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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. Index Terms--Computer modeling, grid resistance, grounding, measurements, optimization of grounding grids, safety, step potential, touch potential.

Here, we consider a class of generalized linear chains; that is, the ladder-like chains as a perturbation of a 2 n path by adding consecutive weighted edges between opposite vertices. This class of chains in particular includes a big family of networks that goes from the cycle, unicycle chains up to ladder networks. In this article, we obtain the Green function, the effective resistance, and the Kirchhoff index of ladder-like chains in terms of the Green function, the effective resistance, and the Kirchhoff index of the path. © 2014 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the considered network has some symmetries, which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster's n-th formula. [ABSTRACT FROM AUTHOR]