**3. System Overview**

#### *3.1. Description*

The system described in [11] is named *Wi-DACIS*, standing for wind-driven air compression and isobaric storage. It utilises the technologies previously mentioned in Section 2. A wind-driven, direct drive air compressor replaces the gearbox system in a conventional geared offshore wind turbine. The high-pressure air exhausted from the compressor can either be immediately expanded to generate electricity or passed into an energy bag air storage system. This provides flexibility to the otherwise intermittent renewable energy supply from the turbine. Because primary energy from the wind is used directly to compress air before it is ever converted into electricity, this constitutes a GIES system.

Being direct drive, the problem of intake swept volume must be considered. In a similar manner to the pumped heat system described in [6], the solution is to supply air to the primary compressor at a pressure higher than ambient. However, instead of the closed loop utilised by [6], *Wi-DACIS* employs a prior stage of compression, which absorbs air from the environment, compressing it from ambient conditions to a suitable pressure for the wind-driven compressor.

In [11], the *Wi-DACIS* system was originally described with two pressures of air store: a high-pressure store fed by the wind-driven compressor, and an additional mediumpressure store fed by the first stage compressor. While the authors believe that there could be significant merit to the additional flexibility provided by the medium-pressure store, the full cost/benefit analysis of such a store is beyond the scope of this paper and will be addressed in future work.

The classification of *Wi-DACIS* as a purely GIES system is dependent on the form that the first stage of compression takes. If it is driven by electricity from the grid, as is assumed for the analysis in Section 4, then it acts as a hybridisation of standalone and GIES systems, as some fraction of the energy in storage has been absorbed from the grid. The ratio of standalone to GIES utility is then dependent on the relative powers of the two compressor stages.

However, if the first stage of compression is run by some non-grid method (i.e., one in which electricity from the grid is not required, such as solar or wave power), then *Wi-DACIS* performs as a wholly GIES system. The possibility of using a form of trompe compressor as a method of offshore first-stage compression is also discussed in [11], using the water head created by wave heights to push volumes of water to a depth, pressurising the air entrained within that water.

Figure 4 shows the *Wi-DACIS* system in its hybrid GIES-standalone configuration, utilising a single high-pressure air store.

Important components and parameters for the *Wi-DACIS* system are:


**Figure 4.** The *Wi-DACIS* system in an adiabatic main stage configuration. In an isothermal configuration, HXU and TES are not present.

#### *3.2. Possible Configurations*

An important consideration in a *Wi-DACIS* system is whether the main stage compressor is adiabatic or isothermal. This decision dictates several system parameters, including the relative powers (or relative pressure ratios, depending on which values are set) of the two compressors. Because the product of *p* and *V* remains constant throughout isothermal compression, if the main stage compressor is isothermal, the relative powers of the two stages can be described as:

$$\frac{P\_G}{P\_W} = \frac{\ln(r\_1)}{\ln(r\_2)}.\tag{11}$$

By comparison, if the main stage compressor is adiabatic, the relative powers can be described as:

$$\frac{P\_G}{P\_W} = \frac{\chi \ln(r\_1)}{(r\_2)^{\chi} - 1}.\tag{12}$$

Figure 5 shows that, for a set upper pressure *r*1*r*2, an adiabatic main stage will result in a smaller grid-powered compressor. Given that the *Wi-DACIS* system intends the mainstage compressor to have a reasonably high power compared to the first-stage compressor (certainly *PG/PW* < 1), this limits the acceptable relative pressure ratios. In the example given in Figure 5, where *r*1*r*<sup>2</sup> = 200, *r*<sup>2</sup> would therefore need to be greater than 9 for an adiabatic main stage or greater than 14 for an isothermal one.

**Figure 5.** Power ratios for an isothermal and an adiabatic main stage of compression, where the upper pressure, *r*1*r*2, is set.

The choice between isothermal and adiabatic compression also affects the required inlet swept volume, as is described in Section 2.3. For any given intake pressure and pressure ratio, an adiabatic compressor will require a lower intake swept volume than an isothermal one. This is due to the additional work done in adiabatic compression to heat the gas. As previously mentioned, the upper temperature is a limiting factor in the adiabatic case, but multi-stage compression is possible to keep this temperature within reasonable limits (by taking heat from the air at several points during the compression process).

With both of these effects taken into consideration, an adiabatic main stage appears to be the clear choice. However, this is also dependent on the relative costs of the compressors. Regardless of whether the main stage compressor is isothermal or adiabatic, heat exchange of some kind will be required, either in the form of inter-stage cooling, or to strip the heat from the air for storage. Assuming, then, that the isothermal and adiabatic compressors and heat exchangers are of similar costs, an important measure of the viability of adiabatic main stage compression is whether the thermal energy storage (TES) required by an adiabatic compressor is cost-competitive with the high-pressure energy bag system. Given that the costs calculations for the energy bags in Section 2.4 only include material costs, the same will be applied to the TES.

#### **4. System Analysis**

#### *4.1. Simulation Data and Assumptions*

Simulations of the *Wi-DACIS* system have been run for both the isothermal and adiabatic main-stage compressor configurations. These will provide insight into the relationship between various *Wi-DACIS* parameters, as well as providing a reasonable minimum size for the energy store and some sense of the profitability of such a system.

Wind speed data for 2015 were obtained from the UK Met Office Integrated Data Archive System (MIDAS) [30]. This took the form of sea-level wind speed data, which were converted to wind speed at turbine-height with:

$$
\mu(z) = \frac{\mu\_\*}{\kappa} \left[ \ln \left( \frac{z}{z\_0} \right) \right],
\tag{13}
$$

where *u*(*z*) is the wind speed at altitude *z*, *u*\* is the friction velocity, *κ* is the Von Kármán constant (~0.4) and *z*<sup>0</sup> is the roughness length (~0.0002 m for open sea) [31,32].

Hourly data from 12 locations were used (Figure 6). These sites were chosen due to the availability of sufficient wind speed data over the given period. Several of these sites would not necessarily be suitable for a *Wi-DACIS* system, due to their location on the continental shelf implying relatively shallow water. However, the data at these sites are sufficiently representative of generic offshore wind data to be suitable in the analysis. Figure 6 includes the approximate outline of the continental shelf, showing the closeness of the sites to relatively deep water. Figure 7 shows the worldwide water depth map. It is clear that a depth of 2000 m is closely accessible for much of the world's coastline.

**Figure 6.** Map of the 12 wind data point locations. Letters used to differentiate between sites. Adapted from [33] (Map Data: ©2022 Google, GeoBasis-DE/BKG ©2009).

**Figure 7.** Map of worldwide water depth. Adapted from [34].

The wind speed data were converted to energy generation data using the real power curve of the reference turbine, shown in Figure 8 [23]. The energy generation data could then be used in the simulation to calculate the energy flow in the system via air volumetric flow rates.

**Figure 8.** Power curve for reference wind turbine. Adapted from [23].

UK day-ahead electricity price data over the same 2015 time period were taken from [35]. It is assumed that the system operates with a merchant contract, using the hourly day-ahead electricity prices as a basis for decision-making. This is in contrast to many UK wind farms, which operate on the Contracts for Difference (CfD) scheme, wherein a single price is agreed upon per unit of electricity supplied to the grid, regardless of instantaneous electricity value. The revenue of a conventional wind turbine on the CfD scheme will also be considered for the sake of comparison.

The simulation assumes that the *Wi-DACIS* wind-driven compressor is capable of performing at part-load to the same extent as the conventional reference turbine. Optimal part-load performance would be made possible with a compressor design similar to the one described in [6], which allows individual compression cylinders to be deactivated via automated active valve control. It is expected that these operations could be performed at much shorter timescales than is required for the turbine blades to adjust pitch, meaning that overall part-load performance should not be affected.

The grid-powered isothermal compressor is assumed to be of sufficient power to provide the necessary volumetric flowrate to the main stage compressor at its nameplate capacity. It is also assumed to have no variation in efficiency at partial load.

In order to gain some measure of the cost of each iteration, unit costs were applied to each element of the system. Reasonable values for *a*, *b* and *c* from Equation (9) were found that satisfied the condition of a single optimum at *D* ≈ 20 m and gave a cost of roughly 50 £/m3, indicated by [26]. The total energy bag storage was calculated as multiples of these optimal bags, with an additional smaller bag (if necessary) at a less optimal cost. It is assumed that each energy bag can store a parcel of air for as long as is required between the charging and discharging cycles. This is a reasonable assumption given the store sizes considered (<200 h).

#### *4.2. Methodology*

The initial inputs for the simulation can be split into system parameters and unit costs. The system parameters tested in the simulation are presented in Table 2.


**Table 2.** System parameters for *Wi-DACIS* simulations.

For each combination of store capacity and swept volume, the system powers, inlet and outlet volumetric flowrates, pressure ratios and energy bag sizes were calculated, both for the isothermal and adiabatic configurations. The initial state of charge (SoC) assumed for the store was 50% of the maximum charge. Operation over the year time period was then simulated for each system and at each site.

The simulation was performed assuming perfect knowledge of a year of day-ahead electricity prices and wind availability. A modified version of the price-matching algorithm found in [36] was used to find the optimal store and compressor power usage at each hour time interval.

The income (revenue) was calculated as a summation of the hour-wise multiplication of instantaneous electricity price and instantaneous expander power. Similarly, the expenditure was calculated as a summation of the hour-wise multiplication of instantaneous electricity price and the instantaneous power of the first-stage, grid-powered compressor.

For the configuration where the wind-driven stage is adiabatic, the required capacity of the thermal energy store was calculated using the work done by the adiabatic compressor from Equation (2), and the temperature was found by:

$$T\_{store} = T\_{ref} r\_2 r\_{\prime} \tag{14}$$

where *Tref* is the ambient temperature of the air. In a packed gravel bed TES, using a thermal medium (quartzite) with a specific heat capacity of 850 J/kg·K, the required mass was found:

$$m\_{quartzite} = \frac{W\_{Hcut}}{850 \cdot \left(T\_{store} - T\_{ref}\right)}.\tag{15}$$

The thermal medium was given a material cost of 0.1 GBP/kg [37]. A mass overrating factor of 2 was then applied.

An estimate of the steel required for the thermal store was obtained using a random sphere packing density ~0.64, quartzite and steel densities of 2700 kg/m<sup>3</sup> and 8000 kg/m3, respectively, and assuming a TES store with a height to diameter aspect ratio of 2 and 20 mm thick walls (considered to be very conservative):

$$V\_{\text{stor}} = \frac{m\_{\text{quartz}}}{0.64 \times 2700} \,\text{\textdegree} \tag{16}$$

$$m\_{steel} \approx 0.646 \left( m\_{quartz} \right)^{2/3}.\tag{17}$$

The cost of worked steel for wind turbines is in the order of 2 GBP/kg, based on assertions made by Henrik Stiesdal on several occasions, including at Floating Offshore Wind UK (30 October 2018) and the EWEA Floating Wind Power Debate (18 November 2015). Steel was therefore costed at 2 GBP/kg. The capital costs per unit power for the compressors and expanders were chosen partly from values in [2,13,38–40] and partly on the idea that a conventional wind turbine costs ~1 GBP/W and replacing the expensive gearbox element with an expensive compressor element will not change that value too significantly. These costs are summarised in Table 3. It should be noted that the cost (GBP/kW) for compressor and expander machinery is dependent on several factors, including its rated power—larger machines generally cost less per unit power [39–41]. In order to take advantage of the scalability in the *Wi-DACIS* system, it is likely that several turbines would be fed by a single

grid-powered compressor and would feed into a single expander. Although a single turbine has been simulated, this scalability has been accounted for in the capital costs chosen.

**Table 3.** Per-unit power capital costs for the compressor/expander machinery. Based on values in [2,13,38–40].


To reasonably account for losses in the system, the efficiencies shown in Table 4 were applied in the simulation. As with cost, the efficiency of machinery can be affected by its rated power [42,43]. The large scale of the machines used in *Wi-DACIS* means that the upper range of efficiencies is certainly accessible.

**Table 4.** Efficiencies of the system machinery used. Based on values in [44–48].


\* The efficiency value of the main stage compressor is given as 1 because it is a relative efficiency, which will be used to compare with alternative wind + storage systems in Section 4.5. The result of applying the COMG efficiency is that the pure transmission efficiency of the Wi-DACIS system will be 90% of the transmission efficiency of a conventional turbine.

The range of cost and efficiency values shown were used in data validation testing, whereas the nominal values were used in the main simulation.

The efficiency losses in the grid-powered compressor and the expander were accounted for by increasing the expenditure and decreasing the income by a factor of *η*, while keeping the actual exergy absorbed/sold the same.

Efficiency losses in the energy bags are expected to be extremely small. In this paper, a representative value of 0.98 was chosen. This was applied by increasing the cost of the stores by this factor.

The outputs of the simulations were: instantaneous compressor and expander powers over time, state of charge for the store over time, capital costs, revenue and expenditure (the difference of which is the profit), a one-year return on investment and potentially limiting parameters such as TES temperature and ratio of *PG/PW.*

#### *4.3. Results and Discussion*

Each of the 12 sites used in the simulation exhibited the same behaviours, although the exact values were slightly different due to local wind data. The averaged results of the 12 sites are used in the following figures. Maximum and minimum values given in the text cover all 12 sites.

The primary effect of increasing the inlet swept volume is that the main stage compressor, COMW, becomes a larger proportion of the total system power; alternatively, COMG becomes a smaller proportion. This is caused by the increased ratio *r*2/*r*1, seen in Figure 9.

**Figure 9.** The relationship between the relative power of the main-stage and first-stage compressors and the intake swept volume, in the form of pressure ratio *r*2/*r*1.

Increasing the proportional power of COMW in this way serves to significantly improve the yearly profit (income minus expenditure) of the system, in all iterations. This can be seen in Figure 10, which highlights the improvement of the system with increased *Vswept* (and reduced proportional power of COMG).

**Figure 10.** *Cont*.

**Figure 10.** Income, expenditure and profit for representative isothermal (**above**) and adiabatic (**below**) systems with 200 h of storage. Also shown on the upper x-axes is the proportional power of COMG compared with COMW. Decreasing this ratio improves financial performance.

While the income of the system is reduced by increasing *Vswept*—a function of the total system power reducing as the proportional power of COMW, which is set at 8 MW, increases—the expenditure of the system decreases more quickly, resulting in greater profit. The expenditure is further reduced in the adiabatic case compared with the isothermal case, due to the further increase in the ratio between COMW and COMG powers, a result of the work of Equations (1) and (2).

Due to the effect the swept volume has on the system powers and pressure (and therefore costs), it is useful to show a breakdown of the cost elements with changing *Vswept* for both the isothermal and adiabatic cases. Figure 11 shows a breakdown of the cost elements for a system with 200 h of storage. Figure 12 normalises these costs by the power of the system at each value of *Vswept*.

For the adiabatic case, the reduction in the cost of the thermal energy store with increasing *Vswept* is due to the increasing pressure ratio of COMW. This results in a higher outlet air temperature; the thermal mass is therefore used more effectively. Likewise, the reduction in the cost of the air store is due to a larger proportion of the exergy being stored as heat, as *Vswept* increases.

Given that system capital costs are reduced and profits increased with increased *Vswept*, it is clear that the one-year return on investment (ROI) is significantly affected by increasing the inlet swept volume of the system. This can be seen in Figure 13, using a system with 200 h of storage for demonstration.

**Figure 11.** Breakdown of capital costs for an isothermal (**above**) and adiabatic (**below**) system with 200 h of storage.

**Figure 12.** Breakdown of capital costs shown in Figure 10, normalised by the total discharge power of the system. Isothermal (**above**) and adiabatic (**below**) configurations shown.

**Figure 13.** The relationship between one-year return on investment and inlet swept volume for a representative system with 200 h of storage.

It is therefore desirable for the profitability of the *Wi-DACIS* system to maximise *Vswept* to its upper practical limit.

It is important to determine whether there is an optimal energy storage capacity for the system. Figure 14 shows the ROI of a system with a constant swept volume and changing store size, from 1 to 200 h.

**Figure 14.** The relationship between one-year return on investment and storage capacity for a system with the maximum allowable inlet swept volume.

In fact, a maximum ROI for the system is reached in all cases. At the highest value of *Vswept* (shown in Figure 14), this occurs at ~20 h for the isothermal case and ~15 h for the adiabatic case. Before this point, there is very little value provided by the stores, despite the increased cost of the system compared with a conventional turbine (through the addition of the first-stage compressor and the expander). After this maximum, the increased value offered by the store does not make up for the climbing costs of such a system at present. This is summarised in Figures 15 and 16.

**Figure 15.** The relationship between profit and storage capacity for a representative system with the maximum allowable inlet swept volume.

**Figure 16.** The relationship between total system cost and storage capacity for a representative system with the maximum allowable inlet swept volume.

For the isothermal case, the maximum ROI at each site ranged from 6.4% to 9.8%. For the adiabatic case, the maximum ROI ranged from 8.1% to 13.0%. At all sites, this maximum occurred at the highest value of swept volume, with the optimal store size varying only slightly.

The lowest ROI values (between 0.8% and 1% for the isothermal case and between 1.8% and 2.4% for the adiabatic case) are found when the swept volume is at its lowest and the storage capacity is close to zero, due to the high system costs and minimal benefit provided by the store.

In the adiabatic case, at higher values of swept volume, the air reaches temperatures nearing the limits of sensible heat storage capabilities (~900 K). This could be accounted for with multi-stage adiabatic compression utilising inter-stage cooling.

Using the method and values described in this paper, it seems likely that an adiabatic wind-driven compressor is significantly financially favourable over an isothermal one for the *Wi-DACIS* system. It is advantageous to design the system such that the wind-driven compressor performs the majority of the total work, achieved by designing for maximum swept volume and adiabatic operation. The existence of an optimal store size in each case is also of interest, as it creates a clear system design goal for store size—something that is not seen to be the case for standalone storage in Section 4.5.

#### *4.4. Validation*

In addition to the real wind and electricity price data used in this paper, and the nominal costs and efficiencies based on prior literature, data validation was performed in the form of a Monte Carlo simulation. The ranges of cost and efficiency shown in Tables 3 and 4 were used to create triangular probability distributions for each parameter. For each iteration of the *Wi-DACIS* system (characterised by the values of *Vswept* and store size), random weighted samplings of these distributions were created, and the cost, income, expenditure, profit and ROI values of that iteration were adjusted accordingly. With 10<sup>5</sup> runs in each iteration, a normal distribution was then fit to the result, and the coefficient of variation (that is, the standard deviation normalised by the mean and presented as a percentage) of the ROI was found, as shown in Figure 17.

The coefficient of variation is considerably higher at low values of *Vswept*. At its highest, it reaches 141% in the isothermal case and 51% in the adiabatic case. This is due to the low mean ROI values and higher proportional power of COMG at the minimum swept volume. For some values of cost and efficiency, the ROI at these low *Vswept* iterations can be negative, a result of the losses in the system outweighing the benefits of absorbing and storing the electricity. Clearly a system with such parameters would not be economically viable.

However, at middling and higher values of *Vswept*, the coefficient of variation quickly becomes tolerable, plateauing at around 10–15% for the isothermal case and 7–10% for the adiabatic case. As with the effects of *Vswept* on the variability, the isothermal case is more variable due to the larger proportional power of COMG, resulting in lower profit margins and more chance for an expensive compressor to impact the ROI of the system.

Given that the iterations that have been shown to be more favourable are those with higher values of *Vswept*, the variability calculated due to possible variations in the input parameters is considered to be acceptable.

#### *4.5. Comparison with Other Systems*

Comparing the ROI and capital costs of the *Wi-DACIS* system with alternative wind– storage options is useful in determining whether the system described here has a potential place in the energy grid.

A conventional 8 MW wind turbine (capital cost ~£8 M) on the CfD scheme with a strike price of 40 GBP/MWh has a maximum ROI of 22% using the same wind and price data. Approximately the same maximum ROI was found for a free-market wind turbine over the same time period. The difference in the ROI between these turbines and the

*Wi-DACIS* system supports the generally held belief that it is much more expensive to store a unit of energy than it is to generate it.

**Figure 17.** Results of data validation for isothermal (**above**) and adiabatic (**below**) systems, presented

However, given the necessity for large-scale storage in future energy grids, regardless of its relative profitability, it is useful to compare like-for-like. Therefore, two other wind– storage systems have been simulated, using the same initial logic: a wind turbine with co-located Li-ion battery storage, and a wind turbine connected to both a compressed air energy store (CAES) and the grid.

The efficiencies and costs assumed for these systems are summarised in Table 5.

as the coefficient of variation of the ROI for each iteration.


**Table 5.** Efficiencies and costs of the other wind–storage systems. Costs estimated from [49,50].

The efficiencies were applied in a similar approach as the *Wi-DACIS* simulation. During costing, the store was considered larger by a factor √*<sup>η</sup>* (to apply the same efficiency loss to the beginning and the end of the process), and during revenue calculations, income was reduced by the same factor.

The wind turbine was considered to be acting on the free market in both cases, and the same algorithm (based on [36]) was used to decide whether to sell or store energy, where possible. The power costs provided in Table 5 are the total costs for charging and discharging power. As with the *Wi-DACIS* system, the storage capacity was calculated in hours, from 1 to 200. Figure 18 shows the representative ROI curves for the two systems.

**Figure 18.** The relationship between one-year return on investment and storage capacity for the Li-ion and CAES simulations.

For a set storage capacity, the Li-ion system achieves higher revenue in all cases (due, obviously, to the only simulated difference in the income of the two systems being their efficiencies). However, the CAES system achieves significantly higher ROI values. The maximum ROI values for CAES were between 9.7% and 14.3% and were between 4.9% and 8.4% for Li-ion. These all occur during the lowest possible store size. Comparing Figures 14 and 18, it appears as though the *Wi-DACIS* system is extremely competitive with alternative storage systems, especially at higher storage capacities. Section 4.6 discusses an interesting quirk of *Wi-DACIS* that may give it further viability, from a whole grid perspective.

#### *4.6. Capture Value*

The capture value (CV) of a wind turbine is a measure of how effectively the turbine can achieve the average electricity value over a given time period. Wind power generally has a negative correlation with electricity price—during times of high wind, the wind fleet of a grid is generating more electricity, increasing supply, and thereby reducing the electricity price. Capture value is calculated as:

$$CV = \frac{\sum\_{i=1}^{n} output\_i \times price\_i}{price} \, \times \frac{price\_i}{\sum\_{i=1}^{n} output\_i} \, \, \, \tag{18}$$

where *output* and *price* are the wind electricity output and electricity price at time *i*, and *price* is the average electricity price over the time period [51].

The average capture values are expected to decrease in the future, due to significantly increased wind generation capacity. This is a concern for wind farm operators, due to the uncertainty it creates [51,52]. Less certainty in wind farm output may result in reduced investment in wind farms in the future.

Any system that stores exergy prior to sending electricity to the grid has the potential to lessen the negative impact of this capture value, both for itself (by only selling during times of high electricity price) and for the whole grid (by reducing the wind supply during times of high wind). *Wi-DACIS* is an example of such a system, but so is any co-located wind–storage system. What sets *Wi-DACIS* apart is that it also draws electricity from the grid when the wind turbine is working, via its grid-powered compressor. Because the instantaneous power of this compressor is directly proportional to the instantaneous wind resource, *Wi-DACIS* would serve to draw electricity mainly at times of high wind. When this coincides with times of low electricity value (which will occur increasingly more frequently), *Wi-DACIS* will store this energy. Through this mechanism, *Wi-DACIS* further lessens the capture value problem. This improved capture value could reduce uncertainty in future wind farm investments. However, any system intending to make a significant impact on the capture value of a whole grid would need to account for a significant proportion of the wind generation capacity of that grid.

#### **5. Summary**

The wind-driven GIES system described in this paper has the potential to offer significant generation flexibility to wind power generation. Further costing work must be done before the economic case is fully made. By including some electrically driven compression prior to supplying air to the wind-driven compressor, a solution is found to the problem that large intake swept volumes would otherwise be needed. This allows direct drive machinery to replace the expensive gearbox system in a conventional turbine.

The use of underwater compressed air energy storage in the form of flexible energy bags has natural synergy with floating offshore wind turbines, which may be situated over extremely deep water. It has been shown in a previous paper that these energy bags have an optimum diameter, which was suggested to be approximately 20 m. Any energy store utilising these bags should therefore employ multiple optimally sized bags.

For multiple configurations of the system, simulations were run for both an adiabatic and an isothermal wind-driven compressor. For a set wind turbine and upper pressure, as the allowable volumetric swept intake of the main stage compressor increases:


It is therefore desirable to accommodate the maximum possible swept volume.

It was also found that the adiabatic main stage compressor achieved higher ROI values than the isothermal configuration. This is partly due to the relatively cheap thermal energy storage used in the adiabatic case. The adiabatic case also results in a more favourable ratio of wind-driven to grid-powered compressor powers, resulting in a configuration closer to a pure generation-integrated energy storage system.

There is an optimum value of store size for ROI with the *Wi-DACIS* system, which is generally between 10 and 20 h of rated output. With proper design and sizing, ROI values in the region of 10–15% are certainly possible. A Monte Carlo simulation validated the assumed costs of the system by showing low variability (in the order of 10%) at higher values of *Vswept*, where these ROI values were found.

With the wind data used in this paper, a conventional wind turbine achieves higher ROI values than the *Wi-DACIS* system. However, under the same assumptions, the other wind–storage systems simulated also achieved lower ROI values than the conventional turbine, and the optimum values for these systems were found at the minimum storage capacity, which most closely resembles a standalone wind turbine. The *Wi-DACIS* system performed as well as or better than the alternative storage solutions, especially at higher storage capacities.

The addition of a medium-pressure store may serve to add flexibility to the system, reducing the expenditure by allowing *Wi-DACIS* to draw energy from the grid at times of lower electricity value. This additional store should be analysed in future work.

Further analysis should also be performed on the relative costs of the system elements, as these will dictate proper sizing. The effect that the power ratio between the two compressors has on the overall efficiency of the system is of interest, as an iteration that is closer to standalone storage than GIES may result in a less efficient system. The benefit of overrating of the expander, allowing for quicker discharge of the high-pressure store, should also be investigated.

In this paper, the efficiency of the wind-driven compressor was given in relative terms, with the assumption being that it would be as efficient as a traditional wind turbine transmission system. This should be verified as the development of the adiabatic compressor in [6] continues.

With a sufficient grid presence, *Wi-DACIS* may also act as a capture value balancer, due to its dual mechanisms of storing energy during times of low electricity price (which will increasingly frequently occur during times of high wind) and drawing electricity from the grid during times of high wind availability, thereby increasing demand. With a significant market share of the wind generation capacity of a grid, *Wi-DACIS* could greatly reduce the uncertainty surrounding capture value in wind farms. Further work should be done to determine the value of the *Wi-DACIS* and similar wind-driven systems in an expected future energy network, as the negative correlation between electricity price and wind availability becomes more pronounced in the coming years. This negative correlation may heavily impact conventional wind farms that lack co-located energy storage, at which point systems such as *Wi-DACIS* may have an extremely promising economic case.

**Author Contributions:** Conceptualization, L.S.-S., S.D.G. and D.G.; methodology, L.S.-S. and S.D.G.; software, L.S.-S. and B.C.; validation, L.S.-S. and B.C.; formal analysis, L.S.-S.; investigation, L.S.-S.; writing—original draft preparation, L.S.-S.; writing—review and editing, L.S.-S., S.D.G., D.G. and J.P.R.; visualization, L.S.-S.; supervision, S.D.G., D.G. and J.P.R.; project administration, S.D.G.; funding acquisition, S.D.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to thank the United Kingdom's Engineering and Physical Sciences Research Council (EPSRC) for funding this work through the following research grants: 'Multi-scale Analysis for Facilities for Energy Storage' (Manifest: EP/N032888/1) and 'Generation Integrated Energy Storage - A Paradigm Shift' (EP/P023320/1).

**Data Availability Statement:** Restrictions apply to the availability of wind speed data. Data was obtained from NCAS British Atmospheric Data Centre and the post-processed data are available from the authors with permission of NCAS British Atmospheric Data Centre. Publicly available day-ahead electricity price data were analysed in this study. This data can be found here: https: //transparency.entsoe.eu/dashboard/show. The outcome data presented in this study are available upon reasonable request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.



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