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| Transient Temperature Rise Calculation of Oil Immersed Transformer Winding Based on Sub Cyclic Adaptive Staggered Time Matching Algorithm |
| Liu Gang1, Hao Shiyuan1, Hu Wanjun1, Liu Yunpeng1, 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 |
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Abstract For the time-matching problem of two or more multiple physical fields, the traditional idea generally considers that the physical fields are solved by coupling with fixed equal time steps. This direct coupling algorithm is named conventional serial staggered (CSS), but there are two obvious problems in this time matching method, namely, step size adjustment and coupling point selection. Therefore, this paper proposes a time-matching algorithm based on Sub cyclic adaptive staggered (SCAS).
Firstly, in step size adjustment, the Adaptive Time Stepping algorithm (ATS) is added, and the difference of approximate solutions with different accuracy is used as the basis for time step adjustment. At the same time, for nonlinear problems, the Heuristic time stepping method (HTS) is combined to set the number of iterations as the basis for nonlinear discrimination, which solves the problem that the step size cannot be adjusted in real time under strong nonlinear problems. It can obtain a more appropriate step size each time according to the changing trend of the physical field under the allowable error. The introduction of the ATS-HTS hybrid variable step size method reduces the number of computing time steps greatly.
Secondly, for the problem of coupling point selection, this paper proposes a SCAS time-matching algorithm based on the CSS time-matching algorithm, which uses an adaptive scheme to determine the calculation time window and predetermined coupling points and introduces an exponential smoothing method to ensure its accuracy.
Finally, to verify the effectiveness of the proposed method, a two-dimensional transient single-zone split turn winding model is established. Compared with the traditional CSS algorithm, in terms of accuracy, the average relative error of the flow field of the SCAS algorithm is 0.25%, and the average relative error of the temperature field is 0.45%, which is within the acceptable error range. In terms of efficiency, after combining coupling point selection and step size adaptive selection, the SCAS algorithm has further reduced the number of coupling times and computing time steps, and its overall computing efficiency is nearly 20 times higher than the CSS algorithm.
At the same time, to further illustrate the value of the proposed algorithm in engineering practice, this paper has built a temperature rise experimental platform based on the 110 kV transformer winding model and applied the SCAS time matching algorithm to the heat transfer model. The calculation and experimental results show that the maximum absolute error between the SCAS algorithm and the experiment when reaching the steady state occurs at the temperature measuring point No.4 of the 30-wire cakes, which is 2.7 K, because the temperature rise experiment is affected by several uncontrollable factors. Therefore, the error is within the acceptable range. The computational efficiency of the algorithm proposed in this paper is about 46 times higher than that of the traditional algorithm, and the number of computational steps is about 1/47 of the traditional algorithm, which greatly reduces computational redundancy.
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Received: 01 November 2022
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[1] 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.
[2] 朱涛, 王丰华. 地磁感应电流作用下大型变压器的温升特性计算[J]. 电工技术学报, 2022, 37(8): 1915-1925.
Zhu Tao, Wang Fenghua.Calculation of temperature rise of large transformer under geomagnetically induced current[J]. Transactions of China Electro- technical Society, 2022, 37(8): 1915-1925.
[3] 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]. Auto- mation of Electric Power Systems, 2022, 46(10): 121-137.
[4] 邓永清, 阮江军, 董旭柱, 等. 基于自适应网格控制的10 kV油浸式变压器多物理场仿真计算[J]. 高电压技术, 2022, 48(8): 2924-2933.
Deng Yongqing, Ruan Jiangjun, Dong Xuzhu, et al.Simulation of multi-physical field of 10 kV oil immersed transformer based on adaptive grid con- trol[J]. High Voltage Engineering, 2022, 48(8): 2924-2933.
[5] 武卫革, 杜振斌, 刘刚, 等. 大型油浸式变压器绕组温度场仿真及验证[J]. 华北电力大学学报(自然科学版), 2020, 47(6): 68-74.
Wu Weige, Du Zhenbin, Liu Gang, et al.Simulation and verification of winding temperature field for large oil immersed transformer[J]. Journal of North China Electric Power University (Natural Science Edition), 2020, 47(6): 68-74.
[6] Ruan Jiangjun, Deng Yongqing, Huang Daochun, et al.HST calculation of a 10kV oil-immersed transformer with 3D coupled-field method[J]. IET Electric Power Applications, 2020, 14(5): 921-928.
[7] 唐钊, 刘轩东, 陈铭. 考虑流体动力学的干式变压器热网络模型仿真分析[J]. 电工技术学报, 2022, 37(18): 4777-4787.
Tang Zhao, Liu Xuandong, Chen Ming.Simulation analysis of dry-type transformer thermal network model considering fluid dynamics[J]. Transactions of China Electrotechnical Society, 2022, 37(18): 4777-4787.
[8] 王泽忠, 李明洋, 宣梦真, 等. 单相四柱式变压器直流偏磁下的温升试验及仿真分析[J]. 电工技术学报, 2021, 36(5): 1006-1013.
Wang Zezhong, Li Mingyang, Xuan Mengzhen, et al.Temperature rise test and simulation of single-phase four-column transformer under DC-bias[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(5): 1006-1013.
[9] 刘刚, 王晓晗, 马永强, 等. 基于控制体—迎风有限元法的变压器绕组二维流体场—温度场耦合计算方法研究[J]. 高压电器, 2021, 57(6): 1-9.
Liu Gang, Wang Xiaohan, Ma Yongqiang, et al.Study on coupled calculation method of two dimensional fluid and temperature field of transformer winding based on control volume-upstream FEM[J]. High Voltage Apparatus, 2021, 57(6): 1-9.
[10] 袁发庭, 吕凯, 刘健犇, 等. 基于电磁-热-结构多物理场耦合的铁心电抗器线圈结构优化方法[J]. 电工技术学报, 2022, 37(24): 6431-6441.
Yuan Fating, Lü Kai, Liu Jianben, et al.Coil structures optimization method of iron core reactor based on electromagnetic-thermal-structure multi- physical field coupling[J]. Transactions of China Electrotechnical Society, 2022, 37(24): 6431-6441.
[11] 廖才波, 阮江军, 刘超, 等. 油浸式变压器三维电磁-流体-温度场耦合分析方法[J]. 电力自动化设备, 2015, 35(9): 150-155.
Liao Caibo, Ruan Jiangjun, Liu Chao, et al.Com- prehensive analysis of 3-D electromagnetic-fluid- thermal fields of oil-immersed transformer[J]. Electric Power Automation Equipment, 2015, 35(9): 150-155.
[12] 廖才波, 阮江军, 逯怀东, 等. 油浸式变压器二维电磁-流体-温度场耦合分析方法研究[J]. 科学技术与工程, 2014, 14(36): 67-71.
Liao Caibo, Ruan Jiangjun, Lu Huaidong, et al.2-D coupled electromagnetic-fluid-thermal analysis of oil- immersed transformer[J]. Science Technology and Engineering, 2014, 14(36): 67-71.
[13] 谢裕清. 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.
[14] Jiang Bonan.The least-squares finite element method: theory and applications in computational fluid dynamics and electromagnetics[M]. New York: Springer Science & Business Media, 2013.
[15] Liu Gang, Zheng Zhi, Yuan Dongwei, et al.Simu- lation of fluid-thermal field in oil-immersed trans- former winding based on dimensionless least-squares and upwind finite element method[J]. Energies, 2018, 11(9): 2357.
[16] Liu Gang, Rong Shichang, Wu Weige, et al.A two-dimensional transient fluid-thermal coupling method for temperature rising calculation of trans- former winding based on finite element method[J]. AIP Advances, 2020, 10(3): 035325.
[17] 曹龙飞, 范兴纲, 李大伟, 等. 基于快速有限元的永磁电机绕组涡流损耗半解析高效计算[J]. 电工技术学报, 2023, 38(1): 153-165.
Cao Longfei, Fan Xinggang, Li Dawei et al. Semi analytical and efficient calculation method of eddy current loss in windings of permanent magnet machines based on fast finite element method[J]. Transactions of China Electrotechnical Society, 2023, 38(1): 153-165.
[18] 金亮, 李育增, 杨庆新, 等. 大规模工程电磁场的亿自由度可扩展并行计算方法[J]. 电工技术学报, 2022, 37(3): 589-598.
Jin Liang, Li Yuzeng, Yang Qingxin, et al.Extensible parallel computing method with hundreds of millions of freedoms for large-scale engineering electro- magnetic field[J]. Transactions of China Electro- technical Society, 2022, 37(3): 589-598.
[19] Farhat C, Lesoinne M, Maman N.Mixed explicit/ implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conser- vation and distributed solution[J]. International Journal for Numerical Methods in Fluids, 1995, 21(10): 807-835.
[20] Felippa C A, Park K C.Synthesis tools for structural dynamics and partitioned analysis of coupled systems. In: Ibrahimbegovi'c A[M]. Netherlands: Brank B (eds) NATO advanced research workshop. IOS Press, 2004.
[21] 李彬. 先验误差评估时间自适应方法研究及其在饱和砂土地震液化分析中的应用[D]. 大连: 大连理工大学, 2020.
[22] 赵振, 张树有. 自适应步长顺序耦合法及其在瞬态场耦合问题分析中的应用[J]. 计算机集成制造系统, 2011, 17(7): 1404-1414.
Zhao Zhen, Zhang Shuyou.Self-adaptive step sequential- interaction method and its application in transient- fields coupling problems[J]. Computer Integrated Manufacturing Systems, 2011, 17(7): 1404-1414.
[23] Kassiotis C, Ibrahimbegovic A, Niekamp R, et al.Nonlinear fluid-structure interaction problem. part Ⅰ: implicit partitioned algorithm, nonlinear stability proof and validation examples[J]. Computational Mechanics, 2011, 47(3): 305-323.
[24] 张宇娇, 汪振亮, 徐彬昭, 等. 瞬态电磁-温度场耦合计算中自适应时间步长研究[J]. 电工技术学报, 2018, 33(19): 4468-4475.
Zhang Yujiao, Wang Zhenliang, Xu Binzhao, et al.Research on the adaptive time step in transient calculation of coupled electromagnetic and thermal fields[J]. Transactions of China Electrotechnical Society, 2018, 33(19): 4468-4475.
[25] 刘刚, 靳立鹏, 胡万君, 等. 基于混合有限元法的油浸式变压器稳态流-热耦合场并行计算方法[J/OL]. 高电压技术, https://doi.org/10.13336/j.1003-6520.hve. 20221050.
Liu Gang, Jin Lipeng, Hu Wanjun, et al. A parallel method for steady-state fluid-thermal coupling field of oil-immersed transformer based on hybrid finite element method[J/OL]. High Voltage, https://doi.org/ 10.13336/j.1003-6520.hve. 20221050.
[26] Russo A.Streamline-upwind Petrov/Galerkin method (SUPG) vs residual-free bubbles (RFB)[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(13/14/15/16): 1608-1620.
[27] D'Haese C M F, Putti M, Paniconi C, et al. Assessment of adaptive and heuristic time stepping for variably saturated flow[J]. International Journal for Numerical Methods in Fluids, 2007, 53(7): 1173-1193. |
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2024, Vol. 39 
