## 4 Parameter Derivation
### A Simple Grounding Grid  
Figure 12 shows a relatively simple grounding system that consists of several horizontal and vertical electrodes. The evaluation of this grounding system as a second case study is due to the revision of soil capacitive behavior. The Earth capacitive behavior in the theory of the transmission line is fully justified [17].  
Currently, the frequency response diagrams of the grounding grid represented in Figures 13 and 14, show that initially, at low frequencies, the system is considered to be capacitive, and the ground impedance is high due to this capacitive property. The phase angle diagram of ground frequency response is also distributed between \(-90^{\circ}\) to \(0^{\circ}\). As the frequency increases, the grounding system decreases the capacitive property, and enhances the inductive characteristics. This reduces the impedance magnitude, which pushes the phase angle to zero. Then, the higher the frequency, the more indicative of its inductive property, thus, the impedance magnitude of the grounding system will increase. As expected, the frequency response phase angle will reach around 90 degrees.  
Figure 11: Grounding system effective length.  
Figure 12: A Simple Grounding Grid.  
As explained in [18], the Grcev model uses the electromagnetic formulation to derive the semi-precise equivalent circuit of horizontal and vertical model. Since this model is approximately matched with the real data up to one MHz, we use a comparison of proposed approach to Grcev model it this range of frequency. The formulations founded in [18], despite the accurate solution, are hired, to derive the equivalent circuit of each horizontal and vertical electrodes, individually, while the proposed approach presented here uses only one equivalent circuit for all grounding grid. Therefore, our strategy can be implemented much more easily than the Grcev model.  
The ground potential rise (GPR), or Earth potential rise, is a phenomenon that occurs when large amounts of electricity enter the earth. This is typically caused when substations or high-voltage towers fault, or when lightning strikes occur. When currents of large magnitude enter the earth from a grounding system, not only will the grounding system rise in electrical potential, but so will the surrounding soil as well. The voltages produced by a GPR or Earth potential rise event can be hazardous to both personnel and equipment. As described earlier, the soil has resistance known as soil resistivity, which will allow an electrical potential gradient or voltage drop to occur along the path of the fault current in the soil.  
The resulting potential differences will cause currents to flow into any and all nearby grounded conductive bodies, including concrete, pipes, copper wires and people [25; 26; 27; 28; 29]. The GPR calculated in different soil resistivity is visible in Figure 15. As can be seen, the CIGRE function as an excitation source with a 400 ohm lightning channel is multiplied to the proposed impedance diagram, and GPR is calculated compared to the ideal node within zero potential relatives. The higher the soil resistance, the higher the GPR production will be.