## 4 Discussion and Conclusions  
This study examined the impact of transient events on power transmission lines and power plants by creating LEMP offshoots using Heidler and Rusck functions. In [PERSON]'s field-to-line coupling model, the electric field used in the coupling equations is derived from expressions of [PERSON]'s model for the electric field of a return stroke current propagating at a constant velocity along a vertical channel [28]. The effect of the indirect fall (discharge) of the LEMP sprout on the nearby ETLs was analyzed in the first analysis. Different drop currents of the LEMP sprout were used to obtain the vertical electric field generated by the dispersed charge from the LEMP. This study revealed that an increase in the current of the LEMP leads to an increase in the value of the vertical electric field and the induced voltage. Specifically, the electric field value generated by a 160 kA LEMP at the base of an overhead line 100 m away was \(-\)3.87 kV/m. Additionally, an LEMP of the same magnitude produced a scalar value of 200 kV/m at 1.5 ms at the base of an overhead line 100 m away, depending on the time. This finding supports [PERSON]'s suggestion. Furthermore, the vector component of the vertical electric field was examined for various LEMP current levels. Unlike previous studies in the literature, this study investigates both the vector and scalar components of the vertical electric field for different LEMP values. It was observed that the scalar component (200 kV/m at 100 m away for the same current value) is more destructive than the vector component (\(-\)3.87 kV/m at 100 m away). This study also obtained the magnetic field values generated by the LEMP at different falling current values. The analysis revealed that the magnetic field value in the region where the falling current of the LEMP sprout increases also increases non-linearly. Specifically, a 160 kA LEMP creates a magnetic field intensity of 0.4 mT at the foundation of the overhead line 100 m away in 1.5 ms [38]. It was found that the increase in the propagation speed of LEMP sprouts is directly proportional to the gains in the induced voltage in ETLs and power plants as they approach the speed of light. To prevent this issue, the grounding foundations of the poles on certain lines should be shielded where lightning strikes are most frequent. This will improve electromagnetic compatibility and reduce the risk of indirect impacts. This study analyzed the transient voltage values that arise in ETLs and energy facilities based on the propagation speed of LEMP sprouts, according to the area-line relationship. The results showed that the voltage induced in ETLs and power equipment increases in direct proportion to the speed of propagation of the LEMPs as they approach the speed of light. Furthermore, this study examined the effectiveness of LEMPs in the forward trend of the wave and the electrical conditions they create in the region before falling to the ground. This study looked at the humidity levels in the region where the LEMP sprout fell to the ground, as well as the electrical conditions in high-altitude regions. As the formation time of the LEMP sprout approached, the electric field value increased. Specifically, the electric  
Figure 16: Electric field change (x = 0, I\({}_{0}\) = 15 kA, \(\beta\) = 0.4, h = 15 m, and d = 70 m) when the LEMP channel is initially loaded. (Solution for the function in Equation (34)). field value produced by the 15 kA LEMP at 0.5 \(\upmu\)s in the conductors on the 15 m high pole of the overhead line, which was 70 m away from the point where the channel fell before the channel was formed, was measured as 1.5 kV/m [39]. The fall location of the LEMP sprout can be predicted by selecting electric field values in specific lines within the regions most exposed to LEMPs. Furthermore, the electric field value was analyzed based on the time and distance from the point of impact after the LEMP discharge occurred.