Research on Singularity in Calculation of Induced Electric Field in Pointed Conductors

Abstract

In the electric field environment of thunderstorm, the tip of a grounded object at a high place is more likely to produce corona discharge and finally cause lightning flash. Therefore, the study of the surface electric field of the grounded object tip in the electric field environment has important theoretical value and practical significance for the analysis of the characteristics of the head-on discharge. Due to the strong singularity of the tip structure, the traditional numerical analysis method cannot accurately calculate its surface electric field. Therefore, the traditional literature usually chamfers the conductor tip, but in lightning physics, researchers are most concerned about the maximum field strength in the local area. In order to study the electric field distribution on the tip conductor surface, a semi-analytical boundary element method is proposed to calculate the tip structure directly. Firstly, the analytical formula of the electric field on the tip conductor surface and the boundary element semi-analytical common method are derived, and the tip conductor model is established to calculate the tip electric field excited by the external electric field using the analytical solution and the semi-analytical method. The correctness of the semi-analytical method is verified by calculating the L₂ loss function of the two, and the influence of the tip angle on the semi-analytical calculation results is studied. The results show that for the three-dimensional cone model, the L₂ loss function is 10^-5, which meets the calculation accuracy. The special treatment of the semi-analytical method at the strong singular integral makes the calculation accuracy much higher than that of the Gaussian integral, where the L₂ loss function is greatly reduced. Further, based on the change of tip angle, as the conductor tip becomes sharper, the greater the electric field distortion is, and the greater the L₂ loss function is. The research results provide a method reference for the calculation of the electric field on the tip conductor surface.