By M. Abdel-Salam, et al.,
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33) where [P] is an n x n matrix of the coefficients for n-unknown node potentials, [(P]is an n x l column matrix of the unknown potentials, and [B] is an n x 1column matrix of the sum of known potentials of the bounding electrodes. , 1985). For complex cases,iterative schemes are most eEficient in combination with successive overrelaxation methods. There is no reason why this technique cannot be used for computing the field in multidielectric arrangements. 12, assume the nodes 2, 0, and 4 to be at the interface betweentwodielectricsof permittivities (containing node 1) and c2 (containing node 3).
52): c X Plane re~~angular element. lxyz ar aIxy and Xxy are respectively 332 ax ay The potential and field equations for other elements such as plane triangular, cylindrical, spherical, conical, and torodial elements are reported in the literature ( ~ u t ~ e i s c1989). 2 BoundaryConditions The boundaryconditions are theDirichlet condition at the electrode surface and the Neumann condition at the insulator surface. 54b) where E z d and Eza are the zcomponents of the electric field calculated at any point on the insulator surface when seen from the insulator and surrounding-gas sides, respectively.
The sphere maybe represented by a point charge as an image equal to -Qr/D, located a distance 6 = r2/D away from its center. The imaging technique cannot be extendedto multidielectric media or to three-dimensional fields. 1 Successive Imaging among Cylinders A system of parallel cylindrical conductors, as in gas-insulated switchgear (GIs), is used as an example to explain how the image charges are determined. ,q4. Of course, if they are placed near the ground or its equivalent, each conductor will also have its image (see Fig.
High Voltage Engineering - Theory and Practice by M. Abdel-Salam, et al.,