Multi-Objective Optimization Design of Transformer Base on T-ψ Finite Element Method
Yang Xinsheng1, Zhang Yunpeng2, Xu Guizhi1, Zhang Changgeng1, Fu Weinong3
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China; 2. School of Mechatronic Engineering and Automation Shanghai University Shanghai 200444 China; 3. Department of Electrical Engineering The Hong Kong Polytechnic University Hong Kong 999077 China
Abstract：With rapid increase in capacity and voltage grade of power grid, higher requirement of optimal design of transformer is carried out by clients. In this paper, the optimization design of topology structure of transformer is implemented with the constraints of multi-objective function optimization based on vector potential-scalar magnetic T-ψ finite element method (FEM) to improve transformer performance and reduce cost. Due to the transformer optimization design involves multi-parameters and multi-objective function, an improved generalized differential evolution 3 (GDE3) is employed to achieve fast global optimization. Because of per candidate requires the FEM to verify the characteristics of transformer, which is time cost. In order to reduce the time required for transformer simulation verification, under the premise of ensuring accuracy, a coarser mesh is adopted in the search for excellence, and after the optimal case is determined, the performance parameters of the transformer are compared and verified by combining the refined mesh with finite element method. Compared with the parameters of the original transformer, the copper loss is reduced by 4.5%, the iron loss is increased by 0.81%, but the total loss was reduced by 3.62% and the manufacturing cost is reduced by 3.89%. Adopting the refine mesh, the error of core loss is 0.825%, which is an acceptable range of the engineering application, to verify the correct and validity of this method, and this method also can be applied to optimized design of other electrical equipment.
杨新生, 张云鹏, 徐桂芝, 张长庚, 傅为农. 基于T-ψ 有限元法的多目标函数变压器优化设计[J]. 电工技术学报, 2021, 36(zk1): 75-83.
Yang Xinsheng, Zhang Yunpeng, Xu Guizhi, Zhang Changgeng, Fu Weinong. Multi-Objective Optimization Design of Transformer Base on T-ψ Finite Element Method. Transactions of China Electrotechnical Society, 2021, 36(zk1): 75-83.
[1] 井永腾, 王宁, 李岩, 等. 电磁-热-流弱耦合的变压器绕组温升研究[J]. 电机与控制学报, 2019, 23(10): 41-48. Jing Yongteng, Wang Ning, Li Yan, et al.Research on temperature rise of transformer windings with electromagnetic-thermal-flow weak coupling[J]. Electric Machines and Control, 2019, 23(10): 41-48. [2] Ugale R T, Mejari K D, Chaudhari B N.Intermediate voltage variation-based interconnecting transformer design for voltage and phase angle control with coupled field FEA studies[J]. IEEE Transactions on Industrial Electronics, 2018, 65(8): 6077-6088. [3] 王竹荣, 崔杜武, 张毅坤, 等. 基于遗传算法的整流变压器的优化设计[J]. 电工技术学报, 2004, 19(5): 6-9. Wang Zhurong, Cui Duwu, Zhang Yikun, et al.Optimization design based on genetic algorithm for rectifier transformer[J]. Transactions of China Electro- technical Society, 2004, 19(5): 6-9. [4] 潘再平, 张震, 潘晓弘. 基于QPSO算法的电力变压器优化设计[J]. 电工技术学报, 2013, 28(11): 42-47. Pan Zaiping, Zhang Zhen, Pan Xiaohong.Optimal design of power transformers using quantum-behaved particle swarm optimization[J]. Transactions of China Electrotechnical Society, 2013, 28(11): 42-47. [5] 杨玉岗, 吴瑶, 黄伟义. 旋转式松耦合变压器的绕组优化设计[J]. 电工技术学报, 2019, 34(13): 2782-2792. Yang Yugang, Wu Yao, Huang Weiyi.The optimized design of winding for rotary loosely coupled trans- former[J]. Transactions of China Electrotechnical Society, 2019, 34(13): 2782-2792. [6] 石建, 李琳, 程志光, 等. 电力变压器油箱磁屏蔽的优化设计[J]. 电气技术, 2013, 14(2): 7-11. Shi Jian, Li Lin, Chen Zhiguang, et al.Optimization design of magnetic shields onto power transformer tank[J]. Electrical Engineering, 2013, 14(2): 7-11. [7] Coelho L D S, Mariani V C, Guerra F A, et al. Multiobjective optimization of transformer design using a chaotic evolutionary approach[J]. IEEE Transactions on Magnetics, 2014, 50(2): 669-672. [8] Gómez-Lorente D, Triguero I, Gil C, et al.Multi- objective evolutionary algorithms for the design of grid-connected solar tracking systems[J]. Inter- national Journal of Electrical Power & Energy Systems, 2014, 61: 371-379. [9] Wang Qingsong, Niu Shuangxia, Yang Lin.Design optimization and comparative study of novel dual-PM excited machines[J]. IEEE Transactions on Industrial Electronics, 2017, 64(12): 9924-9933. [10] Zhao Xing, Niu Shuangxia.Design of a novel parallel-hybrid-excited vernier reluctance machine with improved utilization of redundant winding harmonics[J]. IEEE Transactions on Industrial Elec- tronics, 2018, 65(11): 9056-9067. [11] Zhao Xing, Niu Shuangxia.Design and optimization of a new magnetic-geared pole-changing hybrid exci- tation machine[J]. IEEE Transactions on Industrial Electronics, 2017, 64(12): 9943-9952. [12] 江友华, 帅禄玮, 吴琦娜, 等. 基于量子粒子群的双向电子变压器输出端谐振参数优化[J]. 电力系统自动化, 2020, 44(11): 171-190. Jiang Youhua, Shuai Luwei, Wu Qina, et al.Opti- mization of resonance parameter for output port of bi-directional electronic transformer based on quantum particle swarm[J]. Automation Electric Power Systems, 2020, 44(11): 171-190. [13] 曹小鹏, 陈武, 宁光富, 等. 基于多目标遗传算法的大功率高频变压器优化设计[J]. 中国电机工程学报, 2018, 38(5): 1348-1355. Cao Xiaopeng, Chen Wu, Ning Guangfu, et al.Optimization design of high-power high-frequency transformer based on multi-objective genetic algo- rithm[J]. Proceedings of the CSEE, 2018, 38(5): 1348-1355. [14] 李祥林, 李金阳, 杨光勇, 等. 电励磁双定子场调制电机的多目标优化设计分析[J]. 电工技术学报, 2020, 35(5): 972-982. Li Xianglin, Li Jinyang, Yang Guangyong, et al.Multi-objective optimization analysis of electric- excitation double-stator field-modulated machine[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 972-982. [15] 肖龙, 伍梁, 李新, 等. 高频LLC变换器平面磁集成矩阵变压器的优化设计[J]. 电工技术学报, 2020, 35(4): 758-766. Xiao Long, Wu Liang, Li Xin, et al.Optimal design of planar magnetic integrated matrix transformer for high frequency LLC converter[J]. Transactions of China Electrotechnical Society, 2020, 35(4): 758-766. [16] 周兵凯, 杨晓峰, 张智, 等. 能量路由器中双有源桥直流变换器多目标优化控制策略[J]. 电工技术学报, 2020, 35(14): 3030-3040. Zhou Bingkai, Yang Xiaofeng, Zhang Zhi, et al.Multi-objective optimization control strategy of dual- active-bridge DC-DC converter in electric energy router application[J]. Transactions of China Electro- technical Society, 2020, 35(14): 3030-3040. [17] 刘明凯, 王占山, 邢彦丽. 基于强化多目标差分进化算法的电-气互联系统最优潮流计算[J]. 电工技术学报, 2021, 36(11): 2220-2229. Liu Mingkai, Wang Zhanshan, Xing Yanli.Enhanced multi-objective differential evolutionary algorithm based optimal power elow calculation for integrated electricity and gas systems[J]. Transactions of China Electrotechnical Society, 2021, 36(11): 2220-2229. [18] Lei Gang, Wang Tianshi, Zhu Jianguo, et al.Robust multiobjective and multidisciplinary design optimi- zation of electrical drive systems[J]. CES Transa- ctions on Electrical Machines and Systems, 2018, 2(4): 409-416. [19] Lampinen J. De’s selection rule for multiobjective optimization[R]. Lappeenranta University of Tech- nology, Department of Information Technology, 2001-03-04. [20] Kukkonen S, Lampinen J.GDE3: the third evolution step of generalized differential evolution[C]//2005 IEEE Congress on Evolutionary Computation, Edinburgh, UK, 2005: 443-450. [21] IEC 60076-1:2011 Power transformers-Part 1: General[S]. [22] Ahn H M, Lee B J, Hahn S C.An efficient investigation of coupled electromagnetic-thermal- fluid numerical model for temperature rise prediction of power transformer[C]//IEEE Proceedings of the 2011 International Conference on Electrical Machines and Systems (ICEMS), Beijing, 2011: 1-4. [23] Bertotti G, Fiorillo F, Soardo G.Dependence of power losses on peak magnetization and magneti- zation frequency in grain-oriented and non-oriented 3% SiFe[J]. IEEE Transactions on Magnetics, 1987, 23(5): 3520-3522. [24] Lin Dingsheng, Zhou Ping, Fu Weinong, et al.A dynamic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis[J]. IEEE Transactions on Magnetics, 2004, 40(2): 1318-1321. [25] Lei Gang, Zhu Jiangguo, Guo Youguang, et al.A review of design optimization methods for electrical machines[J]. Energies, 2017, 10(12): 1-31. [26] Demenko A.Eddy current computation in 3-Dimensional models for electrical machine applications[C]//2006 12th International Power Electronics and Motion Control Conference, Portoroz, Slovenia, 2006: 1931-1936. [27] Zhao Yanpu.Robust full-wave maxwell solver in time-domain using magnetic vector potential with edge elements[J]. IET Science, Measurement & Tech- nology, 2017, 11(6): 746-752. [28] Zhou Ping, Badics Z, Lin Dingsheng, et al.Nonlinear t-$\omega $ formulation including motion for multiply connected 3-D problems[J]. IEEE Transactions on Magnetics, 2008, 44(6): 718-721. [29] Preis K, Biro O, Buchgraber G, et al.Thermal- electromagnetic coupling in the finite-element simu- lation of power transformers[J]. IEEE Transactions on Magnetics, 2006, 42(4): 999-1002. [30] Li Longnü, Fu Weinong, Ho S L, et al.Numerical analysis and optimization of lobe-type magnetic shielding in a 334MVA single-phase auto- trans- former[J]. IEEE Transactions on Magnetics, 2014, 50(11): 1-4. [31] 谢德馨, 姚缨英, 白保东. 三维涡流场的有限元分析[M]. 北京: 机械工业出版社, 2001.
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