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

Abstract

PurposeTo 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.Design/methodology/approachAnalytical 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.FindingsIt 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.Practical implicationsThe 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.Originality/valueFor 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.

Numerical modelling on partial discharge in HVDC XLPE cable

“…Time interval between two PD events is long, and the present discharge event is therefore with little influence on the gas temperature and pressure of the following event. Electrical conductivity of air is therefore assumed to be constant (He et al, 2016;Alisoy et al, 2005;Alisoy et al, 2004).…”

Combined kinetic charging of particles on the precipitating electrode in a corona field

“…In this expression, the time constant τ is determined by equation (7) in the case when the surface conductivity of the particle is equal to zero (γ s = 0); in the case of γ s = 0, τ is determined as [19,21,26]…”

“…(i) The contact between the particle and the electrode is ideal (no asperity) and the surface conductivity of the particle (γ s ) is zero. In the case when γ s = 0, the free charges precipitated on the particle cannot be distributed homogeneously on the surface and, because of this, the electrical field E 1 on the particle becomes nonhomogeneous [19,21]. An electric double layer forms at the contact region of the polarized particle precipitated from the corona field onto the electrode surface.…”

An advanced model of partial discharge in electrical insulation

“…For instance, if the insulation is delaminated, one can have a situation where only a minor part of cavity surface takes part in a spark, due to small discharge surface (spark channel width of the order of magnitude of a few microns), and insufficient surface conductivity of the surface, Figure 4a. In some cases, it is possible to obtain an analytic expression for the voltage and charge distribution, respectively quantities C b and C c , [2][3][4][5]. They researched the influence of variable applied frequency on the physics of discharge process, on voltage and charge distribution, as well as on the stochasticity of the process.…”