Abstract：As the advancement of Industry 4.0 continues, the power and energy sectors are rapidly undergoing intelligent and digital transformation, leading to the emergence of digital twin technology in the field of electrical equipment. As critical primary equipment, power transformers greatly benefit from the development of digital twin models, which enhance operational reliability, maintenance efficiency, and fault prediction capabilities. However, model-driven digital twin models are often constrained by slow computation speeds. To address this issue, this paper constructs a simplified field-circuit coupled model for oil-immersed power transformers using Modelica, aimed at reducing computational complexity. Additionally, to further enhance computational efficiency, the proper orthogonal decomposition (POD) method is applied to the field computation section for order reduction. Firstly, we investigate the heat generation, heat dissipation mechanisms, and oil flow circulation of a 35 kV, 800 kV·A scaled-down oil-immersed self-cooled (Oil Natural Air Natural, ONAN) converter transformer prototype. Based on this, a simplified method for coupling thermal and circuit calculations and an equivalent modeling approach for the temperature rise of the converter transformer are proposed. Subsequently, the implementation method and encapsulation form of the thermal circuit coupled model using Modelica are discussed. POD is then employed to reduce the order of the field computation section. Finally, temperature rise experiments on the converter transformer are conducted, and the model's computational data is compared with the experimental results. The comparison between the model’s computational data and the experimental results reveals significant differences in the range of 0.5 to 2 hours, with the maximum discrepancy reaching 9.8 K at the top sampling point. As the operating time increases, the temperature rise difference gradually diminishes, and the temperatures converge in the steady state. Whether the radiator is considered significantly impacts both the magnitude of the winding temperature rise and the hotspot location. In the steady state, excluding the radiator results in a maximum temperature error of 11.39 K between the model’s calculations and the experimental data, whereas the proposed model's maximum temperature error is 1.37 K, and the full-order model's maximum temperature error is 0.82 K. In terms of computational efficiency, the proposed model takes a total of 3.328 hours under the temperature rise condition, which is 258.65 times faster than the full-order three-dimensional model. Compared to the full-order field-circuit coupled model, the computational speed is increased by 5.1 times. From the analysis of the model's computational results and the experimental data, the following conclusions can be drawn: (1) The proposed model has a maximum temperature error of 1.37 K compared to the experimental results, making it suitable for temperature rise calculations and winding hotspot analysis of converter transformers. (2) For oil-immersed self-cooled converter transformers, excluding the complete oil flow circulation with the radiator in temperature rise calculations may lead to significant deviations in both the magnitude and location of the winding hotspot temperature rise compared to actual conditions. (3) The proposed model effectively reduces computational costs through the thermal circuit coupling and POD order reduction methods. Compared to the full-order three-dimensional model, the computation speed is increased by 258.65 times, and compared to the full-order field-circuit coupled model, the computation speed is increased by 5.1 times, better meeting the timeliness requirements of digital twin models.
杨帆, 胡星宇, 王鹏博. 油浸式电力变压器温升计算场路耦合和降阶模型研究[J]. 电工技术学报, 2025, 40(13): 4071-4084.
Yang Fan, Hu Xingyu, Wang Pengbo. Study on Temperature Rise Calculation and Reduced-Order Model of Oil-Immersed Transformer with Field-Circuit Coupling. Transactions of China Electrotechnical Society, 2025, 40(13): 4071-4084.
[1] 罗豪, 成立, 杨丽君, 等. 虚实融合的变压器内绝缘状态孪生方法[J]. 电工技术学报, 2024, 39(23): 7628-7638. Luo Hao, Cheng Li, Yang Lijun, et al.The state twinning method of transformer internal insulation by virtual-real fusion[J]. Transactions of China Electro-technical Society, 2024, 39(23): 7628-7638. [2] 王伟杰, 雍明超, 黄金魁, 等. 高压设备数字孪生体构建及状态分析技术研究[J].高压电器, 2023, 59(11): 119-128. Wang Weijie, Yong Mingchao, Huang Jinkui, et al.Research on construction of condition analysis technology of digital twin for high voltage equipment[J]. High Voltage Apparatus, 2023, 59(11): 119-128. [3] 刘云鹏, 刘一瑾, 刘刚, 等. 电力变压器智能运维的数字孪生体构想[J]. 中国电机工程学报, 2023, 43(22): 8636-8651. Liu Yunpeng, Liu Yijin, Liu Gang, et al.Digital twin conception of intelligent operation and maintenance of power transformer[J]. Proceedings of the CSEE, 2023, 43(22): 8636-8651. [4] 许剑冰, 冯霄峰, 徐海波, 等. 基于数字孪生的安全稳定控制系统试验验证展望[J]. 电力系统自动化, 2024, 48(5): 1-10. XuJianbing, Feng Xiaofeng, Xu Haibo, et al. Prospects for experimental verification of safety and stability control systems based on digital twins[J]. Automation of Electric Power Systems, 2024, 48(5): 1-10. [5] 刘刚, 郝世缘, 朱章宸, 等. 基于动态模态分解-自适应变步长油浸式电力变压器绕组瞬态温升快速计算方法[J]. 电工技术学报, 2024, 39(12): 3895-3906. Liu Gang, Hao Shiyuan, Zhu Zhangchen, et al.Research on rapid calculation method of transient temperature rise of winding of dynamic mode decom-position-adaptive time stepping oil-immersed power transformer[J]. Transactions of China Electrotec-hnical Society, 2024, 39(12): 3895-3906. [6] 中国电力企业联合会科技开发服务中心. 电力行业数字孪生技术应用白皮书[R/OL].(2022-07-02)[2024-06-10]. https://www.thepaper.cn/newsDetail_forward_19289460. [7] 和敬涵, 张佳宝, 李猛, 等. 基于孪生模型的模块化多电平换流器保护[J]. 电力系统自动化, 2023, 47(21): 119-126. He, Jinghan, Zhang, Jiabao, Li, Meng, et al.Protection of modular multilevel converters based on twin models[J]. Automation of Electric Power Systems, 47(21): 119-126. [8] 杨帆, 吴涛, 廖瑞金, 等. 数字孪生在电力装备领域中的应用于实现方法[J]. 高电压技术, 2021, 47(5): 1505-1521. Yang Fan, Wu Tao, Liao Ruijin, et al.Application and implementation method of digital twin in electric equipment[J]. High Voltage Engineering, 2021, 47(5): 1505-1521. [9] 张重远, 刘迪程, 高成龙, 等. 基于Twin Builder的110 kV油浸式变压器3维磁场降阶模型及损耗分析[J]. 高电压技术, 2024, 50(3): 941-951. Zhang Zhongyuan, Liu Dicheng, Gao Chenglong, et al.Three-dimensional magnetic field model order reduction and loss analysis of 110 kV oil-immersed transformer based on Twin Builder[J]. High Voltage Engineering, 2024, 50(3): 941-951. [10] 王源, 李兴宝, 杨明月, 等. 基于热电类比理论的光纤复合低压电缆温度分布特性研究[J]. 电气技术, 2021, 22(3): 44-51. Wang Yuan, Li Xingbao, Yang Mingyue, et al.Research on temperature distribution characteristics of optical fiber composite low voltage cable based on thermoelectric analogy theory[J]. Electrical Engineering, 2021, 22(3): 44-51. [11] Jiang Genghui, Kang Ming, Cai Zhenwei, et al.Online reconstruction of 3D temperature field fused with POD-based reduced order approach and sparse sensor data[J]. International Journal of Thermal Sciences, 2022, 175: 107489. [12] Pla F, Herrero H.Reduced basis method applied to eigenvalue problems from convection[J]. International Journal of Bifurcation and Chaos, 2019, 29(3): 1950028. [13] 张宇娇, 赵志涛, 徐斌, 等. 基于U-net卷积神经网络的电磁场快速计算方法[J]. 电工技术学报, 2024, 39(9): 2730-2743. Zhang Yujiao, Zhao Zhitao, Xu Bin, et al.Fast calculation method of electromagnetic field based on U-net convolutional neural network[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2730-2742. [14] Rommel D P, Di Maio D, Tinga T.Transformer hot spot temperature prediction based on basic operator information[J]. International Journal of Electrical Power and Energy Systems, 2021, 124: 106340. [15] Tan Youbo, Yu Xiaoling, Zang Ying, et al.Improving the flow and thermal uniformities of transformer disc-type windings using a self-blocking oil circuit[J]. International Communications in Heat and Mass Transfer, 2023, 148: 107083. [16] 刘刚, 胡万君, 郝世缘, 等. 油浸式变压器绕组瞬态温升降阶快速计算方法[J]. 电工技术学报, 2024, 39(3): 643-657. Liu Gang, Hu Wanjun, Hao Shiyuan, et al.Reduced order calculation method of steady temperature rise of oil immersed power transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 643-657. [17] Chi Cheng, Yang Fan, Ren Zhuoxiang, et al.Reduced order model based on combined POD/LDEIM-Q for nonlinear thermoelectric coupling[J]. IEEE Transactions on Magnetics, 2022, 58(9): 7402304. [18] Liu Yunpeng, Zhao Qingxian, Liu Gang, et al.A real-time solution method for three-dimensional steady temperature field of transformer windings based on mechanism-embedded cascade network[J]. Case Studies in Thermal Engineering, 2024, 58: 104444. [19] Delussu F, Manzione D, Meo R, et al.Experiments and comparison of digital twinning of photovoltaic panels by machine learning models and a cyber-physical model in Modelica[J]. IEEE Transactions on Industrial Informatics, 2022, 18(6): 4018-4028. [20] Masoom A, Mahseredjian J, Ould-Bachir T, et al.MSEMT: an advanced Modelica library for power system electromagnetic transient studies[J]. IEEE Transactions on Power Delivery, 2022, 37(4): 2453-2463. [21] Nobile F.Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models[J]. Mathematical and Computer Modelling 2009, 49(11-12): 2152-2160. [22] Fritzson P.Principles of Object-Oriented Modeling and Simulation with Modelica 3. 3: A Cyber-Physical Approach[M]. 2nd ed. Piscataway: IEEE Press, 2015. [23] 徐天光, 王永庆, 朱超, 等. 变压器用片式散热器散热性能数值模拟及试验研究[J]. 电力工程技术, 2020, 39(5): 178-184. Xu Tianguang, Wang Yongqing, Zhu Chao, et al.Numerical simulation and experimental study on heat transfer performance of panel-type radiators of transformers[J]. Electric Power Engineering Technology, 2020, 39(5): 178-184. [24] Chi Cheng, Yang Fan, Xu Chong, et al.A multi-scale thermal-fluid coupling model for ONAN transformer considering entire circulating oil systems[J]. Inter-national Journal of Electrical Power and Energy Systems, 2022, 135: 107614. [25] 王路伽, 蔡镇潞, 邱亚博, 等. 计及风量损耗的油浸风冷外置冷却系统散热效率优化方法[J]. 电工技术学报, 2023, 38(17): 4767-4778. WangLujia, Cai Zhenlu, QiuYabo, et al. Heat dissipation efficiency optimization method for ONAF external cooling system taking into account airflow losses[J]. Transactions of China Electrotechnical Society, 2023 38(17): 4767-4778. [26] Zienkiewicz O C, Taylor R L, Nithiarasu P.The Finite Element Method for Fluid Dynamics[M]. 6th ed. Builington, MA: Butter-worth-Heinemann, 2005. [27] 谢裕请. 油浸式电力变压器流场及温度场耦合有限元方法研究[D]. 北京: 华北电力大学, 2017. Xie Yuqing.Study on flow field and temperature field coupling finite element methods in oil-immersed power transformer[D]. Beijing: North China Electric Power University, 2017. [28] 陶文铨. 数值传热学[M]. 西安: 西安交通大学出版社, 2001. [29] Wang Yi, Yu Bo, Cao Zhizhu, et al.A comparative study of POD interpolation and POD projection methods for fast and accurate prediction of heat transfer problems[J]. International Journal of Heat and Mass Transfer, 2012, 55(17-18): 4827-4836. [30] 刘刚, 荣世昌, 武卫革, 等. 基于混合有限元法和降阶技术的油浸式变压器绕组2维瞬态流-热耦合场分析[J]. 高电压技术, 2022, 48(5): 1695-1705. Liu Gang, Rong Shichang, Wu Weige, et al.Two-dimensional transient flow-thermal coupling field analysis of oil-immersed transformer windings based on hybrid finite element method and reduced-order technology[J]. High Voltage Engineering, 2022 48(5): 1695-1705. [31] International Electrotechnical Commission.Power transformers-part 2: temperature rise for liquid-immersed transformers: IEC 60076-2[S]. Geneva: IEC, 2011.
2025, Vol. 40 
