基于Bezier曲面四边形边界元法的特高压绝缘子串电场计算  

Calculation of UHV Insulators String Electric Fields Based on Bezier Surface Quadrilateral BEM

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,湖北宜昌443002

出　　处：《华北电力大学学报（自然科学版）》2017年第3期39-44,共6页Journal of North China Electric Power University：Natural Science Edition

基　　金：国家自然科学基金资助项目(51577105)

摘　　要：在三维静电场的边界元计算中,为了快速、精确计算电位和电场强度分布,提出了用双2次Bezier曲面四边形拟合实际积分面的Bezier曲面四边形边界元方法。该方法利用二阶剖分单元的节点坐标信息来构造双2次Bezier曲面参数方程,再利用Bezier曲面参数方程和面积比值法构造对应于Bezier曲面4个顶点节点的形状函数;以Bezier曲面4个顶点节点为计算节点,大大减少了计算节点数;与一阶平面四边形边界元法相比,双2次Bezier曲面能够更好地拟合实际积分面,提高计算精度。并且可通过精细后处理技术将模型表面的函数值精细显示。算例结果表明,Bezier曲面四边形边界元法与传统边界元法相比,在网格剖分节点数相同时,计算精度得到了提高。在计算精度相同条件下,该方法中的节点数量降低,减少了计算机内存的使用。最后,将Bezier曲面四边形边界元法应用于交流特高压绝缘子串电场的计算。In the boundary element calculation of three-dimensional electrostatic field, in order to calculate the intensity distribution of electric potential and electric field quickly and accurately, Bezier surface quadrilateral boundary element method （ BEM ） which uses the double quadric Bezier surface quadrilateral to fit the actual integral surface is proposed in this paper. This method uses second-order segmentation element＇ s node coordinates to construct double quadric Bezier surface parameter equation and uses Bezier surface parameter equation and area ratio method to construct shape functions corresponding to Bezier surface＇ s four vertex nodes. The number of node can be obviously decreased if the four vertex nodes are used as the computational node. Double quadric Bezier surface quadrilateral will fit the actual integral surface better when compared with the first-order plane quadrilateral BEM. So, Bezier surface quadrilateral BEM can improve calculation accuracy. And the function value of the model surface can be accurately displayed by the fine post-processing technique. The calculating results show that Bezier surface quadrilateral BEM has more accurate calculation results than the traditional BEM if they have the same grid segmentation nodes. Under the condition of same calculation accuracy, the Bezier surface quadrilateral BEM obviously requires fewer nodes, which needs less computer memory. Finally, the Bezier surface quadrilateral BEM are applied to the calculation of AC UHV insulator string electric field.

关 键 词：静电场计算 BERNSTEIN基函数 BEZIER曲面 边界元法 精细后处理 

分 类 号：TM151[电气工程—电工理论与新技术]