, Zhao Dongming, et al.A review on the utilization of energy storage system for the flexible and safe operation of renewable energy microgrids[J]. Proceedings of the CSEE, 2020, 40(1): 1-18, 369. [4] 张怡静, 李智, 时艳强, 等. 基于储能惯量支撑的受端电网频率优化控制方法[J]. 电工技术学报, 2024, 39(11): 3556-3568. Zhang Yijing, Li Zhi, Shi Yanqiang, et al.Optimal frequency control method of receiving power grid based on energy storage inertia support[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3556-3568. [5] 石梦舒, 许小峰, 张继广, 等. 考虑电-氢市场的虚拟电厂两阶段优化策略研究[J]. 发电技术, 2023, 44(5): 645-655. Shi Mengshu, Xu Xiaofeng, Zhang Jiguang, et al.A two-stage optimization strategy for virtual power plants considering the electricity-hydrogen market[J]. Power Generation Technology, 2023, 44(5): 645-655. [6] Chen Yahong, Xu Wei, Liu Yi, et al.Modeling and transient response analysis of doubly-fed variable speed pumped storage unit in pumping mode[J]. IEEE Transactions on Industrial Electronics, 2023, 70(10): 9935-9947. [7] 庄凯勋, 孙建军, 丁理杰, 等. 提升双馈变速抽水蓄能机组频率响应特性的控制策略[J]. 电工技术学报, 2023, 38(23): 6292-6304. Chuang Kaihsun, Sun Jianjun, Ding Lijie, et al.A control strategy with improved frequency response characteristics of variable speed DFIM pumped storage[J]. Transactions of China Electrotechnical Society, 2023, 38(23): 6292-6304. [8] 吴洋, 苏承国, 郭超雨, 等. 考虑风电出力不确定性的风电-抽水蓄能互补系统短期优化调度[J]. 可再生能源, 2023, 41(9): 1222-1231. Wu Yang, Su Chengguo, Guo Chaoyu, et al.Short-term optimal scheduling of wind farms and pumped-storage hydropower plant complementary system considering wind power output uncertainty[J]. Renewable Energy Resources, 2023, 41(9): 1222-1231. [9] 欧阳晨曦, 赵志高, 李旭东, 等. 海水可变速抽水蓄能与风电联合运行优化研究[J]. 水利水电快报, 2023, 44(5): 65-72. Ouyang Chenxi, Zhao Zhigao, Li Xudong, et al.Operation optimization of combined system of seawater pumped storage with variable-speed units and wind power[J]. Express Water Resources & Hydropower Information, 2023, 44(5): 65-72. [10] 文劲宇, 周博, 魏利屾. 中国未来电力系统储电网初探[J]. 电力系统保护与控制, 2022, 50(7): 1-10. Wen Jinyu, Zhou Bo, Wei Lishen.Preliminary study on an energy storage grid for future power system in China[J]. Power System Protection and Control, 2022, 50(7): 1-10. [11] 李辉, 黄樟坚, 刘海涛, 等. 交流励磁抽水蓄能机组快速功率响应控制策略[J]. 电力自动化设备, 2017, 37(11): 156-161, 175. Li Hui, Huang Zhangjian, Liu Haitao, et al.Control strategy of rapid power response for AC excited pump storage unit[J]. Electric Power Automation Equipment, 2017, 37(11): 156-161, 175. [12] 徐斌, 金龙云, 熊健, 等. 抽水蓄能电站全功率变频控制策略[J]. 电力电子技术, 2020, 54(7): 33-35. Xu Bin, Jin Longyun, Xiong Jian, et al.Control strategy of full power variable in pumping storage power station[J]. Power Electronics, 2020, 54(7): 33-35. [13] 李文锋, 张健, 卜广全, 等. 抽蓄电站和经多端柔性直流电网接入的大规模新能源间的协调互补优化控制方案[J]. 电力系统保护与控制, 2017, 45(23): 130-135. Li Wenfeng, Zhang Jian, Bu Guangquan, et al.A coordinate complementary optimization control scheme between pumped storage station and large-scale new renewable integrated through VSC-MTDC[J]. Power System Protection and Control, 2017, 45(23): 130-135. [14] 衣传宝, 梁廷婷, 汪卫平, 等. 全功率变速抽水蓄能机组无功优先控制策略研究[J]. 电力电容器与无功补偿, 2021, 42(1): 25-31. Yi Chuanbao, Liang Tingting, Wang Weiping, et al.Study on reactive power priority control strategy of variable speed pumped storage unit with full-sized converter[J]. Power Capacitor & Reactive Power Compensation, 2021, 42(1): 25-31. [15] 王廷涛, 苗世洪, 姚福星, 等. 计及频率电压稳定性约束的电力系统多层级储能协同优化运行策略[J]. 电工技术学报, 2024, 39(21): 6759-6777. Wang Tingtao, Miao Shihong, Yao Fuxing, et al.Multi-level energy storage collaborative optimization operation strategy for power systems considering frequency and voltage stability constraints[J]. Tran-sactions of China Electrotechnical Society, 2024, 39(21): 6759-6777. [16] 朱珠, 潘文霞, 刘铜锤, 等. 变速抽蓄机组频率响应机理模型与性能研究[J]. 电网技术, 2023, 47(2): 463-474. Zhu Zhu, Pan Wenxia, Liu Tongchui, et al.Frequency response mechanism modeling and performance analysis of adjustable-speed pumped storage unit[J]. Power System Technology, 2023, 47(2): 463-474. [17] 陈超, 汪卫平, 刘海滨, 等. 全功率变速抽水蓄能机组用于提升电网频率稳定性控制策略研究[J]. 水电与抽水蓄能, 2020, 6(5): 68-72. Chen Chao, Wang Weiping, Liu Haibin, et al.Study on the control strategy of FSC-VSPS for improving the frequency stability of power grid[J]. Hydropower and Pumped Storage, 2020, 6(5): 68-72. [18] Jha P K, Prajapat G P, Bansal S K, et al.Mode identification and small signal stability analysis of variable speed wind power systems[C]//2020 International Conference on Power Electronics & IoT Applications in Renewable Energy and its Control (PARC), Mathura, India, 2020: 286-291. [19] 王方洲, 谭甜源, 刘开培, 等. 可变速抽蓄机组与直驱风电机组联合运行系统的小信号稳定分析[J]. 电力自动化设备, 2021, 41(7): 65-72. Wang Fangzhou, Tan Tianyuan, Liu Kaipei, et al.Small-signal stability analysis of combined operation system of variable-speed pumped storage unit and direct-drive wind turbine unit[J]. Electric Power Automation Equipment, 2021, 41(7): 65-72. [20] 史华勃, 王渝红, 滕予非, 等. 全功率变速抽水蓄能机组快速功率模式小信号建模[J]. 电力系统自动化, 2022, 46(4): 162-169. Shi Huabo, Wang Yuhong, Teng Yufei, et al.Small signal modeling of variable-speed pumped storage unit with full-size converter in fast-power mode[J]. Automation of Electric Power Systems, 2022, 46(4): 162-169. [21] 程佩芬, 李崇涛, 傅闯, 等. 基于状态空间法的高压直流输电系统电磁暂态简化模型的解析算法[J]. 电工技术学报, 2019, 34(6): 1230-1239. Cheng Peifen, Li Chongtao, Fu Chuang, et al.An analytic solution for simplified electromagnetic transient model of HVDC transmission system based on state space method[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1230-1239. [22] 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 impedance[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4130-4146. [23] 刘俊良, 杜雄, 管勃, 等. 变工作点下的逆变器并网系统建模与稳定性分析[J]. 电网技术, 2022, 46(9): 3642-3650. Liu Junliang, Du Xiong, Guan Bo, et al.Impedance modeling and stability analysis for grid-connected inverter containing operating point variables[J]. Power System Technology, 2022, 46(9): 3642-3650. [24] 王国宁, 杜雄, 邹小明, 等. 用于三相并网逆变器稳定性分析的自导纳和伴随导纳建模[J]. 中国电机工程学报, 2017, 37(14): 3973-3981, 4275. Wang Guoning, Du Xiong, Zou Xiaoming, et al.Self and accompanying admittance model for three-phase grid-tied inverter stability analysis[J]. Proceedings of the CSEE, 2017, 37(14): 3973-3981, 4275. [25] 杜程茂, 杜雄, 苏婧媛, 等. 定子电流控制的双馈风机导纳建模与次同步振荡风险分析[J]. 电力系统自动化, 2023, 47(13): 159-167. Du Chengmao, Du Xiong, Su Jingyuan, et al.Admittance modeling and subsynchronous oscillation risk analysis of DFIG-based wind turbine with stator current control[J]. Automation of Electric Power Systems, 2023, 47(13): 159-167. [26] Vieto I, Du Xiong, Nian Heng, et al.Frequency-domain coupling in two-level VSC small-signal dynamics[C]//2017 IEEE 18th Workshop on Control and Modeling for Power Electronics (COMPEL), Stanford, CA, USA, 2017: 1-8. [27] Working Group Prime Mover and Energy Supply. Hydraulic turbine and turbine control models for system dynamic studies[J]. IEEE Transactions on Power Systems, 1992, 7(1): 167-179.
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