## 3 Evaluation of the Model Under Controlled Synthetic Conditions
### Very Large Horizontal Electrode in Homogeneous Soil  
The proposed model allows for the incorporation of electrodes made from materials other than conventional copper and its alloys. This makes it possible to evaluate, from a thermal perspective, the suitability of alternative conductive materials whose implementation in grounding electrodes may offer economic advantages. As an application example, a large synthetic electrode is considered, which could represent a simplified version of the grounding electrode used in a large-scale photovoltaic installation. Two scenarios are used: one in which bare copper conductors are used, and another in which stainless steel is used instead. In both cases, the electrode conductors have a radius of 7 mm and are buried horizontally at a depth of 0.5 m in a 50 \(\Omega\cdot\)m homogeneous soil. Due to the large size of the electrode, and in order to avoid excessively long computation times, a segmentation of two elements per meter is assumed. It is acknowledged that the resulting potentials overestimate the actual values since--as is well known--refining the segmentation of the  
Figure 13: Soil resistivity and temperature versus the radial distance from some electrode segments.  
conductors leads to results that more closely approximate the real values. The same applies to temperatures: the calculated values overestimate the actual temperatures at any point on the electrode or in the surrounding soil. Figure 14 shows, in the left panels from top to bottom (a) and (c), the node potentials of the electrode made of hard-drawn copper and zinc-coated steel, respectively. Table 1 summarizes the thermal and electrical properties of both materials used in the proposed model.  
In the right panels, also from top to bottom (b) and (d), the temperatures of the segments of the hard-drawn copper and zinc-coated steel electrodes are shown. As observed in the figure, the injection point corresponds to the location where the highest temperature is reached in both cases. Note in particular the significant difference in the grounding potential between the two electrodes, which results from the influence of the internal resistance of the material. The model indicates that higher material resistivity leads to a higher temperature at the injection point, with the associated risk that the connection to  
\begin{table}
\begin{tabular}{c c c c} \hline
**Property** & **Copper** & **Zinc-Coated Steel** & **Units** \\ \hline Electrical resistivity & 1.72 \(\times\) 10\({}^{-8}\) & 2\(-\)7 \(\times\) 10\({}^{-7}\) & \(\Omega\cdot\)m \\ Thermal conductivity & 390–401 & 15–50 & W/(m\(\cdot\)K) \\ Specific heat capacity & 385 & \(\sim\)490 & J/(kg\(\cdot\)K) \\ Density & 8960 & \(\sim\)7800 & kg/m\({}^{3}\) \\ Melting point & 1085 & \(\sim\)1370 (steel), 420 (Zn) & \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 1: Thermal and electrical properties used for copper and zinc-coated steel.  
Figure 14: Node potentials (**a**,**c**) and electrode temperature profiles (**b**,**d**) for two different conductor materials.  
the grounding electrode could be interrupted due to material melting. Indeed, numerical simulations using this large-scale electrode, made from stainless steel with a resistivity of 6.9 \(\times\) 10\({}^{-7}\)\(\Omega\cdot\)m, show that the injection point segment reaches the melting temperature of the material in approximately 0.4 s under a 10 kA current.