Transients associated with partial discharges in ellipsoidal and spheroidal voids are derived in terms of the induced charges on the electrode. The relationship between the induced charge and the properties which are usually measured are discussed. Formulas are obtained from which conclusions can be drawn about the effects of the gas within the void as well as the size, shape, and location of voids. The method is illustrated by applying it to a spheroidal void in a simple disk-type gas-insulated-substation (GIS) spacer. It is found that the nonattaching gas generates an induced charge that is approximately an order of magnitude larger than that generated by the attaching gas. Inception voltages, however, are higher in the latter case by a factor of about 1.5 to 3. The induced charge is therefore proportional to the inverse of the distance from the axis of the electrode system to the center of the void.
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