快速计算架空与水平双层大地埋地导体间互阻抗的矩函数方法

Moment Function Method of Fast Mutual Impedance Calculation Between Overhead and Underground Conductor in Horizontal Two-layered Soil

架空导体和水平分层大地中埋地导体之间的互阻抗是众多电磁兼容问题分析的基础,该阻抗表达式为含无穷上限的高振荡复积分。提出了一种采用矩函数方法快速计算该积分的方案,将互阻抗积分表达式分割为定积分和含有无穷上限的尾积分,并分别采用合适的方法予以快速计算。对于其中的定积分部分,首先采用样条函数拟合被积函数,此时,定积分部分可用矩函数解析表示;对于含有无穷上限的尾积分,将积分核用其渐进函数代替,该渐进积分核函数可采用指数积分表示。由于矩函数采用解析式计算,本文方法完全避免了振荡积分的计算,是一种高效的计算高振荡积分的方法。本文方法可以用于电磁兼容或者电磁暂态问题中涉及的架空导体和埋地导体之间互阻抗的计算。

It is a dispensable step for many electromagnetic compatiblity problems to calculate the mutual impendance between the o- verhead and the underground conductors in a multi-layered soil. To this end, an efficient approach is proposed in this paper. The ex- pression of the mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts inten- tionaUy in the first place, i. e. , the definite and the tail integral respectively. The definite integral is calculated using the proposed mo- ment functions after fitting the integrand into a serial of spline functions, and the tail integral is replaced by an exponential integral with an asymptotic integrand. The advantage of the proposed approach is that the calculation of oscillatory integral is completely avoided due to the fact that the moment function is evaluated analytically. Numerica! examples justify the proposed approach in many cases with different combination of parameters. The proposed approach can be used in the electromagnetic compatibility analysis between o- verhead and underground conductors.