Generalization of the quadratic charge-voltage relation of impulse corona in air

On the one hand, a quadratic relationship between the charge Q
_i
of the first corona and the associated inception voltage U
_i
has been recently put in evidence for a 1m point-plane air gap submitted to impulse voltages. On the other hand, different models have been proposed to evaluate that relation for coaxial geometries and conductor-plane also submitted to impulse voltages. The aim of this paper is to put in evidence the quadratic charge-voltage relations for all the configurations and to discuss how the assumptions made for one configuration can be exported to the other electrodes geometries.