After setting up, the voltage is applied. Figure 2 shows the electric field distribution and the 3D model, indicating that the electric field distribution within the slice is uniform, with an electric field value of 22.7 MV/m.

As shown in Figure 3, the maximum field strength at the scratch location on the XLPE slice model is 23.2 MV/m, while the electric field strength in the non-scratch areas of the same slice is only 14.7 MV/m. Figure 4 presents the 3D electric field distribution of the XLPE scratch model, showing significant electric field distortion at the scratch compared to the defect-free condition. Scratches not only damage the surface of the insulation, reducing the insulation thickness at the scratch, but also cause changes in the relative dielectric constant at the air gap and XLPE main insulation interface, leading to electric field distortion.

To study the changes in field strength around the scratch, the slice was sectioned perpendicularly to the scratch direction, as shown in Figure 5. Hx represents the distance from the bottom of the slice to the top, and electric fields along paths I, II, III, and IV were analyzed for variation patterns. Figure 6 shows the electric field intensity changes corresponding to the cross-sectional paths of the slice. When Hx = 0 mm, it represents the bottom end of the slice. Along path I, the field strength gradually increases between HⅠ = 3.0–5.8 mm, reaching a maximum of 15.6 MV/m at HⅠ = 5.8 mm. Along path II, the field strength uniformly rises between HⅡ = 3.0–4.5 mm, with significant changes from 4.5 to 5.8 mm. Figure 4 shows that path II bends at the scratch, causing severe field distortion, with the field strength peaking at 23.2 MV/m at HⅡ = 5.8 mm, about 1.6 times that of the non-defective area. Path III shows a similar trend to path I, with the field strength peaking at 18.39 MV/m at HⅢ = 5.0 mm. Path IV resembles path II, with significant field distortion between 3.0 and 4.5 mm, and the field strength peaking at 23.0 MV/m at HⅣ = 4.5 mm, as shown in Figure 5.

The XLPE surface moisture model shows that under pure water conditions, the electric field strength at the interface between the water film and the slice is 22.4 MV/m, which is consistent with normal conditions. As shown in Figure 7, in the presence of contaminated water, the field strength is 10 MV/m, and the non-moist areas have an electric field strength of 13 MV/m. The maximum potential difference between the contaminated in the contaminated water and the slice interface reaches about 2 kV, with the highest field strength at the contaminated-slice interface being 18.5 MV/m. Figure 8 shows the 3D electric field distribution of the XLPE moisture model, where contaminated water adheres to the upper surface of the moisture model without gaps. When the same voltage is applied, the thickness of the XLPE layer remains consistent, leading to uniform field distribution, but the field strength changes at the contaminated particle-XLPE interface.

Figure 9 shows the relationship between the electric field strength and the distance from the center of the model surface to the side (Xx) within 10 mm, focusing on the interface between contaminateds in the contaminated water and the XLPE model. Figure 10 presents a line graph of electric field strength variations within 10 mm of Xx, showing significant fluctuations along the Xx direction due to the severe impact of contaminated particles in the contaminated water on field strength. When Xx ≤ 0.5 mm, the field strength varies between 3.2 and 5.5 MV/m, peaking at 18.5 MV/m, which is 1.22–1.4 times the normal value. This is because the larger the contaminated water area on the XLPE moisture model surface, the more conductive impurities in the water, increasing its conductivity and enhancing the nearby electric field. The water film is prone to electroosmosis under the electric field, inducing water tree growth (Xiufeng and Xianri, 2017; Shaw and Shaw, 2010; Yang et al., 2021a), significantly affecting the insulation performance of the material.

As shown in Figure 11, the maximum field strength at the contaminated particle-XLPE insulation interface is 20.5 MV/m, nearly 1.5 times the normal condition of 13.6 MV/m. Figure 12 shows the 3D electric field distribution of the XLPE contaminated model, with the metal conductive contaminateds affecting field strength changes.

Figure 13 shows a line graph of electric field strength variations within 1 mm of the center of different radius particles to the side (Lx) on the XLPE slice. The graph shows that the electric field strength at the XLPE interface gradually increases with the radius of the contaminated particles. When Lx = R, the field strength at the contaminated-model interface peaks. When R = 0.3 mm, the maximum field strength is 14.68 MV/m, and it increases regularly with larger contaminated radii, peaking at 18.1 MV/m when R = 0.6 mm. When R = 0.7 mm, the field strength distortion at the contaminated-model interface is the highest, with a field strength of 20.5 MV/m, 1.5 times that of the normal XLPE surface. Thus, a slight increase in contaminated radius leads to an increase in field strength, with larger particles causing greater field distortion at the interface.

Power frequency voltage pressurization experiments were conducted according to the national standard GB/T 1048.1-2006, “Test Methods for Electrical Strength of Insulating Materials.” The breakdown voltage of samples with different defects under different voltage levels, as well as normal defect-free samples, was compared and analyzed to investigate the breakdown voltage under various defects. The schematic diagram and experimental platform are shown in Figure 14. The entire pressurization experimental platform consists of a voltage regulator, protective resistor, experimental electrode, transformer, divider, oscilloscope, and outputterminal.

Several cross-linked polyethylene (XLPE) insulation slices were customized from a cable manufacturer, as shown in Figure 15. The XLPE slices were rinsed with anhydrous ethanol to remove surface dust and dirt, then air-dried under natural conditions. Subsequently, they were sequentially placed using sterile tweezers according to their group and order to avoid any interference from other conditions affecting the experimental results.

After drying, four types of sample groups were prepared: normal defect-free, scratched, moisture-exposed, and metal particle-contaminated slices, as shown in Figure 16.

Bostrom et al. (2003); Bartnikas and Eichhorn (1983); Hagen and Ildstad (1993); Marzinotto et al. (2006); Urbanczyk (2011); Yang et al. (2021b); Yang et al. (2024) indicate that the greater the dielectric constant of impurities and the sharper the shape of defects, the more severe the distortion of the electric field inside the insulation. Therefore, when preparing defect slices, the following points should be noted:

(1) When creating scratched defect samples, it is essential to strictly control the length, width, and height of the scratches, using a hydraulic cutter to ensure the reliability of variables in each group.

For scratched slices, 5 groups of experiments are set up, with each group consisting of the same 10 slices. As shown in Figure 17. When conducting breakdown experiments with scratched slices for different experimental groups, the following points should be noted:

(1) Divide the five groups into a, b, c, d, e, each with ten slices of the same specification.

For moisture slices, five experimental groups were also set up, with each group consisting of ten slices, as shown in Figure 18. The following points should be noted:

(1) Divide the 5 groups into a, b, c, d, e, each with 10 slices of the same specification.

For contaminated slices, also, five experimental groups were also set up, with each group consisting of ten slices, as shown in Figure 19. The following points should be noted:

(1) Divide the 5 groups into a, b, c, d, e, each with 10 slices of the same specification.

For each defect sample, five groups of as-similar-as-possible samples should be created, and the average breakdown voltage was recorded. The experimental data are shown in Table 2.

The average breakdown voltage results are shown in Figure 20. The average breakdown voltage of normal XLPE slices is 129.6 kV. For the scratched group slices, the average breakdown voltage varies significantly depending on the experimental setup. Groups 1 and 2, with the same scratch depth, showed higher breakdown voltage with shorter scratch lengths. Groups 1, 3, and 4, with the same scratch length and depths of 0.5, 0.2, and 0.6 mm, had average breakdown voltages of 58.1, 72.1, and 49.9 kV, respectively. The deeper the scratch, the lower the breakdown voltage, with the most significant intergroup variation and impact on breakdown voltage. For slices with contaminated water droplets, the average breakdown voltage is 69.7 kV, 0.53 times that of the normal slices, with stable breakdown voltage across the groups. For contaminated particle slices, the average breakdown voltage is 59.2 kV, 0.46 times that of normal slices. The average breakdown voltage difference among the five groups was 0.7, 1.7, 1.8, and 3.8 kV. The larger the contaminated particle radius, the more significant the impact on the breakdown voltage of the XLPE slices.