## 3 Application to Real Cases for Validation of the Method
### Grounding Grid of the Loeches Substation  
Loeches is a large substation located in Loeches (Madrid), with approximate dimensions of 350 m in length by 250 m in width. The substation, owned by UFD DISTRIB. ELECTRIC. S.A. (UFD) has voltage levels of 132 kV, 45 kV, and 15 kV, and is located next to another large substation owned by Red Electrica de Espana, with a voltage level of 220 kV. In Figure 7, the 45 kV/15 kV section of the UFD substation is outlined in red.  
The auxiliar current electrode used, consisting of four copper rods connected in parallel and spaced approximately 2 m apart, was installed at a distance of about 100 m from the substation perimeter fence (green dot). In Figure 7, the position of the auxiliary current  
Figure 6: Representation of the different measurement procedure parameters as a function of the distance from the edge of the Balaidos grid. An interconnected case with other grounding system is also considered. The dashed line represents the edge of the electrode.  
Figure 7: In the (**a**), the Loeches substation is marked in red. The blue dot is the auxiliary current electrode 211 m away from the grid edge. (Courtesy of UFD DISTRIB. ELECTRIC. S.A.) The grounding grid is shown in the (**b**).  
electrode is shown as a blue dot. To measure the substation grounding resistance, an auxiliary voltage electrode was used, consisting of a rod driven into the ground at an approximate distance of 40 m from the substation perimeter fence, in the direction of the current electrode.  
Based on the technical data of the grounding electrode shown in the right panel of Figure 7, it is easy to calculate \(k_{\rho}=0.00787\)\(\Omega/\Omega\)m and \(k_{c}(x)\), along the yellow line shown in Figure 7, to finally evaluate \(k_{m}(x)\) according to (7). For this final step, \(D_{1}=271\) m, and \(D_{2}\) will take two values, 271 m and 211 m from the auxiliary electrode, since the coordinate origin on the ground is the point (X0 = 35 m, Y0 = 0). With respect to this coordinate origin, the potential probe is located at the point with coordinates (Xp = 35 m, Yo = 211 m, Zp = 0).  
Figure 8 shows the results of the analysis. The solid blue line represents, as in previous examples, the field measurement values of the electrode resistance using the FOPM \(R_{G}^{meas}(x)\). These values are expressed as unit resistance, knowing that the estimated soil resistivity is \(\rho=59.5\)\(\Omega\)m. The solid red and being lines represent the corrected values of \(R_{G}^{meas}(x)\) using the correction coefficient \(k_{m}\) evaluated with \(D_{2}=211\) m and \(D_{2}=271\) m, respectively, and \(D_{1}=271\) m, according to (7). Finally, the magenta dashed line shows the average of both corrections, corresponding to the estimated resistance of the electrode. The figure also shows the value measured by the potential probe 40 m from the perimeter fence, which corresponds to a distance of 211 m from the coordinate origin. As can be seen in the figure, the estimated value for the grounding resistance, obtained by correcting the field-measured values at any distance from the potential probe, is constant and has a value of \(R_{G}=0.007875\)\(\Omega\), in full agreement with the theoretical value associated with the electrode.