## 1 Introduction  
Lightning activity has become a major cause of intermittent disturbances in power systems, significantly affecting the quality of power distribution. This is due to the fact that high-, medium- and low-voltage lines are more elevated than surrounding buildings, making them more susceptible to direct or indirect lightning electromagnetic pulses (LEMPs). [PERSON] carried out a primary hypothetical investigation of lightning-induced surges in power transmission lines with the following objectives: This research investigated the reasons for lightning strikes on transmission lines [1]. In 1929, [PERSON] utilized [PERSON]'s hypothesis to reveal that the field induced by lightning cannot vanish immediately [2]. An article written by [PERSON] in 1935 was the first in the current literature to consider the inducing effect of vertical lightning paths on the ground due to a lightning strike [3]. In an editorial distributed in 1948, [PERSON], unlike [PERSON] and [PERSON], calculated the induced voltages resulting from vertical lightning strikes using more complex assumptions. [PERSON] claimed it was essential to consider the magnetic impact in addition to the electrostatic effects. The study emphasized that this consideration is significant for the regions near a lightning strike point [4]. In 1958, [PERSON] calculated induced voltages for energy transmission lines (ETLs) with short and long ranges and developed a closed-form expression with a global standard [5; 6]. [PERSON]'s approach failed to consider a precise analytical formulation for vertical electric fields (VEFs), which was developed by [PERSON] et al. [7]. Compared to [PERSON]'s results, [PERSON] et al. 's study pointed out differences in the surge voltages caused by an LEMP. Although [PERSON] also addressed this issue, its practical effects on different LEMP flows and overhead lines have not been studied in detail. Therefore, there is a need for an in-depth investigation of [PERSON]'s impact on the calculation of electric areas, induced voltages and the indirect lightning performance of overhead lines. A similar study was carried out for medium-voltage lines. In this study, the LEMP status was investigated using the 3D finite-difference time-domain (FDTD) method. It is advantageous for analyzing LEMP because it can handle non-uniform conductors over lossy ground [8]. Another study determined the current and electric field values of lightning's return stroke [9]. Induced voltages and fields were investigated based on the lightning strike angle with a constant current value by [PERSON] [10]. [PERSON] carried out insulation work to protect against lightning-induced overvoltages in medium-voltage overhead lines [11]. In a similar literature study, a numerical analysis of both the lightning current pulse and the electromagnetic field propagating in the far field was performed using a revised modified transmission line model with exponential decay (MTLE) for high-rise buildings with conductive ground [12]. In another work, theoretical models, numerical simulations and experimental tests for determining the pulses propagating between the windings of transformers subjected to lightning strikes were discussed [13]. In another study, the impact of a grounded wind tower, ground conductivity, permittivity, the depth of the cable and its position from the return stroke on the lightning-induced electromagnetic fields on a cable sheath was investigated [14]. In another work in the literature, a new numerical method was proposed to reconstruct the waveform of a distant electric field due to a lightning strike on a tall structure [15]. In another literature study, an approximate formula was proposed for evaluating the peak values of lightning-induced voltages in the presence of highly resistive soils [16]. Finally, another recent study in the literature discussed the widespread use of the FDTD method, one of the full-wave numerical approaches, to simulate electromagnetic transients in earthing structures, such as earthing grids for substations [17].