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50). By proper numbering of the nodes, the matrix [ T I takes the form of a narrow diagonal bandof symmetrical structure. The order of [TIcan reach several thousands to cover an entire two-dimensional field. However, its bandwidth is about 5-15. Fortunately, techniques have been developed for efficiently solving such sparse matrix equations, which can signi~cantly decrease the computation time (Jennings, 1977)). Figure 2. l1 shows a comparisonof the finite-element(FE) andchargesimulation (CS) techniques for calculating the electric field at the contacts within a gas-insulated switchgear.
5). Errors in this method result, among other things, from the nonhomogeneity of the paper resistivity, its dependence on the ambient humidity, and the contact resistance to the electrodes. In this analog, the continuous field is replaced by a discrete set of points as depicted by a mesh of resistors (Fig. 6). Replacement of the continuous field by discrete resistors does, of course, introduce an errorarising from the finite mesh size. This error may be reduced by reducing the mesh size. 4 Electrolytic tank model of athree-corecablerepresentedat instant when one core is at zero voltage, the same as the sheath.
25) where ria is the distance from q: to the point a and Uia is a unit vector along the direction from qi to a. A s a practical application, thesuccessive imaging technique has been used to calculate equipotential contours foran overhead transmission line with two circuits and two ground wires (Fig. 8). 2 Successive Imaging between Spheres Given two spheres located near, and isolated from, each other, with potentials V I and Vz, the sameimagingprocess asthat described above for parallel cylinders can easily be adopted here with n = 2, but only if the spheres are far from ground.