Experimental Modelling of the Breakdown Voltage of Air Using Design of Experiments

Many experimental and numerical studies were devoted to the electric discharge of air, and some mathematical models were proposed for the critical breakdown voltage. As this latter depends on several parameters, it is difficult to find a formula, theoretical or experimental, which considers many factors. The aim of this paper is to model the critical breakdown voltage in a "Sphere-Sphere" electrodes system by using the methodology of experimental designs. Several factors were considered, such as geometrical factors (inter-electrodes interval, diameter of the electrodes) and climatic factors (temperature, humidity). Two factorial centred faces experimental designs (CCF) were carried out, a first one for the geometrical factors and a second one for the climatic factors. The obtained results made it possible to propose mathematical models and to study the interactions between the various factors.