## 3 Results and Discussions
### Comparative Analysis of LIVs over Gaussian, Conical, and Flat Terrains  
Figures 5 and 6 show the variations in LIVs for Configurations A and B, respectively. The results were calculated at the two ends and the center of the distribution line located 300 m horizontally from the mountain center and 10 m above the flat ground. The mountain is set to 250 m in height and 400 m in width. The mountain conductivity and relative permittivity are set the same as that of ground soil. Figure 5 illustrates the LIVs of the overhead distribution line under Configuration A and the maximum LIVs are shown in Table 1. Figure 5a-c presents the results calculated over three different terrains when lightning strikes at SL1. Simulation results reveal that a notable reduction in the induced overvoltage was observed when lightning strikes at SL1, due to the terrain obstruction. Compared with flat ground, induced voltages at the close end of the line decrease by 18% for a Gaussian-shaped mountain and 22% for a cone-shaped mountain seen in Table 1. Additionally, the peak arrival time of the induced voltages varies with the mountain shape. For the Gaussian-shaped mountain, the peak occurs earlier at the close end of the line than in the cone-shaped mountain case, while at the center and remote end of the line, the peak arrives later. Results for lightning strikes at SL2 are shown in Figure 5d,f: the presence of a mountain enhances the overvoltage when lightning strikes at SL2 of a Gaussian-shaped and cone-shaped mountain. Compared to flat ground, induced voltages at the line close end increased by approximately 56% and 43%, respectively. Consistent with the SL1 case, induced voltages along the overhead distribution line are slightly higher for the Gaussian-shaped mountain than for the cone-shaped mountain. Nevertheless, the peak arrival times at the close end, center, and remote end of the line are slightly delayed for the Gaussian-shaped mountain case. Figure 5g-i depicts the variations in LIVs when lightning strikes at SL3. Under this condition, as in the case of SL1, the propagation of the lightning EM fields is affected by the terrain-induced shielding effect. Compared to flat ground, the presence of the mountain leads to an  
Figure 4: Comparison of results obtained from [PERSON] et al. [31] with that from our 3-D FDTD model adopted in this study for calculating the LIVs when lightning strikes a cone-shaped mountain with different inline angles. approximate 10% decrease in the LIVs for both Gaussian-shaped and cone-shaped terrains. Nonetheless, voltage waveforms and peak values remain largely consistent between the two mountain geometries, possibly due to increased separation between the lightning strike location and the distribution line in the case of SL3. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Strike Location** & **Terrains** & **Close End (kV)** & **Center (kV)** & **Remote End (kV)** \\ \hline SL1 & Flat ground & 17.62 & 11.09 & 20.50 \\  & Gaussian-shaped & 15.57 & 4.59 & 15.89 \\  & Cone-shaped & 14.59 & 2.57 & 13.14 \\ SL2 & Flat ground & 17.70 & 11.12 & 20.54 \\  & Gaussian-shaped & 25.51 & 23.65 & 44.17 \\  & Cone-shaped & 23.99 & 23.33 & 43.08 \\ SL3 & Flat ground & 17.56 & 11.07 & 20.48 \\  & Gaussian-shaped & 17.07 & 11.04 & 20.16 \\  & Cone-shaped & 16.90 & 10.9 & 19.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum LIVs of different terrains in Configuration A.  
Figure 5: Comparison among the lightning-induced voltages for Configuration A over different terrains, including flat ground, Gaussian-shaped, and cone-shaped mountains. LIVs of line close end, center, and remote end when lightning strikes at (**a–c**) SL1, (**d–f**) SL2, (**g–i**) SL3, respectively. Figure 6 illustrates the LIVs of the overhead line for Configuration B with the maximum LIVs presented in Table 2. Except for the configuration of the overhead line, all other settings remain the same as those in Configuration A.