## 4 Simulations and Analysis
### Electric Field Simulation in Defect  
To simulate the electric field distribution within the insulation defect, the COMSOL Multiphysics 6.2 simulation software was used for modeling and analysis. Since the insulation defect region is the primary discharge area, a segment of the cable near the defect was selected for simulation, as shown in Figure 15. The main components of the simulation model are the cable conductor and the XLPE insulation layer. A through-defect penetrating the insulation layer is placed at the center of the model, with a variable size. The defect region is divided into two parts: the upper part is filled with water, and the lower part with air. The thicknesses of the water and air layers are adjustable to simulate the gradual intrusion of water into the defect. Since breakdown typically occurs near the voltage peak, where the electric field strength is at its maximum, the analysis can be simplified to focus on the electric field distribution at the voltage peak under electrostatic conditions. The relative permittivity of air is set to 1, that of the liquid to 80, and that of XLPE to 2.2, with a thickness of 2 mm. The cable core material is copper, modeled as an equipotential body with a potential of 318 V, while the liquid layer is set to a ground potential.  
As the liquid gradually penetrates the insulation defect, the thickness of the water layer increases while the thickness of the air layer decreases. The electric field distributions corresponding to different water layer thicknesses within the defect are shown in Figure 16a, with the defect width fixed at 1.1 mm. As the water layer becomes thicker, the electric field distribution changes significantly. When the water layer thickness reaches 0.5 mm, the electric field shows a certain degree of concentration at the interface between the water and air layers. However, the overall field strength remains relatively low, around 2.5 kV/cm, with the field near the conductor core at approximately 1.5 kV/cm. As the water layer thickness increases to 1.0 mm, the concentration of the electric field at the interface becomes more pronounced, forming a localized high-field region where the maximum electric field strength at the interface reaches 4-5 kV/cm. When the water layer thickness further increases to 1.5 mm, the electric field strength around the entire air column reaches 4-5 kV/cm. In highly non-uniform electric fields, the breakdown strength of air is  
Figure 14: Statistics of intermittent arcs under different liquid conductivities.  
approximately 3-10 kV/cm, which can lead to electrical breakdown and the formation of an arc within the defect.  
The electric field distribution for different insulation defect sizes is shown in Figure 16b, with the water layer thickness maintained at 1 mm. When the defect width is 1.1 mm, the electric field is concentrated at the interface between the water layer and the air layer. As the defect width increases to 1.6 mm, the degree of field non-uniformity decreases, with the high-field region concentrated at the interface among the air, water, and insulating medium. Further increasing the defect width to 2.3 mm results in a more uniform electric field distribution within the air layer. The increase in defect width allows the electric field to be more evenly distributed throughout the defect area, thereby reducing the concentration of local field strength and lowering the likelihood of breakdown occurrence. On the other hand, a wider defect facilitates greater liquid infiltration and contact with the conductor core, creating a direct conductive path between the core and the ground through the liquid, leading to leakage current and a decrease in arc occurrence frequency.  
Figure 16: Electric field strength distribution in insulation defects: (**a**) with different water layer thicknesses; (**b**) with different defect sizes.  
Figure 15: Schematic diagram of the simulation model.