Optimal Cooperative Management of Energy Storage Systems to Deal with Over

17 Pages·2017·5.73 MB·English

energies
Article
Optimal Cooperative Management of Energy Storage
Systems to Deal with Over- and Under-Voltages
GhassemMokhtari1,*,GhavameddinNourbakhsh2,AmjadAnvari-Moghadam3,
NegarehGhasemi2andAminmohammadSaberian2
1 CSIROAustraliane-HealthResearchCenter,Brisbane4029,Australia
2 SchoolofElectricalEngineering&ComputerScience,QueenslandUniversityofTechnology,Brisbane4000,
Australia;[email protected](G.N.);[email protected](N.G.);[email protected](A.S.)
3 DepartmentofEnergyTechnology,AlborgUniversity,Alborg9220,Denmark;[email protected]
* Correspondence:[email protected];Tel.:[phone]
AcademicEditor:WilliamHolderbaum
Received:4January2017;Accepted:28February2017;Published:2March2017
Abstract: Thispaperpresentsanoptimalcooperativevoltagecontrolapproach,whichcoordinates
storageunitsinadistributionnetwork. Thistechniqueisdevelopedforstoragesystems’activepower
managementwithalocalstrategytoproviderobustvoltagecontrolandadistributedstrategyto
deliver optimal storage utilization. Accordingly, three control criteria based on predefined node
voltagelimitsareusedfornetworkoperationincludingnormal,over-voltage,andunder-voltage
controlmodes. Thecontributionofstorageunitsforvoltagesupportisdeterminedusingthecontrol
modesandthecoordinationstrategiesproposedinthispaper. Thistechniqueisevaluatedintwocase
studiestoassessitscapability.
Keywords: storage;optimalcontrol;over-voltage;under-voltage;cooperativecontrol
1. Introduction
Due to their significant benefit for customers and utilities, renewable energy resources are
increasingly utilized in power systems around the world. However, the traditional distribution
networksarenotdesignedtoaccommodaterenewableenergyresources[1]. Assuch,powerquality
issues gradually are becoming the main concern for future grids with high utilization of these
sources[2]. Withthehighintegrationofrenewableenergygenerationindistributionnetworks,voltage
violationsmayoccurduringhighgenerationandpeakloadperiods,astheseeventsdonothappenat
thesametime[3]. Normally,over-voltageoccursduringpeakgenerationtimes,whileunder-voltage
isexperiencedduringpeakloaddemandperiods. Nationalstandardsusuallyspecifythatallnode
voltages in a network must be kept within a range (usually between 0.94 and 1.06 per unit (pu)).
Violation of these limits can cause problems for sensitive consuming and generating facilities [4].
Hence,bothover-andunder-voltageissuescancreatemajorobstaclesforpenetrationofrenewable
energygenerationinfuturedistributionnetworks[5]. Normally,theunbalancebetweentheloadand
generationatanyperiodisthemaincauseoftheissues[6].
Severalapproachesareproposedinliteraturetomitigatevoltageissuesindistributionnetworks.
Thesemethodscanbecategorizedintotwobroadclasses.Thefirstclassusescustomerresources—such
asrenewableenergysourceactivepower[7],renewableenergysourcereactivepower[8],andsmart
loads[9]—toavoidover-andunder-voltages, whilethesecondclassusesutility-ownedresources
suchasadistributionstaticsynchronouscompensator(D-STATCOM)[10]andon-loadtap-changer
(OLTC)[11]todealwiththesameissues.
Storageunitshaveshowntohaveattractiveperipheralutilizationfeatures,includingreductionin
generation/loadmismatch[12],frequencyregulation[13],andpeakshaving[14]. Ingeneral,themain
Energies2017,10,293;doi:10.3390/en10030293 www.mdpi.com/journal/energies
Energies2017,10,293 2of17
applicationsofstorageunitsinpowersystemscanbedividedintotwocategories. Inthefirstcategory,
thestorageactiveorreactivepowerareusedtoprovidepowerqualityimprovementinthedistribution
network [15]. For instance, Reference [2] uses storage active and reactive power for loading and
voltage support in the distribution network. In another reference, storage active power is used to
providefrequencycontrolinthedistributionnetwork[13]. Peakshavingandloadlevelingareother
applicationsofstorageunitsinwhichstorageunitscharginganddischargingwillbeusedtoreduce
thepeakgenerationandpeakdemand[16]. Inthesecondapplication,thestorageunitsareutilizedto
improveself-consumptioninresidentialsectors[17].
Indistributionnetworks,includingbothmedium-andlow-voltagefeeders,storageunitsusually
areusedfortwomainpurposes. Customersasthemainstakeholdersusestorageunitstoimprove
theirself-consumptionandtoreducetheirelectricitybill. Normallyinthiscase,thestorageunitsare
managedbycustomers,basedontheirgoals. However,astoragecoordinationstrategyisrequired
whenanetworkisfacedwithpowerqualityissues.
Supervisorycontrolcoordinationisnotapracticalstrategyinadistributionnetworkduetoits
complexityandreliabilityissues[12]. However,combinedlocalanddistributedcontrolcoordination
approachescanprovidepromisingfeaturesforfuturedistributionnetworkswithhighutilizationof
energyresources[2]. Acombinedlocalanddistributedcontrolstrategyisproposedinthispaperto
coordinatemultiplestorageunitsdealingwithover-andunder-voltageissuesindistributionnetworks.
Thelocalcontrolapproachusespointofcommoncoupling(PCC)busvoltageasareferencetocontrol
storageunits’activepowerinordertoavoidviolatingvoltagelimits. Simultaneously,adistributed
controlstrategyisusedasasupplementaryschemetoprovideoptimalutilizationofstorageunits.
Itisworthnothingthatweconsiderbatteriesasthestorageunitsduetotheircommonutilizationin
distributionnetworks.
2. ProposedApproach
Inordertooptimallycoordinateandmanagetheoperationofenergystorageunitsinatypical
distribution network, it is crucial to consider the aims and objectives of the asset owners. Given
anormaloperatingcondition(i.e.,intheabsenceofnetworkvoltageand/orloadingissues),thestorage
unitsaremainlydispatchedinawaytoimprovetheself-consumptionandreducetheelectricitybillsif
theyareownedby“customers”.Inthiscase,normally,alocalcontrolarchitectureisneededtomeetthe
notedobjectives. However,withutilityasthestorageowner,theaimwillbetodealwiththenetwork
problemsinanefficientway,whichinturnnecessitatesacoordinatedcontrolarchitecture. Therefore,
efficientcontrolofstorageunitsgreatlydependsonthesystem’sobjectives,relatedsecurity/technical
constraints,andoperatingmodes.
Thispaperproposesanefficientcooperativecontrolapproach(whichincludesbothlocaland
distributedcontrolapproaches)todealwithover-andunder-voltageissuesindistributionnetwork.
AscanbeseeninFigure1,thelocalcontrolapproachusesthestorageunitsatPCCbusvoltagesto
determinethecontributionoftheseunitsforarobustvoltagecontrol,whilethedistributedcontrol
approachdeterminestheoptimalcontributionofstorageunitsforvoltagesupport.
Energies2017,10,293 3of17
Energies 2017, 10, 293 3 of 17
Energies 2017, 10, 293 3 of 17

Figure 1. Proposed control structure for storage unit.
Figure1.Proposedcontrolstructureforstorageunit.
Figure 1. Proposed control structure for storage unit.
2.1. Local Voltage Control Strategy
2.1. LocalVoltageControlStrategy
2.1. Local Voltage Control Strategy
The local control approach uses the storage units at PCC bus voltages to determine the
TThhee loloccaallc ocnotnrotrloalp parpoparcohauchse sutshees sttohrea gsetournaigtse autPnCitsC batu sPvCoClt agbeuss tovdolettaegrmesi nteo thdeetceornmtriinbeu ttiohne
contribution of these units for a robust voltage control. In order to determine the triggering criteria
ocofnthtreisbeuutinonit soffo trhaesreo ubunsittsv foolrt aag reocbounsttr vool.ltIangoe rcdoenrttroold. eInte ormrdienre ttoh deettreigrmgeirnien gthcer ittreigrigaefroinrgth ceriltoecraial
for the local controllers, three control modes are defined for network operation, as given in Figure 2.
cfoorn tthroel lleorcsa,lt chorenetrcoollnetrrso, ltmhroede ecsoanrterodl emfinodedesf oarren detewfionrekd ofopre rnaettiwono,raks ogpivereantiionnF, iagsu greiv2e.n in Figure 2.

Figure 2. Network control modes based on voltage limits.
Figure 2. Network control modes based on voltage limits.
Figure2.Networkcontrolmodesbasedonvoltagelimits.
If the voltages of all storage units are in the desirable range (between (cid:1848)(cid:3039)(cid:3042)(cid:3050)(cid:3032)(cid:3045) and (cid:1848)(cid:3048)(cid:3043)(cid:3043)(cid:3032)(cid:3045)), the
If the voltages of all storage units are in the desirable range (between (cid:1848)(cid:3031)(cid:3039)(cid:3042)(cid:3050)(cid:3032)(cid:3045) and (cid:1848)(cid:3031)(cid:3048)(cid:3043)(cid:3043)(cid:3032)(cid:3045)), the
netwIofrkth ceonvtorlotal gmesodoef iasl lnostromraagl.e Tuhneritesfoarree, sitnortahgee duensiitrsa bcalen rbaen guese(db efotwr eoe(cid:3031)thnerV plouwrerpoasn(cid:3031)eds sVuucphp ear)s,
network control mode is normal. Therefore, storage units can be used for other dpurposes sudch as
power buffering and so on. The second control mode engages when the voltage at any of the storage
thenetworkcontrolmodeisnormal. Therefore,storageunitscanbeusedforotherpurposessuchas
puonwit ebru bsuesff eexricnege dasn d(cid:1848) s(cid:3048)o(cid:3043)(cid:3043) o(cid:3032)n(cid:3045).. ITnh teh sies ccoansde, csotnortraogle m uondites egnog atog eths ew ohveenr -tvhoe lvtaogltea cgoen attr oaln ym oofd teh ea nsdto trhageye
puonwit ebrubsuesff eerxicnegedans d(cid:1848)(cid:3030)s(cid:3048)o(cid:3043)(cid:3043)o(cid:3032)n(cid:3045).. ITnh tehsies ccoansde, csotnortraoglem uondites egnog atog ethsew ohveenr-tvhoelvtaogltea gcoenattroaln ymoofdteh eansdto trhageye
start to collaborate w(cid:3030)iuthpp eerach other in coordinating their charging rate to achieve robust and efficient
unitbusesexceedsV . Inthiscase,storageunitsgototheover-voltagecontrolmodeandthey
start to collaborate wicth each other in coordinating their charging rate to achieve robust and efficient
over-voltage prevention. This coordination continues until all the bus voltages go to the desirable
starttocollaboratewitheachotherincoordinatingtheirchargingratetoachieverobustandefficient
over-voltage prevention. This coordination continues until all the bus voltages go to the desirable
range and the network goes to the normal mode.
over-voltageprevention. Thiscoordinationcontinuesuntilallthebusvoltagesgotothedesirable
range and the network goes to the normal mode.
Finally, under-voltage control mode is treated similar to the over-voltage control mode, where
rangeandthenetworkgoestothenormalmode.
(cid:1848)(cid:3039)(cid:3042)(cid:3050)(cid:3032)F(cid:3045)i naanldly ,(cid:1848) u(cid:3039)(cid:3042)n(cid:3050)d(cid:3032)e(cid:3045)r -dveotletramgein ceo tnhtero slt amrto adned is s ttorepa otefd t hsiism ciolanrt rtool tmheo doev.e Irt- vshooltuaglde bceo nntortoeld m thodate t, hweh aeimre
(cid:1848)o(cid:3030)(cid:3030)f(cid:3039) (cid:3042)o(cid:3050)v(cid:3032)F(cid:3045)ei rna-a noldlry ,u(cid:1848)(cid:3031)(cid:3031)n(cid:3039)u(cid:3042)dn(cid:3050)ed(cid:3032)r(cid:3045)e- vrd-oveltotealrtgmaeg iencoecn tothrneot lrs otialsr ttm oa onaddve ositidos pat norefy at thbeiudss c sovinimotlriaolatlir nmgtoo dtheteh. Iept esorhvmoeuirs-lsvdio bblletea nglioemteictdos nt(htir.aeot. l,t h(cid:1848)me(cid:3039) (cid:3042)oa(cid:3050)dim(cid:3032)e(cid:3045),
waoaainnfhm ddoe vr(cid:1848)(cid:1848)oe(cid:3043)ef(cid:3048)(cid:3048)rV(cid:3043)(cid:3043)o-(cid:3043)(cid:3043)c vl(cid:3032)(cid:3032)ooe(cid:3045)(cid:3045)wrr))e -..ru o anrndudenrV-dvdleoorwl-tevraogdleet atcegoremnctiornonelt rtiohs letiosst ataorvtaoavindod iadsntayon pbyoubfsu tvhsiivosilcoaoltainnttigrno gtlhmteh oepdpeere.mrImtississhisobiublell edlilbmimeitnistos (t(iei.de.e.,.t ,h(cid:1848)Va(cid:3043)(cid:3043)(cid:3039)ptl(cid:3042)o(cid:3050)twh(cid:3032)ee(cid:3045)r
E(cid:3043)uapcphe rstorage unit is supported by both local and distributed controllers. As soon as the voltage
andV ).
at a sEtoparcahg set uornaigt eb uusn viti oisla stuesp p(cid:1848)o(cid:3039)r(cid:3042)t(cid:3050)e(cid:3032)d(cid:3045) boyr b (cid:1848)ot(cid:3048)h(cid:3043) (cid:3043)l(cid:3032)o(cid:3045)c, atlh aen lodc dali sctorinbturotellde rc uonptdraotlelesr ist.s A resf esoreonnc ae sp tohwe evro, latas gine
at a storage unit bus violates (cid:1848)(cid:3030)(cid:3039)(cid:3042)(cid:3050)(cid:3032)(cid:3045) or (cid:1848)(cid:3030)(cid:3048)(cid:3043)(cid:3043)(cid:3032)(cid:3045), the local controller updates its reference power, as in
(1). (cid:3030) (cid:3030)
(1).
Energies2017,10,293 4of17
Energies 2017, 10, 293 4 of 17
Eachstorageunitissupportedbybothlocalanddistributedcontrollers. Assoonasthevoltageat
astorageunitbusviolatesVlower orVupper,thelocalcontrollerupdatesitsreferencepower,asin(1).
c c
 m ·(V[k]−Vupper) V[k]>Vupper
i,o i c i c
Pl,i[k]=mi,o·(Vi0[k]V−clowVecru<ppVeri[)k]<ViV[ckup]pe>r Vcupp er (1)
P [k] = −m0·(VV[lkow]e−rV<lowVer)[k]V<[kV]u<pVpelrower (1)
l,i  i,u ic c i i c c
 −m ·(V[k]−Vlower) V[k] <Vlower
i,u i c i c
where Pl,i is the local contribution of storage unit, and mi,o and mi,u are the droop coefficients. As
wsthoerraegPe unisittsh eshloocualldc ostnatrrti btuo tciohnarogfes toorr adgisecuhnairtg,aen adt mcritiacanld limmitsa raentdh eudsero tohpeicro mefafixciimenutsm.A caspstaobrialigtey
l,i i,o i,u
uinn iptsersmhiosusilbdles tliamrtitt,o thceh darrgoeopo rcodeifsficchieanrgt eis aptrcorpiotisceadl laism iint sEqanudatiuosnes t(h2)e iarnmd (a3x)i.m um capability in
permissiblelimit,thedroopcoefficientisproposedasinEquations(2)and(3).
Pava.
m =| i | (2)
i,o VuppePr a−vVa.upper
m = | p i c | (2)
i,o Vupper−Vupper
p c
Pava.
m =| i | (3)
i,u VlowePr −avVa.lower
mi,u = |Vlopweri−Vclower | (3)
p c
where (cid:1842)(cid:3028)(cid:3049)(cid:3028). is the maximum available power in storage unit i.
(cid:3036)
wherePava.isthemaximumavailablepowerinstorageuniti.
Adiditionally, to show that the network mode is changed, a local voltage control flag is used, as
Additionally, to show that the network mode is changed, a local voltage control flag is used,
given in (4).
asgivenin(4).
Lflag[k]L=flag[k−]10=1−101 VVcclloowwVVereViVir[[<ikk[<[V]k]ki]><][Vk><VVi][cculk<oVVpw]pVceeul<rrocpuwpppVeeerrrcu pper (4(4) )
i c
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tthhee ssttoorraaggeeu unnitits tsatratrstst otoc hcahragregoe rodri sdcihscahrgaergteo tdoe adlewali twhiothve or-voerr-u onrd uern-dveorlt-avgoeltaisgseu eisss.uAelst.h Aoultghhouthgihs
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anentewtworokr.k I.nI nthtihsi salaglgoroirtihthmm, t,hthe ereresosouurcreces sinin aa nneettwwoorrkk aarree rreepprreesseenntteedd bbyy aa ggrraapphh ((VV,, EE)),, wwhheerree VV
mmooddeellss ggrraapphh vveerrttiicceess aanndd EE mmooddeellss tthhee ggrraapphh eeddggeess,, aanndd ppaaiirr ((ii,, jj)) iiss mmeemmbbeerr ooff EE iiff tthheerree iiss aann eeddggee
bbeettwweeeenn vveerrttiicceess jj aanndd ii.. AAnn eexxaammppllee ooff tthhiiss ggrraapphh mmooddeell iiss sshhoowwnn iinn FFiigguurree 33..

FFiigguurree 33.. GGrraapphh mmooddeell ooff rreessoouurrcceess..
FFoorr eeaacchh vveerrtteexx,, tthhee sseett NNi sshhoowwss iittss nneeiigghhbboorrss,, aass ggiivveenn iinn ((55))..
i
N ={j∈v|(i, j)∈E} (5)
i
N = {j ∈ v|(i,j) ∈ E} (5)
i
Based on this technique, for each resource in node i, a parameter named information state (λ(t)) is
i
defined, which will be updated as in (6) to achieve a specific control objective [1].
.
λ(t)= d λ(t)
i ij j (6)
j∈Ni
Energies2017,10,293 5of17
Basedonthistechnique,foreachresourceinnodei,aparameternamedinformationstate(λ (t))
i
isdefined,whichwillbeupdatedasin(6)toachieveaspecificcontrolobjective[1].
. ∑
λ (t) = d λ (t) (6)
i ij j
Energies 2017, 10, 293 j∈Ni 5 of 17
wwhheerree ddiijj iiss aa ccooeeffffiicciieenntt ddeeffiinneedd aass iinn EEqquuaattiioonn ((77)) [[1188]]..
cc
dd== jjii (7)
ijij ∑ cc (7)
kiki
kk∈∈NNii
wwhheerree ccij mmooddeellss tthhee ccoommmmuunniiccaattiioonn lliinnkk bbeettwweeeenn rreessoouurrccee ii aanndd jj.. IInn aa ddiissccrreettee ttiimmee ddoommaaiinn,, ((77)) ccaann
ij
bbee sshhoowwnn iinn mmaattrriixx ffoorrmmaatt aass ggiivveenn iinn ((88))..
λ[k+1]=D·λ[k] (8)
λ[k+1] = D·λ[k] (8)
This algorithm has been applied in applications which require fair sharing among resources [19].
For eTxahmispalleg,o irni t[h2m], thhaiss abpepenroaapcphl iies dusineda ptop plircoavtiiodnes fwaihr ischharreinqgu iorfe afcatiirvseh paoriwngera ammoonnggr estsooruargcee su[n1i9ts].
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iasm aolnsog puhseodto vtoo ltpariocv(PidVe) -ostpotriamgaels yusttileimzaotifoan loowf -rveosoltuagrceens e[t2w1o].r kB.aIsnerde coenn ttlhitee rnatoutered, tlhitiesraaptuprreosa,c hthies
palrsoopuosseedd tdoisptrroibvuidteedo pcotinmtraollu sttirliuzcattuiorne ofofrr eas ostuorrcaegse[ 2u1n]i.tB ias siemdpolnemtheennteodte idn ltihteirsa ptuarpeesr,,t hase sphroopwons eidn
Fdiigsturribe u4t.e dcontrolstructureforastorageunitisimplementedinthispaper,asshowninFigure4.
Pmin, Pmax Dflag V
i i Logic II i Equation (4) i
Lflag
Dflagi i Dflag , j∈N
Logic I j i
|P |
l,i
P
d,i Equations (14)-(17)
λ, P' , j∈N
j v,j i
λ, P'
i v,i
Figure 4. Proposed structure for distributed controller.
Figure4.Proposedstructurefordistributedcontroller.
The maximum and minimum power of a storage unit depends on the control mode of the
The maximum and minimum power of a storage unit depends on the control mode of the
network. Lflag is a local index of a network control mode. However, to extend the network mode to
network. Lflagisalocalindexofanetworkcontrolmode. However, toextendthenetworkmode
all storage units, (cid:1830)(cid:1858)(cid:1864)(cid:1853)(cid:1859) is also defined. A value is assigned to this index based on the following
toallstorageunits,Dfla(cid:3036)g isalsodefined. Avalueisassignedtothisindexbasedonthefollowing
i
arguments: Logic 1: is followed to charge all storage units during over-voltages and discharge during
arguments: Logic1: isfollowedtochargeallstorageunitsduringover-voltagesanddischargeduring
under-voltages; Logic 2: is followed to determine the maximum and minimum of a storage unit’s
under-voltages; Logic 2: is followed to determine the maximum and minimum of a storage unit’s
contributed power. These logics are formulated as follows:
contributedpower. Theselogicsareformulatedasfollows:
LogicL 1o:g ic1:
Dflagi =0 if LfDlagflia=gi0= an0dif aLllf laDgfila=g 0=a0ndajl∈l ND flagj =0 j ∈ Ni
Dflag =1ifLflag =j1oranyofi Dflag =1 j ∈ N
Dflagi =1 if LfDlafglia=gi1= o−r a1niyf Loff laDigfla=g−=11orja∈nyNof Dfjlag = −1 ij ∈ N
i i j i j i
LDofglaicg2i:=−1 if Lflagi =−1 or any of Dflag =−1 j∈N
j i
Pmin =0 Pmax = Pava. if Dflag =1
Logic 2: i i i i
Pmin = −Pava. Pmax =0 if Dflag = −1
Pmin =0 Pmax =Pava. i if Dflaig =1 i i
i i i i
Pmin =−Pava. Pmax =0 if Dflag =−1
i i i i
In this paper, the aim is to use a consensus approach to provide an optimal utilization of storage
units in voltage support. To achieve this objective, the utilization function of each storage unit is
defined as (9).
Ci(|Pd,i |)=|Pd,i |·ηi (9)
Energies2017,10,293 6of17
Inthispaper,theaimistouseaconsensusapproachtoprovideanoptimalutilizationofstorage
units in voltage support. To achieve this objective, the utilization function of each storage unit is
definedas(9).
C(|P |) = |P |·η (9)
i d,i d,i i
whereP isthedistributedcontributionofstorageunit,andη isthestorageunitefficiency.
d,i i
Asnotedin[21],theefficiencyofthestorageunitreduceswhenitspowerincreases. Therefore,
thestorageefficiencydependsonitsoutputpower,asgivenin(10).
η = a −b·|P | (10)
i i i d,i
wherea andb arecoefficientsthatdependonthetypeofstorageunit.Thesevaluescanbedifferentfor
i i
chargingordischarging. However,forthesakeofsimplicity,inthispaper,fixedvaluesareconsidered.
So,thecostfunctionforeachstorageunitcanbeshownasin(11).
C(|P |) = a ·|P |−b·|P |2 (11)
i d,i i d,i i d,i
Inordertoachieveanoptimalutilizationofenergystorageunits,theobjectivecontrolfunctionis
definedasin(12).
n
Max∑ C(|P |)
i d,i
i=1
n n
s.t.∑ |P | =∑ |P | (12)
d,i l,i
i=1 i=1
Pmin ≤ P ≤ Pmax for i =1,...,n
i d,i i
where n is the number of storage units. The optimal solution of this function can be written as
in(13)[21].
n n
(∑ ai − ∑ |P |)
λ∗ = i=12bi i=1 l,i (13)
n
∑ 1
i=12bi
whereλ∗ istheoptimalincrementalcostforeachstorageunit.
Inthispaper,toachievethenotedoptimalpoint,theiterativeprocessin[21]isusedtooptimize
thecostfunctionforstorageunits,whichincludesthefollowingdistributedupdatingrules.
∑
λ [k+1] = d ·λ [k]+α·P [k] (14)
i ij j v,i
j∈Ni
−λ [k+1]+a
|P [k+1]| = ( i i) (15)
d,i 2·b
i
P(cid:48) [k+1] = P [k]+(|P [k+1]|−|P [k]|) (16)
v,i v,i d,i d,i
P [k+1] = ∑ d ·P(cid:48) [k] (17)
v,i ij v,j
j∈Ni
whereP isthedifferencebetweenthecurrentstateofbatterychargewithrespecttothevalueinthe
v,i
lasttimeinterval. Thisisthevaluesharedbytheneighborstocontribute,assetinthealgorithm.
Inmatrixform,thenotedequationscanbeshownintheformsgivenin(18)–(21).
λ[k+1] = D·λ[k]+α·I ·P [k] (18)
n V
|P [k+1]| = B·λ[k]+F (19)
d
P [k+1]−|P [k+1]| = P [k]−|P [k]| (20)
v d v d
Energies2017,10,293 7of17
P [k+1] = D·B·(D−I )·λ[k]+(D+α·D·B)·P [k] (21)
v n v
where
F = [ a1 a2 ... an ]T (22)
2b1 2b2 2bn
B = diag([ −1 −1 ... −1 ]) (23)
2b1 2b2 2bn
basedon[21],theseequationsconvergeto:
λ[∞] = [ λ∗ λ∗ ... λ∗]n = λ∗·1n (24)
1 ·|P [∞]| =1 ·B·λ[∞]+1 ·F (25)
n d n n
Pv[∞] = [ 0 0 ... 0]n = 0n (26)
1 ·(P [∞]−|P [∞]|) =1 (P [0]−|P [0]|) (27)
n v d n v d
byinitiatingP andP in(27)through(28):
v d
P [0] = −|P |
v,i l,i (28)
P [0] =0
d,i n
Wecanrewrite(27)using(25),asin(29):
n
1 ·|P [∞]| = −1 (P [0]) = ∑|P [0]| (29)
n d n v l,i
i=1
Therefore,(29)canberewrittenas:
∑n |P [0]| = −∑n 1 ·λ∗+∑n ai (30)
l,i 2·b 2·b
i=1 i=1 i i=1 i
n n
(∑ ai − ∑ |P |)
λ∗ = i=12bi i=1 l,i (31)
n
∑ 1
i=12bi
So,thestorageunits’incrementalcostconvergestotheoptimalpoint.Theproposedmixedcontrol
approachcanprovidearobustandoptimalover-andunder-voltagecontrolinadistributionnetwork.
Tostudythedynamicoperationofthistechnique,thenetworkinternalstates—suchasvoltageand
currentofPVsandstorageunits—arenotconsidered,astheseparametershavefasterresponsetimes
comparedwithstorageunitoutputpower[2]. Inotherwords,theseparametersarestabilizedfaster
thanoutputpower. Therefore,theproposedcontrolapproachdeterminesthedynamicofthenetwork,
asgiveninFigure5,whichillustratestheproposedapproachwithaflowchart.
Energies2017,10,293 8of17
Energies 2017, 10, 293 8 of 17
Energies 2017, 10, 293 Start 8 of 17
kS=tka+rt1
( ) ( )
Pl,i[k]=mi,o Vi[k]−Vclower Samkp=likn+g1 PCC Pl,i[k]=mi,o Vi[k]−Vcupper
Lflag[k]=−1 bus voltage Lflag[k]=1
i i
( ) ( )
Pl,i[k]=mYie,osVi[k]−Vclower Sampling PCC Pl,i[k]=mi,o ViY[ke]s−Vcupper
Lflag[k]=−1 No bus voltage Yes Lflag[k]=1
V[k]i<Vlower V[k]>1 V[k]i>Vupper
i c i i c
Yes Yes
No No Yes No
V[k]<Vlower V[k]>1 V[k]>Vupper
i c Yes P [k]=0 i P [k]=0 Yes i c
V[k]<Vlower l,i l,i V[k]>Vupper
iNo d Lflagi[k]=−1 Lflagi[k]=1 i Ndo
No Yes P [k]=0 P [k]=0 Yes No
VLPif[Nll,aki[og]ki<][kV=]d0lo=we0r Lflla,igi[k]=−1 Lfll,aigi[k]=1 VLPif[ll,kai[g]k>i][kV=N]du0=oppe0r
Pl,i[k]=0 λ[k+1]=d .λ[k]+α.P [k] Pl,i[k]=0
Lflagi[k]=0 i|P [k+1j∈]N|=i (ij−λji[k+1]+av,ii) Lflagi[k]=0
P'v,i[kλ+i|[1kP]Pdd+,,v=ii,[i1[kP]kv+=,i+[1jk1∈]]N]|=i+=d((ij−|.λPλdjid,[[i[kikj22k.]P+..++bb'1ivα1,]j]+[.|Pk−av],ii|[)Pkd],i[k]|)
P' [k+1]=P [k]+(j∈|NPi [k+i1]|−|P [k]|)
v,i v,i d,i d,i
P [k+1]=d .P' [k]
Figure 5. Flowcv,hiart of the pijrovp,josed approach.
Figure5.Flowchartoftjh∈Nei proposedapproach.
3. Case Studies
Figure 5. Flowchart of the proposed approach.
3. CaseStudies
3.1. Case 1
3. Case Studies
3.1. Case1
In the first case, the aim is to compare the performance of the proposed approach with other
3.1. Case 1
Ianppthroeafichresst lcisatseed, itnh ethae ilmiterisattuorec. oTmwpo aarpeptrhoeacpheesr,f oinrcmluadnincge aocftitvhee pporwoepro csuerdtaialmppenrot a(AchPCw) iatnhdo ther
approstaocrhaIegnse tluhisnet ieft idrfsaitin rc atshsheae,r ltiinhtgee rafaoimtru vrieso .lttoTa wgceoo msaupppappreor orttha eac shp eleisrs,ftoeindrmc ilanun d[c2ien, 7og]f, atahcrteei vpceoronppsoiodwseereder dac pufporrrt oatahiclemh pewunirttph(o AostePh Ceorf) and
storagcaopempurponaairctihsfoeansi .rl iAsst hesidam riipnnl etgh aefn oldirt esvtraaontludtaraegr.d eT rwsaudop iaappl onprertotwaacoshrelkis sw, tieintdhcl usinidxi n[b2gu, s7ae]cs,t,i avthreer epeco owPnVesrsi dcaunerdrte atdihlmrfeoeern sttt o(hAreaPgpCe u)u ranpnitodss e of
compisast orsirismaogunel .auAtnedist iwmfaiitprh l stehhaean rdidnifgfse trfaoennr dtv vaoorldlttaarggaeed ssiuuapplppnooerrtttw aaopsr pklrisowtaecidth heinss. iT[x2h,b7isu] ,t seaesrste ,s tychostrneesmeid PiesVr seshdoa wfnodnr ittnhh eFr eipgeuusrrtpeo o6rs.a eTg hoeefu nits
tceocmhnpiacrails odna. tAa soifm tphlee annedtw sotarnk daanrdd rraedsioaul rnceetsw aorrek swhiothw sni xi nb uTsaebs,l eths r1e–e 3P. VIns aonrdd ethr retoe setxoarmagien eu nthites
issimulatedwiththedifferentvoltagesupportapproaches. ThistestsystemisshowninFigure6.
pise srifmorumlaatnecde w oift hth teh ev odlitfafegree nsut pvoplotratg aep spurpopaocrhte asp cpornosaicdheersin. Tgh disif tfeesrte nsyt snteemtw iosr skh mowond eins, Fai gguernee 6ra. tTiohne
ThetechnicaldataofthenetworkandresourcesareshowninTables1–3. Inordertoexaminethe
ptercohfniliec agli vdeant ain oFfi gtuhere n7e itsw uosrekd afonrd P rVess.o urces are shown in Tables 1–3. In order to examine the
performanceofthevoltagesupportapproachesconsideringdifferentnetworkmodes,ageneration
performance of the voltage support approaches considering different network modes, a generation
profilegiveninFigure7isusedforPVs.
profile given in Figure 7 is used for PVs.

Figure 6. Six-bus test system.

Table 1. Network parameters.
Figure 6. Six-bus test system.
Figure6.Six-bustestsystem.
Network voltage level 10 kV
Table 1. Network parameters.
Line impedance between buses 0.3766 + 0.2550i
Table1.Networkparameters.
LNoeatdw ionr ke avcohl tbaugse (lkevWel) 101 0k0V
Line impedance between buses 0.3766 + 0.2550i
Networkvoltagelevel 10kV
Load in each bus (kW) 100
Lineimpedancebetweenbuses 0.3766+0.2550i
Loadineachbus(kW) 100
Energies2017,10,293 9of17
Table2.PVsparameters.
Energies 2017, 10, 293 9 of 17
Energies 2017, 10, 293 9 of 17
PV 1 2 3
Location(bTuTasba)blele 2 2. . PPVV3ss ppaarraammeetetre4sr.s . 5
Rating(kPWPVV) 200011 212000 33 1000
LoLcoactaiotinon ( b(buuss)) 33 44 5 5
TRabaRtlaienti3gn. g(S k(tkWoWr)a) ge2u200n00i0t0s ’p110a00r00a 0m 1e0t10e00r0 s0.
Table 3. Storage units’ parameters.
StoragTeabUlen 3it. Storage 1units’ para2meters. 3
Storage Unit 1 2 3
LocatiSotnor(abgues )Unit 3 1 24 3 5
Location (bus) 3 4 5
Rating(kW) 600 400 550
LocRaattiionng ((kbWus)) 6030 4040 5505
a 0.91 0.91 0.91
Riatinga (i kW) 06.0910 04.9010 0.9515 0
b 0.04 0.03 0.02
i aib i 00..0941 00.0.93 1 0.002.9 1
bi 0.04 0.03 0.02

Figure 7. Generation profile of PVs.
Figure7.GenerationprofileofPVs.

In the first scenario, the performance of APC approach [7] is considered for voltage support. The
parameters of this control approFaicghu froer 7 e.a Gche nPeVra itsi ogniv perno ifnil eT oafb lPeV 4s. . Figure 8 shows the bus voltages
In the first scenario, the performance of APC approach [7] is considered for voltage support.
and PV generation when this control coordination approach is applied to deal with over-voltages.
TheparametersofthiscontrolapproachforeachPVisgiveninTable4.Figure8showsthebusvoltages
In theA fsi rist tc asnce bnea sreieon, tihn et hpise rffigourmre,a dnucrei nogf tA =P 0C–2 a0p0 ps raonadc ht = [ 74]0 0is– 6c0o0n ss,i adlel rveodlt afgoers v aorlet alegses tshuapnp tohert . The
andPpVargamecnreeittericarastl i oloifmn tihwt,i sthh ceeornnefttorhroeils, ancpoo pcnrutorrtaoacilhlmc foeonort r eidsa icrnehqa PutiViore nids afgopirvp tehrneo aiPncV hTs’a ipsbolaewp e4pr. . FlHiiegoduwrteeov 8edr s,e hdaoulwrwinsgi tt hth e=o 2bv0u0es–r 4-v0vo0ol tlatgaegse s.
Aansdi tPcsV,a angse bbnueesr s4ae taeinondn i5wn vhotheltnaisg tehfisi gsp uacsrosen t,htrdeo uclr rciitonicogarld tliim=nai0tt,i –Po2Vn0 sa0 apts ptharoensadec bhtu i=sse as4 p0wp0il–lli 6ehd0av0 teos 1 ,d9a1el.a4ll5 v wkoWiltth aa gnodve se1r2a-.v6r5eo lkltWeasg sest.h anthe
power curtailment, respectively.
criticallimAist ,itt hcaenre bfeo rsee,enn oinc tuhritsa fiilgmureen, tdiusrrinegq ut i=r e0d–2f0o0r st ahnedP tV =s 4’0p0o–6w0e0r s., Halol wvoeltvaegre,sd aurrei lnegsst th=a2n0 t0h–e4 00s,
asbucsri4ticaanld lim5ivt,o tlhtaergeefosrpe,a nsso tchuertcarilimticeanlt lisim reiqt,uPirVeds faotrt thhees PeVbsu’ speoswweri.l lHhoawveev1e9r,1 d.4u5rikngW t a= n2d001–240.605 kW
Table 4. Active power curtailment (APC) parameters.
powesr, caus rbtuasi l4m aenndt 5, rveoslptaegcetsiv pealsys. the critical limit, PVs at these buses will have 191.45 kW and 12.65 kW
power curtailment, respectively. Vcri. 1.05 pu
Droop coefficient of PV 1 20 kW/V
Table4.AcDtirvoeopp cooweffeicriecnut rotfa PilVm 2e nt(A10P kCW)/pVa rameters.
Table 4. ADcrtoiovpe cpooewffiecrie cnut rotfa PilVm 3e nt (A1P0C k)W p/aVr ameters.
VVcrcir.i. 11.0.055p puu
DDrrooooppc cooeeffiffcicieienntto offP PVV1 1 2020k WkW//VV
DDrrooooppc cooeeffiffcicieienntto offP PVV2 2 1010k WkW//VV
DDrrooooppc cooeeffiffcicieienntto offP PVV3 3 1010k WkW//VV

(a)

(a)
Figure8.Cont.
Energies2017,10,293 10of17
Energies 2017, 10, 293 10 of 17
Energies 2017, 10, 293 10 of 17

(b)
Figure 8. Voltage support simulation results based on APC approach, (a) bus voltages; (b) PVs’ power
Figure 8. Voltage support simulation results based on APC approach, (a) bus voltages; (b) PVs’
curtailment.
powercurtailment.
(b)
In the second scenario, the performance of distributed fair power sharing [2] is considered for
Figure 8. Voltage support simulation results based on APC approach, (a) bus voltages; (b) PVs’ power
Itnhet hsetosreagcoe nudnistsc.e Inna trhiois, ctahsee,p tehref olarsmt naondcee ooff tdhies tnreibtwuoterkd ifsa cironpsoidweerreds haas rtihneg c[r2it]iciasl cnoondsei dweirtehd thfeo rthe
curtailment.
storagaeimu ntoi trse.gIunlathtei sitcsa vsoel,ttahgee ltaos tlensso dtheaonf 1t.h05e npuet, wwoitrhk eiqsucaoln sshidareirnegd oaf ssttohreagceri tuincaitls.n Tohdee rwesiuthltitnhge aim
toregvuollatategeists Ianvn todhl etp asogewceoentrod o lsfec ssetnsoatrrhaioga,en t hu1en. 0pit5esr pfaourrem, swahnioctweh onef qidnui saFtrliigbsuuhrtaeerd i9 nf. agTirho pefo sswttooerrr aasghgeae ruiunngni ti[st2 s]c .oisTn chtoreinbsruiedtseeur deldtui rnfiognr gv to =lt ages
200–t3h0e0 s sto troa gdee uanl iwtsi. tIhn othvies rc-avsoel, ttahgee l.a Tsth neo sdhea orfi nthge o nfe tthweo rskto irsa cgoen suidneitrse da ta tsh teh es tceraitdicya-l sntoadtee iwndithic athtee that
andpowerofstorageunitsareshowninFigure9. Thestorageunitscontributeduringt=200–300sto
the faaiimr s thoa rreeg iusl aatceh iitesv veodl,t aagse i nto t hlees sf otlhlaonw 1in.0g5; pu, with equal sharing of storage units. The resulting
dealwithover-voltage. Thesharingofthestorageunitsatthesteady-stateindicatethatthefairshare
voltages and power of storage units are shown in Figure 9. The storage units contribute during t =
P 208.19
isachieve2d00,–a3s00in s ttoh edefaol lwloitwh ionvger;-voltage. The sh1ari=ng of the= s0t.o3r4a7ge units at the steady-state indicate that
the fair share is achieved, as in the follPo1wPi1nma=gx; 20680.019 =0.3 47
Pmax 600
1 PP12 ==210388..1799==00..334477
P2 P1Pm2=maxax 1364800.0079 =0. 347
Pmax 400
2P3 PP=3P2Pmm32aaxx ==1119394508005...07088944==00=..3344770 .347
in thiBsa csaesde oisn 4 t8h6e. 3c7o6s2t fkuWnc.t ion definePd3m foaxr tPh3Pm3eax s=t15o9505r5.a0804g=e0 u.34n7i ts, the total cost of storage units’ utiliz ation
Basedonthecostfunctiondefinedforthestorageunits,thetotalcostofstorageunits’utilization
Based on the cost function defined for the storage units, the total cost of storage units’ utilization
inthiscaseis486.3762kW.
in this case is 486.3762 kW.

(a)
(a)

((bb))

Figure9. Voltagesupportsimulationresultsbasedonapproachin[1],(a)busvoltages;(b)storage
units’charging.