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Copyright2010CleanPowerResearch 1

PVPowerOutputVariability:CorrelationCoefficients

ThomasE.HoffandRichardPerez

CleanPowerResearch

www.cleanpower.com

Draft,November11,2010

AbstractUtilityplannersandoperatorsareresponsibleforguidingwherePVsystemsarelocatedandare

accountableforsystemreliability.TheyareconcernedabouthowshorttermPVsystemoutputchanges

mayaffectutilitysystemstability.Thatis,theyareconcernedaboutPVpoweroutputvariability.

Thispaperintroducesanovelapproachtoestimatethemaximumshorttermoutputvariabilitythata

fleetofPVsystemsplacesonanyconsideredpowergrid.Akeyinputtothisapproachisthecorrelation,

orabsencethereof,existingbetweenindividualinstallationsinthefleetattheconsideredvariability

timescale.

ShorttermPVpoweroutputvariabilityisdrivenbychangesintheclearnessindex.Thus,thepaper

focusesonanalyzingthecorrelationcoefficientofthechangeintheclearnessindexbetweentwo

locationsasafunctionofdistance,timeinterval,andotherparameters. Thepaperpresentsamethod

toestimatecorrelationcoefficientsthatuseslocationspecificinputparameters.Themethodappearsto

becapableofdescribingsitepaircorrelationacrosstimeintervalsfromsecondstohours.

Themethodisderivedempiricallyandvalidatedusing12yearsofhourlysatellitederiveddatafrom

SolarAnywhereinthreegeographicregionsintheUnitedStates(Southwest,SouthernGreatPlains,and

Hawaii).Resultsattimeintervalslessthanonehourarecorroboratedusingfindingsfromrecent

investigationsthatwerebasedon10secondtooneminutedatasets.

Thestrengthandstructureofthemethodissummarizedbythreefundamentalfindingsthatboth

confirmandextendconclusionsfrompreviousstudies:

1. Correlationcoefficientsdecreasepredictablywithincreasingdistance.2. Correlationcoefficientsdecreaseatasimilarratewhenevaluatedversusdistancedividedbytheconsideredvariabilitytimeinterval.3. Theaccuracyofresultsisimprovedbyincludinganimpliedcloudspeedterm.

ThepresentapproachhaspotentialfinancialbenefitstosystemsthatareconcernedaboutPVpower

outputvariability,rangingfromdistributionfeederstobalancingregions.

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Copyright2010CleanPowerResearch 2

IntroductionPVcapacityisincreasingonutilitysystems.Asaresult,utilityplannersandoperatorsaregrowingmore

concernedaboutpotentialimpactsofpowersupplyvariabilitycausedbytransientclouds.Utilitiesand

controlsystemoperatorsneedtoadapttheirplanning,scheduling,andoperatingstrategiesto

accommodatethisvariabilitywhileatthesametimemaintainingexistingstandardsofreliability.

Itisimpossibletoeffectivelymanagethesesystems,however,withoutaclearunderstandingofPV

outputvariabilityorthemethodstoquantifyit.Whetherforecastingloadsandschedulingcapacity

severalhoursaheadorplanningforreserveresourcesyearsintothefuture,theindustryneedstobe

abletoquantifyexpectedoutputvariabilityforfleetsofuptohundredsofthousandsofPVsystems

spreadacrosslargegeographicalterritories.Underestimatingreserverequirementsmayresultina

failuretomeetreliabilitystandardsandanunstablepowersystem.Overestimatingreserve

requirementsmayresultinanunnecessaryexpenditureofcapitalandhigheroperatingcosts.

ThepresentobjectiveistodevelopanalyticalmethodsandtoolstoquantifyPVfleetoutputvariability.

Variabilityintimeintervalsrangingfromafewsecondstoafewminutesisofprimaryinterestsincecontrolareareservesaredispatchedoverthesetimeintervals.Forexample,regulationreservesmight

bedispatchedatanISOeveryfivesecondsthroughabroadcastsignal.KnowledgeaboutPVfleet

variabilityinfivesecondintervalscouldbeusedtodeterminetheresourcesnecessarytoprovide

frequencyregulationserviceinresponsetopowerfluctuations.

VariabilityofaPVfleetisthusameasureofthemagnitudeofchangesinitsaggregatepoweroutput

correspondingtothedefinedtimeintervalandtakenoverarepresentativestudyperiod.Notethatitis

thechangeinoutput,ratherthantheoutputitself,thatisdesired. Alsonotethat,foreachtimeinterval

thechangeinoutputmayvaryinbothmagnitudeandsign(positiveandnegative). Astatisticalmetricis

thereforeemployedinordertoquantifyvariability:thestandarddeviationofthechangeinfleetpower

output.

Itishelpfultographicallyillustratewhatismeantbyoutputvariability.TheleftsideofFigure1presents

10secondirradiancedata(PVpoweroutputisalmostdirectlyproportionaltoirradiance)andtheright

sideofthefigurepresentsthechangeinirradianceusinga10secondtimeintervalforanetworkof25

weathermonitoringstationsina400meterby400metergridlocatedatCordeliaJunction,CAon

November7,2010(HoffandNorris,2010).Thelightgraylinescorrespondtoirradianceandvariability

forasinglelocationandthedarkredlinescorrespondtoaverageirradiancedistributedacross25

locations.Resultssuggestthatspreadingcapacityacross25locationsratherthanconcentratingitata

singlelocationreducesvariabilitybymorethan70percentinthisparticularinstance.

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Copyright

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Copyright2010CleanPowerResearch 4

outputvariabilitytobethestandarddeviationofthechangeinoutputoversometimeinterval(suchas

oneminute),usingdatatakenfromsometimeperiod(suchasoneyear).

Thesimplifiedmodelcoveredthespecialcasewhenthechangeinoutputbetweenlocationsis

uncorrelated(i.e.,cloudimpactsatonesitearetoodistanttohavepredictableeffectsatanotherforthe

consideredtimescale),fleetcapacityisequallydistributed,andthevarianceateachlocationisthesame. Undertheseconditions,HoffandPerezshowedthatfleetoutputvariabilityequalstheoutput

variabilityatanyonelocationdividedbythesquarerootofthenumberoflocations:1

(1)

whereisthestandarddeviationofthechangeinoutputofthefleetusingatimeintervaloft, isthestandarddeviationofthechangeinoutputofthefleetconcentratedatasinglelocation,andNisthenumberofuncorrelatedlocations.

MillsandWiser(2010)havederivedasimilarresultthatrelatesvariabilitytothesquarerootofthe

numberofsystemswhenthelocationsareuncorrelated.

MaximumOutputVariabilityEquation(1)hasimportantimplicationsforutilityplanners.Itallowsthemtodeterminereserve

capacityrequirementstomitigateworstcasefleetvariability. Forexample,supposethatthevariability

ofasinglesystemwas10kWperminuteandtherewere100uncorrelatedidenticalsystemsinthefleet.

Totalfleetvariabilityequals0.1MW(

perminute. Theplannercouldthenapplythedesired

confidencelevel(e.g.,theymaychoose3standarddeviations)todeterminetherequiredreserve

capacity(e.g.,3x0.1MW=0.3MW).

Thiscalculationisapplicablewhentwofundamentalconditionsaresatisfied:(1)theoutputvariabilityat

asinglelocationcanbequantifiedand(2)thechangeinoutputvariabilitybetweenlocationsis

uncorrelated.

Considerthefirstcondition. Oneapproachtodeterminingsinglelocationvariability( )istoanalyze

historicalsolarresourcedataforthelocationofinterest.Thedatawouldneedtohavebeencollectedat

aratethataccommodatesthetimeintervalofinterest(perhapsdowntoafewseconds)overa

substantialandrepresentativeperiodoftime(perhapsoverseveralyears).Suchhighspeed,high

resolutiondataisnotgenerallyavailable.2

Analternativeapproachistoconstructadatasetthatsimulatesworstcasevariabilityconditions.The

theoreticallyworstcasevariabilityofasinglePVplantwouldbethatitcyclesalternatelybetween0and

100percentofitsratedoutputeverytimeinterval.Forexample,supposethatthePVplantisratedat1

1SeeEquation(8)inHoffandPerez(2010).2OneofthefewexamplesofthissortofdataisprovidedbyKuszamaul,et.al.(2010).

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Copyright2010CleanPowerResearch 5

MWandthetimeintervalofinterestis1minute.AsillustratedinTable1,maximumvariabilityoccurs

whenthePVplantisatfullpowerat12:00,zeropowerat12:01,fullpowerat12:02,etc.Asillustrated

intherightsideofthetable,thecorrespondingchangeinpowerfluctuatesbetween 1and1MW.The

standarddeviation3ofthechangeinpoweroutputequals1MWperminute.Thatis,a1MWPVplant

thatisexhibitingmaximumvariabilityovera1minutetimeintervalhasa1MWperminutestandard

deviation.Thiswouldimplythat1MWofreservecapacityisrequiredtocompensatefortheoutput

variabilityforasingleplant.

Table1.Maximumchangeinpoweroutputatonelocation.

Time Power(MW) Change(MW/min)

12:00 1 1

12:01 0 +1

12:02 1 1

12:03 0 +1

12:04 1

SupposethatthePVfleetcapacitywassplitbetweentwolocationsandeachweretoexhibit

maximumoutputvariability.Twopossiblescenariosexist.Thefirstscenario,illustratedinTable2,

assumesthatbothplantsturnonandoffsimultaneously.Aswasthecasewhereallcapacityis

concentratedatasinglelocation,thechangeinoutputfluctuatesbetween 1and1MWandthe

standarddeviationforthisscenariois1MWperminute.

Thesecondscenario,illustratedinTable3,assumesthattheplantscycleonandoffalternatelywitha

timeshiftof1minute.Inthiscase,thechangeinoutputfromthefirstlocationcancelsthechangein

outputatthesecondlocation.Theresultofthisscenarioisastandarddeviationof0MWperminute.

Itisincorrecttoconclude,however,thattheupperboundofoutputvariabilityfor1MWofPVis1MW

perminutebecausethisisthelargervalueofthetwoscenarios(thefirstequals1MWperminuteand

thesecondequals0MWperminute).Thisisbecauseeachofthetwoscenariosviolatestheassumed

conditionthatthelocationsareuncorrelated.Specifically,thechangeinoutputbetweenthetwo

locationshasperfectpositivecorrelationinthefirstscenario(i.e.,correlationcoefficientequals1)and

perfectnegativecorrelationinthesecondscenario(i.e.,correlationcoefficientequals 1).

3ThestandarddeviationofarandomvariableXequalsthesquarerootoftheexpectedvalueofXsquaredminusthesquareoftheexpectedvalueofX. EX EX.

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Table2.Maximumchangeinpoweroutputattwolocations(scenario1).

Time Power(MW) Change(MW/min)

Plant1 Plant2

Fleet

(1+2)

12:00 0.5 0.5 1 112:01 0 0 0 +1

12:02 0.5 0.5 1 1

12:03 0 0 0 +1

12:04 0.5 0.5 1

Table3.Maximumchangeinpoweroutputattwolocations(scenario2).

Time Power(MW) Change(MW/min)

Plant1 Plant2 Fleet1+2

12:00 0.5 0 0.5 0

12:01 0 0.5 0.5 0

12:02 0.5 0 0.5 0

12:03 0 0.5 0.5 0

12:04 0.5 0 0.5

FeasibleMaximumOutputVariabilityThesescenariosdemonstratethatitisimpossiblefortwosystemstoexhibitthebehaviorofworstcase

varianceindividually(bycyclingonandoffateachinterval)withouthavingeitherperfectpositiveor

perfectnegativecorrelation.Indeed,foreachsystemtoexhibititsmaximumvariance,itsoutput

changesmustbeexactlyintempowiththetimeinterval,looselyanalogoustoeachmemberofan

orchestrafollowingintimetoitsconductor,inwhichcasethesystemswouldbydefinitionhaveperfect

correlation(whetherpositiveornegative).Bythisreasoning,themaximumoutputvariabilityscenario

describedabove(1MWofvariabilityforeach1MWoffleetcapacity)isimpossible.Whenthesystems

havelessthanperfectcorrelation,asmustbethecaseforanyrealworldfleet,thevariabilityofthe

combinedfleetmustbelessthanthetotalfleetcapacity.

Tocorrecttheworstcasescenario,retaintheassumptionthateachpowerchangeiseitheratransition

fromzerooutputtofulloutputorfromfulloutputtozerooutput. Thisassumptioninitselfishighly

conservativesincetheimpactsofcloudtransientsonPVsystemswillalmostneverproducechanges

withmagnitudesashighas100percentofratedoutputandwillgenerallyproducechangesmuchless

than100percent.Asfortiming,ratherthanbeingsynchronized,eachsystemisassumedtocycleonand

offinarandomfashion,representingfleetsofPVsystemswithoutputsthatareuncorrelated.

RandomtimingofpoweroutputchangesisillustratedforasinglelocationinTable4fora1MWPV

system.Supposethatitis12:00andthetimeintervalis1minute.Thereisa50percentchancethatthe

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7/30/2019 075_PVPowerOutputVariabilityCorrelationCoefficients

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CorrelationversusDistanceBackground:CriticalFactorsAffectingCorrelationThecriticalfactorsthataffectoutputvariabilityaretheclearnessofthesky,sunposition,andPVfleet

orientation(i.e.,dimensions,plantspacing,numberofplants,etc.).Toimproveaccuracy,HoffandPerez

(2010)introducedaparametercalledtheDispersionFactor.TheDispersionFactorisaparameterthat

incorporatesthelayoutofafleetofPVsystems,thetimescalesofconcern,andthemotionofcloud

interferencesoverthePVfleet.HoffandPerezdemonstratedthatrelativeoutputvariabilityresulting

fromthedeploymentofmultipleplantsdecreasedquasiexponentiallyasafunctionofthegenerating

resourcesDispersionFactor.Theirresultsdemonstratedthatrelativeoutputvariability(1)decreasesas

thedistancebetweensitesincreases;(2)decreasesmoreslowlyasthetimeintervalincreases;and(3)

decreasesmoreslowlyasthecloudtransitspeedincreases.

MillsandWiser(2010)analyzedmeasuredoneminuteinsolationdataoveranextendedperiodoftime

for23timesynchronizedsitesintheSouthernGreatPlainsnetworkoftheAtmosphericRadiation

Measurement(ARM)program.Theirresultsdemonstrated7

thatthecorrelationofthechangeintheglobalclearskyindex(1)decreasesasthedistancebetweensitesincreasesand(2)decreasesmore

slowlyasthetimeintervalincreases.

Perezet.al.(2010b)analyzedthecorrelationbetweenthevariabilityobservedattwoneighboringsites

asafunctionoftheirdistanceandoftheconsideredvariabilitytimescale.Theauthorsused20second

tooneminutedatatoconstructvirtualnetworksat24USlocationsfromtheARMprogram(Stokesand

Schwartz,1994)andtheSURFRADNetworkandcloudspeedderivedfromSolarAnywhere(2010)to

calculatethestationpaircorrelationsfordistancesrangingfrom100metersto100kmandfrom

variabilitytimescalesrangingfrom20secondsto15minutes.Theirresultsdemonstratedthatthe

correlationof

the

change

in

global

clear

sky

index

(1)

decreases

as

the

distance

between

sites

increases

and(2)decreasesmoreslowlyasthetimeintervalincreases.

Theconsistentconclusions8ofthesestudiesarethatcorrelation:(1)decreasesasthedistancebetween

sitesincreasesand(2)decreasesmoreslowlyasthetimeintervalincreases.HoffandPerez(2010)add

thatthecorrelationdecreasesmoreslowlyasthespeedofthecloudsincreases.

ObjectiveUtilityplannersclearlyrequireatoolthatcanreliablyquantifythemaximumoutputvariabilityofPV

fleetsusingamanageableamountofdataandanalysis.Equation(3)wouldpotentiallymeetthis

requirementifthechangeinoutputbetweenlocationswereuncorrelated(i.e.,correlationcoefficientis

zero).Inrealfleets,PVsystemswillgenerallyhavesomedegreeofcorrelation,soanyplanningtoolwill

havetoincorporatecorrelationeffectsincalculatingactualfleetvariability.

Thispapertakesasteptowardsageneralmethodbyanalyzingthecorrelationcoefficientofthechange

inclearnessindexbetweentwolocationsasafunctionofdistance,timeinterval,andotherparameters.

7SeeFigure5inMillsandWiser(2010).8TheresultsapplytoeitherchangesinPVoutputdirectlyorchangesintheclearskyindex

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ItuseshourlyglobalhorizontalinsolationdatafromSolarAnywhere(2010)tocalculatecorrelation

coefficientsfor70,000scenariosacrossthreeseparategeographicregionsintheUnitedStates

(Southwest,SouthernGreatPlains,andHawaii).Thecorrelationcoefficientstakenfromthesescenarios

arethencomparedtoamethodthatcouldproveusefulwhenintegratedintoutilityplanningand

operationstool.Recognizingthatthemethodmustalsobevalidatedforshortertimeintervals(several

secondstoseveralminutes),itsresultsarecomparedtostudiesbasedon10second,20second,and1

minuteinsolationdatasets.

ApproachHoffandPerez(2010)definedPVfleetvariabilityasthestandarddeviationofitspoweroutputchanges

usingaselectedsamplingtimeinterval(e.g.,suchasoneminuteoronehour)andanalysisperiod(such

asoneyear),asexpressedrelativetothefleetcapacity.Tosimplifythework,theyformulateditinterms

ofthechangeininsolationratherthanthechangeinPVpower.

Asstatedearlier,skyclearnessandsunpositiondrivethechangesinshorttermoutputforindividualPV

systems.MillsandWiser(2010)andPerez,et.al(2010)subsequentlyisolatedtherandomcomponentofoutputchangeandexaminedchangesattributableonlytochangesinglobalclearsky(orclearness)

index.Theglobalclearnessindexequalsthemeasuredglobalhorizontalinsolationdividedbytheclear

skyinsolation.

ThispapercontinuesinthedirectionofMillsandWiser(2010)andPerez,et.al.(2010)andfocuseson

changesintheglobalclearnessindex.

ChangeinGlobalClearnessIndexTheglobalclearnessindexataspecificpointintimeistypicallyreferredtoasKt*.Itequalsthe

measuredglobalhorizontalinsolation(GHI)dividedbytheclearskyinsolation.Thispaperreferstothe

changeintheindexbetweentwopointsintimeas Kt*.Sincethechangeoccursoversomespecified

timeinterval, t,atsomespecificlocationn,thevariableisfullyqualifiedas,

.Thisonly

representsonepairofpointsintime.Asetofvaluesisidentifiedbyconventionbyboldingthevariable.

Thus,

isthesetofchangesintheclearnessindicesataspecificlocationusingaspecifictime

intervaloveraspecifictimeperiod.

,,

,,, ,, ,,

(4)

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Copyright2010CleanPowerResearch 11

Table5illustrateshowtocalculatethechangeinclearnessindex(Kt*)duringconditionsofrapidly

changinginsolation.Forexample, Kt*between12:00and12:01equalsthedifferencebetweenKt*at

12:01andKt*at12:00(0.51.0= 0.5).

Table5.Exampleofhowtocalculatechangeinclearnessindex(Kt*)using t=1minute.

Time GHI ClearskyGHI Kt* Kt*

12:00 1.0 1.0 1.0 0.5

12:01 0.5 1.0 0.5 0.5

12:02 0.0 1.0 0.0 +0.5

12:03 0.5 1.0 0.5 +0.5

12:04 1.0 1.0 1.0

Correlationanddependenceinstatisticsareanyofabroadclassofstatisticalrelationshipsbetweentwo

ormorerandomvariablesorobserveddatavalues(Wikipedia2010).Let

and

represent

twosetsofobserveddatavaluesforthechangeintheclearnessindexthathaveameanof0and

standarddeviations,and.9

Pearsonsproductmomentcorrelationcoefficient(typicallyreferredtosimplyasthecorrelation

coefficient)equalstheexpectedvalueof times dividedbythecorrespondingstandarddeviations.

,

(5)

Theanalysisisperformedasfollows:

1. Selectageographicregionforanalysis2. Selectalocationforthefirstpartofthepair3. Selectalocationforthesecondpartofthepair4. Selectatimeintervalfortheanalysis5. Selectaclearskyirradiancelevelbin6. Obtaindetailedinsolationdata7. Calculatethecorrelationcoefficient108. Repeatthecalculationforallsetsoflocationpairs,timeintervals,andclearskyirradiancebins.

9TheexpectedvalueofKt*equals0aslongasthestartingandendingGHIvaluesarethesame.Thisconditionis

satisfiedwhenthetimeperiodoftheanalysisisperformedoveronedaybecausethestartingandendingGHIboth

equal0.Itwillalsobeapproximatelytruewhentheanalysisencompassesmanydatapoints(aswouldbethecase,

forexample,ofananalysisofonehourofdatausingaoneminutetimeinterval).

10AppendixBillustrateshowtocalculateKt*correlationcoefficients.

7/30/2019 075_PVPowerOutputVariabilityCorrelationCoefficients

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7/30/2019 075_PVPowerOutputVariabilityCorrelationCoefficients

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Copyright2010CleanPowerResearch 20

ThepaperusedhourlyglobalhorizontalinsolationdatafromSolarAnywheretovalidatethemethodby

calculatingcorrelationcoefficientsfor70,000scenariosacrossthreeseparategeographicregionsinthe

UnitedStates(Southwest,SouthernGreatPlains,andHawaii),whilevaryingdistance,timeinterval,

insolationbin,andotherparameters.Theseempiricalcorrelationcoefficientscomparedfavorablywith

thosederivedbythemethod. Themethodwasthenshowntobeindependentofselectedtimeinterval,

suchthathourlysatellitedatacouldbeusedtocalculatecorrelationcoefficientsforveryshorttime

intervals(severalsecondstoseveralminutes).Theseextrapolatedresultswerevalidatedusingresults

fromstudiesthatarebasedon20secondtooneminuteinsolationdata.

Thepaperhadseveralimportantfindings.First,correlationcoefficientsdecreasedwithincreasing

distance.Second,correlationcoefficientsdecreasedatasimilarratewhenplottedversusdistance

dividedbytimeinterval.Third,theaccuracyofresultswasfurtherimprovedwhenanimpliedspeed

termisintroducedintotheanalysis.Together,theseresultsprovidedthebasisforvalidatingthe

generalizedmethod.Themethod,basedoninputparametersfromhourlySolarAnywheredata,

producedcorrelationcoefficientsforshorttimeintervals(secondstominutes)thatcomparedquitewell

toresultsfromindependentstudiesthatused10second,20second,andoneminutedatasets.

Thepreliminaryconclusionofthisworkisthattheapproachvalidatedinthispapercanbeusedto

identifytheconditionsunderwhichthechangeinoutputbetweenlocationsareuncorrelated.Asa

result,itcanbeusedtosatisfyoneoftheinitialmotivationsofthisstudy:thedesiretoequiputility

plannerswithatoolcapableofplacinganupperboundonthemaximumoutputvariabilityofafleetof

PVsystemsusingamanageableamountofdataandanalysis.

Theresults,however,mayhavefurtherimplications.Inparticular,theresultsmaybethebasisfor

quantifyingoutputvariabilityevenwhencorrelationexists.

NextStepsThisstudydemonstratedtheabilitytopredictcorrelationcoefficientsusingtimeintervalsof1to4hours

usingmultiyeardatasets.Resultsalsosuggestedthatthemethodisvalidforshorttimeintervalswhen

comparedtohighspeedstudies,againbasedonlongtimeperioddatasets.

Thenextstepswillbetofurthervalidatetheresultsforshorttimeintervalsusingmeasuredhigher

speeddata.Plansincludetheuseof:1kmx1kmgrid,hourSolarAnywheredatainselectedlocations;

1kmx1kmgrid,oneminuteextrapolatedSolarAnywheredatainselectedlocations;andadditional10

seconddatafromthemobile,highdensitynetworkdescribedearlier(HoffandNorris,2010).A

particularlyimportantfocusofthisworkwillbetoassessthemethodsabilitytopredictcorrelation

betweenlocationsovershorttimeperiodsaswellaslongtimeperiods(severalhoursversusseveral

years).

AcknowledgementsPortionsofthisstudywerefundedunderaCaliforniaSolarInitiative(CSI)GrantAgreementtitled

AdvancedModelingandVerificationforHighPenetrationPV.TheCaliforniaPublicUtilities

CommissionistheFundingApprover,ItronistheProgramManager,andPG&EistheFunding

7/30/2019 075_PVPowerOutputVariabilityCorrelationCoefficients

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Copyright2010CleanPowerResearch 21

Distributor.ThankstoBenNorris(CleanPowerResearch)whodesigned,implemented,andoperated

themobileirradiancenetworkandprovidedvaluablecommentsonthepaper.ThankstoJeffRessler

(CleanPowerResearch)forhiscomments.Opinionsexpressedhereinarethoseoftheauthorsonly.

ReferencesHoff,T.E.,Perez,R.2010.QuantifyingPVpowerOutputVariability.SolarEnergy84(2010)17821793.

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Forecasted7daysAheadandArchivalDatabacktoJanuary1,1998.www.SolarAnywhere.com.

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7/30/2019 075_PVPowerOutputVariabilityCorrelationCoefficients

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1.0 1.

tequals0.5

m2) Clear

#2 #11.0 1.

1.0 1.

0.0 1.

1.0 1.

1.0 1.

tequals0

m2) Clear

#2 #11.0 1.

1.0 1.

0.0 1.

0.0 1.

1.0 1.

ure13.Chan

earch

exampleso

correlation

Datatocalc

SkyI(kW/m2

#21.0

1.0

1.0

1.0

1.0

SkyI(kW/m2

#21.0

1.0

1.0

1.0

1.0

SkyI(kW/m2

#21.0

1.0

1.0

1.0

1.0

geinclearne

howtocalc

coefficients.

ulatecorrela

) Clearness

#11.0

0.0

0.0

1.0

1.0

) Clearness

#11.0

0.0

0.0

1.0

1.0

) Clearness

#11.0

0.0

0.0

1.0

1.0

ssindexforL

latethecha

tioncoefficie

Index C

#21.0

0.0

0.0

1.0

1.0

Index C

#21.0

1.0

0.0

1.0

1.0

Index C

#21.0

1.0

0.0

0.0

1.0

ocation2vs.

ngeinthecl

nts.

angeinClear

#11.0

0.0

+1.0

0.0

angeinClear

#11.0

0.0

+1.0

0.0

angeinClear

#11.0

0.0

+1.0

0.0

Location1.

arnessindex

essIndex

#21.0

0.0

+1.0

0.0

essIndex

#20.0

1.0

+1.0

0.0

essIndex

#20.0

1.0

0.0

+1.0

23

,