水平分层土壤中点电流源电流场的计算

Calculation of Current Field due to a Point Source in Multi-layer Soil

为解决地网仿真计算中多层土壤点电流源的格林函数计算复杂问题,以典型4层水平分层土壤模型为例,对点电流源格林函数公式进行了化简。因为格林函数的计算中涉及到含有贝塞尔函数的广义积分,被积函数高速振荡,难以数值积分。通过对被积函数的分析,提取衰减较慢的成分,给出了级数形式的解析表达式;对剩余部分,按照贝塞尔函数的零点分区间进行积分,收敛很快,提高了计算效率。最后使用数值方法给出了地电流的分布图像。

The computation of Green＇s Functions in multi-layer earth, which plays an important role in the analysis of grounding systems, are difficult for their complex expressions. In order to improve the computation, the Green＇s Functions in a typical 4-layer soil are analyzed in this paper. First, by introducing some parameters uk and considering the field point is usually very far from the source point so that the source can be treated as being located at the earth surface, the expressions of Green＇s Functions are simplified. Then, the calculation of Green＇s Functions involving the integration of the oscillatory functions which contain the first order Bessel functions are carried out. To accelerate the integral convergence, the slow decaying parts of the integrant are separated and are integrated through an analytical way, which gives an expression in series form. For the remanent part, the integrating interval is divided into subintervals by zeros of the Bessel function, and the quadrature converges very quickly. By these algorithms, the expense of time for computing Green＇s functions is greatly reduced. Simulation results show its effectiveness. Finally, the current distribution in soil is obtained by using the finite element method, which gives an intuitional image of the earth current.