Abstract：The temperature rise characteristics of electrical equipment directly affect its operational stability and service life. Prolonged high temperatures in localized areas can lead to a gradual decline in insulation performance, potentially causing equipment failure or damage. Therefore, understanding the equipment’s temperature rise and heat flow characteristics is crucial for improving its reliability. However, it is difficult to directly measure internal temperature data in closed or complex electrical equipment. When using numerical simulation methods, one faces challenges such as complex modeling and long computation times that hinder the acquisition of practical temperature data. This paper proposes a thermal network model with self-calibration capabilities that combines physical mechanisms and data-driven algorithms to calibrate the parameters of thermal network components. It enables rapid prediction of temperature rise and heat flow along heat dissipation paths in high-voltage AC vacuum circuit breakers (VCBs) as a function of load current, thereby providing practical support for structural optimization during the design phase and for condition monitoring during operational phases. First, temperature data at different load currents were obtained from multiphysics numerical simulations, and a lumped-parameter thermal network was designed based on these data and the heat-transfer processes. Subsequently, based on theoretical formulas for heat sources and thermal resistance, the paper derives corresponding correction functions and optimizes the correction component using ridge regression and genetic algorithms. It enables self-calibration of parameters during iterative calculations, addressing variations in component parameters with temperature and load current within the thermal network. Model accuracy was validated under 1 575 A and 3 000 A load scenarios, focusing on temperature rise at critical nodes and heat flow along heat-dissipation paths. On a workstation equipped with an Intel Xeon Gold 5218R processor and 128 GB RAM, steady-state multi-physics simulations in ANSYS Workbench 2021b required approximately 8h per operating condition, whereas the thermal network model implemented in Matlab/Simulink 2021a completed the same case in approximately 1 min, yielding an efficiency improvement of about two orders of magnitude. Average prediction errors were 3.7% (3.7 K) for temperature rise and 5.5% (4.3 W) for heat flow. Accordingly, the proposed rapid-prediction approach enables efficient and accurate evaluation across load conditions, substantially benefiting the thermal design, prediction, and assessment of high-voltage AC vacuum circuit breakers. Incorporating parameter self-calibration further improved accuracy: the mean temperature-rise error decreased from 13.6% (uncalibrated) to 5.7% (self-calibrated), a 58% reduction. At nodes sensitive to radiative thermal resistance (5, 6, 8, 9, 10), the mean error fell from 24.4% (maximum 50.0%) to 8.0%, with all errors ≤15%, indicating a marked reduction in local deviations. The thermal network model with self-calibration capabilities can effectively predict the temperature rise and heat flow along heat dissipation paths in a high-voltage AC VCB. Future research will extend the application of this model to transient analysis and incorporate deep learning techniques to enhance prediction accuracy. This model is not only applicable to VCBs but also provides theoretical support and technical reference for the thermal management system design of other electrical equipment.
黄镭, 马慧, 许文迪, 耿英三, 刘志远. 基于热网络模型的高压交流真空断路器温升和热流快速预测方法[J]. 电工技术学报, 2026, 41(6): 2059-2072.
Huang Lei, Ma Hui, Xu Wendi, Geng Yingsan, Liu Zhiyuan. Rapid Prediction Method for Temperature Rise and Heat Flow in High-Voltage AC Vacuum Circuit Breakers Using Thermal Network Model. Transactions of China Electrotechnical Society, 2026, 41(6): 2059-2072.
[1] Yao Xiaofei, Wang Jianhua, Geng Yingsan, et al.Development of a 126kV single-break vacuum circuit breaker and type test[C]//2013 2nd International Conference on Electric Power Equipment-Switching Technology (ICEPE-ST), Matsue, Japan, 2013: 1-4. [2] Li Shengtao, Li Jianying.Condition monitoring and diagnosis of power equipment: review and prospective[J]. High Voltage, 2017, 2(2): 82-91. [3] 林梓圻, 周贺, 牛林华, 等. 隧道敷设条件下超高压电力电缆热-流场耦合分析[J]. 电力工程技术, 2022, 41(3): 216-223. Lin Ziqi, Zhou He, Niu Linhua, et al.Thermal-fluid coupling analysis of ultra-high voltage cables laid in tunnel[J]. Electric Power Engineering Technology, 2022, 41(3): 216-223. [4] 何玉灵, 蒋梦雅, 邱名豪. 同步发电机定子铁心磁-热-固耦合计算分析[J]. 电力工程技术, 2024, 43(4): 208-216. He Yuling, Jiang Mengya, Qiu Minghao.Calculation and analysis of electromagnetic-temperature-stress coupling of the stator core of synchronous generator[J]. Electric Power Engineering Technology, 2024, 43(4): 208-216. [5] Lü Qian, Yu Xiaoling, Tan Youbo, et al.Structure improvement of a 126 kV vacuum circuit breaker using electromagnetic-thermal field coupling simulation[J]. Applied Thermal Engineering, 2019, 160: 114076. [6] Cheng Xian, Du Shuai, Ge Guowei, et al.Electromagnetic-thermal-flow field calculation and optimal design of environment-friendly live tank multi-break vacuum circuit breakers[J]. Electric Power Systems Research, 2023, 217: 109081. [7] Boglietti A, Cavagnino A, Staton D, et al.Evolution and modern approaches for thermal analysis of electrical machines[J]. IEEE Transactions on Industrial Electronics, 2009, 56(3): 871-882. [8] Gan Yunhua, Wang Jianqin, Liang Jialin, et al.Development of thermal equivalent circuit model of heat pipe-based thermal management system for a battery module with cylindrical cells[J]. Applied Thermal Engineering, 2020, 164: 114523. [9] Wang Baosen, Liu Yongqiang, Zhang Bin, et al.Analysis of the temperature characteristics of highspeed train bearings based on a dynamics model and thermal network method[J]. Chinese Journal of Mechanical Engineering, 2022, 35(1): 104. [10] Wockinger D, Bramerdorfer G, Vaschetto S, et al.Approaches for improving lumped parameter thermal networks for outer rotor SPM machines[C]//2021 IEEE Energy Conversion Congress and Exposition (ECCE), Vancouver, BC, Canada, 2021: 3821-3828. [11] 张超, 司马秉奇, 王凯东, 等. 高速永磁电机的三维集总参数热网络模型研究[J]. 电工技术学报, 2025, 40(22): 7193-7203. Zhang Chao, Sima Bingqi, Wang Kaidong, et al.Research of the three-dimensional lumped parameter thermal network model for high-speed permanent magnet motor[J]. Transactions of China Electrotechnical Society, 2025, 40(22): 7193-7203. [12] Jiang Zhuoyuan, Qu Zhiguo, Zhang Jufa, et al.Rapid prediction method for thermal runaway propagation in battery pack based on lumped thermal resistance network and electric circuit analogy[J]. Applied Energy, 2020, 268: 115007. [13] Akbari M, Mostafaei M, Rezaei-Zare A.Estimation of hot-spot heating in OIP transformer bushings due to geomagnetically induced current[J]. IEEE Transactions on Power Delivery, 2023, 38(2): 1277-1285. [14] Akbari M, Rezaei-Zare A.Transformer bushing thermal model for calculation of hot-spot temperature considering oil flow dynamics[J]. IEEE Transactions on Power Delivery, 2021, 36(3): 1726-1734. [15] 林韦弦, 钱乐天, 罗欣, 等. 基于集总参数热网络法的四足机器人温度分布预测[J]. 机器人, 2025, 47(2): 188-199. Lin Weixian, Qian Letian, Luo Xin, et al.Temperature distribution prediction of the quadruped robot based on the lumped-parameter thermal networks[J]. Robot, 2025, 47(2): 188-199. [16] Yang Yun, Xiao Yukun, Du Zhengchun, et al.Datadriven varying state-space model based on thermal network for transient temperature field prediction of motorized spindles[J]. Applied Thermal Engineering, 2023, 219: 119456. [17] 魏书荣, 周海林, 符杨, 等. 基于温度热模型与数据融合驱动的海上风力发电机故障早期预警[J]. 高电压技术, 2025, 51(10): 4945-4956. Wei Shurong, Zhou Hailin, Fu Yang, et al.Early warning of offshore wind turbine failures based on temperature-thermal modeling and data fusion drive[J]. High Voltage Engineering, 2025, 51(10): 4945-4956. [18] Tang Aihua, Huang Yukun, Liu Shangmei, et al.A novel lithium-ion battery state of charge estimation method based on the fusion of neural network and equivalent circuit models[J]. Applied Energy, 2023, 348: 121578. [19] Kirchgässner W, Wallscheid O, Böcker J.Thermal neural networks: Lumped-parameter thermal modeling with state-space machine learning[J]. Engineering Applications of Artificial Intelligence, 2023, 117: 105537. [20] Li Marui, Dong Chaoyu, Yu Xiaodan, et al.Multistep ahead thermal warning network for energy storage system based on the core temperature detection[J]. Scientific Reports, 2021, 11: 15332. [21] Feng Jianghua, Liang Dawei, Zhu Z Q, et al.Improved low-order thermal model for critical temperature estimation of PMSM[J]. IEEE Transactions on Energy Conversion, 2022, 37(1): 413-423. [22] Guo Yujing, Xu Ruihai, Jin Ping.A real-time temperature rise prediction method for PM motor varying working conditions based on the reduced thermal model[J]. Case Studies in Thermal Engineering, 2023, 47: 103098. [23] 冯云南, 吴丽泽, 李焱鑫, 等. 复合圆筒型永磁直线作动器热网络模型与热性能研究[J]. 电工技术学报, 2025, 40(18): 5854-5865. Feng Yunnan, Wu Lize, Li Yanxin, et al.Research on thermal network model and thermal performance of compound tubular permanent magnet linear actuator[J]. Transactions of China Electrotechnical Society, 2025, 40(18): 5854-5865. [24] 师蔚, 骆凯传, 张舟云. 基于热网络法的永磁电机温度在线估计[J]. 电工技术学报, 2023, 38(10): 2686-2697. Shi Wei, Luo Kaichuan, Zhang Zhouyun.On-line temperature estimation of permanent magnet motor based on lumped parameter thermal network method[J]. Transactions of China Electrotechnical Society, 2023, 38(10): 2686-2697. [25] 郭玉敬, 刘溪芃, 金平, 等. 3D精细热网络直接降阶的永磁电机实时温升预测模型研究[J]. 电机与控制学报, 2025, 29(2): 55-64. Guo Yujing, Liu Xipeng, Jin Ping, et al.Research on real-time temperature rise prediction model of PM motors based on 3D detailed thermal network direct order-reduction[J]. Electric Machines and Control, 2025, 29(2): 55-64. [26] 龙柳, 肖凡, 涂春鸣, 等. 基于热网络分区等效策略的Si/SiC混合器件耦合热参数辨识方法[J]. 电工技术学报, 2024, 39(12): 3718-3731. Long Liu, Xiao Fan, Tu Chunming, et al.Enhanced identification approach for RC parameters of Si/SiC hybrid switches based on thermal network partition scheme[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3718-3731. [27] 田野, 卜凯阳, 李楚杉, 等. 用于IGBT模块温度观测的3-D降阶混合型热模型[J]. 电工技术学报, 2024, 39(16): 5104-5120. Tian Ye, Bu Kaiyang, Li Chushan, et al.A hybrid 3-D reduced-order thermal model for temperature observation of IGBT modules[J]. Transactions of China Electrotechnical Society, 2024, 39(16): 5104-5120. [28] 许鹏飞, 杨帆, 刘刚, 等. 110 kV插拔式GIS电缆终端轴向传热分析[J]. 电力工程技术, 2020, 39(5): 30-35. Xu Pengfei, Yang Fan, Liu Gang, et al.Assessment on axial heat transfer of 110 kV plug-in GIS cable terminal[J]. Electric Power Engineering Technology, 2020, 39(5): 30-35.
2026, Vol. 41 
