Optimum pattern of grounding grid by using closed-form solution based on optimized results

Finding the optimum conductor’s pattern for unequally spaced grounding grids can be achieved by using empirical formulas or optimization techniques. Empirical formulas give an approximate solution depending on human experience and never cover the entire search space. On the other hand, the optimization techniques generally require a significant effort and time. To overcome the previous issues, this paper presents a closed-form solution based on optimized results. The main motivation behind this formula is the comprehensive study carried out by the authors to find optimum location of grounding grid conductors over different areas. In that work, particle swarm optimization technique (PSO) has been adapted with combined integration matrix method (CIMM) to facilitate the study. In this paper, the results obtained previously were summarized in the proposed formula. The proposed formula gives the optimum design of unequally grounding grids by specifying the conductor’s locations as percentage of the side length for square and rectangular shapes. As long as the side length and the number of conductors are given, the location of each conductor as a percentage of the side length can be obtained. The effect of adding driven rods and the stratified soil conditions on the results of the optimized design were investigated. The validity of the proposed closed-form solution was verified experimentally.