A general empirical formula of current-voltage characteristics for point-to-plane geometry corona discharges

With a point-to-plane geometry, the experimental investigation of the current-voltage characteristics in corona discharges demonstrated that existing empirical formulae met with some physical difficulties in explaining the results. By mathematically processing the experimental data and applying the updated knowledge of corona inception, a new general formula in characterizing the relationship of corona current-voltage was derived and expressed as I = K(V - V₀)ⁿ. It was demonstrated that the exponent n falls into a limited scope of 1.5-2.0, and there always exists an optimal exponent n in the scope, which can be determined by maximizing the R-square of regression. Of all the potentially influential factors, it was disclosed that the point radius has the strongest influence on the optimal exponent n, and the effects of ambient conditions and corona polarities are not noticeable. The optimal exponent n holds a fixed value of 2.0 for microscopic points and of 1.5 for large points with a radius in millimetres, but changes decreasingly with the radius for the points of microns. For given experimental conditions, the optimal exponent n almost does not change with the inter-electrode distance. Furthermore, it was demonstrated that the formula is applicable not only for both negative and positive coronas in point-to-plane geometries but also for both polarities in point-to-ring geometries. With the optimal exponent n, the formula can well explain the inconsistencies met by other existing formulae and best represent the characteristics of corona current-voltage with an accuracy of 1 νm.