## 2 The Model Backgrounds  
To calculate the electrical parameters of a grounding electrode, the simplest model assumes that the conductors are non-resistive PEC, so that the electrode as a whole is equipotential [9]. The incoming current through the injection point is distributed throughout the conductor and is filtered to ground through its surface so that the electrode becomes equipotential. The injection point is not important, and only the magnitude of the fault current is the initial relevant information. The leakage current to the ground in each part of the electrode is calculated without difficulty. With this information, the grounding resistance and potentials at the ground surface, with which step and touch potentials are evaluated, are calculated. Such potentials are important magnitudes since they characterize the electrical behavior of the electrode [10]. When the conductors that form part of the electrode have internal resistance, the electrode is no longer equipotential as a whole, and the injection point becomes important. The model that best describes the behavior of an electrode of this nature is the aforementioned CBM. According to this model, the electrode is divided into branches and nodes, and circuit theory is applied to each branch and each node. A complete description of the model can be found in the aforementioned reference [7], which describes the CBM of a buried electrode in a semi-infinite multilayer soil. The application of the model supplies the currents flowing through the branches and the leakage currents to the ground of each branch. With this information, the potential at any point on the ground can be calculated. Figure 1 shows in the top a horizontal rod which is divided into N branches. The branch potential \(U_{k}\) and the leakage current \(I_{k}\) in each branch are also shown. At the bottom, the CBM  
is shown. At each node of the circuit, the potential \(V_{\rm t}\) and the source of nodal leakage current \(J_{t}\) are located. The internal currents \(i_{k}\) that run inside the conductor are also shown. Node potentials and branch potentials are closely related, as also are the nodal leakage currents and branch leakage currents. The branch potentials \(U_{k}\) depend on the currents filtered to the ground by all other branches \(I_{m}\), including the branch \(k\) itself. Assuming that the electrode lies on the same soil layer with resistivity \(\rho\), it can be stated that  
\[U_{k}=\sum_{m=1}^{N}I_{m}\cdot Z_{km} \tag{1}\]  
where the impedance \(Z_{km}\), called transverse impedance, has the following expression for a multi-layered soil,  
\[Z_{km}=\frac{\rho}{4\pi}\int dl_{m}\Bigg{[}\frac{1}{\overrightarrow{r_{k}- \overrightarrow{r}_{m}}}+\int\limits_{0}^{\infty}(f(\lambda)e^{-\lambda(z_{k }-z_{m})}+g(\lambda)e^{\lambda(z_{k}-z_{m})})J_{0}(\lambda r)d\lambda\Bigg{]} \tag{2}\]  
As stated before, \(\rho\) is the soil resistivity around the branch \(m\), and the functions \(f(\lambda)\) and \(g(\lambda)\) stand for the contribution of the other soil layers to the potential, which are calculated by imposing the boundary conditions at each layer interface [7]. The branch potentials \(U_{k}\) and the leakage currents \(I_{m}\) are then related with the node potentials \(V_{k}\) and currents \(J_{m}\), which satisfy the CBM equations. Next, the influence of a partial coverage of the electrodes will be introduced in the model.