Stress control for sphere-sphere and sphere-plane electrode configurations

The highest potential gradient between a sphere and plane has been calculated by the method of images for various gap-length/sphere-diameter ratios. It is shown that, if the distance between the plane and the most distant point on the sphere is fixed at S, while the sphere diameter is allowed to vary, the highest stress on the sphere surface has the minimum attainable value of 5 16/S times the voltage, and the gap length is then 1 4 times the sphere radius. Measurements made at voltages up to 200kV for a fixed value of S confirm that, to an accuracy of within 1 or 2%, the minimum breakdown voltage occurs for the sphere diameter that makes the stress a minimum. The relevance of this result to the design of a stress shield surmounting a high-voltage terminal is discussed. The potential gradient has also been calculated between three spheres of variable diameter having their centres in line at a fixed distance d apart. It has been deduced that the highest gradient on the spheres is a minimum when the diameters are 2d/3, d/3 and d/3, corresponding to imposed voltages of V, 0, 0, or about 5d/9, 4d/9 and 4d/9 when the voltages are V, ¿ V/2 and ¿ V/2. This applies when the two lower-voltage electrodes are of equal diameter, but results are also given for various combinations of electrode diameter. The values quoted are discussed in terms of choosing suitable diameters of spherical stress shield for use on the terminals of 3-phase transformers during induced overpotential tests.