## 3 Evaluation of the Model Under Controlled Synthetic Conditions
### Horizontal Grid in Homogeneous Soil  
The electrode consists of a basic horizontal grid composed of bare copper rods with a radius of 5 mm, buried at a depth of 0.5 m in homogeneous soil with a resistivity of 50 \(\Omega\cdot\)m. The fault current injection point--an important consideration in real electrodes with internal resistance--is located at the geometric center of the grid, the point P(0, 0, \(-\)0.5), with a current magnitude of 10 kA. This current value was selected because it is on the same order of magnitude as that generated by lightning strikes and is capable of producing high temperatures over short time intervals. In typical fault scenarios, the currents diverted to the grounding system are usually much lower; however, they could also lead to significant temperature rises if not for the prompt action of protection devices, which limit the duration of fault current flow through the grounding electrodes. Figure 5 provides a graphical representation of the electrode. For the calculation of electrical parameters and the temperature profile, each rod of the electrode is divided into a number of segments per meter of conductor. The temperature profile computation algorithm is applied to the soil surrounding each segment. The calculation is carried out following the flowchart shown in Figure 4, using a time loop of 20 steps for a total fault duration of 0.5 s. The initial soil temperature has been set to \(T_{s}\)(0) = 20 \({}^{\circ}\)C. In each simulation, the three models presented in (19) for the temperature dependence of soil resistivity are applied. For the purpose of comparing results, two different segmentations of the rods have been considered: 7 segments per meter and 11 segments per meter of conductor. The potential acquired by the electrode corresponds to the potential at the fault current injection point. The time evolution of the electrode potential under various scenarios is shown in Figure 6.  
The left panel of Figure 6 shows the electrode potential as a function of fault duration for the three soil resistivity models dependent on temperature, using a segmentation of seven segments per meter for the rods that make up the electrode. The right panel presents the same results but using a finer segmentation of 11 segments per meter. In this right panel, the saturation effect of the segment equivalent radius is clearly observed, limiting it to no more than one-fourth of the segment length. This effect becomes more pronounced as the segmentation becomes finer. For this reason, the potential curves tend to flatten,meaning that the potential no longer decreases over time, indicating that the actual value of the potential may be lower than that shown in the curves and, therefore, the plotted values should be considered as an upper bound for the grounding potential. Figure 7 illustrates the potential acquired by each node of the electrode, defined as the junction between adjacent segments, at the end of the considered time interval. The figure refers to the application of Model 1 for temperature to the electrode, using a segmentation of \(11\) pieces per meter. The figure shows that the injection node acquires the highest potential, although, in this example, the differences among the various nodes are not significant. This behavior consistently occurs when the electrode is not large in size and is made of a highly conductive material [24]. Figure 5: The test electrode with numbered rods. Figure 6: Grounding potential for the different soil resistivity models and the two types of electrode segmentation. Figure 8 shows the variation over time of the maximum temperature reached by the electrode, which corresponds to one of the segments into which the rods are divided. The solid-colored lines correspond to the segmentation of 7 segments per meter, while the dotted lines represent the finer segmentation of 11 segments per meter. Figure 9 shows the temperature acquired by each segment of the electrode, represented by a point, at the final instant of the time period considered.