三维电场多极子曲面边界元方法研究  

Fast Multipole Curved Boundary Element Method for 3D Electrostatic Field

作　　者：王泽忠[1] 石雨鑫[1] Wang Zezhong;Shi Yuxin(Beijing Key Laboratory of High Voltage&EMC North China Electric Power University Beijing 102206 China)

机构地区：[1]高电压与电磁兼容北京市重点实验室(华北电力大学),北京102206

出　　处：《电工技术学报》2018年第24期5797-5804,共8页Transactions of China Electrotechnical Society

基　　金：中央高校基本科研业务费(2017XS006)资助项目

摘　　要：电力系统中存在大量的静电场问题,边界元法可以有效地分析小规模问题,但是对于大规模问题的分析能力有限。为解决这一问题,通过多极子方法加速基于坐标变换的曲面边界元法,形成多极子曲面边界元法。为适应曲面边界元特点,改进多极子方法中树结构的划分方法。多极子曲面边界元继承了两种方法的优点,通过曲面单元增加计算精度,通过多极子方法加快计算速度,减少内存占用,扩大求解规模。使用不同模型验证了该算法在计算精度和计算效率上有明显优势。应用该算法分析了±350kV单桥臂换流阀屏蔽系统的表面电场强度。多极子曲面边界元法的计算精度高、计算速度快、资源占用少,可以用于分析大规模静电场问题。There are a large number of electrostatic field problems in the power system.For example,the boundary element method(BEM)can effectively analyze the small scale problems,but its ability to analyze large scale problems is limited.In order to solve this problem,the fast multipole method(FMM)was used to accelerate the curved boundary element method(CBEM)based on coordinate transformation,then the fast multipole curved boundary element method(FMCBEM)was proposed.In order to adapt to the features of CBEM,the method of generating the oc-tree structure in FMM was improved.The FMCBEM combines the advantages of the two methods.Through the curved element the calculation precision is increased.Through FMM,the computation time and memory requirement are reduced,and the solution scale is enlarged.Different examples were used to verify that the algorithm has obvious advantages in computational accuracy and efficiency.In addition,the surface electric field intensity of±350kV single bridge converter valve shield system was analyzed.It is shown that the FMCBEM has high accuracy,fast speed and less memory requirement,which can be used to analyze large scale electrostatic field problems.

关 键 词：静电场 边界元 曲面单元 多极子方法 

分 类 号：TM15[电气工程—电工理论与新技术]