## 2 Analytical Methodology for the Calculation of Electric Field Strength
In this, the corresponding electrode is used as the point of reference  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]2 First electrode station configuration—Plan view of six frames in linear arrangement, having each one placed parallel to the dam axis (similar to Figure 8 in [2]). and the electric current is the product of the electric current density \(J_{\mu_{x}\_{0}}\) or \(J_{mt}\), and the respective peripheral surface of the electrode \(S_{p\_{e}d}\). The electric field strength of the \(k\)-th electrode is analysed in its components \(E_{x-k}\) and \(E_{y-k}\), on xOx\({}^{\prime}\) and yOy\({}^{\prime}\) axes (as in Figure 5), utilising the coordinates \((x_{k},y_{k})\) of the electrode (\(x\),\(y\)) of the point of interest (canvas points) and the corresponding distance \(r_{k}\):  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]3  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]4  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]5  
Through superposition, all the electric field strengths of each single electrode are added up on the axes xOx\({}^{\prime}\) and yOy\({}^{\prime}\), as follows:  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]6  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]7  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]8  
The calculation of the absolute electric potential is performed numerically along the main directions xOx\({}^{\prime}\) and yOy\({}^{\prime}\) at various points of the canvas with respect to either \"infinity\". \[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]9  
Figure 1.0  
Figure 1.1 Basic principle of electric field strength analysis of an electrode in xOx\({}^{\prime}\) and yOy\({}^{\prime}\) axes (similar to Figure 9 in [2]). Similarly, from the respective potential difference for specific lengths, the respective average electric field strength values are calculated:  
Figure 1.2  
The resistance of remote earth is determined from the comparison of all operation scenarios:  
Figure 1.3  
Thus, all the variables required for the preliminary study are calculated. * _Determination of areas ensuring electric field strength and voltage limits according to IEC TS 62544:2013 and CIGRE B4.61 675:2017_: In order for the operating conditions of the electrode station to be safe--under any operating conditions--whether it concerns the specialised maintenance staff, or people and living beings, in the areas of direct access, limits are set for the electric field strength, touch voltage, step voltage, metal-to-metal touch voltage, and absolute voltage with respect to remote earth. In particular, taking the most unfavourable limits from the general guidelines of IEC TS 62544:2013 [27] (p. 32) and CIGRE B4.61 675:2017 [1] (p. 65), as well as recommendations about the pipe-to-soil potential difference based on the applied provisions of cathodic protection [35], the necessary conditions that must be met (as they are also summarised in SS2.5. of [2]) are as follows: 1. Electric field strength (potential gradient) for continuous operating conditions in water should be smaller than or equal to 1.25 V/m (for marine mammals, while it could be up to 2.5 V/m when concerning humans). 2. Electric field strength (potential gradient) for transient operating conditions in water should be smaller than or equal to 15 V/m. 3. Potential difference between metal equipment and soil for continuous operating conditions should be smaller than or equal to 4 V. Practically, on the safe side, it could be taken as the corresponding limit for the absolute potential with respect to remote earth. 4.