1. School of Electrical Engineering Guizhou University Guiyang 550025 China 2. Electric Power Research institute Guizhou Power Grid Co. Ltd Guiyang 550000
Abstract：With the photovoltaic (PV) industry expanding into mountainous areas, power stations now face rugged terrain and frequent cloud cover. These converters increase operational differences among multi-converter units. Transient stability analysis becomes more complex as a result. Developing detailed full-order models typically leads to increased computational demands, higher storage requirements, and greater analytical complexity due to the high-dimensional state variables and intricate control interactions. However, after differentiated coherency partitioning of the system, the established equivalent model can significantly reduce the complexity of system stability analysis while maintaining the accuracy of the original system model description. In recent years, several system equivalence modeling methods have been proposed. However, most fail to effectively integrate the impacts of system coherency partition and the dynamic parameters of control loops, limiting their ability to accurately capture the system’s dynamic behavior. To overcome these shortcomings, the Coherent Partition Equivalent Aggregation (CPEA) method is proposed which combines coherent partition and control loop aggregation. This method constructs simplified yet precise equivalent models of multi-converter systems in mountain PV power stations by partitioning based on their dynamic characteristics and aggregating their state variables. Firstly, a coherency discrimination criterion is established based on the voltage vector control mechanism of the phase-locked loop (PLL), using the deviation in the q-axis voltage component at the converter output as the criterion. The partition of converters within the same bus and between different bus is carried out in turn: all converters within the same bus that satisfy the coherence criterion are partitioned together, while those that don’t are split into subgroups, which may belong to the original bus cluster or form independent clusters. The single coherence partition formed in the bus continues to participate in the inter-busbar partitioning. If multiple groups exist within a bus, cross-bus partitioning is prohibited. This results in the system being represented as either an equivalent single-machine or a multi-machine model. Next, through state variable equivalent transformation techniques, the equivalent electrical parameters of grid-connected converters, as well as the parameters of their inner and outer control loops and PLL, are derived to form the equivalent single-machine models for each coherence partition. Finally, a system of the equivalent multi-machine model is constructed according to the partitioning results. The method was validated using the SIMULINK and the RT-LAB real-time hardware-in-the-loop (HIL) platform. The simulation results show that the partitioning and aggregated equivalent results are consistent with the theoretical analysis in the case of single-phase ground fault and three-phase short-circuit fault, which effectively confirms the accuracy of the coherence criterion and the ability of the equivalent model to accurately replicate the dynamic characteristics of the original system. For the equivalent modeling of multi-converter systems in mountain PV power stations, this paper proposes a dynamic mechanism-based CPEA method. Through theoretical analysis, numerical computation, and simulation validation, the following conclusions are obtained: (1) Owing to complex terrain and varying local micro-meteorological conditions, the operational characteristics of grid-connected converters in mountain PV power stations exhibit significant heterogeneity. Moreover, the spatial distribution of converters influences the equivalent line impedance and the dynamic change of synchronous angular. Hence, an appropriate partitioning is essential for accurate equivalent modeling. Using the deviation of the q-axis voltage component at the converter output as the partitioning criterion enables partitioning based on large-disturbance instability mechanisms. This approach also considerably reduces computational complexity. (2) The state variable equivalence transformation approach is employed for parameter aggregation, enabling the construction of a multi-machine equivalent model for the AC system. This equivalent model achieves effective system dimensionality reduction while preserving dynamic behaviors, including control loop responses and PLL synchronization characteristics.
[1] 兰天楷, 孙华东, 王琦, 等. 考虑分布式新能源的有源综合负荷模型[J]. 电工技术学报, 2024, 39(23): 7365-7378. Lan Tiankai, Sun Huadong, Wang Qi, et al.Active synthesis load model considering distributed renewable energy source[J]. Transactions of China Electrotechnical Society, 2024, 39(23): 7365-7378. [2] 孙秋野, 李大双, 王睿, 等. “双高” 电力系统: 一种新的稳定判据和稳定性分类探讨[J]. 中国电机工程学报, 2024, 44(8): 3016-3036. Sun Qiuye, Li Dashuang, Wang Rui, et al.Power system with high shares of renewables and power electronics: a new stability criterion and classification[J]. Proceedings of the CSEE, 2024, 44(8): 3016-3036. [3] 谢小荣, 贺静波, 毛航银, 等. “双高” 电力系统稳定性的新问题及分类探讨[J]. 中国电机工程学报, 2021, 41(2): 461-475. Xie Xiaorong, He Jingbo, Mao Hangyin, et al.New issues and classification of power system stability with high shares of renewables and power electronics[J]. Proceedings of the CSEE, 2021, 41(2): 461-475. [4] 赵鹏臻, 谢宁, 殷佳敏, 等. 适应新型电力系统发展趋势的配电网集中-分布式形态及其分层分区方法[J]. 智慧电力, 2023, 51(1): 94-100. Zhao Pengzhen, Xie Ning, Yin Jiamin, et al.Centralized-distributed pattern of distribution network and its hierarchical partition method adapting to development trend of new power system[J]. Smart Power, 2023, 51(1): 94-100. [5] 黄萌, 舒思睿, 李锡林, 等. 面向同步稳定性的电力电子并网变流器分析与控制研究综述[J]. 电工技术学报, 2024, 39(19): 5978-5994. Huang Meng, Shu Sirui, Li Xilin, et al.A review of synchronization-stability-oriented analysis and control of power electronic grid-connected converters[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 5978-5994. [6] 杨苓, 陈燕东, 罗安, 等. 多机并网系统的两带阻滤波器高频振荡抑制方法[J]. 中国电机工程学报, 2019, 39(8): 2242-2252, 7. Yang Ling, Chen Yandong, Luo An, et al.High-frequency oscillation suppression method by two Notch filters for multi-inverter grid-connected system[J]. Proceedings of the CSEE, 2019, 39(8): 2242-2252, 7. [7] Ashraf S M, Chakrabarti S.A single machine equivalent-based approach for online tracking of power system transient stability[J]. IEEE Transactions on Power Systems, 2021, 36(3): 1688-1696. [8] 郭昊, 刘崇茹, 吕懿澎, 等. 基于单机扫描与曲线形状聚类的风电场分群等值方法[J/OL]. 电工技术学报, 2025: 1-14. (2025-09-11). https://link.cnki.net/doi/10.19595/j.cnki.1000-6753.tces.241759. Guo Hao, Liu Chongru, Lü Yipeng, et al. A method for grouping and equivalent modeling of wind farms based on single-machine scanning and curve shape clustering[J/OL]. Transactions of China Electrotechnical Society, 2025: 1-14. (2025-09-11). https://link.cnki.net/doi/10.19595/j.cnki.1000-6753.tces.241759. [9] 郑天悦, 邓俊, 王潇桐, 等. 基于电压与功率分布特性的新能源场站等值建模方法[J]. 电力系统保护与控制, 2024, 52(22): 47-58. Zheng Tianyue, Deng Jun, Wang Xiaotong, et al.Equivalent modeling method based on voltage and power distribution characteristics of a renewable energy station[J]. Power System Protection and Control, 2024, 52(22): 47-58. [10] Liu Yushuang, Geng Hua, He Changjun, et al.Equivalent aggregated modeling of multi-VSC system for transient synchronization stability analysis[J]. IEEE Transactions on Power Systems, 2024, 39(2): 4296-4310. [11] 张磊, 晁璞璞, 金泳霖, 等. 适用于电网频率响应分析的直驱型风电场实用化等值方法[J]. 电力系统自动化, 2025, 49(14): 200-207. Zhang Lei, Chao Pupu, Jin Yonglin, et al.Practical equivalent method for direct-drive wind farms applicable to frequency response analysis of power grids[J]. Automation of Electric Power Systems, 2025, 49(14): 200-207. [12] 张子傲, 李岩松, 任必兴, 等. 电力系统Koopman动态等值方法[J/OL]. 电工技术学报, 2025: 1-16. (2025-04-08). https://link.cnki.net/doi/10.19595/j.cnki.1000-6753.tces.242346. Zhang Ziao, Li Yansong, Ren Bixing, et al. Dynamic equivalencing method for power systems based on koopman theory[J/OL]. Transactions of China Electrotechnical Society, 2025: 1-16. (2025-04-08). https://link.cnki.net/doi/10.19595/j.cnki.1000-6753.tces.242346. [13] 赵学深, 朱琳, 郭力, 等. 基于等值单机非线性模型的多换流器并联直流系统暂态稳定性分析及控制参数整定方法[J]. 中国电机工程学报, 2023, 43(4): 1389-1402. Zhao Xueshen, Zhu Lin, Guo Li, et al.Transient stability analysis and control parameters tuning method of multi-converters DC power system based on equivalent single-converter nonlinear model[J]. Proceedings of the CSEE, 2023, 43(4): 1389-1402. [14] 王丽娟, 王森, 骆梦贺, 等. 基于AHP-GIS的山地光伏项目选址适宜性评价: 以云南省会泽县为例[J/OL]. 太阳能学报, 2024: 1-10. (2024-11-06). https://link.cnki.net/doi/10.19912/j.0254-0096.tynxb.2024-1182. Wang Lijuan, Wang Sen, Luo Menghe, et al. Ahp-gis-based siting suitability evaluation of pv projects in mountainous regions: a case study of Huize county, Yunnan province[J/OL]. Acta Energiae Solaris Sinica, 2024: 1-10. (2024-11-06). https://link.cnki.net/doi/10.19912/j.0254-0096.tynxb.2024-1182. [15] 张锐, 马铭遥, 马文婷, 等. 基于数据驱动的山地电站光伏组串融合模型[J]. 太阳能学报, 2024, 45(7): 517-524. Zhang Rui, Ma Mingyao, Ma Wenting, et al.Data-driven photovoltaic string fusion model of mountain power plant[J]. Acta Energiae Solaris Sinica, 2024, 45(7): 517-524. [16] Li Dongsheng, Shen Chen, Liu Ye, et al.A dynamic equivalent method for PMSG-WTG based wind farms considering wind speeds and fault severities[J]. IEEE Transactions on Power Systems, 2024, 39(2): 3738-3751. [17] 李东晟, 沈沉, 吴林林, 等. 适用于风电集群的分群指标求解及自适应等值建模方法[J]. 电力系统自动化, 2024, 48(24): 166-173. Li Dongsheng, Shen Chen, Wu Linlin, et al.Clustering indicator solution and adaptive equivalent modeling method for wind power clusters[J]. Automation of Electric Power Systems, 2024, 48(24): 166-173. [18] He Xiuqiang, Geng Hua.PLL synchronization stability of grid-connected multiconverter systems[J]. IEEE Transactions on Industry Applications, 2021, 58(1): 830-842. [19] Gupta A P, Mitra A, Mohapatra A, et al.A multi-machine equivalent model of a wind farm considering LVRT characteristic and wake effect[J]. IEEE Transactions on Sustainable Energy, 2022, 13(3): 1396-1407. [20] 罗聪, 陈燕东, 谢志为, 等. 计及电压动态的构网型变流器多机并联系统暂态建模与稳定域估计[J]. 电工技术学报, 2025, 40(9): 2752-2765. Luo Cong, Chen Yandong, Xie Zhiwei, et al.Transient model and stability region estimation for multiple paralleled grid-forming inverter system[J]. Transactions of China Electrotechnical Society, 2025, 40(9): 2752-2765. [21] 刘子文, 曹博源, 崔晓丹, 等. 基于等效电势动态相似性的直驱式风电场分群等值方法[J]. 电力自动化设备, 2024, 44(11): 79-87. Liu Ziwen, Cao Boyuan, Cui Xiaodan, et al.Clustering equivalence method for direct-drive wind farm based on dynamic similarity of equivalent potential[J]. Electric Power Automation Equipment, 2024, 44(11): 79-87. [22] 张永新, 李飞, 张榴晨, 等. 基于线路阻抗聚类的分布式光伏电站等效建模[J]. 太阳能学报, 2022, 43(5): 312-318. Zhang Yongxin, Li Fei, Zhang Liuchen, et al.Equivalent modeling of distributed photovoltaic power stations based on line impedance clustering[J]. Acta Energiae Solaris Sinica, 2022, 43(5): 312-318. [23] 易相彤, 沈超, 彭也伦, 等. 基于同调等值的多变流器系统聚合降阶建模[J]. 中国电机工程学报, 2022, 42(15): 5664-5675. Yi Xiangtong, Shen Chao, Peng Yelun, et al.Aggregation reduced-order modeling of multi-converter systems based on coherency equivalence method[J]. Proceedings of the CSEE, 2022, 42(15): 5664-5675. [24] 赵博元, 路晨, 陈磊, 等. 锁相环动态对切换延迟导致的暂态过电压的影响[J]. 电网技术, 2025, 49(1): 284-294. Zhao Boyuan, Lu Chen, Chen Lei, et al.Impact of phase-locked loop dynamics on transient over-voltage in VSC due to switching delays[J]. Power System Technology, 2025, 49(1): 284-294. [25] 潘尔生, 王智冬, 王栋, 等. 基于锁相环同步控制的双馈风机弱电网接入稳定性分析[J]. 高电压技术, 2020, 46(1): 170-178. Pan Ersheng, Wang Zhidong, Wang Dong, et al.Stability analysis of phase-locked loop synchronized DFIGs in weak grids[J]. High Voltage Engineering, 2020, 46(1): 170-178. [26] Lin Pengfeng, Meng Qingzuo, Zhu Miao, et al. Dynamic circuit-based unified power regulation for hybrid AC/DC/DS microgrids: a comprehensive approach to static and transient control[J]. IEEE Transactions on Industrial Electronics, 2025, PP(99): 1-12. [27] 郑宇婷, 肖凡, 谢伟杰, 等. 基于并网变流器电流稳定运行域的锁相环参数设计方法[J]. 电工技术学报, 2025, 40(10): 3181-3194. Zheng Yuting, Xiao Fan, Xie Weijie, et al.A phase-locked loop parameter design method based on current stable operation domain of grid-connected converter[J]. Transactions of China Electrotechnical Society, 2025, 40(10): 3181-3194. [28] 林顺富, 李寅, 戴烨敏, 等. 考虑谐波耦合的多变流器并网系统建模及交直流谐波交互特性分析[J]. 电力系统保护与控制, 2023, 51(10): 65-77. Lin Shunfu, Li Yin, Dai Yemin, et al.Modeling of a multiple grid-connected-converter system considering harmonic coupling and analysis of AC/DC harmonic interaction characteristics[J]. Power System Protection and Control, 2023, 51(10): 65-77. [29] Achlerkar P D, Ketan Panigrahi B.Recursive least squares-based adaptive parameter estimation scheme for signal transformation and grid synchronization[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(2): 2427-2439. [30] 倪以信, 陈寿孙, 张宝霖. 动态电力系统的理论和分析[M]. 北京: 清华大学出版社, 2002: 133-134. [31] 刘鑫蕊, 夏天, 任瀚文, 等. 锁相环扰动影响下的并联变换器扰动前馈补偿及动态特性改进控制方法[J/OL]. 控制理论与应用, 2025: 1-9. (2025-07-17). https://kns.cnki.net/kcms/detail/44.1240.TP.20250716.1837.096.html. Liu Xinrui, Xia Tian, Ren Hanwen, et al. Disturbance feedforward compensation and dynamic characteristic improvement control method of parallel converter under the influence of PLL disturbance[J/OL]. Control Theory & Applications, 2025: 1-9. (2025-07-17). https://kns.cnki.net/kcms/detail/44.1240.TP.20250716.1837.096.html. [32] 刘林, 曹鑫, 钱梦飞, 等. 永磁同步电机电流环PI控制器参数整定及优化[J]. 电机与控制学报, 2023, 27(10): 131-140. Liu Lin, Cao Xin, Qian Mengfei, et al.Parameter tuning and optimization of PI controller for current loop of PMSM[J]. Electric Machines and Control, 2023, 27(10): 131-140.
