ANEWBRAZILIANENERGYPORTFOLIO:THECASEFORSUNANDWATER By ErikJacobBrown ADISSERTATION Submittedto MichiganStateUniversity inpartialful˝llmentoftherequirements forthedegreeof MechanicalEngineeringDoctorofPhilosophy 2021 ABSTRACT ANEWBRAZILIANENERGYPORTFOLIO:THECASEFORSUNANDWATER By ErikJacobBrown TheAmazonisadelicateecosystemthathasglobal-scaleenvironmentalandclimatological impact,andisatriskofoverdevelopment,over-modi˝cationanddestruction.Issuesassoci- atedwiththeinstallationandoperationoftraditionalreservoir-damsystemsintheAmazon areexamined,anditissuggestedtosupplementthecurrentBrazilianenergyportfolioand replacefuturedamplanswithhybridin-streamgeneratorandphotovoltaicsystemstopro- videfordistributedrenewablemicrogridsaswellason-gridpowerneeds.Thesesystemscan beinstalledatvariousscales,fromasingle-householdo˙-gridimplementation,upthrough andincludingo˙settingorreplacingcurrentandfutureplannedlarge-scaledamsforon-grid use.Thissolutiono˙ersasociallyandenvironmentallysaferalternativetodams,byre- ducingoreliminatingseveralissueswithreservoir-baseddams:deforestationforreservoirs, ˛oodingfromreservoirs,displacementoflocalfamilies,inhibitionofsedimentandmarine lifetransport,andgreenhousegasemissions.The˝nancialandenergeticfeasibilityofthe proposedsystemiscompared,includingtransmissioncosts,toseveralcommonelectri˝cation methods.Othersupportingtopicsarealsoinvestigated,suchasthe˝sh-friendlydesignof in-streamdevices,andthemaximumreachoftheproposedhybridmicrogridsystemrelative tothein-streamdeploymentsites. ThisisdedicatedtomydarlingwifeKathryn,toourcherishedchildrenwhoarehereand ontheirway,andtoallofthosewhohelpedandsupportedmealongtheway. iii ACKNOWLEDGEMENTS IwouldliketothankmyNSFprojectsponsorsforthewonderfulopportunitytotakepart inthisproject.AspecialthankstoDr.Müllerforrecognizingandprovidingmewiththe project,time,andwisdomyousharedthroughoutmydegree. iv TABLEOFCONTENTS LISTOFTABLES ................................... viii LISTOFFIGURES ................................... ix CHAPTER1INTRODUCTION ........................... 1 1.1EnvironmentalandSocialIssueswithDams..................4 1.1.1EnvironmentalIssueswithDams....................4 1.1.1.1DeforestationandFlooding..................4 1.1.1.2SedimentTransportBlockage.................5 1.1.1.3GreenhouseGasEmissions...................5 1.1.2EcologicalImpact.............................6 1.1.3SocialIssueswithDams.........................6 1.1.3.1DisplacementbyFlooding...................7 1.1.3.2DisplacementbyFoodSourceChange............7 1.1.3.3DisplacementbyModernization................7 1.1.3.4AwarenessofLocalIssues...................7 1.2Drivers.......................................8 CHAPTER2SUGGESTEDENERGYPORTFOLIO ................ 9 2.1CurrentBrazilianAmazonBasinEnergySituation...............9 2.1.1CurrentEnergyPortfolio.........................9 2.1.2GenerationPlantsDistribution.....................10 2.1.3AmazonianEnergyPotential.......................11 2.1.3.1HydraulicEnergyPotential..................11 2.1.3.2PhotovoltaicandEolicEnergyPotential...........12 2.1.3.3Bio-EnergyPotential......................12 2.2RecommendedEnergyEnhancement......................14 2.2.1LocalCommunities:O˙-GridSolutionMethodology..........14 2.2.1.1LoadDevelopment.......................17 2.2.1.2Equipmentselectionandpreliminary˝nancialanalysis...22 2.2.1.3GenerationDeterminationandDetailedFinancialAnalysis.25 2.2.1.4O˙-gridmicrogrids:thenaturalreachofrivers........46 2.2.2FinancialInterests:On-GridSolutionMethodology..........49 2.2.2.1LoadDevelopment.......................50 2.2.2.2GenerationDetermination...................50 2.2.2.3FinancialAnalysisandDiscussion...............52 CHAPTER3ENHANCEMENTOFGRIDSTABILITYWITHFLOATINGSO- LARPANELS ............................. 55 3.1Background....................................55 3.2AnOverviewoftheCurrentBrazilianElectricPowerSystem.........59 v 3.2.1UnderproductionofDams........................60 3.2.2WindandPVPowerinBrazil......................62 3.3EnvironmentalandSocialImpactofDams...................66 3.4FloatingPVSystemsonHydropowerDamReservoirs.............67 3.5GenerationAdequacyAssessment........................69 3.6SystemModeling.................................70 3.6.1WindTurbineOutputPower.......................71 3.6.2OutputPowerofPVSystems......................72 3.6.3GenerationModel.............................73 3.6.4LoadModel................................74 3.6.5GenerationReserveModel........................75 3.7CaseStudies....................................76 3.7.1CapacityfactorofPVsystemattheproposedlocations........76 3.7.2AttributesofPVpowertothepeakloadshaving...........77 3.7.3Systemadequacy.............................78 3.7.3.1Systemreliabilityt18......83 3.7.3.2Systemreliabilityprojection..........84 3.7.4ResultsandDiscussion..........................85 3.8Conclusion.....................................86 CHAPTER4IN-STREAMTURBINESASFISH-FRIENDLYTECHNOLOGY .. 88 4.1Background....................................88 4.2TurbineInstallation................................89 4.2.1DamTurbine...............................89 4.2.2Run-of-RiverTurbine...........................90 4.2.3In-StreamTurbine............................90 4.3FishInjuryMechanisms.............................92 4.3.1PhysicalStrike..............................92 4.3.2PressureChanges.............................94 4.3.3Shear....................................96 4.3.4Turbulence................................97 4.3.5CurrentTraditionalCon˝gurationFish-FriendlyDesigns.......97 4.3.6Sound...................................98 4.4FishSafeTurbineDesign.............................98 4.4.1PhysicalStrike..............................99 4.4.2PressureChange,Shear,andTurbulence................101 4.4.3Sound...................................102 4.4.4BypassesandLadders..........................104 4.4.5In-StreamTurbinesinFarms.......................106 4.4.6ElectromagneticEmissions........................106 4.5MarineSafetyandAquaticHealth........................107 4.6LiteratureSummary...............................107 4.7Design.......................................108 4.8Simulation.....................................111 4.8.1ModelandMesh.............................111 vi 4.8.2Setup...................................111 4.8.3Results...................................116 4.8.3.1PowerCoe˚cient........................117 4.8.3.2Pressure.............................118 4.8.3.3StrainRate...........................119 4.8.4PostprocessingRoutine..........................121 4.8.4.1Method.............................121 4.8.4.2Output.............................122 4.8.4.3Discussion............................123 4.8.5Conclusion.................................127 CHAPTER5CLOSINGREMARKSANDGLOBALIMPLICATIONS ....... 130 APPENDICES ...................................... 131 APPENDIXAGISFileSources ........................ 132 APPENDIXBMATLABSampleScript .................... 133 APPENDIXCExcelVBASampleScript ................... 163 BIBLIOGRAPHY .................................... 187 vii LISTOFTABLES Table2.1:Cablesusedasbasisforinvestigation....................46 Table3.1:Currentinstalledpowercapacitiesandprojectionofcapacityplanning increasebyyear2023.............................60 Table3.2:Damsunderproduction............................63 Table3.3:InstalledPVcapacityandthehorizontalsolarirradiationfordi˙erent countries....................................65 Table3.4:Braziliansystemdata.............................81 Table3.5:AnnualreliabilityindicesofTS...................81 Table3.6:AnnualreliabilityindicesofthesystembeforeandafteraddingFPVsystem83 Table3.7:Annualreliabilityindicesofthesystemwithloadincrease.........83 Table3.8:Annualreliabilityindicesofthesystemwithloadincrease ojection 84 Table3.9:SRIFconsideringdi˙erentreliabilityindices.................85 Table4.1:TurbineDesignParameters..........................110 viii LISTOFFIGURES Figure1.1:TheAmazonBasinandtheAmazonExtendedorLegalBasin......2 Figure1.2:TheAmazonExtendedorLegalBasinandmajorSouthAmericanrivers3 Figure2.1:The2017PowerCapacityoftheBrazilianSIN(source:[126])......10 Figure2.2:ThecurrentandfuturepowerlinesoftheSIN(source:[125]).......11 Figure2.3:Brazilianisolatedsystemlocations(source:[125]).............12 Figure2.4:SnapshotofBrazilianenergybalance(source:[123])............13 Figure2.5:OperationalGenerationPlantsinBrazilianAmazon(source:[9]).....14 Figure2.6:OperationalHydraulicPlantsandTransmissionLinesinBrazilianAma- zon(source:[9])................................15 Figure2.7:TheLegalAmazonandmajorBraziliansub-basins............16 Figure2.8:ThehydraulicpotentialinBrazil(source:[7])...............17 Figure2.9:ThedirectnormalsolarirradiationpotentialintheAmazon,assuming anoverall12%conversione˚ciency(datasource:[111])..........18 Figure2.10:TheeolicpotentialintheAmazonat50meterheight,assumingan overall45%conversione˚ciency(datasource:[111])...........19 Figure2.11:Amazonianenergysolutionportfolio....................20 Figure2.12:Pictorialcomprisalofassumedo˙-gridloadwithonepossiblescenario ofusagetimes.................................20 Figure2.13:Temporalcurveofassumedo˙-gridload..................21 Figure2.14:Optionforpossibleloadbyutilizingsmartloadmanagementsystem...22 Figure2.15:Developedloadmodels1-8.They-axisisthepowerconsumption,in watts,andthex-axisisthetimeofday,inhours.Thegreencurverep- resentstheoptimaltotalgenerationcalculated,comprisedoftheyellow (PV)andblue(in-stream)curves,thatmeetorexceedtheload(the blackcurve)..................................23 ix Figure2.16:Potentialpower"availableforfutureloadreduction........23 Figure2.17:Developedloadmodels1-8.They-axisisthepowerconsumption,in watts,andthex-axisisthetimeofday,inhours.Thegreencurverep- resentstheoptimaltotalgenerationcalculated,comprisedoftheyellow (PV)andblue(in-stream)curves,whoseintegratedpower-timearea meetsthatfortheload(theareaunderblackcurve)............24 Figure2.18:Singlehouseholdloadpro˝lewithsuggestedgenerationpro˝les......29 Figure2.19:Curveofbasecostovertheinvestigatedrangeof˛owvelocities,costs calculatedovera30yearequipmentlifespan................29 Figure2.20:Locationsofsamplesitesoverlaidontopofriverpaths,withmarkers representingtherivervelocityavailableatthatlocation,basedon Q 90 ..38 Figure2.21:ComparisonofproposedUPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Thecostsasso- ciatedwiththeelectricgridextensionisshownbythepurplerange, adieselgeneratorisshownbythebrownrangeandthe2019Brazil- ianNorthregionresidentialandruraltari˙sareshownbytheblack range.Thex-axisisthedistancefromthecommunitytothenearest existingtransmissionline,inkm,andthey-axisisthecalculatedcost inUSD/kWhover30years..........................39 Figure2.22:ComparisonofproposedUPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Damconstruction withdistributionlinesisshownbythegoldrange,withnounderreport- ingfactorincluded;theotherrangesarethesameas2.21.Thex-axisis thedistancefromthecommunitytotheoptimalin-streamgeneration site,inkm,andthey-axisisthecalculatedcostinUSD/kWhover30years.40 Figure2.23:ComparisonofproposedUPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Anewdamcon- structionwithdistributionlinesisshownbythegoldrange,withan underreportingfactorof1.96USD/USDincluded,adieselgeneratoris shownbythebrownrangeandthe2019BrazilianNorthregionresiden- tialandruraltari˙sareshownbytheblackrange.SeeFigure2.22for axes.......................................41 x Figure2.24:ComparisonofproposedPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Thecostsas- sociatedwiththeelectricgridextensionisshownbythepurplerange, adieselgeneratorisshownbythebrownrangeandthe2019Brazilian Northregionresidentialandruraltari˙sareshownbytheblackrange. SeeFigure2.21foraxes............................42 Figure2.25:ComparisonofproposedPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Anewdamcon- structionwithdistributionlinesisshownbythegoldrange,withnoun- derreportingfactorincluded,adieselgeneratorisshownbythebrown rangeandthe2019BrazilianNorthregionresidentialandruraltari˙s areshownbytheblackrange.SeeFigure2.22foraxes...........43 Figure2.26:ComparisonofproposedPCsolution(greendiamonds)withseveral commonenergygenerationanddistributionmethods.Anewdamcon- structionwithdistributionlinesisshownbythegoldrange,withan underreportingfactorof1.96USD/USDincluded,adieselgeneratoris shownbythebrownrangeandthe2019BrazilianNorthregionresiden- tialandruraltari˙sareshownbytheblackrange.SeeFigure2.22for axes.......................................44 Figure2.27:Reachoflosslesscablesatvariousgoalcostofenergylevels........49 Figure2.28:Loadmodeldevelopmentprocessforon-gridsystem............51 Figure2.29:Loadmodeldevelopmentprocessforon-gridsystem............53 Figure2.30:Loadmodeldevelopmentprocessforon-gridsystem............54 Figure3.1:Brazilianinterconnectedsystem[130].....................61 Figure3.2:DirectnormalirradiationinBrazilfrom[193]..........64 Figure3.3:GlobalhorizontalirradiationinBrazilfrom[193]........65 Figure3.4:PotentialofaveragePhotovoltaicpowerinBrazilfrom[193]..66 Figure3.5:PercentageofpotentialwindpowerinBrazil[193].............67 Figure3.6:IntegratedPVsystemwithhydropowerinstalledcapacityworldwide...68 Figure3.7:FloatingPVsystemonreservoirinwhichmarinelifeand˝shingactivity arenotdisruptedbyplacingPVsystemsonthereservoir.........69 xi Figure3.8:CapacityfactorofPVsystematseveraldamlo........77 Figure3.9:CapacityfactorofPVsystematseveraldamlo........78 Figure3.10:CapacityfactorofPVsystematseveraldamlo........79 Figure3.11:CapacityfactorofPVsystematseveraldamlo........80 Figure3.12:Contributionofgrid-connectedPVsystemtodailypeakshaving.....80 Figure3.13:Attributionofgrid-connectedPVsystemtoassistHydropowerpeak loadshifting..................................81 Figure4.1:Canonical˝shinjuryriskmechanisms(from:[36]).............89 Figure4.2:Schematicsofturbinecon˝gurations(a)cross-sectionofadamorrun- of-riverhousing,(b)traditionaldam,(c)run-of-river,(d)in-streamturbine91 Figure4.3:Survivalofrainbowtrout( Oncorhynchusmykiss )basedonstrikespeed (modi˝edfrom:[6])..............................93 Figure4.4:Dose-Responsechartofmortalityvs.pressureforjuvenileChinook salmon,intermsoftheratioofacclimationtominimumpressures,and thenaturallogoftheratioonthebottomaxis(modi˝edfrom:[32])...95 Figure4.5:Experimenttoquantifytolerableshearstresseson˝sh(from:[112])...96 Figure4.6:AMoonWrasse( Thalassomalunare )evadinganin-streamturbine(from: [79])......................................99 Figure4.7:PressureTracesatVariousRadiialongaTidalStreamTurbine.The legendshowstheradialdistancesintermsoftheratioofagivenradius tothetipradius.(modi˝edfrom:[198])..................102 Figure4.8:Shearrateoftidalstreamturbine(from:[198])..............102 Figure4.9:SoundlevelsmeasuredintheMississippiRivernearMemphis,75meters awayfromthebargeand21metersfromtheturbine,shownbythesolid lineswithoutmarkers.Thelineswithmarkersshowthehearingability ofcertain˝sh.(from:[21])..........................104 Figure4.10:Ductedrotormodelfromthreeviews:˛owdirection,obliqueandtop..112 xii Figure4.11:Cross-sectionofthein-streamgenerator,withasimpli˝edrim-drive generator.Theblackblocksarebearings,thedarkblueblocksare magnets(rotatingwiththeblades),andtheredblocksarethestator windingsandcore(stationarywithshroud).................113 Figure4.12:In-streamgeneratorinariverchannel....................113 Figure4.13:Numericdomain...............................114 Figure4.14:Ductedrotormesh:domainsideview....................114 Figure4.15:Ductedrotormesh:rotorbladeview....................115 Figure4.16:Mass˛owratedi˙erencebetweeninletandoutletnormalizedbyinlet mass˛owrateoveriterationcount......................116 Figure4.17:Torquecoe˚cientoveriterationcount...................117 Figure4.18:Plotofpowercoe˚cientovertipspeedratio,basedontherotorand ductareas...................................118 Figure4.19:Plotofpressureratioovertipspeedratio,atthreeacclimationpressures: 1atm,1.5atm,and2atm..........................119 Figure4.20:Plotofmaximumnegativepressurerateofchangeovertipspeedratio..120 Figure4.21:Plotofmaximumdomainstrainrateovertipspeedratio.........121 Figure4.22:Plotofpercentofbladesurroundingvolumeabovecriteriaof4951/s overtipspeedratio..............................122 Figure4.23:Designedtrianglevelocitiesoverbladespan................123 Figure4.24:Designedbladeangledi˙erenceacrossbladeoverbladespan.......124 Figure4.25:ComparisonofdesignedbladetrianglevelocitieswithCFDoutput....124 Figure4.26:Spanwisepro˝lesofangulardi˙erencebetweendesignandCFDoutput.125 Figure4.27:Relative˛owvelocityvectorsandcontoursat10%squareradialspan..125 Figure4.28:Relative˛owvelocityvectorsandcontoursat50%squareradialspan..125 Figure4.29:Relative˛owvelocityvectorsandcontoursat90%squareradialspan..126 xiii Figure4.30:Relative˛owvelocitystreamlinesandcontoursat10%squareradialspan126 Figure4.31:Relative˛owvelocitystreamlinesandcontoursat50%squareradialspan126 Figure4.32:Relative˛owvelocitystreamlinesandcontoursat90%squareradialspan127 Figure4.33:Relative˛owvelocityvectorsandcontoursat10%squareradialspan, usingnodalvalues..............................127 Figure4.34:Relative˛owvelocityvectorsandcontoursat50%squareradialspan, usingnodalvalues..............................128 Figure4.35:Relative˛owvelocityvectorsandcontoursat90%squareradialspan, usingnodalvalues..............................128 xiv CHAPTER1 INTRODUCTION TheAmazonBasinisthelargestdrainagebasinintheworld,withanareaof7.8million squarekilometers[197].TheAmazonismadeupofeightcountries:Brazil,Bolivia,Peru, Ecuador,Guyana,Venezuela,andSuriname.WithinBrazil,whichaccountsforaround 64%oftheAmazonBasin'sarea[197],eightstatesarewithintheboundsoftheAmazon: Amazonas,Para,Maranhao,Rondonia,Roraima,Acre,Amapa,MatoGrosso,andalsoa ninthstate,Tocantins,iftheso-called`LegalAmazon'isconsidered(seeFigures1.1and1.2 forvisualsoftheregionsofinterest,withandwithoutriversshown,andAppendixAfor shape˝lesources).TheAmazonBasinalsocontainstheworld'slargestrainforest,covering 6.7millionsquarekilometers,andishometotensofthousandsofspeciesofmammals,˝sh, insects,andplantlife[40].OftenreferredtoastheAmazonregionisacrucial ecosystem,whosehealthcanlargelydeterminetheenvironmentalandclimatologicalhealth oftherestofEarthaswell.DuetoBrazilcontainingmostoftheareaoftheAmazon,the policiesandactionsoftheBraziliangovernmentandpeopleshavealargee˙ectontheoverall healthoftheAmazon.MisuseofthenaturalresourcesoftheBrazilianAmazonhavebeena historicalissue,andstillpersist.Misusecanhaveseveralforms:deforestationforlanduse, poachingandwildlifetrading,excessivemining,waterandairpollution,andintroductionof overly-invasivepowergenerationsystems.Duetotheintensepublice˙ortoftheBrazilian governmentoverthelast15yearstoincreaseitscitizens'qualityoflifeandprotectionagainst misuseofthenaturalresourceswithintheirborders,focusingontheBrazilianportionofthe Amazon,calledtheBrazilianAmazonBasinfromhereon,canbeane˙ectiveindicatorofthe Amazonasawhole.TheBraziliangovernmentandrelatedindividualinstitutionsrelease severalcrucialdatasetswithinformationon:population,nationalpowergrid(calledthe NationalInterconnectedSystem,orSINfromthePortuguesewording),deforestation,energy availability,andutilizationofnaturalresources.Withtheaforementionedinformation,itis 1 Figure1.1:TheAmazonBasinandtheAmazonExtendedorLegalBasin possibletomakeconclusionsaboutwhatthecurrentandpossiblefutureenergyresources andneedsareintheBrazilianAmazonBasin,whichcanactasaproxyfortherestofthe Amazon,wheredatamaynotbeasreadilyavailable. Thequestionsofinteresthereare:whoneeds(andwants)electricpower,howmuchdo theyneed,howtogetthempower,andatwhatcost(˝nancially,socially,andenvironmen- tally)?TheBraziliangovernmentaddressedsometheseissuesin2003withthestartofthe LightforAllprogram(LuzparaTodos,orLPT,inPortuguese).ThegoalofLPTwas, similartoitspredecessor,LuzparaCampo,toincreaseruralelectri˝cationinBrazil,headed bytheMinistryofMinesandEnergy(MME)department.Accordingtothe2010Brazilian census,LPTreachedapproximatelya98.7%electri˝cationrateinBrazil[86].Theincrease inelectri˝cationratewasachievedprimarilyintwoways:increasingthestockoflarge-scale 2 Figure1.2:TheAmazonExtendedorLegalBasinandmajorSouthAmericanrivers hydraulicpower,andprovidingsmallthermalgeneratorsforo˙-gridcommunities.Though thismethodologymayhavepartiallysolvedtheissueofgettingpowertothepeopleinneed, itdidnotanswerthequestionofwhatsocialandecologicalcoststhesolutionhas.Someof thecostsassociatedwiththelargescalehydropoweranddistributedthermalsystemsare: displacementoffamiliesandcommunitiesfromreservoirconstruction,disruptionofsediment andecologicaltransport,enhancedgreenhousegasemission,andriskofenvironmentalspill whiletransportingthermalstock.TheseissuesarereviewedinSection1.1. Withthesesocialandenvironmentalcostsinmind,naturallyanotherquestionarisesof howshouldtheincreaseinpowerdemandbemetinthefuture?ShouldBrazilcontinue withthesamemethodology,orchangetoanewoutlookforenergygeneration?Authors suchas[115]recommendchangingtoaviewpoint,meaningmodelingpractices andresourceutilizationwithnaturalprocesses.These`natural'systemscaninclude:solar, wind,biomass,andin-stream(alsocalledhydrokinetic)turbines.Thegenerationsystems 3 thatarenotconsideredtoembodythespiritofcanincludetraditionalreservoir- basedhydropowerdamsandthermalsystemsthatrequireriskyfueltransportorharmful environmentalemissions.InBrazil,thenon-`natural'methodologyhasbeentraditionally employed,withlargedamhydropowerleadingthecountry'senergymarket. Futureinstalledpowergenerationsystemsshouldbesizedandlocatedcarefullyfora realisticandreasonableuseoftheproducedpower.Inotherwords,thereneedstobe separateconsiderationforpowerthepandpowerthatisrequiredbybigindustry andmetropolis.ForindividualfamiliesorcommunitiesintheAmazon,smallsystems(on theorderof500Wattsperperson/household)shouldbeimplemented,andforbigindustry or˝nancialinterests,scaled-upversionsofsimilarsystemscanbeutilized.Inparticular,in- streamturbinesandphotovoltaicsystemsareexaminedhereas˛exibleandfriendlyoptions atbothscales,whichcanreduceoreliminatefurthersocialandenvironmentalimplications ofenergygenerationinBrazil.ThiswillbediscussedfurtherinChapter2. 1.1 EnvironmentalandSocialIssueswithDams 1.1.1 EnvironmentalIssueswithDams Itisacommonlyheldbeliefthatallhydropoweriscompletely`green'and`friendly',however, itisnotentirelytrue.Dam(andthusreservoir)basedhydropowersystemspresentseveral environmentalissues:deforestationand˛ooding,sedimenttransportblockage,greenhouse gasemission,aswellasseveralecologicalissues,suchas˝shmigrationblockage,marinelife injuryriskduetotheturbines,andalsobehaviorchangesduetothepresenceofthedam andturbines. 1.1.1.1 DeforestationandFlooding Inordertoproducetheelevationchangedesignedtodrivetheturbinesinadamatagiven water˛owrate,andtohelpcombatlowwaterlevelsduringwatershortageevents,reservoirs 4 aredugfromthegroundandare˝lledupfromthesupplyingriver.Thematerialremoval processoftenrequiresnearbyforestandfaunatoberemovedalongwiththesoil,resulting indeforestationthatisproportionaltotheareaofthereservoir.Theareaofexcavation willthen˛oodwithwaterfromtheriverthatwillstagnateatthedam.Dependingonthe seasonandontheclimatologicalconditions,thewaterlevelwillriseandfall,resultingin apartially˝lledreservoir,ordependingonthee˚cacyoftheplanningforthemaximum ˛oodedvolume,couldresultinthelocalareabecominginundatedwith˛oodwaterthat spilledoutofthereservoir.Themodi˝edlandscapeofthenewwater-landinterfacewillalso shiftovertime,duetothemotionofthewaterinthereservoir˛owingtowardsthedamand overthenearbyland,causingmoredeforestation;thetrees,fauna,andloosenedsediments willbeintroducedintothereservoir,wheretheywilleithersinktothebottomandbuildup overtime,orwillcontinuedownriveroverthespillway. 1.1.1.2 SedimentTransportBlockage Duetotheirgenerallyhigherdensitycomparedtowater,sedimentstendtosinktothe bottomofriversandreservoirs,andwilltravelneartotheriverbed.Withoutthepresence ofadam,thesedimentsthatmovealongtheriverbedwouldtransporttowardstheocean wheretheywouldbeburied.Withdamsinstalled,however,thesesedimentscannotpassby aseasily,andinsteadtheybuildupinthereservoirinfrontofthedam. 1.1.1.3 GreenhouseGasEmissions TropicalbiomessuchastheAmazon,containingmostoftheworld'swetlands,aremajor producers,transporters,andsinksofcarbonduetotheirhightemperatures,precipitation rates,humidity,stocksofbiomass,amongotherfactors[120].Thevastareasofwetlandsand riversintheAmazonhavebeenfoundtobemajorcontributorsintheglobalcarboncycle, contributinganestimated470Tgofcarbon(C)fromcarbondioxide(CO2)riverineevasion [148]and42.7Tgofmethane(CH4)eachyear[132].Thislargepotentialforcarbonemission 5 inthenaturalcarboncyclehasbeenhypothesizedtobedisruptedbytheintroductionof dams.Ithasbeenshownthatthedeforestationassociatedwiththecreationofthedam reservoirsleadstoenhancedgreenhousegasemissionstotheatmosphere[74].Showing whetherreservoir-baseddamsingeneralleadtoanetsourceorsinkofcarbon(intheform ofCH4andCO2)hasnotbeenmadeconcreteintheliteratureyet.Measurementshavebeen takentocalculatethegrossemissionsoncedamsareinstalled,however,netemissionsrequire measurementsfrombeforeandafterthedamswereinstalled,whichhasbeenperformedon onlyonetropicaldam:thePetitSautprojectinFrenchGuiana[1].Anotherissuewiththe currentliteratureisthatnoteverysourceofcarbonwasconsideredineachexperiment:for afull,consistentcomparisonateachdam,di˙usionandebullition(bubbling)ofbothCH4 andCO2,bothupstreamanddownstreamofthedamneedtobemeasured[65]. 1.1.2 EcologicalImpact Damspresentseveralecologicalriskstolocalmarinelife: ‹ Habitatandmigrationblockage ‹ Physicalinjury ‹ Behaviorimpact TheseimpactswillbereviewedindetailinChapter4. 1.1.3 SocialIssueswithDams Alongwiththeenvironmentalissuesassociatedwithdam-basedhydropower,therearealso severalsocialissues:householddisplacementby˛ooding,foodsourcechanges,orbylo- calchangestothesocialorphysicalinfrastructure(`modernization'),aswellasdiverting awarenessoflocalissuesawayfromthearea,suchasforaccesstoelectricity. 6 1.1.3.1 DisplacementbyFlooding Themostimmediateissueforhouseholdsneartodamprojectsis˛ooding.Whenthereservoir iscreated,nearbylandmighthavetobeconvertedto˛oodedareatoprovideforthedam requiredheight,dependingonthedamdesignandthelocallandscape.Additionally,the damdesignersmaynothaveaccountedfortheextremityofseasonalchangesinclimateand riverhydraulicsortheexactcontourofthelandsurroundingthereservoirthatshouldnot be˛ooded,whichmayresultinalargerareabecoming˛oodedthanoriginallyplanned. 1.1.3.2 DisplacementbyFoodSourceChange AswasmentionedinSection1.1.1,oneoftheenvironmentalissueswithdamsistheblockage ofmigrating˝sh.Thecommunitiesthatrelyonthemarinelifemaylosetheircommon˝shing spots,andwouldhavetomovefurtherawayfromhome,allowinglesstimeeachdaytocollect food[38]. 1.1.3.3 DisplacementbyModernization Agenerallyslowerdeveloping,butequallyconcerningissuewiththedevelopmentofdams isthesocialtransformationofthearealocaltotheprojectsite.Thetransformationscan include,butarenotlimitedto:conversionofundevelopedareasintotouristsightseeingloca- tions,settlingoflocalareabyprojectworkers,orconstrictivepurchaseoflandssurrounding existingcommunitiesforprojectorpublicuse[64]. 1.1.3.4 AwarenessofLocalIssues Withtheintroductionofdams,itispossiblethattheoutsideviewofthelocalpeoplemay shift;itcouldbeseenthatbecausetheyareclosetoalargepowerproducingstructure,that theydonotneedfurtherassistanceforaccesstoelectricity;itcouldevengoasfarasbeing viewedaswealthyorwell-o˙,simplyduetobeingclosetoadam.However,therealityis 7 thateveninwell-developedareas,thecommunitiesclosetoadamandtransmissionlinemay stillnothaveaccesstoelectricity,andmayrelyontraditionalmeansfordailylife,suchas kerosenelampsinsteadofelectriclights[60]. 1.2 Drivers TheBrazilianEnergyResearchCompany(EPEinPortuguese)estimatedthatthereis almost2GWoftraditionalhydropowerplannedtobebuiltintheBrazilianAmazonBasin between2018and2027,aswellasover3000kmofpowerlinesplanned[51].Theamount ofplannedhydropowerincreasestoover8GWwhenconsideringhydropowerthatarein variousotherstagesofplanning,thatcouldbeacceptedintotheBrazilianten-yearplanat anytime[9].Itcanbeshownthatatthe2010Brazilianelectri˝cationrate,itispossibleto provideelectricitytoallhouseholdsthatwerereportedtobewithoutenergybyinstalling orprovidinggridconnectionsofapproximately500MWofratedpower(seeSection2.2.1). Thisdi˙erenceinplannedversusneededpowerforthepeopledemonstratestheneedto askquestionsposedinSection1,namely,whereistheplannedpowergoingandwhois itbene˝tting?Thegoalofthisworkistosuggestandinvestigatealternativestocurrent centralizeddam-basedpowerplans,inordertoprovidethegreatestbene˝ttoboththelocal communitiesinneedofelectricityaccess,aswellasthegrowing˝nancialinterestsinthe Amazonwhilealsotoreducingoreliminatingenvironmentalandsocialimpacts. 8 CHAPTER2 SUGGESTEDENERGYPORTFOLIO 2.1 CurrentBrazilianAmazonBasinEnergySituation 2.1.1 CurrentEnergyPortfolio Asof2017,therearetwodominatingpowergenerationsourcesinBrazil;68%oftheenergy feedingintoBrazil'snationalpowergridisfromhydropower,and22%isfromthermal systems(oil,gas,biomass,etc.)asisshowninFigure2.1[126].Theremaining10%is fromallotherformsofenergy:wind,solar,nuclear,andothers.Themostdramaticchange inpowerplansforthefutureisforsolar:thereisanearly4-foldplannedincreaseinthe solarcapacityforthegrid.Theplannedincreaseinsolarisstillrelativelysmallcompared tothe11GWofpossibledam-basedhydropowerplannedoverthesametimeframe.To distributethegeneratedpowertothecountry,thecurrentnationalelectricgridextends eastwardandsouthwardfromthecitiesofPortoVelhoandManaus,towardstheeastern borderandsoutherntipofBrazil.Theareabetweenandwestwardofthosetwocitiesand alsonorthofManausisnearlydevoidofgridconnections,ascanbeseeninFigure2.2. TheareabetweenManausandPortoVelhoisshowntohavenoplansfortransmissionline extension;however,itisunlikelythatthiswillremainundevelopedinthefuture,duetothe highhydraulicpotentialintheMadeiraandTapajósrivers.Therearealsoo˙-gridsystems (calledisolatedsystemsbyONS,theBrazilianelectricgridoperatinggovernmentagency) toprovidepowerforthepeoplewhowerenotgivenaconnectiontothecurrentelectricgrid. Theseo˙-gridsystemscancompriseoneormoreofthefollowing:thermalorgasgenerators, waterturbines,solarpanels,orwindturbines.Brazilprovidespowertoatleast246ofthese o˙-gridsites,almostallofwhicharesuppliedbythermalanddieselgenerators,servicing approximately760,000citizens[128].Avisualizationofthelocationsoftheo˙-gridsystems 9 Figure2.1:The2017PowerCapacityoftheBrazilianSIN(source:[126]) in2009canbefoundinFigure2.3.ItistobenotedthatalthoughFigure2.2showsthat thereareplanstoextendthenationalgridfromManausnorthwardintoRoraima,Brazil currentlydoesnotclassifythestateofRoraimaasbeing`on-the-grid',andallpowerin Roraimaisgeneratedbyo˙-gridmeans. 2.1.2 GenerationPlantsDistribution ThepowerforthegridcomesfromvariousplantsthroughoutBrazil,andisredistributed amongthedi˙erentregionsofBrazil(North,South,etc.),asisshowninFigure2.4.The excessenergyisthenexportedtoneighboringcountries.ItcanbeinferredfromFigure2.2 thatBrazilintendstoincreasetheirenergytradewithotherSouthAmericancountries,due totheplannedtransmissionlineleadingnorthintoVenezuela.Thepossiblefutureelectric 10 Figure2.2:ThecurrentandfuturepowerlinesoftheSIN(source:[125]) gridsystem,calledtheofthewouldaimatincreasingelectricexportation.All oftheoperationalgenerationplantlocationsforBrazilareshowninFigure2.5,andallof theoperationalAmazonianhydraulicplantlocationsareshowninFigure2.6. 2.1.3 AmazonianEnergyPotential 2.1.3.1 HydraulicEnergyPotential Threeofthemostenergy-importantsub-basinswithintheAmazonBasinaretheMadeira, TapajósandXingusub-basins(Figure2.7),duetotheirlargehydraulicpotentials,shownin Figure2.8.Eachofthesethreesub-basins,shownindarkblue,havearound15-30GWof hydraulicpotential,mostofwhichisuntappedinto. 11 Figure2.3:Brazilianisolatedsystemlocations(source:[125]) 2.1.3.2 PhotovoltaicandEolicEnergyPotential Thephotovoltaic(PV,orsolar)andeolic(wind)potentialenergydensitiesareshownin Figures2.9and2.10.ThesolartoeolicpotentialratioformostoftheAmazonisaround9, showingthatformostoftheAmazon,windisnotaviableoption.Therearelocationsnear theoceanbordersandfurtherawayfromtheforestedareasoftheAmazonthataremore suitedforwind;theeolicpotentialisrelativelylowintheinterioroftheAmazonatheights below50meters. 2.1.3.3 Bio-EnergyPotential Thereareseveraloptionstopursuebiomassenergysystemsthathavebeenreviewedinliter- ature.Traditionalmethodsofutilizingdedicatedbiomasscropsandtheirassociatedwastes arenotconsideredasanoptionhereduetothelikelyoutcomeofincreaseddeforestationin theAmazonandtheconversionofrich,greenhousegasabsorbinglandintodegraded˝elds 12 Figure2.4:SnapshotofBrazilianenergybalance(source:[123]) [56].However,thereareseveralalternativesourcesforfeedstockthathavebeenpresented intheliterature.Forexample,[13]suggestsusing˛oatingwoodfromtheMadeiraRiverto powerbiomassgenerators.Otherssuggestusingmunicipalsolidwastetoproducevarious chiporpelletbiomassforms[68].ItisrecommendedthatexistingbiomasssourcesinBrazil bepursued,suchason-siteconversionoffarm-basedanimalorexistingcropwasteproducts, andnottopursueoptionsthatcouldleadtofurtherdestructionofthenaturallanduseof BrazilortheAmazon. 13 Figure2.5:OperationalGenerationPlantsinBrazilianAmazon(source:[9]) 2.2 RecommendedEnergyEnhancement FortheBrazilianAmazonBasin,thereareseveralpartiestoconsiderwithvaryingdegrees ofinterestandpolarizeddirectionsofneeds.Figure2.2showsthecategoriesofAmazonian energybene˝ciariesandthesuggestedenergysolutionthatisrecommendedtosatisfytheir needs.The˝rstsplitofscale-of-interestsisbetweeno˙-gridandon-grid:theo˙-gridneeds ortheneedsofthelocalcommunities,examinedinSection2.2.1,aresmallerinscalethanthe on-gridneeds,examinedinSection2.2.2,whicharetheneedsofthecountry,orofgrowing ˝nancialinterests. 2.2.1 LocalCommunities:O˙-GridSolutionMethodology Thequestionsofwhoneedspoweraswellashowmuchtheyneedarenaturallyaccompanied bythequestion:whydotheyneedpower?Therearetwomainanswerstothisquestion: 14 Figure2.6:OperationalHydraulicPlantsandTransmissionLinesinBrazilianAmazon (source:[9]) the˝rstanswerbeingthat,simply,thehouseholdhaslittletonoaccesstopowerandwould liketohaveaccommodationsforlights,refrigeration,etc.Thesecondanswerisexpanding ˝nancialinterests:industrialandcommercialneedsforpowertoincreasemanufacturing, distribution,and/ore˚ciency.Theneedsofthosewhowouldanswerwitheitherthe˝rst orthesecondresponsearefundamentallythesame,i.e.theyneedpower,butthemethod toprovidepowerandtheamountneededcanbeverydi˙erent.Thisdi˙erenceispolarized intheAmazon,duetoaportionofthepopulationlivinginruralregionsoftheAmazon, possiblydeepwithintherainforestitself,farawayfromanycity.Thedistributionofpower tothesepeoplewholivefarfromthenationalgridbecomesdi˚cultandcostly,intermsof bothinfrastructureinvestmentandlandscapemodi˝cation.Forthepeoplewhoarefaraway fromthecurrentgrid,itmakesmoresensetoutilizethenaturalresourcesinthenearby regiontoproducethepowerlocally.Forthecommunitiesandhouseholdsthatareclose 15 Figure2.7:TheLegalAmazonandmajorBraziliansub-basins tothecurrentelectricgrid,orthosewhowillbeclosetothefuturelineextensions,itis recommendedtosimplyprovidethemwithadirecttie-intothegrid.Forthosewhodo not˝tintothesecategories,ano˙-gridsolutionisnecessary.Theprocessfordevelopinga solutionforfutureo˙-gridsystemswasasfollows: 1. Developaloadmodelforanindividualhousehold ‹ Pickcommonhouseholddevices ‹ Assumedailyusagehabits ‹ Providesmartload-managementconceptstoreducemaximumload 2. Determinegenerationtomeetload ‹ Determine`sunnyhours'thatsolarenergyisavailable,aswellasitspotential ‹ Determinethemaximum`non-sunny'loadtobemetwithin-streamturbines 16 Figure2.8:ThehydraulicpotentialinBrazil(source:[7]) ‹ SizePVtomeetdi˙erencebetweenhydroandpeakload 3. Scalesolutionuptonumberofhouseholdsofinterest 4. Perform˝nancialanalysis 2.2.1.1 LoadDevelopment The˝rststageofdevelopingaloadmodelistoselectthedevicesthatare`commonnecessities' forthecommunitiesofinterest.ForthecaseoftheAmazono˙-gridcommunities,the followingdeviceswerechosentoconstitutetheloadmodel: 1. Refrigerator 2. Lights 17 Figure2.9:ThedirectnormalsolarirradiationpotentialintheAmazon,assumingan overall12%conversione˚ciency(datasource:[111]) 3. Fans 4. Television 5. Smallstandalonefreezer Withthedevicesknown,thenextstepistoassumedeviceinstantaneouspowerrequirements anddailyusagehabitsforthedevices.Thesimplestcase,aswellastheworstcasescenario, istoassumethatalldevicesareusedat100%capacityfor24hourseachday.Another possibilityistoassumethattherefrigeratorandfreezeraretheonlydevicesthatrunall day,inordertokeepfoodpreserved,andthattheotherdevicesfollowtheloadcurveshown inFigure2.12and2.13.Thisloadmodelassumesthathouseholdsareoutworking,playing, andanyotherdailyactivityduringthehoursthatthesunisout,andthatthehousehold needslightsandfansduringtheeveningandmorninghourswhenthefamilyisinthehouse. Additionally,themodelassumesthatthehouseholdwatchesTVforacouplehoursoncethe sunbeginstoset. 18 Figure2.10:TheeolicpotentialintheAmazonat50meterheight,assuminganoverall 45%conversione˚ciency(datasource:[111]) Anotherpossiblecasefortheloadmodelistointroducesmartloadmanagementsystems thatcanreducethemaximumconstantloadand/orthepeakload.Oneexampleofasmart loadmanagementsystemwouldbetoutilizeasimpletimingcircuitonthemoreconsistently useddevices,particularlythehigherpowerdevicesliketherefrigerator,toonlyrunwhen needed.Forthecaseoftherefrigerator,thiscouldmeanonlyturningitonforafewhours intheeveningwhenthedoorwillbeopenforusage,andtokeepitonjustlongenoughto keepthecontentscooluntilthenextday,seeFigure2.14. Alongwiththesetwoloadmodels,severalothersweredeveloped,allofwhichareshown togetherinFigures2.15and2.17,forloadsmetwithandwithoutbatteries,respectively. Loadmodels1-4representneedsthatarelikelymorealignedwiththeo˙-gridcommunities thathavenotyethadelectricaccess:thesecommunitieslikelyhavelowerpowerexpectations, andcouldsimplyenjoyhavingaccesstodailyneeded/desireddevices.Loadmodels5-8would likelybeenjoyedbyanycommunity,previouslypoweredornot,however,theseloadmodels arebettersuitedforpreviouslypoweredcommunities.Thisisduetotheinclusionofmore devicesincludedthatthesecommunitiescouldbealreadyusedtohavingatleastpart-time 19 Figure2.11:Amazonianenergysolutionportfolio Figure2.12:Pictorialcomprisalofassumedo˙-gridloadwithonepossiblescenarioof usagetimes 20 Figure2.13:Temporalcurveofassumedo˙-gridload (suchasairconditioning),butwillbemoreexpensiveandthuspossiblymoredi˚cultto persuadethefundingbodiestoaccept. Theloadmodelsareshownwiththeiroptimally-lowequipmentcostgenerationcurves(see Section2.2.1.3fordetails).Itcanbeseenforthepro˝lesthathaveanoptimumgeneration mixtureconsistingofbothPVandIST(asopposedtopureIST),thatthereisoftenmore energydeliveredwhencomparedtotheload.Thisovershootleadstoanexcessinpowerthat willbeunusedwithoutbatteryorgridstorage;however,thisenergycanberepurposed,such asprovidinghouseholdcoolingusingthefreezerwithasplitA/Csystem,asshowninFigure 2.16asanequivalentreducedload.Itisrecommendedtonotusebatteries,ifpossible, frombotha˝nancialandenvironmentalperspective.Environmentally-safebatteries,such assaltwater-basedtechnology,canbeveryexpensivetopurchase,andcheaper,standard lead-acidbatteries,canbeenvironmentallydamagingtodisposeofattheendoftheirlife. Thelead-acidbatteriesinthattheycanbeleftinthedirtorwaterlocallyifeasydisposal proceduresarenotplannedfororactedon. 21 2.2.1.2 Equipmentselectionandpreliminary˝nancialanalysis The˝nancialanalysisbeginswithpricingcomponents.Fortheo˙-gridsolarsystem,the followingitemswerechosenasa˝nancialreferencesetup: ‹ PeimerSG33OPpanels(0.504USD/Watt) ‹ SolarlandSLB0103universaltiltbracket(0.172USD/Watt) ‹ SchneiderConextSW4024inverter(0.440USD/Watt) ‹ Assumedapproximately0.1USD/Wattforcablingandcouplings ThePeimarpanelsareratedat330Watts,andhave72cells.Thepanelsoutputatamaxi- mumof36.4VoltsDC(VDC),butlikelyatnormaloperatingconditions(NOCT)willoutput closerto30VDC,whichiswithinthe20-34VDCinputrequiredfortheSchneiderinverter, withouttheassistanceofavoltagetransformer.TheSchneiderinverterallowsfor120or 240Voutput,whichcan˝ttheneedsofmostexistingo˙-griddevices.Theseitemsyielded Figure2.14:Optionforpossibleloadbyutilizingsmartloadmanagementsystem 22 Figure2.15:Developedloadmodels1-8.They-axisisthepowerconsumption,inwatts, andthex-axisisthetimeofday,inhours.Thegreencurverepresentstheoptimaltotal generationcalculated,comprisedoftheyellow(PV)andblue(in-stream)curves,thatmeet orexceedtheload(theblackcurve). Figure2.16:Potentialpower"availableforfutureloadreduction 23 Figure2.17:Developedloadmodels1-8.They-axisisthepowerconsumption,inwatts, andthex-axisisthetimeofday,inhours.Thegreencurverepresentstheoptimaltotal generationcalculated,comprisedoftheyellow(PV)andblue(in-stream)curves,whose integratedpower-timeareameetsthatfortheload(theareaunderblackcurve). aPVsystemcostof1.04USD/Watt.Atthetimeofdevelopingthissolution,littledata isavailableonthepriceofin-streamtechnology.Inindustry,onlyoneready-from-the-shelf pricedatapointwasfound:SmartHydro,basedinGermany,o˙ersacompleteo˙-gridIST packagefor12,490Euroor14,580Euro,dependingontheavailable˛owvelocityanddesired mooringcon˝guration[173].Thispricecanbeequatedto,atmaximumgeneratoroutput, 2.69-3.44USD/Watt.Atasimilartime,[48]commentedthatthecostofISTtechnologyis around2.5USD/Watt,alsonotingthebene˝tofbeingenvironmentallysafe.Combiningthe ISTandPVsystemscosts,andscalingbytheunitload,itiscalculatedthatthecostofthe o˙-gridsolutionisbetween1.34and3.01USD/Watt.Thecostforallreporteddamsinthe AmazonBasinis3.67USD/Watt,andevenhigherfortheBrazilianAmazonapproximately 5.50USD/Watt[70].Comparingthecosts,itisshownthatthesolutionproposedherecan beeconomicallyviableandadvantageousoverdams;amoredetailedanalysisispresented todeterminethespatialextentandspanofthisstatement,seeSection2.2.1.3. 24 2.2.1.3 GenerationDeterminationandDetailedFinancialAnalysis Aftertheloadmodelsweredeveloped,thegenerationrequiredtomeetthatloadisde- termined.Duetotheenergypotentialsdiscussedin2.1.3fortheAmazonianregion,itis recommendedtoutilizehydraulic(within-streamturbines)andsolarenergysources,aswas showninFigure2.2.Thenumberofin-streamturbinesdependsonthemaximumloadduring `non-sunny'hoursaswellasconstraintsfromtheriver:theaveragedepthandtransverse˛ow velocitypro˝les,theintermittencyofavailabilityofthe˛owvelocity,thedepthandwidth oftheriver,andthedistancefromtherivertothecommunity.TheISTsaretobeplaced inthenearest,highestvelocityriverstretchestothecommunity,andthepowersharedand distributedtothehouseholdsandcommonbuildings.ThenumberofPVpanelsdependson thedi˙erencebetweentheconstanthydro-metloadandthepeakload,thetimeofdayofthe maximumdi˙erencebetweenthetwo,andthespeci˝ccoordinatelocationintheAmazon. ThePVpanelsaresuggestedtobeplacedontheroofsoftheindividualhouseholdsoron topofcentralcommunitybuildings,bothofwhichwillprovidethecommunitieswiththe mostconvenientsolution,andhopefullyprovidethestrongestfeelingof`self-ownership'for thesolution;theindividualpeopleandfamiliescanfeelthattheywereconsideredandcared fordirectly. Toevaluatethedetailed˝nancialanalysis,aMicrosoftExcelVBA-basedscriptwas developedtobeabletotestawiderangeofconditions,toautomaticallyextractdatafrom aninternetsource[136],tologicallylocateandtabulateriverconditionsfromaprovided dataset[41],andtofacilitaterigidsolverinput-output,andtobeabletomoreeasilyand consistentlyadapttothesolutionoutputsignals,seeAppendixC.Thescriptisorganized withthefollowinglogic:userinputisprovidedonanExcelsheet,whichwillbereferredto alphabeticallyhere,whichisthenpassedontosheetthatwillserveastheoutput forthe˝nalscriptresults.Fromsheetthecoordinatesofinterestarepassedthrough, alongwiththenumberofcommunityhouseholds,andanoptionalcommunityname;the coordinatesareusedtolookupthehourlysolardataoveroneyearusinganotherexcelVBA 25 scriptprovidedbyRenewables.ninja[136]thatpullsfromsheetOnsheetarethe followingvariables:theuser'srenewables.ninjaAPID,thecoordinatesofinterest,thesize ofthePVplanttodesign(1kW),thedesiredsolarmodel(MERRA-2),thetiltandazimuth oftheplannedpanels(0 ),andtheadditionalsystemloss(10%).Foreachcommunity's coordinateset,thePVdataisextractedfromsheettosheetwithanassumedplant sizeof1kW.Theyearofhourlydataisaveragedforeachhouroftheday,whichwillbe scaledbytherequiredhourlyPVratedpoweratthecurrentsolveriterationonsheet ThePVratedpowerisusedasascalingfactoroverthe1kWscriptinputplantsizebecause thesolardataestimatestherelativee˚ciencyofthepanel,utilizingaparameterizedenergy performancemodelpresentedby[85],Equation(2.3).ThesolarscriptusestheMERRA-2 globalreanalysisdatatoextractthelocation-speci˝c2-meterdisplacementheight(T2M,zero windlog-pro˝levelocity),airtemperatureandirradiancetoestimatethemoduletemperature viaanempiricalrelationshiptocalculatethemoduleheatingandrelativee˚ciency.The relativepowerperformanceequationpresentedby[85]isthensolved,usingthefree-standing moduletemperaturerisecoe˚cient,Equation(2.2),whichisreproducedhereasEquations (2.1)-(2.4). T mod = T amb + c T G (2.1) c T =0 : 035 o CW 1 m 2 (2.2) rel =1+ k 1 ln( G 0 )+ k 2 ln( G 0 ) 2 + T 0 k 3 + k 4 ln( G 0 )+ k 5 ln( G 0 ) 2 + k 6 T 0 2 (2.3) P = P STC G G STC rel (2.4) Where G 0 = G G STC , T 0 = T mod T mod STC , G STC =1000 W=m 2 , T mod STC =25 o C , G is thein-placeirradiance,and T amb isT2Mand k 1 k 6 arefoundfromexperimentaldata. OncethePVdataisimported,theapproximately30-yearaverageriver˛owrateand˛ow velocitywasretrievedfromatabulatedsheetofcoordinatedata,sheetatthenearest riverlocationtothecommunitycoordinate(foundbyusingautomatedlogictosearchfor nearestreasonably-high˛owrate, O (100 1000) ).Theriver˛owandcross-sectionalarea 26 datacomesfromaleaf-hydro-˛ood(LHF)hydraulicmodel,carriedoutata2kmresolution fortheentiretyoftheAmazonRiverbasin[41].Oncethenearestriverhasbeen found,thenthehighestrivervelocityinthesurroundingtabularregion(foundbyusing similarlogictothepreviousstepto˝ndtabulardirectionofriver)ispassedbacktosheet wherethesolversetupanditerationcanproceed.Theturbinedeliveredpoweriscalculated fromtherivervelocityfoundpreviouslyviauseofacurve˝tfromdataavailableonthe SmartHydroPowerwebsite[173],orequaltotherated5000Watthefull-rated2.8m/s. Equation(2.5)showsthepowercurve˝t,where P IST isthegenerator-includedpowerof thein-streamunit,and C 1 isthefree-streamvelocityfoundforthegivenriverlocation. Thein-streamunitisassumedtobeabletooperateatthecalculatedlevel24/7,onaverage throughouttheyear. P IST = 8 > > < > > : 196 : 43 C 1 3 : 1336 ; if C 1 < 2 : 8 m=s 5 ; 000 ; if C 1 =2 : 8 m=s (2.5) AnonlinearGeneralizedReducedGradient(nGRG)algorithmwasutilizedwithinthe VBAenvironment,usingMicrosoftExcel'ssolvertoevaluatethegenerationtomeetthe loadwhileminimizingcost.ThenGRGmethodisa.nonlinearextensionofthesimplex methodforlinearprogramming"[97].Accordingto[96]and[97],thisalgorithmseeksto solveaseriesofsimpli˝ed,orreducedequations,whicharesummarizedinEquations2.6- 2.13: minimizeF ( x ) (2.6) subjecttol 0 (2.12) Where ischosentosatisfytheboundsontheoriginalconstraints.Intheoriginalfunction form,thisisequivalenttosolving: f ( y; x + i d )=0 (2.13) whereonlyyisunknown(theoround"constraints),whichcanbesolvedwiththe Newton-Raphsonroot-searchingmethod. Thegenerationcostswerecalculatedovertherangeof1-2.8m/sofriver˛owspeed, with2.8chosenasthemaximumforthein-streamgenerator'sratedmaximumpowerlevel, assumingthatthereiscut-outcontrol.TheresultsareshowninareshowninFigures2.18 and2.19.Iftheloadpro˝leismodi˝edthentheresultsabovewillchangeaccordingly.For example,ifthepeakloadisincreasedthenthetotalcostwillalsolikelyincrease,likewise forincreasingthemaximumloadduring`non-sunny'hours(inotherwords,therearetwo peakloadstoconsider:sunnyandnon-sunny).Themagnitudeofe˙ectofthechangewill bedependentontheseverityoftheloadchange,aswellasthe˛owvelocityinquestion: athigh˛owvelocity,changingthepeaknon-sunnyloadwillhavelessofane˙ectontotal costduetothehydraulicpotentialbeinghigherthanatlowvelocity.Anotherchangethat 28 Figure2.18:Singlehouseholdloadpro˝lewithsuggestedgenerationpro˝les Figure2.19:Curveofbasecostovertheinvestigatedrangeof˛owvelocities,costs calculatedovera30yearequipmentlifespan 29 willhaveasigni˝cante˙ectontheaboveresultisthetemporalusageofthedevices:PV isusedtoshavethepeakload,soiftoomanydevices(namely,highpowerdeviceslikethe refrigerator)areusedaroundsunrise/sunsetthenthecostswilllikelyincrease,asPVdoes nothaveenoughpotentialatareasonablescaletoshavethepeakloadwithoutbatteries. Thenextstepwastocalculatethecablecostsassociatedwiththeparticularoptimal generationcasetomeettheload.TheSmartHydroPowerunitcomeswith50metersof cabling,whichmaybesu˚cientifthegeneratorisnotfarfromshorerightneartothe community.Requiringtheturbinetoberightnexttothecommunityisconvenient,butnot necessarilyalwaysthemostenergeticallyor˝nanciallyfeasibleoption.Theoptimalscenario wouldbethatthecommunityhashigh˛owvelocitywaterwithinapproximately50meters ofthewater'sedge,whereatminimumthecablingprovidedcouldtransmitpowertoshore. However,asitispossiblethatmostcommunitiesarenotrightnexttoriverlocationswith high˛owvelocity,allowingthein-streamdevicestobeplacedfurtherawayandtransmitthe poweroverlongercablesisapossiblesolutiontokeepcostslowandpowercapacitiescloserto ratedlevels.Withlongercables,costswillalsoincreaseinproportiontotheturbinesystem ratingaswellasthedistancetothenearesthigh-velocityriverlocation.Tocalculatethe cablecosts,thefollowingisassumed:amaximumdistanceof60kmbetweenthecommunity andtheISGdeploymentsitewasallowedinthescript(approximatelyhalfofatypical mediumvoltagelinemaximumlength),anda10AmericanWireGauge(AWG)o˙-the-shelf spoolwouldbeusedasabasisforcosts(rangingfrom0.82to1.18USD/meter,whichwas approximatedas1USD/m).Thecablecostrangeexaminedhereis1,000-6,000USD/km, representingusingonlyacablebundle(ormorelikely,multiplecables)uptoalow-cost distributionnetwork(transformers,externalconductors,andotherelectricalcomponents). ItisnotedthatthePVsystemisnotunderconsiderationwhenexaminingthecablingdue totheproposedplacementofthePVpanelsbeingontheroofsofthecommunity,thus,will alwaysbeashortdistanceawayfromwherethepowerisused.SeeSection2.2.1.4forfurther detailsandresultsonthetheoreticalmaximumdistancethatcanbeservicedatagivencost 30 ofenergygoal.Itisassumedthatthe50metersofcableissu˚cienttoreachfromthe turbinestotheshore,whereconversion(from3 ˚ to1 ˚ )andtransformation(fromgenerator voltageto120or240V)cantakeplace,andthenthepowertransmittedtothecommunity (whichcanthenberecti˝edifnecessary),or,thegeneratorphasescanbekinto singlephase(connectingtooneofthethreephasesandtheneutralline,orbyusingtwolive phases),forlowpowersituations,andthentransmittedtothecommunity. Tohaveabasisforcomparisonwiththecalculatedcostoftheproposedsolution,several possiblecommonBrazilianenergygenerationordistributionmethodswereestimated:an extensionofthecurrentnationalelectricgrid,thebuildingofanewdamwithdistribution lines,usingadieselgenerator,andalsothe2019BrazilianNorthregiontari˙s.Thoughthe tari˙srepresenttheaveragechargeforelectricitywhileinterconnectedtothenationalgrid, itisrecognizedthatthisratemaynotbeaccurateforcommunitiesthatarefarfromthegrid withouttheaidofextragovernmentincentiveprograms,duetothelargecostsincurredto extendthegridoveralongdistance.Regardless,thetari˙sactasaguide forthecoste˙ectivenessofaproject,inthatifaproposedsystemcouldmeetorbelowercost thanthetari˙s,itcouldbeastrongincentiveforfurtherexaminationbythegovernment (ANEEL,EPE,ONS,MME,etc.)forutilizationevenbeyondo˙-gridcommunities. The˝rstmodeofenergyprovisionisanextensionofthenationalgridviaanewtransmis- sion/distributionlinenetwork.Tocalculatethegridextensioncosts,twomajorperspectives tocalculatethelinecostsweredeveloped:1)useBraziliangovernmentreporteddataasa situationalabsolute;ifthecurrentmethodtosupplyanyregionwithpoweristobuild230 kVlineuptothepointofdistribution,thenthatislikelyhowitwillbedoneforgridstability andreliability,andsotheperspectiveisanaccuratebasisor2)usearangeofelectricalcom- ponent(highvoltage(HV),mediumvoltage(MV),andlowvoltage(LV)lines,transformers, etc.)pricingfromtheliteraturetomodelatransmissionsystem.Forbothscenariosawide possiblerangeoflinecostswerefound,fromapproximately6,000USD/km,attemptingto developacheaperlow-to-mediumvoltagedistribution/transmissionline,[55]upto80,000- 31 410,000USD/km,calculatedfromexistingandplannedHVtransmissionlinesintheBrazil- ianAmazonregion([129],[127],[122]).Itisunclearatthistimewhichvaluewouldbemost representativeofextendingatransmissionlinedeeperintotheheartoftheAmazon,where existingroadwaysandconstructionright-of-wayshavenotyetbeenestablished,theterrain maybehighlyvariable,andnativelandsandprotectedareasmaybepresentthatprevent building,etc.,thusarangeofpossiblecostsisconsidered. TheBrazilianlinecostswereusedontheirownastotalcostperkilometer,duetono additionalinformationbeingprovidedaboutwhetherornotthesearetotalprojectcosts,or somesubsetofthetotal.Thus,theBraziliancostestimateswillbedubbedcosts, asthelinecostsareassumedtocapturealltransmissioncosts,asopposedtojusta cost,whichhereismeanttorefertothecostofthecablealone.Additionally,substation costswerealsonotincluded,assumingthatthedistancesandloadswillnotbesigni˝cant enoughforsubstationstoberequired.FromBraziliandata,itiscalculatedthatanHVline couldextendanywherefrom4to168km(onaverage ˘ 77km)([129],[127],[122])between substations.AslongastheHVlinedoesnotextendfaroutsideoftheapproximaterangeof 77-160km,theassumptionofnotpricingasubstationshouldhold.Equation(2.14)shows thecalculationofabsolutegridextensioncostsinUSD: C ONS tot = CC L (2.14) where C ONS tot isthetotalgridextensioncostbasedondatafromtheBraziliangovernment entityONS, CC isthecablecostperkilometercalculatedfromthedata,and L isthelength ofcableextension. Theliteraturecomponentcostswereuseddi˙erently:insteadofassumingthatthecable costisthecost,thecablecostsareonlyonecomponentofthewholesystem, whichisbuiltupfromthefollowing: ‹ HV,MV,andLVcablecosts ‹ transformers 32 ‹ householdconversionequipmentandconnectioncosts TheLVlinecostsarecalculatedfromanassumedinter-housedistanceof25meters[155]with acablecostbetween10,611USD/kmand12,000USD/km([133],[155]),andtheMVline isassumedtocarrythepoweroveramaximumdistanceof120kilometerstothe community[46]atacostbetween6,000USD/kmand30,580USD/km([55],[99])atwhich pointtheHVlinemakesuptheremainingdistance,withacostrangingfrom90,000USD/km to192,000USD/km,dependingonoperatingvoltage[46].Thetransformersareassumed tocostbetween39and1,000USDperratedkW([133],[155]),thehouseholdequipmentis assumedtocostbetween263and367USDperhousehold([133],[155]),andthehousehold connectioncostis149USDperhousehold[133].Theoperationandmaintenancecostsare assumedtobebetween2-3%forthetransformersandcables,respectively([133],[155]). Thetransformersareassumedtohave18%lossesanda10yearlifespan[133].Thetotal cablelengthcanbecalculatedbyEquation(2.15),andthetotalgridextensioncostswere calculatedwithEquation(2.16). L total = L LV + L MV + L HV (2.15) Where L isthelengthofcableforaparticularvoltagecategory,ortotallength. C COMP tot = 8 > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > : (1+ OM MV ) CC MV L MV + ::: (1+ OM LV ) CC LV HH d ihs + ::: (1+ OM tr ) (1+ LF tr ) ( T=t tr ) ( C tr P peak HH ) ; if L MV 120 km CC HV L HV +(1+ OM MV ) CC MV 120+ ::: (1+ OM LV ) CC LV HH d ihs + ::: (1+ OM tr ) (1+ LF tr ) ( T=t tr ) ( C tr P peak HH ) ; otherwise (2.16) 33 Where OM istheoperationandmaintenancecostoftheparticularequipmentinpercentof cablecost, CC isthecablecostofagivenvoltagecategoryfoundinliteratureinUSD/km, HH isthenumberofhouseholdsexamined, d ihs istheinter-householddistance, LF tr ;t tr ;C tr arethelossfactor,lifetime,andunitcostofthetransformersinpercent,years,andUSD/kW, respectively,and P peak isthepeakratedloadpowerlevel. Thenextmodeofenergyprovisiontocomparetheproposedsolutiontoistheconstruction ofanewfull-scaledamwithtransmissionlinesbuilttobringthepowertothecommunity. Equation(2.17)showsthetotalestimatedcostcalculationofdamconstructionandpower transmission. C dam tot = C dam UR P peak HH + OM dam P MWh + CC BR L (2.17) Where C dam istheaveragecalculatedcostofdamconstruction(5.5USD/W)intheAma- zonBasinandBrazil([135],[189]), UR istheaverageglobaldamconstructioncosttypical underreportingratio(valuesofeither1USD/USDor1.96USD/USD[10]wereconsidered here), P peak and P MWh arethepeakpowerandenergyusageoverayearinWandMWh, respectively, OM dam istheoperationandmaintenanceforadam(2.31or5.8USD/MWh) [87], CC BR isthecablecostfortransmission,assumingthatthecurrentBrazilianmethod forpowertransmissionapplies,andHVcableswillbeusedformostofthedistance,and L isthedistanceofcable.Aswasmentionedforthegridextensioncalculation,theBrazilian transmissionlinecostsareusedatthetotallinecost,assumingthatallcostsareincluded (right-of-way,projectedoperationandmaintenance,etc.),duetoalackofinformationon projectcostcomponents.BoththegridextensionandthedamconstructionusetheBrazil- ianlinecosts,becauseunlikewithadecentralizedmicrogrid,thereliabilityofthenational systems(whetheritisanewdamorthegriditself)isundercloserscrutinybyanyinterests- at-large,andsoitisassumedherethatthetraditionalHVlinewillbeinstalledtoreducerisk ofoutagesiftheloadspikesbecometoolarge.Similartothegridextension,atransmission networkwasalsocalculatedfromcomponentsinliterature,whichyieldsacostcalculatedby 34 Equation(2.18). C dam tot = 8 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > : C dam UR P peak HH + OM dam P MWh + ::: (1+ OM MV ) CC MV L MV + ::: (1+ OM LV ) CC LV HH d ihs + ::: (1+ OM tr ) (1+ LF tr ) ( T=t tr ) ( C tr P peak HH ) ; if L MV 120 km C dam UR P peak HH + OM dam P MWh + ::: CC HV L HV +(1+ OM MV ) CC MV 120+ ::: (1+ OM LV ) CC LV HH d ihs + ::: (1+ OM tr ) (1+ LF tr ) ( T=t tr ) ( C tr P peak HH ) ; otherwise (2.18) Theratingofaconventionaldamthatcouldbeinstalledinthesameriver locationasthein-streamsiteiscalculatedbyEquations(2.19)and(2.20)wereutilizedalong withthehydraulicdatausedtocalculatetherivervelocity.Thetotalheadiscalculatedfrom thesumofthestatichead(waterheight, h andelevation, z )acrossthesite,andthekinetic headatthesite.Thisisconvertedintoanequivalenttotalpressureandmultipliedbythe ˛owrate( Q 90 )atthesitetoobtainthemaximumtheoreticalextractableriverinepower. H total =( h 2 + z 2 ) ( h 1 + z 1 )+ C 1 2 2 g (2.19) P dam = ˆ g H total Q 90 (2.20) Onlyaportionofthetotalpowercalculatedwillbedivertedtowardsthecommunity,whereas mostofthepowerisassumedtobedirectedtotheexistingelectricgrid.Itisassumedthatthe communitywouldthenbechargedonlyforthepowerutilized,equivalenttothecumulative communityloads, P community = HH P peak P dam P dam . Onemajordi˙erencebetweenthegridextensionandthedamconstructionistherisk of˛oodingandassociatedcommunitydisplacementoncethereservoiris˝lled.Toestimate 35 thereachofthereservoir,theaveragereservoirradiuswascalculatedwithrespecttothe nameplatecapacityofeachdam: R res ˇ q 1 : 58 P nameplate =ˇ (2.21) Where P nameplate isthecalculatedtheoreticalcapacityofthedaminMW,and1.58isthe calculatedaverageconversionforBrazilianAmazondamsin km 2 =MW .Withthereservoir areadetermined,aconstantradiuscircularshapeisassumed,neglectingthelocaltopography, allowingforsimplecalculationofthereachof˛ooding.Ifthecommunityiswithintheradius ofthecalculatedreservoir,thenitisconcludedthatitispossiblethatthereisariskof ˛oodingforthatcommunity,andinstallingafull-scaledamatthein-streamsitecouldlead todisplacementofthatcommunity.Thesitesatriskof˛oodingaremarkedwithared`x' inFigures2.22-2.23and2.25-2.26. Thelastmodeofenergyprovisionexaminedisadieselgenerator.Tocalculatethecost ofenergyofadieselgenerator,typicalusagefromanAmazoniancommunityinthestateof Amapawascalculated.From[144],usingthepowerrating(90kW)andyearlyallottedfuel consumption(27,600liters),anestimatedaverageloadof75%wascalculatedusingpower- consumptionscurves/tablesforsimilarlysizeddieselgenerators(80-100kW)atafuelrate of ˘ 4.99gal/hr.Fromthisgeneratorload,thenumberofhouseholdsthatthedevicecould equivalentlysupportwascalculated,basedonaUPCpeakloadof350Wand1,490Wfor PC,yielding192and45households,respectively.Therearetwousagecasesconsideredfor adieselgenerator:meetingthesameloadpatternastheproposedsolution,andmeetingan all-dayconstant,all-devicesload(500Wfor135householdsand1,540Wfor43households, forUPCandPC,respectively).Thelatterisconsideredastheest-caseforhaving constantaccesstoalldevicesallday;however,thefuelcostswouldlikelybetooexpensivefor manyhouseholds,andaswasmentionedin[144],wouldnotbefundedinthefuelallowance (likelytobegrantedenoughfuelforapproximately4hoursperdayofusage,not24),and sothiscaseisconsideredasatheoreticallowerlimitforthegivenexaminedconditions.The dieselgeneratorwasquotedtocost44,151.52USD[144].Tocalculatethefuelcosts,the 36 Brazilian2019averagedieselcost[14]wasconvertedintoUSD,whichwasfoundtobe2.60 USD/gal.ThecostofdieselgeneratorisshowninEquation(2.22). C diesel tot = C generator + CR fuel 2 : 60 8760 T (2.22) Where CR fuel istheconsumptionrateofdieselfuelbythegenerator. ToexplorethepossiblerangeoftheproposedsolutioncostsintheAmazon,several samplesiteswerechosen,basedoncurrentlyplanneddams,aswellasafewofplanneddams thatwerehaltedforenvironmental/socialreasons,withtheadditionofafewextrasitesto distributethelocationsmoreevenlyamongthethreesub-basinsshowninFigure2.20.These sitesactasproxiesforcommunitiesthatcouldbepresentattheselocations,andcanserve aslocationalcasestudiesforexaminingtheproposedsolutionasbeingaviablealternative forfull-sizedlargescaledamsprovidinglocalpower.Figures2.21-2.26showtheresultsof themicrogridsizingcalculationbycomparingthecalculatedproposedsolutioncostsagainst thecalculatedcostsforanelectricgridextension(Figures2.21and2.24)andagainstanew damconstructionwithdistributionlines(Figures2.22-2.23and2.25-2.26),wherearedx symbolizesapossiblecommunity˛ooding/displacement,dependingonthereservoirbuilt forthedam.ThecostsareshownintermsofUSD/kWh,whichwascalculatedbydividing thetotalcostsbytheloadenergyusageperhousehold(hh)peryear,1,544kWh/hhor7,048 kWh/hhforUPCandPC,respectively,withtheexceptionofthelow-costdiesel,which hasayearlyusageat4,380kWh/hh,andthenmultiplyingbythenumberofhouseholdsin question. Figure2.21examinesseveralcablecostsonthefeasibilityoftheproposedsolutionas comparedtoanextensionofthecurrentelectricgrid,adieselgenerator,andthe2019tari˙s forapreviouslyunpoweredcommunity(UPC).Thesamplesitesshowthatarangeofcosts werecalculated,dependingonthelocalrivervelocities,andtheirdistancetothecommunity. Attheextrema,forthelowendofcablecosts(1,000USD/km),therearetwosamplesites whoserivervelocitiesare0.74and0.84m/sthathavecostsabovethehighdieselgenerator 37 Figure2.20:Locationsofsamplesitesoverlaidontopofriverpaths,withmarkers representingtherivervelocityavailableatthatlocation,basedon Q 90 . level,thereforethesemaynotbene˝tfromtheproposedmixasmuchasothersites,and therearearoundsevensitesthathavealowercostthanthe2019ruraltari˙,whichseemsto associatewithrivervelocitiesabove1.54m/sthatarealsogenerallyclosetohigh-velocity riverlocations,thatmaymostconsistentlybene˝tfromtheproposedenergymix.Three ofthesesevensitesalsoarewithin ˘ 90kmfromacurrenttransmissionline,socouldalso potentiallyreceiveagridconnection,ifthelowextensioncostscanbemet,andnomajor substationorelectricalsupportingstructureneedstobebuilttosupporttheadditional load.Thereareanotherthreesiteswhosecostsareinbetweenthetwotari˙s,thatcould alsobene˝tfromtheenergymix,withtheexceptionofonesitethatis ˘ 100kmfroman existingtransmissionline,thatcouldalsobene˝tfromalow-costgridconnection.The remainingsiteshavecoststhatliesomewhereinbetweenthe2019residentialtari˙andthe highcostofdiesellines,andarethuscompetitivewiththecurrentdieselgeneratormethodof supplyingpowertoo˙-gridcommunities;thecommunitiesthatstillneedpowercouldbene˝t 38 Figure2.21:ComparisonofproposedUPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Thecostsassociatedwiththeelectricgrid extensionisshownbythepurplerange,adieselgeneratorisshownbythebrownrangeand the2019BrazilianNorthregionresidentialandruraltari˙sareshownbytheblackrange. Thex-axisisthedistancefromthecommunitytothenearestexistingtransmissionline,in km,andthey-axisisthecalculatedcostinUSD/kWhover30years. 39 Figure2.22:ComparisonofproposedUPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Damconstructionwithdistributionlinesis shownbythegoldrange,withnounderreportingfactorincluded;theotherrangesarethe sameas2.21.Thex-axisisthedistancefromthecommunitytotheoptimalin-stream generationsite,inkm,andthey-axisisthecalculatedcostinUSD/kWhover30years. 40 Figure2.23:ComparisonofproposedUPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Anewdamconstructionwithdistribution linesisshownbythegoldrange,withanunderreportingfactorof1.96USD/USDincluded, adieselgeneratorisshownbythebrownrangeandthe2019BrazilianNorthregion residentialandruraltari˙sareshownbytheblackrange.SeeFigure2.22foraxes. 41 Figure2.24:ComparisonofproposedPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Thecostsassociatedwiththeelectricgrid extensionisshownbythepurplerange,adieselgeneratorisshownbythebrownrangeand the2019BrazilianNorthregionresidentialandruraltari˙sareshownbytheblackrange. SeeFigure2.21foraxes. 42 Figure2.25:ComparisonofproposedPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Anewdamconstructionwithdistribution linesisshownbythegoldrange,withnounderreportingfactorincluded,adieselgenerator isshownbythebrownrangeandthe2019BrazilianNorthregionresidentialandrural tari˙sareshownbytheblackrange.SeeFigure2.22foraxes. 43 Figure2.26:ComparisonofproposedPCsolution(greendiamonds)withseveralcommon energygenerationanddistributionmethods.Anewdamconstructionwithdistribution linesisshownbythegoldrange,withanunderreportingfactorof1.96USD/USDincluded, adieselgeneratorisshownbythebrownrangeandthe2019BrazilianNorthregion residentialandruraltari˙sareshownbytheblackrange.SeeFigure2.22foraxes. 44 fromtheproposedsolution,andnotneedtodependonfossilfuelsorgovernmentfuelcredits. Increasingthecablecostfrom1,000USD/kmto3,000and6,000yieldstheexpectedresult ofthecostsassociatedwiththein-streamgenerationtoincrease,andwithoutthepresence ofabattery,thetotalprojectcostincreases.Thetwositesthathadcalculatedcostsabove thehighdieselgeneratorlineincreaseincosttoapointwheretheyarenolongershownon thehighercablecostplots,butforthesitesthathavecoststhatwerecomparabletothe tari˙sordieselgenerator,thegroupingofpointsremainsconsistentlyinthecost-competitive rangeoverthecablecostsconsideredhere. Figures2.22and2.23examineseveralcablecostsonthefeasibilityoftheproposed solutionascomparedtotheconstructionofanewfull-scaledam,adieselgenerator,and the2019tari˙sforapreviouslyunpoweredcommunity.AsitwasfoundfromFigure2.21, thereisarangeofcostsandthusfeasibilityoftheproposedsolutionoverthesamplesites. Thedistributionofresultsforthesitesisconsistentwiththeaforementionedresults,with theexceptionsomesitesacrosstheexaminedcablecostrangethatarenotas˝nancially feasibleastheothers:thesesiteshaveahighercostthanthefull-scaledam,butareat riskfor˛ooding.Forthesesites,comparingthecoststoadieselgeneratorleadstothe conclusionthattheproposedenergymixiscompetitive,evenifnotmorecost-e˙ectively thanadam,wheretheenvironmentalandsocialsafetycomparedtothefulldamordiesel generatorcouldbeconsideredtomakeupthedi˙erence.Againincreasingthecablecosts from1,000USD/kmto3,000and6,000yieldstworesponsesfromthesamplesitecosts: sitesthatwerelesscompetitivebecomeevenlesscompetitive(somesiteshavecoststhatare hightobeshownintherangeofthe˝gures),andtherestremainfairlywellgroupedinthe competitiverange.Resultsforapreviouslypoweredcommunity(PC)indicateverysimilar trendstotheUPCcase,butataslightlymorecost-e˙ectiverate(seeFigures2.24to2.26). Theresultsalsoremainconsistentoverthecostofcablingconsidered.Theexaminedvalues ofunderreportedcostsfordamalsodidnotchangetheoverallresultingtrend:thelower costratesolutions(thosearoundorbelowthetari˙s)are˝nanciallybene˝cialwiththe1.96 45 Table2.1:Cablesusedasbasisforinvestigation CableV(V)I(A)USD/m 1600150.849 2600305.157 36009510.335 460032512.830 underreportingratio(thoughtmoresothancomparedtothefactorofunity),andthesites thathavehighercostsarestilllesscompetitivecomparatively. 2.2.1.4 O˙-gridmicrogrids:thenaturalreachofrivers Anotherperspectiveonprovidingpowertothelocalcommunitiesisinsteadofaskinghow economicallytheycanreceivepower,askinghowfarcanthecommunitybefromahigh- enoughvelocityriverandreceiveelectricityatagivengoalcostofenergy?Conversely,the questioncouldalsoberivervelocitytoreachacertaindistance?To˝ndthe maximumdistanceofservice,therearetwopathsthatcouldbeused:coupledanduncoupled solutionprocedures.Thecoupledsolutioninvolvesincludingthecablecostdirectlywithin thescriptusedtodeterminetheoptimalriverlocationsimultaneouswiththegeneration determination,minimizingdistanceand(andthus,cablecost)andmaximizingrivervelocity available.Forthisstudy,theuncoupledmethodisusedforasimpli˝edexaminationof cablecostdecoupledfromthegenerationsystemcosts.Forthismethod,thegeneration systemissizedtomeettheloadandthenthecablecostsarecalculatedbasedontheoutput. Thecablesusedintheanalysisareseveralspools:thediametersare18AWG, 16AWG,12AWG,and250MCM,rangingincostfromapproximately0.8to12.8USD/meter, seeTable2.1fordetailsofeachcable.Thepowercarryingcapabilityofthecableiscalculated fromthemaximumratedvoltageandthetypicalamperagecarryingabilityforthatcable, assumingapowerfactorofunity(voltageinphasewithcurrent,ortherealpowerisequal totheelectricpower, I V ). Tocalculatethee˙ectiverangeofthegenerationsystem,thecostlevelsof0.40USD/kWh 46 and0.12USD/kWhareusedasabasis,correspondingtoadieselgeneratormeetingthesame loadpro˝leasthesuggestedenergyportfolioandthe2019NorthRegionBrazilianrural tari˙[8],respectively.Thecostandcarryingcapacityofthecablesareusedtocalculatethe theoreticalpowertransmissioncost,uptoatypicalmediumvoltagelineusageof120km [47].After120km,itisassumedthatahighvoltagelinehastobeutilized,increasingthe cablecostforthedistancesgreaterthan120kmto90USD/m[47].Itisassumedthatfor thesizeofcommunityexamined,anadditionaldeviceforhighvoltagetransformationwill berequired,butthatthepricewillbesmallinproportiontotheassumedtotalsystemcosts. Foramuchsmallerorlargercommunity,thisassumptionwillnotholdasstrongly,andhigh voltagetransformer(s)wouldhavetobeaddedtothecosts. Thefollowingsystemofconstraints(Equations2.23-2.25)aresolved,andthenan analyticalequationformaximumextensiondistanceissolved(Equation2.26): Minimize ( C b;eq ) (2.23) Where C b;eq isthetotalsystemequipmentcostwithoutcabling,inUSD,andiscalculated as: C b;eq = UC ISG P r;ISG + UC PV P r;PV .Where _ W;r istheratedpoweroftheISGor PVsystems. P ISG ( t )+ P PV ( t ) Load ( t ) (2.24) Where P istheinstantaneouspowerdeliveredbytheISGorPVsystemsattime-of-dayt. N ISG 0& N PV 0 (2.25) Where N isthenumberofISGorPVgeneratingunits. D MV = gCoE kphy HH T C b;eq CC MV TF (2.26) Where D MV isthedistanceofextensionusingamediumorlowvoltageline(LVorMV, simplynamedMVhere)inkm. gCoE;kphy;HH;T;CC MV ;andTF are:thegoalcost ofenergyinUSD/kWh,theloadkWh/yearperhousehold,thenumberofhouseholds,the 47 numberofyearsforthelifetimeoftheequipment,thecablecostoftheMVlineinUSD/km, andtheturbinefactor,respectively.TheturbinefactorisaratioofthedesignedISGrated powertothetheoreticalmaximumpowerthatthelinecancarry.Iftheextensiondistance D MV isfoundtobegreaterthan120km,thenasecondequationisused: D HV = gCoE kphy HH T C b;eq CC MV 120 TF CC HV (2.27) Where D HV isthedistanceofextensionusingahighvoltage(HV)line.Itfollowsthatif Equation2.27isused,thenthetotaldistanceofreachofthesystemis D total = D HV +120 . CC HV isthecablecostofahighvoltageline,inUSD/km.Theturbinefactorisnotincluded inthehighvoltagelinecalculationassumingthatforthesystemratedpowerinquestionfor atypicalo˙-gridcommunitywillbewell-belowthecapacityofanHVline. AscanbeseenfromFigure2.27thebehaviorofthecurvesbeforetheextensiondistance reaches120kmisgenerallywell-behaved,inthatasimpleconceptualsimpli˝cationcanbe made:asahigher˛owvelocityisavailable,thefartherthatthegenerationmixcanreachat agivenpricepoint.Afterthe120kmcrossover,thereisachangeinthemagnitudeofslope thecurvesbeingdependentonthecostbasisandcableofinterest;however,theoveralltrend staysconsistent:thehigherthe˛owvelocityavailable,thefartherawayfromtheriverthat thecommunitycanbelocatedandhavepowerprovidedina˝nancially-incentivemanner. Forseveralcables,thereisanotherslopechangearound1.6m/s(cable#4)or2.3-2.4m/s (cables#1or3),whichiscausedbytheassumptionofTFnotbeingabletogobelowunity, inotherwords,atleastonefullcablehastobesized,andnotafractionofone.Thisyields acurvethatincreasesmoreslowlyinextensiondistanceover˛owvelocity,whencompared withacurvethatwouldallowtheTFtofallbelowunity.Themaximumrenewablegrid servicedistanceisfoundtobeapproximately150kminthe˛owrangeinvestigated.Ata distributiondistanceof150kmfromariverlocationthathasa˛owvelocitygreaterthan2.6 m/s,approximately43.6%oftheAmazonianareacouldbene˝tfromtheserviceandmeet the0.40USD/kWhgoalcostofenergy,or35.5%fortheNorthernruraltari˙. 48 Figure2.27:Reachoflosslesscablesatvariousgoalcostofenergylevels 2.2.2 FinancialInterests:On-GridSolutionMethodology Similartotheprocessfordevelopingtheo˙-gridsolution,theon-gridsolutioniscomprised ofthefollowingsteps: 1. Developaloadmodel ‹ Determineratedpowertoreplace Underproductionofcurrentdams Replacingplanneddams ‹ Scaleratedpowertocurrentgridtrend ‹ Con˝rmthatratedpowerismet 2. Determinegenerationtomeetload 49 3. Perform˝nancialanalysis 2.2.2.1 LoadDevelopment The˝rststageistodevelopaloadmodel,whichrepresentsthepowerneedsofthecountry incontrasttoindividualcommunities.Theloadmodelischosenasonethatestimates thecontributionstothegridfromthefutureplannedhydropower,aswellasmakingup forcurrentdamunderproduction.However,itisnotsu˚cientforaloadmodelinthis analysistobeequaltoaconstantovertime,becauseitisanunrealisticassumptionthat theload(andthus,theload-followinghydro)willbeconstantatalltimes.Instead,thenet underproductionandplannedpower(approximately12GW)areusedasascalingfactor, withloadandgenerationdatafromONSbeingthereferencebasisforscaling.Theprocess forscalingisshownintheinput-outputstructureinFigure2.28.Thenameplatecapacity oftheinstalledhydropoweraswellasthetimehistoryofactualsuppliedgenerationis reportedbyONS[124].Theyearlyaverageactualgeneratedhydropoweriscalculatedviaa temporalintegral,whichisthenusedtocalculatetheratiooftheaveragepowerdelivered totheaveragenameplatecapacityfortheyear.Thisratio,aswellastheratioofaverage actualdeliveredhydropowertotheassumedaverageload(themodeleddeliveredpowerto thegrid),areusedtoscalethenetloadcurveforthesolution.Theloadcurvewillhavethe sametemporalshapeastheactualgridhydropowergeneration.Thisloadcurverepresents anexpectationofhowtheinstalledon-gridcomponentscouldbeutilizedinreplacementof theplanneddamsando˙setofunderproducedpower,inthescenariothattheloadinjection istemporallycurtailedsothatitfollowstheexistinggridloadbehavior. 2.2.2.2 GenerationDetermination Aswassuggestedfortheo˙-gridsystems,isitrecommendedtomeetthemodeledloadfor theon-gridsystemwithamixtureofin-streamturbinesandsolarpanels.Oneofthemajor di˙erencesbetweenthetwosolutionsisscale:theon-gridwillhaveamuchhigherpower 50 Figure2.28:Loadmodeldevelopmentprocessforon-gridsystem requirementforgeneration,duetothelargedamplansforandtheunderproductionfrom severallargedams.Anotherdi˙erencebetweenthetwosolutionsisthatitisrecommended thatthesolarpanelsbeinstalledto˛oatonexistingdamreservoirs,insteadofwithin communitiesonrooftops.Thereareseveralcountriesthatarebeginningtodevelop˛oating solarpower:China,Japan,theUnitedKingdom,andBrazil,duetoseveralnotedpositive e˙ectsoverstandalonesolarandhydrosystems,ifdesignedwithadequatespacing[77]: ‹ Increasedpaneloutputduetoincreasedcooling ‹ increasedwatersavingduetodecreasedreservoirevaporation ‹ Decreasedalgalblooms,andincreasedwaterquality ‹ Decreasedgreenhousegasemissionsfromreservoir ‹ Decreasedplantcostofenergyandresultingtari˙s Forfurtherdiscussionandinvestigationinto˛oatingsolarpanels,seeChapter3. 51 Unliketheo˙-gridsolution,theon-gridcaseisamoreproblemtosolve,as theneedtominimallymeetaloadisnotanexplicitcondition;Brazilroutinelysellspower toneighboringcountries,andhasalsohadissueswithseverelocalizedoutages,thusBrazil couldbene˝tfromanincreasedgridreliabilityfromtheincreasednumberofgenerators.As such,thecalculatedloadpro˝leservesasasoftguide,ratherthanahardlimit,meaningthat thegenerationdesignedtomeettheloadhasincreased˛exibility.Usingthesamepanels fortheo˙-gridcase,coveringonly1%ofthereservoirsofunderproducingdams,the˛oating PVsystemcouldgenerateanddeliver7GWoutofthe12GWdesigned.The1%coverage equatesapproximately72.7 km 2 outofof7,262 km 2 totalavailablesurfacearea(atotalof 13,565 km 2 wasfound,buttheChavedoVazreservoirwasignored,duetoitsunrealistic reportedareaversusthepowerandsizeofthedam).ISGsmakeupthedi˙erenceof6GWat thefull-rated V 90 of2.8m/s.Thegenerationthatwascalculatedtomeet(andlikelyexceed) theloadmodelisshowninFigure2.29.Forthisgenerationscenario,anextra66.1GWhis addedtothegrid.Anotherpossibilityforagenerationmixturecanbefoundbyassuming thegridactsasabatteryforthesystem,andsoanypowergeneratedwillbestored bythegrid,e˙ectivelyreducingthetotalMWhneededtomeettherequiredload.Shown inFigure2.30,thisreducestherequiredin-streamratedcapacity(thenumberofdevices), wherethe˛oatingPVsystemstillcoversonly1%oftheexistingreservoirsurfaces. 2.2.2.3 FinancialAnalysisandDiscussion ForthePVsystem,itisrecommendedthatthepanelsbeinstalled˛oatingonexisting reservoirs,whichisreportedtoadd18%costovertraditionalland-basedsystems[164]. Thecostoftheproposedenergymixtureforon-gridusagewascalculatedtobe0.017-0.019 USD/kWh,over30years(assuming365daysperyearoperation).Thedamsthatcould besizedtomeetthesameload(12GWofratedpower),assumingthesameyearlyusage astheproposedsolutionandinstallationcostof5.5USD/W,werecalculatedtooperateat 0.052USD/kWh,showingthattheon-gridsolutioncouldbeaneconomicallyviableportfolio 52 Figure2.29:Loadmodeldevelopmentprocessforon-gridsystem additionforBrazil.Duetothebasin-scaledistributionofthereservoirsandriversinquestion, cablingcostswerenotincludedintheon-grid˝nancialanalysis,butwouldbeacrucialdetail toincludeinfutureworktodecide˝nancialfeasibility,oratleast,themostcost-e˙ective magnitudeofpowertoproduceat(attheshown10GW,orat100GW,etc.).Toestimate anequivalentvaluecomparedtothereplaceddams,the˛owvelocityofapproximately1.73 m/swasfoundtoyieldasimilarcostperkWhofelectricitysupply.Fromhydraulicdata, assumingthatriversarerepresentedby˛owratesofgreaterthan100 m 3 =s ,thisminimum velocitycriterionispresentinapproximately5,353kmworthofequivalentriverlengthin thegridcells.Thefoundriverlengthscanprovidesu˚cientspacingto˝tthe5.26million turbines(witha10diameterspacinginbetweenturbines)evenifonlyasingleonemeter diameterturbineisplacedineachrow.Thiswarrantsanotheroptimizationproblem,where 53 Figure2.30:Loadmodeldevelopmentprocessforon-gridsystem thenumberofturbinesineachrowcanbeincreased(oranequivalentblockageratio),as wellasthediameterofeachturbine,balancedagainstthepossiblehydraulice˙ectsonthe marineenvironmentaswellasthecablecostsassociatedwithtransferringpowerfromthat locationtothenationalelectricgrid. 54 CHAPTER3 ENHANCEMENTOFGRIDSTABILITYWITHFLOATINGSOLAR PANELS Thischapterhasbeenreproducedasoriginallypublished:SamerSulaeman,ErikBrown, RaulQuispe-Abad,NorbertMüller.FloatingPVsystemasanalternativepathwaytothe amazondamunderproduction.RenewableandSustainableEnergyReviews,Volume135, 2021.110082.ISSN1364-0321,https://doi.org/10.1016/j.rser.2020.110082. 3.1 Background Oneofthenumerous,andperhapsmosttransformative,changesthatthepowergrid isundergoingistheinclusionofrenewableenergyresources.Inrecentyears,thepene- trationofgrid-levelrenewableresourcessuchaswindpowerandphotovoltaic(PV)sys- temshastremendouslyincreasedduetopolitical,environmental,andeconomicalincentives. Therapidinvestmenttowardincreasingthepenetrationlevelofrenewableenergysources hasbecomeoneofthepossiblesolutionstoreducegreenhousegasemissions,amongother social-environmentalissuesrelatedtoelectricpowerproduction,aimingtoreplacetheneed forfossil-fueledgenerators.Globally,theinvestmenttowardinstallinglargewindandPV farms,andhydropowerplants(dams)haveincreasedintherecentyears,largelybecause ofthebelievedbene˝toverfossilfuelgenerationsystemsinregardsto:environmentalcon- cerns,globalwarmingawareness,andeconomicincentives.Windpower,PVsystems,and hydropowerplantshavereceivedmoreattentionespeciallyinregionswheretheoutputpower ofthesesourcesispotentiallyhigh.IntheUS,theprojectionofwindpowerandPVsystem integrationisassumedtoreach 35% and 19% respectivelyby2050[186].Inothercountries suchasBrazilabout 68% oftheelectricalenergyiscurrentlycomingfromlargedams,while thecontributionofotherenergysourcesisaround 32% [130].However,theBraziliangov- ernmentisplanningtobuildmoredamstomeetthefutureincreasedpowerdemand[130]. 55 Ontheotherhand,manyenvironmentalandsocialconcernsassociatedwithhydropower plantsexpansionintheAmazonregionarestillofconcern,someoftheseconcernshave alreadybeenstudiedandextensivelyaddressedintheliterature[72,98,169,177,20,178]. Theutilizationofanadditionallybalancedmixofenergysourcesmaypotentiallyprovide analternativepathwaytoavoidtheenvironmentalandsocialimpactofdamexpansionin Brazilwhilemeetingtheincreasingpowerdemand. Oneofthepromisingapplicationsofagenerationmixthathasgainedattentionrecentlyis theintegrationof˛oatingPV(FPV)systemsonthereservoirofdams.Somecountriessuch asChinahavealreadyaggregatedasmuchas150MWofFPVsystemson˛oodedminingsites andconnectedtothenationalgrid[154,194].OthercountriessuchasJapanalreadyhave installed22.66MWofFPVsystems;whilecountriessuchasCanada,SingaporeandIndia contributetoasmallamountofworldwideinstallationofPVsystemalongsidehydropower plants[154,194].IntheUS,despitethefactthatinvestmenttowardimplementingFPV systemislimited,astudybySpenceretal.[175]showsthattheinvestmentofFPVsystems onman-madewaterbodiescouldpotentiallyproduceupto 10% ofcurrentnationalpower supply.InBrazil,wheremostoftheelectricalenergyiscurrentlycomingfromlargedams, installingFPVsystemsonthereservoirsofhydropowerplantsisstillinitsearlystages. Recently,FPVpilotprojectswereannouncedbytheBraziliangovernmentforthereservoirs ofthehydroelectricpowerplantsofBalbina(StateofAmazonas)andSobradinho(Stateof Bahia)[71].Althoughthemaingoalofthesepilotprojectsistoevaluatetheperformanceof FPVsystemsunderdi˙erentclimaticconditions,thecurrentexperienceswiththeinstalled FPVsystemsworldwiderevealsomeadvantagesofhybridsystemdeployment,especiallyon reservoirsofdams.Suchahybridsystemalreadyo˙ersahigherpowerdispatch˛exibility thatPVpowerprovidesespeciallyduringhighdemandtimes(i.e.,daytimewhentheoutput ofPVsystemispotentiallyhigh),andaddingmore˛exibilitytotheoperatortodispatch powergeneratedbyhydropowerplantsassuchtobeusedduringnightandearlymorning hours[154,194]. 56 Intheliterature,severalauthorshaveevaluatedpossiblescenariosthatcanbeimple- mentedtominimizetheenvironmentalandsocialimpactsassociatedwithreservoirsinthe AmazonBasinasaresultofbuildingnewlargehydropowerplants.In[12],theauthorseval- uatedtheBrazilianelectricnetworkexpansionconsideringreplacinglargedamswithwind powerplants.Theauthors'˝ndingssuggestthatwindpowerhaslimitedpotentialasthe investmenttowardmorewindpowerinstallationincreases.Withthelimiteddeploymentof PVsystemsinBrazil,severalauthorshavealsodiscussedthepotentialelectricalbene˝tsof PVsystemsinbothgrid-connectedando˙-gridapplications,aswellasthepotentialsocial andenvironmentalbene˝ts,especiallyinruralando˙-gridcommunities.In[17,18,16],the authorshaveevaluatedthetransmissionexpansionandlocation-basedmarginalpricealong withotherissuessuchasenergyimport/exportbetweenBrazilandneighboringcountries. Others[168,42,114]haveevaluatedthedeploymentofPVsystemsintheruralareaswhere themaingridistoofarawaytoallowforeconomically-feasibleexpansion. Large-scaledeploymentofPVsystemsinBrazilalsohasbeeninvestigatedwithregard togrid-connectedandbuilding-integratedsystemsandtheirpotentialbene˝tstotheelectric grid[103,153,11].In[145],aliteraturereviewofFPVsystemcon˝guration,application, anditsimpactonwaterevaporationandCO2reductionhavebeendiscussed.Ithasbeen concludedthatusingtheFPVsystemhasahighpotentialofreducingCO2emissionsand waterevaporation.In[179],asustainablehydro-solarmodelisproposedasanalternativeto thecurrentmodelofpowerproductioninBrazil.[121]evaluatesdi˙erentFPVtechnologies andtheirperformance,andtheauthorsconcludethattheFPVsystemperformanceismainly dependentuponthetechnologyusedandthelocationofthePVsystem.Anotherbene˝t isthatthedeploymentofFPVcouldalsoleadtomorefavorablepoliciestowardsfuture considerationoflarge-scaledeploymentofPVsystemsinBrazil.[200]alsohasshownthat ahybridFPV-hydropowersystemimprovestheenergye˚ciencyofthehydropowerplant. In[151],theelectricalandeconomicbene˝tsofinstallingaFPVsystemonthetropical GaviãoreservoirinNortheastBrazilhavebeenevaluated.Theauthorshavethatisiteco- 57 nomicallyviable,besidestheenvironmentalbene˝ts,itisalsoeconomicallyviable.Further, [137]examinestheenvironmentalandsocio-economicimpactsoflarge-scaledeploymentof photovoltaicsystemsinBrazil.In[170],acasestudyonthehydroelectricplantsofthe SãoFranciscoRiverbasinhasbeenpresented,whereinthetechnicalandeconomicalpro- ceduresforsizingtheFPVsystemandthecoordinationwithhydroelectricplantoperation havebeenevaluated.Besidestheenvironmentalgain,theresultsalsoindicateinstalling FPVcouldpotentiallyincreasethehydroelectricplantproduction˛exibilityby76%andthe capacityfactorby17.3%onaverage. Autilizationofmixedgenerationresourcesmaypotentiallyprovideanalternativeap- proachthatcanbefullyimplementedandutilizedtoavoidtheenvironmentalandsocial impactofdamexpansioninBrazilwhilemeetingtheincreasedpowerdemand.Thework presentedherefocusesonassessingthecontributionofFPVtotheadequacyofgenerating capacityoftheBrazilianelectricsystem.ThecapacitiesofFPVsystemsaredesignedtoo˙- setthehydropowerdamunderproductionandanalternativepathwaytolargedamexpansion isproposed.FPVsystemsareinstalledandintegratedalongsidetheexistingdamstoo˙set thecurrentunderproductioncapacities,enhancetheexistingpowersourcesandprovidean alternativepathwaytomeettheincreasingpowerdemand.Systemadequacyisevaluated bycalculatingsystemreliabilityindicesbeforeandafteraddingFPVsystems.Further,the correlationbetweenPVoutputandsystemloadisevaluated,andtheenvironmentaland socialconcernsassociatedwithdamexpansionintheAmazonBasinarebrie˛ydiscussed. Thisworkevaluatesthebene˝tsofaddingFPVsystemsonthesystemadequacyandisnot intendedforsecurityassessment.Themaincontributionsofthisworkare:1)Evaluating thepotentialcontributionof˛oatingPVsystemstotheBrazilianpowergrid.2)Investi- gatingtheenhancementtheexistingpowersourcesbyinstallingFPVonexistingreservoirs toprovideanalternativepathwaytomeettheincreasingpowerdemand.3)Evaluatingthe correlationbetweenFPVoutputandsystemload.4)Evaluatingthecontributionoflarge- scaledeploymentofFPVsystemstothesystemadequacy.Systemadequacyisevaluated 58 withrespecttothecurrentunderproductionofdamsandtherequiredcapacitiesofFPVsys- temsthatareneededtoo˙setthecurrentunderproductionofdams.Inaddition,reliability assessmentisusedtoevaluatethepotentialbene˝tstowardinstallingFPVsystemsonthe reservoirsontheoverallsystemreliability.AdequacyofgeneratingcapacityoftheBrazilian electricsystemisevaluatedinseveralcasestudieswithdi˙erentscenarios.Systemreliability improvement,intermsofreliabilityindices,isalsoevaluatedwithandwithouttheaddition ofaFPVsystem.Metricscommonlyusedforreportingbulkpowersystemreliabilityare utilizedinthiswork:lossofloadprobability(LOLP),LossofEnergyExpectation(LOEE), expecteddemandnotsupplied(EDNS),andlossofloadfrequency(LOLF).Also,theen- vironmentalandsocialconcernsassociatedwithdamexpansionintheAmazonBasinare brie˛ydiscussed. Theremainderofthispaperisorganizedasfollows.Section3.2presentsanoverview ofthecurrentpowersysteminBrazil.Section3.3discussestheenvironmentalandsocial impactofhydropowerdamexpansion.Section3.4discussesanalternativepathwaytodam expansionandtheproposedsolution.Section3.5describestheadequacyofpowersystemand evaluationofreliabilityindices.Section3.6presentssystemmodeling.Section3.7provides severalcasestudies,results,anddiscussionsthereof.Section3.8providesconcludingremarks. 3.2 AnOverviewoftheCurrentBrazilianElectricPowerSystem TheOperatoroftheNationalElectricitySystem(ONS),whichisresponsibleforthe coordinationandcontrolofthegenerationandtransmissioninstallationsintheNational inter-connectedsystemofBrazilunderthesupervisionandregulationoftheNationalElec- tricEnergyAgency(ANEEL)haslistedthecurrentinstalledpowercapacitiesincluding transmissionlineexpansionneedtomeettheincreasingdemand[30].Thesestatisticsare listedinTable3.1. Currently,thelargestpowersourceintheBrazilianpowernetworkisthehydropower dams,withaninstalledcapacityexceeds109GWanditisprojectedtoincreaseto114.395 59 Table3.1:Currentinstalledpowercapacitiesandprojectionofcapacityplanningincrease byyear2023 Power Installed Projected Percentage source Capacity Capacity ofCapacity (2018) (2023) Increase (GW) (GW) (%) Hydro 109.058 114.449 4.710 Thermal+Gas 12.821 17.780 27.890 4.614 4.900 5.830 Coal 2.672 3.0170 11.430 Biomass 13.696 14.028 2.370 Nuclear 1.980 1.980 0.000 Wind 14.142 17.177 17.670 Solar(PV) 1.780 3.630 50.960 Others 0.779 1.000 22.100 Total 161.552 177.961 9.220 GWbytheyear2023[130].OtherresourcessuchaswindandPVpowercontributeto asmallerpercentagecomparingwithhydroelectricpowerplantsasindicatedinTable3.1. Currently,solarpowercontributestoonly 1% ofthesystemtotalinstalledcapacity,on theotherhand,windcontributetoaround 9% .However,theprojectionofPVpowerin theyear2023willincreaseby 51% whilewindpowerisprojectedtoincreaseby 17 : 7% . However,theBraziliangovernmenthasrecentlypreviewedseveralpilot-projectson˛oating PV(FPV),thislargelybecauseofthehighincidenceofsolarradiationthatpowersPV systems[103,114,42,11].Withtheneedformoregeneratingcapacityexpansion,the Braziliangovernmentisplanningtoexpandtheexistingtransmissionlinestomeetthegrown demand,especiallywiththelargestpowersources(hydropowerdams)beinglocatedfaraway fromthemajorloads.Fig.3.1showstheinterconnectedsystemofBrazilasadoptedfrom [130]. 3.2.1 UnderproductionofDams Damswithreservoirsactasnaturalhydraulicbatteriesthatresisthigh-frequencychanges towaterlevels.Thereservoirs,however,cannotadjustsu˚cientlyforlong-termorsevere 60 Figure3.1:Brazilianinterconnectedsystem[130]. changesinrainfallorotherclimatologicalfactors.Asaresult,damsystemscannotalways producetheiraverageratedpowerwhenwaterlevelsarebelowanacceptableleveltoproduce theheaddropnecessaryfortheinstalledturbines.Anotherfactorthatcana˙ecttheability ofthedamsystemtoproducepoweriseconomicfeasibility;dependingontheloadonthe electricgridsystematagiventimeoftheday,itmaynotbepro˝tabletoruntheturbinesat highloadorpossiblyatall.WaterestimationsfortheAmazonBasinindicateadryingtrend intheSouthernandEasternregions[178,110].Thisisdecreasingthewatersuppliesand a˙ectingthereliabilityofpowergeneration[178,110].TheJiraudamandSantoAntoniodam ontheMadeiraRiverinBrazil,completedin2013,areestimatedtogenerateonlyafraction oftheprojectedpower(3GWeach)duetothesmallerstoragecapacityofrun-of-the-river reservoir[178,167].BeloMontedamontheXinguRiver,completedin2016,isalsoestimated toproduceonly4.46MWoftheprojectedpower(11.23GW)[100,167,110].Anotherfactor a˙ectingthepowergenerationisthedeforestationintheAmazonRiverBasin,whichisbeing 61 investigatedby[178].IntheXinguBasin,thelocationoftheBeloMontedam,withchanges inrainfall,theprojectionsofforestlosscouldreach 40% by2050,andcouldpotentiallylead to 25% reductionofthecurrentpowercapacity[178,116].InBrazil,itcanbeestimated thatthereisaround12GWofunderproductionofratedcapacityconsideringoperational dams[30].Thenominalcapacitiesofthedams,˝scalpowerproductionandunderproduction percentageascalculatedfromthereportedvaluesin2018by[30]areshowninTable3.2. 3.2.2 WindandPVPowerinBrazil InBrazil,thelargeststateintheAmazonisthestateofAmazonas,withalargesurface areaof1,559,148 km 2 .AsshowninFigurestheAmazonregionhasastrongsolar radiationandhighpotentialofPVpoweroutput[193].Despitetheseasonalvariationand climatecharacteristicsalongtheBrazilianterritory,thetotaldailyaveragevalueofsolar irradiationasrecordedfor16yearsshowsthattheglobalirradiationisfairly uniformwithamaximumdailyaveragevaluereaches46.2 kWh=m 2 .Further,thedaily averageofPVpotentialpowerasrecordedforthesameperiodoftimealongtheBrazilian territoryrangesbetween kWh=kWp ,withyearlyaveragerangesbetween kWh=kWp .TheamountofsolarradiationandpotentialofPValongBrazilianterritoryis considerablyhighcomparingtothemajorityoftheEuropeancountrieswheremoreinvest- mentstowardsPVpowerinstallationhavegainedagreatmomentum[22].AlthoughBrazil hasonaverageahighPVpowerpotentialcomparedtosomeleadingcountries,suchasJapan withGHIofwithatotalinstalledcapacityof56,162MW ,Germany withGHIof withatotalinstalledcapacityof45,452MW andFrance withGHIof withatotalinstalledcapacityof10,562MW asshowninTable3.3,Brazilhasonlyaccumu- lated2,296MWofPVsystemsofar[104].Accordingto[130],Brazilisplanningtoincrease theinvestmenttowardsPVinstallationstobringthetotalprojectedcapacityto4,241MW bytheyear2024.However,windpowerhasreceivedmoreinvestmentsinBrazilalongthe coastalareaswherethepotentialofwindspeedishighasshowninFig.3.5.Noticeably, 62 Table3.2:Damsunderproduction DamName Nominal Capacity (MW) Fiscally Re- ported Power (MW) Percent under Rating (%) AdoPopin- haki 22.600 16.950 25.0 AltoBened- itoNovo 6.500 2.192 66.3 Balbina 250.000 249.750 0.1 Bariri 143.100 136.800 4.4 BeloMonte 11233.100 3938.570 64.9 Bugres 24.120 11.120 53.9 Cachoeirado Ronca 0.900 0.340 62.2 Calheiros 19.528 19.000 2.7 Canastra 44.800 42.500 5.13 Capigui 4.470 3.760 15.8 Capivari 18.738 18.090 3.5 Cedros 8.400 7.280 13.3 CelsoRamos 12.816 5.600 56.3 ChavedoVaz 1.600 0.680 57.5 Paranoá 30.000 29.700 1.0 Passode Ajuricaba 6.200 3.200 48.3 PassodoIn- ferno 4.900 1.332 10.6 Coaracy Nunes 78.000 76.952 1.3 Venâncio 3.820 1.600 58.1 CongonhalI 1.816 1.616 11.0 CristoRei 1.800 0.960 46.6 Ernestina 4.960 4.800 3.2 Estreito 1050.000 1048.000 0.2 F 3.972 3.792 4.5 Ferraria Gomes 252.000 168.000 33.3 FontesNova 131.900 130.300 1.3 Forquilha 1.118 1.0000 10.5 Glória 13.800 11.360 17.7 DamName Nominal Capacity (MW) Fiscally Re- ported Power (MW) Percent under Rating (%) PedrinhoI 16.200 16.040 1.0 PereiraPas- sos 99.900 99.110 0.8 Piabanha 20.000 9.000 55.0 Porto Colômbia 320.000 319.200 0.3 Primavera 25.700 24.740 3.7 RioFortuna 6.990 6.850 2.0 Ronuro 1.040 0.874 15.9 SantaCruz 0.550 0.364 33.8 SantaCruz 1.500 1.400 6.7 SantaLuzia Alto 29.250 28.500 2.6 SantaRosa 1.580 1.400 11.4 Santana 0.650 0.500 23.1 SantoAnto- nio 3150.400 2286.100 27.4 S ~ a oDomin- gosII 24.660 24.300 1.5 S ~ a o Lourenço 29.990 29.100 3.0 S ~ a oManoel 700.000 175.000 75.0 S ~ a oPedro 2.160 1.500 30.5 Tudelândia 2.547 2.400 5.8 WalterRossi 16.500 15.780 4.4 Ypê 30.000 27.400 8.7 Mello 10.680 9.540 10.7 Nilo Peçanha 380.030 378.420 0.4 Mascarenhas 198.000 189.000 4.5 Marumbi 9.600 4.800 50.0 MarcoBaldo 16.750 16.550 1.2 Jirau 3750.000 2100.000 44.0 Itiquira 157.400 156.000 0.9 Itapebi 462.000 456.000 1.3 asmentionedinSection3.2,solarpowerhasmorepotentialthanwindpowerespeciallyin theAmazonregionlargelydueto:windpowerhavinglesspotentialpowerespeciallyinthe 63 Figure3.2:DirectnormalirradiationinBrazilfrom[193]. Amazonregionwherethetall,denseforestsandlow-pressuregradientsareconcentrated, highpotentialofPVpowerwithintheBrazilianterritory,andchangingpoliciestowarda morebalancedgenerationmixinvestment[103,114,42,11].Therefore,inthiswork,wind powerisnotconsideredasanalternativesolutiontodamexpansionintheAmazonBasin. However,adequacyassessmentofBrazilianpowernetworkisevaluatedforgenerationmix includingtheexistingwindfarmsandPVsystems. 64 Figure3.3:GlobalhorizontalirradiationinBrazilfrom[193]. Table3.3:InstalledPVcapacityandthehorizontalsolarirradiationfordi˙erentcountries Country YearlyAverage Installed Grid-connected O˙-grid GHI( kWh=m 2 ) Capacity(MW) (MW) (MW) China 175,400 175,032 368 Japan 56,162 55,989 173 U.S.A 62,498 62,498 Germany 45,452 45402 50 India 34,831 34,831 Italy 20,107 20,107 Australia 10,953 10,669 284 France 10,562 10,532 30 SouthKorea 10,505 10,505 Spain 5,659 5,513 146 Brazil 2,296 1796 500 65 Figure3.4:PotentialofaveragePhotovoltaicpowerinBrazilfrom[193]. 3.3 EnvironmentalandSocialImpactofDams Contrarytopopularbelief,thenotionofhydraulicdamswithreservoirsbeingcompletely greenisinaccurate.Damscauseenvironmentalandsocialissues,someofwhichare:increase greenhousegasemission[176,66,63,59,58,57],increaselikelihoodoftoxicmethylation [180,62],increaseevaporationofriverwater[58],interruptionorcompleteblockageofwater- borneanimalmigrationandnaturallivingpatterns,anddeforestationandunnaturallevels of˛oodingforthedamreservoir.Theseenvironmentalissuesarealsosimultaneouslysocial issues,withtheadditionofforcedrelocationoflocalpeoplesfortheintroductionofthedam 66 Figure3.5:PercentageofpotentialwindpowerinBrazil[193]. andreservoirviathedestructionofthelocalareaforthereservoiritself,orfromtheresulting ˛oodingfrom˝llingthereservoir[61]. 3.4 FloatingPVSystemsonHydropowerDamReservoirs Theadditionofo˙-gridPVsystemsandgrid-levelPVsystems˛oatingonthereservoirof damscanhelppreventsocialandenvironmentalissuesassociatedwithdamsfromworsening inthefuturebyo˙settingtheplannedneedforpowerfromdams.Integratinggrid-levelFPV systemstoexistingdamsaddmore˛exibilitytotheoperationoflargedamsbyallowinglarge damstooperatenotfollowingbase-loadbutratherloadfollowingapproach.Theinvestment towardintegratingsuchalternativesystemsopenupmoreopportunitiesfordeploymentof environmentally-friendlyandyete˚cientpowersourcesthatcansupplythecurrentand futurepowerneedsofthecountry,bothonando˙ofthegrid.Despitethefactthatthe deploymentoflargescalegrid-connectedFPVsystemsarestillinearlystages,thedeploy- mentofPVsystemsalongsideexistingdamsor˛oatingonthereservoirshasbeenrecently 67 gainingmoreattention.AsdepictedinFig.3.6,globally,ChinaandJapanareleading onPVsystemsinstallationwithtotalcapacityof376.50MWand22.66MW,respectively. OthercountriessuchasCanada(0.0005MW),Singapore(0.005MW)andIndia(0.06MW) contributetoasmallamountofworldwideinstallationofPVsystemalongsidehydropower plants.Meanwhile,othercountriessuchasAfghanistan,Azerbaijan,Colombia,Ghana,and theKyrgyzRepublic,developmentofFPVsystemsprojectsareunderprogress[154,194]. Thisislargelybecauseofthefactofhighpotentialande˚ciencyofFPVsysteminstalled onthereservoirofdamsandtheabilitytoprovideanaturalstoragesystemthatcanbe utilizedanddispatchedtoprovideabalancetothesystemoperationincludingtheintermit- tentsources.Furthermore,FPVsystemscanhelpreduceenvironmentalissuesduetothe factthattheFPVsystemsprovidingshadethatminimizewaterevaporation,improvewater qualityandhelp˝shandotherwaterspecies'populationstabilitybutalsosymbiotically increasingthePVsysteme˚ciencybyprovidinganaturalcoolingsystem[196,39,152]. Consideringtheenvironmentalandsocialconcernsassociatedwiththedamexpansionin BrazilasmentionedinSection3.3andherein,theproposedsolutionaimstominimizesuch concernsbyinstallinggridlevelFPVsystems (˛oatingonthereservoirarea) alongsidethe existingdams.TheFPVsystemdesignfacilitateslocal˝shingactivitiesandthecohabitation ofmarinelifewhenPVarraysarepresentedasdepictedinFig.3.7. Figure3.6:IntegratedPVsystemwithhydropowerinstalledcapacityworldwide. 68 Figure3.7:FloatingPVsystemonreservoirinwhichmarinelifeand˝shingactivityare notdisruptedbyplacingPVsystemsonthereservoir. 3.5 GenerationAdequacyAssessment Ingeneral,generationadequacyassessmentisusedtoevaluateshort-termandlong-term powergenerationcapacityplanningstudies.Probabilisticmethodsarecommonlyusedin powersystemadequacystudiesastheytakeintoaccountthestochasticnatureofsystem behavior,suchascomponentfailuresandload-levelchanges[23,156,3,29,181].Forpower systemplanningprojects,probabilisticmethodsareusedtoexaminetheabilityandthe adequacyofthetotalgeneratingsystemtomeetthedemand[3].Inaddition,powersystem reliabilityassessmenthasplayedamajorroleinevaluatingthecontributionofvariableenergy resourcestotheadequacyofgenerationsystemforbothoperationandplanningprocess [181].Inthiswork,ananalyticalmethodisusedtoevaluatesystemadequacyandcalculate reliabilityindices.Reliabilityindicessuchasbutnotlimitedto; lossofloadprobability (LOLP) , LossofEnergyExpectation(LOEE) , ExpectedDemandnotSupply(EDNS) and LossofLoadFrequency(LOLF) areamongthemostcommonlyusedindicesasametric tomeasurethecontributionofadditionalgenerationresourcestoadequacyofthesystem [26,25].Theseindicesarebrie˛yde˝nedasfollows[106]: ‹ ALossofLoad(LOL)eventisoneinwhichasystemisunabletomeetitstotal demand. 69 ‹ LossofLoadProbability(LOLP)istheprobabilityofencounteringoneormoreLOL eventsduringagiventimeperiod. ‹ TheEDNSindexisthesumoftheproductsofprobabilitiesoffailurestatesandthe correspondingloadcurtailments.ItisexpressedinMW/yearorGW/year. ‹ LossofLoadExpectation(LOLE)istheexpectednumberofLOLhoursduringagiven timeperiod.Itisexpressedinhr/year. ‹ LossofEnergyExpectation(LOEE)istheexpectedenergythatthesystemisunable toserveasaresultofLOLeventsduringagivenperiod.Itiscalculatedastheweighted sumoftheenergiescurtailedduringtheLOLevents,theweightsbeingtheprobabilities ofthecorrespondingLOLevents.ItisexpressedinMWh/yearorGWh/year. ‹ LossofLoadFrequency(LOLF)istheexpectedfrequencyofencounteringoneormore LOLeventsduringagiventimeperiod. ‹ LossofLoadDuration(LOLD)istheexpecteddurationofLOLeventsoccurringduring agiventimeperiod. 3.6 SystemModeling Duetothecomplexityofthepowersystem,thereliabilityassessmentofthebulkpower systemhasmainlybeenappliedinthreedi˙erenthierarchicallevels[3].Theassessmentof generationadequacy,knownashierarchicallevel-I(HL-I).AtHL-Istudies,thetransmis- sionlinesareconsideredhighlyreliabilityabletotransferthegeneratedpowertoallload points.Whereas,whenbothgenerationunitsandtransmissionsystemsareconsideredin thereliabilityevaluation,itsknownasthereliabilityofcompositesystemorHierarchical level-III)studies.Further,thereliabilityevaluationatHierarchicallevel-IIIII) considerstheentiresystem.However,duetothecomplexityofpowersystemandhighcom- putationtime,reliabilityevaluationattheIIlevelisrarelyattempted.Instead,power 70 systemreliabilityisevaluatedatthreedi˙erentlevelsseparately:generationsystemlevel compositepowersystemlevel),anddistributionlevel[3,49].Inthiswork, reliabilityevaluationatisconsidered.Inthisprocess,thefailuresofgeneratingunits areconsideredtobeindependentevents,sothattheprobabilityoffailureofageneration unitcanbemodeledasMarkoviancomponentswithtwostates, up and down stateswith knownfailureandrepairrates, and respectively( isthefailuretransitionratefrom anupstatetoadownstate,and istherepairtransitionratefromadownstatetoanup state). 3.6.1 WindTurbineOutputPower Windturbinepowercurveprovidesaquantitativerelationshipbetweenwindspeedand theoutputpower.Itdescribestheoperationalcharacteristicsofawindturbinegenerator (WTG). TheoutputpowerthatcanbeextractedfromWTGscanbecalculatedasfollows[89]. P = 1 2 C p ˆAv 3 (3.1) where P istheoutputpower(Watts), ˆ istheairdensity(kg = m 3 ), v isthewindspeed (m = sec), A isthesweptareaoftheturbine(m 2 ),and C p isthepowercoe˚cient. Theoutputpowercurvecombines(3.1)withthephysicalconstraintsinthesystem.The outputpowercurveincludingthephysicalconstraintscanbeexpressedasfollows. P = 8 > > > > > > > > > > < > > > > > > > > > > : 0 if v > < > > : 1 ; if X 0 0 ; otherwise, Thecumulativeprobability P ( X ) foraforcedoutageof X MWorgreatercanbein generalcalculatedusing(3.10). P ( X )= X i P ( X i ) ; 8˘ X i X; (3.10) where P ( X )=1 ; 8˘ X C; Inthecaseofmulti-stategeneratingunits,(3.9)canbemodi˝edasfollows. 73 P ( X )= n X i P ( i ) P ( X C i ) : (3.11) Thecumulativefrequencyofcapacityoutageof X MWcanalsobecalculatedusingthe sameapproachusing(3.12). F ( X )= F i (1 q )+ F j q +( P j P i ) q (3.12) where q and arerespectivelytheprobabilityoffailureandrepairrateofthenewadded unit; P i , P j , F i ,and F j aredeterminedfromtheoldCOPAFT(priortoaddingthenewunit); i istheindexoftheexistingcapacityoutagestate, C i = X ,and j istheindexofexisting capacityoutagestate, C j ,suchthat C j = X C . F i and F j arecumulativefrequenciesof states i and j respectively. 3.6.4 LoadModel Theloadmodelisusuallyexpressedintheformofprobabilityandfrequencydistributionof therandomvariablethatrepresentssystemload[23,24].Theloadmodelcanbeconstructed byscanningthehourlyloaddataofthesystemoverthetimeperiodofstudy,usuallyone year.Ingeneral,theloadmodelcanbebuiltintermsofloadlevel L i withitscommutative probabilityandfrequencyasfollows[23,24]. P L ( L L i )= H ( L L i ) T ; (3.13) F L ( L L i )= ( L1)(seeFigure4.3) ‹ Bladeleadingedgesshouldbekeptasthickandroundedaspossible ‹ Bladespacingshouldbekepthigh ‹ Gapsbetweenrotorbladesandouterwallsshouldbeminimized ‹ Gapsbetweenrotorbladesandgatesorvanesshouldbemaximized Low Risk Figure4.3:Survivalofrainbowtrout( Oncorhynchusmykiss )basedonstrikespeed (modi˝edfrom:[6]) Analternativerecommendationintheliteratureis6-12m/speripheralbladespeedfor minimal˝shstrikerisk[118].Thisrangecouldhavehigherriskthanoriginallythoughtat thehighervelocities,basedonnewdataonrainbowtroutoflengths110to163and182to 236mm,yieldingalengthtobladethicknessratio(L/t)ofapproximately1.14and2.[5] showedthatatstrikespeedsof10and12m/s,ifthe˝shimpactsthebladesatanangle 93 above45and30degreesrelativetothebladesurface,respectively,thesurvivabilityof˝sh dropstoandbelow67%and4.2%.Further,at7m/s,thetested˝shsurvivedat98%or moreatvaryingdegreesofimpactwiththebladesurface(30,60,and90degrees)[5].The 5m/scriteriaisusedhereasaconservativemeasure,allowingforlargerthana2L/tratio betweenthe˝shandtheblades(longer˝shand/orthinnerblades);however,thestrikespeed couldapproach10m/sdependingonthe˝shpresentandbladedesigndeveloped. 4.3.2 PressureChanges Traditionaldam-turbinecon˝gurationsrelyonsmalltolargeheaddi˙erences,whichiscon- vertedintoextractableenergythroughastaticpressuredropacrosstheturbineatadesigned ˛owrate.As˝shentertheturbineintake,theyexperienceanincreasingpressureaboveat- mospheric(dependingonthedepthoftheintakebelowthesurfaceofthereservoir),and thentheyexperiencearapiddecreasein˛uidpressureastheymovethroughtheturbine section,thatcanapproacharatioof4([149],[182])toover10[118]fromthegatestoafter therunnerbladesfortypicalturbines.Alownadirpressurerelativetothepressurethatthe ˝shisadjustedtogivesrisetoseveralissues: ‹ Lowpressurescandisruptthefunctionoftheswimbladder,allowingforeasypredation ‹ Lowminimumpressurescanruptureorgans,suchasswimbladdersandeyes ‹ Pressuresbelowtheworkingvaporpressurecancausecavitation,whichcancause physicaldamageto˝sh,aswellastheaboveissues [32]showedthatthemostimportantfactorforjuvenileChinooksalmon( Oncorhynchus tshawytscha )istheratioofacclimationpressuretominimumpressure,whencomparedto rateofpressurechange,conditionfactorofthe˝sh,andtotaldissolvedgascontentofthe water.Itcanbeseenfromthesameworkthatiftheminimumpressuredoesnotfallbelow aroundhalfoftheacclimationpressureforagiven˝sh(anacclimationtominimumpressure ratioof2),thereisalowprobabilityofinjuryordeathasisshowninFigure4.4.[32] 94 alsoconcludedthatthejuvenileChinooksalmonthatwerestudiedrespondedwelltoslow decompression,however,ishasbeencommentedinliteraturethatother˝shspeciesmight notrespondwelltoevenslowdecompression[143]. Low Risk Figure4.4:Dose-Responsechartofmortalityvs.pressureforjuvenileChinooksalmon,in termsoftheratioofacclimationtominimumpressures,andthenaturallogoftheratioon thebottomaxis(modi˝edfrom:[32]) Alower-pressurecriteriafoundintheliteratureisallowingtheminimumpressuretodrop to30%ofadjustedpressure(apressureratioof3.33)[118].Theauthorcitesa˝gurefrom[34], justifyingthecriteriabyshiftingfocusawayfromnon-anadromous(bassandcrappie)data points.Theoriginalcitedworkrecommendsacriteriaofnotallowingaminimumpressure below60%ofadjustedpressure(apressureratioof1.67)[34].Thestudiesperformedto gatherthedataforthesetworecommendationsiscommentedbytheoriginalauthorasbeing poorlydocumented,haveinadequateornocontrols,andusedonlysmallnumbersof ˝sh"[34],andthusnewer,well-exploredandwell-documenteddataisusedinsubstituteto cometothecriteriausedhere. 95 4.3.3 Shear Similartophysicalstrike,damageduetoshearisduetorelativevelocity,butthevelocityin questionisofthe˛uidinsteadofaphysicalwall.Accordingtoexperimentsandsimulations, around1-2%ofatypicalconventionalturbinedamcon˝gurationwillhaveashearrate (oftenreferredtoas`strainrate')greaterthan4951/s,whichisreportedasthepointwhere injuriesto˝shwilltendtoincrease([112],[35]).Theseregionsaremostlyareasassociated withwakesbehindstructures,suchassupportpiersorstationarygatesorvanes,thoughthe turbinerotorcanalsoproducehighshearratesnearthetips,dependingonthedesignand loads.Thestrainlimitcanbeconvertedtoanequivalentshearstressofslightlylessthan 1600Pa(calculatedfrom5171/s)[35].Theschematicoftheexperimentalsetupby[112]to determinethetolerableshearrateisshowninFigure4.5,whereanozzleisusedtoaccelerate ˛uidinajet,andthenthe˝shareintroducedintothestream. Figure4.5:Experimenttoquantifytolerableshearstresseson˝sh(from:[112]) Otherliteratureusesalowerstrainratecriteriaof1801/s[118].Thislowervalueisused forexaminingthe˛owthroughaturbinepassage,andnottheentiretyoftheturbine rotatingregion.Mostofthe˛owthroughapassageshouldbewell-behavedandwillnot haveashighofstrainratesaswouldbefoundintheboundarylayerneartosolidsurfaces, andsoalowercriteriacanbeusedtoevaluatethisregion.[118]alsocommentsthatinthe 96 boundarylayer,wherethestrainrateishighest,theprobabilityofphysicalstrikeisalsoat itshighest,andsoassumesthatinthenear-wallregion,ifphysicalstrikeriskismitigated (throughdesignbladevelocity),thenthatregioncouldbeconsidered`safe'.However,to examinetheindividuale˙ectsofeachsafetyrisk,usingacriteriathatcanserveasabasis fortheentireturbine˛owregion,thehighercriteriaof4951/scitedhereismoresuitedto evaluatethedesign. 4.3.4 Turbulence Drivenbyshear,thevelocitygradientsassociatedwithturbulencecanhavetwomaine˙ects on˝sh: ‹ Physicalsheardamageof˝shbody ‹ Disorientationbylargescalevorticalstructures(eddies) Experimentswithacontrolledlevelofturbulenceinducedbygeneratedshearstresscanbe performed,anexampleofwhichattemptedtoestimatetheriskofmortalityofsmall˝sh andlarvaebyaship'spropeller([94],[95]).Thestudyconcludedthatalinearrelationship betweensheardevelopedbyaboat'spropellerandlarval,egg,andjuvenile˝shmortality canbepredicted.Itwasshownthatfortheinvestigatedlifecyclestages,thelarval˝sh beingweremostsensitivetoshear.Itispostulatedthatturbulencecanalsoenhancepre- dationbyinducingdisorientationiftheturbulenceintensityishighenough,butquantifying `disorientation'isnotsimple,sonoexplicitcriteriahasbeenfoundastoanacceptablelevel ofturbulence.Ithasbeennotedthatturbulenceanddisorientationcanalsoa˙ectthe˝sh's abilitytoeat,swim,aswellaswheretheychoosetomakeahabitat[174]. 4.3.5 CurrentTraditionalCon˝gurationFish-FriendlyDesigns Afewnoveldesignsfor`˝sh-friendly'turbinesfortraditionalturbinecon˝gurationshave beendeveloped;themostprominentandwell-documentedofthesedesignsaretheAlden 97 turbine,theMinimumGapRunner(MGR),andtheVeryLowHeadturbine(VLH).The Aldenturbine'smainfeaturesarearunnerthatrotateswithitsoutershroud,eliminating relativevelocitybetweenthebladetipandtheouterwall,andalsohasonlythreebladesto reducetheprobabilityofstrike.TheMinimizedGapRunner(MGR)designalleviatessome oftheissuesassociatedwithbladestrikeriskto˝sh,namely,minimizingthegapbetween therunnerbladerootandtipregionsaswellasthehubandouterwall,loweringtherisk of˝shbecomingtrappedandinjured([6],[83]).MJ2setouttodevelopaverylowhead (VLH)turbinethatcanminimizecivilworkscosts,aswellasbeing`˝sh-friendly'[108]. Othercompanieshavealsodevelopedtheirown`˝sh-friendly'concepts,workingtoincrease theeasefor˝shtopassthroughthegateandrunnersectionswithoutharm,suchasGEand Natel([190],[31]). 4.3.6 Sound Thoughnotnecessarilyadirectinjurymechanism,theemittedsoundfromaturbinecanstill haveane˙ecton˝sh.Ithasbeenknownsinceatleastthe1980sthatsoundcana˙ecthow ˝shwillinteractwithregionsarounddamturbines[50],thoughthelevelofbehaviorchange wasnotquanti˝edatthatpointintime.Morerecently,˝shpassagee˚ciencyhasbeen quanti˝edinregardstodirectingsoundpressurewavesatcertainlocationsandincertain directionswithrespecttothedam([159],[78]).Thisissuewillbeexaminedfurtherinsection 4.4.3,whereisitusedasoneoftheconsiderationsfor`˝sh-friendly'in-streamturbinedesign. 4.4 FishSafeTurbineDesign Ithasbeennotedthatin-streamturbineshavearelativelysmallenvironmentalimpact, andcanbeconsideredtobeverylowriskdevices,evenwheninsmallarraycon˝gurations ([43],[150],[131]). 98 4.4.1 PhysicalStrike Forlow-headturbinesinatraditionaldamcon˝guration,ithasbeenreportedthatblade strikeisthemostcriticalissuefor˝shsafety[4].Theissueofimpactwiththerotorblades themselvesisthesameamongin-streamandtraditionaldam-turbinecon˝gurations.How- ever,in-streamturbinesallowthe˝shtopassaroundtheturbineorretreatatanypoint upuntilthe˝shreachestherotorbladesthemselves(seeFigure4.6),givingthe˝shmore timeandspacetoreacttotheturbine.For˝shpassingthroughtheturbinerotatingsection, in-streamturbineshavetheadvantageofgenerallybeinglowersoliditythantheirtraditional counterparts,allowingformorespacebetweenthebladesfor˝shtopassthrough[76]. Figure4.6:AMoonWrasse( Thalassomalunare )evadinganin-streamturbine(from:[79]) Forin-streamturbines,therecouldexistacriticalRPMoftherotorthatcanincrease thechanceof˝shsurvival;thecommondesignRPMforw-spdevicesisaround15- 40RPM([79],[134],[163],[109],[52]).Thereisadesignchoice,however,todesignthe turbineatoneendortheotheroftheaforementionedrange,duetothedi˙erentecological phenomenaordesignconstraints.Atthelowendoftherange,rotatingatverylowRPM canbeseenassaferthanhigherRPMinthecaseof˝shimpactwiththerotatingblades, duetolowRPMdesignsbeingassociatedwithlargeturbinediameters,suchastheCape Sharpturbine(6-8RPM)[37].Theselargediameter,slowrotatingturbinescanallowfor 99 largegapsbetweenthebladesandalsoprovidethe˝shwithmoretimetomaneuveraround theblades,facilitatingmoree˙ective˝shpassage.Towardsthehigherendoftherange, rotatingabove20RPMhasbeennotedasbeingthepointwhere˝shtendtoavoidthelocal areaaroundtheturbine,andthuswouldnotattempttopassthroughtheturbine[199], whichcouldalsoreducetheriskforstrike,thoughthismayintroducemigrationrouteand habitatchoicechanges.[79]showedthatofalloftheobservationsof˝shencounteringa verticalaxisin-streamturbineinarealriverchannel,whiletherotorwasspinningonlytwo individual˝shenteredtherotor(outofapproximately150measurable˝shpassingswiththe rotorpresent),andonlywhenthecurrentspeed(approximately0.25m/s)androtorspeed werelow(17RPM). ThisRPMphenomenacouldhavevaryingimportancetothe˝shattemptingtopass throughdependingonthespecies,channelgeometry,timeofday,numberof˝shinthe group,amongothervariables,aswasshownbyworkfromvariousauthors.Forexample, [185]notedanapproximately0.477probabilityof˝shenteringanOceanRenewablePower Company(ORPC)TurbineGeneratingUnit(TGU)inatidalchannelduringthecombined nightandday,whenitwasrotatingatanaverageof21.4RPM.Itwasalsoshownthat theprobabilityof˝shenteringduringthedaywasmuchlowerthanatnight,ashasbeen indicatedthroughouttheliteratureinregardsto˝shresponsetolightstimuli([187],[33]), particularly,onlyapproximately4%oftheobserved˝shpassedthroughtheturbineduring thedaywhileitwasrotating.[54]alsoshowedthatcertainspeciesof˝shmaystillchoose topassthrougharunnerthatisrotatingabove20RPM,aswasshownbytheavoidanceof only33%forhybridstripedbass( Moronesaxatilis x Moronechrysops ),whilemuchcloserto 100%fortheothertestedspecies(86-100%).Muchlikethewaylighta˙ectsthebehavioral responseof˝shviathevisualsensorysystem,thereasonforthecriticalspeedbeingaround20 ispresumablyduetothenatureoftheinteractionbetweentheturbineemittedsoundwaves andthe˝shauditorysensorysystems:theinnerear,andthelateralline.[192]commented thatthelowfrequencystimuliresultsinanelongated`near˝eldradius',allowingthe˝shto 100 sensethe˛owdisturbancefrommuchfartheraway,whichcouldleadtoincreasedlikelihood ofavoidancemaneuvers.Thein˛uenceofturbinesoundon˝shwillbeexaminedfurtherin section4.4.3. 4.4.2 PressureChange,Shear,andTurbulence Fromcomputationalsimulationsofa5-meterradiusturbinerotatingat21.5RPM(2.25 rad/s),ithasbeenshownthatin-streamturbinescanhavepressuredropsofoneorderof magnitudeormorelessthanatypicalhigh-headdam-turbinecon˝gurations;themaximum ratiooftotalpressurechangewasshowntobeapproximately1.1nearthebladetipinFigure 4.7[198].Therelativelyhighminimumpressurecorrespondstoahighsurvivalrateof˝shin regardtopressuree˙ects,aswellasalowriskofcavitationdamage.Thetimeofdecompres- sionisalsonotedasanimportantfactorin[198],whichisshowntobeapproximatelyofthe sameorderforin-streamturbinesastraditiondam-turbinecon˝gurationswhenconsidering afullbladeresolvedgeometry(BRG)CFDmodel;however,theauthornotesthatthetime fordecompressionislongerbasedontheresultsofBladeElementMomentum(BEM)CFD simulation. Similarly,shearandturbulenceproducedbyatypicalin-streamturbinehavebeenshown tobelowinmostoftheturbine.Theshearrateisshowntopeakaround3001/s(fromblade resolvedgeometryCFDsimulation),whichislessthanthe4951/scriteriafor˝shsafety [198].Thenumericalinvestigationconcludedthattheonlyregionofissueforshearisvery neartothetip(within0.01m,showninFigure4.8);however,itisunlikelythat˝shwould swimnearthetip,andthiscouldbefurthermitigatedwiththeintroductionofashroudor nozzle/di˙useraroundtheperipheryoftherotor,asitwouldbeevenmoredi˚cultfor˝sh toencounterthisregion.Theturbulencelengthscalewasshowntoreachthepeakof1.7m attheendofthedomain(approximately300to400metersaftertheturbine),andthelargest turbulentkineticenergyeddiesbehindthebladetipshavealengthscaleofapproximately10 cm.Forsmall˝shwithswimbladders,thiscouldcausedisorientation,andthusemploying 101 strategiestomitigate˝shaccesstothebladetipswouldbebene˝cialindesign. Pressure Ratio of1.1 Figure4.7:PressureTracesatVariousRadiialongaTidalStreamTurbine.Thelegend showstheradialdistancesintermsoftheratioofagivenradiustothetipradius. (modi˝edfrom:[198]) Figure4.8:Shearrateoftidalstreamturbine(from:[198]) 4.4.3 Sound Fishhavetwomainacousticsensingsystems:theinnerearandthelateralline[140].The twosystemsworkinconcerttoproduceacomplete˛owdisturbanceimageinthe˝sh'sbrain, 102 byanalyzingnear-˝eld(approximately1to2˝shbodylengthsaway)andfar-˝eld(greater than2bodylengths;themaximumrangevarieswiththe˝shspecies)acousticwaves.The innereargenerallyisusedforfar-˝eldhearing,inthefrequencyrangeof50toover2000Hz, whereasthelaterallineisusedfornear-˝eldsensing,inthefrequencyrangeof1to200Hz [140].Accordingto[172],producingexternalinterferencetothenaturalfrequenciesemitted andheardby˝shcana˙ect: ‹ Distributionof˝sh ‹ Growthandreproduction(or`˝tness') ‹ Predator-preyrelationships ‹ Communication Anyexternalnoisesourcecoulda˙ectthesenaturalinteractionsof˝sh,toadegreethat dependsonthefrequencyspectrumemittedbythesource.Manmadedisturbancescanemit loudacousticdisturbances,fromboats,barges,andunderwatermachines.Underwaternoise emittedfromadam-turbinecon˝gurationhasbeenoflittlefocusintheliterature,thoughit canbeanimportantstudyinanattempttominimize˝shentrainmentthroughhydropower plants([107],[113]).Withmindsgearedtowards˝shsafetyandgaininganinsightinto˝sh behaviorrelativetounderwatermachinery,investigationshavebeenconductedtoquantify soundproducedfromin-streamturbines.[21]inparticularconcludedthatthesoundlevel producedbyaTidGenturbineisaboutthesameasthenaturalenvironmentathighwater velocity(byutilizingacylindricalsoundspreadingmodel),andslightlyhigher.Theauthor alsostatesthatatadistanceof21metersaway,itislikelythatsomespeciesof˝shcannot heartheturbine,asshowninFigure4.9.Thismeansthattheturbinewillnotinterfere with˝shinteractionsexceptpossiblyclosetotheturbineitself,wherethe˝shcouldlikely avoidduetothepressuresoundlevelproducedbytheturbinerotation.Ithasbeennoted, however,thatusingtheindividualclassicspreadingmodels(sphericalorcylindrical)canlead 103 toanunderestimateofthesoundlevelsfromthesource([139]).Inanotherinvestigation, [162]concludedthatthereisameasurablechangeto˝shbehaviorfromshort-andlong- termplaybackofapre-recordedturbinesoundtrack,butforthe˝shspeciesstudied,the behavioralchangesinanexperimentalsetupwerenotstatisticallysigni˝cantenoughto determinebehaviorinthecaseofanactualin-streamturbineinnature. Figure4.9:SoundlevelsmeasuredintheMississippiRivernearMemphis,75metersaway fromthebargeand21metersfromtheturbine,shownbythesolidlineswithoutmarkers. Thelineswithmarkersshowthehearingabilityofcertain˝sh.(from:[21]) 4.4.4 BypassesandLadders Traditionaldamcon˝gurationsshouldhavesystemsinplacethatattempttoallow˝shto bypasstheturbineintakeandsafelycontinueswimmingupordownstream.However,these systemscanbeine˙ective,notallowingall˝shtopassthrough,duetotheirgeometricsetup 104 andlocation([2],[45],[117],[188],[105]).Unlessthespeci˝cspeciesisparticularlyadept atjumpingoverobstacles,orlaterallyalteringtheirpathofmotiontoseekopenroutes, manyofthe˝shbypassesorladderscanblockmigrationandnormal˝shbehavior.Several authorshaveinvestigatedalternativestocurrent˝shbypasscon˝gurationstoincreasetheir e˙ectiveness([191],[67],[92],[119]).Unfortunately,mostofthesee˙ortshavebeenmade afterlargedamshavebeenconstructedinmajorwaterways,andinalllikelihood,wouldnot beimplementedduetocost.Utilizingine˙ective˝shbypasssystems,moderndamsprovide onlytwomainoptionstomigrating˝sh:retreatorattempttopassthroughtheturbine. Aladderisde˝nedhereasastructuredesignedtoallow˝shtopassupstreamacrossthe dam.Incontrast,abypassisde˝nedasastructuredesignedtoallow˝shtochoosetoavoid toentertheturbinepenstockandcancontinueswimmingdownstreampastthedam.These twocategorieswillbereferredtoingeneralandcalledsystems.Thereare˝ve maintypesof˝shpassagesystems:pool/weirladders,verticalslotladders,chute˝shway ladders(alsocalledladders),culverts,andelevators[142].Thepool/weirtypeisthe oldestoftheladdertechnologies,madeupofalongrampwithkoroforthe ˝shtojumpinandoutof(orthrough,foranori˝ce/porttype)tomoveupanddownthe ramp,similarlytoalockforaboat.Thechuteorladderissimilartothevertical slotladder,inthattheybothincludestructuralprotrusionsthataredesignedtoproducea ˛owbehaviorthatisadvantageousforthe˝shtotravelthroughwithrespectto˛owspeed, ori˝cesizes,areasforrest,etc.Theculvert-typeladderisaductofsomesortsthatallow natural˛owthroughit(suchasthrougharoadordam),andcanincludeinternalba˜esto keepthe˛owvelocityfrombecomingtoohighfor˝shpassage.Lastly,the˝shelevatorsare themostuniqueofthepassagetechnologies,inthatthe˝sharecollectedinaholdingarea, andaretransportedviaanelevatoroverthedam.Othertypesofpassagesystemsexist, suchasremovingthebarrierto˛ow(damremoval),aswellasthenewer-coined orbiomimeticbypasses,whichattempttomimicnaturalrapidsorriversections[160].The lastmethodistocollectthe˝shandtransporttheminbargesortruckstomovethemto 105 theothersideofthedam,ortransportingtheminhelicopters,givingthemthename [141].Thequestionariseswhethertheseareimplementedsu˚cientlyinnumberand scaleforcurrentdamsystems. 4.4.5 In-StreamTurbinesinFarms Anotherdi˙erencebetweenin-streamanddam-turbinecon˝gurations,isthattoobtainlarge amountsofpower,thein-streamturbinesgenerallyneedtobedesignedinlargernumbersof units.Thisisduetothefactthatin-streamturbinesarenear-zeroheadturbines,andthus relyheavilyon˛owkineticenergytoconverttomechanicalshaftenergy.Placingturbines infarms,however,couldpossiblyleadtoissueswiththenaturalaquaticenvironment,if thespacingbetweenturbinesismadetoosmall(inboththestreamwiseandthecross˛ow directions).Ifthecross-streamspacingbetweenturbinesistoosmall,aquaticlifemighthave amoredi˚culttimemaneuveringaroundtheturbines,andtheblockagee˙ectcouldbecome toogreat,reducingthetotalpoweroutputoftheturbinearray[184]andtheabilityofthe rivertorecoveritsnatural˛owconditions[91].Theoptimumnumberofturbinesandtheir spacingwilldependonthechannelgeometry,˛owcharacteristics,individualturbinedesign, andthetypeandquantityofaquaticlifepresent. 4.4.6 ElectromagneticEmissions Thepossibleissuewithelectromagnetic˝elds(EMFs)emittedfromgeneratorsandpower transfercablesisinterferencewithnavigation,foraging,ordevelopmentbyaquaticlife, particularly˝shthataredependentonorsensitivetomagneticorelectric˝elds,suchas sharks,salmonoids,seaturtles,andwhalesanddolphins([44],[53]).Incurrentliterature, therehavebeenno˝ndingsthatindicatethatEMFfromsingledeviceswillnegativelya˙ect aquaticlife[15].ThelevelofEMFwilllocallyincreasewiththenumberofgenerators andcablesinthewater,however,nocurrentliteraturehasbeenfoundtoquantifythe compoundinge˙ectoftheEMFonaquaticlife. 106 4.5 MarineSafetyandAquaticHealth Dependingonthelocationoftheturbine,marinelifemaybecomprisedofmuchmore thanonly˝sh:mammals,crustaceans,andinsectandplantlifeallmayusethewaterways forfood,reproduction,ormigration.Thebehaviorofeachspecieswilldi˙er,sodesigning forasmanydi˙erentreactionsandneedsaspossiblemayprovetobeachallenge.From possiblymodifyingthebehaviorofmammalsandbirds([19],[80],[69])todisruptingcrab metamorphosis[138],turbinescana˙ectmarinelifeinvariousways.Monitoringtheresponse ofmarinelifetotheexistenceandoperationoftheturbine,andthehydrodynamicsandsound producedcanbedi˚cult,evenwithcurrentactiveacoustictechnology[101]. Alongwiththelifesupportedbytheriverineenvironment,theorganicandinorganic materialstransportedbythe˛owalsoplayanimportantroleintheecosystem.Thesedi- ments,comprisedoforganicandinorganiccomponentsofsoils,silts,sands,andsolids,as wellastrappedgasesandun-dissolvedcompoundsareneededbyplankton,farmland,and marinelifethroughouttheriver.Thesedimentsprovidenutrients,abalanceofwaterquality, andhabitatforaquaticlife.Ithasbeenshownthatin-streamturbinesa˙ectthesediment dynamicsofariverbychangingthelocalbedformfromscouringbelowtheturbineandde- positingsedimenttowardstheoutsideofthechannelanddownstream([81],[82])depending ontheshapeoftheriverandthe˛owvelocity.Theseverityofthein˛uenceoftheturbine onthesedimentdynamicsisrelatedtotheblockageratiooftheturbinedevice(s),though noexistingliteraturewasfoundtoprovideafunctionalrelationshipbetweenthem. 4.6 LiteratureSummary Thecanonicalinjurymechanismsofdam-turbinecon˝gurationshavebeenreviewed,and appliedto˝shsafeturbinedesignwiththeadditionofRPMandsoundconsiderations.It hasbeenshownthatin-streamturbinescanoperatewithlowrisktothesurroundingaquatic environmentwithrespecttophysicalstrike,pressure,shear,andturbulenceifthefollowing areincludedinthedesignprocess: 107 ‹ Keeptipstrikevelocitybelow5m/s(balanceofRPM,freestreamvelocity,androtor radius) ‹ OperateatlowRPM(atorbelow20RPM) ‹ Longbladechordandgapsbetweenbladeslarge(dependingonsizeoflargest˝sh presentinwaterway) ‹ Eliminateorminimizegapdistancesbetweenstationaryandmovingparts ‹ Keepdistancebetweenturbinesaslargeaspossible,ifplacedinfarms ‹ Mitigate˝shaccesstobladetipregion ‹ Keepstrainratelessthan4951/s ‹ Keeppressureratiolessthan2 Itistobenotedthatthesedesigncriteriaarefromtheavailabledataintheliterature, correspondingtothestudiedspeciesinquestion:futureexperimentswillshowhowwellthese parameterswillholdforother˝shspecies.Itisrecommendedthatin-streamtechnology befurtherinvestigated,particularlyexaminingin-situmarineinteractionwiththeturbine. Oneofthemaingapsinthecurrentknowledgeisthee˙ectofthesoundproducedbya singlerealinstalledturbineandbyafarmofturbines.Itisrecommendedtoperformshort andlongtermexperimentsbeforeandaftertheinstallationofrealturbineunit(s)tofully understandthelocaltemporale˙ectsonaquaticlifeaswellastomonitorthebehavior changeinnativemarinespecies.Acceptablecriteriaforsafesoundlevelsshouldthenbe establishedtominimizetheinterferencewiththelocalaquaticlifeandshouldbeincluded inthesuggestedlistofdesigncriteriafor˝sh-friendlydesign. 4.7 Design ThelessonsfromSection4.4wereappliedinthepreliminarydesignprocessforanin- streamturbine.Oneofthemostsimplewaystodesignaturbineisaparametricapproach; 108 importantandrestrictingparametersarechosenbyorsetforthedesigner,thatwhencom- binedwithbasicturbomachineryand˛uiddynamicprinciplesallowforthecalculationof bladeshapeatthemeanradiallocation(generally,thearea-averagedmean).Theseimpor- tantparameterswilldependonthescopeoftheintendeduseoftheturbine,butcouldlikely include:rotortipmaximumdiameter(intheformoftheminimum˛owdepth),ratedpower extraction,mean˛owvelocity(or˛owrate,knowingchannelbathymetry),androtorRPM. Oncethemeanbladeanglesarecalculatedfromtheparameters,thedesignerpicksaradial distributionofloadingorspeci˝cworkontheblade,withthecommoninitialchoicefora traditionalbladebeingameaningthattheswirl(orcircumferential)velocity isscaledfromthemeanasinverselyproportionaltotheradius.Fortheparticulardesign discussedhere,thepreliminaryparametersthatdeterminedthemeanbladeanglesare: ‹ Maximumstrikespeedlessthan5m/s ‹ Rotationrateequalto20RPM ‹ Flowvelocityequalto1m/s Wherethestrikespeedisusedhereasthehypotenuseofthetriangleformedbytherotational velocityandtherotorinletvelocity,whichassumesthatthe˝shismovingintheriverby simplyfollowingthe˛owatthesamespeedasthemean˛owvelocity.Inotherwords,the strikespeedisequaltothebladeinletrelativevelocity,whichisassumedtobethemaximum velocityatwhichthe˝shwillriskcontactingthebladesurface.Themaximumstrikespeed, alongwiththeRPMand˛owvelocity,determinesthemaximumdiameteroftheturbine. The˛owvelocityischosenaswhatwouldbetypicalfortheriverofinterest,inthiscasethe AmazonRiver.TheRPMischoseninthiscasetobethehypothesizedcriticalpointfor˝sh safety,favoringlowimpactvelocityintheeventof˝shcontactwiththerotorblades. Theinitialestimationofratedpowerextractionisdeterminedbytheaforementioned parameters,aswellasthemeancircumferentialvelocity(chosenastheoutletbladeangleat theaverageradius).Themeancircumferentialvelocityisscaledintheradialdirectionusing 109 afree-vortexpro˝leassumption(4.1), K = constant = C r (4.1) andallotherbladeanglesarecalculatedateachradiallocation.Thebladeoutletcircumfer- entialvelocityiscalculatedasthevalueatwhichtheBetzlimitisreachedforabarerotor (4.2), P Betz =_ m KE 1 =0 : 5 ˆ C 3 1 A turbine (4.2) assumingthatthereisnopre-swirlintotherotor(4.3),andthattherotorhas100%blade e˚ciency(relativetoBetz)(4.4).Inotherwords,themeanbladeswirlisdeterminedwhen theresultingpowerfromtheEulerturbineequationmatchesthepowerreportedfromthe idealBetzequation. P barerotor = ! U r C ;wherevaluesarecalculatedatr mean (4.3) P barerotor = P available = P Betz ;if =100% (4.4) Therotorisencasedinaduct,mainlytomitigate˝shaccesstothebladetips,aswellas increasingtheratedpowerextractionoftheturbineoverabarerotor.Thedesignisevaluated inopen-watere˚ciencyaswellasthemaximumstrainrateandminimumpressurearefound numericallywithaCFDsimulationinanin˝nitemediaenvironment,seeSection4.8.The turbinedesignissummarizedinTable4.1. Table4.1:TurbineDesignParameters TurbineDesign Parameter Value TipDiameter 1.25m HubDiameter 0.4m RPM 20RPM MeanOutletBladeAngle 25.8 RatedPower 325W 110 4.8 Simulation 4.8.1 ModelandMesh TheaforementionedturbinedesignwasmodeledinBladeGenandSiemensNX,andimported intoANSYSWorkbenchformeshingandComputationalFluidDynamics(CFD)simulation. Themeshcomprisedofamixtureof12.5milliontetrahedralandhexahedralelementsforthe turbine,shroud,and˛owdomain.Themeshqualitywasmeasuredintermsoftheskewness andtheorthogonalquality:themaximumelementskewnesswasequalto0.851andthe minimumorthogonalqualitywasequalto0.182.Thegeometricmodelandsimulationmesh areshowninFigures4.10to4.15. Thisrotorisdesignedtobehubless,andinsteaddrivesageneratorattherim,suchis shownin4.11.Thehublessdesignischosenduetothepossiblebene˝tthatifany˝shor debrismanagetoresistthenaturalbypass˛owandmakeitpastthetrashrack(notshown), thattheopencenteraswellasthebackward-leanedbladescanhelptopassthe˝shordebris throughwithoutcontactingtheblades. Excludingapossibletrashrack,electricalcables,andamooringdevice(a˛oatorcables), thein-streamdeviceisshowninariverin4.12. 4.8.2 Setup Theturbinewassimulatedinatransient,full-wheel3D˛owenvironment.Theturbulence closureproblemwashandledwiththe k ! ShearStressTransport(SST)model,inorder toenhancetheaccuracyoftheturbulencemodelingneartothebladewallsaswellasfarout intothe˛uid.Thisisdonebycombiningthestandard k and k ! closuremodels,and blendingthembetweenwallandfree-streamregions.Equations(4.5)through(4.8)show thesetofequationsthataresolvedinANSYSFluent,withthe k ! SSTclosuremodel. Thedi˙erencebetweenthestandard k ! andtheSSTmodelisinthefunctionalformof theturbulentviscosity t andtheturbulentPrandtlnumbers ˙ k and ˙ ! thatareusedto 111 Figure4.10:Ductedrotormodelfromthreeviews:˛owdirection,obliqueandtop 112 Figure4.11:Cross-sectionofthein-streamgenerator,withasimpli˝edrim-drivegenerator. Theblackblocksarebearings,thedarkblueblocksaremagnets(rotatingwiththeblades), andtheredblocksarethestatorwindingsandcore(stationarywithshroud). Figure4.12:In-streamgeneratorinariverchannel 113 D 5D 5D 10D 15D Figure4.13:Numericdomain Figure4.14:Ductedrotormesh:domainsideview calculate k and ! in(4.7)and(4.8).TheSSTmodelusedahyperbolictangentfunction toblend k ! and k ,insteadofpurelyusing k ! .Theproduction(G),dissipation (-Y),andusersourceterms(S)forbothkand ! aresimilaramongthestandardandSST k ! models,withafewconstantsandcalculationlogiccomponentsthatsetthemapart. @ˆ @t + r ( ˆ~v )= S m (4.5) @ @t ( ˆ~v )+ r ( ˆ~v~v )= p + r ( ˝ )+ ˆ~g + ~ F (4.6) @ @t ( ˆk )+ @ @x i ( ˆku i )= @ @x j k @k @x j )+ e G k Y k + S k (4.7) 114 Figure4.15:Ductedrotormesh:rotorbladeview @ @t ( ˆ! )+ @ @x i ( ˆ!u i )= @ @x j ! @! @x j )+ G ! Y ! + D ! + S ! (4.8) Theboundaryconditionsweresetas:velocityinlet(at1m/s),apressure-outlet(atzero gauge),andtheotherouterdomainsurfacesweresettosymmetryconditions,tosimulate aturbinefarawayfromthefreesurfaceorriverwalls.Thespatialandtemporal˝nite di˙erenceschemeswereallevaluatedatsecondorder,andthepressure-velocityvariables werecoupled,withaCourantnumberof2.Tomodelthemotionoftherotor,asliding meshtechniquewasimplemented.Amultipleframeofreferencemodelwasused,providing thecylinderof˛uidthatrepresentedtheturbine-turned˛owameshmotionat2.09rad/s, andthesametreatmentwasgiventothewallsassociatedwiththat˛uidzone.The˛ow domainwasinitializedwiththeinletconditions,andwassolvedimplicitlywithatimestep 115 Figure4.16:Mass˛owratedi˙erencebetweeninletandoutletnormalizedbyinletmass˛ow rateoveriterationcount ofonemillisecond.Thesolutionwasallowedtotime-stepforatleasttwofullbladerotations (6000timesteps),andwasallowed100iterationsateachtimesteptoconvergethetracked variablestoaresidualof1E-5.Thesimulationisconsideredconvergedoncethemass˛ow ratedi˙erencebetweeninletandoutletreachedasemi-steadylevel,andthetorquecoe˚cient onthebladesreachesaquasi-steadylevel(˛uctuationsareaboutaconstantmeanvalue), asisshowninFigures4.16and4.17. 4.8.3 Results TheinitialdesigncasewassimulatedataTSRofapproximately0.65.TheTSRwasvaried from1.87towards0byvaryingthein˛owvelocity,mimickinglargechangesinseasonalriver ˛owrates,whilethegeneratormaintainsconstantRPM.Theperformanceoftheturbine designwasmeasuredintermsofitsabilitytomeettheaforementioned˝sh-friendlycriteria aswellasitsabilitytoproducepower.Theshaftpowerisreportedintermsofthepower coe˚cient,andthe`˝sh-friendliness'ofthedesignismeasuredintermsofthemaximum strainrateandtheminimumpressureencounteredinthe˛ow.Theresultscalculatedfrom 116 Figure4.17:Torquecoe˚cientoveriterationcount FluentareshowninFigures4.18-4.22. 4.8.3.1 PowerCoe˚cient Figure4.18showstherangeofthetypicalperformancemetricforin-streamdevices,the powercoe˚cient,overtheinvestigatedtipspeedratio.Themaximumfoundpowercoef- ˝cientis0.239usingtherotordiameterasthebasisformaximumkinetic˛ux,or0.208 whenconsideringtheductoutermostdiameter,occurringataTSRofapproximately0.871. Comparingthispeakpowercoe˚cienttotheso-calledBetzlimityieldsarelativee˚ciency of35-40%,comparingtoabarerotor,1-Dmomentumbasis.However,aswasmentionedin Section4.2.3,thisconceptofamaximumpoweroffree-˛owingdeviceshasbeeninvestigated intheliteratureforvariousdevice-environmentcon˝gurations,withnoclearansweryetas tothetrueupperlimit,orthemostaccuratebasisforcalculation.Takingtheanalysisof Betzonestepfurther,usingtheresultsoftherotordiskmodel,equations(4.9)and(4.10) canbeusedtoevaluateasomewhatmorerealisticvalueformaximumpowercoe˚cientthan 117 Figure4.18:Plotofpowercoe˚cientovertipspeedratio,basedontherotorandductareas Betz[102]: 2 = (1 a 2 )(4 a 2 1) 2 (1 3 a 2 ) (4.9) C p;max = 8 729 [ 64 5 x 5 +72 x 4 +124 x 3 +38 x 2 63 x 12 ln ( x ) 4 x 1 ] x =0 : 25 x =(1 3 a 2 ) (4.10) Usingthesetwoequationsallowsforthecalculationofamaximumpowercoe˚cientequalto 0.391atthesametipspeedratioasthepeakpowerfromCFD.Thisincreasesthee˚ciency ofthedesigntoaround53-61%whenutilizingrotordisktheoryoverpureactuatordisk theory;however,thisisstillinaccuratebasisasnoductisconsideredineitherdiskanalysis. 4.8.3.2 Pressure Figure4.19showsthepressureratiooftheminimum(ornadir)pressureencounteredinthe ˛owtovarioushypotheticalacclimationpressuresof˝sh.Thepressureratioremainslower than2overtherangeofacclimationpressuresformostofthedesignpointsconsidered.At 118 Figure4.19:Plotofpressureratioovertipspeedratio,atthreeacclimationpressures:1 atm,1.5atm,and2atm acclimationpressureshigherthan2atm,thepeakperformancepointandhighervelocities wouldpresenttoohighofapressureratiotokeepinjuryprobabilitiesataminimum.This maynotbeaproblem,however,dependingontheplacementoftheturbinewithinariver channel,becauseabottom-dwelling˝shmaynotmovequicklyorcloseenoughtowardsthe surfacetoswimthroughtheturbine-a˙ected˛owiftheturbinewasnotplacedon/verynear tothebottom.Similarly,themaximumnegativerateofpressurechangeisshowntobe acceptablewhencomparedwiththeindustry-used550kPa/scriteria[118],downtoaTSR ofapproximately0.65. 4.8.3.3 StrainRate Figures4.21and4.22showthemaximumstrainrate(orshearrate)inthe˛ow,andthe percentofthebladesurfacesabovethemaximumcriteria.Figure4.21showsthatonahyper- 119 Figure4.20:Plotofmaximumnegativepressurerateofchangeovertipspeedratio. localmaximumstrainbasis,noneoftheexamineddesignconditionshaveanacceptablylow levelofshear;inotherwords,evenifonemeshelementexperiencesover-criteriastrainrate, thenthedesignfails.However,Figure4.22tellsadi˙erentstorybyexaminingtheentire high-strainregion,namely,neartothebladesurface,andthepercentofthebladesurface thatisabovethecriteria.Itisfoundthatatatipspeedratioof0.871andabove,thepercent ofthebladesurface(calculatedbyelementvolume)thatisabovethecriteriaisnearlynull; onlyaverysmallnumberofelementsneartheblade"tip"(thebladerootforthehubless, rim-drivendesignconsideredhere)couldpresentrisk.Tofurtheravoidrisk,thepresenceof theductcanmitigate˝sh'saccesstothetip,andthehublessopencentercanencourage(by lowerpressurechangeand˛owresistance)˝shtoswimthroughwithoutneedingtoswim pasttheblades. 120 Figure4.21:Plotofmaximumdomainstrainrateovertipspeedratio 4.8.4 PostprocessingRoutine AftertheinitialresultswerecalculatedusingANSYSFluent'sGUI-basedroutines,aseparate analysiswasdoneusingMATLABtoanalyzetheCFDresultstocomparetothedesign. 4.8.4.1 Method Tobettervisualizeandanalyzetheperformanceofthesimulatedmachine,itwasdesiredto examinethe˛owandturbomachinevariablesqualitativelyandquantitatively.ANSYSFlu- entdoesnoteasilyallowfull-wheel3Denvironmentsimulationwithintheturbomachinery toolset(onlyarepeated˛owpassagewithatraditionalhubandcase).Therefore,anyanal- ysisneedstobedonewithgeneralFluentvisualization/evaluationtools(simplegeometry- boundplotting,postprocessingofelemental˛owvalues,etc.),orneedstobedeveloped externally,andprovidedthesimulationresultdata.Inthiscase,an"unwrappviewof 121 Figure4.22:Plotofpercentofbladesurroundingvolumeabovecriteriaof4951/sovertip speedratio the˛owpassageswasdesired(visualizationona2Daxial-tangentialdirectionalplane),so MATLABwaschosenasthebestenvironmentforanalysisforitsstrongvisualizationtoolset, seeAppendixB.ThesimulationresultswereexportedfromFluentfortheentiretyofthe rotationaldomain,exportingcell-centerevaluatedvalues(becauseFluentisavolumetric approach,thesevaluesarenotinterpolatedlikenodalvalues)ofallvariables.Thiswasalso doneforthebladewallregionsaswell,tocaptureonlythenear-to-bladeregionsforthemost accurateturbomachinerycalculations. 4.8.4.2 Output Figures4.23-4.32showtheoutputfromtheMATLABscript.Figures4.23-4.26showthe initialfree-vortexbladevelocitytriangledesign,andthecomparisonwiththenear-blade dataoutputfromFluent.Figures4.27-4.32focusonthe2Dvisualizationofa˛owpassage 122 Figure4.23:Designedtrianglevelocitiesoverbladespan oneithersideofoneblade,intermsoftherelative˛owvelocities:vectors,contours,and streamlines,atthreeroot-of-the-sum-of-the-square(RSS)radialspanlocations:10%,50% and90%. 4.8.4.3 Discussion AscanbeseenfromFigures4.27-4.32,therelative˛owvelocitycontoursdidnotcalculateas wereexpectedwhenusingcell-centeredexportedvaluesfromFluent.Startingatatangential arclengthpositionofapproximately0meters,thereareperiodic-looking(somemultiplicative intervalofpi*radius)linedisturbancestothedata.ThiscanbemosteasilyseeninFigures 4.27and4.30,whereitcanbeseenthattherearephysicaldatapointswithinthemeshless bladeinteriorvolume.Thisissuewasattemptedtoberesolved,however,no˝xwasfound duringthetimeofthiswork;theinterpolationfunction(otherthanScatteredInterpolant) andtechniquewaschanged(linear,nearestneighbor,naturalneighbor)tonoavail.It 123 Figure4.24:Designedbladeangledi˙erenceacrossbladeoverbladespan Figure4.25:ComparisonofdesignedbladetrianglevelocitieswithCFDoutput 124 Figure4.26:Spanwisepro˝lesofangulardi˙erencebetweendesignandCFDoutput Figure4.27:Relative˛owvelocityvectorsandcontoursat10%squareradialspan Figure4.28:Relative˛owvelocityvectorsandcontoursat50%squareradialspan wasdeemedthatthisissueisembeddedwithinFluent'sexportroutine,andsothenode- basedvalues(interpolatedbyFluentfromthecellcenters)wereexportedtoassistinthe visualrepresentationofthe˛owpassages.Thecell-centeredvalueswereretainedforany quantitativecalculations(suchasthespan-averageangulardi˙erencefromdesign),butthe 125 Figure4.29:Relative˛owvelocityvectorsandcontoursat90%squareradialspan Figure4.30:Relative˛owvelocitystreamlinesandcontoursat10%squareradialspan Figure4.31:Relative˛owvelocitystreamlinesandcontoursat50%squareradialspan valuesareexaminedwithasenseofconservativecaution.Figures4.33-4.35showsomeofthe relativevectorandcontouroutputscalculatedusingthenodaldataexportfromFluent.It canbeseenfromFigures4.27-4.35thattherelativevelocityvectorsalignfairlywellwiththe bladeshapesthroughthe˛owpassages.Figure4.26indicatesthat,whencalculatedusingthe cell-centeredvalues,themass-averagespandi˙erencebetweenthedesignedrelativevelocity 126 Figure4.32:Relative˛owvelocitystreamlinesandcontoursat90%squareradialspan Figure4.33:Relative˛owvelocityvectorsandcontoursat10%squareradialspan,using nodalvalues angles( )andtheCFDcalculatedanglesareapproximately4and11degrees,attheleading andtrailingedges,respectively.Fortheabsolutevelocityangles( ),thecalculatedmass- averageddi˙erencesareapproximately5and22degrees,attheleadingandtailingedges. Therelativeangledi˙erencecanbequalitativelyseeninFigures4.27-4.35inthattherelative ˛owiswell-alignedwiththebladesurfaces,withanoticeabledi˙erenceofafewdegreesatthe leadingandtrailingedges,leadingtoreducede˚ciencyvialessswirldi˙erence thandesigned. 4.8.5 Conclusion ConsideringtheresultsshowninSection4.8.3,thedesignedin-streamdeviceachievesthe goalofbeing˝shfriendlybasedonthe˝ndingsinSection4.3,withthecaveatsmentioned 127 Figure4.34:Relative˛owvelocityvectorsandcontoursat50%squareradialspan,using nodalvalues Figure4.35:Relative˛owvelocityvectorsandcontoursat90%squareradialspan,using nodalvalues overthetipspeedratiorangeinvestigatedhere.Itisnoteworthytomentionaninteresting pointthattheliteraturementionedhereinyieldedessentiallytwodi˙erentsetsofcriteriaand thustwodi˙erentdesignsfor"˝turbines:MJ2'svery-low-head(VLH)turbine basedpredominantlyonthereviewworkofOdehetal.andtheAldenturbine,withwork andsupportbyAldenLabs,Voith,theEnvironmentalPowerResearchInstitute(EPRI), andtheDepartmentofEnergy(DoE)basedonthenewerexperimentationandinnovation. Theworkpresentedhereismainlybasedonthefoundationofthelatterdesign,withthe additionofothernovelresearchdocumentedintheliteratureinanattempttoaccumulate themassofcurrentknowledgeintoadesignthatiscapableofbeingplacednaturallyintoa free˛owingriverwithoutsigni˝cantlydisturbingorharmingthemarinelifepresent.Based onthecriteriacompiledanddocumentedbyOdehandutilizedbyMJ2,itcouldbesaidthat thedesignpresentedhereusesconservativecriteria,andcouldpossiblyuselessrestrictive valuesforpressure,strikevelocity,etc.andmaintainahighlevelof˝shsafety.Neverthe- 128 less,untilthedesignwouldbemanufacturedanddeployedinsoloandfarmcon˝gurations, thetruebehavioralimpactonthemarinelifecanonlybestipulatedon,whichcanhope- fullysomedayaddtotheknowledgebaseonmarineenergyextractioninteractionwiththe surroundingenvironment,oratleastbene˝tfromandbeenhancedbyfuturework.Itis notedthattheemittedsoundlevelsofthisparticulardesignwerenotcalculatedduringthe simulationprocess.Thisisleftforfuturetoworktoinvestigateforfurtherunderstandingof theinteractionofthisturbinedesignwiththesurroundingenvironment.Additionally,the designwassimulatedinane˙ectivelyopenenvironment(ablockageratiolessthan0.01); futureworkwouldinvolvesimulatingtheturbinewithaspeci˝cchannelgeometry oranequivalentsigni˝cantblockageratio,whilealsoexaminingthee˙ectonadynamic open-channelsurface. 129 CHAPTER5 CLOSINGREMARKSANDGLOBALIMPLICATIONS ThelessonslearnedfromtheAmazoncanalsobegeneralizedtootherregionsoftheworld, suchasAfricaandIndia,whereaccesstoanationalpowergridandanabundanceofnatural energysourcesmaybelimitedbygeographic,˝nancial,orsocialsituations.Thereare severalchallengesthatneedtobeplannedforandovercomewhenutilizingthetechnologies andenergygenerationstrategiespresentedhere,including: ‹ Guidingviewpointstowardsglobalenvironmentalandsocialsafetyandhealthover ˝nancialinterests ‹ Overcominglocalpeople'sopinionofy-backyard",oftencomingfromexperi- encewithlargehydro ‹ Creatinginterestofthelocalpeopleaswellthegoverningbodiesandindustrytoaccept new" ‹ Workingwiththeappropriategovernmentagenciesandindustriestofundtheprojects ‹ Sharingthebene˝tsofdistributed,renewablepowerwiththepublic Theseissuestaketimeandmulti-disciplinaryplanningtoovercome,however,withenough publicinterestandinvolvement,workingbetweenallinterestedandbene˝ttingpartiesis possible.Embracingdecentralizedrenewablepowergeneration,suchasrooftopand˛oating solar,aswellasin-streamtechnologiescouldbeakeyfactorinimprovingglobalqualityof lifeandmeetingenvironmentalgoalstowardsafuture-friendlyglobalenergymarket. 130 APPENDICES 131 APPENDIXA GISFILESOURCES Shape˝leandGISsourcesutilized: ‹ Background:NaturalEarth: http://www.naturalearthdata.com/ ‹ SouthAmericawithboundaries: https://tapiquen-sig.jimdofree.com/english -version/free-downloads/south-america/ ‹ Brazilwithboundaries:IBGE: https://www.ibge.gov.br/estatisticas/downloa ds-estatisticas.html ‹ GISsoftware:QGIS: https://www.qgis.org/en/site/ ‹ Brazilianenergygenerationlocations:ANEEL: https://www.aneel.gov.br/infor macoes-geograficas ‹ Braziliantransmissionlines:ONS: http://www.ons.org.br/paginas/sobre-o-sin /mapas 132 APPENDIXB MATLABSAMPLESCRIPT %BEGINSCRIPT %ThisscripttakesASCIIoutputdatafromtherotatingregion aroundthe %turbineandextractsdatanecessarytoexaminetheflowthrough theblade %passages. clearall clc closeall %Inputs %UsermustinputR^2locationsaswellasmachinetipandhub diameters. R_squared_locs=[0.1,0.5,0.9]; %numberofradialsamplesdesired orfromfile tip_diameter=1.25; %m hub_diameter=0.4; %m N_blades=3; %~,tocalculatebladespacing blade_face_mesh_size=0.005; %inmeters rotating_body_mesh_size=0.01; %inmeters beta2_mean=25.82; %atR=0.41,geometricmean alpha1=90; %nopre = swirl N=20; %RPM c_inf=1; %m/s 133 %Bladetriangleknownsandcalcs tip_radius=tip_diameter/2; hub_radius=hub_diameter/2; R_mean_geometric=(tip_radius+hub_radius)/2; R_mean_square= sqrt (tip_radius^2+hub_radius^2); omega=N * pi /30; %rad/s c1=(2/3) * c_inf; %fromBetzderivation,alpha %Initializedata for i=1: length (R_squared_locs) sq_radii(i)= sqrt (R_squared_locs(i) * (tip_radius^2 = hub_radius^2)+hub_radius^2); end %Importdatafileofinterest blades=importdata("..."); turbine=importdata("..."); [num_rows,num_cols]= size (turbine.data); [num_rows_blades,num_cols_blades]= size (blades.data); blade_spacing=2 * pi * sq_radii/N_blades; %ExtractDesiredDataintoMatrices,turbineregion radii_data_loc= find ( strcmp (turbine.colheaders,'radial = coordinate')); radial_coord_unsorted=turbine.data(:,radii_data_loc); tangential_data_loc= find ( strcmp (turbine.colheaders,'angular = coordinate')); tangential_coord_unsorted=turbine.data(:,tangential_data_loc); axial_data_loc= find ( strcmp (turbine.colheaders,'axial = coordinate ')); 134 axial_coord_unsorted=turbine.data(:,axial_data_loc); rel_tan_vel_data_loc= find ( strcmp (turbine.colheaders,'rel = tangential = velocity')); rel_tan_vel_mag_unsorted=turbine.data(:,rel_tan_vel_data_loc); tan_vel_data_loc= find ( strcmp (turbine.colheaders,'tangential = velocity')); tan_vel_mag_unsorted=turbine.data(:,tan_vel_data_loc); axial_vel_data_loc= find ( strcmp (turbine.colheaders,' axial = velocity')); axial_vel_mag_unsorted=turbine.data(:,axial_vel_data_loc); radial_vel_data_loc= find ( strcmp (turbine.colheaders,' radial = velocity')); radial_vel_mag_unsorted=turbine.data(:,radial_vel_data_loc); rel_vel_mag_data_loc= find ( strcmp (turbine.colheaders,'rel = velocity = magnitude')); rel_vel_mag_unsorted=turbine.data(:,rel_vel_mag_data_loc); rel_vel_ang_data_loc= find ( strcmp (turbine.colheaders,'relative = velocity = angle')); rel_vel_ang_unsorted=turbine.data(:,rel_vel_ang_data_loc); vel_ang_data_loc= find ( strcmp (turbine.colheaders,' velocity = angle')); vel_ang_unsorted=turbine.data(:,vel_ang_data_loc); %ExtractDesiredDataintoMatrices,onblades radii_data_loc_blades= find ( strcmp (blades.colheaders,'radial = coordinate')); radial_coord_blades_unsorted=blades.data(:,radii_data_loc_blades ); 135 tangential_data_loc_blades= find ( strcmp (blades.colheaders,' angular = coordinate')); tangential_coord_blades_unsorted=blades.data(:, tangential_data_loc_blades); axial_data_loc_blades= find ( strcmp (blades.colheaders,'axial = coordinate')); axial_coord_blades_unsorted=blades.data(:,axial_data_loc_blades) ; %Sortandindexmatricesbasedonradii %turbine [radial_coord,sortindex]= sort (radial_coord_unsorted,'ascend'); tangential_coord=tangential_coord_unsorted(sortindex); axial_coord=axial_coord_unsorted(sortindex); rel_tan_vel_mag=rel_tan_vel_mag_unsorted(sortindex); tan_vel_mag=tan_vel_mag_unsorted(sortindex); axial_vel_mag=axial_vel_mag_unsorted(sortindex); rel_vel_mag=rel_vel_mag_unsorted(sortindex); radial_vel_mag=radial_vel_mag_unsorted(sortindex); rel_vel_angle=rad2deg(rel_vel_ang_unsorted(sortindex)); vel_angle=rad2deg(vel_ang_unsorted(sortindex)); %blades [radial_coord_blades,sortindex_blades]= sort ( radial_coord_blades_unsorted); axial_coord_blades=axial_coord_blades_unsorted(sortindex_blades) ; tangential_coord_blades=tangential_coord_blades_unsorted( sortindex_blades); 136 clear ("blades") clear ("turbine") %Onlyincludedataathuborabovetocomparetomeanlinedesign %turbine hub_loc= find ( abs (radial_coord = hub_radius)==... min ( abs (radial_coord = hub_radius))); radial_coord_hubup=radial_coord(hub_loc: end ); axial_coord_hubup=axial_coord(hub_loc: end ); tangential_coord_hubup=tangential_coord(hub_loc: end ); rel_tan_vel_mag_hubup=rel_tan_vel_mag(hub_loc: end ); tan_vel_mag_hubup=tan_vel_mag(hub_loc: end ); axial_vel_mag_hubup=axial_vel_mag(hub_loc: end ); rel_vel_mag_hubup=rel_vel_mag(hub_loc: end ); radial_vel_mag_hubup=radial_vel_mag(hub_loc: end ); rel_vel_angle_hubup=rel_vel_angle(hub_loc: end ); vel_angle_hubup=vel_angle(hub_loc: end ); %blades hub_loc_blades= find ( abs (radial_coord_blades = hub_radius)==... min ( abs (radial_coord_blades = hub_radius))); radial_coord_blades_hubup=radial_coord_blades(hub_loc_blades: end ); axial_coord_blades_hubup=axial_coord_blades(hub_loc_blades: end ); tangential_coord_blades_hubup=tangential_coord_blades( hub_loc_blades: end ); leading_edge_axial= max (axial_coord_blades_hubup); trailing_edge_axial= min (axial_coord_blades_hubup); crit=0.1; %PICKrangeofaxiallocationstouse(highercrit, 137 likelyhigherradialvariation) leading_dist_error=100 * abs ((leading_edge_axial = axial_coord_hubup)/leading_edge_axial); trailing_dist_error=100 * abs ((trailing_edge_axial = axial_coord_hubup)/trailing_edge_axial); sep_locs_nonzero_leading= find (leading_dist_error<=crit); sep_locs_nonzero_trailing= find (trailing_dist_error<=crit); %CalculatefromFluentandcomparetodesign %Findleadingandtrailingedgepointsfromdataforbladeinlet andoutlet %station1,inlet radial_coord_analysis1_nonunique=radial_coord_hubup( sep_locs_nonzero_leading); axial_coord_analysis1_nonunique=axial_coord_hubup( sep_locs_nonzero_leading); tang_vel_analysis1_nonunique=tan_vel_mag_hubup( sep_locs_nonzero_leading); rel_tang_vel_analysis1_nonunique=rel_tan_vel_mag_hubup( sep_locs_nonzero_leading); axial_vel_analysis1_nonunique=axial_vel_mag_hubup( sep_locs_nonzero_leading); radial_vel_analysis1_nonunique=radial_vel_mag_hubup( sep_locs_nonzero_leading); rel_vel_ang_analysis1_nonunique=rel_vel_angle_hubup( sep_locs_nonzero_leading); vel_ang_analysis1_nonunique=vel_angle_hubup( sep_locs_nonzero_leading); 138 %onlyuseuniquevaluesforinterpolationlater [radial_coord_analysis1,unique1index]=unique( radial_coord_analysis1_nonunique); axial_coord_analysis1=axial_coord_analysis1_nonunique( unique1index); tang_vel_analysis1=tang_vel_analysis1_nonunique(unique1index); rel_tang_vel_analysis1=rel_tang_vel_analysis1_nonunique( unique1index); axial_vel_analysis1=axial_vel_analysis1_nonunique(unique1index); radial_vel_analysis1=radial_vel_analysis1_nonunique(unique1index ); rel_vel_ang_analysis1=rel_vel_ang_analysis1_nonunique( unique1index); vel_ang_analysis1=vel_ang_analysis1_nonunique(unique1index); Wu1_analysis=rel_tang_vel_analysis1; Wm1_analysis= sqrt (axial_vel_analysis1.^2+radial_vel_analysis1 .^2); Cu1_analysis=tang_vel_analysis1; Cm1_analysis= sqrt (axial_vel_analysis1.^2+radial_vel_analysis1 .^2); W1_analysis= sqrt (Wu1_analysis.^2+Wm1_analysis.^2); C1_analysis= sqrt (Cu1_analysis.^2+Cm1_analysis.^2); U1_analysis_check=Cu1_analysis = Wu1_analysis; beta1_analysis=asind( = axial_vel_analysis1./W1_analysis); % = axial b/cflowin = zdirection alpha1_analysis=asind( = axial_vel_analysis1./C1_analysis); % = axialb/cflowin = zdirection 139 %station2,outlet radial_coord_analysis2_nonunique=radial_coord_hubup( sep_locs_nonzero_trailing); axial_coord_analysis2_nonunique=axial_coord_hubup( sep_locs_nonzero_trailing); tang_vel_analysis2_nonunique=tan_vel_mag_hubup( sep_locs_nonzero_trailing); rel_tang_vel_analysis2_nonunique=rel_tan_vel_mag_hubup( sep_locs_nonzero_trailing); axial_vel_analysis2_nonunique=axial_vel_mag_hubup( sep_locs_nonzero_trailing); radial_vel_analysis2_nonunique=radial_vel_mag_hubup( sep_locs_nonzero_trailing); rel_vel_ang_analysis2_nonunique=rel_vel_angle_hubup( sep_locs_nonzero_trailing); vel_ang_analysis2_nonunique=vel_angle_hubup( sep_locs_nonzero_trailing); %onlyuseuniquevaluesforinterpolationlater [radial_coord_analysis2,unique2index]=unique( radial_coord_analysis2_nonunique); axial_coord_analysis2=axial_coord_analysis2_nonunique( unique2index); tang_vel_analysis2=tang_vel_analysis2_nonunique(unique2index); rel_tang_vel_analysis2=rel_tang_vel_analysis2_nonunique( unique2index); axial_vel_analysis2=axial_vel_analysis2_nonunique(unique2index); radial_vel_analysis2=radial_vel_analysis2_nonunique(unique2index 140 ); rel_vel_ang_analysis2=rel_vel_ang_analysis2_nonunique( unique2index); vel_ang_analysis2=vel_ang_analysis2_nonunique(unique2index); Wu2_analysis=rel_tang_vel_analysis2; Wm2_analysis= sqrt (axial_vel_analysis2.^2+radial_vel_analysis2 .^2); Cu2_analysis=tang_vel_analysis2; Cm2_analysis= sqrt (axial_vel_analysis2.^2+radial_vel_analysis2 .^2); W2_analysis= sqrt (Wu2_analysis.^2+Wm2_analysis.^2); C2_analysis= sqrt (Cu2_analysis.^2+Cm2_analysis.^2); U2_analysis_check=Cu2_analysis = Wu2_analysis; beta2_analysis=asind( = axial_vel_analysis2./W2_analysis); % = axial b/cflowin = zdirection alpha2_analysis=asind( = axial_vel_analysis2./C2_analysis); % = axialb/cflowin = zdirection %Separatedatabyradiallocations %CalculateBladeTriangles,useradiifromfluentanalysis radii_span1=radial_coord_analysis1; radii_span2=radial_coord_analysis2; blade_velocity1=omega * radii_span1; blade_velocity2=omega * radii_span2; r_geo_loc= find ( abs (radii_span2 = R_mean_geometric)== min ( abs ( radii_span2 = R_mean_geometric))); r_geo=radii_span2(r_geo_loc); ifisempty (r_geo_loc) 141 r_geo_loc= find ((radii_span2>=0.999 * R_mean_geometric)&... (radii_span2<=1.001 * R_mean_geometric)); r_geo=radii_span2(r_geo_loc); end iflength (r_geo_loc)>1 distance_error=r_geo = R_mean_geometric; error_min_loc= find ( abs (distance_error)== min ( abs ( distance_error)),'first'); r_geo_loc_min_error=r_geo_loc(error_min_loc); r_geo=radii_span2(r_geo_loc_min_error); else r_geo_loc_min_error=r_geo_loc; end %Location1,turbineinlet alpha1_span=alpha1 * ones( length (radii_span1),1); c1_span=c1 * ones( length (radii_span1),1); cm1_span=sind(alpha1_span). * c1_span; cu1_span=cosd(alpha1_span). * c1_span; U1_span=blade_velocity1; %assumeconstantrpmandradii w1_span= sqrt (c1_span.^2+U1_span.^2); wu1_span= = (U1_span = cu1_span); wm1_span=cm1_span; beta1_span=asind(wm1_span./w1_span); %Location2,turbineoutlet cm2_span= interp1 (radii_span1,cm1_span,radii_span2,'linear',' extrap'); %assumeconstantmassflowthrough %useextrapincaseradiidontlineupexactly 142 U2_span=blade_velocity2; %constantbladerpmandradius wm2_span=cm2_span; %cm=wm w2_mean=wm2_span(r_geo_loc_min_error)/sind(beta2_mean); wu2_mean= sqrt (w2_mean^2 = wm2_span(r_geo_loc_min_error)^2); cu2_mean=U2_span(r_geo_loc_min_error) = wu2_mean; cu2_span=cu2_mean * (R_mean_geometric./radii_span2); %shouldbe squaremean,butnotusedinorig.design c2_span= sqrt (cu2_span.^2+cm2_span.^2); alpha2_span=asind(cm2_span./c2_span); wu2_span= = (U2_span = cu2_span); w2_span= sqrt (wm2_span.^2+wu2_span.^2); beta2_span=asind(wm2_span./w2_span); %interpolatevariablesatstation2to1fordifference calculations w2_resamp= interp1 (radii_span2,w2_span,radii_span1); c2_resamp= interp1 (radii_span2,c2_span,radii_span1); wu2_resamp= interp1 (radii_span2,wu2_span,radii_span1); cu2_resamp= interp1 (radii_span2,cu2_span,radii_span1); beta2_resamp= interp1 (radii_span2,beta2_span,radii_span1); alpha2_resamp= interp1 (radii_span2,alpha2_span,radii_span1); %plotdesignvariables ab1= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (beta1_analysis,radial_coord_analysis1) hold on plot (rel_vel_ang_analysis1,radial_coord_analysis1) legend ('\beta1_{calc}','\beta1_{fluent}') 143 subplot (2,2,2) plot (beta2_analysis,radial_coord_analysis2) hold on plot (rel_vel_ang_analysis2,radial_coord_analysis2) legend ('\beta2_{calc}','\beta2_{fluent}') subplot (2,2,3) plot (alpha1_analysis,radial_coord_analysis1) hold on plot (vel_ang_analysis1,radial_coord_analysis1) legend ('\alpha1_{calc}','\alpha1_{fluent}') subplot (2,2,4) plot (alpha2_analysis,radial_coord_analysis2) hold on plot (vel_ang_analysis2,radial_coord_analysis2) legend ('\alpha2_{calc}','\alpha2_{fluent}') saveas(ab1,"AngleDifference_fluenttome.png") ab2= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (beta1_analysis,radial_coord_analysis1) hold on plot (rel_vel_ang_analysis1 = 90,radial_coord_analysis1) legend ('\beta1_{calc}','\beta1_{fluent}') subplot (2,2,2) plot (beta2_analysis,radial_coord_analysis2) hold on plot (rel_vel_ang_analysis2 = 90,radial_coord_analysis2) legend ('\beta2_{calc}','\beta2_{fluent}') 144 subplot (2,2,3) plot (alpha1_analysis,radial_coord_analysis1) hold on plot ( = vel_ang_analysis1 = 90,radial_coord_analysis1) legend ('\alpha1_{calc}','\alpha1_{fluent}') subplot (2,2,4) plot (alpha2_analysis,radial_coord_analysis2) hold on plot ( = vel_ang_analysis2 = 90,radial_coord_analysis2) legend ('\alpha2_{calc}','\alpha2_{fluent}') saveas(ab2,"AngleDifference_fluenttome_adjusted.png") ad1= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (beta1_analysis = rel_vel_ang_analysis1,radial_coord_analysis1) legend ('\beta1_{calc} = \beta1_{fluent}','location','southoutside') subplot (2,2,2) plot (beta2_analysis = rel_vel_ang_analysis2,radial_coord_analysis2) legend ('\beta2_{calc} = \beta2_{fluent}','location','southoutside') subplot (2,2,3) plot (alpha1_analysis = vel_ang_analysis1,radial_coord_analysis1) legend ('\alpha1_{calc} = \alpha1_{fluent}','location','southoutside' ) subplot (2,2,4) plot (alpha2_analysis = vel_ang_analysis2,radial_coord_analysis2) legend ('\alpha2_{calc} = \alpha2_{fluent}','location','southoutside' ) saveas(ad1,"BladeAngleDifference.png") 145 bl1= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (beta1_span,radii_span1,'g == ') hold on plot (beta2_resamp,radii_span1,'g == ') plot (alpha1_span,radii_span1,'r = ') plot (alpha2_resamp,radii_span1,'r = ') hold off legend ('\beta1','\beta2','\alpha1','\alpha2','location',' eastoutside') xlabel ('Angles (degrees)') ylabel ('Radial Position (m)') title ('Design Conditions') %bl2=figure; subplot (2,2,2) plot (w1_span,radii_span1,'g == ') hold on plot (w2_resamp,radii_span1,'g == ') plot (c1_span,radii_span1,'r = ') plot (c2_resamp,radii_span1,'r = ') hold off legend ('W1','W2','C1','C2','location','eastoutside') xlabel ('Velocity (m/s)') ylabel ('Radial Position (m)') title ('Design Conditions') %bl3=figure; subplot (2,2,3) 146 plot (wu1_span,radii_span1,'g == ') hold on plot (wu2_resamp,radii_span1,'g == ') plot (cu1_span,radii_span1,'r = ') plot (cu2_resamp,radii_span1,'r = ') hold off legend ('Wu1','Wu2','Cu1','Cu2','location','eastoutside') xlabel ('Velocity (m/s)') ylabel ('Radial Position (m)') title ('Design Conditions') %bl4=figure; subplot (2,2,4) plot (wu2_resamp = wu1_span,radii_span1,'g == ') hold on plot (cu2_resamp = cu1_span,radii_span1,'r = ') hold off legend ('Wu2 = Wu1','Cu2 = Cu1','location','eastoutside') xlabel ('Velocity Change across Blade (m/s)') ylabel ('Radial Position (m)') title ('Design Conditions') saveas(bl1,"DesignConditions.png") bl20= figure ('Position', get (0,'Screensize')); plot (beta2_resamp = beta1_span,radii_span1,'g == ') hold on plot (alpha2_resamp = alpha1_span,radii_span1,'r = ') hold off legend ('\beta2 = \beta1','\alpha2 = \alpha1','location','southoutside' 147 ) xlabel ('Angle Change across Blade (degree)') ylabel ('Radial Position (m)') title ('Design Conditions') saveas(bl20,"DesignAngleDIfference.png") %plotbladevelocitycheck blch1= figure ('Position', get (0,'Screensize')); plot (U1_analysis_check,radial_coord_analysis1,'k = ') hold on plot (U2_analysis_check,radial_coord_analysis2,'r = ') plot (U1_span,radii_span1,'go = ') plot (U2_span,radii_span2,'b. = ') legend ('U1_{fluent}','U2_{fluent}','U1_{design}','U2_{design}',' location','southoutside') saveas(blch1,"UvelCheck.png") %plotfluentvs.designvariables bl5= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (W1_analysis,radial_coord_analysis1,'k = ') hold on plot (W2_analysis,radial_coord_analysis2,'r = ') plot (w1_span,radii_span1,'g == ') plot (w2_span,radii_span2,'b == ') hold off legend ('W1_{fluent}','W2_{fluent}','W1_{design}','W2_{design}',' location','eastoutside') %bl6=figure; 148 subplot (2,2,2) plot (C1_analysis,radial_coord_analysis1,'k = ') hold on plot (C2_analysis,radial_coord_analysis2,'r = ') plot (c1_span,radii_span1,'g == ') plot (c2_span,radii_span2,'b == ') hold off legend ('C1_{fluent}','C2_{fluent}','C1_{design}','C2_{design}',' location','eastoutside') %bl7=figure; subplot (2,2,3) plot (beta1_analysis,radial_coord_analysis1,'k = ') hold on plot (beta2_analysis,radial_coord_analysis2,'r = ') plot (beta1_span,radii_span1,'g == ') plot (beta2_span,radii_span2,'b == ') hold off legend ('\beta1_{fluent}','\beta2_{fluent}','\beta1_{design}','\ beta2_{design}','location','eastoutside') %bl8=figure; subplot (2,2,4) plot (alpha1_analysis,radial_coord_analysis1,'k = ') hold on plot (alpha2_analysis,radial_coord_analysis2,'r = ') plot (alpha1_span,radii_span1,'g == ') plot (alpha2_span,radii_span2,'b == ') hold off 149 legend ('\alpha1_{fluent}','\alpha2_{fluent}','\alpha1_{design}','\ alpha2_{design}','location','eastoutside') saveas(bl5,"FluentDesignComparison.png") %CalculateaveragedifferencesbetweenFluentanddesign deltaBeta1=beta1_analysis = beta1_span; deltaBeta2=beta2_analysis = beta2_span; deltaAlpha1=alpha1_analysis = alpha1_span; deltaAlpha2=alpha2_analysis = alpha2_span; cumulative_avg_beta1=0; cumulative_avg_beta2=0; cumulative_avg_alpha1=0; cumulative_avg_alpha2=0; for i=2: length (radial_coord_analysis1) cumulative_avg_beta1=cumulative_avg_beta1+0.5 * (deltaBeta1( i)+deltaBeta1(i = 1)) * (radial_coord_analysis1(i)^2 = radial_coord_analysis1(i = 1)^2); cumulative_avg_alpha1=cumulative_avg_alpha1+0.5 * ( deltaAlpha1(i)+deltaAlpha1(i = 1)) * (radial_coord_analysis1( i)^2 = radial_coord_analysis1(i = 1)^2); end for i=2: length (radial_coord_analysis2) cumulative_avg_beta2=cumulative_avg_beta2+0.5 * (deltaBeta2( i)+deltaBeta2(i = 1)) * (radial_coord_analysis2(i)^2 = radial_coord_analysis2(i = 1)^2); cumulative_avg_alpha2=cumulative_avg_alpha2+0.5 * ( deltaAlpha2(i)+deltaAlpha2(i = 1)) * (radial_coord_analysis2( i)^2 = radial_coord_analysis2(i = 1)^2); 150 end beta1_diff_area_avg=cumulative_avg_beta1/(tip_radius^2 = hub_radius^2); beta2_diff_area_avg=cumulative_avg_beta2/(tip_radius^2 = hub_radius^2); alpha1_diff_area_avg=cumulative_avg_alpha1/(tip_radius^2 = hub_radius^2); alpha2_diff_area_avg=cumulative_avg_alpha2/(tip_radius^2 = hub_radius^2); fprintf ('Area Averaged Quantities: \n') fprintf (' beta1diff = %g,\n beta2diff = %g,\n alpha1diff = %g,\n alpha2diff = %g,\n',... [beta1_diff_area_avg,beta2_diff_area_avg, alpha1_diff_area_avg,alpha2_diff_area_avg]) cumulative_mass_avg_beta1=0; cumulative_mass_avg_beta2=0; cumulative_mass_avg_alpha1=0; cumulative_mass_avg_alpha2=0; for i=2: length (radial_coord_analysis1) cumulative_mass_avg_beta1=cumulative_mass_avg_beta1+0.5 * ( deltaBeta1(i)+deltaBeta1(i = 1)) * ((radial_coord_analysis1(i )^2 = radial_coord_analysis1(i = 1)^2). * cm1_span(i)); cumulative_mass_avg_alpha1=cumulative_mass_avg_alpha1+ 0.5 * (deltaAlpha1(i)+deltaAlpha1(i = 1)) * (( radial_coord_analysis1(i)^2 = radial_coord_analysis1(i = 1) ^2). * cm1_span(i)); end 151 for i=2: length (radial_coord_analysis2) cumulative_mass_avg_beta2=cumulative_mass_avg_beta2+0.5 * ( deltaBeta2(i)+deltaBeta2(i = 1)) * ((radial_coord_analysis2(i )^2 = radial_coord_analysis2(i = 1)^2). * cm2_span(i)); cumulative_mass_avg_alpha2=cumulative_mass_avg_alpha2+ 0.5 * (deltaAlpha2(i)+deltaAlpha2(i = 1)) * (( radial_coord_analysis2(i)^2 = radial_coord_analysis2(i = 1) ^2). * cm2_span(i)); end beta1_diff_mass_avg=cumulative_mass_avg_beta1/((tip_radius^2 = hub_radius^2). * c1); beta2_diff_mass_avg=cumulative_mass_avg_beta2/((tip_radius^2 = hub_radius^2). * c1); alpha1_diff_mass_avg=cumulative_mass_avg_alpha1/((tip_radius^2 = hub_radius^2). * c1); alpha2_diff_mass_avg=cumulative_mass_avg_alpha2/((tip_radius^2 = hub_radius^2). * c1); fprintf ('Mass Averaged Quantities: \n') fprintf (' beta1diff = %g,\n beta2diff = %g,\n alpha1diff = %g,\n alpha2diff = %g,\n',... [beta1_diff_mass_avg,beta2_diff_mass_avg, alpha1_diff_mass_avg,alpha2_diff_mass_avg]) bl9= figure ('Position', get (0,'Screensize')); subplot (2,2,1) plot (deltaBeta1,radial_coord_analysis1,'k = ') hold on plot (deltaBeta2,radial_coord_analysis2,'r = ') 152 hold off legend ('\beta1_{fluent} = \beta1_{design}','\beta2_{fluent} = \beta2_{ design}','location','southoutside') %bl10=figure; subplot (2,2,2) plot (deltaAlpha1,radial_coord_analysis1,'k = ') hold on plot (deltaAlpha2,radial_coord_analysis2,'r = ') hold off legend ('\alpha1_{fluent} = \alpha1_{design}','\alpha2_{fluent} = \ alpha2_{design}','location','southoutside') subplot (2,2,3) text (0,1,strcat('\beta_1 mass average difference:',{' '}, num2str (beta1_diff_mass_avg),' degrees')) text (0,0,strcat('\beta_2 mass average difference:',{' '}, num2str (beta2_diff_mass_avg),' degrees')) xlim([ = 1,2]) ylim([ = 1,2]) axis off subplot (2,2,4) text (0,1,strcat('\alpha_1 mass average difference:',{' '}, num2str (alpha1_diff_mass_avg),' degrees')) text (0,0,strcat('\alpha_2 mass average difference:',{' '}, num2str (alpha2_diff_mass_avg),' degrees')) xlim([ = 1,2]) ylim([ = 1,2]) axis off 153 saveas(bl9,"FluentCalcBladeAngleDifference.png") %Findradiiofinterest %forturbineregion sep_locs= zeros (num_rows, length (sq_radii)); for k=1: length (sq_radii) for i=1:num_rows if radial_coord(i)>sq_radii(k) = rotating_body_mesh_size /2&&... radial_coord(i)sq_radii(k) = blade_face_mesh_size/2&&... radial_coord_blades(i)=long_val) Then ExitFor Else cCol=cCol+1 EndIf Next j column_select=cCol rRow=2 For j=2Tonum_velocity_rows = 1 If (Cells(rRow,1).Value>=lat_val And Cells(rRow+1, 1).Value<=lat_val) Then ExitFor Else rRow=rRow+1 EndIf Next j row_select=rRow 'Findhighestvelocitywithin(loopnum * 2)km Application.Wait( Now +1E = 05) Worksheets("FlowRates_Q90").Activate 170 cCol=column_select rRow=row_select highestvalue=Cells(rRow,cCol).Value For j= = loopnumToloopnum For k= = loopnumToloopnum If Cells(rRow+k,cCol+j).Value>=highestvalue Then highestvalue=Cells(rRow+k,cCol+j).Value column_inter=cCol+j row_inter=rRow+k j_inter= Abs (j) k_inter= Abs (k) Else EndIf Next k Next j IfCStr (column_inter)="0" Then column_final=column_select row_final=row_select distance_at_min=0 Else column_final=column_inter row_final=row_inter distance_at_min=(4 * j_inter * j_inter+4 * k_inter * k_inter)^0.5 EndIf If distance_at_min>2 * loopnum_max Then ExitFor 171 EndIf 'Changeflowvelocity Application.Wait( Now +1E = 05) Worksheets("Solver_withoutbatteries").Activate Worksheets("Solver_withoutbatteries").Range("$H"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(row_final, column_final).Value Worksheets("Solver_withoutbatteries").Range("$R"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(row_final,1).Value Worksheets("Solver_withoutbatteries").Range("$S"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(1,column_final). Value Worksheets("Solver_withoutbatteries").Range("$T"&i+2).Value =Worksheets("FlowRates_Q90").Cells(row_final,column_final). Value 'use2.8m/slimitforsmarthydromonofloatturbine,changefor others 'inputroundinglogic Worksheets("Solver_withoutbatteries").Activate If Worksheets("Solver_withoutbatteries").Range("H"&i+2). Value>2.8 Then Worksheets("Solver_withoutbatteries").Range("I"&i+2).Value= 2.8 Else Worksheets("Solver_withoutbatteries").Range("I"&i+2).Value= Worksheets("Solver_withoutbatteries").Range("H"&i+2). Value 172 EndIf Worksheets("case2_gen").Range("$F$2").Value=Worksheets(" Solver_withoutbatteries").Range("I"&i+2).Value Application.Wait( Now +1E = 05) Worksheets("case2_gen").Activate Application.Run"Solver.xlam!SolverReset" 'setupnewanalysis 'SolverOk(SetCell,MaxMinVal,ValueOf,ByChange,Engine, EngineDesc) '1Maximize '2Minimize '3Matchaspecificvalue Application.Run"Solver.xlam!SolverOk","$Q$28",2,,"$J$8,$E$6 ",2,"GRG Nonlinear" 'SolverOptions(MaxTime,Iterations,Precision,AssumeLinear, StepThru, 'Estimates,Derivatives,SearchOption,IntTolerance,Scaling, Convergence,AssumeNonNeg, 'PopulationSize,RandomSeed,MultiStart,RequireBounds, MutationRate,MaxSubproblems, 'MaxIntegerSols,SolveWithout,MaxTimeNoImp) Application.Run"Solver.xlam!SolverOptions",_ 100000,100000,1E = 12,False,False,_ 2,2,1,1,True,1E = 12,True,_ 100,[],False,True,0.075,100000,_ 100000,False,30 'addconstraints 173 'SolverAdd(CellRef,Relation,FormulaText) '1<= '2= '3>= '4CellsreferencedbyCellRefmusthavefinalvaluesthat areintegers. '5CellsreferencedbyCellRefmusthavefinalvaluesof either0(zero)or1. '6CellsreferencedbyCellRefmusthavefinalvaluesthat arealldifferentandintegers. Application.Run"Solver.xlam!SolverAdd","$J$8",4,0 Application.Run"Solver.xlam!SolverAdd","$E$6",4,0 Application.Run"Solver.xlam!SolverAdd","$L$4:$L$28",3,"$D$4: $D$28" 'runtheanalysis 'SolverSolve(UserFinish,ShowRef) result=Application.Run("Solver.xlam!SolverSolve",True) 'finishtheanalysis 'SolverFinish(KeepFinal,ReportArray,OutlineReports) Application.Run"Solver.xlam!SolverFinish" 'reportonsuccessofanalysis 'Result=0,Solutionfound,optimalityandconstraints satisfied '1,Converged,constraintssatisfied '2,Cannotimprove,constraintssatisfied '3,Stoppedatmaximumiterations '4,Solverdidnotconverge 174 '5,Nofeasiblesolution '6Solverstoppedatuser'srequest. '7TheconditionsforAssumeLinearModelarenotsatisfied . '8TheproblemistoolargeforSolvertohandle. '9Solverencounteredanerrorvalueinatargetor constraintcell. '10Stopchosenwhenmaximumtimelimitwasreached. '11Thereisnotenoughmemoryavailabletosolvethe problem. '12AnotherExcelinstanceisusingSOLVER.DLL.Tryagain later. '13Errorinmodel.Pleaseverifythatallcellsand constraintsarevalid. '14 = Solverfoundanintegersolutionwithintolerance.All constraintsaresatisfied(14). '15 = Stopchosenwhenthemaximumnumberof[integeror feasible]solutionswasreached(15). '16 = Stopchosenwhenthemaximumnumberof[integer] subproblemswasreached(16). '17 = Solverconvergedinprobabilitytoaglobalsolution (17). '18 = Allvariablesmusthavebothupperandlowerbounds (18). '19 = Variableboundsconflictinbinaryoralldifferent constraint(19). '20 = Lowerandupperboundsonvariablesallownofeasible 175 solution(20). If result=14 Or result=0 Then 'SetInfoBox=CreateObject("WScript.Shell") ''Setthemessageboxtocloseafter10seconds 'CHKTime=0.5 'SelectCaseInfoBox.Popup("Solverfoundasolution,Result#" +CStr(Result),_ 'CHKTime,"SOLUTIONFOUND",0) 'Case1, = 1 'EndSelect 'MsgBox"Solverfoundasolution,Result#"+CStr(Result), vbInformation,"SOLUTIONFOUND" GoToREPORTING Else 'MsgBox"Solverwasunabletofindasolution,Result#"+ CStr(Result),vbExclamation,"SOLUTIONNOTFOUND" 'ExitFor GoToERRORFOR EndIf ERRORFOR: Application.Wait( Now +1E = 05) Worksheets("case2_gen").Range("E6").Value=1 Worksheets("case2_gen").Range("J8").Value=10 Application.Wait( Now +1E = 05) Worksheets("case2_gen").Activate Application.Run"Solver.xlam!SolverReset" Application.Run"Solver.xlam!SolverOk","$Q$28",2,,"$J$8, 176 $E$6",2,"GRG Nonlinear" Application.Run"Solver.xlam!SolverOptions",_ 100000,100000,1E = 12,False,False,_ 2,2,1,1,True,1E = 12,True,_ 100,[],False,True,0.075,100000,_ 100000,False,30 Application.Run"Solver.xlam!SolverAdd","$J$8",4,0 Application.Run"Solver.xlam!SolverAdd","$E$6",4,0 Application.Run"Solver.xlam!SolverAdd","$L$4:$L$28",3," $D$4:$D$28" result=Application.Run("Solver.xlam!SolverSolve",True) Application.Run"Solver.xlam!SolverFinish" If result=14 Or result=0 Then GoToREPORTING Else GoToERRORFOR2 EndIf ERRORFOR2: Application.Wait( Now +1E = 05) Worksheets("case2_gen").Range("E6").Value=10 Worksheets("case2_gen").Range("J8").Value=1 Application.Wait( Now +1E = 05) Worksheets("case2_gen").Activate Application.Run"Solver.xlam!SolverReset" Application.Run"Solver.xlam!SolverOk","$Q$28",2,,"$J$8, $E$6",2,"GRG Nonlinear" Application.Run"Solver.xlam!SolverOptions",_ 177 100000,100000,1E = 12,False,False,_ 2,2,1,1,True,1E = 12,True,_ 100,[],False,True,0.075,100000,_ 100000,False,30 Application.Run"Solver.xlam!SolverAdd","$J$8",4,0 Application.Run"Solver.xlam!SolverAdd","$E$6",4,0 Application.Run"Solver.xlam!SolverAdd","$L$4:$L$28",3," $D$4:$D$28" result=Application.Run("Solver.xlam!SolverSolve",True) Application.Run"Solver.xlam!SolverFinish" If result=14 Or result=0 Then GoToREPORTING Else GoToERRORFOR3 EndIf ERRORFOR3: Application.Wait( Now +1E = 05) Worksheets("case2_gen").Range("E6").Value=1 Worksheets("case2_gen").Range("J8").Value=100 Application.Wait( Now +1E = 05) Worksheets("case2_gen").Activate Application.Run"Solver.xlam!SolverReset" Application.Run"Solver.xlam!SolverOk","$Q$28",2,,"$J$8, $E$6",2,"GRG Nonlinear" Application.Run"Solver.xlam!SolverOptions",_ 100000,100000,1E = 12,False,False,_ 2,2,1,1,True,1E = 12,True,_ 178 100,[],False,True,0.075,100000,_ 100000,False,30 Application.Run"Solver.xlam!SolverAdd","$J$8",4,0 Application.Run"Solver.xlam!SolverAdd","$E$6",4,0 Application.Run"Solver.xlam!SolverAdd","$L$4:$L$28",3," $D$4:$D$28" result=Application.Run("Solver.xlam!SolverSolve",True) Application.Run"Solver.xlam!SolverFinish" If result=14 Or result=0 Then GoToREPORTING Else GoToERRORFOR4 EndIf ERRORFOR4: Application.Wait( Now +1E = 05) Worksheets("case2_gen").Range("E6").Value=100 Worksheets("case2_gen").Range("J8").Value=1 Application.Wait( Now +1E = 05) Worksheets("case2_gen").Activate Application.Run"Solver.xlam!SolverReset" Application.Run"Solver.xlam!SolverOk","$Q$28",2,,"$J$8, $E$6",2,"GRG Nonlinear" Application.Run"Solver.xlam!SolverOptions",_ 100000,100000,1E = 12,False,False,_ 2,2,1,1,True,1E = 12,True,_ 100,[],False,True,0.075,100000,_ 100000,False,30 179 Application.Run"Solver.xlam!SolverAdd","$J$8",4,0 Application.Run"Solver.xlam!SolverAdd","$E$6",4,0 Application.Run"Solver.xlam!SolverAdd","$L$4:$L$28",3," $D$4:$D$28" result=Application.Run("Solver.xlam!SolverSolve",True) Application.Run"Solver.xlam!SolverFinish" If result=14 Or result=0 Then GoToREPORTING Else GoToREPORTING EndIf REPORTING: turbinerating=Worksheets("case2_gen").Range("Q4").Value numberhouseholds=Worksheets("Solver_withoutbatteries").Range(" G"&i+2).Value loopnum_double= CDbl (loopnum) Application.Wait( Now +1E = 05) Worksheets("DistanceCostCurves").Activate 'Keeptrackofcostcurve,andadd1000$USDper1kmofcabling, per24kWofhydro(40A * 600V) If turbinerating>24000 Then householdcost=Worksheets("case2_gen").Range("$Q$12").Value+ (1000 * distance_at_min) * (turbinerating/24000)/ numberhouseholds Else householdcost=Worksheets("case2_gen").Range("$Q$12").Value+ (1000 * distance_at_min)/numberhouseholds 180 EndIf Cells(i+2,loopnum+2).Value=householdcost Cells(i+2+17+1,loopnum+2).Value=distance_at_min If householdcost0.9 * Round (Cells(row_final,column_final).Value ,0)) Then If (j= = 1 Or (j=0 And k= = 1)) Then River_loc_col_pre=column_final+j River_loc_row_pre=row_final+k River_flow_pre=Cells(row_final+k,column_final 181 +j).Value EndIf If (j=1 Or (j=0 And k=1)) Then River_loc_col_post=column_final+j River_loc_row_post=row_final+k River_flow_post=Cells(row_final+k, column_final+j).Value EndIf If River_loc_col_pre=0 Or River_loc_col_post=0 Then If (k= = 1 Or (k=0 And j= = 1)) Then River_loc_col_pre=column_final+j River_loc_row_pre=row_final+k River_flow_pre=Cells(row_final+k, column_final+j).Value EndIf If (k=1 Or (k=0 And j=1)) Then River_loc_col_post=column_final+j River_loc_row_post=row_final+k River_flow_post=Cells(row_final+k, column_final+j).Value EndIf EndIf EndIf Next k Next j 'calculatedamatISTinsertionlocation 182 Application.Wait( Now +1E = 05) Worksheets("Elevations").Activate Elevation_site=Cells(row_final,column_final) Elevation_pre=Cells(River_loc_row_pre,River_loc_col_pre) Elevation_post=Cells(River_loc_row_post,River_loc_col_post) Application.Wait( Now +1E = 05) Worksheets("Depths").Activate Depth_site=Cells(row_final,column_final) Depth_pre=Cells(River_loc_row_pre,River_loc_col_pre) Depth_post=Cells(River_loc_row_post,River_loc_col_post) Application.Wait( Now +1E = 05) Worksheets("RiverVelocities_Q90").Activate Velocity_site=Cells(row_final,column_final) Velocity_pre=Cells(River_loc_row_pre,River_loc_col_pre) Velocity_post=Cells(River_loc_row_post,River_loc_col_post) Head_site=Elevation_site+Depth_site+0.5 * Velocity_site * Velocity_site/9.81 Head_pre=Elevation_pre+Depth_pre+0.5 * Velocity_pre * Velocity_pre/9.81 Head_post=Elevation_post+Depth_post+0.5 * Velocity_post * Velocity_post/9.81 Dam_potential_site=highestvalue * 998.2 * 9.81 * ( WorksheetFunction.Max( Abs (Head_pre = Head_site), Abs ( Head_site = Head_post))) EndIf Next loopnum Application.Wait( Now +1E = 05) 183 Worksheets("Solver_withoutbatteries").Activate Worksheets("Solver_withoutbatteries").Range("$H"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(lat_min_loc, long_min_loc).Value If Worksheets("Solver_withoutbatteries").Range("H"&i+2). Value>2.8 Then Worksheets("Solver_withoutbatteries").Range("I"&i+2).Value= 2.8 Else Worksheets("Solver_withoutbatteries").Range("I"&i+2).Value= Worksheets("Solver_withoutbatteries").Range("H"&i+2). Value EndIf Worksheets("Solver_withoutbatteries").Range("$R"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(lat_min_loc,1). Value Worksheets("Solver_withoutbatteries").Range("$S"&i+2).Value =Worksheets("RiverVelocities_Q90").Cells(1,long_min_loc). Value Worksheets("Solver_withoutbatteries").Range("$T"&i+2).Value =Worksheets("FlowRates_Q90").Cells(lat_min_loc,long_min_loc ).Value Worksheets("Solver_withoutbatteries").Range("J"&i+2).Value= householdcost_minimum Worksheets("Solver_withoutbatteries").Range("K"&i+2).Value= householdcost_minimum * numberhouseholds Worksheets("Solver_withoutbatteries").Range("N"&i+2).Value= 184 number_generators_minimum Worksheets("Solver_withoutbatteries").Range("O"&i+2).Value= number_panels_minimum Worksheets("Solver_withoutbatteries").Range("P"&i+2).Value= diff_minimum Worksheets("Solver_withoutbatteries").Range("Q"&i+2).Value= result Worksheets("Solver_withoutbatteries").Range("J"&i+2). NumberFormat="###,###,###,###" Worksheets("Solver_withoutbatteries").Range("K"&i+2). NumberFormat="###,###,###,###" Worksheets("Solver_withoutbatteries").Range("L"&i+2). NumberFormat="###,###,###,###" Worksheets("Solver_withoutbatteries").Range("M"&i+2). NumberFormat="###,###,###,###" Worksheets("Solver_withoutbatteries").Range("N"&i+2). NumberFormat="###,###,###,##0" Worksheets("Solver_withoutbatteries").Range("O"&i+2). NumberFormat="###,###,###,##0" Worksheets("Solver_withoutbatteries").Range("P"&i+2). 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