# Attenuation of Lightning-Induced Effects on Overhead Distribution Systems in Urban Areas
## 1 Introduction  
The continuous growth of overhead distribution systems requires a constant improvement in terms of power quality and system reliability. One of the most critical events causing a fault on an overhead distribution line is undoubtedly represented by lightning events [1, 2]. On overhead distribution systems, lightning damage can be caused by two main categories: direct events and indirect events. While the first one is typical of lightning directly striking the electrical infrastructure and is extremely dangerous, the second one represents lightning discharges striking in the proximity of the overhead line and causing line overvoltage due to the coupling with the electromagnetic fields. The events belonging to this latter category, even if less dangerous, have a higher frequency of occurrence and can lead to a high number of flashovers if the line insulation level is low [1]. The analysis of lightning-induced voltages on distribution systems has been deeply researched, focusing on the effects caused by the soil parameters [3, 4, 5] and on the possible mitigation measures, such as the installation of shield wires and surge arrests [3, 6, 7]. Distribution lines in urban areas are usually installed in cable. However, in some countries, they are installed as overhead lines located close to buildings. In those particular cases, buildings play a non-negligible role in the interactions between lightning strike and overhead line in cases of direct and indirect events. Concerning direct events, the presence of a building reduces the probability that the lightning directly hits the power line, playing the same role as a shield wire, which protects the distribution lines from direct events according to the well-known electrogeometrical criterion [5]. On the other hand, the role of buildings close to overhead lines during indirect events has been less analyzed. The interactions of buildings with lightning events was examined by [8, 9], which analyzed the electromagnetic fields induced inside the buildings directly struck by lightning. Other works, based on experimental tests, focused their efforts on the evaluation of how the presence of buildings modified the behavior of the electromagnetic fields irradiated by the lightning discharge [10]. In principle, the most rigorous and precise approach for the evaluation of this particular case should be based on a full-wave approach, where the complete geometry including the channel, the building, the overhead line, and the ground is modeled as proposed in [11]. The most valuable works in this field have been proposed by the authors of [12], who presented the attenuation of the electromagnetic fields produced by lightning discharges due to the presence of buildings by means of specific functions applied to the closed-form expressions of the electromagnetic fields valid for open terrain Validation of this approach was given by comparison with a Finite Element Method (FEM)-based field calculation (used as a benchmark). The functions obtained in [12] enabled calculation of the induced voltage on a specific overhead distribution line starting from the electromagnetic fields' expressions valid for open terrain, which are usually implemented in the well-known Finite Difference Time Domain (FDTD) numerical codes, such as LIOV [13] and LIGHT-PESTO [14]. However, application of the same functions obtained and validated in some specific cases seems unjustified for different cases, since cases can be different in terms of striking point, channel-base parameters, lightning channel parameters, and line characteristics. This paper proposes an analysis of the lightning-induced voltages on distribution systems with the presence of nearby buildings. The analysis was performed computing the EM fields by means of the FEM software COMSOL [15] and using them as input to the field-to-line coupling code with LIGHT-PESTO [14]. The analysis aims at providing an estimation of the attenuation due to the buildings, which can be useful in the design of Lightning Protection Systems (LPS).