基于A,Ф-A的变压器三维涡流场时域有限元POD降阶方法及其应用  

Time Domain Finite Element POD Order Reduction Method for 3D Eddy Current Field of Transformer Based on A,Ф-A and its Application

作　　者：朱章宸 刘尧 刘刚[1] 刘云鹏[1] ZHU Zhangchen;LIU Yao;LIU Gang;LIU Yunpeng(Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense(North China Electric Power University),Baoding 071003,China;Construction Branch of State Grid Chongqing Electric Power Company,Chongqing 409800,China)

机构地区：[1]河北省输变电设备安全防御重点实验室(华北电力大学),河北保定071003 [2]国网重庆市电力公司建设分公司,四川重庆409800

出　　处：《华北电力大学学报(自然科学版)》2025年第1期82-94,共13页Journal of North China Electric Power University:Natural Science Edition

基　　金：国家重点研发计划项目(2021YFB2401703);中央高校基本科研业务费专项资金资助项目(2022MS073).

摘　　要：为解决三维涡流场时域求解时间长和存储空间需求较多的问题,首先基于A,Ф-A的三维涡流场时域有限元法结合POD(Proper Orthogonal Decomposition,POD)降阶算法实现了三维涡流场的高效计算。其次,以国际TEAM第21基准问题的模型B为例,通过对比分析实测数据与自编程序和COMSOL的计算结果,验证了A,Ф-A的三维涡流场时域有限元求解方法的有效性。然后,通过POD不同阶数的降阶算例验证了POD降阶方法的有效性。最后,利用所提的基于A,Ф-A三维涡流场时域有限元法计算了一台三相变压器进行额定运行工况下的涡流场,并将计算结果与COMSOL仿真结果进行了对比。同时,还分析了三相变压器在负荷减少过程中的相电流和磁场变化,并分析了降阶模型阶数对计算时间和精度的影响,结果表明:15阶降阶模型耗时约为全阶耗时1/10,并且在方程降阶后各时间步的加速比最大,可达到70~165倍,在计算涡流损耗时相对误差不超过4.59%,计算精度相对较高。To solve the problems of long solution time in the time domain and high storage space requirements for three-dimensional eddy current fields,we firstly combined the 3D eddy current field time-domain finite element method based on A,Ф-A with the POD(Proper Orthogonal Decomposition,POD)reduction algorithm to achieve efficient calculation of 3D eddy current fields.Secondly,taking Model B of the international TEAM Problem 21 as an example,we verified the effectiveness of the time-domain finite element method for solving the three-dimensional eddy current field of A,Ф-A by comparing and analyzing the measured data with the calculation results of the self-designed program and COMSOL.Then,the effectiveness of the POD reduction method was verified by reduction examples of different orders of POD.Finally,we calculated the eddy current field of a three-phase transformer under rated operating conditions by using the time-domain finite element method based on A,Ф-A three-dimensional eddy current field proposed in this article,and compared the calculation results with those obtained from COMSOL simulation results.At the same time,we also analyzed the changes in phase current and magnetic field of three-phase transformers during load reduction,and analyzed the impact of the order of the reduced order model on calculation time and accuracy.The results show that the 15-order reduced order model takes about 1/10 of the full order time,and the acceleration ratio at each time step after equation reduction is the highest,reaching 70~165 times.The relative error in calculating eddy current losses does not exceed 4.59%,indicating relatively high calculation accuracy.

关 键 词：三维涡流场 三相变压器 A Ф-A方法 POD降阶方法 

分 类 号：TM401[电气工程—电器]