### Abstract:

Abstract In order to achieve lightning protection and electromagnetic compatibility (EMC) requirements, a proper grounding system is needed. Furthermore, the Earth Surface Potential (ESP) due to discharging current into grounding system in case of abnormal conditions has to be known. The Main objectives of the grounding system are, I) To guarantee the integrity of the equipments and continuity of the service under the fault conditions (providing means to carry and dissipate electrical currents into ground). II) To safeguard those people that working or walking in the surroundings of the grounded installations are not exposed to dangerous electrical shocks. To attain these targets, the equivalent electrical grounding resistance (Rg) of the system must be low enough to assure that fault currents dissipate mainly through the grounding grid into the earth, while maximum potential difference between close points into the earth’s surface must be kept under certain tolerances (step, touch, and mesh voltages). A lot of efforts had been taken to answer the very important question, which is, how the Earth Surface Potential due to discharging current into grounding system can be calculated. Many researches are published to present information about step and touch voltages, some of these publications depend on the experimental works on a scale model and the other depend on some empirical function that depend also on the results from experimental. Scale model in an electrolytic tank to simulate the lightning events on earth is presented to measure the Earth Surface Potential (ESP) on the surface of the water and also to study the transient performance of the grounding grid when it subjects to lightning like (Impulse current), in order to know something about the behaviour of the grid structure, i.e. is there a transient behaviour that needs complex models or is a static model sufficient and also give evidence to computer model. Impulse current tests were performed on 16(4 x 4) meshes. On the other hand, an old, but still easy to implement technique depend on Charge Simulation Method (CSM) is proposed to calculate the fields with the equivalent charges, the attractiveness of the CSM, when compared with the Finite Element and Finite Difference Method emanates from its simplicity in representing the equipotential surfaces of the electrodes, its application to unbounded arrangements whose boundaries extend to infinity, its direct determination to the electric field and its calculation speed. The results of the method are compared to experimental measurement results, empirical formulas in an IEEE standard and also to the other technique like (Boundary Element Method) that is often used to calculate Earth Surface Potential. In the field of grounding system design, the optimization means to find a grounding system which is able to safeguard those people that working or walking in the surroundings of the grounded installations and on the other hand has minimal cost. A new technique combining Evolutionary Algorithm with CSM field computation is proposed for optimization the design of grounding grids. The basic design quantities of the grounding grids are the ground resistance (Rg), touch voltage (Vt), step voltage (Vs) and the cost of the grounding system design. These mentioned quantities depend on the grid parameters, which are its side lengths, radius of grid conductors and length of vertical rods.