ALTERNATIVEMETHODSFORMITIGATINGNATURALPHOTOVOLTAICVARIABILITY:DYNAMICHVACLOADCOMPENSATIONANDCURTAILEDPV

POWER

BY

JOHNALEXANDERMAGERKOIII

THESIS

SubmittedinpartialfulfillmentoftherequirementsforthedegreeofMasterofScienceinElectricalandComputerEngineering

intheGraduateCollegeoftheUniversityofIllinoisatUrbana-Champaign,2016

Urbana,Illinois

Adviser: ProfessorPhilipKrein

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AbstractContinuedintegrationofrenewableenergyresourcesontotheelectricgridincreasesvariabilityand

decreasesgridstability.Energystoragecanhelpmitigatesomeoftheseeffects,butconventionalenergy

storagesuchasbatteriesistypicallyexpensiveandhasotherdisadvantagessuchasroundtrip

inefficiencyandlimitedlifetime.Real,high-speedsolarpaneldataisusedtocharacterizethestochastic

energyoutputofPVsources,andthenumerouschallengesfacedandmethodsusedwhenmanipulating

thisreal-lifedatasetaredetailed.Twoalternativemethodsarethenpresentedtoabsorborreducethe

variabilityimposeduponthegridbyPVorothergeneration.(1)DynamicHVACloadcompensationis

showntoabsorbor“filter”short-termPVvariabilityandactaseffectivegridinertia.Aproposed

Butterworthfilterpowertargettechniquebalancesenergystoragedemandswithdecreased

uncertainty.Asmall-scalemodelofavariablespeedblowerandfanisusedtoprovideaconversion

betweenfanspeedandpowerconsumedandtoestimatefilteringlimitationsimposedbyundesirable

acousticeffects.Consideringtheacoustic,physical,andthermallimitationssimultaneously,thevariation

absorptionorfilteringcapabilityofdynamicHVACloadcompensationisanalyzedforvariousbuilding

sizesandon-sitePVpenetrations.Theresultingreductioninbatterystoragecapacityandutilizationis

brieflyinvestigated.(2)PVoperatingreservecurtailmentisintroduced.ThesameButterworthfilter

powerset-pointisused,itsimplementationisshownasfeasiblethroughsimulation,andthevariability

reductionisquantifiedintwodifferentways.TheclaimismadethatPVshouldbetreatedandpriced

likeconventionalgridgeneration,whichisresponsibleforbothenergyandregulationcapabilities.PV

operatingreservecurtailmentisthenshowntobeeconomicallyfavorableforatleastsomelevelof

reserve.Finally,aproposedmetricofoptimalityispresentedthatbalancesenergyproductionwith

decreasedvariability.

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Acknowledgments

Tomyever-supportivefamilywhohasledbyexampleandprovidedtheencouragementandadvicethat

enabledmetoreachthismilestone.

ThisworkwasprimarilysupportedbytheGraingerCenterforElectricMachineryandElectromechanics

attheUniversityofIllinoiswithadditionalsupportfromtheSiebelEnergyInstitute.

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Contents

1. IntroductionandMotivation..............................................................................................................1

1.1. Windandsolaras“negativeloads”............................................................................................1

1.2. Variabilityandinertiainthegrid................................................................................................2

1.3. Understandingandquantifyingtheproblem.............................................................................3

1.4. Energystorageandproposedalternatives.................................................................................3

1.4.1. Traditionalenergystoragesolutions......................................................................................3

1.4.2. VariablespeeddrivesinHVAC................................................................................................4

1.4.3. CurtailedPVpower.................................................................................................................6

2. High-speedSolarData........................................................................................................................7

2.1. Dataacquisitionhistory..............................................................................................................7

2.2. Capturingallpossibledynamics..................................................................................................8

2.2.1. Demonstratingsmoothdynamicsduringcharacteristicallynoisyperiod..............................8

2.2.2. Verificationduringflickeringshadows.................................................................................10

2.2.3. Investigationofdynamicsintermsofpotentialenergyloss................................................11

2.3. Dataprocessingchallengesandapproaches............................................................................13

2.3.1. Missingdata..........................................................................................................................13

2.3.2. Substituteddataforpublicuse.............................................................................................14

2.3.3. Datasynchronization............................................................................................................16

2.3.4. Parametercalculation...........................................................................................................17

2.4. Slowmetercurrentsaturationandactiontaken......................................................................20

2.5. PublicandauxiliaryusesforPVdataset...................................................................................20

3. DynamicHVACLoadCompensation.................................................................................................22

3.1. Desiredsolarpowervariationabsorption................................................................................22

3.2. Scalemodelsetupandfan-power/-speedprofiling..................................................................25

3.2.1. Smallblowercharacterization..............................................................................................26

3.2.2. Scalingassumptions..............................................................................................................27

3.3. Variationabsorptioncapability.................................................................................................27

v

3.3.1. Amplitudevariancebounds..................................................................................................28

3.3.2. Rampratelimit.....................................................................................................................29

3.4. EffectivenessofdynamicHVACcompensation.........................................................................32

3.4.1. Reducedbatterystoragerequirement.................................................................................34

4. PVOperatingReserveCurtailment...................................................................................................36

4.1. Operatingreservecurtailmentscheme....................................................................................36

4.2. PVsystemsasagridresource...................................................................................................37

4.3. EconomicjustificationofPVcurtailment..................................................................................38

4.4. Measuresofvariabilityandoptimality.....................................................................................40

5. Implementationanalysis..................................................................................................................43

5.1. Incrementalconductance–areview........................................................................................43

5.1.1. Conventionalalgorithm........................................................................................................43

5.1.2. Modifiedalgorithm...............................................................................................................44

5.2. Modelingprocedureandverification.......................................................................................45

5.2.1. Stage1:Basecase.................................................................................................................46

5.2.2. Stage2:Averagecircuitmodel.............................................................................................46

5.2.3. Stage3:Constantcurtailment..............................................................................................47

5.2.4. Look-uptablecreation..........................................................................................................48

5.2.5. Butterworthcalculation........................................................................................................50

5.2.6. Results..................................................................................................................................51

5.3. Economicjustificationforimplementation..............................................................................51

6. Conclusion........................................................................................................................................54

6.1. Futurework...............................................................................................................................55

References..................................................................................................................................................57

1

1. IntroductionandMotivationIntermittentrenewableenergyresourcesarerapidlybecomingsignificantplayersinthepower

generationlandscape[1],buttheyhavebeenshowntobeextremelyvariable,evenovershorttime

scalesofsecondstotensofseconds.Solarinparticularcanexhibitrapidpowerchangesinthevicinityof

80%peakpowerondayswhereintermittentcloudsblockthesun.Figure1.1representsonesuchtypical

daywithintermittentcloudcover.Thisunpredictabilitycoupledwithreducedtraditionalgenerationthat

solarisreplacingthreatensthestabilityandreliabilityoftheelectricgrid[2].Thedefaultsolutionto

thesechallengesistypicallyenergystorageintheformofbatteries,butthisthesisfocusesoncheap,

partial,alternativesolutionsthatprovidenumerousbenefitswithouttheneedforsignificantadditional

costorhardware.

Figure1.1.Samplepoweroutputfrom20WsolarpaneldemonstratingrapidchangesinPVpoweroutput.

1.1. Windandsolaras“negativeloads”Thefundamentalkeytosuccessfuloperationoftheelectricgridismaintainingpowerbalanceatall

times.Thatmeansthatateveryinstantintimepowerdemandedmustbemetbypowersupplied.

Thankstoanumberofmarketstructuresandgridcontrols,small-tomid-sizeelectricityconsumers

couldturnonandoffanyelectricload,unannounced,atanytime,andthegridcouldmaintainstable

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operation.Whenwindandsolarenergygeneration,specificallyphotovoltaics(PV),wereintroducedto

thegrid,theyweretreatedinthesamewayasloadshadbeen;independentlyownedwindandsolar

couldproducelargelyunregulatedamountsofpowerwheneveritwasavailable.Despitebeingelectric

generationunits,neitherwindnorsolarwereoriginallyresponsibleformaintainingstabilityorreliability

oftheelectricgrid.Incontrast,theywereincreasingvariabilityanduncertainty.Forthisreason,these

renewableresourcesweredeemed“negativeload”astheybehavedjustliketypicalelectricloadsmight

withtheexceptionthattheyproducedpowerratherthanconsumedit,andthereforeutilitycompanies

couldnotchargethemforthepowerfloworvariationinpowerthattheyproduced.Paymentstructures

forelectricityavailabilityinsuranceorelectricitypricesforreverseflowareoutsidethescopeofthis

thesis;however,thecostofvariabilityimposeduponthegridisrelevant.Arguably,aswindandsolar

becomeincreasinglysignificantsourcesofenergyandastheircostscontinuetofall,they,asgeneration

sources,shouldberesponsibleformitigatingsome,ifnotall,oftheirvariability.Thefocusofthisthesis

isentirelyonsolarPVgeneration,thoughmanyofthesameproblemsandpotentialsolutionsexistfor

windorotherresourcesaswell.

1.2. VariabilityandinertiainthegridUnlesseverygeneratorandloadschedulesitsfutureactivities,temporaryimbalanceswillbeintrinsicto

thegrid,andthisisnormal;smallload-changevariationsoccurallthetime,andthegridhasoperated

satisfactorilywiththeseandmuchlargerdisturbances(suchaslightning,faults,orgeneratoroutages)

formanydecades.Thekeytogridstabilityistheinertiafoundmostlyinlargeturbinegenerators.Any

timeagriddisturbanceoccurs,therotationalspeedoftheon-linegeneratorschanges,buttheirlarge

inertiakeepsthemmoving.Thisformofenergystoragepermitsgovernorsorotherfastcontrol

mechanismstomaintainsynchronousoperationofgeneratorsandthusstabilityofthegrid.

Unfortunately,PVgeneratorsconnecttothegridthroughpowerelectronicinverters,andtheydonot

possessanyinherentinertiaorsignificantenergystorage;changesinirradianceonasolarpanel

translatetonearinstantaneouschangesinelectricalpoweroutput.Ontopofthis,asPVproducesmore

andmorepower,traditionalgeneratorswillbetakenoff-line,furtherreducingtheavailablestabilizing

inertiaonthegridandreplacingpredictable,controllablegenerationwithhithertostochasticsources.

IEEEstandard1547compoundedalloftheseissuesbyrequiringinverterstodisconnectduringfaults,

thoughsuchstandardshavebeenrevisedinrecentyearstoallowforlow-voltageridethrough[3].

Nevertheless,thetakeawayisthatcontinuedpenetrationofdistributedPVsystemsisnotsustainable

unlesstheuncertaintyandstabilityissuescanbeaddressed.

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1.3. UnderstandingandquantifyingtheproblemToaddresstheissueofPVvariability,itisimportanttoidentifytherelevanttimescalesusinglong-term,

reallifesolardata.Nootherrandompatterngeneratorcanaccuratelysimulatethestochasticityofreal-

lifechangesinirradiance,atleastnotuntilitiswellunderstood.Oneofthemajorfociofthisthesisisto

quantifythevariabilityatvarioustimescalesandensurethatallpossibledynamicswerecapturedand

consideredwhenperformingthisanalysis.Previousworkhasdifferedinitsdefinitionofhigh-frequency

solardatawithsamplingratesrangingfrom1min[4]to20s[5],[6]andtoppingoutatabout1Hz[7],

[8].Aswillbeshown,allofthesefallwellshortofthesamplingfrequencyrequiredtocaptureall

possiblefluctuations.Chapter2willdetailtheoriginsofthereal-lifedatausedandtheassertionthatthe

testsetupcapturedallpossibledynamics,discusschallengesencounteredinusingtherawdataset,

outlinetheproceduresusedtocleanupthedatasetandmakeituseable,andpresentsomeresultson

whatwasdeemedtobethemagnitudeofvariationassociatedwithvarioustimescales.

1.4. EnergystorageandproposedalternativesAfterdeterminingtheextentofvariabilityduringtheday,thequestionbecomeshowtomitigateit.In

thisthesis,thefocusislargelyonshort-termdiurnalstorageasopposedtoovernight,multi-day,or

seasonalstoragerequirements(thoughthermalstorageforsuchdurationsispossible,suchasfull-day

energystoragewithice[9]orphasechangematerials[10]).Todate,therearethreemainstrategiesfor

absorptionormitigationofPVinducedgridvariationswithbatterystoragebeingthemostcommon

approach.Theothertwoaregenerallycalleddemand-sideresponseandcurtailedPV.Variationson

thesetwolatterstrategieswillbethefocusofthisthesis.

1.4.1. Traditionalenergystoragesolutions

Traditionalenergystoragetypicallyconsistsofalargebankofbatteries(orsupercapacitors)[11]–[13].

TheseunitseitherconnecttothePVstringDCbus(Figure1.2.a)orthroughabidirectionalconverterto

anaccircuitbreakerorgrid(Figure1.2.b).Therearesomepositiveaspectsofbatteriesasavariability

reductionsolution.Thesystemcanbehighlymodularandisthereforeexpandableandrelativelyeasyto

implementasapost-marketsolution.Unlikethealternativesolutionsthatwillbepresented,batteries

canalsoenablelong-termenergystorageinplaceof,oreveninadditionto,short-termvariability

reduction.Suchcapabilityhighlightsthecyclinglimitationassociatedwithbatteries,however.Batteries

designedforlong-termdeepdischargeareusuallynotalsocapableofshort,high-powerburstswithout

degradingthebatterylifetime(thenumberoftimesitcanbechargedanddischargedbeforerequiring

replacement).Inaddition,allbatterystoragesolutionspresentpossiblechemicalandfirehazards;they

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alsosufferfromround-tripinefficiencies,i.e.energylossesassociatedwithvoltageconversion,

Coulombicefficiencies,andotherlossesassociatedwithcharginganddischarging.Perhapsthelargest

downsidetobatterystorageiscost.Long-termgoalsof$150/kWhand$0.010/kWh/cycle

($10/MWh/cycle)ofcycledenergyhavebeendiscussedforstorage[14].Incontrast,thetwo

alternativesproposedherecostverylittletoimplementandshouldbecheaperalternativesoverall,

evenwhentakingintoaccountthecostofenergylosses.Othersolutionssuchassupercapacitorbanks

orflywheelswerenotinvestigated,thoughtheysufferfromtheirownshort-comings,primarilycost.

(a)

(b)

Figure1.2.EnergyflowforaPVsystemwithbatterystoragewhere(a)thebatteryisconnectedtothedcbusand(b)the

batteryisconnectedthroughabidirectionalinverterontothegridside.

1.4.2. VariablespeeddrivesinHVAC

Energy-efficientbuildings,includingseveralnet-zeroenergycommercialbuildings,havebeen

constructedaroundtheglobe.Researchactivitiesonthistopichaveincreasedinrecentyears[15]–[18],

andmanyoccupantshaveshowninterestinhavingnet-zeroenergybuildingsastheirfutureofficessuch

asthenewApple“Spaceship”inCupertino,California[19].Energyefficientornet-zeroenergybuildings

oftenincludeonsitephotovoltaic(PV)solarpanelsthat,asmentioned,providenon-constantpowerthat

canvaryrapidly.ConsideringthisinconstancytorepresentanunwantedacsignalfromaPVsystem,a

suitablefiltercouldbeimplementedbutwouldrequirestorage.Ifinsteadoneutilizesthethermal

storagecapacityorthermalinertiainherentinabuilding,thenHVAC(heating,ventilation,andair-

conditioning)systemadjustmentcanemulateelectricalstorage,muchlikeanelectricswingbus[20]–

SolarPanel dc/dcConverter dc/acInverter PowerGrid

dc/dcConverter

SolarPanel dc/dcConverter dc/acInverter PowerGrid

dc/dcConverter dc/acInverter

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[24].Toclarify,afterconvertingelectricitytothermalenergy,thereversewouldnottakeplaceassuch

conversionisinefficient.Instead,the“release”stageofthisenergystoragewouldbeexperiencedwhen

anHVACsystemconsumeslessenergythanitotherwisewouldtoheatorcoolthegivenspace.Suchan

electricswingbuscouldoffsetfastvariationsoflocalsolarpowerfromagridperspectivewithreduced

needforconventionalstorage.Thescalingpotentialissizeable,giventhatnearly40%ofannualU.S.

energyisconsumedinresidentialandcommercialbuildings[25]withnearlyhalfofthatconsumedby

HVACsystems[26].

ThisthesiswilldemonstrateinChapter3howintelligentcontrolofHVACdrivescancompensate,within

predeterminedfrequencyandamplitudelimits,foronsitesolarpowerovershorttimeintervalswithout

disruptingbuildingtemperatureandcomfort.Theprocessisbasedonconceptsin[20]–[22].In

particular,[20]showshowbandwidthconceptscantakeadvantageofHVACdynamicadjustmentto

offsetenergyresourcevariability.Powerelectronicsenablesthiscontrolviadc-dcconverters,inverter-

baseddrives,andotherexistinghardware,asillustratedinFigure1.3.Theresultsformallytake

advantageofthermalenergystorage,butinthisthesistheemphasisisonmitigatingfastdynamic

variability,moreakintotreatingHVACasaccessingthermalinertia.Utilizingthermalinertiacanalleviate

theneedforinherentlyexpensive,fast-varying,grid-side(orbuilding-side)resources.Thisisnearly

equivalenttoplacingalow-passfilteronabuilding’snetgenerationandusage,requiringgrid-side

assistanceonlywhenchangesinload-sidedemandpersistbeyondanextendedinterval[27].Giventhe

slowthermalresponseofabuilding,wemightanticipatethattimescalesofafewminutesorfastercan

beusedtoadvantagetooffsetresourcevariabilitywithoutnoticeableimpactonoccupants.

Figure1.3.Energyflowinsideabuildingwithvarioustypesofconvertersthatmaybeutilizedtoimplementdynamicenergy

filtering.

AfundamentaladvantageofHVACadjustmentforeffectivedynamicthermalstorageisthatitis

relativelyeasytoimplement.Conventionalbuildingenergymanagementsystemsandthermostatsare

designedtoperforminslowcontrolloops,ontimescalesofminutes.HVACadjustmentcanusetime-

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scaleseparationandstayawayfromthis“effectivedc”loopaction.Inthissense,anacfeedforward

signalisinjectedintoadrivetoadjustpowerflowonfasttimescales,whileavoidinginterferenceon

slowtimescales.TheaverageperformanceoftheHVACsystemremainsintact,andthefastadjustment

canbemadetransparenttousers.

1.4.3. CurtailedPVpower

Insteadofusingstorageelementsorcreativealternativessuchasdynamicloadcompensationwith

HVAC,PVvariabilitycanbepartiallyreducedatthesource,whichinthisanalysiswouldmeanatthe

photovoltaicmodule.ThisistheideaofPVcurtailmentbasedonoperatingreserve:sacrificingabitof

energyproductionforareductioninuncertaintyandvariability.PVcurtailmentisnotespeciallynew,

butitistypicallyusedasalastresortwhenvoltageriseondistributionlinesbecomesproblematic[28].

Runningwithoperatingreserveisalsonotnewandhasbeenshowntobeeconomicalforwindenergy

[29],butpoorimplementationandworriesaboutcosteffectivenessmayhavepreviouslylimitedits

adoptionforPV.

CostinparticularhastypicallybeencalculatedwiththemindsetthatPVis,andshouldbe,treatedas

negativeload.Therefore,curtailmenthasanopportunitycostequaltothecostofenergy(below

$0.05/kWhforsystemswith25yearwarranties)timestheamountofenergysacrificed.Thisthesiswill

makethecaseinChapter4thatthisisanincompletepicturesinceintermittencyandinconsistentgrid

supportcapabilitiesmeanthatPVsystemscannotbetradedagainstmostelectricitygeneration

resources.Acomparablecoststructurewouldincludestorage.ContinuingcostreductionsthattakePV

belowcostparityintroducemoredirectopportunitiesformitigatingintermittencyandprovidingactive

gridsupport.Chapter4willdiscusshowdecreasesinPVsystemcostscanbeleveragedagainststorage

andgridsupporttoprovide“true”system-levelcostparitycomparabletolarge,cyclingutilityplants.

Curtailmenthastypicallybeentreatedasanad-hocsolutiontoproblemssuchasovervoltage[30].Ithas

beendoneoutofnecessityandthereforeonlyaffectsperiodsofhighorpeakpoweroutput.Ithasalso

beenunidirectional–abletobackoffofpowerproduction,butunabletoprovideadditionalpower

capability.Theproposedmethodofoperatingreservecurtailmentprovidesbothpositiveandnegative

operatingheadroom,enablesvariabilityreductionthroughoutthefullsolarday,anddoesnotrestrict

overvoltageprotectionalgorithms.Ifimplementedproperly,PVcurtailmentwithoperatingreserve

couldeconomicallytransformPVintoagridresourceratherthanagridnuisanceandenabledeeper

penetrationofPVwithoutdestabilizingthegrid.Chapter5detailssuchaproposedoperatingreserve

curtailmentimplementation.

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2. High-speedSolarDataAlargeportionoftheresultsinthisthesisareeitherderivedfromdirectanalysisofsolardataor

simulationsthatdependuponit.Therefore,itisimperativetodiscusstheoriginofthehigh-speedsolar

datasetused,theprocessingmethodsfromwhichtheuseablemetricswerederived,andthe

assumptionsmadeinestimatinghigh-speedchangesinsolarpower.Afterall,photovoltaicarraysand

panelsaretypicallyconnectedthroughmaximumpowerpoint(MPP)controllerstothegrid,anditis

thusthevariabilityoftheMPPpowerthatistrulyseenbythegridoranet-zerobuilding.Inaddition,the

rawdatacontainednumerousimperfectionsandinconsistenciesthatpresentedprocessingchallenges,

sotheassumptionsmadeaswellasapproachesusedincreatingacontinuous,useabledatasetwillbe

presented.Finally,thesolardatarepresentsavaluableresource,notonlyforthisthesiswork,but

potentiallyfornumerousothersinterestedinthereal-life,long-term,high-frequencysolardata.Forthis

reason,theessentialcontentisslatedforeventualpublication,andtheadditionalprocessingsteps

performedontherawdataarepresented.

2.1. DataacquisitionhistoryProfessorRobertPilawaoftheUniversityofIllinoisUrbana-Champaignandhisstudentsdesignedand

implementedafastsolardataacquisitionsetupin2012[31].While[31]describestheexperimental

setupinmoredepth,hereisasummaryasitpertainstothiswork:Duringdatacollection,two,identical,

rooftop-mounted,20W,PVpanels,connectedtotwodifferentmeters,wereplacedsidebysideto

eliminatespatialvariationasmuchaspossible.OnemeterwasaKeithley2420thatperformedasweep

acrossthecurrent-voltage(I-V)curveevery2.5-3.9seconds,andtheotherwasanAgilent34410Athat

recordedshort-circuitcurrentat5kHz.ThedataacquisitionmechanismisdepictedinFigure2.1.The

sweepsfromtheKeithley(“slow”)meterenableustocalculateopen-circuitvoltage(VOC),short-circuit

current,andMPPvoltage,current,andpower(VMPP,IMPP,PMPP).TheAgilent(“fast”or“high-speed”)data

provideshigh-frequencyshort-circuitcurrentreadings(ISC)that,aswillbeshown,canbeusedto

calculatehigh-frequencychangesintheavailablepower.Toclarify,bothmetersmeasuredshort-circuit

current,butinthisthesisISCwillalmostalwaysrefertothefastdata.Slowshort-circuitcurrentdatawas

usedforverificationofmeasurementaccuracyagainstthefastmeterandasacheckofinstrument

synchronization.

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Figure2.1.Solardataacquisitionhardwaresetup[31].

2.2. CapturingallpossibledynamicsFivekHzshort-circuitdatawasrecordedbythefastmetertoensurethatallpossibledynamicswere

captured.Theexplanationforwhyshort-circuitcurrentshouldcapture(oratleastindicate)the

presenceoffast,irradiance-baseddynamicshasbeenaddressed[32].Whenitcomestosolarpanels,

thefastestdynamicsarelikelytobeshadow-based,inducedprimarilybycloudsandflyingobjects.

Considerthefastestdynamicthatcouldreasonablybeexpected:ashadowfromapassingbird.A

CanadaGoosehasatypicalcruisingspeedof40mph(64km/h)[33]andaminimumwingchordof

about0.4m[34].Thismeanstheshadowcouldpassontheorderof1/45thofasecond.Bysamplingat5

kHz,eventhishypotheticaloccurrencecouldberecreatedwithmorethan110datapoints.Atmospheric

noisehasthepotentialtoinducestillfasterdynamicsbutgiventhebroadareacoveredbysolararrays,

theeffectsareassumedtoaverageoutbyspatialvariationandwillnotbespecificallyaddressedinthis

thesis.Rigorouslydemonstratingthatallofthesedynamicswerecapturedusingnumericaldatais

difficult.Thefollowingsubsectionswilldescribeproposedsolutionsthatrelyuponknowledgeof

reasonablyexpecteddisturbances.Theywillshowthatevenflickeringshadowsarefullycapturedat100

Hz,andthatfasterdynamicsaresufficientlyinsignificantastonotbeconsidered.

2.2.1. Demonstratingsmoothdynamicsduringcharacteristicallynoisyperiod

Thedominantandmostfrequentdynamicsinsolardata,otherthanbasicdiurnalvariation,arecaused

bypassingclouds,sothefirstandsimplesttestistovisuallyensurethateventhemostrapidtransients

arecapturedbythefastmeter.Thatistosaythatenoughsamplesweretakensuchthattheoriginal

signalcouldbeaccuratelyrecreated,whichwouldbeevidentifthedatawere“smooth”anddidnot

containvisualjumpsordiscontinuitiesbetweensamples.Todemonstratethatindeedthesamplingrate

issufficient,oneofthedynamicdaysintheentiredataset,namelyMarch31st,2013,isclosely

investigatedinFigure2.2.Onthisday,thesolarpanelsexperiencedintermittentcloudcoverandrapid

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rampratesasseeninthetopimageofFigure2.2.Thesubsequentimagesdepictsomeofthemost

dynamicsubsetsofdatafromthatdaytodemonstratethatevenduringsomeofthemostvariable

moments,allpossibledynamicswerecapturedintheirentirety.Infact,thebottomsub-figureinthis

casestillcontains100,000datapoints,providinganexceptionally“smooth”recreationoftheanalog

irradiancechange.

Figure2.2.Sampledaycontainingnumerousrapidtransients(top)andsubsequentclose-upviews.

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2.2.2. Verificationduringflickeringshadows

Variabilityinsolarirradiancecanarisefromsourcesotherthanclouds.Whiletypicallylessfrequent,the

fastestdynamicsarealmostalwayscausedbytheflickeringshadowsoflargebugs,birds,orairplanes

passingbetweenthepanelandthesun.Inordertomoreeasilyidentifytheiroccurrence,ahigh-pass

Butterworthfilterwasappliedtotheraw,short-circuitcurrentdata(thick,bluelineinFigure2.3)and

anyultra-narrowspikesweresingledout.Thespikesofinterestdonothavethecharacteristiccurveson

eitherside;suchinstancesareabyproductofanonidealfilterappliedtorapidcloudtransients.Example

powerdipsofinterestarecircledinFigure2.3andappearasblipsonmoderatetimescales(secondsto

hours).Nevertheless,zoominginonthesecircledregionsasinFigure2.4revealsthateventhefine

detailsofthesetransientsarefullycapturedat5kHz.Instance#4(Figure2.4onright)revealsfourlocal

minimathatmightbearesultofabirdflyingacrossthefourcolumnsofcellsonthesolarpaneltested.

Whilea100Hzsubsamplingdoesnotcapturethesecell-leveldynamics,itdoescapturethepanel-level

powerdipwith3-4points.Fromapanelenergyproductionperspective,thisisshowntobesufficientin

Section2.2.3.

Figure2.3.SamplesolardatafromJuly16th,2013containingmultiple,veryrapiddipsinpoweroutput(circled).

11

Figure2.4.Highlyzoomed-inviewsofthetwomostsignificantcircledinstancesfromFigure2.3.

2.2.3. Investigationofdynamicsintermsofpotentialenergyloss

Insection2.2.2,thefastestexpectedclassofshadingdynamicswereeasilycapturedbya5kHzsignal,

andcouldlargelyberecreatedwithasamplingfrequencyofjust100Hz.Thequestionthenbecomes:

Arethereunknownsourcesofdynamicsinsolarpower,andeveniftheyexist,aretheysignificant

enoughtobeworthcaringabout?Forexample,atmosphericnoisewasmentionedinSection2.2,butif

itseffectonsolarpoweroutputdoesnotmeaningfullychangethepotentialoutputpower,then

arguably,itisnotworthtracking.Uptothispoint,high-speedvariationswereobservedintheshort-

circuitcurrent,but[32]arguesthatatleasttofirstorder,high-speedvariationsinpowercanbe

obtainedfromthehigh-frequencyshort-circuitdatainconjunctionwithslowerI-Vsweepdata.Thefull

processwillnotbeoutlinedhereasthiscanbefoundin[32];onlytheresultispresentedhere.

Assumingthatamaximumpowerpointtracker(MPPT)withconstantupdaterateisusedtomaximize

poweroutputfromaPVpanel,thenfastdynamicswillresultindecreasedpoweroutputuntiltheMPPT

updatestothenewMPPvoltage.Thecumulativeenergymissedduringtheseperiodsissummedfora

given10daysampleasdiscussedinSection2.3.1.Then,theenergysacrificedforagivenMPPTupdate

rateisdividedbythetotalpossibleenergyavailable(assumedtobethesameastheMPPmeasuredat5

kHz).ThisratioisplottedagainstthegivenupdateratesinFigure2.5.Notethatifanydynamics

thereforeexistabove100Hz,forexample,theenergysacrificedwillonlybeabout1partin4000.Atthis

point,thepotentialenergylostorgainedbyknowingthehighestfrequencyvariationisnegligible.

Perfectinsightintotheanalogvariationswouldonlyamounttoabout$0.35ofenergyproductionvalue

fora250Wpaneloveritslifetime[32].Therefore,whatmeaningfulirradiancedynamicsexistare

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arguablycapturedcompletelywith100Hzdata,andanyadditionalhigh-speeddynamicsarenotworth

investigatingforMPPTpurposes.

Figure2.5.Modeledenergysacrificeof10,10-daysampleswithvaryingMPPTupdateratesandmeaninboldedblack.

Entriesinlegendrepresentfinaldayin10-dayseries.

Whileperhapslessinsightfultopowerengineersthansacrificedenergy,fastFouriertransform(FFT)

analysisofthreeverydifferentdayscorroboratedthe100Hzconclusion.Figure2.6depictstheFFTsofa

cloudless(smooth)day,alargelyovercast(noisy)day,andadaywithacloudlessmorningandpartly

cloudyafternoon(partiallynoisy).Eachhasdifferingcharacteristicsatlowerfrequencies,butabove100

Hz(oreven50Hz)thefrequencycontentiswellbelowonepartinonemillionwiththeexceptionofthe

180Hzcoupledgridharmonic.Atthesescales,frequencycontentiseffectivelynegligibleandisonthe

orderoffinemeasurementaccuracyanyway.

13

Figure2.6.Full-dayFFTsof5kHzshort-circuitcurrentforthreedifferentdays.

2.3. DataprocessingchallengesandapproachesTherawdataset,asthenameimplies,wasnotimmediatelyconducivetoanalysis.Missingdata,

formattinginconsistencies,anddataratevariabilityweretheprimaryobstacles.Morespecificdetails,

alongwiththestrategiesusedtocorrectoravoidtheseunexpectedobstacles,areoutlinedinthe

followingsections.Additionally,therawdatadidnotdirectlyprovideuswiththedesiredparameters,

namelyhigh-frequencyvaluesforthemaximumpowerpoint(MPP)power.Asafirststeptowardthis

end,thefinalsubsectionwilladdresstheprocedureusedtocalculateslowMPPvaluesfromcurrent-

voltage(I-V)sweeps.

2.3.1. Missingdata

Thefirstproblemencounteredwasthatoflocalmissingdataornon-sequiturtimestamps.Suchgaps

aretobeexpectedfromreal-lifedatasetsduetoequipmentglitchesorfailures,instanceswherethe

codewasupdated,orotherincidences.Thefirststeptoaddressthisproblemwastoidentifyandflag

missingorunexpecteddata.Thiswasaccomplishedbycomputercodethatrecordedanyinstances

whereactualtimestampsdidnotfallwithinwindowsofreasonablyexpectedtimestamps.Asampleof

theoutputdataisshowninFigure2.7withredboxesindicatingmissingsegments.Apartialdayis

missingfortheafternoonofMarch28th,2013,andafulldayismissingonApril12th,2013.

14

Figure2.7.Solarpanelshort-circuitcurrentvs.timewithhighlightedmissingdatasegments.

SuitabledatasubstitutionsfromotherportionsofthedatasetarediscussedinTable2.1,butforthe

energysacrificeanalysisofSection2.2.3,adifferentapproachwastaken.Tendifferent,randomly

selected,non-overlapping,10-daysamples(100totaldays)weretakenfromtheroughly500daysof

datatoobtainarepresentativesampleoflong-termsolardata.Thiswasaccomplishedbyrandomly

selectingastartingday,andthenproceedingtousethatdayandtheninesubsequentdays,provided

thatnoneofthemoverlappedwithothersamplesorcontainedasegmentofmissingdata.Forexample,

ifthefirstrandomnumbergeneratedcorrespondedtoMarch31st,2013,thenthesegmentofdata

spanningMarch31st,2013toApril9th,2013wouldbeusedsinceFigure2.7indicatesthatitdoesnot

containasegmentofmissingdata.Asacounterexample,ifthenextrandomnumberhappenedto

correspondtoApril7th,2013,thentheselectionwouldbeinvalidatedandanewrandomstartingdate

selectedsincethesegmentbeginningwithApril7thoverlapswiththefirstsample(andcontainsmissing

dataforApril12th,2013).Thisprocesswasselectedbecauseitcontainedrepresentativesegmentsfrom

alltimesofyear,incorporatedlong-termeffectsthatmightappearinmulti-dayweatherpatterns,and

enableddirectuseofthesolardatawithoutadditionalcomplicationsoruncertainty.

2.3.2. SubstituteddataforpublicuseThelong-term,high-speedPVdatasetisusefulforanalysisinthisthesis,butithaslongbeenagoalto

prepareaversionforpublicuse.Thefinalizeddatasetprovidesonecontinuousyearofdatathatcanbe

usedinsimulationstoaccuratelyrepresentreal-lifepoweroutputsfromapanel.Nomatterthestart

datechosen,though,no365consecutivedayswerewithoutsomemissingdatasegments.Dismissing

thework-aroundmentionedinSection2.3.1,missingorincompletedaysthushadtobesubstituted.To

avoidintroducingsuddenchangesorstarkweatherpatterncontrasts,wholedaysweresubstitutedeven

whenpartialdatawasavailable.Table2.1summarizesallincompletedaysbetweenNovember1st,2012

andNovember1st,2013,theportionandtypeofdatamissing,andtherespectivedailysubstitutes.

31-Mar-2013 12 AM 07-Apr-2013 12 AM 14-Apr-2013 12 AM

Shor

t-circ

uit c

urre

nt (A

)

00.20.40.60.8

11.21.41.6

15

Table2.1.SummaryofDayswithMissingDataandSubstitutionsUsed

MissingDay PartMissing MissingSlowand/orFastMeterData

ReplacementDay ScalingFactor

11/23/2012 1minsection Fast 11/23/2013 1.0000000

12/02/2012 Allday Slow 12/02/2013 1.0000000

02/26/2013 Partialday Slow 10/05/2012 1.0000000

02/27/2013 Morning Both 10/02/2012 0.9163347

03/28/2013 Afternoon Both 03/21/2013 1.0405904

04/12/2013 Allday Both 08/13/2013 1.0000000

07/27/2013 Partialday Slow 07/27/2012 1.0000000

08/05/2013 Partialday Slow 08/05/2012 1.0000000

08/29/2013 Partialday Slow 08/12/2012 1.0000000

08/31/2013 Partialday Slow 08/20/2012 1.0000000

09/02/2013 Partialday Slow 08/10/2012 1.0000000

10/14/2013 Partialday Both 10/25/2012 1.0000000

Substitutedayswerechosenwiththefollowingpreference:

1. Ifanon-repeated,completeday(containingalldata)wasavailablefromoneyeareitherprioror

subsequent,thisdaywasselectedasareplacement.

2. Else,ifanon-repeated,completedaywasavailablefromanequidistanttimeawayfromthe

WinterorSummersolstice,thisdaywasselectedasareplacement.Inotherwords,the

replacementdaywouldbeasmanydaysafterthesolsticeastheoriginalwasbeforeit,orvice

versa.

3. Else,dayswithsimilarhistoricweatherpatternsandtemperatureswereselectedwitha

preferencefordaysclosetotheoriginaldate(inapriororsubsequentyear)andsecondary

preferencefordaysclosetoanequidistantWinterorSummersolsticecounterpart(asin2).

Typically,unityscalingfactorswerechosen,butincaseswherepartialdataexisted,substitutedata

couldbescaledslightlytobettermatchtheoriginaldata.

16

2.3.3. Datasynchronization

Inshort,datasynchronizationwasaccomplishedbyaligningdatawithmatching,correspondingtime

stamps.Inreality,however,theprocesswasabitmoreinvolved.Firstofall,therewasnoconsistentfile

length,duration,ornumberofdatapointsperfile.Forexample,thefastshort-circuitcurrentdata

variedinratebetweenabout5010Hzto5014Hzwiththefirstfilerecordingatabout5250Hzandtime

stampsspanningbetween57and59seconds.Settinganominalincrementof200𝜇s(inverseof5kHz)

thereforecausedsignificantoffsetsoverthetensofthousandsofsecondsrecordedeachday.Toresolve

thisoffsetandenablesynchronizationwiththeslowsweepdata,thecomputerprogramhaditsown

masterclockwhichitwouldincrementwiththemeanperiodTmeanbetweendatasamplesasdetermined

bythefollowingsimpleequation:

𝑻𝒎𝒆𝒂𝒏 =𝒕𝒆𝒏𝒅 − 𝒕𝒔𝒕𝒂𝒓𝒕

#𝒔𝒂𝒎𝒑𝒍𝒆𝒔𝒊𝒏𝒇𝒊𝒍𝒆 (2.1)

Whiletimestampsonlyhadprecisiondownto0.01s,thiswasovershadowedbythefactthattheslowI-

Vsweepsdidnotidentifytimestampsbetweenregionsofthesweep.Thatistosaythattheopen-circuit

voltage,MPPvalues,andshort-circuitcurrentmeasurementstookplaceambiguouslywithinthe2.5-3.9

seconddurationofeachsweep.

Toimprovesynchronizationofdata,rawshort-circuitdatafrombothfastandslowsetswerecompared

overa±1swindow.Sincewewouldexpecttheshort-circuitcurrenttobethesameonbothpanels(the

onemeasuredbythefastmeterandtheonemeasuredbytheslowmeter),itwasreasonabletoassume

thatsimilarvaluesshouldberecordedatthesameinstantintime,andthuswecouldadjusttheslow

metertimestamptobettermatchtheinterpolatedtimestampofthefastmeter.Thiswasaccomplished

bymaximizingthecorrelationofthetwocurrentmeasurementsoverthecourseofeachday.Ifnisthe

totalnumberofpointsinadayandmisthemaximumsampleoffsettobeconsidered,thenthemost

likelytimestampoffsetfortheslowmeterwillbethevalueoftoffsetthatmaximizes

𝑻𝒐𝒇𝒇𝒔𝒆𝒕 = 𝐦𝐚𝐱 𝑰𝑺𝑪𝒔𝒍𝒐𝒘 𝒕 ×𝑰𝑺𝑪𝒇𝒂𝒔𝒕 𝒕 − 𝒕𝒐𝒇𝒇𝒔𝒆𝒕

𝒕<𝒏=𝒎

𝒕<𝒎

, −𝒎 < 𝒕𝒐𝒇𝒇𝒔𝒆𝒕 < 𝒎 (2.2)

Theeffectivenessofthiscalculationispresentedatsevenequallyspacedpointsthroughouteachdayto

visuallyverifythatthecalculatedoffsetimprovedoverallalignmentofshort-circuitdataintime.A

sampleoftwoofthesevenwindowsfrom3/31/2013isshowninFigure2.8.Thesesamplesvisually

depictbetteralignmentofdatafromthetwoseparatemetersduringperiodsofrapidirradiance

changes.Thesolidbluecurverepresentsthehigh-speedshort-circuitdata,thereddashedline

representstheslowmetershort-circuitcurrentwithoriginaltimestampsandthegreendottedline

17

representsmeasurementsfromtheslowmeterwithoptimaloffset.Inanidealcase,theapparent

verticesoftheslowmeterwouldliepreciselyontopofthesmooth,high-speeddataasifbeingsampled

fromthesamedataset.Notethatthisanalysiswasonlyperformedforthetwoshort-circuit

measurements.I-Vsweepdataandopen-circuitvoltagewouldhaveadditionaloffsetsastheywere

recordedsubsequenttotheshort-circuitcurrentontheslowmeter.However,aligningthese

parametersusingthesamemethodwouldassumethatincreasesanddecreasescorrelatetoincreases

anddecreasesinshort-circuitcurrent,whichmaynotalwaysbetrue,especiallygiventhevariabilityof

wherewithintheI-VsweepMPPvaluesoccurred.

Figure2.8.TwosamplewindowsofdataalignmentfromMarch31st,2013showingbetterdataalignmentwithtimeoffset.

2.3.4. ParametercalculationEvenafterallofthedatawassynchronizedandmissingdatasegmentsfilled,someofthedesired

parametershadtobecalculatedbeforetheywereused.The5kHzdatacameinanimmediatelyusable

form,buttheslowI-Vcurvedatarequiredspecificprocessingtechniquesinordertoobtainshort-circuit

current,open-circuitvoltage,MPPcurrent,MPPvoltage,andMPPpowervalues.Slowshort-circuit

currentdataconsistsofthreedatapointsnear0V,thesquaresymbolsinFigure2.9.Open-circuit

voltages(VOC)wereobtainedfromthesweepsthatcrossedthevoltageaxis,thetrianglesymbolsin

Figure2.9.MPPvoltage,current,andpowertookthemostprocessing.InFigure2.9,theMPPregion

contains100pointsonthe“knee”oftheI-Vcurve.AscanbeseeninFigure2.10,themeasurements

containacombinationofhigh-frequencyfluctuationsandmeasurementnoise.Simplypickingthepoint

withthepeakvaluecanleadtomisleadingandinaccurateMPPvalues.Toalleviatethis,a4th-order

polynomialleast-squaresfitwasappliedtothedatatocapturetheoverallnatureofthesweep.

18

Figure2.9.Slow,current-voltage(I-V),full-rangesweepcontainingdatapointsneartheshort-circuit,open-circuit,and

maximumpowerpointregion.

Figure2.10.SlowI-VsweepinMPPregionandmaxpowercurvewithpolynomialleastsquaresfits.

Implementinga4th-orderfitinsteadofthe2nd-orderpolynomialusedin[31]increasedtheregression

coefficientfromR2=0.95toR2=0.995foratypicalMPPsweep.Higher-orderpolynomialsorother

functionsmaybeusedinstead,butthe4th-orderpolynomialcapturestheexpectedshapeofthepower

curvewell.Ratherthansolvingforthepeakalgebraically,itwascomputationallymoreefficientto

evaluatethepolynomialfunctionat500equallyspacedpointsoverthesamerangeofvoltagesasthe

originalMPPregionandthenselectthemaximumvaluefromthisfinelydiscretizedset.

19

Forinstanceswhereapeakvaluewasnotfound,thepolynomialkeptincreasingordecreasing

monotonicallybecausetheslowmetermissedtheMPP.Inthiscase,themaximuminterpolatedvalue

(anendpoint)waschosenastheMPP.AnexampleisprovidedinFigure2.11inwhichthreeconsecutive

MPPsweepsareshownwiththemiddle(orange)sweepfailingtospanthepeakpowervalue.This

failureislikelyduetoasuddendropinirradiancefollowingapreviouslyincreasingtrend.Accordingto

theprocedurementionedabove,theMPPpowerwouldbethatassociatedwiththepowerattheleft

endofthemiddlecurve,or16.00Vinthisspecificinstance.Sometimesthefluctuationsweresofast

thatwithinasinglesweep,thepolynomialapproximationgeneratedtwopeaks(orpotentiallymoreifa

higher-orderpolynomialweretobeused).Figure2.12exemplifiessuchascenario,wherethe

polynomialwasapoorapproximationoftherawdata.Incaseslikethis,themaximumvalueoftheraw

sweepdata(marked)waschoseninsteadofthepolynomialpeak.Moregenerally,polynomial

approximationswithR2<0.99weredeemedinvalidandtherawdatapeakusedinstead.Thepolynomial

fitisonlybeneficialifitcloselyrepresentstheoriginaldata.Thus,theinstanceoftwopeaksinFigure

2.12wouldberuledoutduetoapoorpolynomialfit.Aftercomputingvaluesfromtheslowmeterdata,

theresultsweresynchronizedwiththefastmetermeasurementsusingtimestampsrecordedinboth

datasets.

Figure2.11.ThreeconsecutiveMPPpowercurvesweepswiththemiddlesweepmissingtheMPP.

20

Figure2.12.RapidtransientduringMPPsweepandassociatedpoorfitpolynomialapproximation.

2.4. SlowmetercurrentsaturationandactiontakenWhenverifyingthedatasynchronizationinSection2.3.3,itwasobservedthatslowmeterI-Vsweep

currentssaturatedatapproximately1.35-1.375Adespitesimultaneousfastmetershort-circuit

measurementsrecordinghighercurrents,uptoalmost1.8Aattimes.Saturationaffectsabouthalfof

therecordeddaysafterApril2nd,2013,andwaslikelyaresultofanimproperrangesetting.This

deductionisbackedbytwopiecesofevidence.First,thebeginningoftheinaccuratedatacoincideswith

abreakinthedataduringwhichdatarecordingformatswerechanged.Secondly,thesaturationpointis

justslightlygreaterthantheratedpeakcurrentof1.29A.Thismeansthe1.35Aset-pointwouldbe

suitableformostinstancesexceptforwhenthesunappearedbetweencloudsonbright,partlycloudy

days.Intheshortterm,nothingmuchcanbedoneabouttheinaccuratedata.ResultsofSection2.2.3

mightbeslightlyskewedandcouldberecalculatedwithonlydaysunaffectedbythesaturation.Longer

term,theproposedpublisheddatasetalreadyexcludesanypotentiallyinaccuratesweepdataanda

repeatexperimentfordataacquisitionisencouraged.

2.5. PublicandauxiliaryusesforPVdatasetTheprimarypurposeofthehigh-speedsolardata,asitpertainstothisthesis,istoobtainarealisticdata

settobettermodeleffectsofsolarpowervariability.Asmentioned,though,acleaned-upversionofthe

long-termPVdatasetisintendedforpublicuse.Thankstolessonslearnedthroughutilizationofthe

high-speeddata,afewchangesweremade.Timestampsandfilelengthweremademoreconsistent

acrosstheslowandfastmeterdata;sweepdatawassimplifieddowntothekeypointsofinterestsuch

asMPPcurrentandopen-circuitvoltage;andthankstotheanalysisperformedonthedynamiccontent,

21

high-speeddatacouldbedown-sampled(afterpassingamedianfiltertoeliminatemeasurementnoise)

tojust100Hztoreducefilesizeswithoutlosingsubstantiveinformation.

AsinSection2.2.2,findingthefastestdynamicstookconsiderableeffort.TheButterworthfilterusedto

isolaterapidchangeshadtobeappliedtobillionsofpointsperdayandanomalieshadtobeidentified

manually.Withthedown-sampleddataset,thissearchbecomesmucheasier.Themedianfilterapplied

beforedown-samplingeliminatespresumedmeasurementandatmosphericnoiseenablinga

computationallysimplederivativetobetaken.Stringsofdatawithlargederivativesshouldindicatea

rapiddynamicandcanbefurtherinvestigated.

22

3. DynamicHVACLoadCompensationDynamicloadcompensationisavariability-reducingalternativetochemicalstorage.Itcanberelatively

cheapandeasytoimplement,provideeffectivegridinertia,andreducevariabilityofonsitePVpower

variations[35],[36].Whenheating,ventilation,andairconditioning(HVAC)systemsaretobeusedas

theloadmedium,though,dynamicloadcompensationalsohasitslimits.Thischapterfocuseson

variablespeeddrivesinvolvedindynamicHVACcompensationwithmultipleportionshavingbeen

previouslypublishedin[35],[36].

HVAC-implementedenergyresourcefilteringhasbothupperandlowerfrequencybandboundsbeyond

whichitshouldnotoperate.Thelowerfrequencylimit,meaningthelowestupdaterateforHVACspeed

andpowercommands,isestablishedtoshieldbuildingusersfromsubstantialtemperatureswings,

ideallykeepingvariationsimperceptible.Anupperfrequencylimit,meaningthehighestupdateratefor

HVACspeedandpowercommands,isneededsuchthatthefollowingconditionsaremet:(1)HVAC

drivesarecapableofresponding,(2)unduewearandtearisnotinducedondrivesormechanicalparts,

and(3)updateratesdonotcreatediscomfortingaudiblepitchoramplitudechanges.

Frequencydomainanalysisisperformedtoillustrateavailablefilteringpotential,andapproximateupper

andlowerfrequencyboundsarediscussed.ThisanalysisutilizesPVdatafromthehigh-frequencydata

setpresentedinChapter2.IftheHVACsystemcaneffectivelyfilterpowerusageoverausefulfrequency

band,thepowergridwillthenbebetterabletoprovideandabsorbslowerchangesindemandto

balancethelonger-termbuildingenergyflow.Conventionalonsiteenergystoragecouldabsorb

additionalpowershortagesandsurpluseswhereHVACfallsshort,suchaschangesextendingoutsideof

frequencybandboundaries.Asaresult,theelectricgridbenefitsfromamuchslowervariedenergy

demand,andconventionalenergystoragesizeissubstantiallyreduced.Thischapterwillinvestigate

whathigh-frequencyvariationstherearetoremoveandhowtheyweredetermined.Itwillalsopresent

thefandriveexperimentperformedandthebandwidthpermissibleforfilteringcapabilities.Finally,

simulatedfilteringcapabilityofdynamicallycontrolledHVACsystemsispresentedforvariouscaseswith

differingsizesofPVinstallationsandHVAClimitations.

3.1. DesiredsolarpowervariationabsorptionInanidealscenariowheredynamicHVACloadcompensationhasinfinitestoragecapacityand

instantaneousresponsetimes,fixedpowertargetscanbeset,andsolarenergyvariationcanbefiltered

completelybytheHVACsystem(withoutbeingimposedonthepowergrid).Inotherwords,theideal

23

systemwouldstoreorreleasebuildingthermalenergyviatheHVACsystemsothatthecombinedpower

ofthePVsystemandHVACperturbationwouldexactlymatchthedesiredpowertargetateach

moment.Withthefrequencydomainanalysis,wemodeltheeffectsofanidealizedHVACsystemthat

offsetsvariationsbypassingthesolardatathroughvariouslow-passfilters,eachwithadifferentcut-off

frequency,toobtainthedesiredpowertargets.Formostoftheanalysisinthissection,rawdatacame

fromJune15th,2013,shownasday1(hours0-16)inFigure3.1.

Figure3.1.SolarpowerprofilefromJune15th-18th,2013(only4a.m.to8p.m.shownperday).

Figure3.2showslow-passfilteredsolarpanelpowertargetsfromJune15th,2013underfilterswith1,

5,15,and30mincut-offtimeconstants.Powervaluesarenormalizedtoacloud-freedailymaximum.

Figure3.2.IdealsolarpowerprofileseenfromthegridafterHVACfilteringeffect.

24

Figure3.3showsthepowerthattheidealHVACsystemwouldneedtoabsorborsupplyinorderto

realizethefilteredoutputsofFigure3.2.Thispowerwouldbeimposedontopofabaselinepower

consumptiondictatedbyconventionalthermostaticcontrols.Asamplebaselineprofileandprofilewith

dynamicfilteringimposedonitareshowninFigure3.4.Inthefigure,theprofileisgivenintermsof

commandedHVACfanspeeds,butthegeneralideaisthesame;increasedspeedsabovethebaseline

correspondtopositivepowerdemandorpowerneedingtobeabsorbed,whiledecreasedspeedsbelow

thebaselineprofilecorrespondtonegativepowerdemand.

Figure3.3.SolarpowertobefilteredbytheHVACsystems.

Figure3.4.FandrivespeedprofilewithoutandwithdynamicHVACfilteringsuperimposed.

25

Inreality,HVACsystemshavelimitedfilteringcapability,soacompromisebetweenpowerdemandand

certaintyofnetpoweroutputisneeded.Byfollowingthegeneralorlarge-featuretrendsinthesolar

data,loadcompensationpowerdemandsaredecreased,whilestillprovidingincreasedconfidencethat

netpowerinthenextmomentwillnotvarydrasticallyfromitscurrentlevel.Figure3.5illustratesthe

differenceinfilteringpowerrequiredbetweentwodifferentset-pointalgorithms.Inone,setpoints

consistofButterworthfilteroutputwithanuppercut-offpointof15min,whileintheother,15min

sample-and-holdvalues(takenfromthefiltereddata)constituteconstantobligationsetpoints.As

wouldbeexpected,theconstantobligationrequireslongerperiodsofincreasedpowercompensation

whencomparedtothefilteredpowersetpoint,especiallyintimesofslowerdynamics.

Figure3.5.FilterpowerrequestedofHVACcompensationforJune15th,2013.

CompensationinFigure3.5stillneglectsramprate,thermal,andacousticlimitationsoftheHVAC

system.Suchlimitationsandtheireffectarediscussedinsubsequentsections.

3.2. Scalemodelsetupandfan-power/-speedprofilingAscalemodelHVACtestbedwasimplementedtodemonstrateandvalidatethepotentialofanHVAC

systemtofilterenergycontent.Thisproofofconceptblowersetupneededtobecharacterizedto

understandtherelationbetweenrotationalspeedandpowerconsumed.Duringtheexperiment,

acousticvariationswererecordedandanalyzedforlateruse.Oncevalidated,scaledupfiltering

capabilitiescouldbecalculatedgivenproperassumptions.

26

3.2.1. Smallblowercharacterization

Asmallfandrivewasusedtofollowscaledresponsestovariousband-limitedsolarpowerprofiles.Since

thecontrolleracceptsfan-speedsasinputandnotpower,aconversionwasnecessary.Forour

experiment,theelectricalsynchronousfandrivespeed𝜈inHzanditspower𝑃inwattsarerelatedby

𝑷 𝝂 = 𝟏. 𝟔𝟐𝟔𝟔×𝟏𝟎=𝟒𝝂𝟑 + 𝟐. 𝟗𝟗𝟗𝟕×𝟏𝟎=𝟑𝝂𝟐 + 𝟕. 𝟕𝟗𝟐𝟓×𝟏𝟎=𝟑𝝂 + 𝟕. 𝟖𝟎𝟔𝟒 (3.1)

wherethecoefficientswereidentifiedbyaleastsquaresfitasinFigure3.6.

Figure3.6.Small-scalemotorblowerpowervs.electricalspeed.

Acousticeffectsofthefandrivewererecordedwithahighfidelitymicrophonetotestwhethermachine

speedupdateratescausedistractingsounds.Figure3.7showstheexperimentalsetup.A1/3HP,three-

phase,four-pole,inductionmachinewascoupledwithafanblower.AYaskawaCIMR-F7U23P7drive

wasusedtocontrolthefanspeedthroughfrequencyandvoltage.Thedrivewasexternallyprogrammed

byaTIMSP430microcontrollertoadjustfanspeedwitha0.02supdateratetofollowthesolarpower

profileswithhighfidelity.

27

Figure3.7.Experimentalsetupforrecordingacousticeffectsofvariousfanspeedprofiles.

3.2.2. Scalingassumptions

Acousticeffectsofthesmall-scaleblowerwererecordedatunityscaletoemulatetheairflowthrough

anindividualventinaroom.ThemeritsofthischoicearediscussedinSection3.3.2.Electrically,blower

powerresultswerescaleduptobuildinglevelbeforebeingfedintoafull-scale,filtering-potential

simulation.ScalingwasassumedlinearasafractionofpeakpowerbothforthePVdataandHVAC

variablespeeddrives.Itwasassumedthatbothsystemsarefairlymodularwithincreasedcapacity

typicallyresultingfromanincreasednumberofunits.ThisisabetterapproximationforPVsystemsthan

HVACascentralizedblowersareoftenmuchlargerthanthefanusedinthisexperimentandmaynot

scaleexactlylinearly.Peakbuilding-levelpowervalueswerebasedonprojectedpowerconsumptionof

theElectricalandComputerEngineeringBuilding(ECEB)with1.5MWpdesignedsolarcapacity[37]and

about18.6%ofthispeakpoweranticipatedforaverageloadconditions.SinceECEBisexpectedtobe

nearlynet-zero,itsaverageloadshouldapproximatelyequalthecapacityfactoroftheinstalledPV

generationforIllinois,andhencetheestimateof18.6%peakcapacity[38].

3.3. VariationabsorptioncapabilityThelimitationofanydynamicloadcompensationtechniqueisthatitrequiresfullcooperationonthe

partoftheload,whichmayormaynotinterferewithitseffectivenessatperformingtheoriginally

intendedtask.Theabsolutepowercapabilityisalsoafactor.Ifperformanceofthenativetaskis

prioritizedoverdynamicloadcompensation,thenthecapacitytoabsorbvariabilitywillbereduced.This

willalsobetrueiftheloadpowerisinsufficienttomeetthedemandedcompensation.Variablespeed

28

drivesinHVACsystemsexperienceanumberofsuchlimitations.Thereare,ofcourse,peakpower

limitationsassociatedwiththefastestpossiblefandrivespeedavailableandminimumpowerlimitations

associatedwithvariablespeeddrivesoperatingat0Hz(offorstandbymode).Inourexperiment,these

limitswereovershadowedbyanallowablerangeofspeedsassociatedwithamplitudevariationthatis

discussedinSection3.3.1.Thenthereareramplimits.Fanscannotaccelerateordeceleratefasterthana

givenrateforreasonsdiscussedinSection3.3.2.Whileramprateslimitloadcompensation’supper

frequencybound,thermalvariationtypicallylimitsthelowerfrequencybound.Absorbingor“releasing”

electricalenergyintothermalenergyaltersthetemperatureofabuilding.WorkbyCao[35]estimates

thatfilteringcapabilityassociatedwitha15mincutofffilterorfastercouldbeimplementedinlarge

structureswithoutalteringthetemperaturetoogreatlyastobenoticeablebyoccupants.

3.3.1. Amplitudevariancebounds

Whenmoreorlessenergyisdissipatedintovariablespeeddrives,airflowseitherincreaseordecrease

relativetotheirbaselinespeed.Thesechangesinairflowhavedifferingacousticamplitudes.Therefore,

absoluteminimumandmaximumfanspeedsweredefinedbasedonanobjectiveofimperceptible

acoustics.Aseriesofacousticstests,injecting1minsinusoidalspeedcommandswithvarious

amplitudesintothemotordrivecontroller,wereconducted.Taking60Hzasabaseline,thesinusoidal

amplitudesvary±5%,±10%,…,±45%.TherespectiverecordednoiseenvelopesindBareshownin

Figure3.8.Alsoshownisthepeak-to-peakamplitudeofeachcurvecomparedtothebaselinemagnitude

togenerateanormalizedexpectationaboutamplitudevariations.Asverifiedbysubjectivehuman

hearingtests,thespeedvariationcorrespondingto0dBinFigure3.8,orequivalentlyapeak-to-peak

changeequaltothebaselinemagnitude(±16%),seemstobeimperceptible.Thismeansthatabout50

Hzand70Hzareappropriateminimumandmaximumfanspeedlimitsfora60Hzbase.Notethatthis

introducesamorestringentconstraintontheoverallHVACfilteringcapabilitythanthemaximumand

minimumpowerlimits.Filteringcapabilitywiththisnarrowerconstraintisconsideredinthefarright

columninTable3.1inSection3.4.

29

Figure3.8.Acousticnoiseamplitude(top)andrelativeamplitudechangecomparedtobaseline(bottom)forvarious

sinusoidalfanspeedprofiles.

3.3.2. Rampratelimit

Inconventional,thermostaticallycontrolledenvironments,HVACblowermotordrivesnormallyoperate

atfixedfrequenciesasmightbeobservedinredinFigure3.4.Imposeadditionalfilteringdynamics,

however,andthefanspeedwilllikelyvaryconstantly,muchlikethebluecurveinFigure3.4.Ifthis

variationisrapidenoughitwillattractunwantedattentionfrombuildingoccupants,soaramplimit

shouldbeimposedtoneverallowcommandeddynamicstoexceedacertainrate.Todeterminethis

allowablelimit,approximately1minofsolarpowerdatafromJune15th,2013at10:00AMwasusedfor

audioanalysis.Thissamplewaschosenbecauseitincludedamixofrelativelyconstant(±3%)andrapidly

varying(±20%)power.Thescenariotestedwasforabuildinginwhich50%oftheaveragepowerwould

comefromsolarandabout45%ofthisaverageloadwouldbeattributabletotheHVACsystem[26].

Variousrampratelimitswereappliedandtheresearchteamcommentedonwhichtheyfoundtobe

highlynoticeable.Intheend,theteamagreedthata9Hz/sramp-limitedprofilesignificantlyreduced

theattentiondrawntotheblower’soperation,thoughtheyadmittedthatthechangeswouldstill

probablybedistractingifoccupantsweretofocusonthem.Inthisexperiment,9Hz/smeansthatthe

motordrivewouldrampfromastandstilltopeakspeed(cappedatabout90Hz)in10s.

30

AspreviouslymentionedinSection3.2.2,unscaledacousticmeasurementsinthisexperimentwere

takenfroma0.5maway.Theideawastoemulateairflowoutofasinglevent,butinsuchasetupmotor

soundsdominatenoiseproduction.Incontrast,motorsandblowersinmorerealisticHVACsystemsare

distantfromtheoccupants,hencedampeningthesoundofallbutthechangingairflow.Therefore,real

rampratelimitsandamplitudelimitscouldlikelyberelaxed,andarepeatexperimentwithatypicalair

ventsandductsisrecommended.Still,initialresultsandsubjectiveperspectivesindicatethata9Hz/s

frequencyrampappearstobeaplausibleupperlimit.Acommandedspeedprofileabidingbythis

limitation(inadditiontothehard-setmax/minlimit)isshownasadashedlineinFigure3.9alongwith

thepurelycapacity-limitedspeedprofile.Notethattheminimumandmaximumvaluesineffectin

Figure3.9are0%and~120%ofbaselinespeed(60Hz),evenoverthecourseofjust1min.Therefore,

thelinearfrequencychangelimitsareenforcedanytimethedesiredfrequencychangeexceeds9

Hz/sec.

Figure3.9.Commandedspeedprofilewithspeedcapsandramp-limiting.

Anunfortunatesideeffectoframplimitingisthatduringperiodsofrapidpowerfluctuationthereare

timesduringwhichtheHVACfilterisslowenoughtobecounterproductive.ThisiseasiertoseeinFigure

3.10whentheramplimitedpowercompensation(dottedorangeline)iscomparedtotheidealpower

compensation(solidlightgraycurve).Insuchcases,aproportional-derivative(PD)controlmight

producebetterperformance.

31

Figure3.10.Desiredpowercompensationrequestedfromfull-scaleHVACsystemswithandwithoutspeedclampsandramp

limiting.

Ramp-rateacousticchangeswhenfollowingafilteredprofileasinFigure3.9canbedecomposedinto

changesinamplitudeandchangesinfrequency.Thesedominantfrequenciescanoriginatefrommotor

propertiesorstructuralresonancesandcorrespondtodifferentoperatingregions.Figure3.11highlights

therecordedsoundfrequencyamplitudesacrosstheaudiblespectrumwhenmovingfromahigh-speed

“Loud”regiontoalowspeed“Quiet”region.Theregionsaredesignatedinthetoppartofthefigureby

thelight(pink)regionaround20sandthedarker(green)regionaround32s.Themiddledepictsthe

frequencycontentforcomparisonoffrequencyamplitudes.Obviously,louderperiodswillcontain

greaterbroadbandfrequencycontent,buttofocusonjustthepitchchanges,thebottomportionof

Figure3.11normalizesthepeakfrequencyamplitudes.Thisisolatesthepitchesfromchangesin

amplitude.Theencircledregionsindicatedominantfrequenciesthatariseorbecomenoticeablyabsent

relativetobaselineoperation.Therefore,whilenotanexplicitconstraint,frequencychangesshouldnot

beignoredastheywilllikelycontributetotheconspicuousnessofspeedchanges.

32

Figure3.11.Soundamplitudesacrossaudiblefrequencyspectrumforthebaseline,“Loud”sample,and“Quiet”sample.

3.4. EffectivenessofdynamicHVACcompensationDependingonthePVcapacityinstalledandtherelativesizeofthebuildingload,thecapabilityof

dynamicloadcompensationwilldiffer.Table3.1summarizescapabilitiesfordifferentbuildingtypes

withaveragesolarpowerinstallationsrangingfrom25%to100%ofaveragebuildingload.Figure3.12

depictsthesamedataingraphicalform.Tounderstandtheoriginsoftheseresults,a1minsampleof

thispotentialpowercompensationwasdepictedingrayinSection3.3.2,Figure3.10.Thefiltering

capabilitiesofTable3.1formaximumandminimumlimitationswerefoundbyintegratingthearea

underthedashed(blue)curvesandsolid(lightgray)curvesandthenfindingtheratiobetweenthetwo.

Theramp-limitedcaseismorecomplicatedbecause,asobservedinFigure3.10,thepowerconsumption

representedbythedotted(orange)curveiseffectivelytime-delayedrelativetotheidealfilter.Table3.1

confirmsthisunfortunatesideeffectwithramp-limitedfilteringpercentagesthatarestrictlylessthanor

equaltothecapacitylimitedcase.

33

Table3.1.FilteringCapabilityPercentageComparedtoIdealHVACFilter

UpperFilter

Limit(periodinmin)

Max/MinLimitedFilteringCapacity

Ramp-RateLimitedFilteringCapacity

AcousticAmplitude&Ramp-RateLimitedFilteringCapability

AverageSo

larC

apacity

(as%

oftotallo

ad)

100

1 73.20% 57.90% 47.00%5 70.70% 65.40% 44.50%15 66.90% 63.90% 39.90%30 65.20% 62.90% 37.70%

50

1 89.50% 74.20% 62.20%5 85.80% 79.40% 61.00%15 84.70% 81.10% 56.00%30 83.50% 80.80% 54.40%

25

1 98.80% 92.30% 80.30%5 96.60% 91.70% 77.70%15 95.90% 93.00% 75.40%30 95.70% 93.40% 73.70%

Thereareafewgeneraltake-awaypointsfromTable3.1orFigure3.12.Mostobviously,thefiltering

capabilityofHVACsystemsapproachestheidealcase(100%desiredfiltering)astheaveragepowerofa

solarinstallationdecreasesinrelativesizetotheaverageHVACpower.Decreasingoreliminating

limitationssuchasramprateandacousticamplitudeofcoursepermitsincreasedcapabilityaswell.

Moresubtly,whiletheidealHVACfilterincreasesineffectivenesswithshorterperiodfilters(lessenergy

tofilter),realisticimplementationsincludingramplimitingcontrolsperformmoreideallyforlongerfilter

cut-offperiods(30or15min)duetotheslowerdynamics.Fortunately,thiscoincideswithutility

aspirationsofmoreconstantpoweroverperiodsof15ormoreminutes[20].

Inthescenariosstudied,notalldesiredvariationcouldbeabsorbedthroughdynamicHVAC

compensation.However,inbuildingswithoccupancysensors,lessstringentlimitationscouldbesetin

unoccupiedroomsorzones,enablingincreasedenergystoragepotential.Dynamicloadcompensation

mightalsobesufficientifsomePVvariationcouldbeeliminatedatthestart,aswillbediscussedin

Chapter4.Otherwise,themissedorunfilteredenergymustbeabsorbedbyotherenergystorage

mechanisms,asmentionedinSection1.4.1.

34

Figure3.12.GraphicalrepresentationofTable3.1.

3.4.1. Reducedbatterystoragerequirement

Implementingdynamicloadcompensationshouldrequirenomorethananoutercontrolloopbuilton

topofexistingthermostaticcontrolsandvariablespeeddrives,whicharebecomingthenorminnew

commercialbuildings.Therefore,thecostofimplementationisalmostcertaintobelowerthanthe

additionalbatterystoragethatitismeanttooffset.Resultsfromaten-daysamplesuggestthatabattery

storageunitcouldbedowngradedinsizebyatleast25%withthedynamicHVACcompensationstrategy

discussed[39].Thebenefitsofdynamicloadcompensationarevisiblypresentaswell.Onesampledayis

providedinFigure3.13andindicatesthereductioninbatterydemand(filled-inregions)whendynamic

HVACloadcompensationisimplementedvs.thebaselinecaseofrawsolarpower(middlevs.top).

Figure3.13alsoincludesanadditionalscenariowheretheprincipleofdynamicloadcompensationis

extendedtoalargewaterreservoirusedforchilledbeamcooling(bottom).Inthiscase,batterystorage

requirementsarenearlyeliminated.

35

Figure3.13.Gridandbatteryenergycontributionfor:rawsolarprofile(top),filteredsolarprofileusingjustHVAC(middle),

andfilteredsolarprofilewithHVACandwatertankactingasdynamicloadcompensators(bottom).

Anotherbenefitofdynamicloadcompensationisthereductionofenergyenteringandexitingthe

battery,degradingbatterylifetime.Comparedtothebaselinecase,HVACfilteringcanreduceenergy

cyclingbymorethan25%foranovercastday,andnearlyeliminateenergycyclingwhencombinedwith

dynamicloadcompensationofaverylargewatertank.Whileexcessthermallossesassociatedwith

increasedtemperaturegradientshavenotyetbeenconsidered,thereispotentialforsignificantenergy

savingsfromreducedpowerelectroniclossesandbatterycyclinginefficiencies.

36

4. PVOperatingReserveCurtailmentPVoperatingreservecurtailmentcaneliminateshort-termsolarpowervariabilitybypartiallycontrolling

thepowerproductionofaPVpanelorsystem.Inotherwords,thetechniqueenablesmorepredictable

poweroutputbyattemptingtosupplycertainpowerset-pointsratherthansimplytrackingthenatural

dynamics.PVoperatingreservecurtailmenthasbeenshowntoeffectivelyandeconomicallypreventthe

productionofsignificantvariabilityatthepanellevel[40].Thischapterrestatesmanyofthearguments

andfindingspreviouslypublishedin[40].Asanoverview,thischapterfocusesonwhatismeantby

dynamicoperatingreservecurtailment,theelectricalbenefitsthatPVsystemscanprovide,the

economicargumentforwhysomelevelofreserve-basedcurtailmentmakessense,andafewdifferent

variabilityandoptimalitymetrics.

4.1. OperatingreservecurtailmentschemeBothcurtailmentandreservecanhavemultipledefinitionsdependingupontheapplication.Forthis

thesis,curtailmentmeansoperationofaPVpanelatsomepowerset-pointbelowitsMPPwhilereserve

isthepower(orpercentageofpower)availableontopofthecommandedset-point.Dynamicoperating

reservecurtailmentisthecombinationofthesetwoinatime-varyingenvironment.Toclarify,operating

reservecurtailmentisnotequivalenttocontinuousoperationatanominalfractionofMPPoutput.

Instead,anominalfractionisset,andthenalow-passfiltercontrolorotherslowstrategyisusedto

calculateaslow-changingset-pointorpowertarget.Inthisway,aPVsystemactivelyoffsetssomeofits

ownvariability.Theset-pointscouldalsocomefromhistoricalsolardata,weatherforecasts,generic

outputprofiles,15minconstantorfirst-ordergridcommands,orcombinationsoftheseorotherinputs.

Toillustratetheconcept,aPVsystememployingoperatingreservecurtailmentwithalow-passfilter

wassimulatedandanalyzedonthesameJune15th,2003datausedthroughoutChapter3.Muchlike

Section2.2.3,variationsintheMPPpower(notcurrentorvoltage)wereofconcern.AsubsetofMPP

powerdataandthecalculatedreservepowers(nominal10%heldinreserve)isseenasthesolid,jagged

curves(gray)nearthetopofFigure4.1.Theheavy,dottedanddash-dottedcurves(inred)are

calculatedfroma1st-orderlow-passButterworthfilterappliedtothepeakandreservepowercurves.

Sincethesefiltersarecausalandslow-changing,ahigh-probabilityestimateofthenextmoment’s

powertargetcouldbefoundthroughextrapolationmethodsbasedonpastdata.RelativetotheMPP

filteredset-point,excessesorshortagesimposeduponthegridarecalledfluctuationsandis

representedasthejagged,dashedcurveneartheaxis(pink)inFigure4.1.Ifpurecurtailmentis

permitted,thenallinstancesofexcesspowercanbeeliminated.Additionally,ifthereserveset-pointis

37

usedinsteadoftheMPPset-point,thenpowershort-fallscanbepartiallyorcompletelysuppliedthanks

totheavailablepowerreserve.Suchascenariowith10%reservecanbedescribedastheheavier,solid,

mostlyflatcurvenearzero(purple)inFigure4.1.Notethatamajorityofthetime,thepowertarget

couldbeachieved(fluctuationfromset-points=0)andthatresidualdeviationsarereducedin

magnitudecomparedtotheMPPcase.

Figure4.1.MPPPVpoweravailable,reservepower,associated"filtered"powertargets,andremainingfluctuationsimposed

uponthegrid.

Amodifiedincrementalconductancealgorithmwasdesignedandsimulatedthatwouldoperateatthe

powertargetwhenpossibleandmaximizepoweroutputwhenexperiencingashortage.Chapter5

containsdetailsoftheproject,thealgorithm,andsimulatedresults.

4.2. PVsystemsasagridresourceWhenphotovoltaictechnologywasnewandinherentlyexpensive,itmadesensetocontinuously

operateatpeakcapacitytomaximizeenergyoutput.Unfortunately,thismeantthatsolarinstallations

behavedlike“negativeload”gridconnections–introducingstochasticvariability,producingunregulated

poweroutput,andpotentiallydegradingsystemdynamicperformance[41].AsthecostofPVcontinues

todecrease,however,itmaybetimetotransitionfromPVasaliabilitytoPVasagridresource.Whenit

comestotraditionalspinninggeneration,activegridsupport,implyingdynamiccontrol,isessentialfor

full-functionsupply-sideresources.WithoutsimilarcontrolsforPVsystems,modelsofPVgeneration(as

38

in[42])typicallyaddfossilfuelreservecapacitytohelpoffsetintermittency.However,wedonothave

tooperatePVthisway.Itcannotonlyoffsetsomeofitsownvariability,butalso,togetherwithan

“active”grid-readyinverter,itcanactuallyoffergridsupportbeyondwhatconventionalgeneration

provides.

Notincludingenergystorage,someexamplesofactivegridsupportinclude:

• Voltagesupport–Reactivepowercapabilitytohelpregulatelocalvoltage.

• Frequencysupport,includingregulationupanddown–Realpoweradjustmenttomaintain

fixedfrequency.

• Operatingreserves–Additionalcapacitythatcanbeconnectedwhenrequired.

• Rampratecapability–Trackexpectedloadrampingatneararbitraryrates.

• Stabilitymaintenance–Rapidlyrespondtofaults,lineremovalsorinsertions,orlarge

instantaneousloadchanges.

TheinvertersforgridconnectioninmanyPVsystemsoperateatunitypowerfactorandmaximum

powercapacityatalltimes,andthereforedonotprovideanyoftheseactivesupportcapabilities.The

situationischangingrapidlyinEurope,however,asrequirementsforactiveinvertersmovetoward

standardization[43].Reactivepowerandvoltagesupportarefeasibleinthesedesigns,andthe

implementationofreservecouldmeanavailableinvertercapacityevenduringtimesofpeakpower

production.Low-voltageridethrough,requiringcontinuedoperationthroughanexternalfault,is

emerginginPVsystems.Frequencysupportandotherregulationrequirementstendtobeone-sided,

requiringpowerreductionduringover-frequencyconditionsorpowercurtailmentinsomesituations

[30].Operatingreservecurtailmentcouldexpandthiscapabilitytoincludesomelevelofpowerincrease

duringunder-frequencyconditions.Broaderactivegridsupportistypicallyassociatedwithstorage,but

dynamiccontrolsforactivegridfunctionsarepossibleevenwithsmallinverters[44].

4.3. EconomicjustificationofPVcurtailmentAllofthepotentialbenefitsofPVcurtailmentwithoperatingreservemustbemadeeconomically

competitiveagainstalternativesolutions.Thissectionarguesthatsomereservecapacitydoesmake

economicsensegivengridsupportasaninherentrequirementofsupply-sideresources.

Forsometangiblemetrics,considerthecostofPVenergytobeabout$0.05/kWh[45]andthecostof

conventionalspinningreservetobe$0.0058/kWh[42].Photovoltaic(PV)energysystemshavequoted

installationcostsatorbelowUS$2perpeakwattacrossscalesfromresidential[46]toutility[47].In

39

systemswith25yearwarranties,thismeansthatelectricityisproducedbelow$0.05/kWhatthis

installedcost.Asasidenote,thisapproachescostparity,atwhichPVenergyproductioncostsare

comparabletothosefromotherfuelsmeasuredatdistributionpointsinthegrid[45].Thecostof

operatingreserveshasbeenexploredindepthbyNREL[42]andaveragesabout$5.80/MWh,orthe

$0.0058/kWhfigure.ConventionalPVpracticetreatsanyenergysacrificedashavinganopportunitycost

of$0.05/kWh;however,thisneglectsthecostofregulationwhicheithermustbesuppliedbytraditional

generationorbatterystorage.Batterystorage,forcomparison,hastargetcostsof$250/kWh,installed

[14].Assuminglineardegradation,morethan40,000equivalentcycleswouldbenecessarytobecost

competitivewithspinningreserves.Thisisunlikelywithmodernbatterytechnology.

ConsiderinsteadthescenarioinwhichthevalueofaPVsystemasagenerationresourceismaximized

ratherthanjusttheenergyproduction.Saythat,onaverage,10%ofavailablepowerissetasideforgrid

support.Therefore,thecostofthisreservewouldbe10%oftheoverallcostofenergy,withthecaveat

thattheremainingenergyisnowabout10%moreexpensive.Afterall,forthesameinstalledsystem,

10%reservemeansthatyouwouldonlybereceiving90%asmuchenergyaswithoutreserve.

Mathematically,thecostofreserveiscalculatedtobe

𝑪𝒓 =𝑷𝒔𝒐𝒍𝒂𝒓𝟏 − 𝝌

⋅ 𝝌 (4.1)

wherethecostofsolarenergyislabeledasPsolarandthereservefractionasχ.WeseeinFigure4.2the

costofPVoperatingreservecurtailmentplottedovervariousamountsofreserve.Thecircles(blue)

curverepresentstheapproximatecostofmodernPVtechnology,asdiscussed,whilethetriangles

(orange)curverepresentsahypotheticalfuturecostasPVcontinuestogetcheaper.Thesolid(yellow)

linerepresentsthecostofspinningreserve,belowwhichPVreservehasacostadvantage.

Aswouldbeexpectedfrom(4.1),increasingreservecorrespondstosignificantlyincreasedcost.Thisis

becauselargeramountsofreserveconstitutelargerfractionsofthebaselinePVcostandeffectively

causetheremainingenergytobemoreexpensive.Incontrast,smallpercentagesofreservecostvery

little.ThismeansthatforanyPVpricelevel,includingtheverypessimisticgray(squares)costcurvein

Figure4.2,somepercentageofreserveischeaperthanconventionalreserveresources. Curtailmentcost

issueserodeasPVinstalledcostscontinuetofallandasPVinvertersbecomeresponsibleformorethan

justenergyconversion.Inthisanalysis,noeconomicvaluewasattributedtopotentialPVinvertergrid

supportcapabilities,thoughthesecouldcertainlydefraysomereservecosts.

40

Figure4.2.Opportunitycostofreservefordifferentpricesofsolarascomparedtoconventionalreserves.

4.4. MeasuresofvariabilityandoptimalityPVvariabilitycanbedefinedinanumberofdifferentways.Section4.1referstovariabilityasthe

deviationfromthelow-passfilteredpeakpowerprofile.Thiscanbedefinedinatleasttwodifferent

ways-eitherthemaximumabsolutedifferenceortheintegralofpowerdifferences.Thissection

presentshowtheoperatingreservecurtailmentschemereducesvariabilityinbothmetrics.Additionally,

whilethefocusofthisthesisistoreducevariability,thevalueofrenewableenergyisnottobeignored,

soonemeasureofoptimalityispresentedthattriestomaximizeenergyproductionwhileminimizing

variabilityimposeduponthegrid.

Letusfirstconsidervariabilityasdefinedbythepeakdifferencebetweenthepoweravailableandthe

outputpowersetpoint.Allowingforcurtailmentmeansthatonlynegativevariability(powerbelowthe

setpointthatcannotbesupplied)willpersist,becausepositivevariabilitywouldrepresentanexcess

thatcouldbecurtailedtomeetthesetpoint.Figure4.3showscomparativeoperationonadaywith

substantialcloudcovervariationandintermittency.Intheleftplot,actualsolarproduction(scaledtoan

arbitrarypowerpeak)isshownasthelighttrace,andthedesiredoutputbasedonalow-passfilter

invertersetpoint,butnoreserve,isshownasthedarktrace.Allnegativevariabilityisimposeddirectly

onthegrid,andassuch,themaximum,traditional(spinning)operatingreservewouldbetheratioofthe

negativepeakinvariabilitytothepositivepeakinthesolardata,inthiscaseabout5/11.5or43%.Inthe

rightplot,thesamecontrolisemployedwithanominal85%operatingsetpoint.Thisallowsforsome

$0.00

$0.01

$0.02

$0.03

$0.04

$0.05

0% 10% 20% 30% 40% 50%

Opp

ortu

nity

Cos

t of R

eser

ve ($

/kW

h)

PV Reserve as Percentage of Peak Energy Possible

$0.05 $0.04 Current Cost of Traditional Reserves $0.10

41

negativevariabilitytobereducedbyutilizingsomereservepowercapability,andthusthereisa

substantialreductioninvariabilityimposedonthegrid.Theoperatingreserverequirementdropsto

3.6/11.5or31%;thedropisnotquitea1:1reduction(15%PVfor12%conventional),butitisstill

substantial.

Thealternative,integraldefinitionofvariabilityisperhapsbettersuitedtobatterystoragemetrics

ratherthanspinningreservesasitrepresentswatt-hoursofenergystorageratherthanjustwatts.A

claimed“reductioninvariability”wouldbethedifferencebetweenthebasecaseandthereservecase

fluctuationintegral.Thiscorrespondstothedifferencetakenbetweentheintegralsofthebottom

(purple)curvesinFigure4.3.

Figure4.3.Variabilitymitigationoveradaywithsubstantialsolarintermittency(June15th,2013).Leftplot:noreserve

capability.Rightplot:nominal15%reserve.

TheintegraldefinitionofvariabilitywasusedtocalculatetheoptimalPVreservepercentage.Generally

speaking,increasingthenominalreservewillreducevariabilitybutincreaseenergysacrifice.Muchlike

theabsolutevariabilityrelatedtospinningreservereductions,theintegralvariabilitydoesnottradeoff

withenergysacrificeina1:1manner.Instead,itisnonlinearanddependsuponthe“type”ofdayasit

pertainstovariousamountsofcloudcover.Figure4.4showsthereductionratiovs.thenominal

curtailmentlevelforthesamethreedaysasFigure2.6.Eachtypeofdayexperiencesalevelofreserve

abovewhichincreasedreservehasdiminishingreturns.Thepeakofthiscurverepresentsonemeasure

ofoptimalityasthemarginalbenefitofincreasedreserveismaximizedatthispoint.Thispointof

optimaloperationtypicallysupportstheoverallcost-benefitanalysis,too.

42

AccordingtoFigure4.2,moderndaysystemsoperatingwith0-10%reservecorrespondtodirectenergy

reductioncoststhatarelowerthanreducedoperatingreservecostsinthepowergrid.Forexample,in

Figure4.4anoptimaltrade-offisobservedatabout8%reservefortheovercastday.Givena$2/WPV

system,acurtailmentof8%translatestoeffectiveoperatingreservescosting$174/kWand$4.35/MWh

usinganapproachsimilarto(4.1).Thesevaluesaresubstantiallylowerthanexistinggridreserve

methods,andforclearandovercastdaysthisislikelytobethecase.Dayswithintermittentcloudcover

posealargerobstacletovariabilityreductionsotheoptimalenergyvs.variabilitypointmaylietothe

rightofthecross-overcostinFigure4.2andmaythusbecostlimitedandnotquiteideal.

Figure4.4.Cost-benefitcurvesforfindingoptimalreservepercentage.

TheoptimalitycurvesofFigure4.4indicatethatthebestreservelevelshouldadapttoconditions.

Thoughoutsidethescopeofthisthesis,ahybridapproachoflow-passfilteringandweatherforecasting

mayleadtoimprovedenergycaptureandvariabilityreduction.Forexample,weatherforecastsfor

partialorfulldayscouldbedistributedtocontrolalgorithmsthroughinternetconnectivityandset

recommendedreservecapacitybasedonpredictedcloudcovertypeandquantity.Then,thelow-pass

Butterworthfilterwouldusetheupdatedcurtailmentlevelwhendeterminingpowerset-points.

Alternatively,reservepercentagescouldbedynamicallyincreasedanddecreasedbasedonthe

perceivedvolatility,relaxingduringperiodsofclearskyandslowchangesandincreasingduringperiods

ofpartialcloudcover.

43

5. ImplementationanalysisTheproofofconceptSimulinkmodelpresentedheredemonstratesthesuccessfulmodificationofan

incrementalconductancemaximumpowerpointtracking(MPPT)algorithmtoachievethedesired,

arbitrarypoweroutput.Morespecifically,themodelsetsatargetpoweroutputbasedon“filtered”

historical,curtailedsolardataandthenoperatesatvaryinglevelsofcurtailmenttobestmatchthe

desiredoutput.Thiscapabilityiscoineddesiredpowerpointtracking(DPPT).

Asabroadoverview,Section5.1reviewstheconventionaloperationoftheincrementalconductance

algorithmandintroducesthemodificationusedtooperateatpointsawayfromtheMPP.Section5.2

thenbuildsupthemodelpiecebypiece,beginningwithasimplecontrolloopandevolvingintothefinal

controlsystemwithcrosscomparisonsandverificationsbetweenversionsalongtheway.Thefinal

outputtosomesampledatamaybefoundattheconclusionofthissection.Section5.3thenprovides

somebriefeconomicjustificationandanalternativeperspectiveforwhytradinguncertaintyforenergy

productionmightmakesense.

5.1. Incrementalconductance–areviewTheproposedimplementationofpowercurtailmentisbasedonanincrementalconductanceMPPT

algorithm,soitisimportanttounderstanditstypicaloperationbeforeproceeding.Inaddition,ahigh

leveldescriptionofhowDPPTadaptsthisalgorithmispresented.

5.1.1. ConventionalalgorithmIncrementalconductancereliesuponmeasurementsbeingtakenatdiscreteinstancesintime.Ateach

timestepthealgorithmcomparesthelatestvoltageandcurrentmeasurementstotheprior

measurementsandthencalculatesthedifferencetoobtain∆Vand∆I.Bycomparingtheinstantaneous

conductance,I/V,tothenegativeofthediscretechangeinconductance,-∆I/∆V,adecisioncanbemade

toeitherincreaseordecreasetheoperatingvoltagesetpoint.Thederivationoftheincremental

conductancerelationshipisasfollows:Theslopeis0atpeakpoweronthepowervs.operatingvoltage

curve(Figure5.1).ThisMPPisindicatedinthefigurebythecirclesatopeachirradiancecurve.Put

simply,

𝒅𝑷𝒅𝑽

= 𝟎 (6.1)

attheMPP.Next,weexpandoutthepowerPintoitsvoltageandcurrentcomponentsandevaluatethe

derivativeusingtheproductrule.

44

𝒅𝑷𝒅𝑽

=𝒅(𝑰 ⋅ 𝑽)𝒅𝑽

=𝒅𝑰𝒅𝑽

𝑽 +𝒅𝑽𝒅𝑽

𝑰 =𝒅𝑰𝒅𝑽

𝑽 + 𝑰 = 𝟎 (6.2)

Weapproximatethatforrapidsampling(fasterthanthedynamicsfoundinthesolardata)wecan

replacetheinstantaneousderivativewitharatioofdiscretizeddifferences.

𝒅𝑰𝒅𝑽

≈∆𝑰∆𝑽

(6.3)

Implementingthisapproximationandsimplifyingtheexpressionintotwoconductanceterms,wehave

∆𝑰∆𝑽

+𝑰𝑽= 𝟎 →

∆𝑰∆𝑽

= −𝑰𝑽

(6.4)

wherethetermontheleftoftheequalssigniscalledtheincrementalconductanceandthetermonthe

rightistheinstantaneousconductance.

Figure5.1.Powervs.operatingvoltagecurvesforthreedifferentirradiancelevels.

Thefinalstepfortheincrementalconductancealgorithmistoeitherincrementordecrementthe

operatingvoltage(x-axisinFigure5.1).ConsideringthatdP/dVisgreaterthan0totheleftoftheMPP

wecanusethefinalexpressionin(6.2)and(6.4)toinferthatwhentheincrementalconductanceis

greaterthanthenegativeofinstantaneousconductance,theoperatingpointislikewisetotheleftofthe

MPPandthatthevoltagesetpointshouldbeincremented.Thecomplimentarystateandactionsfor

dP/dVlessthan0likewisehold.

5.1.2. ModifiedalgorithmTheconventionalalgorithmpresentedintheprevioussubsectionisdesignedtooperateatpeakpower,

butforDPPT,itismostoftenthecasethatthedesiredoperatingpointwillnotbetheMPP.Itwas

thereforenecessarytogeneralizetheincrementalconductancealgorithmtoaccepttargetoperating

45

pointsbelowtheMPPandcorrespondingnon-zeroslopes.Mathematically,ratherthansearchingforthe

zeroslopepointasin(6.1),wearenowsearchingforwhere

𝒅𝑷𝒅𝑽

= 𝐒 (6.5)

whereSisthevariableforslope.FollowingthesameprocedureasinSection5.1.1,weobtain

∆𝑰∆𝑽

=𝑺 − 𝑰𝑽

(6.6)

atourdesiredoperatingpoint.Justasbefore,iftheincrementalconductanceisgreaterthanthe

negativeofthisnew,modified,instantaneousconductance,thentheoperatingpointistotheleftofthe

DPPandthusthevoltagesetpointshouldbeincremented.Thecomplimentarystateandactionsagain

hold.

Figure5.2representssuchascenariowherethepowerdemandedis90%ofpeakpowerforthat

irradiance.Thetargetpowerandassociatedslopeareindicatedbythegreendotandstraightlinethat

passesthroughit.Notethatonlythenon-shadedregiontotherightofeachMPPisutilized.Eventhough

therearetwopointsatwhichoutputpowerequalsthedesiredfractionofpeakpower,theslopetothe

leftoftheMPPislargelyconstant,whichleadstopoorconditioningofthelook-upvaluestobe

discussedinSection5.2.4.

Figure5.2.Usefulregionofpowervs.operatingvoltagecurves(non-graysection)withanewtargetpower(greendot)and

associatedpowervs.voltageslopeindicatedonthepeakirradiancecurve.

5.2. Modelingprocedureandverification

Toensureaccuracyofthefinalresult,thesimulationwasbuiltinmultiplestageswitheachsuccessive

stageaddingeitheranewsubsystemorasimplifyingapproximation.Additionally,thesimulationutilized

90%

46

PVdatafromthefinalizeddatasetpresentedinChapter2tomodeltheresponsetoreal-lifePVpower

profiles.

5.2.1. Stage1:Basecase

Thebasecaseconsistedofaclassicalincrementalconductancealgorithmwrappedaroundaboost

converter.TheboostconverterwasimplementedwithamodelMOSFETanddiodeaswellasPWM

generatorbuiltfromatrianglewaveformgenerator,theoutputfromthecontrolloop,anda

comparator.Theoutputoftheboostconverterwasconnectedtoafixed-voltagebusof95.2V.Suchan

arbitraryvalueistheresultofascalingapproximation.Initialmodelplanswereforamore-typical235W

panelwith30VMPPtobeconnectedthroughtheboostconvertertoanidealvoltage-sourcedinverteras

inFigure5.3.Theconfigurationmightresembleatypicalmicroinverterthatconnectsasinglesolarpanel

directlytotheacelectricgrid.Inordertooutputa120VRMSwaveformtothegrid,theboostconverter

wouldneedtosupplya170Vdcbus(foranidealinverter).Inordertotransformthepanelparameters

fromChapter2(20W,16.8VMPP)intothoseforthe235Wpaneldesired,alinearscalingapproachwas

taken,muchlikeSection3.2.2.Thatis,aconverterboosting30Vto170Vwasassumedtohavelinearly

proportionaldynamicpropertiestooneboosting16.8Vto95.2V.

Figure5.3.BlockdiagramillustratingtheenvisionedimplementationofaMPPTboostconverteraspartofamicroinverter.

Inordertopermitnumericalintegrationwithoutasingularsolution,Simulinkrequiredasmallresistance

inserieswitheitherthevoltagesourceoroutputcapacitor.Consequently,an8.13×10=]p.u.resistor

wasinsertedinserieswiththeinfinitebus.Theresistorwasplacedhereinsteadofinserieswiththe

capacitortoavoidexcessESR-relatedvoltagejumpsattheoutput.Theselectedplacementconveniently

resembleslineresistancethatwouldbelikelyencounteredifimplementedinreallife.

5.2.2. Stage2:Averagecircuitmodel

Simulatingjust0.1sofmodeltimeinthebasecasetookconsiderablecomputationalpowerandtime-

probablyover100sona2.4GHzdualcoreprocessor.Significantsolarvariationcausedbycloudsoccurs

overaperiodofafewsecondstominutes,sothesimulationhadtobedrasticallysimplifiedifitwereto

provideanymeaningfulresultsintime.Tothisend,theswitchingcircuitwasreplacedwithanaverage

SolarPanel dc/dcConverter dc/acInverter PowerGrid

47

circuitmodeltoobservetheresponseoftheconverterontimescalesmuchlongerthanafewswitching

periods.

Modificationsfromtheswitchingmodelincludedswitchreplacementandanincreaseinoutput

capacitance.Thediodeinthebasemodelwasreplacedbyadependentcurrentsourcevaluedat

1 − 𝐷 ⋅ 𝐼`where𝐼`istheaverageinductorcurrent;theMOSFETwasreplacedbyadependentvoltage

sourcevaluedat 1 − 𝐷 ⋅ 𝑉bcdwhere𝐷isthecommandeddutyratio;andtheoutputcapacitancewas

increasedsignificantly.Sincetheaveragemodelhasatendencytoexaggerateoscillations,theincreased

capacitorsizedampenstheresponsetocreatesimilaroutputpowerresponsestodutyratio

perturbations.Theoutputpowerwaveformsfromthebasecasewithswitchingandtheaveragecase

arelargelyconsistent(Figure5.4).Differencesincludeaslightphaseshiftduetotheeffectoflocal

averaging,andlargersteady-staterippleinthebasecaseduetotheswitchingripple.

Figure5.4.Poweroutputresponsetostart-updisturbance.

5.2.3. Stage3:Constantcurtailment

Beforeimplementinganyadvancedcontrol,itwasimportanttoensurethatthemodeledboost

convertercouldproperlyoperateatadesiredlevelofcurtailment.Inthisstage,afixedfractionof

reservewasset,namely10%.Figure5.5showsthepoweroutputoftheconverterwith10%reservein

green.Maximumpossiblepowerfromthepanelisshowninorangeandthedesiredoutputpowerof

90%peakpowerisshowninblueforcomparisonwithactualpoweroutput.

48

Figure5.5.Poweroutputwithafixedcurtailment(reserve)commandrelativetoidealcase.

Themodeledconverteroutputcloselytrackstheideal90%peakpowercurvewithtwodistinctfeature

typesofnote.Thefirstissmall,intermittentstepchangesthattypicallybringtheoutputclosertothe

desiredlevel.Whilenotconfirmed,thesearelikelyduetothediscretechangesinlook-uptablevalues.

Asthealgorithmtransitionsfromonebreakpointtoanother,itispossiblethatirregularitiesintheslope

valuealongthex-orpower-axisofFigure5.6couldcausesomejaggedbehavior.Theotherfeatureis

triangularoscillationaboutthedesiredoperatingpoint,mostnotablywhereincreasesinpoweroutput

aredesired.Thisnearinstabilityislikelyaresultoftheboostconverter’snaturallyoccurringrighthalf

planezeroincombinationwithcontrolactionsthataredelayedby0.01sfromthemeasurementstaken

andalimitedset-pointvoltagesteprate.Whenmorepowerisdesired,theconverteroutputvoltagewill

initiallydropbeforerisingagain.However,ifthecontrolmeasuresthisdecrease,then0.01slateritwill

demandthatthenextstepbeanincreaseandonlyaddtopotentialovershoot.

5.2.4. Look-uptablecreation

Oneofthedownsidestotheproposedalgorithmisthatyouneedadvancedknowledgeofthepowervs

voltageslopeforeachlevelofcurtailmentdesired.Unfortunately,thedesiredslopealsochangeswith

irradianceforagivencurtailmentlevel.Therefore,atwo-dimensionallook-uptablewasusedtoindicate

anapproximateslopeforagivencurtailmentlevelandpeakpower(relatedtolevelofirradiance).Figure

5.6isagraphicalrepresentationofthelook-uptablewherethexandyaxesrepresent“inputs”andthe

associatedzvalue“output”atthosecoordinatesrepresentstheslopedP/dVforthoseconditions.

49

Figure5.6.Look-uptableingraphicalform.

Photovoltaiccurrentvs.voltage(I-V)curvesalsohaveatemperaturedependence,buttheseeffectswill

besecondaryinsignificanceandwouldrequirea3-Dlook-uptable,sotemperaturedependencewas

ignoredinthisanalysis.Creationofthislook-uptablewasstillcomplicated,however,andinvolvedthe

followingprocedure:

1. Extractingraw,slowmeter,I-Vsweepdata(asdiscussedinSection2.1)forAugust1st,2013.

2. Groupingwell-behavedI-Vsweeps(asdefined inSection2.3.4) into0.1Wresolutionbinsbased

onthepeakpowerofeach.

3. CalculatingthemeanI-Vsweepforeachbin.

4. DeletingvaluesofP-VpairstotheleftoftheMPP.

5. Performing “localizedmoving average” operations to smooth the P-V data to bemonotonically

decreasing.

6. Calculatingdiscretederivativeswithacentralizeddifferenceapproximation

𝑷𝒊e𝟏 − 𝑷𝒊𝑽𝒊e𝟏 − 𝑽𝒊

≈ 𝐒𝐢e𝟏𝟐

(6.7)

inordertocreateaslopevsvoltageorS-Vcurve.

7. Repeating the “localized moving average” where needed (on non-monotonically decreasing

derivativecurves).

8. UsinglinearinterpolationontheP-Vcurvetocalculateapproximatevoltageassociatedwitheach

discretizedcurtailmentlevelbetween0%and99%ofpeakpower.

50

9. Correlatingeachinterpolatedvoltagewithaslopevalue,againusinglinearinterpolation.

10. Repeatingthisprocess(steps2-9)foreachpeakpowerrangeor“bin”.

11. Running a 5-element-wide windowmoving average across the peak power possible values for

constantcurtailmentratiototryandsmoothouttheratherjaggedoutputdatasurface.

Oncealloftheabovestepswereperformed,theoutputyieldedFigure5.6,whichisthesamedataused

forthelook-uptableintheDPPTalgorithm.

5.2.5. Butterworthcalculation

Oncetheconstantcurtailmentwasfunctional,mostanypiecewisecontinuouspoweroutputsequence

couldbecommanded.Inthisstudy,thesamelow-passButterworthfilterwasimplementedasin

Chapters3and4exceptwithalow-passcutoffof(1/60)Hz(orslowerthan1min).Onceachieved,this

targetpoweroutputwouldpossessmuchslowerdynamicsthantherawsolardata,decreasingthe

uncertaintyassociatedwithsolarpowerfromautilityperspective.Withthisexpectedoperatingpoint,

anytimethatavailablepowerisgreaterthancommandedpowerthesolarpowercanbecurtailedto

producetheexpectedpoweroutput.ThepurplecurveinFigure5.7representspowercommitmentor

commandthatcannotbemetwiththisstrategybecausethereisnoheadroom/reserveduringthose

times.Theintegraloftheseshortcomingsisdefinedtobetheremainingvariability,andmustbemet

withadditionalenergystorageorreservesiftheButterworth-filteredcommitmentistobemet.

Figure5.7.Rawsolardatatogetherwithfiltered,curtailedpowerdemanded,andpowerlackingcurves.

51

5.2.6. Results

ThefinalstepinthismodelcreationwastoimplementtheButterworthfilterintothecontrolloop.The

filtertookasinputrawdatamultipliedbyoneminusthenominalreserveor0.90inthiscase.Theoutput

wasusedtocalculatethenextcurtailmentpercentagecommand,anddividingthecurrentpanelpower

bythefilteroutputprovidedtheneededestimateofpeakpoweravailableatthatinstant.Figure5.8

illustratesasampleofthefinaloutputinwhichthedarkestcurve(black)representstheMPPatall

times,themediumdarknesscurve(blue)isthenominal90%valueforthecasewhere10%reserveis

desired,andthesmooth,dashedcurve(magenta)isafirst-order,low-pass,Butterworthfilterwithcut-

offfrequencyof(1/60)Hz.Thelightcurve(green)representsthemodeledoutputoftheDPPT

algorithm,whichasdesired,tracksthemagentaButterworthcurvewheneverpossible,andmaximizes

poweroutput(tracksorangecurve)wheneverinsufficientpowerisavailable.Again,thereisnotable,

triangularoscillationaboutthefilteredpowersetpoint(Figure5.8)thoughthisvirtuallydisappears

whenlimitedbythepeakpower.

Figure5.8.ActualoutputofDPPTmodelcomparedtocommandedpowerset-pointwithrawMPPdataand10%reserve

curveforreference.

5.3. EconomicjustificationforimplementationSolarpower“reserve”cancertainlylowerthecostofbatterystoragenecessarytomeetpower

commitments,butthequestionisiftheopportunitycostofthereserveisgreaterthanthebatterycost

beingoffset.Toinvestigatethisquestion,twoscenarioswerecompared:(1)MPPsolarpowerisoutput

atalltimes,andsufficientbatterycapacityisrequiredtoabsorballpeaksandsupplyforallvalleys

relativetothefilteredMPPoutput.(2)Thefilteredpoweroutputtargetisbasedona90%nominal

52

poweroutput,overheadorreservepowercanbeutilizedwhenbeneficial,andsolarenergycanbe

“spilled”whennotusefulinmeetingclaimedcommitment.Thesimplifyingassumptionsarethatinboth

scenariosthebatteriesarelosslessandthefilteredpoweroutputcommitmentmustbemetatalltimes

throughouttheday.

Forcase1,rawcapacitywasdeterminedtobethepeakcumulativesumofenergyeithersuppliedor

demandedfromthebatteries.Thisisbecausewewouldneedtoabsorbanypossiblevariationfromthe

filteredpowerintothebatteriestomeetourcommitment.Excessenergyandenergyshortageswould

offsetoneanotherinsaidsummation.Actualbatterycapacitywouldhavetobe~3.33timeslargerthan

therawcapacitysothatthebatterywouldoperatebetween20%and80%stateofcharge(SOC)andso

thatitcouldstartat50%SOCtoequallyhandleapotentialsurplusordeficitofequalmagnitude.

Forcase2,rawcapacityiscalculatedinasimilarmannerexceptthatfullpanelpowermaybeusedwhen

convenientandenergycanbe“spilled”byoperatingthesolarpaneloffofitsMPP.Thesamemultiplier

of3.33willbeusedforconsistency,thoughinreality,sincereserveenergyisverylikelytobeavailable

throughoutthedayandshortagesaretypicallybrief,muchlesssurplus-energycapacitywouldbe

neededandthecentralSOCmightbecloserto70%sothatoverallbatterycapacityrequiredcouldbe

reduced.Alternatively,batterycapacitycouldremainthesameascase1andbeusedfornighttime

energyratherthanpureregulationcapability.

Forthepurposeofthiscalculation,asampledaywasselectedfromtherawdataset.Allpowerand

energyvalueswillbescaledby1000torepresentacommercialsolarinstallationof20kW.Whilebattery

degradationislikelynonlinear,batterycyclinginthisanalysiswascalculatedasthecumulativetotalof

allenergyinandoutasafractionofnecessarybatterycapacity.Thetwoscenarioswerecalculated,and

fullbatterystorage(scenario1)wouldrequire0.399kWhofstoragewhilethereserve-basedmethod

wouldrequireonly0.131kWh.Additionally,thefilteringrequiredforthesampledaywouldcycle

approximately140%ofthebatterycapacityandinscenario2,3.41kWhofenergywouldbesacrificed

overthecourseoftheday.Taking,forexample,thecapacityandcostofaTeslaPowerwallbattery[48]

wecanestimateaperkWcostofbatterystoragetobe

$𝟑𝟎𝟎𝟎𝟔. 𝟒𝒌𝑾𝒉

= $𝟒𝟔𝟖. 𝟕𝟓/𝒌𝑾𝒉 (6.8)

Withtheratedcyclingestimateof5000cycles[49]at1.4cyclesperday,thatyields~9.78years.Callit

10yearsforconvenience.Thereducedbatterystoragerequirementcansave

𝟎. 𝟑𝟗𝟗 − 𝟎. 𝟏𝟑𝟏 𝒌𝑾𝒉× $𝟑𝟎𝟎𝟎𝟔. 𝟒𝒌𝑾𝒉

𝟏𝟎𝒚𝒆𝒂𝒓𝒔= $𝟏𝟐. 𝟓𝟔/𝒚𝒓

(6.9)

53

Theenergysacrificedcanbeviewedintwodifferentways.Ifviewedasanoperatingcost,thenevery

kWhmissedhastheopportunitycostoftheelectricityrateofabout$0.0999/kWh[50].Thus,overone

yeartheopportunitycostwouldbeasubstantial

$𝟎. 𝟎𝟗𝟗𝟗𝒌𝑾𝒉

×𝟑. 𝟒𝟏𝒌𝑾𝒉𝒅𝒂𝒚

×𝟑𝟔𝟓𝒅𝒂𝒚𝒔𝒚𝒓

= $𝟏𝟐𝟒. 𝟑𝟒/𝒚𝒓 (6.10)

However,wearereachingapointwheresolarpowercannolongerbetreatedasanegativeload

withoutgridstabilityconsequences.Ifitistobetreatedasatraditionalgeneratorthatmustprovide

regulationcapabilityandabidebyitsforecastcommitment,thenacostcalculationparadigmshiftis

required.Thecostofregulationbecomespartoftheinitialsolarinstallationorinvestmentfixedcost.At

currentcosts,solarenergyisestimatedtocost$0.05/kWh[45].If10%reserveisassumed,thenthecost

ofthesolarenergygoesupby1/(1-10%)or111%andthereservewillcost10%ofthisnewcostor

𝟏𝟎%×𝟏𝟏𝟏%×$𝟎. 𝟎𝟓𝒌𝑾𝒉

=$𝟎. 𝟎𝟎𝟓𝟓𝟔𝒌𝑾𝒉

(6.11)

Withthisnewperspectiveonthecostofthereserve,thecostperyearbecomes

$𝟎. 𝟎𝟎𝟓𝟓𝟔𝒌𝑾𝒉

×𝟑. 𝟒𝟏𝒌𝑾𝒉𝒅𝒂𝒚

×𝟑𝟔𝟓𝒅𝒂𝒚𝒔𝒚𝒓

=$𝟔. 𝟗𝟏𝒚𝒓

(6.12)

whichisconsiderablylowerthanthebenefitgainedbyreducedenergystorageneeds,whichisalsoan

upfront,fixed,investmentcost.

54

6. ConclusionContinuedintegrationofrenewableenergyresourcesontotheelectricgridincreasesvariabilityand

decreasesgridstability.Energystoragecanhelpmitigatesomeoftheseeffects,buttraditionalenergy

storage,suchasbatteries,istypicallyexpensiveandhasotherdisadvantagessuchasroundtrip

inefficiencyandlimitedlifetime.Real,high-speedsolarpaneldatawasusedtocharacterizethe

stochasticenergyoutputofPVsources,andthenumerouschallengesfacedandmethodsusedwhen

manipulatingthisreal-lifedatasetweredetailed.Twoalternativemethodswerethenpresentedto

absorborreducethevariabilityimposeduponthegridbyPVorothergeneration.

DynamicHVACloadcompensationwasproposedasamethodtoabsorborfiltershort-termPV

variabilityandactaseffectivegridinertiathatisbeingreplacedbynon-inertialgeneration.Aproposed

Butterworthfilterpowertargettechniquebalancedenergystoragedemandswithdecreased

uncertainty.Asmall-scalemodelofavariablespeedblowerandfanwasusedtoestimatefiltering

limitationsimposedbyundesirableacousticeffectsandtoprovideaconversionbetweenfanspeedand

powerconsumed.Physicalceilingandfloorlimitationsaswellasthermallimitationsfurtherconstrain

theavailablefilteringpotential.Consideringalloftheimposedlimitations,thevariationabsorptionor

filteringcapabilityofdynamicHVACloadcompensationwasanalyzedforvariousbuildingsizesandon-

sitesolarpenetrations.Aswouldbeexpected,thelargertherelativesizeoftheHVACpower

consumptiontothePVpowercapacity,thegreaterthesystemabilitytoabsorbvariationsinpower

production.Decreasedlimitationssuchasramprateandamplitudelimitswouldalsoenableincreased

filteringcapability.Thereductioninbatterystoragecapacitywasbrieflyinvestigatedandofnotewas

thesubstantialreductioninenergythathadtopassintoandoutofthebatterywhendynamicload

compensationwasimplemented.

PVoperatingreservecurtailmentwasthenintroducedasawaytoreducevariabilityboththrough

croppingofpowerspikesthroughcurtailmentaswellaspartiallycompensatingpower“valleys”by

utilizingPVoperatingreserve.ThesameButterworthfilterpowertargetmethodwasusedforanalysis,

andthevariabilityquantifiedintermsofabsolutevariationandintegrateddifferencesfromthetarget

setpoint.TheideaofoperatingreservecurtailmentthenledtotheargumentthataspricesofPV

continuetocomedown,thecostofgridregulationshouldbeincludedinthecostofinstalledPVand

renewableresourcesjustasitisforconventionalgridgeneration.PValreadycanactasagridresource

ratherthanagridnuisancebyprovidingrapidresponsetimestofaults,frequencyregulation,ramping

capability,andotherservices.Thismindsetofsolarasagridresourcemakesoperatingreserve

55

curtailmentaneconomicalchoice,andthecostcomparisonwasprovidedforvaryingamountsof

curtailmentandPVpricepoints.Aproposedmetricofoptimalitywaspresentedthatbalancesenergy

productionwithdecreasedvariability.Theresultsindicatethatnoonelevelofoperatingreserve

curtailmentisoptimalforalldays,andthatdependinguponthetypeofcloudcoverexperienced,the

optimalenergy-variabilitypeakmayliebeyondtheeconomicbreak-evenpointandthusbecost

constrained.

Aproof-of-conceptmodelfordesiredpowerpointtrackingor“DPPT”wasdemonstrated.Themodel

wasbuiltupinstages,firstimplementinganMPPTincrementalconductancealgorithm,thenreplacing

theconverterwithanaveragemodelandsimilardynamics,thenoperatingatafixedfractionofthe

MPP,andfinallytrackingadynamicButterworthsignal.Theendresultwasanalgorithmthatcould

calculateandtrackafilteredversionoftherawsolarpanelpoweravailable.Bydemonstratingthatsuch

operationcanbeaccomplishedwithnothingmorethanamodifiedcontrolscheme,thereexistsaclear

pathtoreal-lifeimplementationinphotovoltaicinverterswithoutadditionalhardware.Withthe

paradigmshiftinPVvariabilitymitigationrequirements,implementingsuchachangewillprovidethe

necessaryregulationforpredictablepoweroutputatalowercostthanadditionalinvestmentin

chemicalenergystorage.

6.1. FutureworkWhilethesolardatausedforthisworkwassufficient,rerunningsimulationsforanentireyearormore

ofsolardatawouldleadtomorerealisticresults.Knowingnowthat100Hzeffectivelycapturesall

meaningfuldynamics,andtakinglessonsfromthefirstPVacquisition,arepeatexperimentcouldyielda

continuousdatasetsuitableforlong-termanalysisofvariabilitymitigationtechniques.

RegardingtheHVACanalysis,full-scaledataorexperimentsareessentialtoverifyoradjustthe

assumptionsmadewheninvestigatingdynamicloadcompensation.Withrecentaccesstofanpower

andairflowmeasurements,datafromfull-scaleHVACunitscouldbesubstitutedinforthescaled

approximations.Additionally,correlatedaudiorecordingsfromactuallabsorclassroomswithpower

usagedatacouldleadtobetterramprateandamplitudelimitapproximations.Occupancysensordatais

alsoavailable,sofurtheranalysisisencouragedtodeterminehowmuchofthebuildingisunoccupiedat

agiventimeandwhatadditionalflexibilitythatlendstoHVACpowerfiltering.Alongthesesamelines,

watertankstoragehasagiantpotentialcapacityforthermalenergyabsorptionandlittletono

56

limitationonramprate,soifsuchsystemscanbemoreaccuratelycharacterized,theirthermalinertia

couldsupplementthatofbuildingsandair.

Muchofthisdatacouldbegatheredfromsensorsandfedtocontrolalgorithms,butpublicawareness

wouldbeexcludedfromsuchasetup.Futureworkshouldalmostcertainlyincludepubliceducationof

thevariabilityimposedonthegridbyphotovoltaicfluctuationsandthemitigationtechniquesactively

engagedincombattingit.Theformatcouldbeassimpleasanenergydashboarddisplayingprevented

powervariationandwherethatenergyisbeingstored,diverted,oreliminated.Afterall,short-term

variabilityofrenewablesisoftenoverlooked,soiftheproblemistobeaddressed,peoplefirstneedto

knowthattheproblemexistsandthenneedtoknowwhatsolutionsexistandhowtheywork.

TheDPPTalgorithmstillneedsconsiderableoptimizationrequirementsbeforeoperationalhardware

mayberealized.Ofprimaryconcernisthehigh-frequencyoscillationinpoweroutput,whichwouldbe

undesirabletoconnecttothegrid.Additionally,futureworkwillincludeinvestigatingalternativeset-

pointpowertargets.Forexample,short-termforecastsmaybesubstitutedfortheButterworthfilterset

points.

Tosummarize,bothofthetwoproposedvariabilitymitigationmethodspresentedinthisthesisare

inexpensivealternativestobatterystorage,needinglittlemorethananadvancedcontroltobe

implemented.However,eachmethodisalsoincapableofremovingallvariabilityintroducedbyPV.

Together(withotherthermalstorageoutletspotentiallyutilized),theproposedalternativescan

drasticallydecreaseoreliminatenecessarychemicalenergystorage,provideinexpensivegridstability

resources,andenableincreasedpenetrationofrenewableenergytechnologiesforaclearer,brighter

future.

57

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