Development of mathematical equation for determining breakdown voltage of electrodes gap

Knowledge of spark breakdown for various electrodes gap and geometries is essential when designing gas-insulated high voltage apparatus. Many empirical equations are developed for determining the breakdown voltage through the experimental works, but there are very few mathematical equations to explain the air gap breakdown voltage especially when considering the environmental and physical factors. In this paper, a systematic approached is used to develop a mathematical equation of breakdown voltage for different electrode gaps by using dimensional analysis (DA) technique. DA provides a strategy on restructuring the original dimensional variables of a system into a set of dimensionless products based on the dimensional homogeneity in any relationship between the variables. To verify the model, an experimental work was conducted in order to validate and finalized the developed equation.