The extremal charges method in grounding grid design

The behavior of the electric field in earth generated by a fault current derivation to a grounding grid can adequately be modeled by a Colombian potential that is constant in the grid and its reflected image with respect to the earth´s surface. We aim here at approximating, in an efficient way, the charge distribution that produces this potential by using potential theory methods. First, we describe the extremal charges method that allows one to obtain an approximation to the charge distribution as the solution of an optimization problem, specifically a linear programming problem. Second, we show the accuracy of the method obtaining the potential and the fundamental parameters of a grid. Then, we describe a grid design optimization methodology. The optimal grid performance is the one that achieves the better agreement between the grid resistance and the touch and step voltages. Both parts are illustrated with graphical results showing the accuracy of this new method of grid analysis and design.