Numerical methodology to evaluate unipolar saturation current limit of DC corona discharge in complex geometries

Abstract

The unipolar saturation current limit ($${I}_{sat}$$ I sat ) gives an upper limit to the corona current that can be obtained from a unipolar corona discharge. Therefore, it implies a theoretical limit to the performance of unipolar corona discharge devices. However, it has not been widely used in practice because it is difficult to deal with complex discharge configurations in an analytical way. This study aims to establish and validate a numerical methodology to evaluate the maximum current, which numerically imitates the unipolar saturation current limit. It was shown that the maximum current has the same mathematical definition as the unipolar saturation current. For validation, the maximum current was compared with an analytical solution of the Poisson equation for the coaxial cylinders configuration. The differences between the maximum current and unipolar saturation current limit for the coaxial cylinders, pin-to-plane, and single wire-to-plane configurations were discussed in terms of the assumptions used in the semi-analytical derivation of the unipolar saturation current limit. The validated methodology was applied to a multiple wire-to-plane configuration, for which a semi-analytical expression of the unipolar saturation current limit has not yet been developed. The effects of geometric and operation parameters on the maximum currents of the multiple wire-to-plane configuration were analyzed. The results were regressed into a single formula.