## 3 Experimental Results
### Influence of Grounding Resistance  
As shown in Figure 10, for the first two stages of 3.1 and the first stage of 3.3, sub-cycle arc waveforms were recorded under different grounding resistances, with a cable defect width of 1.5 mm. The arcs were generated under liquid penetration conditions, with a liquid conductivity of 3 mS/cm and grounding resistances set to 10 \(\Omega\), 30 \(\Omega\), 70 \(\Omega\), and 120 \(\Omega\). The experimental results indicate that as the grounding resistance increases from 10 \(\Omega\) to 30 \(\Omega\), the arc current gradually decreases due to the current-limiting effect of the resistance. The current amplitude reduces from 19 A to 8 A, while the arc voltage and current maintain smooth variations, suggesting that the arc remains relatively stable during combustion. At a grounding resistance of 70 \(\Omega\), the voltage and current waveforms exhibit high-frequency components, indicating an unstable arc. When the grounding resistance reaches 120 \(\Omega\), voltage and current waveforms show more pronounced fluctuations, with the current amplitude remaining low, peaking at approximately 1 A. This suggests that high grounding resistance significantly suppresses the discharge process, making it difficult for the arc current to form a stable flow. Since arc generation requires sufficient current to sustain ionization in the defect, the entire process remains weak and unstable. Additionally, the number of observed arc occurrences is significantly reduced.  
As shown in Figure 11, for humid air exposure conditions (3.2), sub-cycle arc waveforms were recorded under different grounding resistances, with a cable defect width of  
Figure 10: Sub-cycle arc waveforms under different grounding resistances in the 1 st and 2 nd stages of liquid penetration and the 1 st stage of liquid immersion conditions.  
Figure 9: Typical fault under immersion conditions: (a) the 1 st stage; (b) the 2 nd stage.  
1.2 mm. The arcs were generated in humid air conditions with a relative humidity of 85% and a liquid conductivity of 3 mS/cm. Compared to the variation pattern of the arc in liquid penetration conditions, the common characteristic between the two is that their amplitudes decrease as the grounding resistance increases. However, due to the extremely short duration of transient arcs, the increase in grounding resistance does not significantly affect the waveform shape, and the current consistently maintains a pulse-like form.  
As shown in Figure 12, for the third stage of 3.1 and the second stage of 3.3, periodic current waveforms were recorded under different grounding resistances, with an insulation defect width of 2.2 mm. The cable was fully immersed in water with a conductivity of 3 mS/cm. Unlike arc discharge conditions, where the arc state is significantly affected by current amplitude, in this case, the liquid within the insulation defect behaves as a persistent nonlinear resistor. The series-connected grounding resistance only influences the current amplitude without significantly altering the waveform shape. The calculations indicate that the minimum fault resistance formed by the liquid in the insulation defect is approximately 700 \(\Omega\). Consequently, as the grounding resistance increases from 10 \(\Omega\) to 120 \(\Omega\), the peak current decreases by only a few milliamps.  
Figure 11: Sub-cycle arc waveforms under different grounding resistances in humid air exposure conditions.  
Figure 12: Periodic current waveforms under different grounding resistances in the 3 rd stage of liquid penetration and the 2 nd stage of liquid immersion conditions.