广义索末菲积分快速算法及架空导线与地下导线间互阻抗的计算

提出一种基于离散复镜像法的广义索末菲积分（GSI）快速计算方法。该方法将GSI表示为离散复镜像近似值和积分校正项之和，其中离散复镜像近似值采用Prony方法得到解析式求出；积分校正项以原积分与逼近积分核之差作为校正积分核，采用自适应积分法求出，架空电力线路与地下通信电缆互阻抗的数值计算结果表明，该方法比常规数值积分方法计算效率可提高20倍以上。

FAST EVALUATION OF GENERALIZED SOMMERFELD INTEGRAL AND THE MUTUAL IMPEDANCE CALCULATION BETWEEN OVERHEAD CONDUCTORS AND UNDERGROUND CONDUCTORS

An efficient approach to calculate the generalized Sommerfeld integral(GSI), which is based on the discrete complex image method, is presented. GSI is separated to the sum of two terms, one of which is the approximate value obtained from an analytical expression by means of Prony's method, another of which is an emendatory integral acquired by an adaptive quadrature. The emendatory integral kernel is the difference between the original and the asymptotic integral kernel and converges very fast. The validity of the method herein is proved by the numerical solution of the mutual impedance between overhead power lines and underground telecommunication lines. It is shown, compared with the conventinal integration method, that the method herein can increase the calculation efficiency more than 20 times.