## 5 Insulator Surface Charge and Electric Field Distribution Under DC Voltage
When the surface charge density decreases with time, it indicates that the parameter \(\partial\rho/\partial t\) is less than 0, a condition where surface conduction dominates. As observed in Figure 11, during the first 40 h, the charge density on the convex and concave surfaces of the insulator fluctuates significantly, indicating an unstable initial charge distribution. Subsequently, the rate of change in surface charge density gradually decreases and stabilizes after approximately 300 h, indicating that the charge accumulation has reached an equilibrium state. The time-varying characteristics of the surface charge density at different locations on the insulator surface (points A, B, and C) are illustrated in Figure 12. We observed that sur  
Figure 11: Transient characteristics of surface charge density on basin-type insulators: (**a**) convex surface; (**b**) concave surface. face charge density at various locations increases gradually over time, with rapid changes during the initial stage. Subsequently, with time, all curves gradually approach stability, indicating that the charge density stabilizes after prolonged accumulation. Temperature significantly influences the charge accumulation process. Locations with higher temperatures (e.g., points A and B) exhibit a faster charge accumulation rate, whereas locations with lower temperatures (e.g., point C) demonstrate a relatively gradual accumulation process. The surface charge density at these locations stabilizes after approximately 300 h.  
Figure 13 illustrates the transient distribution characteristics of the electric field along the insulator surface in the 3 o'clock direction. During the initial 40 h, the electric field exhibits significant variations along the surface of the insulator, particularly on the convex surface. This indicates that the electric field is significantly influenced by the accumulation of surface charges and the distribution of temperature during the initial stage. Subsequently, the variation of the electric field on the convex and concave surfaces gradually decreases. After 300 h, the electric field distribution stabilizes, indicating that the surface charge accumulation approaches equilibrium. Figure 14 illustrates the characteristics of surface charge distribution along various radial directions after 300 h of DC voltage application. The charge distribution exhibits notable variations along different radial directions on both the convex and concave surfaces of the insulator, particularly in the middle region of the insulator surface. This phenomenon is primarily attributed to temperature variations along different radial directions of the insulator surface, which result in differences in the conductivity properties of the insulator. Figure 12: Time-varying characteristics of surface charge density at different locations. Figure 13: Transient characteristics of surface electric field on basin-type insulators: (**a**) convex surface; (**b**) concave surface. Figure 15 illustrates the electric field distribution along different radial directions of the insulator surface. When charge accumulation reaches equilibrium, the electric field distribution varies in different radial directions, with the most pronounced differences observed in the 12 o'clock direction. This phenomenon is primarily attributed to the higher temperature observed in the 12 o'clock direction. Comparative analysis with the surface charge distribution characteristics presented in Figure 11 reveals a direct correlation: the magnitude of variation in charge distribution across different radial directions corresponds proportionally to the magnitude of variation in the electric field. This relationship confirms the direct influence of surface charge on the electric field distribution along the insulator surface [34].