## 5 Conclusions  
In this paper, LIVs along an overhead distribution line are calculated over a Gaussian-shaped mountain using the 3-D FDTD method. The height and width of the mountain, as well as the lightning strike locations, are considered to be the factors influencing the LIVs. The following conclusions are drawn from the results:  
1. Comparative analysis reveals that the influence on LIVs for lightning strikes over complex mountainous terrain is pronounced. Different lightning strike locations correspond to different EM wave propagation paths. For lightning strikes at SL2, the presence of Gaussian-shaped mountainous terrain causes the enhancement in LIVs due to the reflection of EM waves between the mountain and the flat ground. However, the mountain obstructs the propagation of EM waves, which leads to attenuation in LIVs when lightning strikes at SL3.
2. For lightning strikes at SL1 and SL2, the presence of a Gaussian-shaped mountain leads to the enhancement of induced voltages, and this enhancement intensifies further as mountain height increases.
3. For lightning strikes at SL3, the Gaussian-shaped mountain is located between the lightning channel and the overhead distribution line. LIVs decrease compared to those of flat ground due to the shielding effect of the mountain, and this impact becomes more pronounced as the height increases.
4. In the case of a Gaussian-shaped mountain model, the influence of mountain width on the enhancement of LIVs is less significant than that of mountain height. Nonetheless, a sufficiently wide mountain can still result in a stronger EM shielding effect.  
This paper investigates the impact of a single Gaussian-shaped mountain with finite soil conductivity on LIVs along a single overhead distribution line. The results demonstrate that the geometry of mountainous terrain significantly affects the LIVs for different lightning strike locations. However, in practical environments, distribution lines traverse multiple terrain features with varying electrical properties. Therefore, future work should extend the analysis to more complex terrain involving multiple mountains and varying soil dielectric properties. Additionally, two different placement configurations of single conductors are considered in this paper, as the coupling effects of multiple conductors also merit further investigation.  
Conceptualization, [PERSON] ([PERSON]) and Q.Z.; methodology, [PERSON] ([PERSON]) and J.N.; software, J.N. and Y.T.; validation, [PERSON] ([PERSON]), Y.T. and J.N.; formal analysis, [PERSON] ([PERSON]), J.Z. ([PERSON]), and J.N.; data curation, J.N., [PERSON] ([PERSON]), and Y.T.; writing--original draft preparation, J.N.; checking, [PERSON] ([PERSON]), Q.Z., Z.X., Y.W. and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China, grant number 42205082; the Natural Science Foundation of Jiangsu Province, grant number BK20220657; and the PhD Research Startup Foundation of Jiangsu University of Science and Technology, grant number 1032932108.  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to privacy.  
Special thanks to the reviewers for their valuable comments.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l}
2/3-D & Two-/three-dimensional \\ EM & Electromagnetic \\ FDTD & Finite-difference time-domain method \\ FEM & Finite element method \\ LIVs & Lightning-induced voltages \\ MOM & Method of moments \\ PV & Photovoltaic \\ SL & Strike location \\ \end{tabular}