Abstract：Fault analysis in electrical power systems is a crucial prerequisite for designing protection principles and configuring settings. With the increasing integration of renewable energy sources into centralized grids, the distinctive fault characteristics of inverter-type new energy power conversion equipment are becoming more pronounced, directly influencing the performance of protection actions. However, the lack of effective fault equivalent analysis models tailored for new energy stations poses challenges in quantitatively analyzing protection operation boundaries and proposing improvement methods, necessitating the development of novel equivalent analysis methodologies. Currently, fault equivalent analysis for new energy stations can be categorized into single-machine multiplication and multi-machine equivalent analysis methods. The single-machine multiplication method simplifies the calculation process by omitting clustering steps, resulting in reduced computational complexity. However, it often sacrifices accuracy. Conversely, multi-machine equivalent analysis considers various operational variables of units and attempts to group them accordingly. Nevertheless, due to differences in unit output parameters and overhead line parameters among units, errors unavoidably arise in the equivalent calculations. Iterative methods, although applicable for fault calculations in networks with new energy sources, struggle due to the inherent topological characteristics of such stations. During the iterative process, it is necessary to individually correct each inverter-type unit, leading to poor convergence and extended computation times. To address the challenges of multi-machine equivalent analysis and the convergence issues encountered in iterative calculations for multi-node new energy stations, a novel methodology based on forward propagation of terminal unit voltages for deriving station equivalent curves is proposed. By iteratively establishing the mapping relationship between single units and line voltages, and subsequently propagating terminal unit voltages towards the grid connection point to calculate current and voltage phasors, the mapping curve of station grid voltage and current phasors, i.e., the station equivalent curve, is obtained. Representing an entire new energy station in the system topology with a curve enhances equivalent accuracy while simplifying the computation process, thereby reducing the likelihood of convergence issues arising from a high number of nodes during iteration. To validate the accuracy and feasibility of the proposed method, this paper analyzes the impact of errors in single-machine equivalent models on the final station equivalent curve. Assuming the maximum amplitude error occurs in a single unit, the influence of the single-unit equivalent model on the station equivalent curve error is analyzed. Combined with the basic principle of phasor addition, it is shown that under the condition where all units have the maximum error in the same direction, the final error will not exceed the error of the single-machine equivalent model. The error of the equivalent curve calculated with model errors aligns with theoretical analysis results, demonstrating that the proposed method does not amplify errors in single-machine equivalent models during the calculation process. Simulation results indicate that compared to traditional multi-machine equivalent and improved fault equivalent modeling, the average error of short-circuit currents is reduced by 1.13. Moreover, equivalent errors under various operating conditions remain within 0.9. Furthermore, utilizing actual artificial short-circuit test data from Xinjiang to fit single-machine curves, the average equivalent calculation error between curves obtained via the proposed method and experimental waveform data is 3.28.
刘岩, 贾科, 毕天姝, 李伟涛, 徐梓高. 基于末端机组电压前推的逆变型新能源发电场站故障等值计算[J]. 电工技术学报, 2025, 40(1): 96-107.
Liu Yan, Jia Ke, Bi Tianshu, Li Weitao, Xu Zigao. Fault Equivalent Calculation of Inverter Interfaced Renewable Energy Generator Stations Based on Extrapolation of Terminal Unit Voltage. Transactions of China Electrotechnical Society, 2025, 40(1): 96-107.
[1] 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. [2] 古庭赟, 杨骐嘉, 林呈辉, 等. 基于单机等值与选择模态分析的风电场等值建模方法[J]. 电力系统保护与控制, 2020, 48(1): 102-111. Gu Tingyun, Yang Qijia, Lin Chenghui, et al.A wind farm equivalent modeling method based on single-machine equivalent modeling and selection modal analysis[J]. Power System Protection and Control, 2020, 48(1): 102-111. [3] 陆飞. 双馈风电模型分析及机群聚合等值技术研究[D]. 北京: 华北电力大学, 2016. Lu Fei.Model analysis of doubly fed induction generator and research of equivalent aggregation technology for wind farm clusters[D]. Beijing: North China Electric Power University, 2016. [4] 夏玥, 李征, 蔡旭, 等. 基于直驱式永磁同步发电机组的风电场动态建模[J]. 电网技术, 2014, 38(6): 1439-1445. Xia Yue, Li Zheng, Cai Xu, et al.Dynamic modeling of wind farm composed of direct-driven permanent magnet synchronous generators[J]. Power System Technology, 2014, 38(6): 1439-1445. [5] 米增强, 苏勋文, 杨奇逊, 等. 风电场动态等值模型的多机表征方法[J]. 电工技术学报, 2010, 25(5): 162-169. Mi Zengqiang, Su Xunwen, Yang Qixun, et al.Multi-machine representation method for dynamic equivalent model of wind farms[J]. Transactions of China Electrotechnical Society, 2010, 25(5): 162-169. [6] 曹娜, 赵海翔, 任普春, 等. 风电场动态分析中风速模型的建立及应用[J]. 中国电机工程学报, 2007, 27(36): 68-72. Cao Na, Zhao Haixiang, Ren Puchun, et al.Establish and application of wind speed model in wind farm dynamic analysis[J]. Proceedings of the CSEE, 2007, 27(36): 68-72. [7] Wang Peng, Zhang Zhenyuan, Huang Qi, et al.Wind farm dynamic equivalent modeling method for power system probabilistic stability assessment[C]//2019 IEEE Industry Applications Society Annual Meeting, Baltimore, MD, USA, 2019: 1-7. [8] Jin Yuqing, Wu Daming, Ju Ping, et al.Modeling of wind speeds inside a wind farm with application to wind farm aggregate modeling considering LVRT characteristic[J]. IEEE Transactions on Energy Con-version, 2020, 35(1): 508-519. [9] 张星, 李龙源, 胡晓波, 等. 基于风电机组输出时间序列数据分群的风电场动态等值[J]. 电网技术, 2015, 39(10): 2787-2793. Zhang Xing, Li Longyuan, Hu Xiaobo, et al.Wind farm dynamic equivalence based on clustering by output time series data of wind turbine generators[J]. Power System Technology, 2015, 39(10): 2787-2793. [10] 晁璞璞, 李卫星, 金小明, 等. 基于有功响应的双馈型风电场实用化等值方法[J]. 中国电机工程学报, 2018, 38(6): 1639-1646, 1900. Chao Pupu, Li Weixing, Jin Xiaoming, et al.An active power response based practical equivalent method for DFIG wind farms[J]. Proceedings of the CSEE, 2018, 38(6): 1639-1646, 1900. [11] 周佩朋, 李光范, 孙华东, 等. 基于频域阻抗分析的直驱风电场等值建模方法[J]. 中国电机工程学报, 2020, 40(增刊1): 84-90. Zhou Peipeng, Li Guangfan, Sun Huadong, et al.Equivalent modeling method of PMSG wind farm based on frequency domain impedance analysis[J]. Proceedings of CSEE, 2020, 40(S1): 84-90. [12] Zheng Zetian, An Zhi, Shen Chen.Evaluation method for equivalent models of PMSG-based wind farms considering randomness[J]. IEEE Transactions on Sustainable Energy, 2019, 10(3): 1565-1574. [13] Zha Xiaoming, Liao Shuhan, Huang Meng, et al.Dynamic aggregation modeling of grid-connected inverters using hamilton's-action-based coherent equivalence[J]. IEEE Transactions on Industrial Electronics, 2019, 66(8): 6437-6448. [14] 张剑, 何怡刚. 基于轨迹灵敏度分析的永磁直驱风电场等值模型参数辨识[J]. 电工技术学报, 2020, 35(15): 3303-3313. Zhang Jian, He Yigang.Parameters identification of equivalent model of permanent magnet synchronous generator wind farm based on analysis of trajectory sensitivity[J]. Transactions of China Electrotechnical Society, 2020, 35(15): 3303-3313. [15] 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. [16] Shabanikia N, Nia A A, Tabesh A, et al.Weighted dynamic aggregation modeling of induction machine-based wind farms[J]. IEEE Transactions on Sustainable Energy, 2021, 12(3): 1604-1614. [17] Zhou Yuhao, Zhao Long, Hsieh T Y, et al.A multistage dynamic equivalent modeling of a wind farm for the smart grid development[J]. IEEE Transactions on Industry Applications, 2019, 55(5): 4451-4461. [18] Kim D E, El-Sharkawi M A. Dynamic equivalent model of wind power plant using parameter identification[J]. IEEE Transactions on Energy Conversion, 2016, 31(1): 37-45. [19] 潘学萍, 王卫康, 陈海东, 等. 计及低电压穿越影响的感应电动机动态分群[J]. 电工技术学报, 2024, 39(7): 2001-2016. Pan Xueping, Wang Weikang, Chen Haidong, et al.Dynamic clustering of induction motors in new energy power systems considering the impact of LVRT[J] Transactions of China Electrotechnical Society, 2024, 39(7): 2001-2016. [20] Ouyang Jinxin, Diao Yanbo, Zheng Di, et al.Dynamic equivalent model of doubly fed wind farm during electromagnetic transient process[J]. IET Renewable Power Generation, 2017, 11(1): 100-106. [21] Ruan Jiayang, Lu Zongxiang, Qiao Ying, et al.Analysis on applicability problems of the aggregation-based representation of wind farms considering DFIGs' LVRT behaviors[J]. IEEE Transactions on Power Systems, 2016, 31(6): 4953-4965. [22] 安之, 沈沉, 郑泽天, 等. 考虑风电随机性的直驱风机风电场等值模型评价方法[J]. 中国电机工程学报, 2018, 38(22): 6511-6520. An Zhi, Shen Chen, Zheng Zetian, et al.Assessment method for equivalent models of wind farms based on direct-driven wind generators considering randomness[J]. Proceedings of the CSEE, 2018, 38(22): 6511-6520. [23] 贾科, 孔繁哲, 张旸, 等. 基于改进K-均值算法的双馈风场故障等值建模方法[J]. 电网技术, 2023, 47(10): 4161-4169. Jia Ke, Kong Fanzhe, Zhang Yang, et al.Fault equivalent modeling of doubly fed wind farm based on improved K-means algorithm[J]. Power System Technology, 2023, 47(10): 4161-4169. [24] 孙华东, 李佳豪, 李文锋, 等. 大规模电力系统仿真用新能源场站模型结构及建模方法研究(二): 机电暂态模型[J]. 中国电机工程学报, 2023, 43(6): 2190-2201. Sun Huadong, Li Jiahao, Li Wenfeng, et al.Research on model structures and modeling methods of renewable energy station for large-scale power system simulation (II): electromechanical transient model[J]. Proceedings of the CSEE, 2023, 43(6): 2190-2201. [25] 杨杉, 同向前, 刘健, 等. 含分布式电源配电网的短路电流计算方法研究[J]. 电网技术, 2015, 39(7): 1977-1982. Yang Shan, Tong Xiangqian, Liu Jian, et al.Short-circuit current calculation of distribution network with distributed generation[J]. Power System Technology, 2015, 39(7): 1977-1982. [26] 匡晓云, 方煜, 关红兵, 等. 适用于含新能源逆变电源网络的全时域短路电流计算方法[J]. 电力自动化设备, 2020, 40(5): 113-122. Kuang Xiaoyun, Fang Yu, Guan Hongbing, et al.Full-time domain short circuit current calculation method suitable for power network with inverter-interfaced renewable energy source[J]. Electric Power Auto-mation Equipment, 2020, 40(5): 113-122. [27] 尹项根, 张哲, 肖繁, 等. 分布式电源短路计算模型及电网故障计算方法研究[J]. 电力系统保护与控制, 2015, 43(22): 1-9. Yin Xianggen, Zhang Zhe, Xiao Fan, et al.Study on short-circuit calculation model of distributed generators and fault analysis method of power system with distributed generators[J]. Power System Protection and Control, 2015, 43(22): 1-9. [28] Nimpitiwan N, Heydt G T, Ayyanar R, et al.Fault current contribution from synchronous machine and inverter based distributed generators[J]. IEEE Transactions on Power Delivery, 2007, 22(1): 634-641. [29] 贾科, 侯来运, 毕天姝, 等. 基于故障区域局部迭代的工程实用化新能源短路电流计算[J]. 电力系统自动化, 2021, 45(13): 151-158. Jia Ke, Hou Laiyun, Bi Tianshu, et al.Practical engineering calculation of short-circuit current for renewable energy based on local iteration of fault area[J]. Automation of Electric Power Systems, 2021, 45(13): 151-158. [30] 国家市场监督管理总局, 国家标准化管理委员会. 风电场接入电力系统技术规定第1部分:陆上风电: GB/T 19963.1—2021[S]. 北京: 中国标准出版社, 2021. [31] 贾科, 杨彬, 刘浅, 等. 基于逆变型电源暂态电流回代的系统级故障暂态解析[J]. 电力系统自动化, 2022, 46(3): 113-120. Jia Ke, Yang Bin, Liu Qian, et al.Transient analysis of system-level fault based on transient current back-substitution of inverter interfaced generator[J]. Auto-mation of Electric Power Systems, 2022, 46(3): 113-120.
2025, Vol. 40 
