# Trends in Sizing for a Hydrogen Storage System for a 1 GW Offshore Wind Farm

Mattéo T Berthelin, Grégory Pinon

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Mattéo T Berthelin, Grégory Pinon. Trends in Sizing for a Hydrogen Storage System for a 1 GW Offshore Wind Farm. International Journal of Energy Research, 2025, 2025, 10.1155/er/1182085. hal-05438739

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Research Article

# Trends in Sizing for a Hydrogen Storage System for a 1 GW Offshore Wind Farm

**Mattéo T. Berthelin** [ID] and **Grégory Pinon** [ID]

*Mechanical, Energy and Civil Eng. Dept., UNIHAVRE, CNRS, Laboratoire Ondes et Milieux Complexes (LOMC) - Normandie Univ, Le Havre, France*

Correspondence should be addressed to Grégory Pinon; gregory.pinon@univ-le Havre.fr

Received 11 April 2025; Revised 25 August 2025; Accepted 16 October 2025

Guest Editor: Santanu Paul

Copyright © 2025 Mattéo T. Berthelin and Grégory Pinon. International Journal of Energy Research published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Electricity storage is considered as a key component for future grid with high renewables penetration. In the present study, trends in sizing for a hydrogen electricity storage system coupled to a 1 GW offshore wind farm are highlighted. A ‘system approach’ was conducted in order to analyse several scenarios of storage capacity, technologies and even equipment nominal powers. Real wind measurement and national electricity productions and consumptions were used as input data. The impact of wind farm capacity factor, hydrogen storage technology and inter-annual resource variations on the storage system sizing is assessed. A first estimation of the cost of electricity generated by a full offshore facility is performed together with possible added flexibility to the network. Geological storage is identified as the cheapest for all storage capacities and the least impacted by inter-annual variations.

**Keywords:** electricity storage; hydrogen; offshore wind

## 1. Introduction

Electricity storage systems could have an important role in facilitating the integration of renewable energies into power grids [1, 2], especially when it comes to match power generation and demand [3–5]. Hydrogen can be used as low-carbon and dispatchable power storage systems, enabling to smooth renewable power variations through time. It is also identified as suitable for coupling with wind energy [6].

The present study focuses on the modelling, through a ‘system approach’ (i.e., no electrical/mechanical modelling of the equipment), of a hydrogen storage coupled to a 1 GW offshore wind farm for peak shaving and load following purposes. The hydrogen storage system is composed of a proton exchange membrane electrolyser (PEMEL), a storage system and a PEM fuel cell (PEMFC). A Python numerical code is used to identify correlations between:

1. hydrogen storage system sizing and cost of energy production through levelized costs of energy (LCOE). Storage

system sizing in fact means the determination of PEMEL/PEMFC nominal power and storage capacity.

2. hydrogen storage system sizing and added flexibility to the grid for several scenarios.

In the literature, coupling between hydrogen and wind farms in grid support configurations was addressed by several studies, such as [6–11]. In those studies, optimisation methods are used to optimise the sizing of hydrogen storage systems through economic and power reliability criteria. However, the impact of the system's size on those criteria is generally not much analysed, and LCOE are frequently not considered. Trends driving the hydrogen system sizing (i.e., PEMEL/PEMFC nominal power and storage capacity) to minimise LCOE have not been deeply considered so far in the literature. LCOE of multiple storage technologies integrated into the grid have been quantified, by Hunter et al. [12] for instance, but storage technologies' sizing for a given power plant is not addressed. The article aims to find insights about the impact of turbine types, inter-annual resource variations, chosen hydrogen storage technology, on the LCOE from a given in situ offshore wind resource.
<figure><img src="image_4.png" /><figcaption>FIGURE 1: Schematic representation of the implemented methodology.</figcaption></figure>

Furthermore, in one of the presented scenarios, the current study introduces the possibility to move the whole hydrogen storage system offshore. Offshore wind capacity is increasing rapidly and there is a growing interest, especially in North Sea, in coupling this electricity generation with offshore renewable hydrogen production (see [13, 14]). Costs of offshore green hydrogen production is regularly studied [15, 16]. However, no LCOE estimation of a hydrogen system for grid support within an offshore facility is available. The present article proposes a first LCOE evaluation for this configuration.

The following article is organised as follows. The methodology implemented in the numerical code is described in Section 2 followed by techno-economic data for LCOE calculation gathered in Section 3. Finally, results on the impact of the system sizing on LCOE and added flexibility to the grid are presented in Section 4.

## 2. Method

This section aims to describe the input data, the developed methodology and assumptions on which the numerical tool

relies. This is synthesised in Figure 1. Additionally, different scenarios are considered; they are presented in Section 2.2.

A python numerical tool was developed to model the whole device's behaviour through a 'systems approach': no physical/ mechanical modelling of each equipment is considered. This is only a macroscopic analysis based on power fluxes. Even though it is a low fidelity approach, such methods allow investigating a large number of configurations with a fairly reasonable accuracy and very low computational resources. The whole device consists of a 1 GW offshore wind farm coupled with a hydrogen energy storage equipment (itself composed of a PEMEL, a hydrogen storage, and a PEMFC). Computations are performed with an hourly time-step. A schematic representation summarising the numerical code operations is depicted in Figure 1.

2.1. *Input Data*. The present methodology is based on real data measurements from past years, which forms the basis of the computations. Two input files are considered: wind data and French power consumption and production. In the upcoming modelling and to account for annual variability, 8 years of data are considered from 2012 to 2019 because all the pieces of information are accessible for these years.
2.1.1. *Wind Data.* The wind data file was provided to the authors by the Direction Régionale de l'Environnement, de l'Aménagement et du Logement (DREAL), a French national institute responsible for assessing wind turbine projects, especially during the consenting phase. This file contains wind speed measurements that correspond to a virtual met-mast obtained from 20 years hindcast computed by national/regional scale models of *Météo France*. The wind speed database denominated wind data corresponds to an offshore LIDAR measurement at the reference altitude $z_0 = 100$ m near Barfleur in the Cotentin peninsula in France (49,839094°N; -0,789696°O). This offshore location of the LIDAR buoy is very close to an already granted offshore wind farm named 'Centre Manche 1' for a total capacity of 1 GW. A second Offshore Wind Farm called 'Centre Manche 2' is also under consideration in the given zone, for an additional potential capacity of 1 to 1.5 GW. Data is available since the 1st January 2000 (beginning of the measurements), to the 31st December 2019 (last full year of measurements) and are given on a 1 h basis.

Also, wind measurement altitude has a major influence on the energy yield, especially when considering different wind turbine models of increasing rated power. Therefore, to better assess the electricity production, an atmospheric boundary layer with a power law of 1/7 was considered such as:

$$V(z) = V_0 \left(\frac{z}{z_0}\right)^{\frac{1}{7}}, \quad (1)$$

where z will be taken as turbine hub height and so $V(z)$ the wind speed at z. This aspect, together with the wind farm power generation, is detailed in Section 2.3.

2.1.2. *French Power Consumption and Production.* The French power consumption and production data has been retrieved from RTE (Réseau de Transport de l'Électricité), the official French company dedicated to the electricity transport, via the éCO₂mix indicators. This file contains national power consumption and production on an 1/2 hour basis. Therefore, national power production and consumption are averaged to obtain a 1 h time step. Data is available since the 1st January 2012 (no older data can be found) until 31st December 2019 (end of the wind data file). These 8 years perfectly overlap with the wind measurements and will be considered as the common time frame for the analysis. Additionally, the electricity power production is presented sector by sector: nuclear, coal, gas, fuel, wind, solar, power storage by pumping, national import/export, etc. This will reveal to be very useful for evaluating the power demand as described in the following Section 2.2.

2.2. *Evaluating Power Demand.* In the future, such devices (offshore wind farm possibly coupled with hydrogen energy storage) will have to meet the power demand. The use of energy storage will allow to consider the whole device as a 'grid support' type of use, where power surplus could be absorbed and stored and then released in shortage times. In the present article, no modelling of the grid based on a mathematical models of the electric network (such as *Power System Analysis Tools*, see [17, 18]) was implemented in the code. This could be addressed in the prolongation work of the current study.

The core idea of the present study is to make use of real wind measurements, electricity production and consumption data to analyse the possible benefits of adding a energy storage capacity to the offshore wind farm. However, from the past measurements, the offshore wind farm did not exist and the French electricity consumption and production were balanced at any time: in the French electricity production and consumption file, the sum of all electricity production, storage and imports/exports (hereafter denoted national power production) is always equal to French electricity consumption. Therefore, a production capacity needed to be removed from the existing historic production to create a demand that could be filled by the offshore wind farm production.

To create this power demand from these pieces of data, the national power production from nuclear energy was artificially reduced to consider the possible shutdown of old nuclear reactors. The decommissioning of a first nuclear power plant already happened in 2020 in Fessenheim. This scenario will be called 'low variability' and is detailed in the following paragraph (see Section 2.2.1). Another scenario (denoted 'high variability') will be considered by additionally removing the electricity imports, meaning here that the offshore wind farm electricity production being prioritised with respect to the imports. This second scenario is also detailed in Section 2.2.2.

2.2.1. *'Low Variability' Scenario.* In this scenario, electricity demand is evaluated by reducing the French nuclear power production. In France, a dozen of 900 MW nuclear reactor (the oldest ones) will be shut down before 2035 (see [19]), and this was already the case for the Fessenheim reactors in 2020. In this context, this 'low variability' scenario assumes that the power production will be reduced by removing half of the equivalent energy generation of such a 900 MW nuclear reactor.

In fact, in France and for the past years, the average capacity factor of nuclear power was approximately equal to 75% resulting in the production of 900 MW × 8760 h × 75% ≈ 5.9 TWh per year. On the contrary, the commonly encountered value of offshore wind capacity factor is said to be around 40%. So, for a 1 GW farm, a total production of 1 GW × 8760 h × 40% ≈ 3.5 TWh per year is expected, which is a little above half of the mentioned nuclear reactor production (≈2.95 TWh). This is an important assumption of this study, and any other choice could have been possible. For instance, the capacity factor of such offshore wind farms will be discussed in Section 2.3. Other possibilities were considered without changing too much of the created electricity demand.

In practical terms, the 2.95 TWh represents ≈0.77% of the 382.6 TWh of produced electricity by nuclear in 2016 for instance. As it was impossible to determine from which nuclear power plant the electricity was coming, the decision to hourly reduce by ≈0.77% the total nuclear electricity production was made. As a matter of example, if the nuclear electricity production was equal to 50, 000 MW on the 1st January 2016 at noon, the adjusted production will be 50, 000 MW × (1 - 0.0077) = 49, 615 MW). The adjusted nuclear power production is aggregated with the other national electricity production/storage sources and national import/export in what can be called an adjusted national power production.
<figure><img src="image_5.png" /><figcaption>FIGURE 2: Evaluated demand curves in MW for the ‘low variability’ scenario over the 8 year of analysed data.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 3: Evaluated demand curves in MW for the ‘high variability’ scenario over the 8 year of analysed data.</figcaption></figure>

In fact, this adjusted power production is not any more equal to power consumption (as nuclear production was reduced), creating an hourly power demand. Even if the reduction ratio is different for every year, this does not lead to tremendously different power demand curves as shown in Figure 2. One can observed a common seasonal variation trend varying from approximately 450 MW during winter to 250 MW during the summer time. On top of that, higher frequency peaks at the order of 100 to 150 MW or more are identifiable. Peaks of low demand, such as the one observed in October 2016 corresponds to time of the year where national nuclear power production was in major surplus compared to national consumption. This scenario is denominated ‘low variability’ demand because the same trends can be observed in demand within the 8 years of analysed data.

2.2.2. *'High Variability' Scenario.* In this second scenario, half of the equivalent power production of a 900 MW nuclear

reactor is still removed from French nuclear power production. In addition to that, this scenario also consider removing the national power importations from the national power production. The obtained power demand is depicted in Figure 3 for the 8 years of analysed data. This results in much higher peaks in power demand, generally in winter, between 1 to ≈5 GW. One can recognise in the given figure the demand pattern of the ‘low variability’ scenario, between 450 and 350 MW and ad hoc demand peaks specific to each year. To the authors point of view, this scenario may be more representative to real case scenario as, in real life, electricity importations will most probably be decided based on all the electricity generation, the newly offshore wind farm included. It is also more representative of long term/duration energy storage use, charging energy during the summer to deliver it in the winter. It is called ‘high variability’ scenario because this method results in ad hoc and yearly specific demand peaks in the evaluated power demand.
<table><caption>TABLE 1: General information on the different turbine models considered in the study.</caption><thead><tr><td>Turbine model</td><td>Rated power (MW)</td><td>Hub height (m)</td><td>Rotor's radius (m)</td><td>V<sub>cutin</sub> (m/s)</td></tr></thead><tbody><tr><td>GE Haliade 150</td><td>6</td><td>100</td><td>75.5</td><td>3</td></tr><tr><td>MHI V164</td><td>8</td><td>125</td><td>82</td><td>4</td></tr><tr><td>CSSC H210</td><td>12</td><td>145</td><td>105</td><td>3.5</td></tr><tr><td>V236</td><td>15</td><td>162</td><td>118</td><td>3</td></tr><tr><td>SG DD-276</td><td>21.5</td><td>182</td><td>138</td><td>3</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIGURE 4: Estimated power curves of the considered offshore turbine models.</figcaption></figure>

## 2.3. Electricity Generation From Wind

### 2.3.1. Evaluating the Electricity Production.
Using the wind data file, the hourly wind farm's power generation can be computed. The studied wind farm has a total capacity of 1 GW but several wind turbine models can be considered, from an old 6 MW model to an 'in development' 21.5 MW model. In reality, the capacity factor of a wind farm proved to be very dependent on the wind turbine rated power, owing to combined non-linear effects with the cut-in and rated velocities. In the present study and by considering different turbine models, the influence of the wind farm capacity factor on the hydrogen energy storage system will be assessed. Public and general characteristics of each turbine model are gathered in Table 1. From these pieces of information, each turbine's power coefficient $C_p$ and power curve can be reconstructed, as depicted in Figure 4.

For power generation, the wind turbine power $P_{WT}$ is 0 when the wind velocity is below the cut-in velocity $V_{cutin}$. Above this value, $P_{WT}$ is evaluated via Equation (2):

$$P_{WT} = N_t \frac{1}{2} \rho A C_p V(z)^3, \quad (2)$$

where $N_t$ is the number of wind turbines in the farm, $A = \pi R^2$ is the swept area of each considered turbine and $V(z)$ is the wind speed obtained from the wind data file and evaluated at the turbine hub height (see Equation (1)). In the present approach, no detailed wind turbine layout will be considered and no complex computational fluid dynamic (CFD) solver will be used neither. Therefore, wake losses within the wind farm will be estimated to 10%, no matter the turbine model is. This 10% value is frequently encountered in the literature (see [20–22]). To finalise this, the wind farm electricity generation $E_{WT}$ will be evaluated by summing over the full year the hourly estimated power production $P_{WT}$ multiplied by the time step $dt$, which is an hour. In that respect, Section 2.3.2 presents the energy production calculated for the 20 years of wind measurements, showing some interesting features on the wind farm capacity factor.

### 2.3.2. Wind Farm Production Validation.
In order to assess the above-mentioned methodology regarding the 1 GW wind farm electricity generation and its dependency on wind turbine models composing the farm (see Section 2.3), an analysis of the wind farm electricity generation was performed using wind
<figure><img src="image_8.png" /><figcaption>FIGURE 5: Capacity factor/electricity production of the wind farm over the 20 years of wind measurements. Dotted lines represent the 20 years-average, while shaded areas represent half the standard deviation σ/2.</figcaption></figure>

data file. In fact, for the 20 years of wind measurements, electricity generation for a 1 GW wind farm composed of different turbine models and associated capacity factor are depicted in Figure 5.

It is really interesting to observe that, for a similar 1 GW rated power wind farm, electricity production can vary between ≈3 TWh for a farm equipped with the smaller turbines to up to ≈5 TWh for the larger ones. This substantial increase is basically due to higher hub height (that is larger velocities, see Equation (1)) and threshold effects combined with the nonlinearities of Equation (2). As a consequence, one can see in Figure 5 that the wind farm's capacity factor is accordingly increasing with turbine nominal power. In average, capacity factors range from 35% for 6 MW models to ~57% for 21.5 MW models. Therefore, although no detailed wind turbine layout nor CFD solver was used, non linear and threshold effects resulting from the number and capacity of the turbines composing the farm is somehow represented, with capacity factors beyond 50% for new wind turbines generation as already evoked by IEA [23]. Of course, these threshold effects are highly dependent on the cut-in and rated velocities of the turbine (Figure 4). For a given rated power, results can vary depending on these cut-in and rated velocities.

## 2.4. Hydrogen Energy Storage Device

### 2.4.1. Common Features on Storage.
The system considered in the study consists of a 1 GW offshore wind farm and a hydrogen energy storage equipment. This storage equipment is itself composed of a PEMEL, a hydrogen storage and a PEMFC system.

As already mentioned in Section 1, this ‘system approach’ modelling only considers electrical or hydrogen fluxes, and

there is no physical/mechanical modelling of the equipment. Even though it is a low-fidelity approach, such methods allow investigating a large number of configurations with a reasonable accuracy and very low computational resources.

Thus, no modelling at the cell level of PEMEL and PEMFC has been implemented. Moreover, PEMEL and PEMFC flexibility characteristics such as warm-up and shut-down times, load following constants and nominal load ranges were not implemented in the numerical code. In reality, PEM devices have start up times up to 10–15 min maximum, with load following properties in the range of the second. The authors estimated that, considering the hourly resolution of the code, PEM devices’ flexibility properties could be neglected to favour instantaneous behaviour (see [24]). Additionally, no degradation of the equipment is considered.

As a consequence and in the present implementation of the code, all equipments are expected to work instantaneously. For instance, when 700 MW of electrical power arrive in the electrolyser, it is assumed that all the power will be transformed into hydrogen, provided that the user defined rated power of the electrolyser is above 700 MW. This is also applicable for the fuel cell and any other device.

### 2.4.2. Evaluating the Possibility of Offshore Storage.
In the present study, two different options are considered regarding the location of the hydrogen storage device. This facility can either be installed onshore or offshore, as illustrated on Figure 6.

Offshore wind installed capacity is increasing sharply. There is a growing interest, especially in the North Sea, in coupling this capacity with offshore renewable hydrogen production (see [14, 25]). The way this can be achieved with the
<figure><img src="image_9.png" /><figcaption>FIGURE 6: Schematic representation of the two locations considered. Please note that offshore/onshore hydrogen power storage facility size is not at scale compared to the wind farm size.</figcaption></figure>

lowest costs was studied by [15, 16, 26], examining if the electrolyser should either be centralised (being placed on an offshore platform, floating or not, for example) or decentralised (in wind turbine towers, for example), but also examining the transmission costs of hydrogen pipelines (see [13, 25] for additional details). Those studies only focus on hydrogen production, mainly for selling this hydrogen as a raw material. But, to the authors' point of view, there is no study on full offshore hydrogen facility for supporting the grid, for enhancing balancing the network. The present study considers this offshore location as an option, where power-to-hydrogen, hydrogen storage and hydrogen-to-power is managed offshore.

On the schematic representation of Figure 6, the wind farm is set up at sea and an export cable (export cable A) carries the electrical power from the offshore substation to an onshore one for injection into the grid. In the case of onshore hydrogen facility, a second export cable (export cable B) connects the onshore facility to the onshore energy storage device. In the eventuality of offshore hydrogen facility, a second export cable (export cable C) connects this offshore facility to the wind farm's electrical substation.

In the numerical code, the fact that the hydrogen facility is set up either onshore or offshore doesn't affect any more the fluxes within the system. That is to say, the two examples presented in Section 2.6 doesn't depend on the storage location. However, it will affect economic data, since the offshore facility may require additional equipments or higher associated CapEx and OpEx as further described in Section 3. Finally, please be aware that in the present approach, these choices are not incorporated within the framework of any geographical or technical feasibility, especially regarding the offshore hydrogen facility. Some of the technologies considered are dependant on spatial opportunities (geological hydrogen storage for example) and only experimental prototypes or demonstrators of this

kind of facility exists offshore, to the best of the authors' knowledge. Those facts are ignored in the study, the aim being to evaluate what could be the costs of an offshore hydrogen power storage facility in a first approximation.

**2.5. Meeting Power Demand.** The study aims to find out some insights regarding the scaling of a hydrogen energy storage equipment coupled to an 1 GW offshore wind farm. This hydrogen storage is used to spread power variations from the wind farm to better meet demand.

Therefore, every hour, the implemented code computes the following steps:

* From the wind measurements (Section 2.1), the farm electrical power production is calculated (Section 2.3) and compared to the electrical power demand from the French national grid (Section 2.2). Based on this evaluation, two main configurations may be encountered.

* Power excess in the network: If the wind farm's power production is higher than demand, then there is a power excess. The portion of the power required by the network is sent to the grid (flux (1) on Figure 1) and the remaining is sent to the hydrogen storage device. Then, the PEMEL converts electrical power into hydrogen, itself stored in the storage system (flux (2) on Figure 1) and Section 2.4. If any energy conversion limitation occurs, that is to say if the PEMEL system is not powerful enough to convert the whole power excess or if the storage capacity is being reached during conversion, then a power surplus remains. In this case, a local power export through the grid is considered to evacuate this surplus and meet demand (flux (5) on Figure 1).

* Power deficit in the network: If the wind farm's production is lower than demand, then a power support is needed. All the wind farm's electricity is sent to the grid (flux (1) on Figure 1). On top of that, stored hydrogen is converted back into electricity by the PEMFC and sent to the grid as an additional power source (flux (3) on Figure 1 and Section 2.4). If any energy conversion limitation occurs, that is to say if the PEMFC equipment is not powerful enough to provide the whole additional requested power needed or if the hydrogen storage is found empty during conversion, then a power shortage remains. In this case, a local power import through the grid is considered to fill this shortage and meet demand (flux (6) on Figure 1).

As a consequence, every hour, electricity demand is met using wind farm's production, hydrogen storage additional capacity, and eventually local power import/export if the system cannot entirely suffice. Section 2.6 details some temporal evolutions of some selected days for improving reader's understanding. Please note that local power import/export presently is a virtual electricity flux, that allows to quantify how much power from 'outside' the system would be needed in order to meet the demand. However, if offshore wind farm are equipped with such storage devices in a near future, that means that network management rules will need to be modified to account
<figure><img src="image_10.png" /><figcaption>FIGURE 7: Temporal variation of some system's variables, using input data from 7:00 to 19:00 from 01/01/2016 with the low variability scenario, 15 MW turbines, 1 GW PEMEL/PEMFC nominal power for each equipment and 1 GWh tank storage capacity. (a) Evaluating demand. (b) Power generation from wind. (c) Meeting demand.</figcaption></figure>

for this additional flexibility. And hence, in the above-mentioned situation, the national importations or exportation of electricity will be modified accordingly.

## 2.6. Validation via Some Selected Days.
Figures 7 and 8 show the temporal evolution of some variables of the computations for some selected days. Let us analyse these two examples to illustrate the methodology previously described. For both examples, low variability scenario, 15 MW wind turbines, 1 GW PEMEL/PEMFC nominal power for each equipment and 1 GWh tank storage capacity are used in the simulation.

The first example (Figure 7) takes place on the 1st January 2016, from 7:00 to 19:00. The upper plot (a) illustrates how power demand is evaluated according to Section 2.2. Each hour, the equivalent of half an old 900 MW nuclear reactor is removed from the national nuclear power production, resulting in an adjusted national power production, slightly lower than the national electricity consumption. An hourly fluctuating power demand is thus evaluated at the order of ≈395 to ≈415 MW in this precise case.

The middle plot (b) shows the wind farm power generation according to Section 2.3. High wind speeds can be observed for
<figure><img src="image_11.png" /><figcaption>FIGURE 8: Temporal variation of some system's variables, using input data from 15:00 18/01/2016 to 3:00 19/01/2016 with the low variability scenario, 15 MW turbines, 1 GW PEMEL/PEMFC nominal power for each equipment and 1 GWh tank storage capacity. (a) Evaluating demand. (b) Power generation from wind. (c) Meeting demand.</figcaption></figure>

this period of times, and wind farm's electricity production is increasing together with the wind velocity. The wind farm rapidly reaches its rating power (a bit lower than 1 GW considering wake losses) and electricity production is, during the 12 considered hours, higher than demand.

Therefore, power excess is reached (see Section 2.5) as illustrated in the lower plot (c). This plot also depicts how this surplus is managed to meet demand. From 7:00 to 10:00, all the power excess is converted into hydrogen and stored, according to Section 2.5. One can see the

PEMEL power increases as the excess is getting larger, and the hydrogen storage is filling up. The power sent to grid is equal to power demand (demand is met), because all the surplus is absorbed by the hydrogen storage device. Soon after 11:00, the hydrogen storage has reached its capacity. Due to an energy conversion limitation, power excess cannot be absorbed any more and a surplus remains. The power sent to the grid is then higher than demand. Therefore, local power export takes place to evacuate the surplus and meet demand.
<table><caption>TABLE 2: Summary of the different scenarios considered in the study.</caption><thead><tr><td>Variable</td><td>Number of cases</td><td>Description</td></tr></thead><tbody><tr><td>Power demand</td><td>2</td><td>'Low variability' or 'high variability' scenario as described in Section 2.2</td></tr><tr><td>Wind turbines</td><td>5</td><td>Turbines nominal power ranging from 6 to 21.5 MW as described in Section 2.3</td></tr><tr><td>Storage equipment</td><td>3</td><td>Tank, underground pipe or geological hydrogen storage is considered as described in Section 2.4.1.</td></tr><tr><td>Storage location</td><td>2</td><td>Onshore or offshore storage location is considered as described in Section 2.4.2</td></tr></tbody></table>

<table><caption>TABLE 3: Wind farm techno-economic data.</caption><thead><tr><td>Parameter</td><td>Current estimation</td><td>2030 estimation</td><td>References</td></tr></thead><tbody><tr><td>Wind farm</td><td></td><td></td><td></td></tr><tr><td>CapEx (k€/MW)</td><td>3250</td><td>2500</td><td>[27–29]</td></tr><tr><td>OpEx (%CapEx)</td><td>3.7</td><td>3.3</td><td>[27, 30, 31]</td></tr></tbody></table>

The second example (Figure 8) starts on the 17th January 2016 at 15:00, and ends at 3:00 the next day.

The upper plot (a) illustrates how power demand is evaluated according to Section 2.2. Here, the power demand is nearly constant with small variations between ≈454 to ≈458 MW. The middle plot (b) shows the wind farm power generation according to Section 2.3. Wind farm power generation is decreasing all over the day, following wind speed variations. It is first higher than demand, from 15:00 to 21:00, and then lower than demand from 21:00 to 3:00 the next day.

The first hours of this example are similar to the end of the first day described above: hydrogen storage has reached its capacity. Due to an energy conversion limitation, power excess cannot be absorbed any more and a surplus remains. The power sent to the grid is higher than demand. Therefore, local power export takes place to evacuate the surplus and meet demand.

After that, power shortage case is reached (see Section 2.5). From 22:00 to 23:00, hydrogen from the storage is converted into electrical power by the PEMFC and sent to the grid according to Section 2.5. One can see the PEMFC power increases as the shortage of power is getting larger, and the level of stored hydrogen is running down. It is empty within 2 h, because the chosen storage capacity is really small in this example. The power sent to the grid meet demand up to 22:00 because of the PEMFC power support. After 23:00 the hydrogen storage is empty. Due to an energy conversion limitation, power shortage cannot be filled any more and a lack of power remains. The power sent to the grid is lower than the demand and local electricity importation will be needed to meet demand. These two examples well illustrate every aspect of the implemented methodology in the numerical modelling of the system.

2.7. Summary of Scenarios. As a partial conclusion, to model the system in a grid-support objective, an hourly power demand is evaluated. It is evaluated by adjusting *French power consumption and production* data in two different ways, either by removing the equivalent power production of half an old 900 MW nuclear reactor, or by removing half of this old 900 MW nuclear reactor and national electricity importations (see Section 2.2). This results, respectively, in a ‘low variability’ scenario where seasonal and lower scales variations can be

observed, and ‘high variability’ scenario where, in addition these previous patterns, high and ad hoc demand peaks occurs through the year (generally in winter). This second scenario may be more representative of long term evolution of network management and may influence the sizing of the facility.

For the expected 1 GW offshore wind farm electricity generation, five different turbine models, from 6 to 21.5 MW are considered. Turbine nominal power and hub height influencing the wind farm’s capacity factor (see Section 2.3.2) may also influence the scaling of the hydrogen power storage system. All these aspects are taken into account as well.

Additionally, three different storage technologies are considered: geological, underground pipe and tank storage. Techno-economic characteristics vary from one technology to another. Thus, it seems important to perform the study considering the three cases.

Finally, the hydrogen facility may be installed either onshore or offshore. Offshore installation may be much more complex technologically speaking but, on the contrary, such offshore solution may be much more easily acceptable from a societal aspect point of view. Although energy flux remains unchanged, offshore location is associated with higher costs and the study will allow, for a first approximation, to estimate the costs of those offshore technologies.

All these configurations are summarised in Table 2, and the present study aims at drawing some insights in sizing the hydrogen energy storage whole device, making use of the 8 years of common available wind and national production/consumption data.

## 3. Techno-Economic Data

A literature review was performed for accurate modelling of the whole storage system. Each equipment is associated with current and expected (by 2030) technical and economical characteristics. To determine a specific techno-economic value among several studies, the average of all the converging values among those studies was chosen. This section aims to gather these information and describe assumptions underlying some values, particularly regarding the offshore case, for which only few studies were found.
<table><caption>TABLE 4: PEMEL techno-economic data.</caption><thead><tr><th>Parameter</th><th>Current estimation</th><th>2030 estimation</th><th>References</th></tr></thead><tbody><tr><td>Rectifier</td><td></td><td></td><td></td></tr><tr><td>Efficiency (%)</td><td>98.6</td><td>98.6</td><td>[12]</td></tr><tr><td>CapEx (k€/MW)</td><td>130</td><td>60</td><td>[12]</td></tr><tr><td>PEMEL</td><td></td><td></td><td></td></tr><tr><td>Efficiency (%-LHV)</td><td>66</td><td>66</td><td>[12, 24, 32]</td></tr><tr><td>CapEx (k€/MW)</td><td>1500</td><td>625</td><td>[12, 25, 32]</td></tr><tr><td>OpEx (%CapEx)</td><td>2</td><td>1.5</td><td>[12, 25, 32]</td></tr><tr><td>Cells replacement (%CapEx)</td><td>40</td><td>25</td><td>[32]</td></tr><tr><td>Cells lifetime (h)</td><td>45,000</td><td>70,000</td><td>[12, 32]</td></tr><tr><td>Additional offshore platform<sup>a</sup></td><td></td><td></td><td></td></tr><tr><td>CapEx-PEMEL<sup>b</sup> (k€/MW)</td><td>—</td><td>400</td><td>[14, 33]</td></tr><tr><td>OpEx (%CapEx)</td><td>0.5</td><td>0.5</td><td>[25]</td></tr></tbody></table>

Techno-economic data regarding wind farm, PEMEL, the different considered hydrogen storages and PEMFC are gathered, respectively, in Sections 3.1, 3.2, 3.3 and 3.4.

### 3.1. Wind Farm.
Owing to the confidential aspects of each turbine's price and related capital expenditure (CaPex) and operational expenditure (OpEx), general values will be considered based on the costs of previous and announced wind farm projects in France and Europe (see Table 3). CapEx and OpEx are given for the entire wind farm's components, including turbines but also foundations, substations, export cables (export cable A in Figure 6), installation costs, etc. In the case of offshore location for the chosen hydrogen storage, the fact that additional export cables and offshore substation increased capacities would be needed, is not taken into consideration yet and is neglected in the economical assumptions.

### 3.2. PEMEL.
The PEMEL device is composed of a rectifier, to convert AC current from the wind farm to DC current, and the electrolyser itself that converts power into hydrogen through electrolysis. Each equipment is modelled by its low heating value (LHV) efficiency (that does not take the produced water vapour into account). Moreover, the PEMEL operating hours and produced hydrogen are hourly monitored in the code. In fact, if its operating hours exceed the stack lifetime, the stack needs to be replaced. This is automatically done (hypothesis of no down-time) and the associated cost is taken into account in the whole cost estimation. Technical data regarding rectifier, PEMEL and additional offshore platform (in the case of the offshore location) is gathered in Table 4.

Operating a centralised PEMEL at sea would require an offshore platform to support it. While floating vessels may be considered [13, 34], fixed offshore platforms are most common in the literature (see [15, 33]) and some economical calculations were performed to estimate the cost of such a platform by [14, 16, 25]. Based on those studies, offshore platform's CapEx is given per MW of PEMEL installed capacity and with 100 m depth. The weight and size of the rectifier are neglected in the platform's cost estimation.

### 3.3. The Different Hydrogen Storage Solutions.
Produced hydrogen from electrolysis could then be stored in different storage solutions. In the present study, three different storage techniques are considered: geological hydrogen storage (in salt caverns, for example) [12, 35, 36], underground pipe storage [15, 37] and tank storage [38].

A compressor needs to compress the produced hydrogen and adapt the pressure for the desired storage solution. The compressor is modelled by its efficiency (which is not the same depending on the required pressure: 68, 200 or 700 bars), while the storage is defined by its storage capacity, in GWh. Each storage technic differs in terms of economic characteristics and will affect system's sizing, as described in Section 4. Technical data concerning compressor, storage types and eventual offshore platform is gathered in Table 5. Following [39], different compressor efficiencies are used depending on the required pressure for storage.

Concerning the cost of offshore hydrogen storage and associated infrastructures, assumptions needed to be made, since no estimations were found by the authors in the literature. Installing and operating hydrogen storage offshore should be more costly than onshore. Moreover, offshore environment may require additional infrastructures, especially for tank storage.

By the way, regarding tank storage of hydrogen, this is the most common solution used nowadays, essentially for transport applications. In the present study, hydrogen is compressed at 700 bars to reduce tanks' footprint. Moving this technology offshore has sometimes been mentioned in studies addressing the offshore hydrogen hub (see [38] for instance), where massive containers were supported by an offshore platform. In the present study, tank storage supported by an offshore platform, similar to the one supporting PEMEL/PEMFC devices or electrical substation is assumed to be feasible. The cost of an offshore platform is influenced by water depth, and equipment's size and weight to carry. According to [14, 16], the cost of an offshore platform reported to the footprint of a PEMEL is 8.3 k€/m², the equipment weight per surface unit being approximately 130 kg/m². However, hydrogen tanks are ~21 times heavier than PEMEL based on [42], with a weight of 2777 kg/m². Therefore, it is assumed that the cost of an

<footnote><sup>a</sup>Values given for 100 m depth.</footnote>

<footnote><sup>b</sup>Rectifier's weight and size are neglected.</footnote>
<table><caption>TABLE 5: Hydrogen storage techno-economic data.</caption><thead><tr><th>Parameter</th><th>Current estimation</th><th>2030 estimation</th><th>References</th></tr></thead><tbody><tr><td><strong>Compressor</strong></td><td></td><td></td><td></td></tr><tr><td>Efficiency 68 bars<sup>a</sup> (%-LHV)</td><td>93.5</td><td>93.5</td><td>[39]</td></tr><tr><td>Efficiency 200 bars<sup>b</sup> (%-LHV)</td><td>91.5</td><td>91.5</td><td>[39]</td></tr><tr><td>Efficiency 700 bars<sup>c</sup> (%-LHV)</td><td>86.5</td><td>86.5</td><td>[39]</td></tr><tr><td>CapEx (k€/MW)</td><td>39</td><td>15</td><td>[12, 25]</td></tr><tr><td>OpEx (%CapEx)</td><td>4</td><td>4</td><td>[25]</td></tr><tr><td><strong>Tank storage</strong></td><td></td><td></td><td></td></tr><tr><td>CapEx onshore (€/kWh-LHV)</td><td>13.5</td><td>10</td><td>[32, 40, 41]</td></tr><tr><td>OpEx onshore (%CapEx)</td><td>1.5</td><td>1.5</td><td>Assumption</td></tr><tr><td><strong>Underground pipe storage</strong></td><td></td><td></td><td></td></tr><tr><td>CapEx onshore (€/kWh-LHV)</td><td>17.1</td><td>15.3</td><td>[12]</td></tr><tr><td>OpEx onshore (%CapEx)</td><td>1.5</td><td>1.5</td><td>Assumption</td></tr><tr><td>CapEx offshore (€/kWh-LHV)</td><td>25.65</td><td>22.95</td><td>Assumption</td></tr><tr><td>OpEx offshore (%CapEx)</td><td>2.25</td><td>2.25</td><td>Assumption</td></tr><tr><td><strong>Geological storage</strong></td><td></td><td></td><td></td></tr><tr><td>CapEx onshore (€/kWh-LHV)<sup>d</sup></td><td>1.2</td><td>1</td><td>[12, 32, 33]</td></tr><tr><td>OpEx onshore (%CapEx)</td><td>1.5</td><td>1.5</td><td>[32, 33]</td></tr><tr><td>CapEx offshore (€/kWh-LHV)<sup>d</sup></td><td>1.8</td><td>1.5</td><td>Assumption</td></tr><tr><td>OpEx offshore (%CapEx)</td><td>2.25</td><td>2.25</td><td>Assumption</td></tr><tr><td><strong>Additional offshore platform<sup>e</sup></strong></td><td></td><td></td><td></td></tr><tr><td>CapEx-tank storage<sup>f</sup> (€/kWh-LHV)</td><td>—</td><td>24</td><td>[16, 42]</td></tr><tr><td>OpEx (%CapEx)</td><td>0.5</td><td>0.5</td><td>[25]</td></tr></tbody></table>

offshore platform per unit surface of tank storage will also be 21 times higher, that is to say 174 k€/m². Considering specific system size, LHV of hydrogen and assuming 10 m high tanks, the given costs of an offshore platform to support offshore hydrogen tanks can be evaluated at 24€ per kWh installed (LHV). Please note that compressor's weight and size are neglected in this estimation.

Geological hydrogen storage, in salt caverns for example, is considered as a very promising solution owing to its lower associated cost (see [12, 15]). Technical feasibility of onshore geological storage has been assessed by Tarkowski [43] and Papadias and Ahluwalia [37], while some facilities/demonstrators are already operating in the world (see [36]). Offshore geological storage of hydrogen has already been studied from a feasibility point of view by Abreu et al. [35]. However, no demonstrator and associated cost estimations exists so far to the authors' knowledge. Operating such a storage may require an offshore platform itself with additional equipment. In order to make a first approximation, it will be assumed in the present study that offshore geological storage CapEx and OpEx are 1.5 times higher compared to onshore.

Finally, underground pipe storage is considered by Brunik et al. [15] and Papadias and Ahluwalia [37]. Hydrogen storage in underground pipes (separate from the transport and distribution gas network) is feasible almost everywhere, since it doesn't depend on location's spatial properties. Offshore

underground pipe storage is also considered in the study, although no mention of technic/solution was found in the literature. The pipe could basically be laid on the seabed, providing some pre-feasibility study and ad hoc environmental assessments. However, as for offshore geological storage, it is assumed that operating such a storage offshore is more costly. Hence, associated CapEx and OpEx are assumed to be 1.5 times higher than onshore.

### 3.4. PEMFC.
The PEMFC is composed of an inverter, converting DC current from fuel cell to AC current for injection into the grid, and a proper PEMFC that converts hydrogen from the storage into electrical power. Each equipment is modelled by its efficiency (LHV). Similarly to the PEMEL (see Section 3.2) operating hours and produced electricity are hourly monitored in the code. And if its operating hours exceed the stack lifetime, the stack needs to be replaced. This is automatically done (similar hypothesis of no downtime) and the associated cost is taken into account in the whole cost estimation.

Moreover, each hour the power consumed and produced by the PEMFC as well as its operating hours are accounted. If its operating hours exceed the stack lifetime, the stack is replaced (see Section 3). Technical data regarding inverter, PEMFC and additional offshore platform (in the case of the offshore layout) is gathered in Table 6. It is assumed that,

<footnote><sup>a</sup>Required pressure for underground pipe storage.</footnote>

<footnote><sup>b</sup>Required pressure for salt cavern storage.</footnote>

<footnote><sup>c</sup>Required pressure for tank storage.</footnote>

<footnote><sup>d</sup>Electricity storage, offshore wind, hydrogen.</footnote>

<footnote><sup>e</sup>Values given for 100 m depth.</footnote>

<footnote><sup>f</sup>Compressor's weight and size are neglected.</footnote>
<table><caption>TABLE 6: PEMFC system techno-economic data.</caption><thead><tr><th>Parameter</th><th>Current estimation</th><th>2030 estimation</th><th>References</th></tr></thead><tbody><tr><td>PEMFC</td><td></td><td></td><td></td></tr><tr><td>Efficiency (%-LHV)</td><td>45</td><td>50</td><td>[12, 44, 45]</td></tr><tr><td>CapEx (k€/MW)</td><td>1500</td><td>1000</td><td>[12, 44, 45]</td></tr><tr><td>OpEx (%CapEx)</td><td>2</td><td>2</td><td>[12, 44, 45]</td></tr><tr><td>Cells replacement (%CapEx)</td><td>40</td><td>25</td><td>[45]</td></tr><tr><td>Cells lifetime (h)</td><td>70,000</td><td>70,000</td><td>[12, 44, 45]</td></tr><tr><td>Inverter</td><td></td><td></td><td></td></tr><tr><td>Efficiency (%)</td><td>98.6</td><td>98.6</td><td>[12]</td></tr><tr><td>CapEx (k€/MW)</td><td>67</td><td>40</td><td>[12]</td></tr><tr><td>Additional offshore platform<sup>a</sup></td><td></td><td></td><td></td></tr><tr><td>CapEx-PEMFC<sup>b</sup> (k€/MW)</td><td>—</td><td>400</td><td>[14, 33]</td></tr><tr><td>OpEx (%CapEx)</td><td>0.5</td><td>0.5</td><td>[25]</td></tr></tbody></table>

similarly to the PEMEL, PEMFC system requires a fixed off-shore platform to support it. Offshore platform's CapEx is given per MW of PEMFC capacity installed and 100 m depth, based on [14, 25, 33] estimations, assuming that PEMFC and PEMEL weights and sizes are comparable for a given installed capacity. Please note that inverter's weight and size are neglected in the platform's cost estimation.

### 3.5. LCOE Calculations.
Using the above-mentioned equipment for energy production based on the techno-economical assumptions presented above, a LCOE can be calculated. In the present study, LCOE are considered as the economic criteria to analyse the influence of the sizing of the whole system and its economic performances. A simplified calculation of the LCOE is given by Equations (3) and (4) (see [46]). Total life-cycle cost (TLCC) is first computed from the following Equation (3):

$$ \text{TTLC} [\epsilon] = \sum_{Y=0}^{\text{PL}} \sum_{n} \frac{C_n(Y)}{(1 + \text{DR})^Y}, \quad (3) $$

$$ \text{LCOE} [\epsilon/\text{MWh}] = \frac{\sum_{Y=0}^{\text{PL}} \frac{C(Y)}{(1+\text{DR})^Y}}{\sum_{Y=0}^{\text{PL}} \frac{E}{(1+\text{DR})^Y}}, \quad (4) $$

where E is the produced energy for the reference year. As the model does not considered degradation in equipment efficiency, E is constant over the plant lifetime. Statistical variation is obtained by selecting several reference years within the 8 years of common wind and electricity production/consumption data.

Different LCOEs are calculated, according to the different steps of the energy conversion chain in order to identify associated energy costs:

* First, LCOE of wind farm's electricity (denoted LCOE<sub>wf</sub>) is calculated. The energy considered is the quantity of electricity produced (in MWh) in the baseline year (2012 for example) by the farm, while costs are associated with wind farm CapEx and OpEx (Table 3). No input energy price is considered for LCOE<sub>wf</sub>.

* Then, an equivalent of LCOE applied to hydrogen (denoted LCOH) can be calculated. The energy considered is the quantity of hydrogen (in MWh) produced for the baseline year by the PEMEL, while the costs are associated to PEMEL/storage CapEx and OpEx (Tables 4 and 5). Input electricity price for electrolysis is chosen to be the LCOE<sub>wf</sub>.

* Finally, the LCOE of electricity produced via PEMFC (LCOE<sub>via H₂</sub>) can be calculated. The energy considered is the quantity of electricity produced (in MWh) for the baseline year by PEMFC, while costs are associated with PEMFC CapEx and OpEx (Table 6) and the hydrogen input price is chosen to be the LCOH.

## 4. Trends in Systems Sizing

Using the previously detailed methodology (Section 2), the present article aims to explore the impact of system's sizing. That is to say determining optimal PEMEL and PEMFC nominal powers and optimal storage capacities and technologies. All these aspects will be studied and detailed in Section 4.1 using the LCOE<sub>via H₂</sub>, that is to say the LCOE of the electricity going out from the fuel cell (PEMFC). Also, the influence of the turbine rated power, and hence the farm capacity factor, will be assessed in Section 4.2. Additionally, as 8 years of common wind measurements and national electricity productions/consumptions are considered, effects of inter-annual variability will be presented in Section 4.3. Finally, any possible added flexibility to the grid will be evaluated in Section 4.4. In the following, and unless otherwise stated, the year of 2012, the low variability demand scenario and 12 MW rated turbines are selected as a reference baseline.

### 4.1. Storage Cost Influence on LCOE<sub>via H₂</sub>.

Storage technology and capacity may have a major influence on optimal equipment power (PEMEL and PEMFC nominal power) for which LCOE<sub>via H₂</sub> is minimal. As everything is linked, it is complicated to make an initial choice and then, vary the rest. Here, a choice was made to set two initial storage

<footnote>ªValues given for 100 m depth.</footnote>

<footnote>ᵇInverter's weight and size are neglected.</footnote>
<figure><img src="image_12.png" /><figcaption>FIGURE 9: LCOE<sub>via H₂</sub> as function of PEMEL and PEMFC nominal power, for several storage technologies and capacities. 12MW turbines are composing the farm, onshore location and low variability demand are considered.</figcaption></figure>

capacities; the lower one being of 20 GWh (equiv. to a little less
that a day of full farm production) and the higher one of
200 GWh (equiv. to a little more than a week of full farm
production) and make the equipment's nominal power vary.
Figure 9 depicts the obtained LCOE<sub>via H₂</sub> for a farm composed
of 12 MW turbines, for the low variability scenario and storage
onshore, for the reference year of 2012. The left-hand side
corresponds to the lower storage capacity of 20 GWh and the
right-hand side to the higher one of 200 GWh for different
storage technologies (i.e., geological, tank and pipes).

LCOE<sub>via H₂</sub> is represented by a colour. Dark blue represents relatively low values of LCOE<sub>via H₂</sub> (here at the order of ≈400€/MWh), while yellow colours tend to represent extremely expensive ones (≥ 3000€/MWh in this case).

First, as very general comments, several observations/
conclusions can be drawn. In all cases, when the equipment's
nominal power is really unbalanced, the yellow colour along
the different abscissae indicates that the obtained LCOE<sub>via H₂</sub> is
very high. Then, higher storage capacities always give higher
optimal LCOE<sub>via H₂</sub>, even if it keeps at the same order for the
<figure><img src="image_13.png" /><figcaption>FIGURE 10: Observed optimal LCOE<sub>via H₂</sub> as a function of storage capacity for the different storage type and layout. 12 MW turbines are composing the farm and low variability demand is considered.</figcaption></figure>

geological storage (with 408€/MWh and 441€/MWh). However, it nearly doubles with the two other technologies: from ≈540 to ≈810€/MWh for tank storage and from ≈550 to ≈950€/MWh for pipe).

More into the details, a more expensive storage leads to a more powerful optimal equipment and higher associated LCOE<sub>via H₂</sub>. Indeed, for the 20 GWh storage capacity, optimal LCOE<sub>via H₂</sub> are obtained for PEMEL and PEMFC nominal power of 80/70, 250/220 and 350/270 MW for geological/tank/pipe storage, respectively. And associated LCOE<sub>via H₂</sub> precisely are: 408, 530 and 543€/MWh. Although the storage capacity is the same in all cases, the storage technologies considered have different unitary CapEx, the cheapest one being geological and the most expensive one being the pipe storage. In fact, for a given storage capacity, a higher storage unitary CapEx/OpEx leads to a higher total life cycle cost of the system within LCOE calculations. To balance this increase, the PEMFC's electricity production must be increased too (according to LCOE's mathematical definition). This is achievable by increasing the PEMEL and PEMFC nominal power in order to reduce the limitations on energy fluxes within the system: powerful equipment allows bigger hydrogen and electricity fluxes. However, increasing PEMEL and PEMFC nominal powers is also associated with an increase of costs, and thus an increase of the total life cycle cost of the system. According to this mechanism, higher storage technology costs for a given storage capacity result in higher life cycle cost, leading to higher optimal power equipment and associated LCOE<sub>via H₂</sub>.

Similarly, higher storage capacity leads to higher associated LCOE<sub>via H₂</sub>. In fact, considering geological storage only as a matter of example, an increase of the storage capacity from 20 GWh (top left plot of Figure 9) to 200 GWh (top right

plot) results in a shift of PEMEL and PEMFC optimal power from 80 & 70 MW to 380 & 290 MW, respectively. Associated LCOE<sub>via H₂</sub> increases from 408 to 441€/MWh. In this case, the total life cycle cost has also increased mainly because of an increase by 10 of the storage capacity. And this CapEx increase is not directly balanced by much more produced electricity via hydrogen storage. Again and in the present case, increased transformation capacity could be achieved by increasing nominal equipment power (PEMEL and PEMFC) but this also results in an increase in total life cycle cost and hence increased LCOE<sub>via H₂</sub>.

Considering offshore facility, the whole equipment costs are even higher, resulting in an extension of the trends already observed on Figure 9 (Figure A1 in appendix). Finally, it is noteworthy to notice that optimal equipment power in these cases is found near the straight line PEMEL nominal power = PEMFC nominal power. But this point will be further developed in Section 4.2.

From another perspective, Figure 10 focuses on the lowest LCOE<sub>via H₂</sub> that can be achieved (LCOE<sub>via H₂</sub> for optimal equipment power) as a function of storage capacity and for the different storage technologies and locations. From these results, geological storage, both onshore or offshore, allows a large increase of the storage capacity with a minimal increase in LCOE<sub>via H₂</sub>. On the contrary, LCOE<sub>via H₂</sub> generated via tank or pipe storage is rapidly increasing together with storage capacity. It is also surprising to see how high is the tank storage offshore, even higher than offshore pipe whereas it was the contrary onshore. This is mainly due to the techno-economic assumptions underlying LCOE<sub>via H₂</sub> calculations. As described in Section 3, offshore pipe storage is chosen to be 1.5 times more costly than its onshore counterpart. However, tank
storage is assumed to be supported by an offshore platform, resulting in a huge offshore tank storage CapEx. But the main information from this Figure 10 is that, based on the used data for wind measurements and electricity production/consumption, no clear optimal storage capacity appears. And this is valid whatever the storage technology is. In that sense, there is no clear economic optimal but the decision-making process for such storage devices also needs to consider the added flexibility to the network and other non-economic advantages. This aspect will be detailed hereafter in Section 4.4.

From the literature [12, 47], similarly demonstrated that geological hydrogen storage could be more suitable for long term storage, that is to say for large storage capacities. Pipe and tank storage, due to their high unitary storage CapEx, and their high unitary charging and discharging CapEx (associated to PEMEL and PEMFC systems unitary CapEx) appear to be costly, even from the smallest storage capacity considered in the present study. For small scale storage [12], also suggests that batteries or bi-directional pumping could likely be achievable at low cost. In that respect, other storage technologies still for offshore wind electricity generation will be considered in the future as a following of the present work.

Concerning offshore storage technologies, the massive increase in overall system costs results in high LCOE<sub>via H₂</sub>, even at optimal. Generating hydrogen offshore via offshore wind was proven to be cost competitive with onshore generation, primary due to the assumed lower cost of hydrogen pipeline compared to subsea electrical connections as presented by Brunik et al. [15]. In those studies, offshore locations may benefit from cost savings. In those studies, the offshore wind farm is dedicated to off grid green hydrogen production. As already said, hydrogen pipelines in those studies are considered cheaper than sub sea electrical cables. Thus, there are energy transmission cost savings, resulting in an advantage for the offshore facility. However, in the present study, considering power-to-H₂-to-power facilities, there is no such cost savings, resulting in higher LCOE inherent to the full offshore location. Moreover, and in the present study, the facility doesn't benefit from any cost reduction by being moved offshore, although offshore geological storage may be cost competitive with pipe and tank onshore storage at large scales (in the limit of the above-mentioned assumptions). For further details on achievable LCOE<sub>via H₂</sub> for offshore facilities, costs of installation for these storage technologies offshore must be investigated deeper.

As a partial conclusion at this stage of the study, the cheapest storage technology from 20 to 200 GWh appears to be geological storage, either onshore or offshore, compared to its onshore/offshore alternatives. Offshore tank and pipe storages appear to be really expensive, due to their already expensive onshore unitary CapEx. In order to better understand the origin of these costs, Figure 11 depicts the observed optimal LCOE<sub>via H₂</sub> breakdown for onshore geological and pipe storages as a function of storage capacity.

From Figure 11, one can see that input electricity (input elec. in the graphic) represents a large amount of the cost, and even the major one in the case of the geological storage (upper plot of Figure 11). In both cases, this input electricity cost

accounts for approximately 250€/MWh. This cost in very high and represent more than half of the whole cost for all storage capacity in the case of geological storage. This is due to the efficiency of the hydrogen conversion, which is ~29.3% for geological storage. In fact, it means that for 1 unit of electricity generated by the PEMFC, 3.41 units of wind farm generated electricity are required. In details, these 3.41 units will be converted into hydrogen, compressed, and then transformed back into electricity with associated losses. As a matter of fact, with the used techno-economical costs (Table 3 and Section 2.3.2), the wind farm's LCOE is 73.7€/MWh when 12 MW turbine are considered. This basically results in an input electricity cost of 248€/MWh and is independent of the sizing of the hydrogen system and only dependent on the wind farm's LCOE. For pipe storage, conversion efficiency is slightly higher due to better performance of compressor, resulting in a lower input electricity cost.

In the same graph, PEMEL and PEMFC represents the share of PEMEL and PEMFC system cost only, but also including rectifier and inverter. According to the trend highlighted in the previous graphs of Figure 9, optimal equipment nominal power is higher for pipe storage, in order to try to compensate its higher capital cost. It results in a higher total costs of PEMEL and PEMFC systems for pipe storage in the bottom plot of Figure 11. In any case, for a given storage technology, PEMEL and PEMFC system costs are subjected to low variations. Their cost is almost constant no matter the storage capacity is.

Finally and still in Figure 11, storage represents the share in LCOE<sub>via H₂</sub> of storage system cost, including compressor. Effect of storage capital cost is shown again, with a sharp increase for pipe storage when storage capacity increases. When comparing the two plots of Figure 11, it is possible to confirm the trend earlier highlighted: an increase of the storage capacity results in higher LCOE<sub>via H₂</sub> mainly because of increase in the storage cost. An increase in the storage technology CapEx results in higher LCOE<sub>via H₂</sub> because of the increase in storage and optimal equipments powers.

Furthermore, these two plots illustrate the importance of input electricity price in order to achieve low LCOE<sub>via H₂</sub>. Offshore wind LCOE being higher than the one of solar or onshore wind, it affects a lot LCOE<sub>via H₂</sub> since conversion efficiency of the whole process is rather low. Therefore, and regardless of the system sizing and chosen technology, combining hydrogen storage for grid support with offshore wind, within the assumptions underlying the present study, leads to optimal LCOE<sub>via H₂</sub> higher than 250€/MWh. This is rather high but it needs to be considered as first estimation, knowing that:

* An electricity price of 73.7€/MWh is higher than usual electricity prices on the wholesale market.

* The possibility of negative electricity prices, as it was recently encountered in the European market is not assessed in the present study.

* Hydrogen equipment costs for 2030, which the projected year for the present study, are relatively high considering their low round trip efficiencies, also suggested by Hunter et al. [12] and Schmidt et al. [47].
<figure><img src="image_14.png" /><figcaption>FIGURE 11: LCOE<sub>via H<sub>2</sub></sub> breakdown as a function of storage capacity for onshore geological and pipe storages. 12 MW turbines are composing the farm and low variability scenario is considered. For each storage capacity, the PEMEL and PEMFC nominal powers were chosen at optimal.</figcaption></figure>

## 4.2. Turbine Nominal Power Influence on LCOE<sub>via H<sub>2</sub></sub>.

Turbine's model and rated power are directly influencing wind farm capacity factor as presented in Section 2.3.2, which in turns has a major impact on optimal equipment power and associated LCOE<sub>via H<sub>2</sub></sub>. Figure 12 shows LCOE<sub>via H<sub>2</sub></sub> maps for different couples of PEMEL/PEMFC nominal powers. In these graphs, a 200 GWh onshore geological storage with a low demand scenario is selected, still for the reference year.

From these graphs, the first observed general trend is that for each combination, the LCOE<sub>via H<sub>2</sub></sub> is always lower (darker blue colour) for turbines with higher rated powers. One of the possible explanation is that with more powerful turbine, the electricity LCOE is cheaper. And owing to the conversion

efficiency, cheaper input electricity will have a noticeable influence on the final LCOE<sub>via H<sub>2</sub></sub>.

More into details, the LCOE<sub>via H<sub>2</sub></sub> of observed optimal PEMEL/PEMFC nominal powers are different, and there are noticeable patterns. In fact, the lower the rated power, the higher the PEMEL nominal power with respect to PEMFC nominal power needs to be. And, on the contrary, the higher the rated power, the lower the PEMEL nominal power with respect to PEMFC nominal power needs to be. For example, from Figure 12, respective wind farm capacity factors for selected 6, 12 and 21.5 MW turbines are ~37%, 53% and 59% and the obtained optimal (PEMEL/PEMFC) couple of nominal power are: (460 MW/120 MW), (380 MW/280 MW), (320 MW/380 MW). And associated LCOE<sub>via H<sub>2</sub></sub> for
each model is, respectively, 592, 441 and 425€/MWh, which is also in accordance with the above-mentioned aspects.

To explain these patterns in the plots of Figure 12, one can advocate that: on the one hand, to achieve lower LCOE<sub>via H₂</sub>, the PEMFC should produce more power. Hydrogen being the energy vector permitting PEMFC electricity generation, the storage should be able to supply hydrogen to PEMFC as long as possible when it needs to operate. Therefore, hydrogen production from wind farm power surplus (supplied by PEMEL), should be able to balance the hydrogen consumption by PEMFC in power shortage times. But, for relatively low wind farm capacity factor, compared to electricity demand, electricity surplus are sporadic. Therefore, at optimum, PEMEL nominal power tends to increase in order to extract more hydrogen from these occasional electricity surplus. And, on the other hand, optimal PEMFC power tends to decrease, to avoid unnecessary CapEx and to limit hydrogen consumption and balance the lower hydrogen supply. On the contrary, a relatively high capacity factor compared to electricity demand (see lower plot of Figure 12) results in frequent electricity surplus. Optimal PEMEL nominal power tends to decrease, limiting the system total life cycle cost while avoiding the storage saturation. And, on the PEMFC side, nominal power tends to increase to balance hydrogen supply, resulting in higher electricity generation and lower optimal LCOE<sub>via H₂</sub>.

This figure shows that to minimise LCOE<sub>via H₂</sub> for a given storage capacity, a balance should be found between:

1. increasing equipment's nominal powers to decrease imposed limitations on power fluxes (hydrogen production and consumption) and

2. increasing the total life cycle of the system by increasing those equipment's nominal powers leading to increased LCOE<sub>via H₂</sub>.

The wind farm capacity factor, compared to electricity demand, determines the frequency and intensity of power surplus and shortage. An important aspect to consider here is that the electricity demand is evaluated following the methodology described in Section 2.2. For the presented results, the low variability scenario was chosen, but the obtained results for the high variability scenario are depicted in Figure A3 of Appendix A with no much differences. Moreover Figure A2 in appendix illustrates how optimal equipment power is chosen to balance hydrogen fluxes within the system.

### 4.3. Inter-Annual Variability.
Wind farm's capacity factor and power demand may vary from 1 year to another as illustrated in Sections 2.2 and 2.3.2 from real data measurements. In that respect, Figure 13 shows how optimal LCOE<sub>via H₂</sub> is impacted by inter-annual variations. Storage capacity is either 20 GWh or 200 GWh but onshore and the results are presented for all tested turbines with a couple of PEMEL/PEMFC nominal powers as the one obtained from the 2012 simulation. But this last assumption does not have any major influence not to say any visible influence. Then, for this configuration of hydrogen storage device, LCOE<sub>via H₂</sub> is computed for the 8 years of measurements comprised between 2012 and 2020.

<figure><img src="image_15.png" /><figcaption>FIGURE 12: LCOE<sub>via H₂</sub> for different wind turbine models. 200 GWh Onshore geological storage is considered.</figcaption></figure>

Averages LCOE<sub>via H₂</sub> and standard deviations based on these inter-annual variations are thus depicted in Figure 13.

As a first general comment, a higher wind farm capacity factor (higher turbine rated power) combined with a lower
<figure><img src="image_16.png" /><figcaption>FIGURE 13: LCOE<sub>via H<sub>2</sub></sub> variations for optimal equipment power for 2012–2020 simulations and all wind turbine types. The marks represent the 8-year averages and error bars represent two times the standard deviations.</figcaption></figure>

storage cost reduce LCOE<sub>via H<sub>2</sub></sub> inter-annual variations. Indeed, for 6 MW turbines for example, standard deviation of LCOE<sub>via H<sub>2</sub></sub> with pipe storage is higher for 200 GWh than for 20 GWh (cheaper storage because of reduced capacity), since it decreases from 102 to 36€/MWh. Furthermore, for 200 GWh storage capacity, standard deviation of LCOE<sub>via H<sub>2</sub></sub> with pipe/tank/geological storage (unitary storage CapEx in descending order) is, respectively, 102, 74 and 26€/MWh (standard deviation decreasing with overall storage costs). Finally, still considering 200 GWh storage capacity, standard deviation of LCOE<sub>via H<sub>2</sub></sub> with pipe storage and 6/12/21.5 MW (wind farm's capacity factor in ascending order) is, respectively, 102, 46 and 43€/MWh (standard deviation decreasing with higher capacity factors).

As a partial conclusion, from 1 year to another, wind resource and electricity demand may vary, leading to change in electricity surplus and shortage frequency and intensity. Standard deviation is a measurement of how much LCOE<sub>via H<sub>2</sub></sub> is sensible to these changes for different configurations. Within the given assumptions of this study, the results clearly show that geological storage may achieve the lowest LCOE<sub>via H<sub>2</sub></sub> with the lowest uncertainty regarding inter-annual variations for all tested storage capacities (from 20 to 200 GWh). For farm composed of 21.5 MW turbines (high capacity factor and higher electricity generation than the average power demand), LCOE<sub>via H<sub>2</sub></sub> is approximately equal to 400€/MWh with a standard deviation of 8€/MWh. Such a result tends to say that inter-annual variability would be weak, not to say negligible, in comparison to all the other assumptions used in the model. Or conversely, such hydrogen storage devices would be rather insensitive to inter-annual

variations, which could be an important aspect from an investor point of view.

4.4. *System's Scaling Influence on Added Flexibility to the Grid.* Owing to the intermittency of wind energy (as most of other renewable energies) and the variation of electricity consumption, the integration of the wind farm electricity production into the French grid needs to meet the demand. This results in what will be called here local electricity imports/ exports (as shown in Section 2.6) to balance wind farm production with grid demand. The hydrogen storage system is designed to be used to reduce these imports/exports (see Section 2.6), by absorbing electricity during surplus and releasing it during shortage. However, as seen in Figures 7 and 8 in Section 2.6, local imports/exports can be generated, even when the storage system is coupled, due to energy conversion limitations (equipment charging and discharging power lower than power surplus/shortage, or full/empty storage). Thus, in the following, 'local electricity imports/exports' refer to additional quantities of electricity that need to be imported/exported from the French grid to meet the demand when the wind farm coupled with the storage can't achieve it. Local electricity imports/ exports somehow indicate the level of autonomy of the system, since they quantify its dependency to external electrical fluxes to meet the hourly demand. In the present study, they are yearly quantified. And, a reduction of local electricity imports/exports from one sizing to another come out as an increase of the system's autonomy, indicating that it is more resilient or flexible to demand and wind resource variations: the system is less dependant on external flux. Therefore, in order to study the system's flexibility, the notion of *avoided local*
<figure><img src="image_17.png" /><figcaption>FIGURE 14: Avoided local exports as a function of equipment nominal power and storage capacity. The reference year and the baseline configuration are considered.</figcaption></figure>

electricity imports/exports is introduced in Figures 14 and 15. And, to quantify the performance of the energy storage system in achieving this flexibility goal, avoided local electricity imports/exports are calculated. The higher the avoided local electricity imports/exports are, the more efficient the storage system is and the more flexible the network gets.

In the 'low variability' demand scenario, for a given size of the system and over a 1 year simulation, avoided local electricity imports/exports are calculated as:

$$ \text{Avoided local imports}^{\text{low}} = \frac{\text{Imports}_{\text{farm}}^{\text{low}} - \text{Imports}_{\text{farm+sto}}^{\text{low}}}{\text{Imports}_{\text{farm}}^{\text{low}}} \times 100, \quad (5) $$

$$ \text{Avoided local exports}^{\text{low}} = \frac{\text{Exports}_{\text{farm}}^{\text{low}} - \text{Exports}_{\text{farm+sto}}^{\text{low}}}{\text{Exports}_{\text{farm}}^{\text{low}}} \times 100, \quad (6) $$

where Imports/Exports<sub>farm</sub><sup>low</sup> represents yearly local imports/ exports generated when no storage system is coupled, and Imports/Exports<sub>farm+sto</sub><sup>low</sup> represents yearly local imports/ exports generated with the storage system, for a specific size. Avoided imports/exports represent the percentage of imports/exports removed by the energy storage system, when compared to imports/exports generated when the wind farm is in operation without any storage possibility.
<figure><img src="image_18.png" /><figcaption>FIGURE 15: Avoided local imports as a function of equipment nominal power and storage capacity. The reference year and the baseline configuration are considered.</figcaption></figure>

As a matter of example, the integration of the wind farm into the grid without any storage possibility will generate electricity exports each time its production is higher than demand. If avoided local electricity exports are equal to 60% over a year and for a given energy storage size, it means that the equivalent of 60% of electricity exports was removed from the grid by the storage system, compared to the exports generated without any storage (60% of yearly surplus was absorbed).

In the 'high variability' demand scenario, avoided local electricity imports/exports are calculated slightly differently:

$$ \text{Avoided local imports}^{\text{high}} = \frac{\text{Imports}_{\text{farm}}^{\text{high}} - \text{Imports}_{\text{farm+sto}}^{\text{high}}}{\text{Imports}_{\text{farm}}^{\text{low}}} \times 100, \quad (7) $$

$$ \text{Avoided local exports}^{\text{high}} = \frac{\text{Exports}_{\text{farm}}^{\text{high}} - \text{Exports}_{\text{farm+sto}}^{\text{high}}}{\text{Exports}_{\text{farm}}^{\text{low}}} \times 100. \quad (8) $$

The quantity of imports/exports removed from the grid in the high demand scenario is still compared to the yearly imports/exports generated by the wind farm alone in the low demand scenario. This allows to compare the difference in removed imports/exports in both scenario. For example, it might be possible that avoided local imports in the 'high variability' demand case are equal to 103%, meaning that the storage has not only totally balanced wind farm production and demand all over the year of simulation, but is also
able to produce additional power to avoid importations at the national level.

Figures 14 and 15, respectively, shows avoided local exports and imports as a function of equipment nominal power and storage capacity for both low variability and high variability demand scenarios. For these calculations, the reference year and the baseline configuration are considered. Also, to ease the representation, PEMEL/PEMFC nominal powers were chosen to be equal.

Increased equipment nominal powers and storage capacity allows to increase avoided local electricity imports/exports, even until 100% for powerful enough equipment. Furthermore, no major differences between the two scenarios can be observed from the two images of Figure 14.

However two thresholds can be identified from these results: for a given storage capacity, avoided exports are increasing with equipment nominal power until a certain point, where increasing equipment power doesn't affect avoided exports any more. For 100 GWh storage capacity, avoided local electricity exports reach their maximum at approximately 400 MW PEMEL/PEMFC nominal powers. Further increase of the equipment powers has no effect on avoided exports. And similarly, for given equipment nominal powers, avoided local electricity exports are increasing with storage capacity until a certain point, where increasing storage capacity doesn't affect avoided exports any more. For 390 MW PEMEL/PEMFC power, avoided local power exports (upper plot) reach their maximum at approximately 120 GWh storage capacity. Further increase of the storage capacity has no effect on avoided exports. It seems that there is certain equipment nominal power/storage capacity limit beyond which one of these equipment is saturated and further increase doesn't affect avoided exports any more.

Local exports occurs when the hydrogen storage device cannot absorb electricity, that is to say when limitations on energy conversion occurs. If the storage is full during surplus, the limitation on energy conversion is due to storage capacity. But if the equipment is not powerful enough to absorb all electricity surplus, the limitation on energy conversion is due to equipment nominal power.

As a final consideration with respect to avoided local power exports, negligible differences can be observed in Figure 14 between the two scenarios. In both cases, the designed system is able to remove nearly all, not to say all electricity exports when the equipment nominal powers/storage capacity are large enough.

From Figure 15, very similar plots are depicted but for avoided local electricity imports. And very similar trends are obtained. That is to say, the higher the equipment nominal powers and storage capacity are, the higher the avoided local electricity imports are. In the upper plot of Figure 15, even up to 85% of avoided local electricity imports can be obtained for powerful enough equipment in the low variability demand scenario. However, it might be surprising to observe that the 100% of avoided local electricity imports cannot be obtained even with the most powerful equipment and storage capacities. But, even if the total energy produced by the farm with 1 GW × 53% × 8760 h ≈ 4.6 TWh is larger than the ≈2.95 TWh of nuclear electricity yearly removed, this does not consider the

losses in energy conversion from electricity-to-hydrogen-to-electricity. Section 4.1 and especially the results of Figure 11 highlighted this high impact of the relatively low efficiency of energy conversion. Also, another aspect that may be taken into consideration is that saturation or emptiness of the hydrogen storage may happen, even with the largest storage capacities.

Finally, for the lower plot of Figure 15 for the high variability demand scenario, the situation is slightly improved. In this scenario, as the national importations were also first removed, this leaves more space for the storage system and fuel cell to deliver electricity to the network. Therefore, for a given couple of (equipment nominal powers/storage capacity), a higher percentage of avoided local electricity imports is obtained with the high variability scenario than with the low one. This is great because it means that the whole storage system is more efficient with this scenario, which is also the one closer to future real configuration. In fact, in the future, the network regulation and hence the decision to import or export electricity will be taken while knowing the local productions and consumption. Keeping that in mind, it is noticeable that the 100% coverage is not attained, most probably because of the above-mentioned limitations: saturation or emptiness of the storage device, losses via the energy conversions ... But also because sometimes, very high quantities are imported with this scenario, with imported power being up to 5 GW (see Figure 3), which is far beyond the capacity of the considered storage device, limited here to 1 GW. But in a near future, if such storage device develops, it might not be an isolated case. And in such a case, with several storage devices, possibly coupled to different offshore wind farms, the situation may be even more improved.

However, even in this configuration of a single storage device coupled to a single offshore wind farm, more than 100% of avoided local electricity imports can be obtained for a farm equipped with the largest wind turbines and for 2016, as depicted in Figure 16.

## 5. Conclusion

In the present article, a numerical code was developed and used in order to highlight trends in optimal sizing of a hydrogen storage system for a 1 GW offshore wind farm. This hydrogen system is coupled to the wind farm for a 'grid support' type use, for peak shaving and load following purposes. Real wind measurements for a consented offshore site together with historic electricity productions/consumptions for France were used as input data, considering several common years of analysis.

A system's approach was used, that is to say no electrical/ mechanical modelling of the equipment was directly modelled but enabling to compute very numerous configurations with limited computational resources. As common features, the whole system was composed of a PEMEL and a PEMFC of different nominal powers. But several storage technologies (geological, tank and pipes) were considered together with the possibility of localising these devices either onshore or offshore. Also, different turbine sizes and rated powers were considered enlarging the possibilities of analyses. Finally, several assumptions were made with respect to the electricity demand evaluations and also to the CapEx and OpEx of all these
<figure><img src="image_19.png" /><figcaption>FIGURE 16: Avoided local imports as a function of equipment power and storage capacity for 21.5 MW turbines in 2016.</figcaption></figure>

technologies. LCOE and avoided local imports/exports were used as indicators, respectively, for economic performance assessment and grid support efficiency.

From the obtained results, several key trends were observed, some of them being in accordance with already evoked results in the literature, some others being new. A synthetic summary of these findings can be listed below:

* With the current CapEx and OpEx prices, storing electricity via hydrogen storage reveals to be at quite high a LCOE<sub>via H₂</sub>. But these prices are not yet at equilibrium given that the technology is not fully mature.

* The cost of input electricity is responsible for a high portion of this LCOE<sub>via H₂</sub> due to the rather low energy conversion efficiency (elec-to-hydrogen-to-elec). This

very high input electricity price, which is not representative of usual prices encountered on the market, will need to be revisited soon if more and more negative electricity prices are encountered on the wholesale market and/or any other similar situation.

* Regarding the sizing itself, the cost of the storage is the main driver, first owing to the chosen technology (geological/tank/pipe) and second owing to the storage capacity (except for geological).

* Higher storage costs, either due to higher storage capacity or storage technology cost, result in higher optimal equipment nominal powers and associated LCOE<sub>via H₂</sub>.

* Wind farm's capacity factor, resulting here from the turbine selection, influences optimal equipment nominal powers and reduces achievable optimal LCOE<sub>via H₂</sub>.
* Larger storage capacity and more expensive storage technologies are more sensible to wind resource, power demand and inter-annual wind variations.

* LCOE<sub>via H₂</sub> using geological storage is identified as the most economical one with ≈400€/MWh owing to the given assumptions and also as being weakly sensitive to the storage capacity. Furthermore, its sensibility to inter-annual variations is negligible.

* But the conclusions of the present study reveal that, in this study of electricity-to-hydrogen-to-electricity, there is no obvious optimal sizing for a given choice of technology. And this is valid for all the tested configurations.

* A key aspect will be the forthcoming prices of electricity on the wholesale market and how services to the grid could be valued: in other word, will it be possible to receive money for evacuating large quantities of electricity surplus from the grid?

In the near future, other storage technologies for grid support, such as batteries, bi-directional pumping or compressed air energy storage (CAES), will be implemented into the numerical code. Their sizing at the level of a 1 GW offshore wind farm will be studied, enabling comparisons with hydrogen. These technologies, having different round trip efficiencies and marginal costs, will surely need to be sized differently while achieving different LCOE. Although, it is not yet implemented, literature gives insights on what may happen in the model:

* Batteries exhibit really low marginal power costs but high marginal energy costs [12]. They are expected to be widely economical (below 100 €/MWh) for storage durations up to only few hours (i.e., rather powerful equipment at low storage capacity), which is adapted to several grid services such as energy arbitrage, power quality, peaker replacement and others. However, they may be ill-suited for very large scale storage because of their energy storage costs [47] and thus less competitive than technologies that can benefit from underground energy storage, like hydrogen with geological storage but also adiabatic and isothermal CAES.

* On the other hand, CAES may exhibit similar trends than the ones observed in the present article. As for hydrogen with geological storage, at least in 2030, CAES is expected to have high power marginal costs and low energy marginal costs. It would also be adapted to large scale storage, with high storage durations. Pumped hydro storage and thermal storage are from the same kind, and comparisons between those technologies could help determining until which storage duration one technology is more interesting economically than the others. Sizing would also change, and thus achievable impact on grid reliability would not be the same for the same LCOE.

Flexibility characteristics of those technologies, such as load gradient and efficiency degradation, may also be implemented in the code. These improvements and additional possible technologies will still have an objective of improving assessment on

impact on grid and storage system performances, while keeping a relatively low computational cost. Finally, another improvement will considered the possibility of having not only a single wind farm with a single storage capacity but also several storage devices possibly coupled with several wind farms, located in different regions and hence being powered by different wind regimes.

## Appendix A

**Appendix A1. Storage Influence on LCOE<sub>via H₂</sub>.** Figure A1 shows LCOE<sub>via H₂</sub> as function of PEMEL/PEMFC nominal power, for 200 GWh storage capacity, within the offshore facility. This result is an extension of the trend highlighted in Section 4. Costs of technologies suitable for offshore location are higher than onshore. Total life cycle cost of the system is very much increased, and as described in Section 4.1 optimal equipment power and associated LCOE<sub>via H₂</sub> increase.

**Appendix A2. Turbine Influence on LCOE<sub>via H₂</sub>.** Figure A2 shows temporal evolution of H₂ stock for different wind turbines at optimal equipment. A higher capacity factor regarding to demand results in more frequent power surplus and less power shortage. Optimal equipment power, giving the lowest LCOE<sub>via H₂</sub>, is influenced by this change. Optimal PEMEL power tends to decrease, limiting the system total life cycle cost while keeping a high hydrogen supply because of the increase in potentially usable power surplus resource. On the other hand, PEMFC power tends to increase to balance hydrogen supply, resulting in higher power generation and lower optimal LCOE<sub>via H₂</sub> (Figure 12). In Section 4.2, it was explained that this mechanism occurred in order to balance energy flux within the system, and thus reduce LCOE<sub>via H₂</sub>. On Figure A2, one can observe how optimal equipment power for a given turbine have vocation to balance energy fluxes within the storage, in order to allow PEMFC to produce power as most as possible, as described in Section 4.2. PEMEL and PEMFC nominal power decrease/increase with wind farm's capacity factor according to the increase/decrease in power surplus/ power shortage. The mean stock for all turbines is approximately equal to 50%.

Figure A3 shows LCOE<sub>via H₂</sub> as a function of equipment power for all turbines considered and 'high variability' demand. As explained in Section 4.4, this scenario has no impact on PEMFC power production and thus LCOE<sub>via H₂</sub>. A reduction of 5 €/MWh maximum can be observed.

**Appendix A3. Added Flexibility.** Section 4.4 highlighted that changes between 'low variability' demand and 'high variability' demand were negligible. This was due to the low impact of 'high variability' scenario on equipment energy production, and thus LCOE<sub>via H₂</sub>. Figure A4 shows temporal evolution of H₂ stock at optimal equipment for the two demand scenario. One can observe that ad hoc high demand peak barely affects PEMFC production (H₂ stock remains almost unchanged, demand peak for 2012 occurring in February). This results in negligible effects regarding avoided local imports/exports and thus LCOE<sub>via H₂</sub>.
<figure><img src="image_20.png" /><figcaption>FIGURE A1: LCOE<sub>via H<sub>2</sub></sub> as a function of PEMEL/PEMFC system nominal power for different storage technologies and 200 GWh storage capacity within offshore location and reference baseline.</figcaption></figure>

Moreover, the fact that less power imports are removed from the grid in the 'high variability' demand scenario, as highlighted in Section 4.4, can be explained using Figure A4. Indeed, the PEMFC production seems to increase in February 2012 (2012-02 on the graph) due to high demand peaks,

resulting in more removed imports from the grid. However, due to those additional demand peaks, the hydrogen storage is nearly empty during March–April 2012 (2012-03 and 2012-04 on the graph). Much more than in the 'low variability' demand scenario. One can conclude that in the 'high variability'
<figure><img src="image_21.png" /><figcaption>FIGURE A2: Temporal evolution of H₂ stock for 6/12/21.5 MW turbines at optimal equipment power and 200 GWh storage capacity in the reference baseline.</figcaption></figure>

demand scenario, additional imports removed during demand peaks are balanced in the following weeks by additional imports that were not occurring in the other case, because the storage falls empty.

Within the assumptions of the study, it shows that for an energy system sized at the level of a 1 GW offshore wind farm, trying to satisfy demand peaks at the national level has a negligible effect on the system.
<figure><img src="image_22.png" /><figcaption>FIGURE A3: LCOE<sub>via H<sub>2</sub></sub> for different wind turbine models and 'high variability' demand scenario. 200 GWh Onshore geological storage is considered.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>FIGURE A4: Temporal evolution of H₂ stock for the two demand scenarios in the reference baseline.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>FIGURE A5: Avoided power local exports as a function of equipment power and storage capacity for different wind turbine models, in low demand scenario.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>FIGURE A6: Avoided power local imports as a function of equipment power and storage capacity for different wind turbine models, in low demand scenario.</figcaption></figure>
Figure A5 illustrates how wind farm capacity factor and demand influence avoided power exports. Avoided power exports decrease while wind farm's capacity factor increases. A higher capacity factor for the same power demand results in higher and more frequent power surplus. For the same equipment power, less power surplus is absorbed.

Figure A6 illustrates how wind farm capacity factor and demand influence avoided power imports. Similarly to the trend highlighted in Figure A5, avoided power imports increase while wind farm's capacity factor increases. A higher capacity factor for the same power demand results in lower and less frequent power shortage. For the same equipment power, power shortages are more easily filled by the system.

## Data Availability Statement

The data used in this study will be available upon request from the authors.

## Conflicts of Interest

The authors declare no conflicts of interest.

## Funding

The authors acknowledge the financial support from Normandy Region through the Laboratoire d'Excellence Energy, Materials and Clean Combustion Center (LabEx EMC3) and the Graduate School Materials and Energy Sciences (GS-MES).

## Acknowledgments

The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR) and the Normandy Region through the Labex Program EMC3 (ANR-10-LABX-09-01) and the WILIAM project.

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