Boundary Element Methods for Weakly Three Dimensional Quasi-Electrostatic Problems

Abstract

Using perturbation theory, a Boundary Element Method is developed for solving a class of three dimensional electrostatics problems. This class includes problems for which an axially symmetric object is weakly coupled to other objects without symmetry so that the total geometry is three dimensional. A problem which falls into this class is that of a surge arrester located near one or more other arresters. The time required for set up and solution using this method is not significantly greater than that required for solving the axially symmetric problem by itself. A simple empirical formula for error is developed by comparing exact solutions with solutions developed using the method described here.

Calculation of Power Line Fields Between Circular Conductors

“…The conditions under which calculations are performed are mostly high voltage direct current, 2,5,6,8,9,12,[16][17][18]20,22,24,[26][27][28][29][30] although the corona around conductors carrying high voltage alternating current is also of interest. 12,13,15,19,21,26,30 Additionally the surface condition of the conductors may be taken as clean, or coated either intentionally 7 or due to contamination.…”

“…Methods of calculation vary widely, with almost all possible having been tried at one time or another. These include methods of charge simulation, [4][5][6][7]11,13,16,23,28 finite element, 1,4,5,8,9,18,20,27,28 integral equation, 25,28 neural networks, 31 iteration, 2,5,8,28 flux tracing, 2,16,17,24 analytic expansions, 10,23 boundary elements, 22 and finally direct measurement. 15,19,21,29,31 In contrast, verification of calculations involves a more limited repertoire of methods; namely comparison to measurements, 1,2,[6][7][8][9]11,17,21,24,[27][28]…”