## 2 Analytical Methodology for the Calculation of Electric Field Strength  
When configuring an electrode station, a representation of the electrode that is more accurate than that of a point source is required (especially when studying the near-electric field), compared to the point approach of CIGRE B4.61 675:2017 [1] and IEC TS 62344:2013 [27]. After all, in order to limit the electric current density of each electrode and for reasons of reliability alike, more than one electrode must be used. Taking into account the methods and results of [2], the proposed methodology for calculating the electric field gradient, ground potential rise, and resistance to remote earth of electrode stations is summarised in the following steps:  
* _Determination of the minimum number of electrodes and layout configuration_: the minimum number of necessary electrodes \(N_{min\_el}\) is determined, based on the maximum nominal current \(I_{tot}\) flowing through the electrode station as follows: \[N_{min\_el}=\frac{I_{tot}}{I_{el}\times S_{p\_el}}\] (1) where \(J_{el}\) is the electric current density limit per electrode and \(S_{p\_el}\) is the area of the peripheral surface of the electrode. Let it be noted that the limits within which the electric current density will range are dependent upon the model and mode of operation, that is, steady operation (conditions of a duration equal to, or higher than, 10 s) and transient (durations shorter than 10 s are considered as such, for example, faults and brief overloads). Indicatively, the CIGRE B4.61 675:2017 [1], SS5.1.3.5 and IEC TS 62344:2013 [27], SS6.1.6 guidelines suggest that the electric current density be kept within the frame of 6 to 10 A/m\({}^{2}\), with regard to sea, beach, and pond electrodes, to curtail chorine selectivity for parts in contact with the seawater. Moreover, the electric field strength in the vicinity is to be less than 1.25-2 V/m. Nonetheless, current densities are allowed to reach values up to 100 A/m\({}^{2}\), when the electrodes are safely out of reach of persons and animals. Of course, the manufacturer's guidelines must be taken into consideration [33], along with the type of operation [34]. In the case of configuring \(N_{frame}\) frames, with an equal number of electrodes per frame \(N_{el\_frame}\), \(N_{el\_frame}\) is equal to the quotient of the total minimum number of necessary electrodes \(N_{min\_el}\) to the number of frames \(N_{frame}\). If, for reasons of reliability and maintenance, an additional frame is necessary, a total of \(N_{frame}/=(N_{frame}+1)\) are placed. In addition, due to the linear arrangement of the electrodes in the frame, the electric current distribution is not uniform, as has been established in [6; 7], so an incremental correction factor \(\beta\) of the electric current density was taken into account during the pre-study stage (in this case, equal to 6%) [2]. Therefore, the current densities in full load \(J_{fu\_lo}\) and maintenance conditions \(J_{mt}\) are calculated as follows:  
\[J_{fu\_lo}=\frac{(\beta+1)\times I_{tot}}{\left(N_{frame}+1\right)\times N_{el \_frame}\times S_{p\_el}} \tag{2}\]  
\[J_{mt}=\frac{(\beta+1)\times I_{tot}}{N_{frame}\times N_{el\_frame}\times S_ {p\_el}} \tag{3}\]  
In place of the \(I_{tot}\) current, the current intensity of either the steady or the transient state can be placed and the corresponding electric current densities of the electrodes can be obtained. * _Calculation of electric field strength per electrode_: The determination is made by combining two models proposed in [2]. In particular, for the near-field, a linear current source is considered (method \"C\" in [2]). Figure 1 presents a simplified structure, taking into account a zone for the effective height \(L\) in cylindrical coordinates. On the \"left\" part, the electrode is positioned at a distance \(d_{r1}\) from the dam, while the depth of the dam is \(t_{d}\). Hence, the exterior radius of the dam is \(d_{r2}=d_{r1}+t_{d}\).