Partial Discharges in Ellipsoidal and Spheroidal Voids

Transients associated with partial discharges in voids can be described in terms of the charges induced on the terminal electrodes of the system. The relationship between the induced charge and the properties which are usually measured is discussed. The method is illustrated by applying it to a spheroidal void located in a simple disk-type GIS spacer. I N T R O D U C T I O N HE transients which are manifest a t the electrodes T of a system during partial-discharge activity are related to the charges which, in view of Faraday’s ice-pail experiment, are induced on the electrodes. The sources of these induced charges are the charges which, as a result of this partial-discharge activity, are distributed within voids located throughout the system. The induced charge can be expressed as the difference between the charge on the electrode when discharges have occurred, and the charge which would have been on the electrode had the system been discharge free [l]. The direct implementation of this approach could be rather cumbersome a s it requires the solution of Poisson’s equation. A more straightforward approach is possible through an application of the principle of superposition [2,3]. This can be done in two ways depending on whether the analysis is based on the P-field [2] or on the D-field [3] in the dielectric. In practice, the application of the latter is more convenient, and this approach will therefore be employed in the present paper. A discharge in a void results in a deployment of charges on the surface S of the void. The surface-charge density a will attain such values that the field within the void will reduce until the discharge is quenched. In view of the principle of superposition, it is evident that the induced charge related to the charge distribution on S can be expressed [3], in the form in which X is a dimensionless scalar function which depends on the position of dS only. The function X is given by Laplace’s equation where E is the permittivity, [4]. The boundary conditions are A = 1 a t the electrode on which q is distributed, and X = 0 at all other electrodes. In addition, the following condition must be fulfilled a t all dielectric interfaces ax a A E + ( ) + = &-( an an)(3) where A is differentiated in the direction normal to the interface and the signs + and refer to the two sides 0018-0367/80/0400-335$1.00 @ 1080 IEEE Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on October 23, 2009 at 02:59 from IEEE Xplore. Restrictions apply. 338 Crichton et al.: Partial discharges in ellipsoidal and spheroidal voids of the interface. Since Equation (2) is Laplace’s equation, any standard method for the calculation of spacecharge-free electrostatic fields can be used to evaluate A. This is possible since the potential V at a point can be expressed as V = XU, where U is the voltage applied in the field calculation. Viewed from the electrode on which the induced charge q is distributed, the charges deposited on S can be considered, to a first approximation, as an electric dipole configuration since the net charge within the void remains zero. The dipole moment p of the charges deposited on S is given by