Abstract
The design methods of earthing from standards recommend the choice of electrode lengths and propose that the distances between electrodes to be 1–3 times larger than their length. The number of electrodes is determined from the condition of achieving the design earth resistance, while the design ends with the choice of one of the variants. This paper presents the methodology for calculating the earthing system with cylindrical, vertical electrodes arranged in a line. The main variables are the length and the number of earth electrodes, as well as the distance between adjacent ones. Firstly, a set of technologically advantageous values for the earth electrode length is established (e.g., 10 values). For each value of the electrode length and different numbers of electrodes (e.g., 11 values), the distance between adjacent electrodes is determined (e.g., for 110 cases), which leads to the design value resistance. Finally, optimal solutions are identified based on the five optimal applied criteria. The proposed optimal criteria for earthing design are the footprint area, the total earthing volume, the total dispersion surface, the total metal mass, and the investment costs. Comparing the optimal solutions with other technically possible solutions clearly highlights substantial savings concerning space, material, and cost.
Highlights
From the outset, it is emphasized that all computational relations included in the mathematical model of the system of earthing (EG) used in the present research are based on current international standards [1,2,3,4,5,6,7,8]
Examining the respective nomogram offers the possibilities to assess the character of the dependences of the earth electrode resistance on the involved variables, and to evaluate the magnitude of the variations determined by the independent variables
For each value of electrode length and each of the number of the electrodes ne ≥ 2, the minimum value of the distance between adjacent electrodes is numerically identified in order to obtain the total resistance to earth, RP, to a lower value, but as close as possible to RPn = 4 Ω
Summary
It is emphasized that all computational relations included in the mathematical model of the system of earthing (EG) used in the present research are based on current international standards [1,2,3,4,5,6,7,8]. Until the optimum criteria appeared, the EG designers first selected an electrode length suitable for the respective soil [1,3,5,6,7,8], selected several values for the distance between adjacent electrodes, and determined the number of electrodes to achieve the designed earth resistance. Previous publications concerning earthing optimum design refer to structural modifications of the earth grids or systems “in order to equalize the leakage current distribution and the potential of ground surface” [18] or to minimize the shielding effect [19] These contributions do not apply optimal criteria to the calculation of the earthing system itself. Realized, RPn—the design value resistance and ne—the number of electrodes
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