Through optimization techniques it is possible to affect the fielddistribution of a given high voltage arrangement by modifying the shapeof electrodes and insulators. When the modification of the shape ofinsulators is used to control the values of the total field strengthintensity on their surfaces, the reduction in the field values that canbe achieved is nor the same for every high voltage arrangement. In thispaper, the theoretical and practical limits of such techniques areinvestigated. An axially symmetrical configuration that has beenrepeatedly used for optimization tasks has been extended adding agrounded electrode to obtain a 3D-Field. The surface of an insulator hasbeen modified by taking as objective the reduction of the maximum totalfield strength intensity on its surface. The position of the groundedelectrode and the way in which the insulator surface is modified arevaried to study the influence of different parameters in the resultingfield distribution. The possibility of fixing or freeing the end-pointsof the insulator is also studied
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