## 3 Application to Real Cases for Validation of the Method
### Grounding Grid of the Balaidos Substation  
The method described in the previous section will be applied to determine the grounding resistance of an extensive electrode, such as the grounding grid of the Balaidos substation in Vigo, Galicia, Spain. The technical characteristics of the grounding grid are listed below. Specifically, the resistance of the grounding electrode of the Balaidos electrical substation belonging to the Electric Company Union Fenosa, located in Vigo, Galician Community (Spain), will be estimated. Figure 4 shows the geometric structure of the electrode, which is a non-regular grid formed by rods of variable length.  
Figure 4: The Balaidos substation grounding grid.  
Figure 3: The measured grounding resistance profile for the original electrode (red line) and for the damaged electrode (beige line).  
The electrode of 4 mm radius is buried at a depth of 0.8 m and the parameter \(k_{R}=\frac{R_{G}}{\rho}\) is previously known. The value is \(k_{\rho}=0.02766\)\(\Omega/\Omega\)m, which represents the unitary grounding resistance provided that \(\rho=1\)\(\Omega\)m. The measurement using the three-pin method is simulated with the help of an auxiliary current electrode at a distance of 300 m from the long edge of the mesh. Given the large distance between the auxiliary electrode and the grounding grid, we will assume \(D_{1}\approx D_{2}=300\) m in (7). The soil is considered to be a single layer with unit resistivity, and the current injected into the mesh-auxiliary electrode circuit is 1 ampere. The absolute potential generated by the isolated mesh in the surrounding area can be simulated. Specifically, considering the dashed path drawn in the subfigure of Figure 5, the absolute potential at points along this path is shown.  
Figure 6 shows the variation in the measured resistance \(R_{G}^{meas}(x)\) (blue line) with the coordinate \(x\) from the edge of the mesh, as well as the correction factor \(k_{m}(x)\) corresponding to the single grid and theoretically calculated (subfigure blue line). The product \(R_{G}=k_{m}(x)\cdot R_{G}^{meas}(x)\) is shown (red line), which ideally represents the true grounding resistance of the electrode obtained from the measurement at distance x. It can be observed that \(R_{G}\) is almost everywhere constant and equals the true grounding resistance value \(R_{G}=0.02766\)\(\Omega\).  
Figure 6 also illustrates the situation where the Balaidos grid is interconnected with another distant grid that is part of an external grounding system. In this case, a fault either in Balaidos or in the distant installation causes both grounding systems to act as one. The figure shows the field measurement of the combined grounding (orange line), while the magenta line represents the product of this measured resistance by the correction factor \(k_{m}\) from Balaidos grid as isolated. The result is an almost constant graph, which is also equal to the grounding resistance of the interconnection. In this case, \(R_{G}=0.01912\)\(\Omega\), which is 3% lower than the theoretical value of the combined grounding system \(R_{G}=0.01963\)\(\Omega\).  
Figure 5: Balaidos grid with the indicative line on the ground where the absolute potential is measured by the three-pin method (blue line) when auxiliar rod is 300 m far away. The absolute potential created by the isolated grid is also shown (red line).