## 4 Parameter Derivation
### A Complicated Grounding Grid  
The grounding system under consideration in this section, as shown in Figure 16, includes several circular electrodes, a number of vertical rods, and numerous horizontal electrodes that are interconnected. Their apparent characteristics, in terms of length and positioning, have been adjusted  
Figure 14: Phase angle of a simple grounding grid; (a) \(\rho=100\)\(\Omega\cdot\)m, (b) \(\rho=300\)\(\Omega\cdot\)m, (c) \(\rho=1000\)\(\Omega\cdot\)m, (d) \(\rho=1800\)\(\Omega\cdot\)m.  
Figure 15: GPR of a simple grounding grid.  
so that the grounding system can be used as a wind turbine system or a high voltage electric tower grid. Thus, the effect of soil ionization dependence on frequency is also evaluated, and the proposed modeling effect is compared with the frequency-independent conditions.  
Figure 17 show the impedance magnitude and its phase angle in several soil resistivity with the effect of frequency-dependent soil ionization. As is observed, the proposed method is well suited to the data extracted from the CDEGS software, which suggests its high accuracy and effectiveness. Conductivity and permittivity are two important electrical properties of soil. Several factors, such as soil compaction, temperature, moisture, and grain size, affect soil conductivity and permittivity. Soil ionization occurs because of the electric field enhancement in soil when subjected to high impulse current discharge, which in turn causes the electric breakdown of air voids enclosed between soil particles. The air breakdown causes current to flow in the voids, and this is usually in the form of an arc. The growth of the arc within the whole soil structure is further described as containing many discrete breakdown channels and branching in nature. Soil medium is a mixture of fragmented mineral materials, organic matter, and gases. The size and distribution of both the soil particles and the air-filled pores are not uniform. To facilitate the computations for engineering purposes, the soil can be represented by an ordered network of soil particles and air voids, as shown in Figure 4. The impulse current mostly flows through the soil particles when there is no ionization, because of the much lower soil resistance. Therefore, the soil ionization phenomena are very important to be considered. If soil ionization is assumed to be frequency independent, Figure 18 are obtained, and the outcomes of the proposed algorithm will still match the data extracted from the CDEGS finite element software. It can be concluded that the impedance of the typical grounding grids buried in soil changes as a function of frequency. The characteristic of the grounding electrode is assessed depending on the soil resistivity. The characteristics of the grounding electrode in low resistivity and high-resistivity soils are dominantly capacitive and inductive, respectively. In both cases of frequency-independent and frequency-dependent, the magnitude and phase angle in all figures varied correspondingly as the frequency increases. In the case of frequency-dependent, the increase of magnitude is a bit higher than the frequency-independent case. On the contrary, the phase angle, in the case of frequency-dependent, increases, but not in the same way as the angle in the case of frequency-independent. There are some spikes in frequency dependent diagrams which rely on the evacuation of the magnetic field at some susceptible points in the soil.  
Figure 16: View of the grounding grid under study.