## 4 Analysis and Discussion  
### Material Parameter Test of Different Samples  
To investigate the differences in DC electrical treeing resistance and partial discharge performance between the two materials, XRD and GPC tests were conducted, aiming to analyze their microstructure and molecular weight characteristics. X-ray diffraction (XRD) [17] is commonly used to analyze the internal structure of crystals and to explore the relationship between a material's microstructure and structural defects. By performing Gauss-Cauchy fitting on the diffraction peaks in the XRD spectrum, the crystallinity and microcrystal size of the sample can be determined. The instrument used in this study was a D8-ADVANCE X-ray diffractometer (Bruker Corporation, Billerica, MA, USA). The parameters were set as follows: tube voltage 40 kV, tube current 30 mA, scan speed 2\({}^{\circ}\)/min, and X-ray wavelength \(\lambda\) = 0.154 nm. The XRD results are shown in Figure 11, where the horizontal axis represents the diffraction angle. The vertical lines indicate the typical crystalline peaks of polyethylene (PE), revealing that the diffraction peaks of both types of cross-linked polyethylene (XLPE) correspond closely to those of PE. As observed in the figure, both XLPE samples exhibit a strong diffraction peak at a diffraction angle 20 = 21.5\({}^{\circ}\), corresponding to the (110) crystal plane of PE. A second diffraction peak appears at 20 = 23.8\({}^{\circ}\), corresponding to the (200) crystal plane of the crystal. The diffraction curve results indicate no significant differences in the aggregated structure of the two materials. Figure 10: PD characteristics in different XLPE samples. The XRD results were subjected to Gaussian peak-fitting analysis. The fitting results indicate that, in addition to the two crystalline peaks, a diffuse peak is observed near the diffraction angle of 20.4\({}^{\circ}\), corresponding to a non-crystalline diffraction peak, which represents the amorphous region. Based on the fitting results, the crystallinity and grain size of the different XLPE samples were further calculated, following the method detailed in the reference [18]. The calculation results are shown in Table 1, where \(D_{hkl}\) denotes the grain size perpendicular to the crystal plane direction (\(hkl\)), and \(X_{c}\) represents the crystallinity. The XRD test results reveal that, between the two XLPE materials, the DC-XLPE exhibits slightly lower crystallinity but somewhat larger grain size, although the differences are not significant. Gel permeation chromatography (GPC), also known as size exclusion chromatography, is a technique that separates solutes based on their size. Different modes of molecular movement result in the separation of molecules with varying molecular weights, thereby enabling the determination of relative molecular weight and its distribution [19]. In this study, the GPC tests were conducted using a high-temperature gel permeation chromatograph, specifically the EcoSEC HLC-8321 GPC/HT (Sowa Denko K.K., Tokyo, Japan), with o-dichlorobenzene as the solvent. The GPC results for the two XLPE samples are shown in Figure 12, where the horizontal axis represents the logarithm of the relative molecular weight. From the molecular weight distribution curves, it can be observed that both XLPE samples exhibit a primary peak corresponding to high molecular weight components. However, the DC sample also shows a minor peak corresponding to low molecular weight components. Additionally, the primary high molecular weight peak of the DC sample is shifted further to the right compared to that of the Cable-XLPE, indicating a larger relative molecular weight in the high molecular weight fraction in the DC sample. The GPC-related experimental results for the different types of XLPE are presented in Table 2. The statistical parameters include the number-average molecular weight \(M_{n}\), weight-average molecular weight \(M_{w}\), \(Z\)-average molecular weight \(M_{z}\), and the polydispersity index \(M_{w}/M_{n}\).