## 3 Experimental Result
### DC Partial Discharge Characteristics of Different Samples  
The variation in the amplitude of PD signals for the two XLPE samples is shown in Figure 9. Figure 9 corresponds to the DC sample. In the early stage of the constant voltage phase, no partial discharge signals were detected until 700 s, when the first PD event occurred. For the initial 3500 s, the maximum discharge magnitude was 500 pC. Subsequently, both the size of the electrical tree and the PD amplitude began to increase rapidly, which can be divided into two distinct stages. The first stage, from 3500 to 4000 s, is characterized by a small dispersion in PD amplitude, showing a linear increasing trend. The second stage extends from 4000 s to breakdown, during which the maximum discharge magnitude increased rapidly, accompanied by some smaller discharge events, with greater dispersion in discharge magnitudes ranging from 1500 pC to 4500 pC. Figure 9 reflects the size of the electrical tree and the partial discharge signals at different times for the Cable sample. Similarly, no partial discharge signals were detected in the early constant voltage phase. PD signals began to appear at 200 s. In the first 2400 s, the maximum discharge magnitude gradually increased to 300 pC. From 2400 s to the breakdown, both the size of the electrical tree and the PD amplitude continued to increase, with a relatively small dispersion in the growth of PD amplitude. It can be observed that changes in PD amplitude are often highly positively correlated with the size of the electrical tree. Therefore, the smaller discharges observed in the second stage of Figure 9 may be attributed to the lateral growth of the electrical tree. Further analysis of the PD characteristics during the growth process of DC electrical trees in different XLPE samples was conducted by statistically analyzing the PD amplitude after each discharge interval, resulting in the q-\(\Delta\)t plots, as shown in Figure 10. By observing the maximum discharge amount corresponding to each discharge interval, both Figure 10,b indicate a trend where the maximum discharge amount first increases and then decreases as the discharge interval increases. When the discharge interval extends to tens or even hundreds of seconds, the corresponding discharge amount tends to be relatively small. Based on the experimental results, it is evident that these small discharges with long intervals typically occur when the electrical tree is relatively small. As the electrical tree grows, both the discharge amount and the average discharge interval decrease significantly. According to the typical DC discharge interval model [16], for the same defect, the longer the discharge interval, the larger the resulting discharge amount should be. Considering the characteristics of electrical trees, the following hypothesis is proposed: when the electrical tree is small, the insulation properties of the sample are relatively strong, leading to a longer electric field recovery time after each PD event, which results in a longer discharge interval and smaller discharge amount. As the electrical tree grows, the discharge amount increases, while the electric field recovery rate after each PD event accelerates, reducing the discharge interval. Therefore, when \(\Delta\)t is small, the discharge amount is positively correlated with \(\Delta\)t,  
Figure 9: PD of different XLPE during DC tree aging. as the charge accumulated from the previous discharge gradually dissipates and the electric field within the tree channel continues to increase. However, when \(\Delta\)t further increases without significant changes in the electric field within the channel, the discharge amount depends only on the size of the electrical tree. Consequently, as the discharge interval increases, the maximum discharge amount first rises and then falls.