刘刚, 侯林玉, 纪锋, et al. Application of Automatic Computation Method for Distributed Capacitance of Multi-conductor Based on Finite Element Method[J]. 2020, 46(4): 1226-1233.
刘刚, 侯林玉, 纪锋, et al. Application of Automatic Computation Method for Distributed Capacitance of Multi-conductor Based on Finite Element Method[J]. 2020, 46(4): 1226-1233.DOI:
基于有限元法的多导体分布电容自动计算方法及其应用
摘要
多导体的分布电容参数是电磁暂态问题分析的基础
为了能够准确高效地得到复杂结构多导体间的分布电容
首先基于电磁场理论推导了以感应系数为待求量的方程组
其次给出了方程组系数矩阵中各非零元素的计算方法
然后基于有限元法计算空间电场能量作为方程组的右端项元素
再通过求解方程组得到感应系数矩阵
最后由感应系数矩阵得到分布电容。将该方法应用于具有解析解的双导体传输线模型的分布电容参数计算问题
对比分析了不同截断边界条件和剖分网格下的计算结果
计算结果表明该方法在适当的截断边界条件和剖分尺寸下
电容计算结果最大相对误差<1%
从而验证了所提方法的有效性。将该方法应用于典型架空线路和绕组匝间的分布电容参数计算
所提出的基于有限元方法计算多导体间分布电容的自动求解方法只需在建模时对多各个导体施加一次边界条件
然后利用所提方法实现方程组的构造、求解和分布电容参数提取
从而大大提高了效率。
Abstract
Distributed capacitance parameters of multi-conductors are the basis of electromagnetic transient analysis. In order to accurately and efficiently obtain the distributed capacitance between multi-conductors of complex structures
the equations with induction coefficient as an unknown quantity are derived based on the electromagnetic field theory firstly. Secondly
the calculation methods of non-zero elements in the coefficient matrix of the derived equations are given. Then
based on the finite element method
the electric field energy is calculated as the right-end element of the equation system
and the induction coefficient matrix is obtained by solving the equation system. Finally
the distributed capacitance is obtained by the induction coefficient. The method is applied to the calculation of distributed capacitance parameters of a two-conductor transmission line model with analytic solutions. The results under different truncated boundary conditions and meshes are compared and analyzed. The results show that the maximum relative error of capacitance calculation is small under the appropriate truncated boundary conditions and mesh size. The proposed method is applied to the calculation of distributed capacitance parameters of typical overhead lines and winding turns. The proposed calculation method
in which only the boundary conditions need to be applied to the multi-conductors during the modeling
constructs and solves the equations
and extracts the distributed capacitance parameters automatically