A generalized analytical-numerical method for the calculation of 3-dimensional HV fields

A generalized analytical-numerical method for computing electric fields in 3-dimensional geometries is introduced. It is based on the construction of an analytic function for the electric potential by the limited development of harmonic functions, using coordinate systems appropriate to the configuration studied. The harmonic functions correspond to particular solutions of the Laplace equation obtained by the separation-of-variables technique. Each solution is weighted by an originally unknown numerical factor; the satisfaction of Dirichlet boundary conditions for the potential leads to a system of linear equations for these numerical factors. Their solution first determines the value of the numerical factors; then the electric potential in any point in the region outside the conductors can be calculated by superposition. Applications of the method to two practical HV (high voltage) configurations are given