## 4 Analysis of Pipeline Overvoltage under the Action of Multi-Tower Flow
### The Influence of Lightning Peak Current  
In order to investigate the impact of lightning peak current on lightning overvoltage of natural gas pipelines at the cross-crossing under the influence of lightning stroke conductor, certain parameters were fixed: soil resistivity (\(\rho\)) of 1000 \(\Omega\cdot\)m, spacing between pipelines (\(d_{gp1}\)) of 40 m, and cross angle (\(\beta\)) of 0\({}^{\circ}\). Lightning peak currents of 25 kA, 30 kA, 35 kA, 40 kA, 45 kA, and 50 kA were sequentially selected. The lightning current waveforms of T\({}_{0}\) and T\({}_{\mathrm{R1}}\) tower grounding grids under different lightning peak currents were imported into COMSOL Multiphysics. Figure 5 illustrates these waveforms. The lightning overvoltage amplitude of natural gas pipelines at the cross-crossing of overhead lines is depicted in Figure 7. Figure 8 presents the potential height distribution of the tower grounding grid and crossing natural gas pipeline under different lightning peak currents.  
Based on the results shown in Figure 7a, it can be observed that as the lightning peak current increases, both the induced voltage amplitude of the metal layer and the induced voltage amplitude of the insulation layer of the natural gas pipeline also increase. Specifically, when the lightning peak current is raised from 25 kA to 50 kA, the induced voltage amplitude of the metal layer rises from 22.61 kV to 42.25 kV, while the induced  
Figure 8: The potential height distribution of tower grounding grid and natural gas pipeline at cross-crossing under different lightning amplitudes. (**a**) I0 = 25 kA. (**b**) I0 = 30 kA. (**c**) I0 = 40 kA. (**d**) I0 = 50 kA.  
Figure 7: The influence of lightning peak current on the overvoltage of natural gas pipelines at cross-crossings. (**a**) Induced voltage amplitude of metal layer and insulation layer of pipeline. (**b**) Voltage amplitude of pipeline insulation layer.  
voltage amplitude of the insulation layer increases from 25.55 kV to 47.56 kV. Similarly, Figure 7b illustrates a similar trend in the voltage amplitude of the pipeline insulation layer with respect to the lightning peak current. In this case, as the lightning peak current increases from 25 kA to 50 kA, the voltage amplitude of the pipeline insulation layer increases from 3.46 kV to 7.23 kV, representing a significant increase of 108.96%.  
The reason for studying the variation law mentioned above is that as the amplitude of the lightning current increases, the current flowing into the earth through the tower also increases. This, in turn, leads to an increase in the potential of the tower grounding grid and the surrounding soil, under the same soil resistivity. Consequently, the resistive coupling effect of the gas pipeline is aggravated. Equation (1) demonstrates that this rise in potential will cause the nearby ground potential to increase, resulting in a larger potential difference between the outer insulation layer and the metal layer of the pipeline. Thus, it is evident that the amplitude of the lightning current directly influences the voltage amplitude of the pipeline insulation layer.  
Based on the results shown in Figure 8, it is evident that the potential height of the T\({}_{0}\), T\({}_{\mathrm{R1}}\) tower grounding grid and the surrounding soil increases significantly with the increase in lightning peak current. This can be attributed to the increased flow of scattered lightning through the tower grounding grid. When the soil resistivity remains constant, the potential of both the tower grounding grid and the surrounding soil increases, thereby exacerbating the resistive coupling effect on the natural gas pipeline. At the same time, it can be obviously seen that the potential height at the center of the natural gas pipeline is significantly higher than the potential height at both ends of the natural gas pipeline.