A Fast Calculation Method for Transient Temperature Rise of Oil Immersed Transformer Windings Driven by Fusion of Order Reduction Technology and Monitoring Point Data
Liu Gang1,2, Hu Wanjun1, Liu Yunpeng1,2, Wu Weige3, Li Lin2
1. Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense North China Electric Power University Baoding 071003 China; 2. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China; 3. Hebei Provincial Key Laboratory of Electromagnetic & Structural Performance of Power Transmission and Transformation Equipment Baoding Tianwei Baobian Electric Co. Ltd Baoding 071056 China
Abstract In order to improve the calculation efficiency of transient temperature rise in oil immersed power transformer windings, order reduction technology is one of the most effective methods in current research. This paper considers fully utilizing the order reduction characteristics of POD method and proposes a calculation method that uses temperature information from several discrete monitoring points in the field to quickly invert the physical field. Firstly, the article derives the reduced expression of the full order temperature field of transformers based on the POD method, and on this basis, establishes the relationship between discrete monitoring points and the temperature distribution in the entire field. In this method, the POD modal matrix can be obtained through a single calculation of the snapshot matrix, the modal coefficients are obtained through the temperature information of discrete monitoring points, and the temperature distribution of the winding at each step in the transient process can be obtained by multiplying the above two on this basis. Due to the absence of complex nonlinear calculations and large-scale equation iteration processes, this method theoretically has high computational efficiency. At the same time, in order to ensure the accuracy of temperature field inversion, the selection of monitoring point positions within the field is crucial. Therefore, in order to improve computational accuracy, this paper introduces a discrete point selection strategy based on column principal component QR decomposition. Relevant research results show that using this method for temperature inversion in the entire field has a good upper limit of error. In order to verify the correctness of the method proposed in this article, based on the basic structure of transformer cake windings, an eight zone winding numerical calculation model and corresponding temperature rise test platform were established. The performance of the method was discussed through numerical simulation and experimental results. The relevant results showed that the maximum average calculation deviation of the method proposed in this article in numerical simulation was only 1.03 K, The maximum average relative error does not exceed 5%, the calculation accuracy is within a reasonable range, and the calculation time is only 0.18 s, which has achieved a higher efficiency improvement compared to full order calculations; In the experimental analysis, the maximum error between the calculation results of the method proposed in this article and the measurement results at each time point does not exceed 4.67 K, and the average error of each measurement line cake does not exceed 1.02 K, which is within an acceptable range in engineering. Meanwhile, the algorithm only takes 3.40 s to calculate the corresponding winding temperature field at the corresponding time, which is much shorter than the calculation time of current mainstream numerical methods.
Liu Gang,Hu Wanjun,Liu Yunpeng等. A Fast Calculation Method for Transient Temperature Rise of Oil Immersed Transformer Windings Driven by Fusion of Order Reduction Technology and Monitoring Point Data[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 6162-6174.
[1] 谭又博, 余小玲, 臧英, 等. 谐波电流对换流变压器绕组损耗及温度分布特性的影响[J]. 电工技术学报, 2023, 38(2): 542-553. Tan Youbo, Yu Xiaoling, Zang Ying, et al.The influence of harmonic current on the loss and temperature distribution characteristics of a converter transformer winding[J]. Transactions of China Electro-technical Society, 2023, 38(2): 542-553. [2] 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 decomposition-adaptive time stepping oil-immersed power transformer[J]. Transactions of China Electro-technical Society, 2024, 39(12): 3895-3906 [3] 杜志叶, 肖湃, 郝兆扬, 等. 基于绕组热点温度反馈的特高压交流变压器低频加热干燥方法研究[J]. 电工技术学报, 2022, 37(15): 3888-3896. Du Zhiye, Xiao Pai, Hao Zhaoyang, et al.Study on low-frequency heating and drying method of UHVAC transformer based on temperature feedback of winding hot spots[J]. Transactions of China Electrotechnical Society, 2022, 37(15): 3888-3896. [4] 谢裕清, 李琳, 宋雅吾, 等. 油浸式电力变压器绕组温升的多物理场耦合计算方法[J]. 中国电机工程学报, 2016, 36(21): 5957-5965, 6040. Xie Yuqing, Li Lin, Song Yawu, et al.Multi-physical field coupled method for temperature rise of winding in oil-immersed power transformer[J]. Proceedings of the CSEE, 2016, 36(21): 5957-5965, 6040. [5] 彭丽丹. 电力变压器温度场数值计算研究[D]. 北京: 华北电力大学, 2016. Peng Lidan.Study on numerical calculation of temperature field of power transformer[D]. Beijing: North China Electric Power University, 2016. [6] 邓永清, 阮江军, 董旭柱, 等. 基于流线分析的 10 kV油浸式变压器绕组热点温度反演模型建立及验证研究[J]. 中国电机工程学报, 2023, 43(8): 3191-3203. Deng Yongqing, Ruan Jiangjun, Dong Xuzhu, et al.Establishment and verification of 10 kV oil immersed transformer winding hot spot temperature inversion model based on streamline analysis[J]. Proceedings of the CSEE, 2023, 43(8): 3191-3203. [7] 程书灿, 赵彦普, 张军飞, 等. 电力设备多物理场仿真技术及软件发展现状[J]. 电力系统自动化, 2022, 46(10): 121-137. Cheng Shucan, Zhao Yanpu, Zhang Junfei, et al.State of the art of multiphysics simulation technology and software development for power equipment[J]. Automation of Electric Power Systems, 2022, 46(10): 121-137. [8] 骆小满, 阮江军, 邓永清, 等. 基于多物理场计算和模糊神经网络算法的变压器热点温度反演[J]. 高电压技术, 2020, 46(3): 860-866. Luo Xiaoman, Ruan Jiangjun, Deng Yongqing, et al.Transformer hot-spot temperature inversion based on multi-physics calculation and fuzzy neural network algorithm[J]. High Voltage Engineering, 2020, 46(3): 860-866. [9] Dowell E H.Eigenmode analysis in unsteady aerodynamics-Reduced-order models[J]. AIAA Journal, 1996, 34(8): 1578-1583. [10] Silva W A.Identification of linear and nonlinear aerodynamic impulse responses using digital filter technique[C]//22nd Atmospheric Flight Mechanics Conference, New Orleans, LA, USA, 1997: 584-597. [11] Antoulas A C.Approximation of Large-scale dynamical systems (advances in design and control)[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2005. [12] 齐凯, 韩玉兵, 盛卫星. 基于快速近似幂迭代子空间跟踪算法的自适应分集接收技术[J]. 南京理工大学学报, 2017, 41(1): 90-94. Qi Kai, Han Yubing, Sheng Weixing.Adaptive diversity reception technique based on fast approximated power iteration subspace tracking[J]. Journal of Nanjing University of Science and Technology, 2017, 41(1): 90-94. [13] 丁永龙, 胡琳萍, 张瑞勤. 一种基于迭代子空间直接求逆算法的高效子空间混合算法[J]. 计算物理, 2021, 38(4): 418-422. Ding Yonglong, Hu Linping, Zhang Ruiqin.An efficient subspace hybrid algorithm based on direct inversion in iterative subspace algorithm[J]. Chinese Journal of Computational Physics, 2021, 38(4): 418-422. [14] Maulik R, Lusch B, Balaprakash P.Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders[J]. Physics of Fluids, 2021, 33(3): 037106. [15] 魏代同, 陈星, 陈玉刚, 等. 基于本征正交分解的叶片碰摩系统降阶方法[J]. 航空动力学报, 2022, 37(4): 711-720. Wei Daitong, Chen Xing, Chen Yugang, et al.Reduced order method of blade rubbing system based on proper orthogonal decomposition[J]. Journal of Aerospace Power, 2022, 37(4): 711-720. [16] 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): 2730-2742. 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. [17] 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. [18] 胡万君, 刘刚, 朱章宸, 等. 油浸式电力变压器绕组稳态温升降阶计算方法研究[J]. 中国电机工程学报, 2023, 43(16): 6505-6517. Hu Wanjun, Liu Gang, Zhu Zhangchen, et al.Reduced order calculation method of steady temperature rise of oil immersed power transformer[J]. Proceedings of the CSEE, 2023, 43(16): 6505-6517. [19] Drmač Z, Gugercin S.A new selection operator for the discrete empirical interpolation method - improved a priori error bound and extensions[J]. SIAM Journal on Scientific Computing, 2016, 38(2): A631-A648. [20] 刘刚, 郝世缘, 胡万君, 等. 基于子循环自适应串行交错时间匹配算法的油浸式变压器绕组瞬态温升计算[J]. 电工技术学报, 2024, 39(4): 1185-1197. Liu Gang, Hao Shiyuan, Hu Wanjun, et al.Transient temperature rise calculation of oil immersed transformer winding based on sub cyclic adaptive staggered time matching algorithm[J]. Transactions of China Electrotechnical Society, 2024, 39(4): 1185-1197.
2024, Vol. 39 
