A Refined Simulation Method for the Vibration Characteristics of Transformer Core Considering the Influence of Air Gap under the Perspective of Electro-Magnetic-Mechanical Coupling
Zhao Xiaojun1, Zhang Jiawei1, Wang Haoming1, Miao Yu2, Liu LanRong3
1. Department of Electrical Engineering North China Electric Power University Baoding 071003 China; 2. Electric Power Research Institute of Guizhou Power Grid Co. Ltd Guiyang 550002 China; 3. Hebei Provincial Key Laboratory of Electromagnetic & Structural Performance of Power Transmission and Transformation Equipment Baoding 071056 China
Abstract：Due to the combined effects of Maxwell force and magnetostrictive force, the transformer core inevitably vibrates in actual operation. The vibration of the core can cause noise pollution and loosen components. In severe cases, it may threaten the power supply reliability of the power system. Currently, finite element simulation is usually used to calculate the core vibration, but this method has a long calculation time and low efficiency. This paper proposes a refined modeling and calculation method based on the electromechanical analogy method for core multiphysics coupling characteristics. Firstly, the step overlap area of the transformer core is studied. In the presence of air gaps, the magnetic properties of a single silicon steel sheet are measured, and the equivalent magnetic properties of the overlap area are analyzed through local magnetic circuit modeling to obtain the equivalent magnetic resistance of the overlap area. Based on reasonable assumptions and simplification, the overall equivalent magnetic circuit topology of the transformer is constructed. Secondly, according to the electromechanical-electrical analogy method and mechanical vibration theory, an equivalent vibration loop model in the form of a two-port cascade is established based on the magnetic field distribution characteristics of the lap area to realize the rapid and accurate calculation of the core vibration characteristics. In addition, a vibration test platform for the single-phase three-column transformer core model is built. The data, including vibration displacement, excitation current, and core flux density under different excitation voltages, are compared with the calculation results of the model. The calculation results are in good agreement with the experimental results, which verifies the effectiveness and accuracy of the proposed method. The magnetostrictive vibration characteristics in the lap area are analyzed. The vibration of the lap region is stronger than that of the non-lap area, mainly because the local magnetic flux density in the lap region tends to be saturated, making the magnetostrictive force significantly stronger. In conclusion, the theoretical analysis and experimental results show that the proposed electro-magnetic-mechanical multiphysics coupling calculation method considering the influence of air gap obtains the distribution characteristics of the transformer core magnetic field and reflects the mechanical vibration distribution characteristics caused by a non-uniform magnetic field. Compared with the traditional finite element calculation method, the proposed method greatly saves calculation time and cost.
赵小军, 张佳伟, 王浩名, 苗宇, 刘兰荣. 电-磁-机耦合视域下考虑气隙影响的变压器铁心振动特性精细化模拟方法[J]. 电工技术学报, 2024, 39(14): 4257-4269.
Zhao Xiaojun, Zhang Jiawei, Wang Haoming, Miao Yu, Liu LanRong. A Refined Simulation Method for the Vibration Characteristics of Transformer Core Considering the Influence of Air Gap under the Perspective of Electro-Magnetic-Mechanical Coupling. Transactions of China Electrotechnical Society, 2024, 39(14): 4257-4269.
[1] 王革鹏, 金文德, 曾向阳, 等. 特高压并联电抗器铁心振动的分析与控制研究[J]. 电工技术学报, 2022, 37(9): 2190-2198. Wang Gepeng, Jin Wende, Zeng Xiangyang, et al.Analysis and control research on core vibration of UHV shunt reactor[J]. Transactions of China Elec-trotechnical Society, 2022, 37(9): 2190-2198. [2] 朱叶叶, 汲胜昌, 张凡, 等. 电力变压器振动产生机理及影响因素研究[J]. 西安交通大学学报, 2015, 49(6): 115-125. Zhu Yeye, Ji Shengchang, Zhang Fan, et al.Vibration mechanism and influence factors in power trans-formers[J]. Journal of Xi'an Jiaotong University, 2015, 49(6): 115-125. [3] 白保东, 刘闯, 王佳音. 直流偏磁下变压器振动的仿真及实验研究[J]. 电工技术学报, 2013, 28(增刊2): 427-433. Bai Baodong, Liu Chuang, Wang Jiayin.Simulation and experimental research of transformer vibration under DC magnetic bias[J]. Transactions of China Electrotechnical Society, 2013, 28(S2): 427-433. [4] 赵莉华, 丰遥, 谢荣斌, 等. 油浸式变压器铁心振动特性分析[J]. 电力系统及其自动化学报, 2018, 30(10): 104-110. Zhao Lihua, Feng Yao, Xie Rongbin, et al.Analysis of vibration characteristics for oil-immersed trans-former core[J]. Proceedings of the CSU-EPSA, 2018, 30(10): 104-110. [5] 王佳音, 白保东, 刘宏亮, 等. 直流偏磁对变压器振动噪声的影响[J]. 电工技术学报, 2015, 30(8): 56-61. Wang Jiayin, Bai Baodong, Liu Hongliang, et al.Research on vibration and noise of transformers under DC bias[J]. Transactions of China Electrotechnical Society, 2015, 30(8): 56-61. [6] 赵小军, 张凌云, 刘洋, 等. 机械应力对取向硅钢片综合磁性能影响的实验研究[J]. 电工技术学报, 2022, 37(22): 5776-5787. Zhao Xiaojun, Zhang Lingyun, Liu Yang, et al.Experimental study on the effect of mechanical stress on the comprehensive magnetic properties of the grain-oriented silicon steel[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5776-5787. [7] Shahaj A, Garvey S D.A possible method for magnetostrictive reduction of vibration in large electrical machines[J]. IEEE Transactions on Mag-netics, 2011, 47(2): 374-385. [8] Bartoletti C, Desiderio M, Di Carlo D, et al.Vibro-acoustic techniques to diagnose power trans-formers[J]. IEEE Transactions on Power Delivery, 2004, 19(1): 221-229. [9] Kitagawa W, Ishihara Y, Todaka T, et al.Analysis of structural deformation and vibration of a transformer core by using magnetic property of magnetostri-ction[J]. Electrical Engineering in Japan, 2010, 172(1): 19-26. [10] Moses A.Measurement of magnetostriction and vibration with regard to transformer noise[J]. IEEE Transactions on Magnetics, 1974, 10(2): 154-156. [11] Hilgert T, Vandevelde L, Melkebeek J.Comparison of magnetostriction models for use in calculations of vibrations in magnetic cores[J]. IEEE Transactions on Magnetics, 2008, 44(6): 874-877. [12] Gao Yanhui, Muramatsu K, Hatim M J, et al.The effect of laminated structure on coupled magnetic field and mechanical analyses of iron core and its homogenization technique[J]. IEEE Transactions on Magnetics, 2011, 47(5): 1358-1361. [13] Ebrahimi H, Gao Yanhui, Kameari A, et al.Coupled magneto-mechanical analysis considering permeability variation by stress due to both magnetostriction and electromagnetism[J]. IEEE Transactions on Magnetics, 2013, 49(5): 1621-1624. [14] Gao Yanhui, Muramatsu K, Fujiwara K, et al.Vibration analysis of a reactor driven by an inverter power supply considering electromagnetism and magnetostriction[J]. IEEE Transactions on Magnetics, 2009, 45(10): 4789-4792. [15] Tang Qi, Guo Shufeng, Wang Zhongdong.Magnetic flux distribution in power transformer core with mitred joints[J]. Journal of Applied Physics, 2015, 117(17): 1-4. [16] 祝丽花, 杨庆新, 闫荣格, 等. 考虑磁致伸缩效应电力变压器振动噪声的研究[J]. 电工技术学报, 2013, 28(4): 1-6, 19. Zhu Lihua, Yang Qingxin, Yan Rongge, et al.Research on vibration and noise of power transformer cores including magnetostriction effects[J]. Transa-ctions of China Electrotechnical Society, 2013, 28(4): 1-6, 19. [17] 祝丽花, 王斌, 刘松, 等. 不同负载对干式变压器电磁振动的影响分析[J]. 电工技术学报, 2018, 33(7): 1599-1606. Zhu Lihua, Wang Bin, Liu Song, et al.Research on electromagnetic vibration of dry type transformer under different types of load[J]. Transactions of China Electrotechnical Society, 2018, 33(7): 1599-1606. [18] 张欣, 解超群, 祝丽花, 等. 考虑磁致伸缩效应的电机应力数值仿真与实验[J]. 电工技术学报, 2017, 32(增刊2): 50-55. Zhang Xin, Xie Chaoqun, Zhu Lihua, et al.Numerical simulation and experimental research on stress of motor including magnetostriction effects[J]. Transa-ctions of China Electrotechnical Society, 2017, 32(S2): 50-55. [19] 李维铮, 祝丽花, 石永恒. 电力变压器铁心搭迭区磁等效及磁致振动分析[J]. 电力科学与工程, 2019, 35(10): 29-35. Li Weizheng, Zhu Lihua, Shi Yongheng.Study on the magnetic equivalent and magneto-induced vibration of core overlap region in power transformer[J]. Electric Power Science and Engineering, 2019, 35(10): 29-35. [20] 张鹏宁, 李琳, 纪锋, 等. HVDC阳极饱和电抗器阻尼弹性体降振降噪试验研究[J]. 电网技术, 2017, 41(12): 3839-3845. Zhang Pengning, Li Lin, Ji Feng, et al.Test study on reduction of vibration and noise to damping elastomer in HVDC anode saturable reactor[J]. Power System Technology, 2017, 41(12): 3839-3845. [21] 张鹏宁, 李琳, 程志光, 等. 并联电抗器与变压器模型铁心振动仿真与试验对比[J]. 电工技术学报, 2018, 33(22): 5273-5281. Zhang Pengning, Li Lin, Cheng Zhiguang, et al.Vibration simulation and experiment comparison of shunt reactor and transformer model core[J]. Transa-ctions of China Electrotechnical Society, 2018, 33(22): 5273-5281. [22] 张鹏宁, 李琳, 聂京凯, 等. 考虑铁心磁致伸缩与绕组受力的高压并联电抗器振动研究[J]. 电工技术学报, 2018, 33(13): 3130-3139. Zhang Pengning, Li Lin, Nie Jingkai, et al.Study on the vibration of high voltage shunt reactor considering of magnetostriction and winding force[J]. Transa-ctions of China Electrotechnical Society, 2018, 33(13): 3130-3139. [23] 曹淑瑛, 王博文, 闫荣格, 等. 超磁致伸缩致动器的磁滞非线性动态模型[J]. 中国电机工程学报, 2003, 23(11): 145-149. Cao Shuying, Wang Bowen, Yan Rongge, et al.Dynamic model with hysteretic nonlinearity for a giant magnetostrictive actuator[J]. Proceedings of the CSEE, 2003, 23(11): 145-149. [24] 曹淑瑛, 王博文, 郑加驹, 等. 应用混合遗传算法的超磁致伸缩致动器磁滞模型的参数辨识[J]. 中国电机工程学报, 2004, 24(10): 127-132. Cao Shuying, Wang Bowen, Zheng Jiaju, et al.Parameter identification of hysteretic model for ginat magnetostrictive actuator using hybrid genetic algorithm[J]. Proceedings of the CSEE, 2004, 24(10): 127-132. [25] 曹淑瑛, 郑加驹, 王博文, 等. 基于动态递归神经网络的超磁致伸缩驱动器精密位移控制[J]. 中国电机工程学报, 2006, 26(3): 106-111. Cao Shuying, Zheng Jiaju, Wang Bowen, et al.Precision position control for giant magnetostrictive actuator based on dynamic recurrent neural network[J]. Proceedings of the CSEE, 2006, 26(3): 106-111. [26] 李冰, 王泽忠, 刘海波, 等. 直流偏磁下500kV单相变压器振动噪声的试验研究[J]. 电工技术学报, 2021, 36(13): 2801-2811. Li Bing, Wang Zezhong, Liu Haibo, et al.Experiment on vibro-acoustic characteristic of 500kV single-phase transformer under DC-bias[J]. Transactions of China Electrotechnical Society, 2021, 36(13): 2801-2811. [27] 李姝汛, 杨鑫, 陈泽坤, 等. 计及漏磁的堆栈式超磁致伸缩制动器多物理场耦合建模研究[J]. 电工技术学报, 2023, 38(9): 2277-2288. Li Shuxun, Yang Xin, Chen Zekun, et al.Multi-physics modeling research of stacked giant mag-netostrictive actuator considering magnetic flux leakage[J]. Transactions of China Electrotechnical Society, 2023, 38(9): 2277-2288. [28] 杜永, 程志光, 颜威利, 等. 电力变压器全斜接缝叠片铁心工作条件下的磁性能模拟[J]. 电工技术学报, 2010, 25(3): 14-19. Du Yong, Cheng Zhiguang, Yan Weili, et al.Working magnetic property modeling of the power transformer laminated core with mitred joints[J]. Transactions of China Electrotechnical Society, 2010, 25(3): 14-19. [29] Elleuch M, Poloujadoff M.New transformer model including joint air gaps and lamination anisotropy[J]. IEEE Transactions on Magnetics, 1998, 34(5): 3701-3711. [30] Wang Gepeng, Zeng Xiangyang, Zhao Yongjin.Research on the effect of core joints on transformer noise[J]. IEEE Transactions on Magnetics, 2021, 57(10): 1-6. [31] Li Lingzhi, Du Xuhao, Pan Jie, et al.An engineering model of magnetic flux density and electromagnetic force density at the structural discontinuity within transformer cores[J]. Sensors, 2022, 22(13): 4869. [32] 杨意妹, 祝丽花, 王斌, 等. 考虑磁致伸缩效应的可控饱和电抗器电磁振动分析[J]. 电工电能新技术, 2016, 35(8): 40-45. Yang Yimei, Zhu Lihua, Wang Bin, et al.Analysis on electromagnetic vibration of controllable saturable reactor considering magnetostrictive effects[J]. Advanced Technology of Electrical Engineering and Energy, 2016, 35(8): 40-45. [33] 赵小军, 杜雨彤, 刘洋, 等. 应用磁-机械耦合场频域解法的铁芯直流偏磁振动特性分析[J]. 高电压技术, 2020, 46(4): 1216-1225. Zhao Xiaojun, Du Yutong, Liu Yang, et al.Vibration characteristics analysis of iron core under DC-biased condition by solving coupled magneto-mechanical field in frequency-domain[J]. High Voltage Engin-eering, 2020, 46(4): 1216-1225. [34] 闫荣格, 程云飞. 动静态力共同作用对电抗器铁心振动影响[J]. 电工技术学报, 2023, 38(4): 1104-1114. Yan Rongge, Cheng Yunfei.Influence of dynamic and static forces on vibration of reactor core[J]. Transa-ctions of China Electrotechnical Society, 2023, 38(4): 1104-1114. [35] 赵小军, 张晓欣, 李慧奇, 等. 基于谐波平衡法的变压器直流偏磁电路-磁路频域耦合模型[J]. 电工技术学报, 2014, 29(9): 211-218. Zhao Xiaojun, Zhang Xiaoxin, Li Huiqi, et al.Frequency domain coupled model between magnetic and electric circuits of DC biased transformers by harmonic balance method[J]. Transactions of China Electrotechnical Society, 2014, 29(9): 211-218.
2024, Vol. 39 
