## 3 Application Examples
### Grounding Grid of an Outdoor Transformation Center  
As a second application example, the grounding grid of an outdoor transformation center, like the one shown in Figure 4, will be considered. Such a transformation center is a standard of some of the most important Spanish electrical companies, such as _Iberdrola_ or _Endesa_. The soil is considered uniform with resistivity \(\rho=100\)\(\Omega\)m. The fault current will be set at 1 A, entering one of the corners. The material of the conductors has a resistivity \(\rho_{e}=72\times 10^{-8}\)\(\Omega\)m that corresponds to stainless steel [11]. For this case, it will be assumed that half of the electrode is oxidized (marked in black on Figure 5), forming a uniform layer of thickness \(e=2\) mm of oxidized material, with a resistivity of \(\rho_{ox}=800\)\(\Omega\)m, throughout the length of the conductors affected by corrosion [12]. The segmentation is set to five pieces per meter. Although the resistivity of the oxide layer, and the thickness and length of the affected conductors do not correspond to any real situation, such data are taken from measurements made on similar conductors by the firm _INGESCO Lightning Solutions_, which is recognized in the acknowledgments.  
Figure 3: Some electrical features of the ideal horizontal rod (**upper** panels) and those of coated resistive horizontal rod (**lower** panels).  
Figure 5 shows the GPR produced by the resistive half-covered grid. In this case, the internal resistivity is about forty times greater than that of copper, which is usually considered to be that associated with an ideal conductor.  
In the upper left panel of Figure 6, the GPR of the PEC grid is shown. In the right panel, the node potentials of the ideal electrode are shown. The electrode is equipotential. In the lower panels, the same magnitudes are represented but considering the internal resistance \(\rho_{e}\) of the conductors and the partial oxidation of the electrode. It is shown that the potential profile in the ground is altered in the oxidized half of the electrode, while the potential of the nodes presents a clear, although small, gradient.  
Figure 4: Example of grounding systems for an outdoor transformation center (Author source).  
Figure 5: Ground Potential Rise contour plot from the grounding grid of the transformation center in Figure 4.  
To better appreciate the differences between considering the ideal electrode or including all the limitations, Figure 7 shows, on the left panel, the GPR percentage difference between the two situations, while on the right, the node potentials' percentage difference is shown. As seen in Figure 7, there is more than 10% difference in the potential of the current injection node between the ideal electrode and the real electrode, which also corresponds to the percentage difference in the grounding resistance of the mesh, since the fault current is unitary. Note that although the current input point is at a higher potential than the rest, the differences are not very close to 5%. However, these differences will increase as the electrode becomes larger. To conclude, it is necessary to point out that such a percentage difference may mean, in practice, being outside the regulations regarding installation safety.