A new estimation model of the lightning shielding performance of transmission lines using a fractal approach

The path of the lightning discharge shows characteristics of branching and tortuosity, and the lightning shielding failure of the transmission line also has statistical features. In this paper, an improved leader progression model using a fractal approach is introduced, which considers both the deterministic and stochastic features of the downward lightning leader. Based on the proposed model, the statistical features of lightning shielding failure on transmission lines will be analyzed. First, the fractal dimensions of the downward lightning trajectory in simulation are calculated and the value of breakdown probability constant η will be determined based on the fractal dimensions of natural lightning. Second, using the proposed model the shielding failure probability contour around the transmission line space is also obtained and used to describe the shielding failure zone and then the contour curve is applied to analyzing the characteristics of transmission lines that suffer from direct lightning strokes. Moreover, a method to estimate the lightning shielding failure rate of transmission lines is put forward, and the influence of the line height and the shielding angle of ground wires on the shielding failure rate of transmission lines are also investigated.