Abstract Atmospheric discharges contain random components which the Electrogeometric Model does not take into account, once it is purely geometric and not physical. Some physical models, like the Progressive Leader Model, also do not consider variations in the properties of the air. The Electric Field Deflection (EFD) was recently proposed in literature. This model is sensitive to small variations in the permittivity of the air. To simulate these air variations, a two-dimensional landscape of the electric permittivity was created using fractional Brownian motion (fBm). This technique was combined with EFD to simulate the trajectories of lightning discharges through the Finite Element Method (FEM). This proposed method, called EFD-fBm, was used to analyze the air-termination system of a power transmission line and compared to the Electrogeometric Model. Discharges with current peaks of 2.9, 5.4, 10.1 and 15.7 kA were studied according to the lightning protection standards. The transmission line was analyzed in two transverse planes: a plane with the tower and another one comprising the span between two towers. Landscapes constructed through fBm were used. The proposed model estimated that the efficiency of the air-termination system of the transmission line analyzed was 96.36% for discharges with current peak of 10.1 kA.

中文翻译：

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基于电场偏转和分数布朗运动模型的输电线路接闪器系统效率

摘要 大气放电包含电几何模型不考虑的随机分量，一旦它是纯几何的而不是物理的。一些物理模型，如渐进式领导模型，也没有考虑空气特性的变化。最近在文献中提出了电场偏转 (EFD)。该模型对空气介电常数的微小变化很敏感。为了模拟这些空气变化，使用分数布朗运动 (fBm) 创建了介电常数的二维景观。该技术与 EFD 相结合，通过有限元方法 (FEM) 模拟闪电放电的轨迹。这种被提议的方法，称为 EFD-fBm，用于分析输电线路的接闪器系统并与电气几何模型进行比较。根据防雷标准研究了电流峰值为 2.9、5.4、10.1 和 15.7 kA 的放电。输电线路在两个横向平面上进行了分析：一个平面包含塔架，另一个平面包含两个塔架之间的跨度。使用了通过 fBm 构建的景观。所提出的模型估计，对于电流峰值为 10.1 kA 的放电，所分析的输电线路的接闪器系统的效率为 96.36%。一个带有塔的平面，另一个包含两个塔之间的跨度。使用了通过 fBm 构建的景观。所提出的模型估计，对于电流峰值为 10.1 kA 的放电，所分析的输电线路的接闪器系统的效率为 96.36%。一个带有塔的平面，另一个包含两个塔之间的跨度。使用了通过 fBm 构建的景观。所提出的模型估计，对于电流峰值为 10.1 kA 的放电，所分析的输电线路的接闪器系统的效率为 96.36%。