包含快照选择策略的POD-QDEIM油浸式变压器绕组瞬态温升降阶算法研究及其实验验证  

Research and Experimental Verification of POD-QDEIM Algorithm for Transient Temperature Rise and Reduced Order of Oil Immersed Transformer Windings With Snapshot Selection Strategy

作　　者：刘刚[1] 胡万君 郝世缘 姜雄伟 高成龙 刘云鹏[1] 王文浩 LIU Gang;HU Wanjun;HAO Shiyuan;JIANG Xiongwei;GAO Chenglong;LIU Yunpeng;WANG Wenhao(Hebei Provincial Key Laboratory of Power Transmission Equipment Security Defense(North China Electric Power University),Baoding 071003,Hebei Province,China;Electric Power Research Institute of State Grid Zhejiang Electric Power Company,Hangzhou 310014,Zhejiang Province,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),河北省保定市071003 [2]国网浙江省电力有限公司电力科学研究院,浙江省杭州市310014

出　　处：《中国电机工程学报》2024年第12期4998-5010,I0033,共14页Proceedings of the CSEE

基　　金：国网浙江省电力有限公司科技项目(5211DS220005)。

摘　　要：为了提高采用有限元方法对油浸式电力变压器绕组瞬态温升进行仿真的计算速度,该文提出一种包含快照选择策略的本征正交分解(proper orthogonal decomposition,POD)-基于列主元QR分解的离散经验插值(QR factorization-discrete empirical interpolation method,Q-DEIM)(POD-QDEIM)算法。首先,文章基于最小二乘有限元法与迎风有限元法推导绕组流热耦合计算方程;其次,通过引入POD方法,降低有限元方程阶数提高求解效率;同时提出POD自适应快照选择策略,在保证降阶模型精度的前提下,减小快照矩阵规模;随后,为了改善POD方法求解非线性问题时效率不高的劣势,文章结合基于Q-DEIM方法,通过插值的方法形成方程中的非线性项,从而提高每一时步非线性项的形成效率;最后,基于110 kV油浸式电力变压器绕组基本结构,建立了八分区分匝绕组传热模型以及绕组温升试验装置对所提算法进行验证,仿真及实验结果表明POD-QDEIM降阶算法的计算精度在工程上属于可接受范围,其计算效率较全阶计算提升了近11.72倍,说明该算法在油浸式电力变压器绕组瞬态温升快速仿真领域的工程应用价值。In order to improve the calculation speed of transient temperature rise simulation of oil immersed power transformer windings using FEM,a POD-QDEIM algorithm with snapshot selection strategy is proposed in this paper.First,based on the least square finite element method(LSFEM)and upwind finite element method(UFEM),the thermal coupling calculation model of winding flow is derived.Then,the proper orthogonal decomposition(POD)is introduced to reduce the dimension of finite element equations and improve the efficiency of equation solving.At the same time,POD adaptive snapshot selection strategy is proposed to reduce the size of snapshot matrix on the premise of ensuring the accuracy of reduced order model.Later,in order to improve the low efficiency of POD method in solving nonlinear problems,the paper combines the QR factorization discrete empirical interpolation method(Q-DEIM)based on column principal component QR decomposition to form nonlinear terms in the equation through interpolation,so as to improve the formation efficiency of nonlinear terms in each step.This method is superior to the traditional discrete empirical interpolation method(DEIM)in accuracy and efficiency.Finally,based on the basic structure of 110 kV oil immersed power transformer windings,this paper establishes an eight-zone and turn-winding heat transfer model to verify the proposed algorithm.At the same time,a winding temperature rise test device is built to discuss its engineering application value.The simulation and experimental results show that:the calculation accuracy of POD-QDEIM reduced order algorithm is acceptable in engineering.Its calculation efficiency is nearly 11.72 times higher than that of full order calculation,and nearly 7.05 times higher than that of single thread calculation of current mainstream simulation software Fluent.This shows the engineering application value of this algorithm in the field of rapid simulation of transient temperature rise of oil immersed power transformer windings.

关 键 词：绕组瞬态温升 快照选择策略 本征正交分解 离散经验插值 温升实验 

分 类 号：TM411[电气工程—电器]