## 3 Results and Discussion
### Dielectric Properties of the EL Coating  
The dielectric stability of ZnS:Cu-doped epoxy composites constitutes a critical parameter governing their viability as functional coatings for high-voltage insulators [33; 43]. To comprehensively evaluate this aspect, broadband dielectric spectroscopy was employed to characterize temperature- and frequency-dependent permittivity (\(\epsilon^{\tau}\)) and dielectric loss (tan \(\delta\)) across operational ranges (\(-\)100-160 \({}^{\circ}\)C; 10\({}^{-1}\)\(\sim\)10\({}^{6}\) Hz), with results detailed in Figure 4. The dielectric constant (\(\epsilon_{\tau}\)) profiles reveal three distinct thermal regimes influenced by dominant polarization processes, as shown in Figure 4a,b. At sub-ambient temperatures (\(-\)100-20 \({}^{\circ}\)C), \(\epsilon^{\tau}\) maintains exceptional stability within 4.5-5.5 across all frequencies (Figure 4a), while tan \(\delta\) remains below 0.02 (Figure 4c). This thermodynamically constrained behavior arises from restricted molecular mobility below the material's glass transition temperature (T\({}_{\rm g}\)), where dipolar orientation becomes kinetically inhibited [33; 43]. Within the service temperature window (20-60 \({}^{\circ}\)C), \(\epsilon_{\tau}\) at power frequencies (50-60 Hz) stabilizes at approximately 5-10, closely aligning with values reported for undoped epoxy systems, thus confirming that ZnS:Cu doping preserves the baseline capacitive voltage-division  
Figure 3: Voltage distributions of an insulator string containing 7 insulators. (**a**) Voltage and (**b**) electrical potential distributions of an insulator string with 7 insulators of effective insulation performance. (**c**) Voltage and (**d**) electrical potential distributions of an insulator string containing 2 zero-value insulators. behavior without significantly distorting the dielectric response. At elevated temperatures (>60 \({}^{\circ}\)C), however, a sharp rise in \(\varepsilon_{\mathrm{r}}\) is observed, particularly below 10 Hz, where values reach over 10\({}^{3}\). This anomalous behavior is attributed to the enhanced segmental chain mobility at the temperature over T\({}_{\mathrm{g}}\). In parallel, tan \(\delta\) spectra delineate two distinct thermally activated relaxation processes, as shown in Figure 4c,d. The first, a \(\beta\)-relaxation process occurring in the \(-\)100-20 \({}^{\circ}\)C range, exhibits peak frequencies in the 102-103 Hz [33; 43]. This relaxation is attributed to interfacial polarization at the filler-matrix boundaries, facilitated by the higher electron affinity of ZnS:Cu relative to the epoxy host. The second, a high-temperature \(\alpha\)-relaxation process (120-160 \({}^{\circ}\)C), occurs at lower frequencies (10\({}^{0}\)-10\({}^{2}\) Hz). This process is associated with epoxy chain reptation dynamics and coupled Zn\({}^{2+}\) ionic conduction effects near the electrodes. The temperature-dependent dielectric loss behavior adheres to the Havriliak-Negami empirical relation [33; 43]. Furthermore, the electrical conductivity measurements corroborate these dielectric transitions. Experimental data in Figure 5a,b shows that the coating's conductivity remains stable and favorable below 40 \({}^{\circ}\)C, ensuring optimal insulation. However, as the temperature exceeds 40 \({}^{\circ}\)C, which is above T\({}_{\mathrm{g}}\) of the coating material, there is a noticeable increase in the coating's conductivity. This rise stems from enhanced molecular mobility and the activation of charge carriers, which cases the material transitions to a more flexible state. Thus, the coating may not be applied to power equipment under high temperatures at this stage. Figure 4: Frequency-dependent dielectric spectra of ZnS:Cu-doped epoxy composite coating.