Hydrokinetic energy site selection under high seasonality: The i-IHE index

Hydrokinetic energy site selection under high seasonality: The i-IHE index R. Carballo a , D.M. Fouz a,* , I. L´ opez a , G. Iglesias b,c a ´ Area de Ingeniería Hidr´ aulica, EPSE, Campus Terra, Universidade de Santiago de Compostela, 27002, Lugo, Spain b School of Engineering and Architecture &MaREI, Environmental Research Institute, University College Cork, College Road, P43 C573, Cork, Ireland c School of Engineering, Computing and Mathematics, University of Plymouth, Marine Building, Drake Circus, PL4 8AA, Plymouth, UK ARTICLE INFO Keywords: Hydrokinetic energy Tidal power River inputs Intra-annual variability Numerical modelling ABSTRACT A novel index is developed to select sites for hydrokinetic energy exploitation in coastal areas with high resource seasonality –the typical case being estuaries whose hydrodynamics are highly influenced by variable river discharges. The intra-annual Integrated Hydrokinetic Energy (i-IHE) index is constructed by means of a new penalty function that modifies the Integrated Hydrokinetic Energy (IHE) index. The i-IHE index thus defined is applied to a case study: the Mi˜ no Estuary (NW Iberian Peninsula), with seasonal variations of up to 1000 % in the riverine discharge. The hydrodynamics are modelled by the state-of-the-art Delft3D-FLOW code using a highresolution 2DH grid. The results confirm a strong variability in the resource, with time periods shorter than seasons. The results obtained for the penalty function throughout the Mi˜ no Estuary, with values ranging between 0.5 and 0.75, show the relevance of the i-IHE index in order to not overestimate the potential of coastal areas subject to large intra-annual variability. Compared to the conventional IHE index, the novel i-IHE index highlights smaller areas with greater energy potential. The larger exploitable energy in these areas, along with the lower costs and fewer restrictions for hydrokinetic energy operation, will be of interest to developers and stakeholders. 1. Introduction Recent climate neutrality objectives and policies highlight the commitment of public bodies towards an energy transition driven by renewable energy sources [1,2]. In this context of energy mix diversification, marine renewable energies [3,4], and in particular tidal stream and hydrokinetic energy, are considered as feasible energy resources in different coastal regions worldwide [5,6], primarily in estuarine areas subject to large tidal ranges and, under certain circumstances, river discharges [7]. The interest of estuaries for hydrokinetic energy operation results from their strong tidal currents caused by large tidal ranges, constrictions [8] and, in some cases, barotropic circulation resulting from river discharges [9,10] or, in specific coastal areas, baroclinic circulation [11,12]. Many studies have analysed the most appropriate areas for hydrokinetic energy operation in many coastal regions by considering different approaches [13–21]. For all the interest of the results obtained, most of them focus on energetic analyses, with environmental and socioeconomic aspects typically not considered in any great detail. It has been shown that the costs of installation and operation together with the restrictions from socioeconomic activities and environmental considerations may greatly differ not only among coastal bodies but also in a given coastal area [22]. With this in view, several works have resorted to more comprehensive economic and environmental approaches when analysing areas where different zones have been proposed for energy operation [23–26]. This is of particular interest in estuaries, coastal bodies which shelter a vast number of socioeconomic activities (e.g., fishing, aquaculture, transportation), being also places of high environmental value, with different figures of protection (e.g., Natura 2000) [27,28], which may pose a threat to energy exploitation. In consequence, an appropriate decision-making process leading to the identification of the best locations for the installation of hydrokinetic energy facilities in estuarine areas should resort to comprehensive approaches considering not only the available resource, but all the different aspects affecting energy exploitation [23,29]. Although final energy project stages require an accurate farm design, for which thorough cost-benefit and environmental site-specific analyses must be developed [30,31], in early-stage projects the main issue is to reduce the uncertainties when planning the installation of a hydrokinetic farm [32]. With this in view, the Integrated Hydrokinetic Energy * Corresponding author. E-mail address: [email protected] (D.M. Fouz). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene https://doi.org/10.1016/j.renene.2024.121695 Received 22 December 2023; Received in revised form 10 October 2024; Accepted 23 October 2024 Renewable Energy 237 (2024) 121695 Available online 24 October 2024 0960-1481/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). (IHE) index has recently been proposed. Its implementation leads to the selection of the most appropriate area for energy exploitation in a coastal region irrespective of the energy conversion technology and farm layout [29]. This index is based on a holistic approach, integrating the three main aspects affecting hydrokinetic energy farm operation: (i) the exploitable energy resource (computation of the hydrokinetic energy index, HE index), (ii) the coastal configuration and their effects on the installation costs (computation of the geospatial cost penalty function, C gp ), and (iii) the socioeconomic and environmental aspects (computation of the geospatial water use penalty function, U gp ). The IHE index indicates suitability for hydrokinetic energy exploitation if IHE ≥1, with larger values indicating greater suitability. The IHE index was previously applied to identifying the most appropriate locations for energy conversion in the Shannon Estuary (W Ireland), leading to an overall improvement with respect to other, more simplistic, currently available procedures. Despite the large river discharges into the Shannon Estuary, this coastal body was shown to behave as a tidally driven waterbody, where the influence of the large fluvial inputs on the total available hydrokinetic resource is scarce, as is apparent from the virtually inexistent intra-annual variations [33]. However, in estuaries subject to large fluvial discharges and a more limited tidal prism than in the case of the Shannon Estuary, the hydrodynamics may be more affected by the discharge variability, resulting in significant intra-annual variability in the hydrokinetic energy resource (e.g. Ref. [34]). In this case, the previously proposed IHE index would not be suited, for it does not consider the intra-annual variability in the hydrokinetic resource. For this reason, its application to the abovementioned estuaries could lead to ill-informed site selection. In this work, a new version of the IHE index is proposed: the intraannual IHE (i-IHE) index, which takes into account the intra-annual variability in the exploitable energy resource. This is done by extending the HE index (the energy resource related part in the IHE index), for which a new parameter accounting for the variability in the resource is computed, and leading to the i-HE index (the energy resource related part in the new i-IHE index). The approach is illustrated through a case study in the Mi˜ no Estuary (NW Iberian Peninsula) (Fig. 1), a shallow and mesotidal coastal region subject to large fluvial inputs [35], which constitutes a paradigm of seasonality in its available energy resource – its hydrodynamics are largely dominated over long periods by river discharges [14]. The Mi˜ no Estuary is subject to the large river inputs of the River Mi˜ no, the most important river in NW Spain and N Portugal, which in turn presents a significant intra-annual flow variability resulting from the precipitation patterns in this region. The largest average monthly flows, with more than 1000 m 3 s –1 , occur in the first part of the year, steadily decreasing up to the last trimester, when they reach their minima, around 100 m 3 s –1 . On this basis, a seasonal behaviour can be described, with average seasonal differences of up to 1000 % (winterautumn), which in turn considerably affect the hydrodynamics of the estuary, and consequently the exploitable hydrokinetic energy resource [14]. Previous works have analysed the suitability of the Mi˜ no Estuary for hydrokinetic energy exploitation from a hydrodynamic standpoint by considering the installation of third-generation hydrokinetic energy converters (HECs) (i.e., those able to operate with water depths of approx. 1.0 m, given its depth-limited configuration), identifying specific areas of interest in the inner and middle estuary [14,36]. Likewise, more recent studies also identified and demonstrated the economic viability of a tidal test site in the outer estuary [37]. Nevertheless, holistic procedures jointly encompassing the seasonality of the energy production and the analysis of socioeconomic and environmental aspects have not been previously applied to this coastal area. The comprehensive analysis of the aforementioned aspects, and in particular the results from the application of the proposed i-IHE index, will provide key information towards an informed decision-making for hydrokinetic energy exploitation in the Mi˜ no Estuary and, more generally, in estuarine areas subject to a marked intra-annual variability in their hydrokinetic energy resource. This study is structured as follows: first, in Section 2, an overall view of the IHE index and the novel i-IHE index are described; in Section 3, the hydrodynamics of the study are accurately characterized by highresolution numerical modelling, and on this basis the spatial distribution of HE index is computed; next, in Section 4, a thorough characterization of the intra-annual variability of the hydrodynamics in the study area leads to the computation of the proposed i-HE index; in Section 4, the C gp and U gp penalty functions are computed; in Section 5, the spatial distribution of the new i-IHE index is obtained by integrating the previous results. Finally, in Section 6, conclusions are drawn. 2. From IHE to i-IHE index. A general overview The Integrated Hydrokinetic Energy (IHE) index represents a holistic tool for selecting the most appropriate locations for hydrokinetic energy exploitation in a coastal region, for which, as previously stated, the different the relevant aspects which affect the decision-making process are considered. The IHE index considers: (i) the exploitable resource, (ii) installation costs, and (iii) socioeconomic and environmental features. It is expressed as: Fig. 1. Location of the Mi˜ no Estuary in NW Spain (a); areas of interest (AOI) for hydrokinetic energy exploitation identified in previous works and location of ADCP (b). R. Carballo et al. Renewable Energy 237 (2024) 121695 2 IHE =HE CgpUgp ,(1) where HE is the Hydrokinetic Energy resource index, which accounts for (i) meaning HE =1 the threshold above which hydrokinetic energy exploitation is suitable from an energetic standpoint, and C gp and U gp stand for the geospatial cost penalty function and geospatial water use penalty function, respectively, accounting for points (ii) and (iii), respectively, and with values ranging from 0 to 1. The HE index is defined as: HE =Ee Eref ,(2) where E e is the exploitable hydrokinetic energy resource (i.e., the energy resource within the cut-in and cut-off limits of a given HEC) during a representative time period (e. g., one year) and E ref the threshold energy resource level which represents the minimum energy resource required for hydrokinetic energy exploitation suitability. As a result, the physical interpretation of the IHE index is straightforward, a larger value implying a more appropriate location for hydrokinetic energy exploitation, with values above 1 indicating suitability for hydrokinetic energy exploitation, which would correspond with a coastal area with HE =1, i.e., the threshold value for suitability from an energetic standpoint, without considering cost and water use penalizations (C gp =1 and U gp =1). As previously stated, IHE index is computed for a given period of time and therefore does not take into account the intra-annual variability in the hydrokinetic resource. Thus, its straightforward application to estuaries whose hydrodynamics are significantly affected by river discharges subject to intra-annual variations would lead to an illinformed decision-making. On this basis, a new version of the IHE index is proposed, the so called intra-annual IHE (i-IHE) index, which reads: i‑IHE =i‑HE CgpUgp ,(3) where i-HE index is the intra-annual hydrokinetic energy index, which is computed as: i‑HE =i‑Egp HE,(4) where i-E gp is a geospatial intra-annual resource variability penalty function (values ranging from 1 to 0), according to which a value of 1 indicates a location where the intra-annual variability of the resource does not impose any type of restriction or limitation to the exploitation of the hydrokinetic resource (i.e., there is virtually no intra-annual variation in the resource). This term is proposed to be computed as: i‑Egp =1− σ (Ee,i) max(Ee,i),(5) where σ (E e,i ) is the standard deviation, and max (E e,i ) the maximum value at each grid cell of E e,i , which represent the exploitable energy over each itime period representative of the intra-annual variation of the resource (e.g., seasons, months). The application of any of these indexes, HE, IHE or i-IHE, leads to the definition of 5 categories (Table 1). These categories are the same for the three indexes. This results from IHE and i-IHE indexes being obtained from HE index by applying different penalization functions (values between 0 and 1), i.e., the use of these categories for selecting areas by using the HE index would be only valid in case of the different penalization functions attaining values of 1 (no penalization). For example, using the IHE index for selecting the areas would be only valid in the case of coastal bodies with virtual or reduced intra-annual resource variability, or in other words i-E gp approximately equal to 1 (no penalization), as it is the case of the Shannon Estuary [33]. It is important to note that the application of the i-E gp function is not restricted by the coastal configuration or the hydrodynamics characteristics of the coastal body, so it can be used to analyse any coastal region of interest. The same applies to the IHE index, and therefore to the resulting i-IHE index. In the case of estuaries or other coastal areas with low resource seasonality, i-E gp will take on values close to unity, and thus the straightforward application of the IHE index would be valid (IHE index ≈i-IHE index). In the following sections, the different parameters of the i-IHE index are explained in detail, with a focus on the extension of the IHE index so as to consider the intra-annual variations in the energy resource, which is illustrated through its application to the Mi˜ no Estuary. 3. Hydrokinetic energy resource (HE) index 3.1. Numerical modelling procedure and validation The first step for obtaining the i-IHE index in a coastal region requires computing the HE index, which provides an estimation of the suitability of a given coastal area in terms of hydrokinetic energy resource. To this end, an accurate characterization of the hydrokinetic energy resource in a coastal region is required, for which a detailed description of its hydrodynamics during an extensive period of time accounting for the total available resource (ideally a complete year), must be conducted [15,29]. With this aim, the open-source code Delft3D-FLOW is applied, which has been successfully used for analysing the hydrokinetic energy resource in estuaries in previous works [8,12, 14,15,23,27,29,33]. It approximates the conservation of mass and momentum equations under the Shallow Water assumption, along with the transport equation for salinity and temperature [38]. This allows the computation of baroclinic flows resulting from the mixing of river discharges and oceanic waters, which may be of interest in coastal bodies subject to large river flows [11,12]. In this work, the hydrodynamics of Mi˜ no Estuary are computed by using a high-resolution 2DH grid of 20 ×20 m of resolution which is interpolated to the most recent high-resolution bathymetric and topographic data available in this area (Fig. 2) (data obtained from Instituto Hidrogr´ afico de la Marina, IHM, and supplemented by own data from survey). Prior to using the model for determining the potential of this area for hydrokinetic energy exploitation, it is calibrated and validated against in situ measurements of flow velocity obtained from an ADCP (Acoustic Doppler Current Profiler) (Fig. 1) deployed for 8 days. To this end, the sensitivity of model results to the variation of different numerical parameters is analysed. The calibration process led to the turbulent eddy viscosity being set to 30 m 2 s −1 . In Fig. 3 the comparison between modelled and in situ xand y-components of flow velocity, Uand V, respectively, is shown. It can be observed that the model reproduces accurately the hydrodynamics in this coastal area, as confirmed by the various statistical parameters (correlation coefficient, R; root mean square error, RMSE; normalized root mean square error, NRMSE; BIAS; scatter index, SI) provided in Table 2. Once the numerical model has been shown to provide accurate hydrodynamic results in Mi˜ no Estuary, it is used to determine the hydrokinetic energy potential. For this purpose, the main tidal harmonics (TOPEX/Poseidon database) [39,40], mean monthly river inputs (Confederaci´ on Hidrogr´ afica del Mi˜ no-Sil, CHMS), and temperature and Table 1 Hydrokinetic energy resource categorization. Category HE/IHE/i-IHE index I<1 II 1 ≤HE <2 III 2 ≤HE <4 IV 4 ≤HE <8 V≥8 R. Carballo et al. Renewable Energy 237 (2024) 121695 3 salinity at the open boundaries (MeteoGalicia, Xunta de Galicia) are considered, with their values being set according to their intra-annual variation. 3.2. Available and exploitable energy resource The available hydrokinetic energy power density at each time step, E a (t) (Wm −2 ), is obtained as [13]: Ea(t) = ρ 2[V(t)]3,(6) where ρ (kgm −3 ) is the seawater density and V(t) (ms −1 ) represents the flow velocity. However, all the available resource cannot be harnessed as a result of HECs only operating within specific velocity ranges. Thus, the exploitable hydrokinetic energy power density at each time step, E e (t) (Wm −2 ) can be computed as [41]: Fig. 2. Numerical grid (a) and its interpolation to the bathymetric data (b) (the grid close the open sea boundary is not plotted for the sake of clarity). Fig. 3. Numerical model results of flow velocities Uand Vagainst ADCP measurements. Table 2 Validation: statistical parameters. Parameter U V R 0.99 0.99 RMSE (ms −1 ) 0.16 0.14 NRMSE (%) 7.66 8.61 SI 0.31 0.38 BIAS (ms −1 ) 0.03 0.02 R. Carballo et al. Renewable Energy 237 (2024) 121695 4 Ee(t) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 0,V(t)<Vci ρ 2[V(t)]3,Vci ≤V(t)<Vco 0,V(t) ≥ Vco ,(7) where V ci (ms −1 ) represents the cut-in velocity and V co (ms −1 ) the cut-off velocity, or the low and high velocity thresholds for device operation. In the present application, and on the basis of the characteristics of the current available HECs, V ci and V co are set to 0.7 and 3.1 m s −1 , respectively [29]. These values can be adapted, if required, in forthcoming applications of the i-IHE index, based on future technological developments. Thus, the mean non-exploitable power density, E ne (Wm −2 ) is obtained as: Ene =Ea−Ee,(8) where E a and E e stand for the mean available and mean exploitable power density over a representative time period, respectively. The resulting spatial distribution of the mean annual E e and E ne in the Mi˜ no Estuary are plotted in Fig. 4. The overall significantly larger figures of E e , ranging from 0.5 to 1 kWm −2 at the potential sites of interest, than E ne , of about 0.02–0.1 kWm −2 , indicates that the lion’s share of the available resource can be harnessed. Finally, as it is the case of other coastal areas of interest for hydrokinetic energy exploitation, the differences between E e and E ne are larger in the areas with greater resource [29]. 3.3. Reference energy and categorization The last step for computing the HE index is non-dimensionalising E e with E ref according to Eq. (2).E ref , which represents the threshold value required for energy exploitation, is set based on a thorough analysis of previous proposed hydrokinetic projects. A value 0.2 kWm −2 is retained, resulting in the five energy categories defined previously (Table 1) [29]. In Fig. 5, the spatial distribution of the HE index within Mi˜ no Estuary is plotted, with indication of the areas where HE ≥1 (i.e., areas suitable for hydrokinetic energy exploitation). The resulting values of the mean value of the HE index within the selected areas of interest, HE mean , along with their resulting categorization and total available surface are provided in Table 3. Fig. 4. Annual spatial distribution of mean E e (a) and mean E ne (b) throughout Mi˜ no Estuary. Fig. 5. Spatial distribution of the HE index throughout Mi˜ no Estuary. Table 3 Categorization of areas of potential interest based on the HE index (HE ≥1). Area HE mean Category Surface (hm 2 ) I 2.04 III 17.30 II 1.81 II 17.98 III 1.44 II 12.53 IV 2.98 III 8.09 V 1.32 II 4.28 The area with the largest energy potential is Area IV, with HE mean =2.98 (category III), followed with a somewhat lower resource by Areas I and II, with HE mean =2.04 and HE mean =1.81, respectively (category III and II, respectively), and finally, with significantly lower resource and near to the viability threshold of energy potential, Areas III and V, with HE mean =1.43 and HE mean = 1.32, respectively (category II). R. Carballo et al. Renewable Energy 237 (2024) 121695 5 4. Intra-annual hydrokinetic energy resource index (i-HE) The hydrokinetic energy resource in a coastal body may be subject to a marked intra-annual variability, resulting from river discharge variations [14,34,42], and to a lesser extent, tidal variability [43–45], which in turn, as previously stated, may affect the exploitation of the hydrokinetic energy resource. The usual approach to consider these effects is by following a temporal characterization, i.e., by comparing different scenarios while considering characteristic seasonal river discharges and thermohaline conditions at open boundaries [7,14,33,34]. However, the resulting variability usually does not show a homogeneous spatial distribution, primarily resulting from the complex geomorphology of estuarine areas, and its influence on the resulting circulation patterns. Thus, the analysis of the intra annual-variability of the hydrokinetic energy resource should be conducted under a geospatial approach. To this end, Fig. 6 shows the spatial distribution of the mean seasonal flow velocity, i.e., mean velocity during a complete season, V m . It can be observed that there is a strong seasonality in the available resource, being winter the season with significantly greater flow velocities, in excess than 1.5 m s −1 over extensive areas in the outer, middle and inner estuary. On the contrary, summer is the season with lower resource, with areas with mean flow velocities greater than 1 m s −1 only present in the mouth of the estuary. The significant greater velocities with increasing river inputs indicates the important contribution of river discharges to the total available resource in this area. In order to fully understand the seasonal spatial variations in the resource, in Figs. 7 and 8 the spatial distribution of the mean seasonal E e and E ne are shown, respectively. As in the case of the annual figures, the larger figures of E e than E ne indicates that the larger part of the resource can be harnesses throughout the year. Nevertheless, the difference between E e and E ne significantly varies, but in this case not only throughout the estuary, but also during the different seasons. In effect, E e attains values of about or close to 1 kWm −2 over different areas during winter and autumn, while during spring and summer, values in excess of 0.5–1 kWm −2 are only attained at the estuary’s mouth. With respect to E ne , its intra-annual variation is also apparent, with overall larger values during winter and autumn, but with specific spatial patterns, which differs from the annual figures. In effect, the large river discharges may lead to strong outflow currents during the whole tidal cycle, even during the flood, which may exceed the cut-in during virtually the tidal cycle. This is apparent during winter with virtually very reduced values of E ne (less than 0.01 kWm −2 ) through the large areas occupied by the main river channel. In this context, the significant variations in the resulting patterns may indicate intra-annual variations in the available resource going far beyond seasonal patterns, i.e., variations in shorter periods than seasons. To assess this, the time distribution of the flow velocity over a complete year at different locations of interest in the outer, middle and inner Fig. 6. Seasonal spatial distribution of V m throughout Mi˜ no Estuary. R. Carballo et al. Renewable Energy 237 (2024) 121695 6 estuary is provided (representative locations in Areas I, II and IV, respectively) is presented in Fig. 9. The results show that, in this area, and as a result of the presence of large river discharges, and the limited tidal prism, time periods of about 1 month are required for an appropriate characterization of the hydrokinetic energy resource. The key role of river discharges is also apparent during winter season, in particular in the middle and inner locations (Areas II and IV, respectively), where outflow velocities in excess of 0.5 m s −1 (cut-in of state-of-the-art HECs) are present during much of the season, thus explaining the virtually negligible E ne figures at specific locations. Based on the previous results, in the present work, the intra-annual variability of the energy resource in the Mi˜ no Estuary is geospatially assessed in terms of the i-IHE index as follows. First, the hydrodynamic results of the complete (annual) simulation are grouped in i29.5-day periods (e.g., an annual scenario would result in a total of 12 complete periods), allowing an accurate characterization of the inequality of the tide during complete lunar months [46], in addition to the variations in river discharges. Next, the mean exploitable power density of each group of data (time periods) is computed as described in Eq. (7) at each cell of the numerical grid. Afterwards, the standard deviation, σ (E e,i ), and the maximum value of the energy resource of the obtained groups, max (E e,i ), are computed at each grid cell. Thus, i-E gp is spatially assessed at each grid cell according to Eq. (5). To analyse the sensitivity of the i-IHE index to the time periods considered, the i-E gp parameter is also computed by considering seasons as the representative time periods. To this end, the numerical results of the complete (annual) simulation are divided in 4 time periods corresponding to seasons of 88.5 days (three 29.5-day periods to also capture the inequality of the tide). The spatial distribution of i-E gp throughout the Mi˜ no Estuary is provided in Fig. 10. It can be observed that the large river flow variations, as opposed to other estuaries with interest for energy exploitation (e.g. Ref. [33]), greatly affect the exploitation of the hydrokinetic energy resource in this coastal area, with values significantly lower than 1, ranging between 0.5 and 0.75 in most of the areas with potential interest for energy exploitation. The consideration of larger periods (seasons) leads to overall larger penalizations, which results from an overestimation of the standard deviation of the exploitable resource (larger variations between periods if seasons are considered instead of 29.5-day periods), along with a larger value of the normalizing maximum value. Thus, in the present study it is found that considering 29.5-day periods instead of seasons leads to more accurate results. Based on the results for i-Egp, it is straightforward to obtain the spatial distribution of i-HE following Eq. (4). The results are shown in Fig. 11 with indication of the areas where i-HE ≥1 (i.e., areas suitable for hydrokinetic energy exploitation). The resulting figures of mean value of i-Egp, i-Egp,mean, and the mean value of i-HE, i-HEmean, Fig. 7. Seasonal spatial distribution of E e throughout Mi˜ no Estuary. R. Carballo et al. Renewable Energy 237 (2024) 121695 7 within the selected areas of interest, along with their resulting categorization and total available surface are provided in Table 4. The area with the largest energy potential is Area IV, with i-HE mean =2.30 (category III), followed by Area I with i-HE mean =1.67, Area II with i-HE mean =1.38, Area III with i-HE mean =1.22, and finally, Area V with i-HE mean =1.05 (all of them corresponding to category II). All of these areas present a marked intra-annual variability, as indicated by similar values of the i-E gp function, between 0.62 and 0.64. Despite the significantly lower values of i-HE relative to HE, as a result of the penalty function i-E gp , the accurate delimitation of areas with greater interest from a resource standpoint for energy conversion as provided by i-HE index leads to a smaller surface of interest, and therefore the reduction of i-HE mean values with respect to HE mean is less marked. In turn, the resulting delimitation of the new areas and i-HE values provide a better definition of the appropriate areas for hydrokinetic energy exploitation and their real potential. Despite the interest of the abovementioned areas for hydrokinetic energy exploitation, from a resource availability standpoint, some of them may be not feasible for the operation of specific technologies, resulting from the unsuitability between their installation and operational requirements and the coastal configuration. Thus, and in spite of the objective of defining the most appropriate area for hydrokinetic energy exploitation irrespective of the energy conversion technology and farm layout, in the present application, 3rd generation HECs are considered (i.e., microturbines able to work with very reduced water depth of approx. 1.0 m), as a consequence of the depth-limited configuration of the Mi˜ no Estuary. Likewise, the narrow cross-sections of this coastal area also limits the definition of feasible areas, which require a minimum width. According to previous works, which investigated the hydrokinetic energy exploitation in waterbodies of width-limited crosssection (e.g., inlets), a minimum width of roughly 150–200 m should be available [47,48]. Finally, besides water depth and width requirements, a total available surface of about 3–5 hm 2 is also required for hydrokinetic projects being commercially viable [49]. On this basis, only Areas I and II are retained for further analysis. 5. Cost and water penalty functions 5.1. Cost penalty function (C gp ) The next step in the computation of the i-IHE index is the determination of the so-called geospatial cost penalty function, C gp , a function independent of specific technologies or farm layouts which relates CAPEX drivers and coastal configuration, and therefore its accurate definition allows us penalizing areas where energy exploitation will incur in larger expenses. CAPEX refers to the capital expenditures of fixed assets, including [22,49]: (i) device acquisition, (ii) cable, (iii) foundations or mooring system, (iv) installation, and (v) grid connection. Among these, cable costs, along with foundations and mooring system costs, depend Fig. 8. Seasonal spatial distribution of E ne throughout Mi˜ no Estuary. R. Carballo et al. Renewable Energy 237 (2024) 121695 8 strongly on the main geomorphological variables (shoreline distance, l, and water depth, h) and are therefore used for developing C gp [29]. A thorough analysis of state-of-the-art formulations for computing these costs [22,30,50–52] leads to the definition of the so-called total cost function, c farm ( € ) to accurately compute the total value of CAPEX which is function of land hof a pre-sized hydrokinetic farm [29]: Fig. 9. Annual time distribution of the flow velocity at the outer (a), middle (b) and inner (c) estuary. Fig. 10. Spatial distribution of i-E gp throughout Mi˜ no Estuary considering 29.5-day periods (a) and seasons (b). R. Carballo et al. Renewable Energy 237 (2024) 121695 9