Overhead high voltage transmission lines are widely used around the world to deliver power to customers because of their low losses and high transmission capability. Well-coordinated insulation systems are capable of withstanding lightning and switching surge voltages. However, flashover is a serious issue to insulation systems, especially if the insulator is covered by a pollution layer. Many experiments in the laboratory have been conducted to investigate this issue. Since most experiments are time-consuming and costly, good mathematical models could contribute to predicting the insulator flashover performance as well as guide the experiments. This dissertation proposes a new statistical model to calculate the flashover probability of insulators under different supply voltages and contamination levels. An insulator model with water particles in the air is simulated to analyze the effects of rain and mist on flashover performance in reality. Additionally, insulator radius and number of sheds affect insulator surface resistivity and leakage distance. These two factors are studied to improve the efficiency of insulator design. This dissertation also discusses the impact of insulator surface hydrophobicity on flashover voltage.

Because arc propagation is a stochastic process, an arc could travel on different paths based on the electric field distribution. Some arc paths jump between insulator sheds instead of travelling along the insulator surfaces. The arc jumping could shorten the leakage distance and intensify the electric field. Therefore, the probabilities of arc jumping at different locations of sheds are also calculated in this dissertation.

The new simulation model is based on numerical electric field calculation and random walk theory. The electric field is calculated by the variable-grid finite difference method. The random walk theory from the Monte Carlo Method is utilized to describe the random propagation process of arc growth. This model will permit insulator engineers to design the reasonable geometry of insulators, to reduce the flashover phenomena under a wide range of operating conditions.

High Voltage Direct Current (HVDC) technology is being considered for several long distance point-to-point overhead transmission lines, because of their lower losses and higher transmission capability, when compared to AC systems. Insulators are used to support and isolate the conductors mechanically and electrically. Composite insulators are gaining popularity for both AC and DC lines, for the reasons of light weight and good performance under contaminated conditions. This research illustrates the electric potential and field computation on HVDC composite insulators by using the charge simulation method. The electric field is calculated under both dry and wet conditions. Under dry conditions, the field distributions along the insulators whose voltage levels range from 500 kV to 1200 kV are calculated and compared. The results indicate that the HVDC insulator produces higher electric field, when compared to AC insulator. Under wet conditions, a 500 kV insulator is modeled with discrete water droplets on the surface. In this case, the field distribution is affected by surface resistivity and separations between droplets. The corona effects on insulators are analyzed for both dry and wet conditions. Corona discharge is created, when electric field strength exceeds the threshold value. Corona and grading rings are placed near the end-fittings of the insulators to reduce occurrence of corona. The dimensions of these rings, specifically their radius, tube thickness and projection from end fittings are optimized. This will help the utilities design proper corona and grading rings to reduce the corona phenomena.