Electric Power Systems Research

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Electric Power Systems Research

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / e p s r

Electrical energy management in unbalanced distribution networks using virtual power plant concept

Mahmoud M. Othman

^a

, Y.G. Hegazy

^b

, Almoataz Y. Abdelaziz

^a,∗

aElectricalPowerandMachineDepartment,FacultyofEngineering,AinShamsUniversity,Cairo,Egypt

bGermanUniversityinCairo,Egypt

a r t i c l e i n f o

Articlehistory:

Received3September2015

Receivedinrevisedform3December2016 Accepted2January2017

Keywords:

Bigbangbigcrunch Distributedgenerators Optimization Virtualpowerplant

a b s t r a c t

Thispaperintegratesdifferentdevelopedoptimizationalgorithmsbasedonmodiﬁcationofthebigbang bigcrunchmethodforvirtualpowerplantrealization.Theproposedalgorithmsaimtomanagethe electricalenergyinunbalanceddistributionnetworksinordertominimizethepurchasedenergyfrom thegrid.Thisgoalisachievedthroughtheoptimalplacementofrenewablebaseddistributedgenerators, optimalschedulingofthecontrollableloadsandoptimaloperationofenergystorageelements.The proposedalgorithmsareimplementedinMATLABenvironmentandtestedontheIEEE37-nodefeeder.

Theresultsshowgreatreductioninthepurchasedenergyfromthegridandthesubsequentdiscussions emphasizethesigniﬁcanceofusingthevirtualpowerplantconceptinmanagingtheelectricalenergy.

1. Introduction

Virtualpowerplant(VPP)isarecentrapidlygrowingconcept thathasmanydefinitions;allthesedefinitionsagreeuponthefact thatVPP is anaggregationof distributedgeneration (DG,small generatingunitsconnectedtothedistributionnetwork)unitsof differenttechnologiesinordertooperateasasinglepowerplant thathastheabilitytocontroltheaggregatedunitsandtomanage theelectricalenergyflowbetweentheseunitsinordertoobtain betteroperationofthesystem[1–6].Fromtheauthorsperspec- tiveVPPcanbeviewedas“Aconcourseofdispatchableandnon dispatchableDGs,energystorageelementsandcontrollableloads accompaniedbyinformationandcommunicationtechnologiesto formasingleimaginarypowerplantthatplans,monitorstheoper- ation,andcoordinatesthepowerflowsbetweenitscomponentto minimizethegenerationcosts,minimizetheproductionofgreen- housegases,maximizetheprofits,andenhancethetradeinsidethe electricitymarket”.

VPPconsistsofthethreemaincomponents,distributedenergy resources(DER),energystorageelements(ESEs)andinformation andcommunicationsystems.DERcanbeeitherdistributedgen- eratorsorcontrollableloadsconnectedtothenetwork,ESEscan storeenergyduringoff-peakperiodsandfeeditduringthepeak

∗ Correspondingauthorat:DepartmentofElectricalPower&Machines,Faculty ofEngineering,AinShamsUniversity,AbdoBashaSquare,Abbassia,11517,Cairo, Egypt.

E-mailaddresses:almoataz[email protected], [email protected](A.Y.Abdelaziz).

periodsandtheinformationandcommunicationsystemsmanages theoperationofotherVPPcomponentsthroughcommunication technologiesinbidirectionalways.

The optimal VPP operation aims at enhancing its operation andminimizingthecostofitsproducedenergy.VPPoptimization methodologydependsonthepowersystemunderstudy;eitherif itisneworexisting.Foranewly-establishedpowersystem,VPP hastheabilitytochoosethecapacityandlocationoftheDGunits andESEs,andthelocationsoftheloadstobecontrolledandthe appropriatecontrolstrategiesandschedules.Ontheotherhand forexistingpowersystems,theseoptionsarelimitedastheloca- tionandsizeoftheDGunitsandESEs,andthelocationsofthe controllableloadsarepre-determined.Thestudiesslantedtoward theoptimizationoftheVPPoperation[7–23]canbecategorized intothreegroups:

1)DGunits’optimalsizingandsiting[7–15]:Researchersinvesti- gatedvariousoptimizationtechniquestodeterminetheoptimal location and size of DG in order to reduce power loss and improve the voltage proﬁle of the power system. Similarly, VPPoptimizationcanbecarriedoutthroughoptimalplacing ofstochasticDGunits(windandphotovoltaic).Otherstudies wereperformed toselect theoptimal capacity of a conven- tionalpowerplantusedincollaborationwithDGunitsaswell aspurchasingenergyfromtheelectricitymarkettosupplythe requiredVPPenergy.

Theoptimizationmethodsusedforoptimalsizingandsiting ofDGunitscouldbeanalytical[7–9],numerical[10–12]and heuristic[13–15].

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andinoptimizingthegenerationofstochasticDGs.

3)Optimal load control scheduling [21–23]: The VPP has the authoritytocontroloreventointerrupttheloadsaccordingto theirimportanceinordertooptimizeitsoperation.

Thispaper presentsthree optimization algorithms basedon modiﬁcationofthebigbangbigcrunch(BB–BC)method[24]for optimalplacementofrenewablebasedDGs,optimalsizingofESEs andoptimalloadcontrolscheduling.Theproposedalgorithmsare integratedtogether inorder tominimizetheenergy purchased fromthegridwhichrealizetheVPPconcept.Theproposedalgo- rithmsareimplementedinMATLABandtestedontheIEEE37-node feeder.Theresultsemphasizethesigniﬁcanceofusingthevirtual powerplantconceptinmanagingtheelectricalenergy.

2. Problemstatement

Theoptimizationproblemunderstudycanbestatedas:

GIVEN:theinputdatacomprisethedistributionfeederstruc- ture,feederloadsvalues,loadtypes,andavailablerenewablebased DGspowerschedule.

Objectivefunctions:theobjectivefunctionistominimizethe annualenergypurchasedfromgridusingEq.(1)

Minimize

96

h=1

P_sub,h×90 (1)

Where:P_sub,histheactivepowerpurchasedfromsubstationatcer- tainhourh.The96valuerepresentsthetotalnumberofhoursof thetypicaldaymodelofthefourseasons(4×24h),the90value representsthenumberofrepetitionofthetypicaldaymodelofthe fourseasons(3monthsforeachseason×30daysperseason).

REQUIRED:todetermineexactlytherequired(optimal)renew- ablebasedDGpowerscheduleandlocation,optimalloadcontrol scheduleandoptimalsizeandoperationscheduleoftheESEsforthe sakeofminimizingtheenergypurchasedfromsubstationwithout violatingthefollowingsystemconstraints:

•Voltagelimits:voltageateachbusshouldbewithinapermissible rangeusually:

0.95p.u.≤V ≤1.05p.u. (2)

•Linesthermallimit(lineAmpacity):itrepresentsthemaximum currentthatthelinecanwithstandatcertainDGpenetration, exceedingthisvalueleadstomeltingoftheline.

I_flow≤I_Thermal (3)

•Powerbalance:thesumofinputpowershouldbeequaltothe sumofoutputactivepowerinadditiontotheactivepowerloss.

Theinputpower mayinclude theDG activepower, theESEs powerandtheactivepowersuppliedbytheutility.Theactive outputpoweristhesumofloadsactivepower.

P_sub+P_ESE+

_P_DG₌

_P_loads ₊_P_loss ₍₄₎

ASSUMPTIONS:Thefollowingassumptionsaremade.

•AlltherenewableDGunitsareworkingataunitypowerfactor.

•Allbusesinthesystemunderstudyaresubjectedtothesame meteorologicalconditions.

•Allloadsparticipatingintheloadcontrolprogrammaybesub- jectedto10%reductionatanyhouroftheday.

•Allloadsarescaledbymultiplyingthembyloadscalingfactor obtainedfromthemodelingstrategypresentedinSection3.

•Controllingmultipleloadsatthesametimeintervalispermitted.

•Theenergycanbefedbacktothesubstation(i.e.grid).

•Anydaymodelforeachseasonstartsat12:00pm

APPROACH: apply themodiﬁed BB–BC methodto solvethe optimizationproblemand ﬁndtheoptimallocation andpower scheduleofDGs,optimalloadcontrolscheduleandoptimalcharg- ingand discharging scheduleof ESEsin order tominimizethe energypurchasedfromsubstation.

3. VPPcomponentsmodeling

3.1. RenewablebasedDGsandloadmodeling

ThemodelpresentedinRef.[25]isused.Thismodelconsiders thestochasticnatureanddependenceofrenewablebasedDGand systemdemand.ThisprobabilisticmodelisbasedonMonteCarlo methodanddiagonalbandcopulaaccordingtothreeyearsofhis- toricalmeteorologicalandsystemdemanddata.Theresultsofthis modelarethemostlikelihoodvaluesofthePVpower,windpower andsystemdemandforthe96hrepresentthefourseason’stypical daymodel.

3.2. Energystorageelementsmodeling

ESEmodelisdescribedusingEqs.(5)and(6)subjectedtothe constraintsfromEqs.(7)to(10)

Discharge: E(t+1)=E(t)+P(t).t/_d,p(t)=−ve (5) Charge: E(t+1)=E(t)+P(t).t.c,p(t)=+ve (6)

Subjectedtopowerlimits:

0≤P(t)._c≤P_max (7)

−P_max≤P(t)/_d≤0 (8)

Storedenergylimits:

0≤E(t)≤Emax (9)

Startingandendinglimits:

E(0)=E_final (10)

WhereE(t)istheenergystoredintheESEattimet.P(t)isthepower oftheESEoutputattimet.tisthetimedurationofeachinterval andequalsto1h._dand_carethedischargeandchargeefﬁciency respectively.P_maxisthemaximumdischargingorchargingrates.

EmaxisthemaximumenergystoredintheESErespectively.Forthe energybalanceoftheESE,theﬁnalstoredenergyinsidetheESE (E_final)attheendofperiodofstudyissettobethesameasinitial storedenergyinsidetheESE(E(0)).

4. Methodology

TheelectricalenergyismanagedwithintheVPPtoachievethe requiredobjectiveusingthefollowingprocedure:

1OptimalallocationofRESinordertoachievetherequiredobjec- tive(i.e.minimizetheenergypurchasedfromgrid).

2Determinationoftheoptimalloadcontrolschedulerequiredto minimizethepurchasedenergywhiletheRESareconnectedto theiroptimallocations.

3DeterminationoftheoptimalpowerscheduleoftheRES,consideringthemdispatchable,requiredtominimizethepurchased energy.

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Fig.1.Fourseasonstypicaldaymodelofaggregatedwindpowerofthetwowindturbines.

Table1

Characteristicsofthewindturbinesavailable.

Features Turbine1 Turbine2

Ratedpower 1MW 1.1MW

Cutinspeed(m/s) 4 4

Ratedspeed(m/s) 13 12

Cutoutspeed(m/s) 21 20

4UsingtheESEstominimizethedifferencesbetweentheoptimal powerschedule(obtainedfrompreviousstep)andactualpower scheduleoftheRES(obtainedfromthemodelpresentedinRef.

[25]).

4.1. OptimalallocationoftheRESforenergyminimization

Theproposedoptimizationalgorithmaimtodeterminetheopti- mallocationsofrenewablebasedDGsinordertominimizethe energypurchasedfromgrid.

ThesupervisedBB–BCisusedforspecifyingtheoptimalloca- tionsofrenewable DGsandtheoptimalhourlypowerschedule ofdispatchabledistributed generators. Theproposedmethodis discussedinthefollowingstepbystepprocedure.

Thefollowingstepbystepproceduresummarizestheproposed method.

1)Generaterandomlytheinitialvaluesofthelocationsforthetwo renewableDGs(windDGandPVDG).

2)Calculatetheannualenergypurchasedfromgridcorresponding toallinitialDGslocationsandtheseasonalhourlypowersched- uleofthewindDGorthePVDGbyrunningunbalancedload ﬂowforthe96h.

3)SelectthebesttwoDGlocationsthatachieveminimumannual energypurchased.

4)UpdatetheDGlocationsusingEq.(11).ThebestDGlocationis keptasaoneofthenewsystemvariables,theDGlocationsare roundedtothenearestinteger.

loc_new=loc_best+up_loc×Randn

it² (11)

WherelocnewisthenewcandidateDGlocation,loc_bestisthebestDG locationduringtheiteration,up_locisthemaximumvaluesofDGs’

locations,Randnisanormallydistributedrandomnumberanditis theiterationstep.

5)Repeatsteps(2–4)untiltheconvergencecriteriaismet,thecon- vergenceisconsideredachievedwhenmorethan50%oftheDGs’

locationsareconvergedtoacertainvalue.

4.2. Optimalloadcontrolforenergyminimization

Theproposedoptimizationalgorithm aims todeterminethe optimalloadcontrol schedulein order tominimizetheenergy purchasedfromgrid.Theproposedmethodisdiscussedinthefol- lowingstepbystepprocedure:

Table2

CharacteristicsofthePVmoduleavailable.

Module characteristics

Watt peak(W)

Opencircuit voltage(V)

Shortcircuit current(A)

Voltageat maximum power(V)

Currentat maximum power(A)

Voltage temperature Coefﬁcient (mV/^◦C)

Current temperature Coefﬁcient (A/^◦C)

Nominalcell operating temperature (^◦C)

Features 53 21.7 3.4 17.4 3.05 88 1.5 43

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Fig.2.Fourseasonstypicaldaymodelofoutputpowerof40,000PVmodules.

Fig.3.Fourseasonstypicaldaymodelofnormalizedsystemdemandproﬁle(loadscalingfactor).

Table3

OptimallocationforrenewableDGsforenergyminimization.

Testcase WindbasedDG

optimallocation

SolarbasedDGoptimal location

Energypurchasedfrom substation(MWh)

Energysuppliedto substation(MWh)

Basecase – – 14315.4 0

RESintegrated 25 7 5282.3 1485.4

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Fig.4.RenumberedIEEE37-nodefeeder.

1)Startwithacertainseason.

2)Deﬁneasetoftheloadsparticipatinginloadcontrolprogram (i.e.#NLnumberofloads).

3)Generaterandomlytheinitialvaluesofthesystemvariables(i.e.

loadlocationstobecontrolledandhours).

4)Performunbalancedloadﬂowtocalculatetheenergyreduction (purchasedfromsubstation)fromthebasecase(i.e.whereno controlisdone)correspondingtoallinitialvariables(control- lableloadsandhours).

5)Selectthebestcontrollableloadandhourthatachievemaximum energyreduction.

6)UpdatetheloadlocationsandhoursusingEqs.(12)and(13).

Keepthebestcontrollableloadandhourasoneofthenewsys- temvariables.Roundtheloadlocationsandhourstothenearest integer.Thenewloadlocationsandhoursareupperandlower bounded.Moreover,theloadlocationsareboundedtothelistof controllableloadsdeﬁnedinStep(2).

lloc_new=lloc_best+up_lloc×Randn

it² (12)

h^new=h^best+24×Randn

it² (13)

Where:lloc_newandh^newarethenewcandidatesloadlocationsand hoursrespectively,lloc_bestandh^bestarethebestloadlocationsand hoursduringtheiterationandup_llocisthemaximumvalueofload locations.

7)RepeatSteps(3)–(6)untiltheconvergencecriterionismet.The convergenceisconsideredachievedwhenmorethan50%ofthe loadlocationsandhoursconvergedtothesamevalues.

8)RemovetheloadlocationdeterminedfromStep(7)fromthe listofcontrollableloadsdeﬁnedinStep(2).Reducethisload by10%duringthehourobtainedfromStep(7).

9)RepeatSteps(2)–(8)toencounterallcontrollableloads.

10)Repeatforotherseasons.

Table4

Listofcontrollableloads.

Feeder IEEE37nodesfeeder

Controllableloads 1,4–6,8–10,12,14,15,17,18–21,23,26–28,30–33,35,36

Table5

Optimalcontrolscheduleforthefourseasons.

Winter Spring Summer Fall

Load Hour Load Hour Load Hour Load Hour

1 9 1 6 1 7 1 7

5 24 14 6 5 6 19 7

32 24 32 6 14 6 32 7

14 9 5 6 32 6 14 7

10 24 10 6 33 6 10 7

4 9 33 5 35 6 33 7

19 9 4 6 19 6 5 7

6 9 19 6 10 6 35 7

33 8 6 6 4 6 4 7

35 8 35 6 6 6 6 7

31 9 31 6 31 6 31 7

9 9 27 6 27 6 27 7

27 9 21 6 21 6 9 7

21 24 23 6 9 6 21 7

23 24 28 6 23 6 23 7

28 9 9 6 28 6 28 6

26 8 17 6 26 6 26 7

36 9 26 6 36 6 36 7

17 9 12 6 17 6 17 7

12 9 36 5 12 6 12 7

18 9 18 6 18 6 18 7

20 9 20 6 20 6 20 7

15 24 15 5 15 6 15 7

30 9 30 6 30 6 30 7

8 9 8 6 8 6 8 7

Table6

Purchasedenergyreductionduetoloadcontrol.

Reductioninenergypurchasedfromsubstation(MWh)

Winter Spring Summer Fall Annual

14.0199 18.1650 22.1698 15.3100 69.6647

Table7

OptimalenergypurchasedfromsubstationusingVPPconcept.

Testcase Energypurchasedfromsubstation(MWh)

Season Winter Spring Summer Fall Annual

Basecase 3074.9 3667.1 4357.3 3216.1 14315.4 RESonlyintegrated 954.8 1155.8 1693.0 1478.7 5282.3 UsingVPPconcept 669.3 533.4 1263.7 1216.0 3682.4

4.3. OptimalpowerscheduleofRESforenergyminimization In ordertoobtaintherequiredpowerschedule,theRESare considereddispatchableandplacedattheoptimallocationsdeter- minedfromA.Theobjectivefunctionistominimizetheenergy purchasedfromsubstation;thisobjectiveisachievedbydetermi- nationofoptimalpowerscheduleoftheDGsrequiredtoreduce thesubstationpowertozeroateachhour.Theproposedmethodis discussedinthefollowingstepbystepprocedure.

1)Startwithﬁrsthour(h=1).

2)Randomlygeneratetheinitialvalues ofthesystemvariables (DGsactivepowers).

3)Performunbalancedloadﬂowtocalculatethesubstationpower correspondingtoallinitialDGs’powers.

4)Selectthe best DGpower that achieve minimum substation power.

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Fig.5.Optimalandactualpowerschedulesforthefourseasons,wind.

Fig.6. Optimalandactualpowerschedulesforthefourseasons,PV.

5)UpdatetheDGspowersusingEq.(14).

P_g^new=P_g^best+upp×Randn

it² (14)

Where:p^new_g isthenewcandidatesDGactivepowers,p^best_g isthe bestDGactivepowersduringtheiteration,anduppisthemaximum valueofDGlocationsandactivepowers.

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Fig.7.OptimalpowerscheduleofESEwithwindDGforenergyminimization,wind.

6)RepeatSteps(4)and(5)untiltheconvergencecriteriaismet, theconvergenceisconsideredachievedwhenmorethan50%of theDGs’powersareconvergedtoacertainvalue.

7)RepeatSteps(2)–(6)forallhoursuntilreachthelasthour(i.e.

h=96)toobtainoptimalpowerschedulefortheDGs.

4.4. OptimalESEsschedulesforenergyminimization

Thissectionaimstodeterminetheoptimaloperationschedule ofESEsconnectedatsamebuswiththeRESinordertoredistribute theactualpowerscheduleof therenewable basedDGs (power obtainedfromthemodelingalgorithmpresentedinRef.[25])to minimizethedifferencesbetweentheactualpowerscheduleof renewableDGsandtherequiredpowerschedule(obtainedfrom partC)thatminimizestheenergypurchased.Theproposedalgo- rithmisdescribedbythefollowingprocedure.

1)Startwithacertainseason.

2)Generate“N”setseachof24randomvaluesofdifferentsigns.

Thesumofthe24valuesineachsetmustequalstozero(each ofthesesetsrepresentsapossibleoperationscheduleofESE).

3)Addeachofthesesetstotheactualpowerscheduleoftherenew- ableDGatthe currentseasontogenerate “N” editedpower

schedule(editedpowerscheduleisthepowerscheduleofthe RESinadditiontotheESEpower).

4)Calculatetherootmeansquareerror(RMSE)betweentheedited powerschedulesand therequired powerscheduleusingEq.

(15).

RMSE=

²⁴

h=1

(P_edited^h −P_required^h )² (15)

5)SelectthebestoperationscheduleoftheESEamongtheNsets (i.e.thesetthatachievesminimumRMSE).

6)UpdateeachESEpowerinallothersetsateachhourusingEq.

(16)takingintoconsiderationtheESEoperationconstraints.

|P_new^h |=|P_best^h |+Pmax×Randn

it² ,∀^h,^N ⁽¹⁶⁾

Where:P_best^h istheoutputpowerathourhofthebestESE operationschedulesetobtainedfromStep(5)andP_new^h isthe updatedoutputpowerathourhofeachoftheremainingsets.

7)RepeatSteps(3)–(6)untiltheconvergencecriterionismet,the convergenceisconsideredachievedwhenmorethan50%ofthe Nsetsconvergedtothesamevalues.

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Fig.8. OptimalpowerscheduleofESEwithwindDGforenergyminimization,PV.

8)Repeatforotherseasons.

5. Testcasesandresults

TheVPPusedinbothstudiesconsistsofthefollowingcompo- nents:

•WindbasedDGofratedcapacityof2.1MW.

•PVbasedDGofratedcapacityof2.12MW.

•Controllableloads.

•TwoenergystorageelementseachconnectedataDGbus.

5.1. ModelofrenewableenergyDGsandsystemdemand

TheconvergedMonteCarlosimulationsofthe96hofthefour seasons(typicaldaymodel)areobtainedfortwowindturbines ofthecharacteristicspresentedin Table1and40,000PV mod- ulesofthecharacteristicspresentedinTable2andforthesystem demand.TheconvergedMCresultsoftheaggregatedpowerofthe twowindturbinesaredisplayedinFig.1andthetotalconverged outputpowerofthe40,000PVmodulesispresentedinFig.2and theloadproﬁleisshowninFig.3.

5.2. ResultsoftheoptimalallocationoftheRESforenergy minimization

The proposed optimization algorithms are implemented in MATLABandtestedontheIEEE37nodesunbalancedfeederpre- sentedinFig.4todeterminetheoptimallocationofwindbasedDG ofpowerscheduleandPVbasedDGofpowerschedule.Theopti- mallocationsoftheRESandthecorrespondingannualenergyare presentedinTable3.

5.3. Resultsofoptimalloadcontrol

ThemethodologydescribedinSection4.2isappliedtotheIEEE 37nodesfeedertoobtaintheoptimalloadcontrolschedulewhile theRESareconnectedtotheiroptimallocations.Thelistofcon- trollableloadsispresentedinTable4.Theoptimalloadcontrol scheduleconsistingoftheloadstobecontrolledarrangedbased ontheirimportanceand thecorrespondingcontrolhourforthe fourseasonsispresentedinTable5.Itisobviousthat,theoptimal hoursforcontrolarethehoursofhighLSFastheloadcontrolduring thesehours’resultsinsigniﬁcantreductionintheenergypurchased fromthesubstation.Thereductionsinenergypurchasedduetoload controlarepresentedinTable6.

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5.4. ResultsofDGsoptimalpowerschedule

ThemethodologydescribedinSection4.3isappliedtotheIEEE 37nodesfeederisusedtoobtaintheoptimalpowerschedulefor theRES,consideringthemdispatchable,inordertominimizethe annualenergypurchasedfromsubstation.Figs.5and6depictthe optimalrequiredpowerschedulesandactualpowerschedulefor bothwindbasedDGandPVbasedDGconnectedtonodes25and7 respectivelyforeachofthefourseasons.Itcouldbenotedthat,itis impossibletoachievetheoptimalrequiredpowerscheduleasthe energyrequiredtoachieveitishigherthantheactualRESenergy.

Thus,insteadofreachingtheoptimalpowerscheduleitisrequired toreachnearoptimalpowerscheduleusingproperESEoperation asdiscussedinthefollowingsection.

5.5. ResultsofoptimalESEsschedules

Theprocedurepreviouslyexplained inSection4.4is usedto determinetheoptimalscheduleofESEsconnectedwiththeRES inordertominimizethedifferencesbetweenactualandrequired powerschedules.

TheeditedpowerscheduleandtheESEoptimalscheduleforthe fourseasonsforthewindDGarepresentedinFig.7andforthePV DGarepresentedinFig.8.Table7presentstheannualenergypur- chasedfromsubstationafterapplyingtheVPPconcept.TheResults showahighreductioninthepurchasedenergyfromthesubstation ascomparedtothebasecaseandthecasewhereRESareonlycon- nectedwithoutloadcontrolorESEs.Thus,theVPPconceptmanages theelectricalenergyinthedistributionnetworksandcanbeused tominimizethepurchasedenergyfromsubstation.

6. Conclusions

Anovelcomprehensivestudyforachievingtheoptimalopera- tionofthevirtualpowerplantispresentedinthispaper.Several optimization algorithms based on modiﬁcation of BB–BC opti- mizationmethodareproposed.Theproposedalgorithmsaimsto determineRESoptimallocation,optimalloadcontrolstrategyand optimaloperationscheduleofenergystorageelementsforthesake ofminimizingtheannualenergypurchasedfromsubstation.The resultsshowahighreductioninthepurchasedenergyfromthe substationascomparedtothebasecaseandthecasewhereRES areonlyconnectedwithoutloadcontrolorESEswhichemphasizes theimportanceofusingVPPconceptin managingtheelectrical energy.

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