## 3 Results and Discussion
### Voltage Distribution Simulation of Insulators and Insulator Strings  
During the operation of high-voltage power systems, there is an obvious potential distribution on the surface of insulators. Obtaining a clear situation of the voltage distribution on the insulator is helpful for better understanding and formulating the insulator voltage characterization strategy based on EL coating. In this study, the finite element analysis (FEA) was employed to investigate the surface potential distribution characteristics under operational conditions by using the COMSOL Multiphysics platform (COMSOL 6.2). The structural model of the insulator used in the simulation is shown in Figure 2a. The relative dielectric constant and electrical conductivity of the insulator's shed, steel cap, steel foot, and cement-based bonded part were set according to the values detailed in Table 1, whose parameters reflect typical material properties derived from standardized testing data and literature benchmarks [41; 42]. The zero-value defects were modeled by modifying the material parameters of cement and ceramic with a relative permittivity of 8000 and a  
Figure 1: The triggering mechanism of EL in ZnS:Cu. conductivity of 0.1 S/m. The model adopts triangle meshing with adaptive refinement at material interfaces to resolve steep potential gradients while maintaining computational efficiency. Boundary conditions were defined to replicate operational scenarios: high-voltage terminal with 10 kV AC excitation (50 Hz), ground terminal with zero potential constraint, and atmospheric boundaries with floating potential with air dielectric properties. For an insulator with effective insulation performance, the simulated potential distribution reveals a characteristic nonlinear voltage gradient along the shed surface, as shown in Figure 2b. The steel cap-to-shed potential difference reaches 2.4 kV under 10 kV voltage. However, when the insulator is damaged and reaches a zero value state, as shown in Figure 2c, the potential difference between the steel cap and the shed decreases significantly (<100 V). In this case, the steel cap and the shed can basically be regarded as being at the same electrical potential. To validate scalability to practical transmission line configurations, a 110 kV voltage-level insulator string comprising seven units was simulated. As shown in Figure 3a,b, the voltage division exhibits characteristic nonlinear distribution along the string for an insulator string with effective insulation performance. There is a potential difference of 17 kV between the steel cap of the terminal insulator and the shed, while there is a potential difference of 15 kv between the central insulators. This pattern is caused by the edge effect, amplified by the mutual capacitance between adjacent insulators. Conversely, the introduction of zero-value insulators dramatically redistributes voltages, as shown in Figure 3c,d. The potential difference between the two ends of the zero-value insulator drops sharply to less than 100 V, while the adjacent insulator experiences a surge to 20 kV. This redistribution adheres to [PERSON]'s voltage law, as the zero-value insulator's near-zero impedance forces neighboring insulators to compensate through elevated electric stresses. These simulations confirm that anomalous voltage redistribution provides a robust indicator for identifying zero-value insulators in the insulator string. This variation in potential difference provides the basic principle of using EL coating to detect zero-value insulators in this work. When the insulator performs with effective insulation, there is a potential difference between the steel cap and the shed, and this potential difference can drive the EL coating to glow. And for insulators with zero-value defects,