Influence of resource definition on defining a WEC optimal size

Influence of resource definition on defining aWEC optimal size

Remy CR Pascal, Felix Gorintin, Gregory S. Payne, David Darbinyan, and Yves Perignon

Abstract—This work is a follow up from two previousstudies which have been investigating the difference inwave resource between sites and the impact this has on theoptimal Wave Energy Converter (WEC) size using scatterdiagrams of the sites only. This study expands these worksby using omni-directional spectra time series to describethe wave resource instead of scatter diagrams. Two wellknown wave energy test sites are considered: EMEC (BilliaCrew) in the North of Scotland and the SEM-REV on theWest coast of France. The sloped IPS buoy is used as acase study, and a succinct description is provided. As inprevious work, only the hydrodynamic power capture isconsidered, and no power-take-off efficiency or cap areintroduced. For both sites, around one full year of data isavailable. Using both the scatter diagrams and the spectradirectly, WEC performance metrics are computed for eachsite and compared. The results show that using spectraltime series instead of the scatter diagrams yield lowerannual energy productions, and that the highest averagecapture width ratio is obtained for larger scale devices.Spectral time series allows also the establishment of asimple O&M model. The effect on device availability ofannual planned downtime days, of annual failure rates of1, 3 and 5 and of operability threshold of 2m and 2.5mare investigated. The results show that larger scales mightindeed have higher availability, but are exposed to higherrisks.

Index Terms—WEC optimization, scale, maintenance, re-source definition

I. INTRODUCTION

THIS work is a follow up from two previous studieswhich have been investigating the difference in

wave resource between sites and the impact this has onthe optimal Wave Energy Converter (WEC) size usingscatter diagrams of the sites only [1], [2]. This studyexpands these works by using omni-directional spectratime series to describe the wave resource instead ofscatter diagrams. The principle is similar to the processemployed in [3], but uses measured spectra instead ofhindcast data which may increase the level of uncer-tainties [4], and explores the impact of such processes

This is article 1643, submitted to the Wave device developmentand testing track.

R. CR Pascal is with INNOSEA Ltd, ETTC, Floor 2 MurchisonHouse, 10 Max Born Crescent, Edinburgh EH9 3BF, UK (email:[email protected])

F. Gorintin is with INNOSEA France, 1 rue de la Noe, CS 12102,44321 Nantes CEDEX 03, France (e-mail: [email protected]).

G. S. Payne is with the Department of Naval Architecture, Ocean& Marine Engineering, University of Strathclyde, HD3.05, HenryDyer Building, 100 Montrose Street, Glasgow G4 0LZ, UK (e-mail:[email protected]).

D. Darbinyan is with the European Marine Energy Center (EMEC)Ltd, Old Academy Business Centre, Stromness, Orkney, KW16 3AW,UK (e-mail: [email protected]).

Y. Perignon is with SEM-REV Executive Board, Centrale Nantes,CNRS (UMR-6598) (e-mail: [email protected]).

over the WEC design period or scale.Two well known wave energy test sites are considered:EMEC (Billia Crew) in the North of Scotland and theSEM-REV on the West coast of France. The same WECis used, and a succinct description is provided. As inprevious work, only the hydrodynamic power captureis considered, and no power-take-off (PTO) efficiencyor cap are introduced.For both sites, around one full year of data is avail-able. This allows the estimation of the correspondingscatter diagram. Then, using both the obtained scatterdiagrams and the spectra directly, the most relevantmetrics introduced in [2] are computed for each siteand compared. A discussion about the impact of usingsummary statistics (scatter diagram) of a site waveresource instead of a more complex description is in-vestigated, and key points relative to the WEC optimalsize are highlighted.A second set of results introduces a finer analysisregarding the importance of the design period on WECavailability considerations. The time series of spectraallows the modeling of the device availability throughthe year. The impact of the WEC design period over theconsequences of failure and of planned maintenance isinvestigated and discussed.

A. Abbreviations and acronyms

Acronyms DefinitionhAEP hydrodynamic Annual Energy ProductionCWR Capture Width RatioaCWR average Capture Width RatioWEC Wave Energy ConverterPTO Power take offLCoE Levelized Cost of EnergyO&M Operation and MaintenanceT Wave periodTmCW Mean capture width periodTE Energy periodHS Significant wave heightCW Capture widthλ WEC geometric scale

II. SITE DATA

The following section describes the data sourcesfor the two sites considered. For each site, a scatterdiagram is computed based on the spectral time series.The scatter diagram resolution follows the recommen-dations of [5]: 1s for the energy period TE , and 0.5mfor the significant wave height HS .

ISSN 2309-1983 Copyright © European Tidal and Wave Energy Conference 2019 1643-1

PASCAL et al.: INFLUENCE OF RESOURCE DEFINITION ON DEFINING A WEC OPTIMAL SIZE

The wave data at Billia Croo site was collectedusing a Datawell Mk3 Waverider buoy during the year2017. The dataset covers almost a full year, with theexception of few short breaks, when the buoy wasrecovered for maintenance. The Waverider buoy wasdeployed at the southern part of the site in a locationwith nominal coordinates of 58◦58.214′N 003◦23.454′W.The spectrum for each 30-minute period was derivedas the average of 9 spectra calculated from the rawdisplacement data, collected at 1.28Hz. The data wasquality controlled on two levels. Raw displacementdata was checked for missing data points and spikes,with a single QC flag assigned to each 30-minuteseries of displacement data. It was followed by QCof bulk wave parameters done for 1-month long time-series, with data being checked for rate of change andacceptable range. The Waverider buoys deployed atBillia Croo are calibrated and serviced on a regularbasis.

In situ data are gathered on the SEM-REV marinetest site [6] - a 1 km2 restricted area located 12 nauticalmiles offshore of Le Croisic on the French Atlantic coast- as part of the whole infrastructure dedicated to thetest at sea of marine renewable energy devices andcomponents. Among other sensors, up to two DatawellWaverider Mk3 buoys have been moored on site since2009 recording displacements nearly 1 km apart (Eastand West corners of the site), and one Waverider Mk3buoy complements the measurement at a more offshorelocation nearly 30 nm west. The water depths for thelocations inside SEM-REV perimeter reach 34 m and 36m LAT respectively, with a tidal amplitude of up to 6.1m. The currents on site remain below 0.5m.s1 for thevast majority of its environmental conditions and thetidal influence over significant wave height only beginsto show for specific sea states during spring tides [7].For the purpose of this study, buoy data recorded at thewest mooring site over the year 2012 are solely used.Vertical displacements of the buoy recorded at 1.28 Hzare thus exploited over 1h time windows in order tocompute omni-directional frequency spectra. Integralparameters are inferred from the spectral distributionof the energy density.

III. METHOD AND METRICS

The WEC and its numerical model used for thisstudy are described in details in [8], [9]. It is a floatingWEC whose PTO system consists of an immersedtube, open at both ends with a piston sliding insidethe tube. The immersed tube is rigidly connected tothe float and energy is generated from the relativemotion between the float - tube assembly and thepiston. The water inside the tube provides the inertialreference to the PTO. A sketch of the device can beseen on the left of figure 1. For numerical modelling,the representation of the PTO has been simplified

and consists of a point mass connected to the floatvia a damper. The damper only allows translationbetween the point mass and the float along a specificinclined direction as can be seen on the right of figure1. It should be noted that through this simplification,the hydrodynamics loads on the tube are neglectedand the inertial reference against which the piston isreacting is considered as constant. This simplificationwas a trade-off to alleviate computational burden andrender practical the parametric study and optimizationwork carried out on the concept (see [8]).

wave directionof propagation

damper

point mass

float wave directionof propagation

rigid mechanicalconnection

piston movingwith respect to

tube

hollow tube

float

water flowing inand out of thetube as thepiston moves

Fig. 1. Schematic of the WEC concept (left) and of its simplifiedrepresentation for modelling purposes (right).

The float is a circular cylinder whose axis is vertical.At scale 1, the cylinder is 0.5m in diameter and draftand has a mass of 98kg. The optimization process onthe PTO described in [8] led to a point mass of 98kg,located 0.25m below the centre of gravity of the float.The optimum damping value found is 326Nsm−1

associated with a damper angle of 50o to the vertical.The numerical modelling was carried out usingWAMIT to compute the hydrodynamic coefficients onthe float and the motions of the float and point-masswere then derived with a bespoke code as a two-bodysystem.

Physically, the WEC design period loosely corre-sponds to the wave period around which the WEC hasthe best capture width performance. This is formallydefined in [2] as corresponding to the mean capturewidth period, noted TmCW and first introduced in [8].When considering the capture width ratio curve of theWEC plotted against wave period, TmCW is the meanof the wave period weighted by the capture width ratioover the period spectrum of interest:

TmCW =1

CWarea

∫spectrum

CW (T )TdT (1)

where CWarea is the area under the capture widthcurve, T the wave period and CW (T ) the WECcapture width value at period T .

B. EMEC

C. SEM-REV

D. WEC model

E. WEC design period

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The geometrical scale λ of the WEC with respect toscale 1 (as defined in section III-A) is related to thedesign period through Froude scaling as follows.

TmCWλ =√λ · TmCW1 (2)

where TmCWλ is the design period of the WEC at scaleλ and TmCW1 is the design period of the WEC at scale1.The WEC CWR curves obtained from the numericalmodel and upscaled (scales 11, 16, 23, 31, 41, 51) arepresented in Fig. 2.

Fig. 2. WEC CWR plotted against wave period for scales 11, 16, 23,31, 41, 51. The curves are scaled up from the CWR curve at scale1 presented in [8], and interpolated to the period resolution of theEmec spectra.

As in [2], the mean power produced by the WECfor a given omni-directional spectrum is obtained bymultiplying in the frequency domain the spectrumand the WEC capture width ratio curve. The linearWEC power is then estimated in the same way as theincident power in a spectrum is computed.

It is however widely accepted that WEC hydrody-namic performances are decreasing as the sea statesteepness is increasing. To avoid associating high en-ergy, steep sea states with unrealisticly high WECenergy production, this performance drop should bemodelled. In this work, a correction factor is thereforeintroduced, based on the steepness parameter Ss [10].Ss values for the considered data varies from 0.01to 0.08 approximately. For Ss < 0.02, the correctioncoefficient is set to 1. For values above, a cos2 typefunction is used to provide a smooth decrease of thecoefficient as SS increases. The equation coefficients areselected such as coef (SS) |SS=1 = 0:

coef = cos

(πSS − 0.02

0.36

)2

for SS > 0.02 (3)

Figure 3 shows the evolution of the correction coeffi-cient as a function of SS for the observed SS range.

Fig. 3. WEC power corrective coefficient as a function of the seastate steepness Ss [10]. Max Ss in data is around 0.08.

For every spectra, the WEC power is estimated asPower = coef (SS) · Powerlinear.This correction coefficient is also applied to the powermatrices which must be generated when estimating themetrics from the scatter diagrams. This is an evolutionof the method used in [2], and therefore slightly differ-ent results could be observed.

1) Metrics from previous study: The most relevantmetrics from [2] are used again in this work. Thosemetrics are:• the hydrodynamic annual energy produced

(hAEP )• the average capture width ratio (aCWR)• percentage of hAEP produced by discarding X%

of the sea states, starting with lowest producingsea states.

Their complete definitions can be found in theprevious study. They can be estimated either using thescatter diagrams of the sites, or directly the 1D spectratime series. These metrics can therefore be comparedand the influence of the resource description on themcan be discussed.In addition to these metrics, further investigation isallowed by the use of 1D spectra time series. Themethod is described below.

2) Definition of availability metrics: In common LCoEmodels, the device availability is a ratio used totake into account downtime on the annual powerproduction of the device. Availability above 90% arenormally expected for a commercially available device[11], however [12] mentioned that due difficulty ofaccess to WECs, lower values might be expected.[2] suggested that these ratio would potentiallybe affected by the device scale. In this study, thedependence of the device availability to the devicescale is therefore investigated by simulating downtimethrough the year at both sites.

First, a planned downtime operation is considered,with possible duration of 20, 30 and 40 days. This

F. WEC power from spectra

G. Metrics

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period is randomly located in the low productionmonths, from May to July.

Second, a number of failures are simulated throughthe year. Failure rates of 1, 3 and 5 critical failuresper year are considered. Failures are randomlyallocated throughout the year. For each failure, thealgorithm then identify the next available weatherwindow for retrieving the device (12 hours withHS < 2m). A 24-hour period is then added forthe WEC repair. Finally, the next available weatherwindow for device redeployment is identified (12hours with HS < 2m). From the failure to the endof the redeployment weather window, the deviceproduction is considered equal to 0. It should be notedthat the algorithm ensures that a failure cannot occurduring the downtime period triggered by a previousfailure. The process involved could be more accurate,but was thought to be satisfactory for the purpose ofthe present study.

The procedure to simulate availability is iterated2000 times for each failure rate and planned down-time duration considered. For each iterations, a devicehAEP is obtained for each scale. Their distributionsand histograms can then be built and investigated.

IV. RESULTS

Fig. 4 and Fig. 5 present the evolution of the hAEPand aCWR for EMEC and SEM-REV sites respectively.Results from scatter diagram where obtained bygenerating JONSWAP spectra with γ of 1 and 3.3 fromthe HS and TE values. These results are comparedwith those of the model based on the actual spectra.

The first observation is that the expected hAEP islower if using the spectral time series, especially in theSEM-REV cases. In this latter case, as the aCWR valuesare in the same order of magnitude, the differencein spectral shape between the actual spectra and theassumed JONSWAP is the main potential explanationfor the large differences. The shallower depth at thissite end extent of intermediate depth up wave asso-ciated to possible wave transformations, have notablybeen shown to significantly modify the spectral contentnear the peak for energetic sea states [4] [13]. Also, aslightly lower spectral resolution compared to EMECdata could have some influence on the computed quan-tities. The aCWR plots also show clearly that using theactual spectra instead of a scatter diagram will inducethe design of larger machine, with a higher designperiod. Indeed, in both cases, the peak of capturewidth ratio is moved towards the higher periods. Thereis some potential explanation for those observations,which could be explored in further details:• the scatter diagram resolution is not high enough

for the low energy, low periods sea states. Thiscould lead to an overestimation of energy produc-tion;

Fig. 4. hAEP and aCWR for the EMEC site.

Fig. 5. hAEP and aCWR for the SEM-REV site.

• the spectral shapes for low periods, low energy seastates are very varied and are not well represented

H. Comparing with scatter diagram

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Fig. 6. Percentage of hAEP at EMEC while discarding 30% of thesea states starting with the least energetic ones.

Fig. 7. Percentage of hAEP at EMEC while discarding 30% of thesea states starting with the least energetic ones.

by a JONSWAP spectral shape.

Figure 6 and Fig. 7 show the effect of discarding thesea states with the lowest incident power representing30% of the annual occurrences for each site. Resultsare shown as percentage of full hAEP plotted againstWEC scale. In both cases, the results shows thatdiscarding the low energy sea states has a verylimited impact on the annual WEC production. Usingthe spectral time series shows that the decrease inproduction is less dependant on scale than usingthe scatter diagrams. Overall, for both sites, andindependently of scale, discarding up to 30% of theannual sea states (starting with the least energetic)does not decrease the hAEP by more than 5%.

Fig. 8 to Fig. 11 show the histograms of the WECmean powers associated with each sea state spectrumof the time series (discarding 30% of the sea statesstarting with the least energetic ones). The associatedcumulative production in % is also shown. Resultsfor scale 16 and 41 are presented, for both sites. Inevery cases, the histograms are concentrated to theleft, towards the low power production sea states,with a long tail towards the high production seastates. The intersections between the mean, median,and 90 and 95 percentile with the normed cumulativeproduction curve show that ignoring this long tail ofhigh production sea states has a very large impacton the hAEP . Therefore, those histograms highlightthe issue of dimensioning correctly a PTO for WECs:

Fig. 8. Histogram and normed cumulative production of WECmean powers, at EMEC for scale 16, after discarding 30% lowestincident power sea states. The median, mean, 90 and 95 percentilesare indicated.

dimension it for the mean or median production seastates, and it will probably no be able to absorb thelarge amount of power during the high energy seastates, and a large portion of the potential hAEP willbe lost. Dimension it for the high energy sea states,and the PTO will probably not be efficient for thelow energy sea states. Finally, while contemplatingthis issue, it is important to remember that thosepower are only mean powers, and not instantaneouspowers within a sea state, which will only increasethe observed variability.

The plots however do show that scale has an effect:the device at scale 16 exhibits histograms that are lesscompressed to the left than the device at scale 41. Thisshould therefore favour the development of smallerdevices, for which the PTO rating problematics shouldbe easier to solve. Similarly, the SEM-REV test site hassmaller sea states, with smaller characteristics periods,and therefore at equal device scale, the histograms aremore compressed at the SEM-REV sites.

[2] suggested that device scale for a givensite should have strong impact on overall deviceavailability. It also mentioned that the ratio of plannedand unplanned maintenance should have differentimpacts depending on scale, with the largest devicesbeing less impacted by planned maintenance.Using the spectral time series, these claims can beexamined and quantified. 2000 annual time seriesof WEC at each scale are generated as described inSection III-D2, for different annual failure rates (1, 3and 5) and number of planned days of downtime (10,20 , 30).

Figure 12 shows notched box-plot and whiskers plotsrepresenting the distribution of availabilities obtained

I. Availability

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Fig. 9. Histogram and normed cumulative production of WECmean powers, at EMEC for scale 41, after discarding 30% lowestincident power sea states. The median, mean, 90 and 95 percentilesare indicated.

Fig. 10. Histogram and normed cumulative production of WECmean powers, at SEM-REV for scale 16, after discarding 30% lowestincident power sea states. The median, mean, 90 and 95 percentilesare indicated.

at EMEC for each failure rate, days of planned down-time and scaled (figures at the SEM-REV site are notpresented, the results are broadly similar).

First, the level of device availability are consistentwith the hypothesis commonly used (∼ 90%) inLCoE models. A failure rate lower than or equal to3 per year is required, and for any scale, bringingthe failure rate down to 1 per year can raise theavailability to 95%. Of course the O&M modelused is simple, and more accurate numbers wouldbe obtained from a model specific to a particular WEC.

One can clearly observe from these simulationsthat increasing the planned maintenance is more

Fig. 11. Histogram and normed cumulative production of WECmean powers, at SEM-REV for scale 41, after discarding 30% lowestincident power sea states. The median, mean, 90 and 95 percentilesare indicated.

detrimental to small devices, whereas increasing thefailure rate has a strong effect on all scales. Indeed,along each column, increasing the number of planneddays of downtime only appears to decrease theavailabilities of the small devices. The effect howeveris limited compared to the effect of increasing thefailure rate. Along each lines (same number of planneddowntime, but increasing failure rate), the availabilityof the smaller devices is lower for the most reliabledevice (failure rate of one a year), but as the failurerate increases, the availability of the larger devices isdecreasing at a higher rate. For the case of 10 days ofdowntime (top row), the availability of larger devicesis indeed lower than the one of small devices for thehigh failure rate case.

Finally, the most important observations is probablythat an O&M model that estimates median availability> 90% is also predicting availability in some casesas low as 60%. The model is also showing that inall cases, the spread between the 1% percentile andthe median (or mean) is increasing for larger devices,confirming the expectation from [2] that for the sameconcept, going to larger scales increase the risk to theannual production of the device.

More details on the distribution of hAEP canbe obtained by examining histograms of the 2000availabilities for the different scales and failures rates.Figure 13 shows the availability histograms at EMEC

for each scale, assuming 10 days of planned downtime,and a failure rate of 3 per year. The histograms showthat indeed the majority of the simulation yieldedmean availability close to 90% for all the scales.However, the risk to have a year with actually verylow availability is shown to be higher for the largescale devices: occurrences as low as 60% availabilityare observed for the largest scale. Interestingly, the

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Fig. 12. Notched boxplots of availability’s for each failure rate and planned downtime days at EMEC as a function of the device scale. Thegreen triangles represents the means, the orange lines the median. The whiskers are set a the 1% an 99% percentile. Black circle representsoutliers. Title represent f for failure rate, d for planned downtime days, o for operability (HS in m).

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Fig. 13. Histograms of availabilities at EMEC, assuming a failure rate =3, 10 days of annual planned downtime, and an operability limit ofHS = 2.0m.

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Fig. 14. Histogram of availabilities at EMEC, for scale 41 andassuming a failure rate =3, and 10 days of annual planned downtime,and an operability at HS = 2.5

histograms show that for all cases, the distribution isvery far from a normal distribution. Approximatingthese distributions with parametric functions wouldbe useful as inputs for LCoE modelling, with theability to realistically take into account the variabilityof the hAEP due to device availability (this is differentfrom variation from year on year resource variability).This possibility arises directly from the availability ofspectral time series, and could not be obtained fromthe scatter diagram alone.

Fig. 14, represents the availability distribution of thedevice at scale 41, for the case failure rate=3 and 10days of planned down time, but raising the operabilitylimit to HS = 2.5m. The figure should be compared tothe subplot corresponding to the same scale (bottomleft) of Fig. 13. Raising the operability has clearlylifted the mean and median availability a few percentup towards 95%, but maybe more significantly, thehistogram is more compressed to the right, with onlyone occurrence below 74%, whereas there is multipleones close to 60% in the Fig. 13 subplot. The risk to thedevice availability is clearly reduced.

V. DISCUSSION

First and foremost, it is important to keep in mindthat the results presented in this article are linked tothe particular WEC considered, and the hypothesesmade to estimate its hydrodynamic performances andits O&M strategy. A different WEC, with differentperformances and variation in the method employedcould potentially produce very different results. Itwould indeed be valuable to investigate in details

the validity of the hypotheses made and their effecton the results. Nonetheless, the study presented herehighlights the benefits of using a detailed resourcedescription and some of the challenges of WEC design.WEC developers are generally encouraged to adaptthe method to their specific case and reproduce someof the results presented.

The use of spectral time series instead of scatterdiagram first appears to have an important effect onthe actual optimal size of a WEC from a point of viewof maximising the potential for hydrodynamic energycapture. In both cases, the curve of capture widthratio obtained using the spectral time series peaks at ahigher design period or scale than the ones drawn fromthe scatter diagrams. Additionally, the use of scatterdiagrams with theoretical spectra is clearly leading toan overestimation of the device hAEP at all scalesinvestigated. The two sites exhibit different results: thehAEP estimations at SEM-REV exhibit much largerdifferences between the methods. The first and obviouspossible reason to explain these observations are thedifferences between the theoretical spectra consideredwhen building the required power matrix and theactual real spectra ( [3], [14]). As a matter of fact, thelarge departure of spectral measurements comparedto modeled distributions in the most energetic seastates has already been documented on SEM-REV,which lead to significant reduction of the availableenergy around the theoretical spectral peak [4] [13].The large extent of intermediate to shallow depths onthe path of propagation for the incoming sea statesremains at this stage a good candidate for spectraltransformation and misfit of standard distributions. Asecond possible explanation is related to the resolutionof the scatter diagrams and related power matrices.The typical resolution is 1s in TE and 0.5m in HS .At the short periods, HS is limited and thereforea band of 0.5m might induces a significant relativeerror, which could possibly introduce a positive biastowards small scale devices which are more efficientat such periods. On the contrary, larger periods aremost normally associated to higher HS , and thereforeerrors of ±0.25m are comparatively less significant. Asthe SEM-REV site is, on average, less energetic thanEMEC, it should be comparatively more impacted bythis issue. This could therefore be part of the reasonwhy the differences in hAEP estimation at SEM-REVare more important than at EMEC.

Further study on this specific issue could provideguidance about an adequate resolution of scatterdiagrams and associated power matrices, especiallyfor low to medium resource sites. In any cases, theobserved differences should encourage WEC designersand evaluators to seek the use of spectral time seriesearly in the design process and in the evaluation ofthe concepts. Using spectral time series, or at leasttime series of sea states parameters, at an early stageof design also highlights the difficulties regardingPTO dimensionning. Deciding on a PTO rating isindeed always a compromise. The distributions of

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mean powers through the year, even after discardingthe less energetic sea states representing up to 30%of the annual occurrences, show that the compromisemight indeed be difficult to satisfy successfullywithout including complex features in the PTO suchas intermediate storage and multiple generators. Thestudy also shows that for a given concept, a choiceof a smaller scale device will reduce the difficulty,suggesting again that early stage development of aconcept should favour comparatively smaller scaledevices, with maybe less complex PTO (withoutintermediate storage, or with a single generator).

The use of spectral time series allowed also theconfirmation of the hypothesis presented at the endof [2], i.e. that larger device might have a higheravailability than smaller devices for a given level ofreliability, but these higher availabilities are associatedwith a higher risk. The larger devices would alsobe installed in smaller number for a given farm’sinstalled power, and therefore the risk associated tothe production of a single devices would potentiallybe more important. Additionally to the observed riskto the production, it should be noted that the failuremodel considered is not linked to sea states or devicecondition. It is however reasonable to assume thatthe risk of failure should be higher in energetic seastates, and it is therefore possible that a failure modeltaking this into consideration would yield even higherrisk to the device hAEP . These high risks are linkedto the dependency of hAEP to the rarely occurringbut most energetic sea states. A model capping itsproduction for high HS , or a concept drasticallyreducing its CWR for higher sea states will exhibitslower risks to its hAEP . This benefit is additionalto the higher survivability often put frontward forsuch concept, but seldom emphasized. The observeddifferences of availabilities between the device scaleare not very large (around 4% of mean and medianavailability variation at most), and are smaller thanwhat could be anticipated. Taking them into accountmight nonetheless have an effect on the selectionof a device size based on LCoE models (see [15]).Further study could focus, for a given case, on thecharacterisation of the availabilities distribution asa function of the device scale, and on the effect ofemploying such distribution to model uncertainty inan LCoE model following a Monte-Carlo approach.

Finally, this approach allows to evaluate at anearly stage in the design process the influence of theoperability limits on the concept power production.While the operability strategy used for the simulationin this study is not entirely realistic, and not based onactual characteristics of the device, it provides insightinto the very high impact that the operability hason the actual device power production, and on thereduction of the risk associated .

CONTRIBUTION

Remy CR Pascal conducted the main part of thestudy, and drafted most of the article. Gregory S. Paynedeveloped the WEC hydrodynamic numerical model,wrote its description and reviewed the manuscript. ,David Darbinyan and Yves Perignon provided and de-scribed the sea state data for EMEC and SEM-REV re-spectively. Felix Gorintin advised on the developmentof the O&M strategy and reviewed the manuscript.

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Influence of resource definition on defining a WEC optimal size