Optimization of Point Absorber Wave Energy Parks MARIANNA GIASSI UURIE 353-18L ISSN 0349-8352 Division of Electricity Department of Engineering Sciences Licentiate Thesis Uppsala, 2018 Abstract Renewableenergiesarebelievedtoplaythekeyroleinassuringafutureofsustainableenergy supplyandlowcarbonemissions.Particularly,thisthesisfocusonwaveenergy,whichiscrea- tedbyextractingthepowerstoredinthewavesoftheoceans. Inorderforwaveenergytobecomeacommercializedformofenergy,modulardeployment ofmanywaveenergyconverters(WECs)togetherwillberequiredintheupcomingfuture.This designwillthusallowtobenefit,amongothers,fromthemodularconstruction,thesharedelec- tricalcablesconnectionsandmoorings,thereductioninthepowerfluctuationsandreductionof deploymentandmaintenancecosts. Whenitcomestoarrays, thecomplexityofthedesignprocessincreaseenormouslycom- paredwiththesingleWEC,giventhemutualinfluenceofmostofthedesignparameters(i.e. hydrodynamicandelectricalinteractions,dimensions,geometricallayout,waveclimateetc.). UppsalaUniversityhasdevelopedandtestedWECssince2001,withthefirstoffshorede- ployment held in 2006. The device is classified as a point absorber and consists in a linear electric generator located on the seabed, driven in the vertical direction by the motion of a floatingbuoyatthesurface. Nowadays,oneofthedifficultiesofthesectoristhatthecostofelectricityisstilltoohigh andnotcompetitive,duetohighcapitalandoperationalcostsandlowsurvivability.Therefore, onesteptotrytoreducethesecostsisthedevelopmentofreliableandfastoptimizationtools forparksofmanyunits. Inthisthesis,afirstattemptofsystematicoptimizationforarraysoftheUppsalaUniversity WEChasbeenproposed. Ageneticalgorithm(GA)hasbeenusedtooptimizethegeometry ofthefloaterandthedampingcoefficientofthegeneratorofasingledevice. Afterwards,the optimallayoutofparksupto14deviceshasbeenstudiedusingtwodifferentcodes,acontinuous andadiscretevariablesrealcodedGA.Moreover,themethodhasbeenextendedtostudyarrays withdevicesofdifferentdimensions. Adeterministicevaluationofsmallarraylayoutsinreal waveclimatehasalsobeencarriedout. Finally,aphysicalscaletesthasbeeninitiatedwhich willallowthevalidationoftheresults. Amulti–parameteroptimizationofwavepowerarraysoftheUppsalaUniversityWEChas been shown to be possible and represents a tool that could help to reduce the total cost of electricity,enhancetheperformanceofwavepowerplantsandimprovethereliability. List of papers Thisthesisisbasedonthefollowingpapers,whicharereferredtointhetext bytheirRomannumerals. I GiassiM.,GötemanM.;Parameteroptimizationinwaveenergy designbyageneticalgorithm;Proceedingsofthe32ndInternational WorkshoponWaterWavesandFloatingBodies,Dalian,China,23-26 April,IWWWFB2017. II GiassiM.,GötemanM.;Layoutdesignofwaveenergyparksbya geneticalgorithm;UnderrevisionforOceanEngineering,2017. III GiassiM.,GötemanM.,ThomasS.,EngströmJ.,ErikssonM.,Isberg J.;Multi-parameteroptimizationofhybridarraysofpointabsorber WaveEnergyConverters;Proceedingsofthe12thEuropeanWaveand TidalEnergyConference,Cork,Ireland,27-31August,EWTEC2017. IV ThomasS.,GiassiM.,GötemanM.,ErikssonM.,IsbergJ.,Engström J.;Optimalconstantdampingcontrolofapointabsorberwithlinear generatorindifferentseastates: comparisonofsimulationandscale test;Proceedingsofthe12thEuropeanWaveandTidalEnergy Conference,Cork,Ireland,27-31August,EWTEC2017. V BozziS.,GiassiM.,MorenoMiquelA.,BizzozeroF.,GruossoG., ArchettiR.,PassoniG.;Wavefarmdesigninrealwaveclimate: the Italianoffshore;Energy,122(378-389),January2017. DOI:10.1016/j.energy.2017.01.094 Reprintsweremadewithpermissionfromthepublishers. Contents 1 Introduction 7 .................................................................................................. 1.1 Waveenergy 7 ..................................................................................... 1.2 UppsalaUniversityconcept 8 ............................................................. 1.3 Waveenergysectorchallenges 8 ........................................................ 1.4 Multi-unitsarrays 9 ............................................................................. 1.5 Researchquestion 11 .......................................................................... 1.6 Structureofthework 11 ..................................................................... 2 Theory 13 ........................................................................................................ 2.1 Waveenergyfarmmodel 13 ............................................................... 2.1.1 Linearwavetheory 13 .......................................................... 2.1.2 Waves-structuresinteraction 16 ........................................... 2.1.3 Dynamicequation 18 ............................................................ 2.2 Optimizationtheory 18 ....................................................................... 2.2.1 Geneticalgorithm 19 ............................................................ 3 Methods 22 ...................................................................................................... 3.1 Simulations 22 ..................................................................................... 3.1.1 Singledeviceoptimization 22 .............................................. 3.1.2 Arraylayoutoptimization 22 ............................................... 3.1.3 Multi-parametersarrayoptimization 24 .............................. 3.1.4 Deterministicarrayevaluation-Acasestudy 27 ............... 3.2 Wavetankexperiments 29 .................................................................. 4 Results 31 ........................................................................................................ 4.1 Singledeviceoptimization 31 ............................................................ 4.1.1 FirstGAvalidation 31 .......................................................... 4.2 Arraylayoutoptimization 32 .............................................................. 4.3 Multi-parametersarrayoptimization 35 ............................................ 4.3.1 SecondGAvalidation 36 ..................................................... 4.4 Deterministicarrayevaluation-Acasestudy 37 .............................. 4.5 Wavetankexperiments 39 .................................................................. 5 Discussion 41 .................................................................................................. 5.1 Costfunction 41 .................................................................................. 5.2 Computationaltime 50 ........................................................................ 5.3 GAparameterssensitivity 51 ............................................................. 6 Conclusions 52 ................................................................................................ 7 Futurework 54 ................................................................................................ 8 Summaryofpapers 55 .................................................................................... 9 Svensksammanfattning 57 ............................................................................. 10 Acknowledgements 58 ................................................................................... References 59 ........................................................................................................ 1. Introduction TheEUenergyandclimateactiongoalistoreducegreenhousegasemissions by 40% by 2030, and that the proportion of renewable energy (RE) will have tocoveratleast27%ofthetotalenergyuse[1]. According to the Swedish energy policy, the share of renewable energy shall beatleast50%oftotalenergyuseby2020and100%by2040[2]. 1.1 Wave energy Renewable energies represent the solutions to a future of sustainable energy supplyandnocarbonemissions. Oceanenergy,i.e. theenergythatcanbehar- vestedfromseawater,isthegeneraltermwhichincludesthefollowingenergy resources: tidal currents, ocean currents, tidal range, waves, ocean thermal energy and salinity gradient. The overall potential of all these resources is enormous. The origin of wave energy is the unbalanced irradiation of the sun at dif- ferent latitudes. Due to this temperature variation on the Earth’s surface, the atmospheric pressure varies and induces motion of air masses from high to lowpressureareas,creatingwinds. Asthewindblowsoverwater,someofthe energy is transfered to the ocean, forming waves, which store this energy as potentialenergy(inthemassofwaterdisplacedfromthemeansealevel)and kinetic energy (in the motion of water particles). The wind speed, the length oftimethewindblowsandthelengthofthegenerationareawillinfluencethe height and the period of the resulting waves [3]. Waves usually travel long distances without much energy loss and therefore are really efficient in the energy transport. The theoretical potential of wave energy in the world has been estimated to be around 3 TW [4]. Like other renewable energy sources, waveenergyisavailablewithseasonalandgeographicalvariability. Theareas with the highest incident wave potential are the western coasts of continents, between40◦−60◦latitude,duetothefluxofregularwesterlywinds(Fig.1.1). Technology to extract wave energy consists nowadays of many different concepts, and they can be classified according to operational principle, loca- tion, power take off (PTO) and directional characteristics, for example. Over thelastdecades,ahugenumberofwaveenergyconverters(WECs)havebeen developed, patented and tested. However, until now, there is no device that has reached the required level of reliability for full scale commercialization. 7 Figure1.1. Annualmeanwavepowerdensity(colors)andannualmeandirectionof thepowerdensityvectors(→)[5] Nevertheless, differentcoastalareaswithdifferentwaveclimateswillrequire different type of technologies, making it more likely that a small number of deviceswillbeconqueringthemarket. TheaverageSwedishenergyfluxalongthewestAtlanticcoastisestimated tobearound5kW/m[6]. Suchwaveclimatesareconsidered"mild"andthey requiresmallratedpowerWECscomparedtoopenAtlanticcoastlikeUKor Portugal,forexample. Largescaleelectricityproductionwillbenefitfromthe deploymentofthedevicesinmulti-unitsarraysorparks: costreductions,mo- dularity,redundancy,powerquality,sharingoftheelectricalcablesandutility scalepowergenerationarejustsomeexamplesoftheadvantagesprovidedby thesesystems. 1.2 Uppsala University concept Uppsala University has been developing a point absorber wave energy con- verter since 2006, which consists of a linear generator located on the seabed, connected via a rope to a floater on the surface (Fig. 1.2). The generator has permanentmagnetsmountedonhissurface,whilethestatorcontainscoilwin- dings. When waves lift the buoy, the relative movement of the magnets with respecttothecoilsinduceelectricityaccordingtoFaraday’slaw. 1.3 Wave energy sector challenges The research during the last decades has resulted in many important achie- vements. However,tobecomecostcompetitivewithotherenergysourcesand togetthesupportandinterestofinvestors, thewaveenergysectorhasstillto faceandsolvemanychallenges. TheEuropeanUnionandtheSwedishEnergy 8 Figure1.2. UppsalaUniversityWECandprincipleofoperation(fromPaperII). Agency have developed and funded specific regulations and action plans to helpthedeliveryofoceanenergy[1],[7],accordingtowhichsomeofthemost significantaspectsthathavetobeaddressedare: • Thereductionofthecostofthetechnology; prototypedemonstrationis difficultandexpensive,duetotheharshmarineenvironment. Moreover, thenumberoftechnologiesunderdevelopmentdecreasesthecapitalcost reductionprogress. • TheEU’stransmissiongridinfrastructuresexpansionsonshoreandoffs- hore to deliver the new generated power; in addition, other infrastruc- turesimprovementsuchasportfacilitiesandspecializedvesselsforde- ploymentoperationandmaintenance. • More knowledge about the environmental impact to mitigate the nega- tiveeffectonthemarineenvironment,aswellasthesocialacceptability. • Development of systems, subsystems and components related to power transmissionquality,controlandmonitoring. • Deviceperformancedevelopment. • Improveinstallation,operationandmaintenancestrategies. • Improving reliability and durability through development of models of predictions; increased knowledge is also needed when it comes to up- scalingconceptualindividualunitstoparks. 1.4 Multi-units arrays There are many ways to reduce the cost of the technology. One option is to deploylargearraysofmanyunits(examplessketchinFig.1.3). Havingapark of wave energy converters instead of one or few bigger units has a lot of ad- vantages: the modular construction, sharing of the electrical cables connecti- ons and moorings, quality and smoothness of the power output, redundancy, maintenancecanbedonewithoutshuttingdowntheentireproduction,higher reliabilitytofailures,higherpowerproductionandcost-effectivedeployment. 9 Figure1.3. Outlineexamplesofarrays. SeabasedAB(topleft), AquamarinePower Oyster(topright),CarnegieCETO(bottomleft),LangleeWavePower(bottomright). However,sincethesystembecomesmuchmorecomplexthanasingleWEC, therearemanyaspectsthatneedtobestudiedandunderstoodbeforetheactual physicalrealizationofthepowerplant,suchas: • Multi-deviceinteractionanalysis(hydrodynamicalandelectrical). • Layoutgeometryofthepowerplant. • Effectofthewaveclimateonthelayout. • Optimalutilizationoftheavailableoceanarea. • Powertakeoffcharacteristicsandcontrolstrategies • Effectsonmarinelifeandcoastalprocesses. • Economicalanalysis(CapEXandOpEXcosts). All the aforementioned aspects will have a direct or indirect influence on the powerproductionoftheplant. Normally,problemswithmultiobjectivegoals are solved by optimization routines. However, optimization of an array of waveenergyconverterisnotaneasytask,althoughveryimportantandcrucial atthisstageofthewaveenergydevelopment. Thecomplexityoftheproblem can be understood by looking at Fig. 1.4, where some of the most important variablesofanarraydesignarerepresented. Arrows represent influence on the "box" or variable they are pointing at. It can be seen that the mutual relations among variables are many and multi- directional. Note that this diagram includes many simplification and that the problem,inreality,canbemuchmorecomplexthanthat. The ideal optimization routine would optimize all these variables simulta- neously, taking in account that, if one variable is changed, automatically all thevariablesthattheboxispointingatwillbemodified. 10