Dimensioning of the Vertical Earth Grounding with Rectangular Contour through Minimizing the Investments Costs

The design of earth grounding (EGR) on optimal criteria has relaunched the seemingly stagnant problem of their dimensioning. The perspective opened by the formulation of technical or economic aim functions becomes engaging for designers, having now the opportunity to argue for the established solutions. If the application of the first three criteria has already been dealt with, such as the ground footprint, the EGR total volume and the total metal mass, the total investment criterion is addressed in the paper. The research also brings a methodological improvement to the case of EGR with vertical electrodes placed after a rectangular contour by fixing the number of electrodes to pare numbers greater than four and looking for correlations between the distance between the electrodes and the length of the electrodes, in order to achieve the chosen rated dispersion resistance. During the searches, identifying a simple, parabolic arc function for the real nonlinear dependence between the vertical electrode dispersion resistance and the electrode length has proven to be a real benefit because it has replaced the solving of transcendental equations with solving second-degree equations. The minimum total investment has different coordinates from the minima of the other optimal criteria, proving once again that they are distinct.