## 3 Insulator Conductivity Measurement  
We designed and constructed a platform for measuring insulator bulk and surface conductivity parameters. We conducted the experiments using the three-electrode method, configuring the electrodes to conform to the IEC 60093 standard [33]. We performed current measurements using a Keithley Model 6485 Picoammeter (Keithley, Solon, OH, USA) with a 10 fA resolution, ensuring high precision. To verify repeatability, we conducted each conductivity measurement three times on five identical samples, achieving a relative error below 5%. The test samples were circular epoxy composite specimens with a thickness of 1 mm and a diameter of 120 mm, possessing material compositions identical to those of the insulator investigated in this study. Prior to testing, we cleaned all samples with anhydrous ethanol to remove surface contaminants, then dried the samples in a vacuum oven at 90 \({}^{\circ}\)C for 48 h to eliminate moisture. We positioned soft conductive rubber (the soft conductive rubber is a commercial product) between the electrodes and samples to ensure optimal electrical contact. The protective resistor of the experimental circuit is 1000 \(\Omega\). The rubber's resistance is 2-3 \(\Omega\). Compared to the sample's resistance of 10\({}^{15}\)\(\Omega\), the conductive rubber's impact is minimal, validating the measurement integrity. To measure stable DC conduction currents and mitigate polarization effects, we extended the measurement duration, particularly under dry conditions. We observed that currents stabilized after approximately 3000 s (50 min), with no further attenuation. We averaged the stable current values to reduce measurement noise, ensuring reliable conductivity calculations. After each experiment, we depolarized the samples by grounding both ends and measured discharge currents before subsequent tests. We confirmed depolarization completion when discharge currents approached 0 pA, allowing the next experiment to proceed. The volume resistivity is derived from the conductive current measured within the sample volume, while the surface resistivity is obtained from the conductive current measured along the insulator surface. As depicted in Figure 2, the electrode configuration diagram illustrates the setup, and for circular samples, both the volume resistivity and surface resistivity are calculated using Equations (20) and (22). \[\rho_{Rv}=\frac{U}{I_{V}}\cdot\frac{S}{e} \tag{20}\]  
\[S=\frac{(d+g)^{2}}{4} \tag{21}\]  
Here, \(\rho_{\mathrm{Rv}}\) is the bulk resistivity, \(U\) is the applied voltage, \(I_{\mathrm{v}}\) is the current through the insulator volume, \(e\) is the insulator thickness, and \(S\) is the effective area. \[\rho_{Rs}=\frac{U}{I_{s}}\cdot\frac{P}{g} \tag{22}\]  
\[P=\pi\cdot(d+g) \tag{23}\]  
Here, \(\rho_{\mathrm{Rs}}\) is the surface resistivity, \(I_{s}\) is the current through the insulator surface, and \(P\) is the effective perimeter. The bulk resistivity parameter measurement platform is depicted in Figure 3. Experiments were conducted under standard atmospheric pressure, with test electrodes positioned within a temperature-controlled oven. Four distinct temperature conditions, \(20\ ^{\circ}\mathrm{C}\), \(40\ ^{\circ}\mathrm{C}\), \(60\ ^{\circ}\mathrm{C}\), and \(80\ ^{\circ}\mathrm{C}\), were set to span the typical operating range of DC GIL insulators, corresponding to conductor heating from currents up to \(3150\) A. Three experimental voltage levels, \(-2\) kV, \(-4\) kV, and \(-6\) kV, were selected to assess resistivity variations, with each set of experiments performed on the same sample to ensure data consistency. The bulk resistivity under various temperature and electric field conditions was determined through final experiments, as illustrated in Figure 4. Under a constant electric field,  
Figure 3: Bulk resistivity measurement platform. Figure 2: Schematic diagram of the electrode device. the volume resistivity decreases as temperature rises.