A methodology for cost-effective analysis of hydrokinetic energy projects

Energy 282 (2023) 128373 Available online 15 July 2023 0360-5442/© 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). A methodology for cost-effective analysis of hydrokinetic energy projects D.M. Fouz a , R. Carballo a , * , I. L´ opez a , X.P. Gonz´ alez a , G. Iglesias b , c a Departamento de Enxe˜ naría Agroforestal, Universidade de Santiago de Compostela, EPSE, Rúa Benigno Ledo s/n, 27002, Lugo, Spain b School of Engineering and Architecture & MaREI, Environmental Research Institute, University College Cork, Ireland c School of Engineering, Computing and Mathematics, University of Plymouth, UK ARTICLE INFO Handling Editor: Soteris Kalogirou Keywords: Tidal stream Tidal energy Marine renewable energy Offshore renewable energy Cost model Energy production model ABSTRACT The cost-effective analysis (CEA) of hydrokinetic farms is typically based on simplistic assumptions regarding the performance and cost structure of hydrokinetic energy converters (HECs) and, in consequence, may lead to illinformed decision-making. In this work, a novel approach to selecting the most appropriate combination of HEC and site within a coastal area is developed, with the accurate computation of the CEA parameters as the cornerstone. The approach, which is illustrated through a case study in the Shannon Estuary (W Ireland), encompasses four models, namely: (i) HEC-site selection model, (ii) energy production model, (iii) CAPEX model, and (iv) OPEX model. By avoiding simplistic assumptions, the proposed approach improves on current procedures and enables developers to accurately compute any cost-effective parameter of interest. In particular, operation and maintenance costs are considered, along with economies of scale, which are typically disregarded in existing procedures. Beyond the interest of the results of the Shannon case study, the approach can be implemented in other regions with potential for hydrokinetic energy conversion. 1. Introduction Coastal areas have supported human activity throughout history in many different ways. In the socioeconomic sphere, these areas have been traditionally used for transport and food supply [1,2]. As a result of the increased public awareness of environmental issues, protected or conservation areas (e.g., Natura 2000) have emerged alongside traditional socioeconomic activities, which have grown significantly (e.g., tourism or heritage) [3,4]. This is also the case of marine renewable energy exploitation, which is posited as a new, promising coastal use [5–12]. Within the different types of marine renewable energies, hydrokinetic energy, primarily resulting from the tide (e.g. Ref. [13]), reinforced in some coastal areas by river discharges and density gradients (e. g. Ref. [14]), is expected to attain a commercial stage in the forthcoming years [15]. The exploitation of this resource is carried out by means of hydrokinetic energy converters (HECs), of which different types exist with varying degrees of technological maturity. Turbine-based solutions, and in particular horizontal axis turbines, are considered to be approaching the commercial stage [16–18]. The state-of-the-art third-- generation HECs are designed to operate with relatively low cut-in velocities (i.e., 0.7–1.0 m/s) [19,20]. As a consequence of this heterogeneity in technological maturity, reliable metrics should be developed to accurately assess the technical and economic viability of hydrokinetic energy projects in decisionmaking processes. As a first approach to technical viability, the Technology Readiness Level (TRL) is usually mentioned as a standard or a metric-based model with several applications in R&D activities, such as the development of HECs [21,22]. However, in order to reduce the uncertainties of hydrokinetic energy projects and ensure their economic viability, the TRL model should be complemented by a cost-effective analysis (CEA), which provides metrics (e.g., LCOE, NPV, IRR) describing the techno-economic performance of technologies under development or proposed projects [23]. The estimation of CEA parameters is usually based on simplified methods, considering either their spatial distribution or, in a simpler approach, delocalised approximations [24]. The main weakness of these approaches is their unrealistic cost structure, which may produce misleading results. In the case of tidal energy projects, the resulting figures typically lack accuracy, which may be seen as a direct consequence of the limitations of the procedure applied, namely [25]: (i) performance computation based on limited and non-reliable HEC data, (ii) consideration of the different economic aspects in terms of expected percentage over the total investment, or (iii) disregard for specific * Corresponding author. E-mail address: [email protected] (R. Carballo). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy https://doi.org/10.1016/j.energy.2023.128373 Received 1 February 2023; Received in revised form 11 May 2023; Accepted 7 July 2023 Energy 282 (2023) 128373 2 aspects, which contributes significantly to real costs. Another aspect closely related to the computation of CEA parameters is the selection of the sites or areas to be subject to this analysis. This selection is typically based merely on the available energy resource [26–28]. In a few cases, a reduced number of geomorphological parameters (e.g., water depth) have also been taken into account [29,30]. Notwithstanding the interest of these methods for a preliminary selection of coastal areas, additional information (e.g., socioeconomic) needs to be considered in more advanced stages. In effect, an appropriate site-selection should also consider aspects such as the coexistence of the energy exploitation with other marine uses, or the site-specific costs of installation and operation [31,32]. In this context, it is important to remark that miscalculated CEA figures may result from not accurately considering specific aspects of cost analysis, such as the operation costs, or from neglecting potential cost reductions through economies of scale [33]. In the case of large coastal areas, the application of the current procedures could result in overly homogeneous CEA figures, as the spatial variability of the energy resource over short distances is not usually accounted for in the computation of these metrics (low to mid resolution energy resource models) [34]. In this research, a novel approach for accurately computing the CEA parameters of hydrokinetic energy projects is developed, leading to a significant improvement with respect to currently available methods. The proposed approach addresses the major difficulties and uncertainties when computing the main aspects affecting the CEA of hydrokinetic energy farms, avoiding simplistic and unreliable assumptions, and improving on current procedures. Thus, the implementation of this novel procedure will lead to the selection of the optimum HEC-site combination for installing a hydrokinetic farm in a coastal area. The novelty of this work lies in the consideration of the following aspects: (i) the energy production, which is assessed by combining highresolution numerical modelling results with spatial analysis algorithms; (ii) the installation costs, whose breakdown in terms of unitary costs is thoroughly analysed, including the effects of economies of scale; (iii) the operation costs, which are computed by means of an ad hoc Operation and Maintenance (O&M) model, including several operational parameters and strategies. Other aspects dealing with the energy transmission or storage related to the specific characteristics of the electrical grid, or the integration with short-term energy storage to help balance the local demand with the varying supply typical of hydrokinetic and tidal farms, are outside the scope of the present work and require specific research [35–40]. The proposed procedure to develop the CEA of hydrokinetic energy projects is applied, for the first time, to a specific case study in the Shannon Estuary (W Ireland) (Fig. 1) and computed in terms of Levelized Cost of Energy (LCOE). Preliminary studies have recognised the potential of this area for hydrokinetic energy exploitation [41,42]. Previous works fully described the hydrokinetic energy resource in the Shannon Estuary, identifying a number of areas as of particular interest [30]. More recent studies highlighted the energy potential of Tarbert Area in the middle estuary (Figs. 1 and 2) by considering: (i) the exploitable resource, (ii) the costs of installation, and (iii) the socioeconomic and environmental pre-existent activities [31,43,44]. The integration of these aspects led to the computation of the Integrated Hydrokinetic Energy (IHE) index and, on this basis, to the delimitation of a large area in the surroundings of Tarbert (≈3 km 2 ) (Fig. 2) with the highest potential, with a value of IHE =4.15 (being IHE =1 the suitability threshold for hydrokinetic energy exploitation). In the present work, this region is retained as a case study for defining the best HEC-site combination by applying the proposed procedure. This paper is structured as follows. In Section 2, a brief overview of the proposed methodology used to compute the CEA is presented. Next, in Section 3, the tools for defining feasible HEC-site combinations are introduced and implemented to the area of interest. Afterwards, the main aspects considered for CEA computation are defined, and the results from its application summarized: (i) energy production (Section 4), (ii) capital expenditures, CAPEX (Section 5), and (iii) operational expenditures, OPEX (Section 6), In Section 7, the integration of results and CEA computation is conducted for the Tarbert Area, and the results compared with available state-of-the-art methodologies. Finally, the major conclusions to this work are depicted in Section 8. 2. General description of the procedure The main objective of this work is to define and apply a new approach to accurately conduct a cost-effective analysis (CEA) of hydrokinetic energy farms, considering all the aspects involved in the process, and thus leading to the identification of the best HEC-site combination within a coastal area. The proposed approach consists of five steps: Fig. 1. Location of Shannon Estuary in W Ireland pinpointing Tarbert Area. D.M. Fouz et al. Energy 282 (2023) 128373 3 (i) The development of an HEC-site selection model (Section 3), which employs the IHE index and spatial analysis algorithms to define different HEC-site combinations, allowing for economies of scale by analysing various farm sizes based on specific criteria (Section 3). (ii) The application of an energy production model leading to the computation of the Annual Energy Production (AEP) of the different HEC-site combinations previously defined, based on high-resolution numerical modelling. (iii) The definition of a Capital Expenditures (CAPEX) model (Section 5), which is based on a detailed breakdown in unitary costs and an ad hoc algorithm for assessing the effects of the economies of scale resulting from the different farms analysed. (iv) The definition of an Operational Expenditures (OPEX) model (Section 6), considering HEC-specific O&M procedures, including Fig. 2. IHE index over the exploitable threshold (IHE ≥1) in the Tarbert Area. Fig. 3. Flowchart of the proposed procedure. D.M. Fouz et al. Energy 282 (2023) 128373 4 the analysis of human and material resources and the definition of specific weather windows. (v) The integration of previous results (ii to iv) to provide reliable CEA parameters for the different HEC-site combinations, leading to the selection of the best alternative. For the sake of clarity, a flowchart of the procedure is provided in Fig. 3. This procedure is illustrated through a case study in the Tarbert Area of the Shannon Estuary (Ireland) [30,31,41,42]. The CEA is carried out in terms of Levelized Cost of Energy (LCOE) – a metric widely used in marine renewable energy projects, including for the selection of sites for hydrokinetic energy farms [24–27,45,46]. 3. HEC-site selection model The first step of the proposed approach is the definition of all the feasible HEC-site combinations. This is a key stage upon which depend several parameters that influence the cost structure (inter alia, the final layout of the farm or maintenance strategies), including the possible effects of the economies of scale and the performance of the plant and, in consequence, the resulting CEA values. With the aim of generalizing the results provided, generic taxonomies of energy converters are considered (Section 3.1), including information about their reliability, which will be retained for its use in further sections. As regards locations, the results of the IHE index in the surroundings of Tarbert are used as a starting point for the definition of different areas with homogeneous levels of energy resource, which are processed to identify the suitable areas under specific criteria by means of spatial analysis algorithms (Section 3.2). 3.1. Characteristics and reliability of the energy converters considered The present work aims to provide results as accurate and realistic as possible in a nascent research field, hydrokinetic energy exploitation. As mentioned above, only horizontal-axis turbine-based devices are approaching commercial maturity, resulting in a lack of reliable economic information of HECs. In order to overcome these limitations, it is usual to resort to general taxonomies of HECs, grouping generic designs with a certain homogeneity, especially in the field of reliability, where surrogate data can be easily available from other renewables (e.g., wind energy). Likewise, despite the assumptions made, this approach is helpful to provide accurate figures of the cost structure of HECs and, in particular, of their costs of installation (Section 5), primarily due to the possibility of complementing their breakdown by means of different data sources, which are assumed to be common or scalable for the whole taxonomy considered [47]. Horizontal-axis turbines are usually classified depending on their seabed fixing as [48]: (i) bottom-fixed and (ii) floating devices. This division is connected with the available water depth and, in consequence, with the diameter of the turbine. Monopile bottom-fixed gravity foundations are usually prescribed up to 20–30 m depth, and floating, moored solutions for deeper areas [31]. This general picture is similar to offshore wind energy facilities, allowing us to use surrogate data to compute accurate reliability figures for HECs under an assembly or subassembly approach. The reader is referred to Ref. [47] for further information about this approach and its procedures. Therefore, in order to select generic energy converter designs, representative of the aforementioned taxonomies and covering the most common horizontal-axis turbines and a wide range of diameters, two different HECs are considered: (i) a floating device of 4.5 m of diameter (F-HEC), which in turn could be applied to most of the areas of interest for hydrokinetic energy exploitation, and (ii) a bottom-fixed converter of 16 m of diameter (BF-HEC), which is of interest in a large number of non-depth limited coastal areas, such as deep estuaries. The main characteristics of the HECs selected, along with their reliability data in terms of average annual number of reparations required, which are retained for its use in further sections, are summarized in Table 1. 3.2. Selection of areas for CEA Previous works have highlighted the energy potential of the Tarbert Area by considering not only its hydrokinetic energy resource, but also its morphological configuration, by applying the TSE ndl index [30], along with socioeconomic and environmental aspects, through the implementation of the IHE index [31]. On the basis of the application of the IHE index, a large area of approx. 3 km 2 with values above a minimum threshold of IHE =1 (i.e., the threshold value of the IHE indicating suitability for hydrokinetic energy exploitation) has been delimited. The definition of suitable smaller areas for energy exploitation requires to take into account the spatial variability of the available resource within this large area; in fact, within it, the maximum value of the IHE index, IHE =4.15, is roughly two times higher than its mean value, IHE =2.10 [31]. The more reduced the area, the greater the IHE index; however, the larger the area considered, the higher the number of HECs, which would result in a cost reduction as a consequence of the economies of scale, not considered in the IHE index. With the aim of defining suitable areas for hydrokinetic energy exploitation considering this spatial variability of the energy resource and the resulting effects on the economies of scale, a complex spatial analysis algorithm (Fig. 3) is developed and applied to the Tarbert Area as follows. First, the entire region delimited by the isoline IHE =1 is subdivided into several sub-areas or polygons by considering isolines of a value ranging from 1 to the maximum value of the IHE index within the whole area by considering a given step. In the present application, a step of 0.2 is proposed; however, this value can be adapted based on the specific characteristics of the site. Second, the mean value of the IHE index at each polygon is computed along with their total surface. Third, the polygons subsequently obtained are rearranged according to their value of mean IHE index in decreasing order (i.e., increasing their total available surface). Finally, some of the polygons obtained are retained for further analysis from the rearranged list. To this end, the selection procedure considers the following criteria, being applied from the top to the bottom of the list. The polygons to be retained must fulfil simultaneously two criteria: (i) to have, at least, a minimum total surface, S min , and (ii) to provide a significant relative increase in the total available surface, ΔS, with respect to the preceding selected polygon in the list. In the present work, these values are established as follows [27,49–54]: S min =5 hm 2 and ΔS =100%. This second criterion allows us to consider the effects of economies of scale on the cost structure of the hydrokinetic farm. 3.3. Application of HEC-site selection model The results of the application of the proposed HEC-site selection model to the Tarbert Area in the Shannon Estuary are provided in Figs. 4 and 5. In Fig. 4, the different polygons obtained by considering isolines of a value ranging from IHE =1 to the maximum value of the IHE index by considering a step =0.2 are plotted (in black). Likewise, in order to facilitate the understanding of the results and of the proposed HEC-site selection model, additional isolines with step =0.6 are also plotted (colour code). A total of 30 polygons are apparent. Finally, as result of the application of the rest of the procedure and the surface criteria given by S min =5 hm 2 and ΔS =100%, in Fig. 5 the polygons retained are plotted. Only five polygons resulting from this procedure are considered for further analysis (A to E), allowing the consideration of the effects of economy scale. In addition, the polygon IHE =1 is also retained. Their main characteristics are presented in Table 2. Based on the characteristics (water depth) of the areas selected, and the characteristics of the selected devices (i.e., surface occupied per unit of HEC and minimum water depth required) (Table 1), a total of seven D.M. Fouz et al. Energy 282 (2023) 128373 5 HEC-site combinations are retained for further CEA: F-HEC can be installed within polygons A to E and IHE =1; in the case of BF-HEC, it can operate only within polygon E. 4. AEP model 4.1. Model description Once defined the different HEC-site combinations resulting from the methodology described in Section 3, the next step in order to assess the techno-economic performance of these combinations is to accurately quantify their annual energy production (AEP). To this end, a highresolution numerical model (Delft3D-FLOW) of the Shannon Estuary is implemented (in its 2DH form) and successfully validated, allowing the simulation of its hydrodynamics during a complete year [55–57]. For further details about the implementation and validation of the numerical model the reader is referred to Refs. [30,31]. Once the hydrodynamics of this coastal area are fully described in spatiotemporal terms, the electric energy production, E e , of a HEC operating during a period of time T can be computed as follows [58]: Ee=ACp ρ 2∫t=T t=0 [V(t)]3dt,(1) where A represents the turbine swept area, C p is the power coefficient which models the efficiency of the HEC selected, ρ stands for the water density and V (t) is the instantaneous vertically averaged flow velocity. However, an accurate computation of this energy production in a Table 1 Main technical characteristics and reliability data of the HECs considered [rotor diameter (Ø), swept area (A), minimum water depth (d min ), total surface in plan view occupied per each device (S unit ), cut-in velocity (V ci ), rated velocity (V r ), cut-off velocity (V co ), rated power (P r ), power coefficient in normal operation (C pNO ), power coefficient in stall control (C pSC ), failure rate (λ)]. HEC Ø (m) A (m 2 ) d min (m) S unit (m 2 ) V ci (m/s) V r (m/s) V co (m/s) P r (kW) C pNO C pSC λ (no/yr) BF-HEC 16.00 200.00 25.00 1920.00 1.00 2.50 3.10 1200.00 0.48 n.a. 4.54 F-HEC 4.50 15.90 7.00 760.00 0.70 2.70 3.75 56.00 0.35 0.20 5.37 Fig. 4. Isolines of the IHE index (0.2 of step for isolines in black and 0.6 for isolines with colour code) within polygon IHE =1. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 5. Delimitation of the resulting polygons (A to E), along with polygon IHE =1. Table 2 Main characteristics of the sites selected [mean value of the IHE index (IHE m ), standard deviation ( σ ), mean water depth (h m ), surface (S), distance between the centroid of the polygon and the base port (d C-BP )]. Polygon IHE m ± σ h m ± σ (m) S (hm 2 ) d C-BP (km) A 3.93 ±0.08 9.22 ±1.09 8.26 1.36 B 3.74 ±0.20 10.00 ±1.68 18.37 1.38 C 3.43 ±0.30 12.02 ±2.96 46.32 1.54 D 3.11 ±0.43 14.34 ±3.69 99.17 1.30 E 2.53 ±0.66 17.21 ±5.00 208.96 1.26 IHE =1 2.15 ±0.80 16.97 ±5.07 297.97 1.48 D.M. Fouz et al. Energy 282 (2023) 128373 6 large coastal region, as is the case of the Tarbert Area, is not straightforward. Given the heterogeneity in terms of available surface of the different sub-areas or polygons of interest selected in Section 3, the spatial variability of the energy resource could result in inaccurate figures of energy production. To avoid this issue, a specific procedure is defined in order to compute the energy production of the different HECsite combinations. Thus, the site-specific hydrodynamic regime of each polygon considered has been reconstructed based on high-resolution numerical results as follows: for each time step of the numerical simulation, the computed values of flow velocity of each grid cell contained in the polygon considered are averaged, constituting a site-specific and time-dependent hydrodynamic regime for each polygon analysed. So, the characteristic velocity at each polygon at each time step, V c (t), can be computed as: Vc(t) = 1 n∑ i=n i=0 Vc(i),(2) where i and t represent the numerical cell number and time step, respectively. Thus, the characteristic mean velocity at each polygon, V c , can be computed as: Vc=1 T∑ t=T t=0[1 n∑ i=n i=0 Vc(i,t)],(3) in this way, the energy production of the different HEC-site combinations can be accurately computed, including the effects of the spatial variability of the energy resource, by combining the time distribution of the characteristic velocity, V c (t), with the characteristics of each HEC considered (Table 1) by means of Eq. (1). 4.2. Application of AEP model The results of the application of the proposed AEP model to the Tarbert Area are provided in Figs. 6 and 7. In Fig. 6, the resulting time distribution of the characteristic velocity during a complete annual year at each polygon is shown. As a result of these time distributions, the following characteristic mean velocities, V c , are attained: 1.20 m/s, 1.05 m/s, 1.16 m/s, 1.12 m/s, 1.03 m/s and 0.98 m/s for polygons A, B, C, D, E, and IHE =1, respectively. In Fig. 7, the figures of AEP and capacity factor (C f ) for the different HEC-site combinations retained are plotted. AEP is computed by combining the site-specific hydrodynamic regime and the power curve of the HECs considered as provided by the device developers. C f is obtained according to Ref. [59]. It can be observed that the polygon where F-HEC produces the largest amount of energy is that with the largest surface, IHE =1 with 174.7 GWh, progressively reducing its energy production as the surface reduces: polygons E with 148.0 GWh, D with 89.9 GWh, C with 45.2 GWh, B with 14.3 GWh, and A with 8.9 GWh. In the case of BF-HEC, its annual energy production in polygon E is 45.1 GWh. This is the result of the significantly larger number of devices in the larger polygons (at least 100% of increase in the total surface with respect the preceding polygon according to the established criteria), which does not indicate a better performance. In fact, the smaller the polygons, the higher their IHE, and therefore the performance in terms of C f could tend to be the opposite. In the case of F-HEC: polygons A with 16.84%, B with 12.07%, C with 15.12%, D with 13.89%, E with 10.95% and IHE =1 with 9.28%. In the case of BF-HEC, its C f in polygon E is 8.42%. This expected tendency does not apply to all cases, e.g. polygon B, given that IHE index also considers, in addition to the energy resource, the total costs although in Fig. 6. Time distribution of the characteristic velocity, V c (t), in the selected polygons. D.M. Fouz et al. Energy 282 (2023) 128373 7 a more simplified way than that proposed in the present work. 5. CAPEX model 5.1. Fundamentals of CAPEX estimation CAPEX stand for the capital expenditures needed for the installation, in the present case, of a hydrokinetic farm. They are usually considered as a one-off expenditure, usually incurred in the first year of the project or in the first payment period (prior to the beginning of the operation of the farm). In consequence, CAPEX group all the construction costs of the plant, commonly representing more than 70% of its total expenses [45]. As a result of their economic magnitude, and in order to make available an accurate assessment of CAPEX, it is necessary to define in detail their cost items and structure, for which a widely used unitary costs model should be defined (Section 5.1) and subsequently implemented (Section 5.2) to compute the CAPEX of the different HEC-site combinations defined in Section 3 — instead of a global percentage, which might produce misleading results. CAPEX is usually broken down into three cost categories [60]: (i) management and engineering costs (CAPEX 1 ), which encompasses the cost of different planning activities needed to ensure the viability of the project and the fulfilment of all its technical requirements (e.g., conceptualization, design, quality management, etc.); (ii) manufacturing costs (CAPEX 2 ), including the cost of the main structural elements of the farm and its equipment (e.g., devices, cabling, foundations or moorings, etc.); and (iii) installation costs (CAPEX 3 ), which include, among others, the expenses of the deployment and grid connection of the plant. The evaluation of these cost categories in the proposed model is explained in detail in Section 5.2. 5.2. Definition of CAPEX model An accurate computation of CAPEX 1 to CAPEX 3 terms is a key point to develop the CEA of a hydrokinetic farm, especially in the case of CAPEX 2 , which has been estimated at about 80% of the total CAPEX [45, 61]. However, this value is highly dependent on the characteristics of the farm and should be accurately computed for each specific project. In this context, the only way to obtain realistic CAPEX figures is, as in the case of a conventional engineering project, to assess them by means of measurements and unitary costs. The definition of these data requires a detailed design of the HEC, e.g., through CAD tools [62], and a reliable breakdown of unitary costs, which is not typically available in the literature. To this end, the use of HEC types and representative generic designs are required. In the present application, a detailed and validated unitary costs model [60,63–65] has been used by combining its breakdown (Table 3) with the specific measurements of the HECs considered, according to their significative taxonomic similarities. For further details about this model and its implementation, the reader is referred to Ref. [60]. Likewise, the present CAPEX model also considers the effects of the economies of scale resulting from the consideration of different farm sizes for installing the selected HECs, for which and ad hoc algorithmic procedure is applied. This procedure is based on a detailed analysis of the farm size (as a function of the installed power, P) and its influence on CAPEX figures for a wide range of proposed hydrokinetic plants, ranging from reduced plants, e.g., 0.5 MW [66], which were planned for the self-sufficiency of local facilities, to large offshore farms, e.g., 50 MW, with remarkable similarities with wind farms [25]. In this context, an increase in the number of HECs may lead to a considerable reduction in the costs in the case of initially proposed small to medium farm sizes; however, as the size of the farm grows, the increase in these effects progressively reduces up to a point at which are maximum [33]. In the present work, these limits have been widely analysed in terms of installed power in tidal energy and other renewables — for farms with installed power over approx. 30 MW the CAPEX presents maximum reductions of about 35% [67–69]. Moreover, as previously established, this reduction is more abrupt in the case of increasing the size of small farms than when approaching the aforementioned limit (i.e., 30 MW), which could be represented through a logarithmic function [70]. Based on these considerations, and by applying a parametric analysis to several hydrokinetic farms within a wide range of installed power (i.e., 0.5–50 MW), the effects of the economies of scale in terms of CAPEX reduction can be computed for hydrokinetic farms below 30 MW as follows: CAPEXred(%) = 100 × [8.4805 ln(P) + 5.8782].(4) Above this limit the CAPEX reduction would be set as a constant (35%). 5.3. Application of CAPEX model The results of the application of the proposed CAPEX model to the 0 50 100 150 200 AEP (GWh) F-HEC BF-HEC A B C D E IHE = 1 Polygon 0 5 10 15 20 Cf (%) Fig. 7. AEP (above) and C f (below) for the selected HEC-site combinations. D.M. Fouz et al. Energy 282 (2023) 128373 8 Tarbert Area are presented in Table 4. As can be observed, CAPEX 2 represents the lion’s share of the total capital investment, followed by CAPEX 1 (about ten times less) and CAPEX 3 (about forty times less). However, their relative importance for the different HEC-site combinations differs widely; in effect, as the surface considered (and therefore the number of HECs) increases, the value of CAPEX 2 significantly increases, whereas this increase in the case of CAPEX 1 is much more contained. This means that in the case of areas of reduced surface (e.g., about 5 hm 2 ), the contribution of CAPEX 1 to the total CAPEX could represent 50% of CAPEX 2 . 6. OPEX model 6.1. Fundamentals of OPEX estimation OPEX represent the expenditures incurred during the operation, in this case, of a hydrokinetic farm. They usually include all the expenses related with the fixed costs of exploitation and both scheduled and unscheduled O&M, such as insurances, taxes, salaries, facilities, etc [25]. In consequence, OPEX are highly influenced by the performance of the plant and the O&M strategy defined for each type of installation. As a general rule, they constitute an important driver of the cost structure of a hydrokinetic farm, reaching average figures greater than 30% of the total expenses [45]; however, they may widely vary amongst hydrokinetic farms depending on their specific characteristics [25]. Resulting from their importance on the cost structure of a hydrokinetic farm, it is necessary to estimate OPEX as realistically as possible, analysing in detail the actual limitations of the state of the art. To this end, an ad hoc OPEX model is developed (Section 6.2) by considering: (i) reliability HEC data (Section 3), (ii) high-resolution hydrodynamic numerical modelling (Section 4), and (iii) several O&M procedures. Finally, this model is applied to estimate the OPEX of the different HEC-site combinations defined for the Tarbert Area (Section 6.3). In spite of their important weight on the cost structure of hydrokinetic farms, the assessment of OPEX is subject to a large number of uncertainties, which results from the lack of knowledge caused by the reduced number of real projects. In order to avoid these difficulties, OPEX estimations usually resort to considering either specific cost items or the total cost as a function of the installed power [46,71] or as percentage of CAPEX [25,72]. Recent works proposed more complex models for specific maintenance items, including O&M schemes based on metocean data [47,73,74]; however, high-resolution site-specific numerical modelling required for accurate OPEX estimations is not usually considered [25]. Moreover, previous studies are focused on specific designs of HECs and only take into account a specific O&M strategy [25,60,63–65]. These weaknesses are considered as a starting point for the development of an ad hoc OPEX model, which is detailed in the subsequent section (Section 6.2). In this regard, prior to the development of an OPEX model, it is necessary to define an appropriate breakdown whose categories would allow a developer to consider all the aforementioned aspects. In the present work, as in the case of CAPEX, a breakdown of OPEX composed of three different categories is considered [25,60,63,75]: (i) insurances and fixed costs (OPEX 1 ), which represent one of the most expensive maintenance costs in renewables [76]; (ii) scheduled or preventive maintenance (OPEX 2 ), covering calendaror condition-based supervising and reconditioning works; and (iii) unscheduled or corrective maintenance (OPEX 3 ), which stands for unplanned repairing operations. The evaluation of these cost categories in the proposed model is explained in detail in Section 6.2. Table 3 CAPEX breakdown: unitary costs. Adapted from [60]. Definition Value Units Cost of occupation of the farm (taxes) 2.00 € /m 2 Cost of carbon steel manufactured for the structure of the nacelle 8.00 € /kg Cost of manufactured carbon steel for PTO frame 4.00 € /kg Cost of manufactured fiberglass for the fairing 10.00 € /kg Cost of thrust bearing 40,000.00 € /MW Cost of brake system 2000.000 € /MW Cost of electrical generator 180,000.00 € /MW Cost of gearbox 35,000.00 € /MW Cost of high-speed shaft 3000.00 € /MW Cost of yaw system 12.00 € /kg Cost of cooling system 15,000.00 € /MW Cost of pressure oil system 15,000.00 € /MW Cost of condition monitoring system 110,000.00 € /MW Cost of protection and connection switches 12.00 € /kg Cost of control system 12.00 € /kg Cost of bilge system 12.00 € /kg Cost of compressed air system 12.00 € /kg Cost of circuit board 12.00 € /kg Cost of added elements 3.00 € /kg Cost of blades 40.00 € /m Cost of pitch system 500.00 € /m Cost of core of the rotor 1000.00 € /m Cost of low-speed shaft 500.00 € /m Cost of base support of the HEC structure 3.00 € /kg Cost of transition structure of the HEC 3.00 € /kg Cost of vertical column of the HEC 3.00 € /kg Cost of elaborated concrete of the ballast 0.20 € /kg Cost of special concrete bags 0.30 € /kg Cost of mooring system (catenary anchor leg mooring) composed by three stud–link chain lines 40.00 € /m Cost of concrete monopile foundation up to 30 m water depth 15,000.00 € /m Cost of protection switch 25,000.00 € /MW Cost of submarine connector 25.00 € /kg Cost of submarine connector installed in the base of the HEC 12.00 € /kg Cost of internal wiring 12.00 € /kg Cost of connection box 12.00 € /kg Cost of umbilical cables 250.00 € /m Cost of rectifiers 100,000.00 € /MW Cost of inverters 100,000.00 € /MW Cost of electrical boxes 20,000.00 € /MW Cost of transformers 40,000.00 € /MW Cost of transformation platform 3.00 € /kg Cost of submarine exportation cables 500.00 € /m Cost of ground exportation cables 150.00 € /m Table 4 CAPEX results (M € ) for the different HEC-site combinations considered. Cost item F-HEC—A F-HEC—B F-HEC—C F-HEC—D F-HEC—E F-HEC—IHE BF-HEC—E CAPEX 1 5.72 5.92 6.48 7.53 9.73 11.38 5.75 CAPEX 2 12.91 22.64 48.02 100.71 213.71 295.90 61.65 HECs 6.50 13.25 30.21 64.74 136.72 190.25 24.11 Foundations n.a. n.a. n.a. n.a. n.a. n.a. 13.54 Moorings 0.70 1.55 4.23 10.87 27.43 37.64 n.a. Cabling 5.71 7.84 13.58 25.10 49.56 68.01 24.00 CAPEX 3 0.15 0.33 0.99 1.77 3.53 5.64 1.40 Power system 0.02 0.04 0.13 0.23 0.47 0.75 0.19 Cabling 0.04 0.08 0.26 0.46 0.92 1.46 0.36 HECs 0.09 0.21 0.60 1.08 2.14 3.42 0.85 CAPEX 18.78 28.89 55.49 110.01 226.97 312.91 68.80 D.M. Fouz et al. Energy 282 (2023) 128373 9 6.2. Definition of OPEX model The approach proposed in this work addresses the abovementioned limitations of current OPEX models by considering: (i) high-resolution site-specific numerical modelling; and (ii) different O&M procedures, as a result of analysing HECs representative of various taxonomies (Section 3). The first aspect is of paramount importance to provide the required accuracy for the definition of weather windows suitable for the O&M works; the second one has an important influence resulting from the differences in the maintenance protocol of floating and bottom-fixed technologies (e.g., number of technicians required, type of vessel, duration of works, etc.). Bearing this in mind, the evaluation of OPEX 1 , OPEX 2 and OPEX 3 is developed as follows. The accurate estimation of OPEX 1 represents a complex task given the low number of real projects developed; thus, reference values should be provided by developers and stakeholders, in particular from the offshore sector [76]. In this regard, as in the case of the abovementioned simplified estimations of OPEX, it is usual to estimate this term as a function of the installed power or as a percentage of the CAPEX. The approach followed in this work is the second, with OPEX 1 computed as a 1.5% of CAPEX, which has shown to provide accurate results [25,72]. Regarding OPEX 2 , it encompasses very heterogeneous maintenance works, covering from cleaning and inspection activities to the replacement of minor components belonging to different systems of the hydrokinetic farm [75]. Thus, this term is the result of several cost items incurred during these works, whose amounts could be highly diverse (e. g., material, staff, transport, etc.). In this respect, the accurate definition of weather windows suitable for conducting maintenance works has a key role in driving the expenses included within the OPEX 2 term [60, 63], and therefore lead to an optimization of resources and costs [75]. The computation of these weather windows requires the definition of specific hydrodynamic conditions, usually in form of threshold values, considering the different weather parameters that could influence the maintenance works and their implication for the security of the infrastructure and workers involved. In this regard there exist different types of vessels to conduct maintenance operations, which can be divided in two large categories [77]: (i) Crew Transport Vessel (CTV) for offshore reparations, and (ii) an Offshore Supply Vessel (OSV), usually equipped with a Remoted Operated Vehicle (ROV), in the case of onshore works. OSV operation requires specific wave, wind and current conditions, whereas CTV operation is only limited in terms of wave height [77]; however, given that specific specialized workers (e.g., divers or Table 5 Hydrodynamic thresholds for the operation and maintenance works using OSV and CTV vessels. Weather criteria OSV O&M CTV O&M Significant wave height, H s (m). Safety and (max.) values 1.50 (2.00) 1.20 (1.50) Tidal currents velocity, V tc (m/s) 1.00 1.00 Wind velocity at 10 m height, U 10 (m/s) 10.00 10.00 Fig. 8. Sketch of the operational protocol for offshore (above) and onshore (below) unplanned reparations (OPEX 3 ). D.M. Fouz et al.