Calculation of electrical field of spherical and cylindrical gas voids in dielectrics by taking surface conductivity into consideration

To determine the electrical field E₁(t) in spherical and cylindrical gas voids existing in an insulator by considering surface conductivity of gas voids having an electrical permittivity of ε₁ and conductivity of γ₁ for DC and AC situations.

Analytical expressions satisfying Laplace equation for inside and outside of the cylindrical and spherical gas voids in an insulator located in an external electrical field having a definite time dependent character, have been derived by considering the surface conductivity of the gas void. The coefficients included by these analytical expressions have been determined by utilizing the continuity equation of the current on the surface of the voids.

It has been demonstrated that the electrical field remains uniform in spherical and cylindrical gas voids when the surface conductivity of gas void has been considered. It has been determined that the contact charging process of different shaped particles has an exponential characteristic, and some expressions have been derived to determine the time constants of this process for practical purposes.

The results have been applied to the problems about contact charging of semi‐spherical and semi‐cylindrical insulated particles located at a charged surface and problems about the calculation of onset discharging voltage of ionization process in dielectric including gas voids.

For spherical and cylindrical gas voids, the onset discharging voltage corresponding to the ionization process occurring in gas voids has increased by increasing the surface conductivity of the void. For the limit value of the surface conductivity, the voids in the insulator behaves like metal particles distributed into the insulator, for this reason, at the outside of the void, especially in the regions where the voids are close to the electrodes and each other, the electrical field will be non‐uniform and will increase. This situation will cause the ignition of the partial discharge and destroy to the insulator.