Delivering energy from hybridised offshore wind-wave parks considering electricity and hydrogen options: an optimisation approach

Contents lists available at ScienceDirect Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan Delivering energy from hybridised offshore wind-wave parks considering electricity and hydrogen options: an optimisation approach Sofia Varotto a, b iD , Ehsan Kazemi-Robati b iD , Bernardo Silva a, b,∗ iD a Faculty of Engineering, University of Porto, Porto, Portugal b Center of Power and Energy Systems, INESC TEC, Porto, Portugal ARTICLE INFO Keywords: Hybrid offshore park Wind power Wave power Offshore hydrogen Battery energy storage Optimal sizing A B S T R A C T Research around the co-location of different renewable energy technologies in offshore sites is increasing due to the potential complementarity of different sources that could decrease the power output variability, and increase reliability. However, further decrease of the power fluctuations and higher economic profitability could be achieved with energy storage. In this work, a model is developed for optimal sizing and energy management of energy storage and delivery solutions to accommodate the hybridisation of an offshore wind park. A set of options is considered for energy storage: the integration of a battery energy storage system (BESS), hydrogen production for direct sale or hydrogen/fuel cell system. For energy delivery, an expansion of the transmission cable, hydrogen pipeline or transportation by ship is evaluated. The case study used to test the model is the offshore farm WindFloat Atlantic located near the coast of Viana do Castelo, Portugal, which is proposed to be hybridised with wave energy converters (WEC). Sensitivity analyses are performed on possible components’ cost variations, hydrogen shipping frequency or sale price. The results show that hydrogen production from the studied offshore hybrid park is profitable, and the transmission through submarine pipeline is competitive with electrical connections by cable. The highest profitability is achieved when pipeline and cable expansion are combined. Hydrogen transportation by ship also appears profitable, in the eventuality that additional submarine transmission facilities cannot be installed. 1. Introduction The effects on the environment of the emission of greenhouse gases, particularly carbon dioxide, have been a concern for the past decades, leading to the awareness that a drastic reduction in fossil fuel consumption is needed to limit the ongoing climate change. In accordance with internationally shared resolutions and agreements towards the decarbonisation of the electrical energy sector, the governments of many countries are implementing initiatives to boost the growth of renewable electricity generation, according to the local availability of primary renewable energy sources (RES). On the other hand, the progress of research and technological advancement, together with the increasing commercialisation of RES generation technologies, is making renewable power plants more and more competitive respect to traditional fossil fuel powered plants. In particular, renewable plants have been expanding to offshore sites, due to the higher availability of areas for installation and of natural resources such as wind, solar and different forms of ocean energy, namely waves, tides or currents. While the environmental benefits of renewable energy are clear, and the economic ones are rising, complications are also emerging from the growing share of fluctuating generation in the energy mix. The dependence of generation on variable and only partially predictable natural resources often creates mismatches between their power output and the electricity demand. Hybrid farms, where generators fed by different renewable sources are located, are emerging in the renewable energy panorama due to their promising features. Co-locating sources with different generation schedules can reduce the variability of the overall power output, particularly when the two sources exhibit temporal complementarity. Although most literature around hybrid farms focuses on onshore applications, many studies have been developed in more recent years around the co-location of renewable sources in sea or ocean sites [1]. Installing different RES technologies at the same site can reduce the investment and maintenance costs. For instance, in offshore farms the electrical connection to shore, which accounts for a significant part of the total installation cost, ∗ Corresponding author at: Faculty of Engineering, University of Porto, Porto, Portugal. Email address: [email protected] (B. Silva). https://doi.org/10.1016/j.segan.2025.101846 Received 13 December 2024; Received in revised form 7 March 2025; Accepted 23 July 2025 Sustainable Energy, Grids and Networks 43 (2025) 101846 Available online 25 July 2025 2352-4677/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). S. Varotto, E. Kazemi-Robati and B. Silva Nomenclature Other symbols S Set of cable sections Parameters Δ𝑡Sampling time 𝑚 𝑟𝑎𝑡𝑒𝑑 H2 ,𝑝 Rated hydrogen mass flow of the pipeline 𝜂 𝑓Fuel cell system efficiency 𝜂 𝑐𝑜𝑚𝑝 Compressor efficiency 𝜂 𝑐𝑜𝑛𝑣 Battery converter efficiency 𝜂 𝑒𝑙 Electrolyser efficiency 𝜂 𝑟𝑒 Rectifier efficiency 𝜋 𝑒 (ℎ)Hourly electricity day-ahead market price 𝜋 ℎHydrogen price 𝑐 𝑖,𝑥 Unitary investment cost of component 𝑥 𝑐 𝑜,𝑥 Unitary operation and maintenance cost of component 𝑥 𝑑𝑏 Discharge duration of battery cells 𝑒 𝑐𝑜𝑚𝑝,H2 Energy consumption of compressor per mass of hydrogen 𝑒 H 2 Specific energy of hydrogen 𝑒 𝑟𝑜,H2 𝑂Energy desalination consumption of system per mass of water 𝑓 𝑎Annualisation factor 𝑓 𝑟,𝑥 Replacement factor of component 𝑥 𝐿 𝑥Lifetime of component 𝑥 𝐿 𝑝𝑎𝑟𝑘 Lifetime of the park 𝑚𝑟𝑎𝑡𝑒𝑑 H2 ,𝑠ℎ Rated hydrogen mass of the tanker ship 𝑚 𝑟𝑎𝑡𝑒𝑑 H2 ,𝑡 Rated hydrogen mass of the tank 𝑁Number of hours in a year 𝑛 𝑤𝑒𝑐 Number of wave energy converters 𝑛𝑤𝑡 Number of wind turbines 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑏𝑐 Power rated of the battery cell 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑒𝑙 Power rated of the electrolyser cell 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑓𝑐 Power rated of the fuel cell 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑝𝑎𝑟𝑘 Power of rated the park 𝑃 𝑔,𝑏𝑎𝑠𝑒 (ℎ) Hourly power to the grid in base case 𝑃𝑝𝑜𝑡 (ℎ) 𝑝𝑎𝑟𝑘 Hourly power potential from the park 𝑃 𝑤𝑒𝑐 (ℎ)Hourly power from a wave energy converter 𝑃𝑤𝑡 (ℎ) Hourly power from a wind turbine 𝑟 Interest rate 𝑅𝑒𝑣 𝑦Yearly revenues of the project 𝑆𝑝𝑟𝑒 𝑐 Apparent power rating of the pre-existing cable 𝑆 𝑐,𝑠𝑒𝑐 Apparent power rating of the cable of section 𝑠𝑒𝑐 𝑠𝑤 𝑒𝑙 (ℎ)Electrolyser switch 𝑡 H2 𝑠𝑎𝑙𝑒 Hydrogen shipping period 𝑣(ℎ)Hourly wind velocity Variables 𝜎 𝑏Battery system size 𝜎 𝑐Additional transmission cables size 𝜎 𝑓Fuel cell system size 𝜎 ℎHydrogen production system size 𝜎 𝑝Pipeline size 𝜎 𝑡Tank size 𝜎 𝑥Size of component 𝑥 𝐸 𝑏(ℎ) Hourly value of energy in the battery system 𝑚 H2 ,𝑒𝑙 (ℎ)Hourly hydrogen mass flow from the electrolysers 𝑚 H 2,𝑓 𝑐 (ℎ) massHourly hydrogen flow to the fuel cell system 𝑚 H 2 ,𝑠𝑜𝑙𝑑 (ℎ) flow Hourly hydrogen mass sold 𝑚 H2,𝑡(ℎ) Hourly hydrogen mass in the tank 𝑛 𝑏𝑐 Number of battery cells 𝑛𝑐 ,sec Number of cables of section sec 𝑛𝑒𝑙 Number of electrolyser cells 𝑛𝑓 𝑐 Number of fuel cells 𝑛𝑠ℎ (ℎ) Number of tanker ships per hour 𝑃 𝑖𝑛 (ℎ) 𝑏 Hourly power input of the battery system 𝑃 𝑜𝑢𝑡( 𝑏ℎ)Hourly power output of the battery system 𝑃𝑐 (ℎ)Hourly power through the transmission cable 𝑃𝑓 (ℎ) Hourly power from fuel cell system 𝑃𝑔 (ℎ) Hourly power to the grid 𝑃ℎ (ℎ)Hourly power to hydrogen production system 𝑃𝑐 𝑜𝑚𝑝(ℎ) Hourly power to hydrogen compressor 𝑃𝑒𝑙 (ℎ) Hourly power to electrolysers 𝑃𝑝𝑎𝑟𝑘 (ℎ) Hourly power from the park 𝑃𝑟𝑜 (ℎ) Hourly power to reverse osmosis desalination can be shared [2]. The utilisation of the available area and the infrastructure can be more efficient than for single-source offshore farms, as was demonstrated by López et al. [3]. Since the potential benefits of co-locating different renewable energy technologies are being investigated, the installation of energy converters using different RES in pre-existing wind parks is being suggested by some studies. Benefits of hybridising offshore wind farms (OWFs) with floating photovoltaic (FPV) in terms of utilisation of the transmission cable were addressed by Golroodbari et al. [4], and increase in energy yield and reduction in variability were reported by Huang and Iglesias [5]. A stochastic optimisation framework was developed by Kazemi-Robati et al. [6] to evaluate the best combinations of wind, FPV and wave to hybridise existing OWFs in selected sites. As wind power is progressively expanding beyond the shallow seas, thanks to the development of floating platforms, ocean energy sources become interesting for hybridisation, as their power density increases in deep waters [2]. The European Union set a goal of 1 GW of marine energy installed capacity by 2030, and 40 GW by 2050 [7], however, the development of ocean energy is slowed down by a series of challenges, related to technology readiness, environmental concerns and availability of connection infrastructures to the grid [8]. This last issue could be mitigated by installing wave or tidal energy converters in co-location with OWFs. The combination of OW and wave farms presents promising synergies between these two generation technologies [2]. A study on co-located OW and WEC in California [9] reported a significant increase in the reliability of a hybrid system respect to wave-only or wind-only configurations. Regarding economic benefits, [10] reports an assessment of hybrid wind-wave farms in comparison to single source farms, by calculating the LCOE considering different percentages of shared costs— infrastructure and operation—for a case study in Norway. The focus of the study by Astariz et al. [11] is on the shadow effect, namely the reduction of wave height within the area of the farm due to wave energy converters (WEC), leading to reduced costs for farm maintenance that become feasible in more adverse climate periods. Economic benefits can stem from the co-location of WEC with other renewables, as stated in [12], due to the higher electricity prices captured by wave power generation respect to the prices at which wind and solar farms normally sell electricity. The economic competitiveness of wave energy farms with OW parks in specific locations was proven by Joensen and Bingham [13], which addressed different sites and wave energy technologies, obtaining for the best case LCOE of 61.8 e/MWh. Higher but still competitive LCOE was found by Ramos et al. [14] for the co-location of a wave energy technology, namely point absorbers, in the offshore farm WindFloat Atlantic, near Viana do Castelo, Portugal. A recent study [15] assessed the co-location potential of floating wind and WEC off the Sustainable Energy, Grids and Networks 43 (2025) 101846 2 S. Varotto, E. Kazemi-Robati and B. Silva coast of continental Portugal, using a Co-Location Feasibility index developed by Astariz and Iglesias [16]. The study concluded that the site of WindFloat Atlantic is the one with the highest generation potential for both wind and wave resources among the examined ones. However, both resources were found to have a higher variability than in other sites, posing challenges for reliable operation of a hybrid farm. To address this issue, one possible solution can be offered by energy storage systems (ESS). As an example, [17] presents a methodology to estimate the energy storage capacity required to achieve energy dispatchability to a local demand from an offshore farm, comparing only-wind and wind-wave configurations. The required storage capacity for hybrid was found to be overall lower than for only-wind, but still necessary to meet the local demand. Several studies are addressing the application of energy storage technologies to offshore farms, in order to understand the most suitable solutions. Arellano-Prieto et al. [18] examined a vast catalogue of energy storage technologies and assessed their suitability for offshore applications. The combination of batteries and hydrogen emerged as an interesting solution, due to some complementarity between their features, such as the operational time scale. A comprehensive assessment of marine renewable energy generation technologies and energy storage systems was carried out by Wang et al. [19], considering also innovative technologies in early stages of development, such as buoyancy and gravity energy storage. Once again, battery energy storage systems (BESS) appear to be the most suitable technology. The optimal sizing of BESS for hybrid offshore farms was assessed in [20], considering battery placement offshore and onshore. As mentioned by Arellano-Prieto et al. [18], hydrogen-based storage systems are an appealing option for offshore electrical energy storage. A study on energy management strategy for battery and hydrogen based ESS applied to hybrid offshore parks proved the effectiveness of this system in reducing power variability and increasing the energy yield of these parks [21]. On the other hand, many studies and projects are being developed around offshore hydrogen production (OHP) for direct hydrogen sale. A review from Ramakrishnan et al. [22] highlighted the potential of OHP from renewables and seawater for increasing the capacity factors of electrolysers. It also underlined the importance of developing integration solutions for locations with limited connections to the electrical grid and optimising the capacity and design of OHP facilities. An assessment of hydrogen production from the WindFloat Atlantic OWF was carried out by Lucas et al. [23]. In the reported case study, hydrogen production capacity was sized to cover most (70 %–93 %) of wind installed capacity. Among the considered scenarios, the lowest hydrogen price that made the project economically feasible was found to be 4.25 e/kg. An optimisation of the hydrogen system sizing could bring more economically feasible configurations to emerge in similar case studies. The optimisation of hydrogen production from OW farms has been addressed in different studies. Convex programming was used by Ma et al. [24] to optimise the sizing and energy management of a hybrid hydrogen-battery ESS for an OWF, and it showed that such ESS considering hydrogen sale can bring a relevant profit improvement. Similar result was obtained by Hou et al. [25], even considering hydrogen prices of 2 e/kg. On the other hand, hydrogen for power-to-power applications— meaning re-converted into power with fuel cells—was found to be not economically convenient. In [26] the same conclusion was reached regarding hydrogen-fuel cell systems, but enriched the storage options by considering ammonia, which became competitive with hydrogen for long-term storage requirements. The authors also concluded that the profitability of hydrogen production systems from OW will increase along with the penetration of renewables in the grid. Different configurations of hydrogen production systems from OW power have been assessed in literature, as for instance in [27] and [28], where the placement of electrolysers onshore, offshore centralised and offshore decentralised are compared. Rogeau et al. [27] concluded that offshore installations will become more profitable in the next decades, even for farms relatively close to land. [29] compared five different scenarios for OW power delivery to land including submarine cable, hydrogen production and transportation by pipeline or ship, hydrogen sale and re-generation of electricity by fuel cell. For the considered system and study case, only cable and hydrogen sale were convenient options. Similarly, in [30], different pathways for electrolysis-based hydrogen production from OW power, including electrolysis on land or offshore, and several storage technologies (compressed, liquid, converted into ammonia or through liquid organic hydrogen carriers), were evaluated. Also d’Amore Domenech et al. [31] evaluated hydrogen transportation by pipeline and by ship—compressed or liquid—for different distance scenarios (100-5000 km), concluding that for shorter distances pipeline is found to be the most economically convenient option. In the reviewed literature, a lack of studies around the integration of energy storage solutions including hydrogen with hybrid offshore farms was found. Moreover, the design of OHP systems’ configurations for hybrid farms is rarely addressed with an optimisation approach. This can lead to sub-optimal designs of energy storage and delivery systems that prove to be economically unfeasible. A comparison with other studies in the examined literature is presented in Table 1. The present paper envisages different options for delivering and storing energy generated by an offshore wind park, hybridised with WEC to double the installed power of the park. The expansion of cable connection capacity to land is evaluated first, and then different options including energy storage—batteries and/or hydrogen—and transmission of hydrogen to land through pipeline or ship are considered. The sizing and operation of energy storage and transmission systems are optimised to obtain the most economically convenient design and operation for different considered configurations. Finally, a sensitivity analysis of the optimisation results to the variation of certain parameters is carried out. The main contributions of this study can be summarised as follows: • The development of a model for optimal combined sizing and energy management of an energy storage and transmission system including batteries, hydrogen—transported by ship or pipeline—and cable for hybridised offshore wind farms. • The inclusion in the optimisation problem of the sizing of power transmission capacity from the offshore farm to land in the form of electrical cable or hydrogen submarine pipeline, separately or in combination. • A set of sensitivity analyses of the sizing to the variation of the most uncertain input parameters, such as component costs, hydrogen prices and shipping frequency, considering a set of different ESS configurations. The rest of the paper is organised as follows: Section 2 presents the methodology followed and the mathematical model formulated for this study; in Section 3, the case study is described and the input data are presented; the results are displayed and discussed in Section 4 together with sensitivity analyses; and finally conclusions are drawn from the outcomes of this study in Section 5. 2. Methodology The present study is an evaluation of different options for energy storage and transmission systems applied to an offshore hybrid park. It is carried out through the optimal sizing and energy management of the mentioned system in a set of possible configurations. The optimisation problem formulated is mixed-integer linear, with the net present value (NPV) as objective function to be maximised. The optimisation is solved using MATLAB R2024a. 2.1. Mathematical model formulation The mathematical model is formulated to represent an offshore hybrid wind-wave park, connected to the grid by a pre-existing cable of fixed capacity. The components that will be optimally sized are additional transmission cables, BESS, hydrogen production system, tank and pipeline, and fuel cell system. Tanker ships of fixed capacity transporting Sustainable Energy, Grids and Networks 43 (2025) 101846 3 S. Varotto, E. Kazemi-Robati and B. Silva Table 1 Comparison of the present work with existing studies. Generation units Energy storage options Energy delivery options H 2 reconver sion - Energy sale Optimisation framework Offshore wind Wave energy con verters - BESS Onshore H 2 pro duction - Offshore H 2 pro duction - H 2 tanker ship H 2 pipeline Electrical export cable Fuel cell H 2 sale Electricity sale at market price ESS sizing Cable/ pipeline sizing Energy man age ment - - [17] ✓ ✓ ✓ ✓ ✓ [20] ✓ ✓ ✓ ✓ ✓ ✓ [21] ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ [22] ✓ ✓ ✓ ✓ ✓ [23] ✓ ✓ ✓ ✓ [24] ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ [25] ✓ ✓ ✓ ✓ ✓ ✓ ✓ [26] ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ [27] ✓ ✓ ✓ ✓ ✓ ✓ [28] ✓ ✓ ✓ ✓✓✓ [29] ✓ ✓ ✓✓✓✓ ✓ [30] ✓ ✓ ✓ ✓ ✓ ✓ ✓ [31] ✓ ✓ ✓ ✓ This study ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ hydrogen from the park to land are also modelled. The system operation is modelled through the hourly values of power among the components, energy in the BESS and hydrogen mass in the tank. All decision variables related to hourly values of power and energy are continuous, as well as the sizes of some components, such as hydrogen pipeline and tank. The charging and discharging components of the energy storage systems, namely the number of battery cells, electrolyzers and fuel cells, as well as the additional transmission cables are, however, represented by integer variables. For this study, a set of configurations of the energy storage and transmission system are evaluated, enabling or disabling the sizing of certain system components from one configuration to another. The symbols indicating the main variables and parameters used in the objective function and the constraints described further on are listed in the nomenclature at the beginning of this paper, some of them in hourly values indicated by (ℎ). 2.1.1. Net present value The formulation of the objective function is expressed in Eq. (1). It must be noted that, for the sake of this estimation of the net present value of the project, all the years along the lifetime of the park are assumed to be the same in terms of meteorological conditions and electricity market prices. Hence, the annual revenues from the considered year are simply annualised and summed to estimate the revenues along the whole lifetime. The optimisation problem is formulated as 1: maximise 𝑁𝑃 𝑉 = −[∑ 𝑥 𝜎 𝑥(𝑐𝑖,𝑥 + 𝑓 𝑎 𝑐 𝑜,𝑥) ]+ 𝑓 𝑎𝑅𝑒𝑣 𝑦 (1) Subject to the constraints that will be described in the following sections. In Eq. (1), 𝑅𝑒𝑣 represents the yearly revenues due to the energy 𝑦 storage and transmission system, calculated as in Eq. (2). The yearly revenues that the park would earn without said additional system, are calculated as the second term of Eq. (2) and subtracted from the total yearly revenues. 𝑅𝑒𝑣 𝑦 = 𝑁 ∑ ℎ=1 [𝑃𝑔(ℎ) 𝜋 𝑒(ℎ) + 𝑚 H 2,𝑠𝑜𝑙𝑑 (ℎ) 𝜋 H2 ] − 𝑁 ∑ ℎ=1 𝑃 𝑔,𝑏𝑎𝑠𝑒(ℎ) 𝜋 𝑒(ℎ) (2) In these formulas, 𝑥 is used for indexing the components, 𝑁is the number of hours in a year, 𝜎 𝑥is the size of the components, 𝑓 𝑎 the annualisation factor, 𝑐 𝑖,𝑥 and 𝑐 𝑜,𝑥 are the investment and operation costs respectively, and finally 𝜋 𝑒 (ℎ) is the hourly day-ahead electricity price and 𝜋 H2 is the hydrogen price. The annualisation factor used to refer all annual expenses—such as operation costs and revenues—along the study horizon to the initial year, is calculated as: 𝑓 𝑎 = 𝐿 𝑝𝑎𝑟𝑘 ∑ 𝑦=1 (1 + 𝑟) −𝑦(3) Where 𝐿 is 𝑝𝑎𝑟𝑘 the lifetime of the park and 𝑟 is the interest rate. The sizes of the components are expressed as: 𝜎 𝑏 = 𝑛 𝑏𝑐 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑏𝑐 (4) 𝜎 ℎ = 𝑛 𝑒𝑙 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑒𝑙 (5) 𝜎 𝑓 = 𝑛 𝑓𝑐 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑓𝑐 (6) 𝜎 𝑡 = 𝑚𝑟𝑎𝑡𝑒𝑑 H 2 ,𝑡 𝑒 H 2(7) 𝜎 𝑝 = 𝑚 𝑟𝑎𝑡𝑒𝑑 H 2 ,𝑝 𝑒 H 2(8) 𝜎 𝑐 = ∑ 𝑠𝑒𝑐∈S 𝑛 𝑐,sec 𝑆 𝑐,sec (9) Being 𝑛𝑏𝑐 , 𝑛𝑒𝑙 , 𝑛 and are integer variables, with subscripts , 𝑓𝑐 𝑛𝑐,sec 𝑏𝑐 𝑒𝑙 and 𝑓 𝑐 indicating battery cells, electrolysers and fuel cells respectively. Subscripts 𝑏, ℎ, 𝑓 , 𝑡, 𝑝 and 𝑐 stand for battery system, hydrogen pro duction system, fuel cell system, tank, pipeline and cable respectively, with sec being the index for cable sections. In particular, 𝑛𝑐 ,sec represents one variable for every considered cable size 𝑆𝑐 ,sec—namely the ones dis played in - - Table 3. 𝑙 is the distance from the point of common connection of the generation units of the park to the grid. The internal park cables between the units are outside the scope of this optimisation. 𝑒H 2 = 33.33 kWh/kg is the specific energy of hydrogen. Another integer variable is the number of ships 𝑛𝑠ℎ (ℎ)that collect and deliver hydrogen from the offshore production system to land, which accounts for one variable every time the ship transportation ⌊ is en ⌋ abled, therefore, within a year of park operation, there are 𝑁∕𝑡 H 2 𝑠𝑎𝑙𝑒 variables, with 𝑡H 2 being the shipping period in hours. In the NPV 𝑠𝑎𝑙𝑒 formulation, the investment cost for ships 𝑐 is considered to be nil 𝑖,𝑠ℎ as the ships are not purchased by the park operator but only rented, and the operation cost corresponding to the rent, 𝑐 , 𝑜,𝑠ℎ is multiplied by the total number of ships over a year: - 𝑛 𝑡𝑜𝑡 𝑠ℎ = 𝑁 ∑ ℎ=1 𝑛 𝑠ℎ (ℎ) (10) The size variables are all constrained to be non negative. 𝜎 𝑥 ≥ 0(11) Depending on the selected configuration, the size variables of the components that are not enabled are constrained to be null. Sustainable Energy, Grids and Networks 43 (2025) 101846 4 S. Varotto, E. Kazemi-Robati and B. Silva The unitary investment costs 𝑐 𝑖,𝑥 associated with every component are calculated as follows, considering that not all components’ sizes are decision variables, since some of them are dependent on others—as for instance the rectifier which is sized depending on the size of the electrolyser. Thus, the costs of certain components are clustered in the NPV formulation, as follows: 𝑐 𝑖,𝑏 =𝑓 𝑟,𝑏𝑐 ⋅𝑐 𝑖,𝑏𝑐 𝑑 𝑏+𝑐 𝑖,𝑐𝑜𝑛𝑣 (12) 𝑐 𝑖,ℎ =𝑓 𝑟,𝑒𝑙 ⋅𝑐 𝑖,𝑒𝑙 +𝑐 𝑖,𝑟𝑜 +𝑐 𝑖,𝑟𝑒 +𝑐 𝑖,𝑐𝑜𝑚𝑝 (13) 𝑐 𝑖,𝑓 =𝑓 𝑟,𝑓𝑐 ⋅𝑐 𝑖,𝑓𝑐 +𝑐 𝑖,𝑖𝑛𝑣 (14) Where 𝑑𝑏 is the charging/discharging duration of the battery, chosen to be 1 h. The subscripts 𝑐𝑜𝑛𝑣, 𝑟𝑜, 𝑟𝑒, 𝑐𝑜𝑚𝑝 and 𝑖𝑛𝑣 stand for battery con verter, reverse osmosis desalination system, rectifier, compressor and inverter respectively. The replacement factor 𝑓𝑟,𝑥 being 𝑥 ∈ [𝑏𝑐, 𝑒𝑙, 𝑓 𝑐] is used to refer the expenses for replacement of components with a shorter lifetime 𝐿 < 𝐿 (battery cells, electrolysers and fuel cells) 𝑥 𝑝𝑎𝑟𝑘 to the initial year: - 𝑓 𝑟,𝑥 =⌈𝐿 𝑝𝑎𝑟𝑘 𝐿 𝑥⌉ −1 ∑ 𝑗=1 (1 + 𝑟) −𝑗𝐿𝑥 (15) Moreover, when the specific component is placed offshore, additional costs must be added to account for the floating platform that has to be built to accommodate it: 𝑐 for the battery system, hydrogen 𝑖,𝑝𝑙 for ,𝑏 𝑐 𝑖,𝑝𝑙,ℎ production system and fuel cell system, and 𝑐𝑖,𝑝𝑙 for ,𝑡 the tank. Unitary operation costs of the above mentioned components are calculated in the same way as in Eqs. (12)–(14), substituting 𝑐 𝑜 for 𝑐 𝑖 . 2.1.2. RES generation units The hybrid park is composed of wind turbines and WEC. The power output 𝑃 (ℎ) of the wind turbines is calculated as a function of 𝑤𝑡 the hourly value of the wind velocity 𝑣(ℎ) at the height of the nacelle, with an approximation of the typical power curve [32] given by (16). 𝑃 𝑤𝑡(ℎ) =⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 0 for 0 ≤ 𝑣(ℎ) ≤ 𝑣 𝑐𝑖 1 2𝑐 𝑃 𝜌 𝑎 𝐴 𝑤𝑡 𝜂 𝑤𝑡 𝑣(ℎ) 3for 𝑣 𝑐𝑖 < 𝑣(ℎ) ≤ 𝑣 𝑟𝑎𝑡𝑒𝑑 𝑃𝑟𝑎𝑡𝑒𝑑 𝑤𝑡 for 𝑣 𝑟𝑎𝑡𝑒𝑑 < 𝑣(ℎ) ≤ 𝑣 𝑐𝑜 0 for 𝑣(ℎ) > 𝑣 𝑐𝑜 (16) Being 𝑣 𝑐𝑖 , 𝑣 𝑐𝑜 and 𝑣 𝑟𝑎𝑡𝑒𝑑 are the wind velocities of cut-in, cut-off and rated respectively, 𝑐𝑃 is the power coefficient, 𝜂𝑤 𝑡 is the electrical efficiency of the turbine, 𝜌 is the air density, considered constant 𝑎 and uniform, and 𝐴𝑤𝑡 is the rotor area of the wind turbine. The power output 𝑃 (ℎ) from the WEC is calculated as a function 𝑤𝑒𝑐 of the hourly wave height and period, using the power matrix from CorPower [33 𝑝𝑜𝑡 ]. The overall hourly generation potential 𝑃( ) of the 𝑝𝑎𝑟𝑘 ℎ park is the sum of the power from these units: 𝑃 𝑝𝑜𝑡 𝑝𝑎𝑟𝑘(ℎ) = 𝑛 𝑤𝑡 𝑃 𝑤𝑡 (ℎ) + 𝑛 𝑤𝑒𝑐 𝑃 𝑤𝑒𝑐 (ℎ) (17) The actual power output of the park 𝑃 (ℎ) is adecis 𝑝𝑎𝑟𝑘 ion variable, since the optimal energy management can involve curtailment due to the transmission limitations or negative electricity prices, that can make generation unfeasible or uneconomical. The power generated is therefore subject to: 0 ≤ 𝑃 𝑝𝑎𝑟𝑘(ℎ)≤ 𝑃 𝑝𝑜𝑡 𝑝𝑎𝑟𝑘(ℎ) (18) 2.1.3. Transmission cable The power flowing through the cable is considered to be always positive, so that the park cannot purchase electricity from the grid. Furthermore, this power is subject to an upper bound equal to the cumulative capacity—considered to be equal to the apparent power—of 𝑝𝑟𝑒 the pre-existing cable 𝑆 𝑐 = 200 MVA and the additional ones sized in the optimisation: 0 ≤ 𝑃 𝑐 (ℎ) ≤ 𝑆 𝑝𝑟𝑒 𝑐+ 𝜎 𝑐(19) The power flowing through the cable is given by: 𝑃 𝑐 (ℎ) = 𝑃 𝑝𝑎𝑟𝑘(ℎ) − 𝑃 𝑖𝑛 𝑏(ℎ) + 𝑃 𝑜𝑢𝑡 𝑏(ℎ) − 𝑃 ℎ(ℎ) + ∗ 𝑃 𝑓 (ℎ) (20) Being: ∗ 𝑃𝑓(ℎ) = { 𝑃𝑓(ℎ)if fuel cell offshore 0if fuel cell onshore (21) 2.1.4. Battery energy storage system The power flow in and out of the battery system is split between two variables, in order to be able to apply the efficiency of the converter to both flows while keeping the model linear. The optimisation ensures that the batteries are not charged and discharged at the same time, since that would cause a power loss due to the converter efficiency. The power charging and discharging the BESS is subject to (22), (23). 0 ≤𝑃 𝑖𝑛 𝑏 (ℎ) ≤ 𝜎 𝑏𝜂 −1 𝑐𝑜𝑛𝑣 (22) 0 ≤𝑃 𝑜𝑢𝑡 𝑏(ℎ) ≤ 𝜎 𝑏 𝜂 𝑐𝑜𝑛𝑣 (23) The energy balance in the battery cells is: 𝐸 𝑏(ℎ) = 𝐸 𝑏(ℎ − 1) + [𝑃𝑖𝑛 𝑏(ℎ − 1) 𝜂 𝑐𝑜𝑛𝑣 − 𝑃 𝑜𝑢𝑡 𝑏(ℎ − 1)∕𝜂 𝑐𝑜𝑛𝑣 ]Δ𝑡 (24) Being Δ𝑡 = 1 h. To avoid excessive battery degradation, the state of charge of battery cells is typically maintained within a certain range, for this study supposed to be [20 %,100 %]. 20 % ⋅ 𝜎 𝑏 𝑑 𝑏≤ 𝐸 𝑏(ℎ) ≤ 𝜎 𝑏 𝑑 𝑏(25) The state of charge at the beginning and at the end of the year must be the same: 𝐸 𝑏 (𝑁) = 𝐸 𝑏(1) (26) 2.1.5. Hydrogen system The hydrogen system is composed of hydrogen production system— including desalination, electrolyser, rectifier and compressor—hydrogen storage tank, re-conversion system—fuel cell and inverter—and hydrogen transmission, which can be implemented with tanker ships delivering hydrogen to land at a given frequency, or with the installation of a submarine pipeline that can transport hydrogen continuously. The modelling of the hydrogen system components is described in the following paragraphs. Production: To produce 1 kg of hydrogen, the power needed to desalinate ocean water, to split it by electrolysis—including the efficiency of the rectifier—and to compress hydrogen to a pressure that is suitable for storage must be considered: 𝑃 ℎ(ℎ) = 𝑃 𝑟𝑜(ℎ) + 𝑃 𝑒𝑙(ℎ) 𝜂 −1 𝑟𝑒 + 𝑃 𝑐𝑜𝑚𝑝 (27) The hydrogen production system is considered to work only when the power that can be generated by the park is at least 5 % of the installed wind and wave power. This in ensured with a binary switch parameter 𝑠𝑤 (ℎ)[ 𝑒𝑙 24]: 𝑠𝑤 𝑒𝑙 (ℎ) = {0 for 𝑃 𝑝𝑜𝑡 𝑝𝑎𝑟𝑘(ℎ) < 5 % 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑝𝑎𝑟𝑘 1 for 𝑃 𝑝𝑜𝑡 𝑝𝑎𝑟𝑘(ℎ) ≥ 5 % ⋅ 𝑃 𝑟𝑎𝑡𝑒𝑑 𝑝𝑎𝑟𝑘 (28) To maintain the model’s linearity, the mass flow of hydrogen produced by the electrolyser is considered to be directly proportional to the power Sustainable Energy, Grids and Networks 43 (2025) 101846 5 S. Varotto, E. Kazemi-Robati and B. Silva consumed, which is considered to be an acceptable approximation for similar studies [26]. 𝑚 H 2 ,𝑒𝑙 (ℎ) = 𝑃 𝑒𝑙(ℎ) 𝜂 𝑒𝑙 𝑒 −1 H 2(29) The minimum mass flow of hydrogen produced is set at 5 % of the electrolyser’s rated mass flow: 𝑠𝑤 𝑒𝑙 (ℎ) ⋅ 5 % ⋅ 𝑚 𝑚𝑎𝑥 𝑒𝑙 ≤ 𝑚 𝑒𝑙 (ℎ) ≤ 𝑠𝑤 𝑒𝑙 (ℎ)𝑚 𝑚𝑎𝑥 𝑒𝑙 (30) Meaning that: 𝑠𝑤 𝑒𝑙 (ℎ) ⋅ 5 % ⋅ 𝜎 ℎ ≤ 𝑃 𝑒𝑙(ℎ) ≤ 𝑠𝑤 𝑒𝑙 (ℎ) 𝜎 ℎ(31) The reverse osmosis desalination system processes ocean water to obtain distilled water to feed the electrolyser, with an energy consumption of 𝑒 𝑟𝑜,H 2 O = 5 ⋅ 10−6 MWh∕kgH 2 O [29]. Considering that 9 kg of water are needed to produce 1 kg of hydrogen, the power consumption per mass flow of hydrogen is given by: 𝑃 𝑟𝑜(ℎ) = 9 ⋅ 𝑒 𝑟𝑜,H 2 O 𝑚 H 2 ,𝑒𝑙 (ℎ) (32) The power consumed by the compressor to increase the pressure of hydrogen to the desired level is calculated as: 𝑃 𝑐𝑜𝑚𝑝(ℎ) = 𝑒 𝑐𝑜𝑚𝑝,H 2 𝑚 H 2 ,𝑒𝑙 (ℎ) (33) Being 𝑒 𝑐𝑜𝑚𝑝,H the 2 energy needed to compress 1 kg of hydrogen [ 24]: 𝑒 𝑐𝑜𝑚𝑝,H 2=𝑐 𝑐𝑝 𝑇 𝑖𝑛 𝜂 𝑐𝑜𝑚𝑝 (𝑝 𝑜𝑢𝑡 𝑝 𝑖𝑛 )𝑘−1 𝑘(34) Where 𝑐𝑐 is 𝑝 the specific heat at constant pressure of hydrogen, 𝑇 𝑖𝑛 the 𝑝𝑜𝑢𝑡 inlet temperature, 𝑝𝑖𝑛 the pressure ratio and 𝑘 the ratio of specific heats of hydrogen. Storage: The mass balance inside the pressure tank is modelled as: 𝑚 H 2 ,𝑡 (ℎ) = 𝑚 H2 ,𝑡 (ℎ − 1) + [ 𝑚 H 2 ,𝑒𝑙 (ℎ − 1) − 𝑚 H 2 ,𝑓 𝑐 (ℎ − 1) − 𝑚 H 2 ,𝑠𝑜𝑙𝑑 (ℎ − 1) ] Δ𝑡(35) Constrained by its size 𝑚 𝑟𝑎𝑡𝑒𝑑 H= 2,𝑡 𝜎 H 𝑡∕𝑒, 2 which is a decision variable, as: 0 ≤ 𝑚 H 2 ,𝑡 (ℎ) ≤𝑚 𝑟𝑎𝑡𝑒𝑑 H 2 ,𝑡 (36) Shipment: The tank is considered to be emptied—fully or partially— with a −1 certain frequency 𝑓H corresponds 2𝑠𝑎𝑙𝑒= 𝑡 . 2𝑠𝑎𝑙𝑒 This H to the frequency of withdrawal by truck in the case where the tank is placed onshore, or by ship in the case where hydrogen is stored offshore and transported to land on tanker ships, in which case the trucks are con sidered to take away the hydrogen as soon as it arrives on land. This is modelled as: - 𝑚H 2 ,𝑠𝑜𝑙𝑑 (ℎ)≥0(37) 𝑚H 2 ,𝑠𝑜𝑙𝑑 (ℎ)⋅Δ𝑡≤ {0 if ℎ∕𝑡 H 2 𝑠𝑎𝑙𝑒 ∉ N 𝑚 H 2 ,𝑡 (ℎ)if ℎ∕𝑡 H 2 𝑠𝑎𝑙𝑒 ∈ N(38) Being N the set of natural numbers. The integer variable corresponding to the hourly number of ships with fixed capacity 𝑚 𝑟𝑎𝑡𝑒𝑑 that H 2 ,𝑠ℎ collect hydrogen and transport it to land constrains the mass flow exiting the tank as: 𝑚 H 2 ,𝑠𝑜𝑙𝑑 (ℎ) ⋅ Δ𝑡 ≤ 𝑛 𝑠ℎ(ℎ)𝑚 𝑟𝑎𝑡𝑒𝑑 H 2 ,𝑠ℎ (39) Pipeline: When the sizing of a hydrogen pipeline is enabled, transportation by ship is no longer considered and the tank is placed onshore, so that it does not require an additional platform. For this reason, the pipeline directly connects the hydrogen production system with the tank onshore, hence its size is directly dependent on the electrolyser size. The mass flow of hydrogen through the pipeline is the same as the one exiting the electrolyser: 𝑚 H 2 ,𝑝 (ℎ) = 𝑚 H 2 ,𝑒𝑙 (ℎ) (40) and subject to: 𝑚 H 2 ,𝑝 (ℎ) ≤ 𝜎 𝑝 𝑒 H 2 (41) Re-conversion: Hydrogen can be “re-converted” into electricity through a fuel cell, whose power output is assumed to be a linear function of the hydrogen mass flow, and is expressed as: 𝑃 𝑓(ℎ) = 𝜂 𝑓𝑒 H 2 𝑚 H 2 ,𝑓 𝑐 (ℎ) (42) Constrained by the size of the fuel cell: 𝑃 𝑓(ℎ) ≤ 𝜎 𝑓(43) The efficiency of the inverter and the fuel cell are accounted for together as efficiency of the fuel cell system 𝜂𝑓 . 2.1.6. Grid connection The overall power balance of the system, calculated at the onshore point of connection with the grid, is given by: 𝑃 𝑔(ℎ) = 𝑃 𝑝𝑎𝑟𝑘 (ℎ) − 𝑃 𝑖𝑛 𝑏(ℎ) + 𝑃 𝑜𝑢𝑡 𝑏(ℎ) − 𝑃 ℎ(ℎ) + 𝑃 𝑓 (ℎ) (44) Lastly, a constraint on maximum power ramping—upwards and downwards—is considered to be applied by the grid operator to the point of connection, equal to 10 % of the pre-installed cable capacity, to limit the power output fluctuations: |||𝑃 𝑔 (ℎ) − 𝑃 𝑔(ℎ − 1)|||≤ 10 % 𝑃 𝑝𝑟𝑒 𝑐(45) 3. Case study The optimisation is performed taking an existing offshore floating wind farm, WindFloat Atlantic, 20 km far from the shore of Viana do Castelo, Portugal, as reference. The currently existing farm includes three Vestas V164 wind turbines of 8.4 MW each, and is connected to shore through a submarine AC cable, 20 km long, operating at the voltage of 60 kV. The cable is however sized to be upgraded to a 200 MVA capacity at a voltage of 150 kV, planned for 2030 [34]. For this case study, an expansion of the farm is hypothesised. 20 wind turbines are added, for a total of 193.2 MW installed. In addition, it is imagined that the park is hybridised with the installation of 500 WEC from CorPower, point absorber type with nominal power of 400 kW (200 MW total), considering the high availability of the wave resource in the area. The addition of WECs increases the annual energy generation of the park by ∼150 % due to the high capacity factor of WECs, even considering the limited transmission capacity of the pre-existing cable (200 MVA), which causes a curtailment of ∼18 % of the total generation potential of the installed units. To reduce this curtailment and increase the economic profitability of the park, different strategies for enhancing energy transmission capacity and energy storage are analysed in this study. 3.1. Market and weather data For the considered case study, year-long hourly time series of real data are used to optimise the energy management of the park throughout a year. The day-ahead hourly spot electricity prices for Portugal are taken from Ember [35]. The year chosen is 2023, in order to use the most recent available data, and since the electricity market prices have been stabilising after peaking in 2021 and 2022, as visible in Fig. 1. Sustainable Energy, Grids and Networks 43 (2025) 101846 6 S. Varotto, E. Kazemi-Robati and B. Silva 2019 2020 2021 2022 2023 Year 0 100 200 300 400 500 600 Day-ahead electricity prices Fig. 1. Distribution of electricity day-ahead market prices in the last five years in Portugal. 2-4 4-6 6-8 8-10 >10 H 2 0% 10% 20% 30% 40% Share of European hydrogen valleys Fig. 2. Distribution of H 2 sale price in European hydrogen valleys [39]. Hydrogen is currently sold and purchased through bilateral con tracts between producers and consumers, and not through a pool market system. Since a detailed market price for hydrogen is not available, a constant price 𝜋 Halong 2 the year is considered as 4.23 e/kg [ - 36], value coherent with the average sale price of hydrogen in European hydrogen valleys, defined as geographical areas where significant amounts of hydrogen are produced and consumed in an integrated ecosystem, according to [37], as shown in Fig. 2. The meteorological data for wind speed, wave height and period are taken from Copernicus Era5 [38]. In the considered year, the site presented a mean wind velocity of 7.84 m/s, and capacity factors for wind power of 30.86 % and for wave of 59.20 %. 3.2. Components data Significant cost reductions are projected in literature for many of the considered technologies, particularly electrolysers, batteries and fuel cells [40,41]. A project like the one considered for this case study could be developed and commissioned in a future scenario when the components’ costs have decreased, hence, cost projections for 2030 are also taken into consideration. However, the cost of several components, namely the most mature technologies such as desalination system, compressor, pipeline and tank, is considered to remain stable in the coming years. The costs of most components are taken from the report by Mongird et al. [42] and the values for year 2023 are calculated by linear interpolation. The costs for battery system components are computed as [43]: 𝑐 𝑖,𝑏 = 𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖,𝑏 + 𝑐 𝑝𝑜𝑤𝑒𝑟 𝑖,𝑏 ∕𝑑 𝑏(46) Table 2 Component costs, projections for 2023 and 2030. Component Investment cost Unit 2023 2030 Battery cells 168.81 115.48 e/kWh Battery converter 235.10 202.66 e/kW Desalination system 7.99 7.99 e/kW Rectifier 104.91 89.29 e/kW Electrolyser cells 944.94 392.86 e/kW Compressor 35.71 35.71 e/kW Tank 18.00 18.00 e/kWh Fuel cells 1059.52 892.86 e/kW Fuel cell inverter 51.64 40.18 e/kW Pipeline 0.50 0.50 e/kW/km Battery platform 93.82 82.02 e/kWh H 2 system platform 295.74 258.54 e/kW Tank platform 4.10 3.58 e/kWh Table 3 Cable ratings and costs for 150 kV XLPE 3-core copper conductor. Cross section mm2 Current rating A Nominal power MVA Cost Me/km 95 300 45.00 2.494 120 340 51.00 2.535 150 375 56.25 2.582 185 420 63.00 2.660 240 480 72.00 2.811 300 530 79.50 2.999 400 590 88.50 3.346 500 655 98.25 3.972 630 715 107.25 4.965 800 775 116.25 6.693 1000 825 123.75 9.144 𝑒𝑛𝑒𝑟𝑔 and the coefficients 𝑐𝑦 [e/kWh] and 𝑐𝑝𝑜𝑤𝑒𝑟 [e/kW] are obtained 𝑖,𝑏 𝑖,𝑏 by minimising the error between the values given by Ref. [42] for different discharge durations 𝑑 𝑏and the curve corresponding to Eq. (46). The cost of floating platforms is estimated with the approach adopted in [27]. The costs per power or energy unit are differentiated according to the power-to-weight or energy-to-weight ratio of the components that the platform must accommodate. Costs of the desalination system are found in [44] and those of the hydrogen tank of type III, suitable for the desired pressure of 350 bar, in [45]. The cost of batteries is divided by that of the battery converter (including the whole power equipment and system integration)—as well as the electrolyzer cells from their rectifier and fuel cells from their inverter—because of their different lifetimes, considered to be 10 years for batteries and 12.5 years for electrolyser cells and fuel cells [42]. All other components are considered to have the same lifetime as the park itself, which is 25 years. The cost of submarine AC cables varies significantly with the capacity. For the selected commercial cables found in technical datasheets of manufacturers [46], a function is used to estimate the costs 𝐶 𝑐,sec (e/km) for different capacities, given as apparent power 𝑆 𝑐,sec (MVA) [47]: 𝐶 𝑐,sec = 𝛼 𝑐,sec + 𝛽 𝑐,sec𝑒 ( 𝛾 𝑐,sec ⋅𝑆 𝑐,sec 10 2) 2 (47) Where the coefficients 𝛼𝑐 ,sec , 𝛽𝑐 ,sec and 𝛾 are calculated by interpola 𝑐,sec tion for the nominal voltage of 150 kV, not included in the voltage levels considered in [ - 47]. The commercial sizes of the cables that the system can include are displayed in Table 3, together with the costs calculated with Eq. (47). The investment cost is then obtained by multiplying this value by the distance of the park to land: 𝑐 𝑖,𝑐,sec = 𝐶 𝑐,sec 𝑙. The operation costs of components are estimated to be a share of the investment cost per year, as reported in Table 4. For the floating platforms, operation costs are assumed to be nil. Sustainable Energy, Grids and Networks 43 (2025) 101846 7 S. Varotto, E. Kazemi-Robati and B. Silva Table 4 Operation and maintenance costs of components as percentage of the investment cost per year. Component O&M cost (%) Battery cells 1 Battery converter 1 Desalination system 3 Rectifier 2 Electrolyser cells 2 Compressor 2 Tank 1 Fuel cells 2 Fuel cell inverter 2 Pipeline 1 Cable 1 Table 5 Summary of the system components included in the sizing for each scenario. Scenario Add. cable BESS H 2 prod. Tank offsh. Tank onsh. Fuel cell Ship Pipel. 1✓ 2 a ✓ b✓ ✓ 3 a ✓ ✓ ✓ b✓ ✓ ✓ 4 a ✓ ✓ ✓ ✓ b✓ ✓ ✓ c✓ ✓ ✓ ✓ 5 a ✓ ✓ ✓ ✓ b✓ ✓ ✓ ✓ ✓ Fig. 3. Legend of symbols representing the components in the scenarios schemes. The cost of sending one tanker ship with a capacity of 5 tons to withdraw hydrogen from the offshore park and bring it to shore is estimated to be 3700 e/ship, approximation based on scenario B2 from [31]. The scenarios that will be examined for this study are outlined in Table 5. Most scenarios include more sub-scenarios, with some variation in terms of components included. The symbols for the system components that will appear in the figures of this section, representing the configurations of the system in the different scenarios, are summarized in Fig. 3. Scenario 1: cable expansion As first option, the expansion of the cable connection to land is evaluated. For the sizing of the connection capacity enhancement, the following assumptions are made: • The new cables are connected in parallel with the pre-existing one; • The voltage level at which the cables work is the same as the preexisting one: 150 kV; • The transmission losses of both the pre-existing and the additional cable are neglected. Given these assumptions, the power from the farm to land is further 𝑝𝑟𝑒 considered as if flowing through one cable with capacity: 𝑆𝑐 + 𝜎 𝑐 . In the following schematic representations of the energy storage and transmission systems in the different scenarios, the system components Fig. 4. Scenario 1, cable expansion. Fig. 5. Scenario 2, BESS with additional cable. Fig. 6. Scenario 3, offshore hydrogen production, fuel cell and shipping. that are considered fixed are drawn in black, and the colour blue represents the components that are optimally sized, as shown in Fig. 4. Scenario 2: battery energy storage system The second option analysed is the addition of a simple BESS with a discharge duration at nominal power 𝑑𝑏 = 1 h. The BESS is located offshore, so it is able to store energy when generation exceeds the capacity of the pre-existing cable, and discharge when the cable is not congested. Other than saving energy from curtailment, batteries can implement en ergy arbitrage between hours of low and high market prices, increasing the overall capture price and therefore the revenues of the park. Scenario 2 also considers the combination of BESS with additional cable ( - Fig. 5). Scenario 3: offshore hydrogen storage The option of a hydrogen storage system is at first considered as being located fully offshore: hydrogen production system, tank and fuel cell are all placed on a floating platform at the offshore point of common coupling of the park generation units. In this scenario, at first hydrogen is produced only to be reconverted into electrical power by means of a fuel cell, and secondly hydrogen sale is considered. Since the installation of a hydrogen pipeline is not envisaged, hydrogen needs to be transported on tanker ships with an assumed storage capacity of 5 tons, which withdraw hydrogen from the tank and carry it to shore (Fig. 6). Scenario 4: hydrogen and pipeline This scenario envisages the installation of a submarine pipeline to transfer hydrogen from the production hub offshore to land, where it is stored and can be either re-converted into electric power by fuel cells or sold to the hydrogen market (Fig. 7). Hydrogen transmission by pipeline is considered to be feasible at high pressures, close to 350 bar (5000 psi), and has relatively low pressure drops of 0.5 %–1 % every 1000 km according to [48]. At a fixed rated mass flow, the cost of pipelines does not vary significantly with the pressure: as more expensive materials are required for higher pressures, lower amounts of material are needed as the diameter decreases [49]. For these reasons, in the developed model, the addition of a pipeline is assumed not to change the configuration of Sustainable Energy, Grids and Networks 43 (2025) 101846 8 S. Varotto, E. Kazemi-Robati and B. Silva Fig. 7. Scenarios 4 configurations (a) without and (b) with hydrogen sale. Fig. 8. Scenarios 5 configurations (a) without BESS and (b) with BESS. the hydrogen production and storage system, as no additional compressors are needed since the pipeline can work at the same pressure as the tank. The sizing of BESS is also considered as an option in this scenario. Scenario 5: cable, hydrogen and pipeline Finally, a comprehensive energy storage and transmission system is analysed, encompassing submarine cable connection expansion, OHP system, submarine hydrogen pipeline and onshore tank. Both cases without and with BESS are considered (Fig. 8). This all-inclusive scenario will be used to perform sensitivity analyses on the cost of components and the price of hydrogen. 4. Results The results of the optimisations performed in the different scenarios are reported and commented on in the following subsections. 4.1. Scenario 1 The optimisation performed for Scenario 1, where only the addition of a submarine cable is envisaged, results in the sizing of an additional cable of 88.5 MVA, for a total transmission capacity of 288.5 MVA. The curtailment is reduced by 66 % respect to the base case of the park working with only the pre-installed transmission capacity, meaning that the curtailed power decreases from 18.05 % in the base case to 6.17 %. 4.2. Scenario 2 The option of Scenario 2 including only batteries placed offshore results in a BESS size of 9.1 MWh, with a negligible curtailment reduction. However, when the additional cable sizing is enabled, the BESS is sized to 20 MWh and the curtailment is reduced to 5.26 %, outperforming the case of Scenario 1 without batteries, as expected. The size of BESS is more than doubled when the transmission capacity is increased, because this allows more freedom for batteries to perform energy arbitrage, since more energy can be delivered to the grid during hours of high electricity Table 6 Optimisation results for Scenario 1 and for Scenario 2 without and with additional cable sizing. Cable MVA BESS MWh NPV Me Curtailment Total Avoided Cable 88.5 – 89.571 6.17 % 11.89 % BESS – 9.1 1.241 17.71 % 0.35 % Both 88.5 20 97.394 5.26 % 12.80 % Power 3340 3360 3380 3400 3420 3440 3460 3480 Hours 0 100 200 300 MW Power generated Power to H 2 production Generation potential Power to the grid Tank state of charge 3340 3360 3380 3400 3420 3440 3460 3480 Hours 0 1 2 kg 10 4 Hydrogen sale 3320 3340 3360 3380 3400 3420 3440 3460 3480 Hours 0 1 2 3 4 5 N. of ships Fig. 9. Hydrogen production and shipment in Scenario 3 during a sample week in May. prices. Table 6 displays the main outputs of Scenarios 1 and 2, where avoided curtailment represents the difference between the curtailment in the base case and in the considered scenario, as percentage of the total generation potential of the park. 4.3. Scenario 3 When the hydrogen system is added, in its full-offshore configuration including hydrogen production system, tank and fuel cell, without considering hydrogen sales, no hydrogen system is sized at all. The model including ship transportation requires extremely long computational time to converge to the optimal solution, due to the high number of integer variables. Hence, it is decided to increase the tolerance gap of the solver from 0.01 % to 1 %, in order to obtain a solution close enough to the optimal in a reasonable time. When hydrogen transportation by tanker ship and sales are enabled, 43.4 MW of electrolysers are installed, and an offshore tank of 891 m 3 (833.28 MWh) that can be emptied by the ships with a daily frequency. The maximum daily number of ships delivering hydrogen from the offshore hub to shore along the considered year is 5, as shown in Fig. 9. Sustainable Energy, Grids and Networks 43 (2025) 101846 9