B样条曲面边界元方法及其在特高压绝缘子串电场计算中的应用  

Research and Application of B-Spline Surface Boundary Element Method for Calculating Ultra-High Voltage Insulator Strings Electric Fields

作　　者：李亚莎[1] 花旭[1] 沈星如 代亚平[1] 

机构地区：[1]三峡大学电气与新能源学院,宜昌443002

出　　处：《电工技术学报》2018年第2期232-237,共6页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金资助项目(51577105)

摘　　要：在计算特高压绝缘子串三维静电场的边界元法中,为了精确确定电场强度和电位分布,提出用双2次B样条曲面拟合实际边界面的B样条曲面边界元法。该方法利用二阶剖分单元的节点坐标信息来求解双2次B样条曲面参数方程,再利用B样条曲面参数方程和面积比值法定义对应于B样条曲面单元4个顶点节点的形状函数;用B样条曲面单元4个顶点作为计算节点,与二阶四边形边界元法相比,计算量大大减少;与线性平面边界元法相比,双2次B样条曲面与实际边界面更接近,从而可以明显提高计算精度。用球形电极和球板电极的电场分布计算进行验算,结果表明:在网格剖分节点数相同时,B样条曲面边界元法的计算精度明显优于线性边界元法。最后,将B样条曲面边界元法应用于交流特高压绝缘子串的电场强度和电位分布计算。In boundary element method（BEM） for calculating 3-D electrostatic fields of ultra-high voltage（UHV） insulator strings, in order to calculate the electric field intensities and the potential distribution accurately, this paper proposes B-spline surface BEM using the double quadric B-spline surface to fit the actual boundary surface. This method uses node coordinates of second-order element to construct double quadric B-spline surface parameter equation, and constructs shape functions corresponding to four vertex nodes of B-spline surface using B-spline surface parameter equation and area ratio method. The B-spline surface BEM takes the four vertex nodes of B-spline surface as the calculating nodes. The calculation will be greatly reduced compared with the second-order quadrilateral BEM, while compared with linear planar BEM, the double quadric B-spline surface is closer to the actual boundary surface, which can improve the calculation precision. The electric field distributions of the spherical electrode and sphere-plate electrode were calculated. The results show that the calculation accuracy of the B-spline surface BEM is better than that of the linear BEM on the condition of same grid nodes. Finally, the B-spline surface BEM is applied to calculate the electric field intensities and the potential distribution of AC UHV insulator strings.

关 键 词：静电场计算 边界元法 B样条曲面 B样条基函数 特高压绝缘子串 

分 类 号：TM151[电气工程—电工理论与新技术]