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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.

High voltage direct current (HVDC) cable is an important part in the electric power transmission and distribution systems. However, very little research has been carried out on partial discharge under direct current (DC) conditions. Niemeyer’s model has been widely used under alternating current (AC) conditions. This paper aims to intend to modify the Niemeyer’s model considering both electric field and charge dynamics under DC conditions, and therefore proposes a numerical model describing partial discharge characteristics in HVDC cable.

This paper intends to understand partial discharge characteristics under DC conditions through numerical modelling. Niemeyer’s model that has been widely used under AC conditions has been modified, taking both electric field and charge dynamics under DC conditions into consideration. The effects of loading level or current through the conductor, cavity location and material properties on partial discharges have also been studied.

Electrical conductivity is important in determining the characteristics of partial discharge under DC conditions and discharges tend to happen in short when the cavity field exceeds the inception level under the parameter values studied in the paper.

Building the numerical model is the purpose of the paper, and there is lack in experiment and the comparison between the simulation results and experiment.

The proposed model provides the numerical model describing partial discharge in HVDC cable and helps understand the partial discharge mechanism under DC voltage.

To the best of the author’s knowledge, this paper is a very early research on the numerical modelling work on partial discharge under DC voltage.