Construction Method of Multi-Scale Fault Analysis Model for Single-Phase Transformer with Internal Short Circuit
Yang Ming1, Zhao Xiaohan1, Sima Wenxia1, Li Gang2, Li Kun3, Ni Heli4
1. State Key Laboratory of Power Transmission Equipment Technology Chongqing University Chongqing 400044 China; 2. China Electric Power Research Institute Beijing 100192 China; 3. TBEA Co. Ltd Changji 831100 China; 4. State Grid Shanghai Municipal Electric Power Company Shanghai 200122 China
Abstract：Internal short circuit is one of the most serious faults in transformers, which can lead to a rapid increase in fault energy in a short period of time and easily cause high-energy discharge and explosion inside the equipment. However, there are many potential combinations of internal short circuit conditions in transformers. The analysis method of field-circuit coupling commonly used by transformer manufacturing enterprises has the problems of excessive time and resource consumption. And it is difficult to model jointly with the external power grid. Existing circuit models face difficulties in multi-scale coupling characterization and parameter calculation of windings. This article focused on the urgent need for transformer short circuit fault analysis. A construction method of multi-scale fault analysis model for single-phase transformer with internal short circuit was proposed. Firstly, based on the multi-scale characteristics of transformer windings and internal short circuit faults, the transformer windings were virtually divided into several sub-windings using axial segmentation. By parametrically scanning the finite element model of the transformer, the self-mutual inductance matrix and resistance matrix of sub-windings was calculated. Secondly, an calculation method was proposed to transform the self-mutual inductance matrix into the coupled leakage inductance matrix, which could effectively characterize the leakage magnetic characteristics between sub-windings. This parameter calculation method could be carried without port short circuit tests, which solved the problem of parameter calculation for existing multi-winding transformer models. Finally, a multi-scale circuit model for transformers was established based on the coupled leakage inductance matrix. By connecting the terminals of each sub-winding based on the electromagnetic connection relationship and the physical process of internal short circuit, transformer fault analysis models for different internal short circuit conditions could be obtained. The problems of low efficiency and poor circuit adaptability in the fault analysis model based on field-circuit coupling were solved. Furthermore, a disk-scale circuit model of an 80 MV·A single-phase transformer was constructed. A comparative simulation was conducted with the finite element model. The results indicated that the errors of the short-circuit impedance and the peak value of the port current at rated operating condition were almost zero. And the simulation time was reduced by about 99.98%. After single inter-turn short circuit faults, the errors of the first peak values of the port currents and short-circuit currents did not exceed 2.5%. The simulation efficiency was improved while ensuring simulation accuracy. Then, based on a certain engineering accident, a developmental inter-turn short circuit analogy simulation analysis was carried out. The errors of the first peak values of the port currents and short-circuit currents after the fault, as well as the local peak values during the fault development process, did not exceed 5.5%. And the duration of the second harmonic percentage of fault differential current accounting for more than 15% of the circuit model was calculated to be 49 ms. It was consistent with the finite element model calculation results. The existing method was 14ms. Therefore, the proposed construction method of multi-scale fault analysis model for single-phase transformer with internal short circuit can accurately simulate the transient characteristics of transformers with internal short circuit under multiple scales and operating conditions. This method provides a basic model for research on equipment accident analysis, traceability, and fault defense.
杨鸣, 赵小涵, 司马文霞, 李刚, 李坤, 倪鹤立. 单相变压器内部短路多尺度故障分析模型构建方法[J]. 电工技术学报, 2025, 40(13): 4085-4099.
Yang Ming, Zhao Xiaohan, Sima Wenxia, Li Gang, Li Kun, Ni Heli. Construction Method of Multi-Scale Fault Analysis Model for Single-Phase Transformer with Internal Short Circuit. Transactions of China Electrotechnical Society, 2025, 40(13): 4085-4099.
[1] 郑玉平, 郝治国, 薛众鑫, 等. 大型电力变压器安全运行与主动保护技术探索[J]. 电力系统自动化, 2023, 47(20): 1-12. Zheng Yuping, Hao Zhiguo, Xue Zhongxin, et al.Exploration of safe operation and active protection technology for large-capacity power transformers[J]. Automation of Electric Power Systems, 2023, 47(20): 1-12. [2] 胡应宏, 李雨, 李阳, 等. 面向柔直换流站高频谐振问题的换流变压器建模与参数辨识[J]. 电工技术学报, 2024, 39(22): 7154-7166. Hu Yinghong, Li Yu, Li Yang, et al.Modeling and parameter identification of converter transformer for high-frequency resonance problem of flexible DC converter station[J]. Transactions of China Electro-technical Society, 2024, 39(22): 7154-7166. [3] Asadi N, Kelk H M.Modeling, analysis, and detection of internal winding faults in power transformers[J]. IEEE Transactions on Power Delivery, 2015, 30(6): 2419-2426. [4] 周利军, 员秀程, 王东阳, 等. 基于电压阻尼振荡的变压器故障绕组识别方法[J]. 电工技术学报, 2024, 39(10): 3218-3231. Zhou Lijun, Yun Xiucheng, Wang Dongyang, et al.Transformer fault winding identification method based on voltage damped oscillation[J]. Transactions of China Electrotechnical Society, 2024, 39(10): 3218-3231. [5] 江涛, 杨传凯, 王荆, 等. 基于健康指数的电力变压器绝缘状态评估方法研究[J]. 高压电器, 2024, 60(5): 124-129. Jiang Tao, Yang Chuankai, Wang Jing, et al.Research on insulation state assessment method of power transformer based on health index[J]. High Voltage Apparatus, 2024, 60(5): 124-129. [6] 罗文萱. 基于胶囊神经网络的电力变压器故障诊断方法研究[J]. 高压电器, 2024, 60(5): 92-98. Luo Wenxuan.Research on fault diagnosis method of power transformer based on capsule networks[J]. High Voltage Apparatus, 2024, 60(5): 92-98. [7] 潘超, 石文鑫, 孟涛. 单相变压器匝间短路电磁特性研究[J]. 高电压技术, 2020, 46(5): 1839-1856. Pan Chao, Shi Wenxin, Meng Tao.Study on electromagnetic characteristics of interturn short circuit of single-phase transformer[J]. High Voltage Engineering, 2020, 46(5): 1839-1856. [8] 闫晨光, 张芃, 徐雅, 等. 换流变压器有载分接开关级间短路故障差动保护动作特性[J]. 电工技术学报, 2023, 38(21): 5878-5888, 5912. Yan Chenguang, Zhang Peng, Xu Ya, et al.Differential protection performance for converter transformer intertap short-circuit faults in on-load tap changers[J]. Transactions of China Electrotechnical Society, 2023, 38(21): 5878-5888, 5912. [9] CIGRE Working Group A2.33. Guide for transformer fire safety practices[R]. Paris: CIGRE, 2013. [10] 刘云鹏, 黎晏霖, 李欢, 等. 基于布里渊光时域峰值边沿分析的变压器绕组局部热点检测[J]. 电工技术学报, 2024, 39(11): 3486-3498. Liu Yunpeng, Li Yanlin, Li Huan, et al.Local hot spot detection of transformer windings based on Brillouin optical time domain peak edge analysis[J]. Transa-ctions of China Electrotechnical Society, 2024, 39(11): 3486-3498. [11] 唐起超, 王赞基, 王维俭. 多绕组电力变压器内部短路稳态分析(一)建模与仿真[J]. 电力系统自动化, 2006, 30(10): 44-47, 74. Tang Qichao, Wang Zanji, Wang Weijian.Steady-state analysis of internal short circuits of multi-winding power transformer part I modeling and simulations[J]. Automation of Electric Power Systems, 2006, 30(10): 44-47, 74. [12] Ahmadi S A, Sanaye-Pasand M, Abedini M, et al.Online sensitive turn-to-turn fault detection in power transformers[J]. IEEE Transactions on Industrial Electronics, 69(12): 13555-13564. [13] Farzin N, Vakilian M, Hajipour E.Transformer turn-to-turn fault protection based on fault-related incremental currents[J]. IEEE Transactions on Power Delivery, 2019, 34(2): 700-709. [14] 邓祥力, 朱宏业, 严康, 等. 基于光纤漏磁场测量的变压器磁平衡保护研究[J]. 电工技术学报, 2024, 39(3): 628-642. Deng Xiangli, Zhu Hongye, Yan Kang, et al.Magnetic balance protection of transformers based on optical fiber leakage magnetic field measurement[J]. Tran-sactions of China Electrotechnical Society, 2024, 39(3): 628-642. [15] 国家能源局. 大型发电机变压器继电保护整定计算导则: DL/T 684—2012[S]. 北京: 中国电力出版社, 2012. [16] 张宗成. 基于小波分析的变压器绕组匝间短路检测方法研究[D]. 北京: 华北电力大学, 2015. Zhang Zongcheng.Study on the methodology of diagnosis for transformer inter-turn short circuit based on wavelet analysis[D]. Beijing: North China Electric Power University, 2015. [17] Prasad U R, Vyjayanthi C, Jaison K.Modeling and detection of inter-turn faults in distribution transformer[C]//2019 8th International Conference on Power Systems (ICPS), Jaipur, India, 2019: 1-6. [18] Biro O, Koczka G, Leber G, et al.Finite element analysis of three-phase three-limb power transformers under DC bias[J]. IEEE Transactions on Magnetics, 2014, 50(2): 565-568. [19] Liu S, Liu Z, Mohammed O A.FE-based modeling of single-phase distribution transformers with winding short circuit faults[J]. IEEE Transactions on Magnetics, 2007, 43(4): 1841-1844. [20] 司马文霞, 孙佳琪, 杨鸣, 等. 计及铁心非线性的变压器空间动态磁场加速计算方法[J]. 电工技术学报, 2025, 40(5): 1559-1574. Sima Wenxia, Sun Jiaqi, Yang Ming, et al.Research on accelerated calculation method of space dynamic magnetic field of transformer considering core nonlinearity[J]. Transactions of China Electrotechnical Society, 2025, 40(5): 1559-1574. [21] 曾麟钧, 林湘宁, 黄景光, 等. 特高压自耦变压器的建模和电磁暂态仿真[J]. 中国电机工程学报, 2010, 30(1): 91-97. Zeng Linjun, Lin Xiangning, Huang Jingguang, et al.Modeling and electromagnetic transient simulation of UHV autotransformer[J]. Proceedings of the CSEE, 2010, 30(1): 91-97. [22] 李姗姗, 张建华. 基于等效电流法的变压器匝间短路故障分析[J]. 变压器, 2020, 57(4): 43-46. Li Shanshan, Zhang Jianhua.Fault analysis of interturn short-circuit in transformer based on equivalent current method[J]. Transformer, 2020, 57(4): 43-46. [23] 韩金华. 一起220kV变压器匝间短路故障分析及仿真计算[J]. 变压器, 2018, 55(9): 70-74. Han Jinhua.Analysis and simulation of 220kV transformer interturn short circuit fault[J]. Transformer, 2018, 55(9): 70-74. [24] 李卓昕, 彭敏放, 黄清秀, 等. 行波反射法在变压器绕组匝间短路故障定位中的应用[J]. 电力系统保护与控制, 2016, 44(21): 84-89. Li Zhuoxin, Peng Minfang, Huang Qingxiu, et al.Application of the traveling-wave reflection method in inter-turn short fault location for transformer[J]. Power System Protection and Control, 2016, 44(21): 84-89. [25] 彭磊, 程养春, 郑丹阳, 等. 可外接分布参数元件的变压器绕组多导体传输线暂态模型及其模块化封装[J]. 高电压技术, 2022, 48(10): 3955-3965. Peng Lei, Cheng Yangchun, Zheng Danyang, et al.Attachable transient model and its modular packaging of transformer winding multi-conductor transmission lines with external distributed parameter components[J]. High Voltage Engineering, 2022, 48(10): 3955-3965. [26] Moradzadeh A, Pourhossein K, Mohammadi-Ivatloo B, et al.Locating inter-turn faults in transformer windings using isometric feature mapping of frequency response traces[J]. IEEE Transactions on Industrial Informatics, 2021, 17(10): 6962-6970. [27] 姚陈果, 胡迪, 赵仲勇, 等. 基于有限元法的电力变压器绕组集总参数电路仿真建模[J]. 高电压技术, 2018, 44(11): 3517-3523. Yao Chenguo, Hu Di, Zhao Zhongyong, et al.Simulation modeling of lumped parameter circuit for power transformer winding based on the finite element method[J]. High Voltage Engineering, 2018, 44(11): 3517-3523. [28] Nurmanova V, Ahangar R A, Aliakhmet K, et al.Simulation and analysis of transformer winding inter-disk and inter-turn faults for online diagnosis[C]// 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC/ I&CPS Europe), Genova, Italy, 2019: 1-5. [29] Bastard P, Bertrand P, Meunier M.A transformer model for winding fault studies[J]. IEEE Transactions on Power Delivery, 1994, 9(2): 690-699. [30] 张杰, 罗隆福, Aggarwal R K, 等. 基于多线圈耦合的新型换流变压器仿真模型设计[J]. 电工技术学报, 2010, 25(11): 68-79. Zhang Jie, Luo Longfu, Aggarwal R K, et al.Simulation model’s design of a new converter transformer based on multi-coil coupling[J]. Transactions of China Electrotechnical Society, 2010, 25(11): 68-79. [31] 刘豪, 刘溪, 王婵, 等. 基于终端测量梯形网络的变压器绕组内部局部放电定位方法[J]. 变压器, 2019, 56(3): 55-61. Liu Hao, Liu Xi, Wang Chan, et al.Method for PD location inside transformer windings based on terminal measurement in ladder network[J]. Transformer, 2019, 56(3): 55-61. [32] Gholami M, Hajipour E, Vakilian M.A single phase transformer equivalent circuit for accurate turn to turn fault modeling[C]//2016 24th Iranian Conference on Electrical Engineering (ICEE), Shiraz, Iran, 2016: 592-597. [33] Zhuang Liman, Johnson B K, Chen Xusheng, et al.A topology-based model for two-winding, shell-type, single-phase transformer inter-turn faults[C]//2016 IEEE/PES Transmission and Distribution Conference and Exposition (T&D), Dallas, TX, USA, 2016: 1-5. [34] Pordanjani S R, Naidjate M, Bracikowski N, et al.Electromagnetic modeling of transformers in EMT-type software by a circuit-based method[J]. IEEE Transactions on Power Delivery, 2022, 37(6): 5402-5413. [35] Yang Ming, Kazemi R, Jazebi S, et al.Retrofitting the BCTRAN transformer model with nonlinear magnetizing branches for the accurate study of low-frequency deep saturating transients[J]. IEEE Transactions on Power Delivery, 2018, 33(5): 2344-2353. [36] 杨鸣, 龙洋, 汪可, 等. 考虑铁芯深度饱和特性的三相三柱变压器改进BCTRAN模型[J]. 中国电机工程学报, 2023, 43(2): 819-831. Yang Ming, Long Yang, Wang Ke, et al.An improved BCTRAN model for three-phase three-limb transformers considering deep saturation of iron core[J]. Proceedings of the CSEE, 2023, 43(2): 819-831. [37] Alvarez-Marino C, de Leon F, Lopez-Fernandez X M. Equivalent circuit for the leakage inductance of multiwinding transformers: unification of terminal and duality models[J]. IEEE Transactions on Power Delivery, 2012, 27(1): 353-361. [38] Henriksen T.How to avoid unstable time domain responses caused by transformer models[J]. IEEE Transactions on Power Delivery, 2002, 17(2): 516-522. [39] Jazebi S, Zirka S E, Lambert M, et al.Duality derived transformer models for low-frequency electromagnetic transients: part I: topological models[J]. IEEE Transactions on Power Delivery, 2016, 31(5): 2410-2419. [40] Martinez J A, Mork B A.Transformer modeling for low- and mid-frequency transients: a review[J]. IEEE Transactions on Power Delivery, 2005, 20(2): 1625-1632. [41] de Leon F, Semlyen A. Efficient calculation of elementary parameters of transformers[J]. IEEE Transactions on Power Delivery, 1992, 7(1): 376-383. [42] Dommel H W. Electromagnetic Transients Program. Reference Manual (EMTP Theory Book)[M]. Portland: Bonneville Power Administration, 1986. [43] 国家电网有限公司. 220kV三相三绕组电力变压器采购标准第26部分:220 kV/240 MVA三相三绕组电力变压器(高-中阻抗14%、高-低阻抗24%,中压69,有载)专用技术规范: Q/GDW 13009.26—2018[S]. 北京: 国家电网有限公司, 2018. [44] Oliveira L M R, Marques Cardoso A J. Leakage inductances calculation for power transformers interturn fault studies[J]. IEEE Transactions on Power Delivery, 30(3): 1213-1220. [45] Kulkarni S V, Khaparde S A.Transformer Engineering: Design and Practice[M]. New York: CRC Press, 2004.
2025, Vol. 40 
