The Field of Rod - Plan Electrodes and Partial Discharge Inception Voltage in Air

The Coordinate transformation allows the
exact calculation of some electrode Configurations.
In this Paper the Prolate Spherical Coordination
transformation is used to Calculate the field of a
hyperboloiderod against Plan electrode. The exact
field is Caculated using two new Parameters:
1) Electrodes Spacing and
2) The radius of Curvature of the tip of the
rod electrode.
The Partial discharge inception voltage in air
is then calculated by numerical integration of the
effective
ionization coefficient over the gap using these
parameters. The PD inception voltage is calception
voltage is Calculated for constant radius of
Curvature Versus electrodes Spacing.
The calculation Shows that for large electrodes
distances the electrodes Spacing is not relevant but
the radius of the curvature of the tip of the rod
electrode is very important. It seems that the form
of the rod shaft is likewise not relevant. The result
can be used for large electrodes distances for evry
form of the rod shaft.