IMICV fault analysis method with multiple PV gridconnected inters for distribution systems

ContentslistsavailableatScienceDirect

Electric

Power

Systems

Research

jou rn al h om 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

IMICV

fault

analysis

method

with

multiple

PV

grid-connected

inverters

for

distribution

systems

Ailson

P.

Moura

_,

_J.A.

_Pec¸

_as

_Lopes

_,

_Adriano

_A.F.

_de

_Moura

_,

Jean

Sumaili

_,

_C.L.

_Moreira

a_{DepartmentofElectricalEngineering,FederalUniversityofCeara,PiciCampus,Brazil} b_{CAPESFoundation,Brazil}

c_{FacultyofElectricalandComputerEngineering,UniversityofPorto,InstitutodeEngenhariadeSistemaseComputadoresdoPorto(INESCPorto),} 4200-465Porto,Portugal

d_{DepartmentofEnvironmentalScienceandTechnology,FederalRuralUniversityofSemi-Arid,Av.FranciscoMota,572BairroCostaeSilva,} Mossoró-RNCEP:59.625-900,Brazil

e_{InstitutodeEngenhariadeSistemaseComputadoresdoPorto(INESCPorto),4200-465Porto,Portugal}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received6June2014

Receivedinrevisedform4September2014 Accepted8September2014

Availableonline29September2014

Keywords: Distributionsystem Faultanalysis Photovoltaic(PV) Powersystem

Grid-connectedphotovoltaicsystem Photovoltaicgenerators

a

b

s

t

r

a

c

t

AnovelfaultsanalysismethodwithmultiplePVgrid-connectedinvertersfordistributionsystemsis proposed.TheaforesaidproposedmethodInverterMatrixImpedanceCurrentVector(IMICV)employs symmetricalcomponentscombinedwithamatrixdenominatedofInverterMatrixImpedanceandwith avectordenominatedImpedance-CurrentVectorwhichareformedbyinspection.Thismatrixandthis vectorareusedtosolvealinearsystemofequationswherethefollowingpost-faultvariablesare:current insubstation,thevoltageatthefaultpointandvoltagesinthePVgrid-connectednodes.Acomparison ofresultsobtainedusingthenewmethodwiththeresultsoftheprofessionalsoftwareANAFASvalidates themethodproposed.Computersimulationsshowthattheproposedmethodforclassicalshuntfaults analysisisefficient,accurateandeasytoprogram.

©2014ElsevierB.V.Allrightsreserved.

1. Introduction

Thesystemofsymmetricalcomponentsisusedtraditionallyfor theanalysisofsymmetricaland asymmetricaloperationof dis-tributionsystems.Faultsingeneralandshort-circuitcurrentsin particulararethemost severeoperatingconditions in distribu-tionsystems.Eachofthedifferentfaults,e.g.,single-line-to-ground (LG),line-to-line(LL),line-to-line-to-ground(LLG)andthree-phase (LLL)canberepresentedbyanequivalentcircuitdiagraminthe sys-temofphasecomponentsandbythisinthesystemofsymmetrical componentsaswell[1–3].

Overthelastyearsenergyshortageandenvironmental prob-lemshavebeenincreasingseriously.Thus,humanitymustadopt renewableenergyandgreenenergyinordertoachievea sustain-abledevelopment.

∗_{Correspondingauthorat:DepartmentofElectricalEngineering,Federal}

Univer-sityofCeara,PiciCampus,Brazil.Tel.:+558532413528;fax:+558533669574. E-mailaddresses:[email protected](A.P.Moura),[email protected](J.A.P.Lopes), [email protected](A.A.F.deMoura),[email protected](J.Sumaili), [email protected](C.L.Moreira).

SincecreationofCzochralskiprocesstomakethefirst gener-ationofsingle-crystalsiliconphotovoltaic,thephotovoltaic(PV) systemshavebeenutilizedasrenewableenergysourcestoproduce electricpower[4].ItisworthnotingthatPVpowerisbecoming cheaperandcheapereveryyear,asaresultitisexpectedtohavea higherpenetrationlevelinpowernetworks.Grid-connectionofPV systemsisaccomplishedthroughtheinverter,whichconvertsdc powergeneratedfromPVmodulestoacpowerusedforordinary electricequipmentspowersupply.

SincegrowthofPVsystemsaccelerates,ithasbecome impor-tantasthePVsystemswillcontributetothefaultcurrentduring afault.SeveralstudiesinvestigatetheimpactofaPVonthefault currentlevelsonafeederusingmainlytime domainsimulation methods[5].Thefollowingcanbecited:PletandGreenproposed inverterfaultmodelsandtheiruseinanetworkfaultanalysis[6]. Moreover,in[7], anovelunsymmetricalfaultsanalysismethod withhybridcompensationformicrogrid distributionsystemsis proposed.Thismethodemploystheactualthree-phasemodelsto handleunsymmetricalfaults.In [8],a faultanalysismethodfor inverter-interfacedDGswasproposed.Themethodaimsto esti-matetheinitialhighcurrentthataninverterinterfacedDGunder voltage control scheme can inject during thefirst cycleof the

fault.Ref.[9]proposedamethodologytoestablishageneralindex focusedon theinsertion of distributed photovoltaic generation andenergystorageusingbatteries.Ting-ChiaOuproposedadirect buildingalgorithmformicrogriddistributiongroundfaultanalysis

[10].In[11],MATLAB/SIMULINKisusedtosimulatesinglephase andthreephasevoltagesourceinverters whichareincreasingly beingusedtointegrateelectricpowergenerationfromsolar pho-tovoltaicwiththeelectricdistributionsystems.Ref.[12],alsoused MATLAB/SIMULINKtopresentamodelofgrid-connectedhybrid AC/DCmicrogrid.Furthermore,dynamicmodelsforeachsystem componentaredevelopedandusedforshort-timetransient sim-ulations.In[13],aPVinverterdynamicmodelinPSCAD/EMTDC isdeveloped.In[14],theauthorsinvestigatedtheimpactsofPV connectionontheprotectionsystemsofadistributionnetwork, especiallywhenpowerflowisreversedinhighpenetration sce-narios.Eventhoughthesubstationmodelwasbuiltinareal-time EMTPtypesimulationenvironmentusingRTDS/RSCAD.However, thepowersystemliteraturedoesnotpresenta simplemethod, whichcanbeusedinrealtime.Thismethodisbasedonsolvinga lin-earsysteminsideaniterativeprocess,meanwhileitcalculatesthe faultcurrent(onfrequencydomain)onradialdistributionsystem connectedwithmultiplePVgeneration.

InthePowerEngineeringandfortheelectricpowerindustry real-timefaultanalysisisorientedtowardapplicationsinthe dis-tributionsystemoperationareaotherthantheplanninganalysis. Theresultsoftheseearlierstudiescanbeusedfordistribution adap-tiverelaycoordinationandsettingswhenfeederreconfigurationis performed,whichcouldbeausefulfuturesmartgridapplication

[15].

Thispaper proposesa single and efficientmethod to calcu-lateshunt fault currentona PV-dominated distributionfeeder. Thenovelfaultsanalysis methodemployssymmetrical compo-nentscombined witha matrix denominated of inverter matrix impedance (IMI) and with a vector denominated impedance-currentvector(ICV)whichareformedbyinspection.Theproposed methodisdenominatedInverterMatrixImpedanceCurrentVector (IMICV).

Thepaperisorganizedasfollows:Firstly,thephotovoltaic sys-temmodelisintroduced.Secondly,acompletedemonstrationof thenewmethodispresented,includinganumericalexample.In fourthsectionthenewmethodisvalidated.Finalconclusionsand referencesarecontainedinthispaperaswell.

2. Modelofthephotovoltaicsystem

AccordingtoGermanstandardVDE4105reducingthepower factor(PF)ofPVgenerationusingfixedPFshouldbetaken,whether inductiveorcapacitive,aimedatimprovingtheoperationofthePV systembythedistributionnetwork.Thus,acompletemodelfora PVsystemmustrepresentactiveandreactivecurrentcomponents. Whenafaultoccursonthefeeder,thePVsystemfeedscurrent tothefault.Duetothecharacteristicsoftheinverter,thefault cur-renthasonlypositivesequencecomponentwhichdependsonthe PVinverterdesign.SincethePVsystemsaredesignedtopushthe maximumpoweravailablefromPVpanelstothesystem,thePV invertertriestopushthispowerevenunderlowvoltage condi-tionswhichoccurduringafault,i.e.,itwilltrytoactlikeaconstant powersource[5].Hence,thecurrentinjectionfromaPVinverter tothesystemcanbeapproximatedasinEq.(1):

Ipost-fault(+)=

P0

|Vpost-fault(+)|PF <(angle(Vpost-fault(+))

−arccos(PF)) (1) whereP0isthepowerfromthePVpanels,Vpostfault(+)istheac

ter-minalpositivesequencepost-faultvoltageandarccos(PF)isthearc cosineofthepowerfactor.

Fig.1.V–IcharacteristicsofaPVsystem.

However, if this current gets to be higher than the maxi-mumcurrentratingoftheinverter,itwilllimitthecurrentatits maximumlevelasshowninEq.(2).Inverterslimittheircurrentto onetotwotimestheratedcurrent[5].

Ipost-fault(+)=|Imax-inverter|<(angle(Vpost-fault(+))−arccos(PF)) (2)

TheV–IcharacteristicsofaPVsystemisshowedinFig.1.

AccordingtoFig.1,thePVsystemfeedscurrenttothefault.If thethreephasevoltagesareaboveofthenominalvoltage,the mag-nitudeoftheinjectedcurrentwillbecalculatedsoastomaintain theinitialactivepower.I.e.thecurrentiscalculatedbytheEq.(1).If thevoltagegetstoolow,themagnitudeofthecurrentwillreachits maximumlimit(Imax)anditwillnotpassthisvalue.Thehorizontal

segment(1)inFig.1presentsthissituation.

3. Newmethodformulation

AcompletedemonstrationoftheIMICVmethodispresented hereafter,illustratedwithanumericalexample.

One of the most powerful matrices used in power system analysisisthebusimpedancematrix(Z-Matrix).TheZ-Matrixis generallyfull,i.e.itcontainselementsineverypositionunlessthere aredisconnectedpartsofthenetwork.Generally,analgorithmfor findingtheZ-Matrixismoredirectandcheapertoimplementthan performinganinversionofadmittancematrix[1].

Thenewmethodemployspositive,negativeandzerosequences componentscombinedwiththeIMIandwithICV.

Initially,theproposedmethodrequires theformationofthe classicalpositiveZ-MatrixandclassicalzeroZ-Matrix[16]which aredemandedtocalculatethepost-faultvoltages.

The iterative process requires the setup of the post-fault voltages.Then,initialpost-faultpositivesequencevoltagesare cal-culatedusingtheequationstofollow:

LLfault

v

i+=1− zi,k

2(zk,k) (3)

LGfault

v

i+=1−

zi,k

2(zk,k)+z0k,k+3zg

(4)

LLGfault

v

i+=1−

zi,k

zk,k+(((zk,k)(z0_k,k+3zg))/(zk,k+z0_k,k+3zg))

(5)

LLLfault

v

i+=1− zi,k zk,k

Fig.2. Connectionsofpositive,negativeandzeroimpedancesdiagram.

where,

v

i+ – Post-fault positive sequence voltage at bus r; Zk,k – diagonalelementsof thebusimpedance matrix(positive

sequence);Z0

k.k–diagonalelementsoftheofthebusimpedance

matrix (zero sequence); Zi,k –off-diagonal elementsof thebus

impedancematrix;Zg–faultimpedance.

BeforebuildingtheIMI,thepowerdistributionsystemmustbe reducedbyaccumulatingofpositivesequenceimpedancesinthe mainfeederandalsointhesecondarybranches.Hence,thisprocess isdenominatedreducedsystemand,ismadeasfollows:Firstly,the accumulationprocessofpositivesequenceimpedancesoccursfrom thesubstationtothefaultwhichconsistsinthreeothersteps:

First step: Accumulation of positive sequence impedance betweenthesubstationandthefirstnodewhereitlocatesaPV generation;

Second step: Accumulation of positive sequence impedance betweenthefirstnodeandthesecondnodewhereitlocatesaPV generation.Similarly,thisstepiscarried outuntilthelast node beforethefault,whereitlocatesaPVgeneration;

Third step: Accumulation of positive sequence impedance betweenthelastnodewhereitlocatesaPVgenerationbeforethe faultandthefaultednode.

Afterwards,theaccumulationofpositivesequenceimpedances occursasfollows:fromthefaultednodeuntilthelastnodeafter thefaultednode.Thisprocesshastwoothersteps:

Fourth step: Accumulation of positive sequence impedance betweenthefaultednodeandthefirstnodewhereitlocatesaPV generation;

Fifth step: Accumulation of positive sequence impedance betweenthefirstnodeandthesecondnodewhereitlocatesaPV generation.Similarly,thisstepiscarriedoutuntilthelastnodeafter thefault.

Finally, it accumulates the positive sequence impedance betweeneachnodewherethereisaPVgenerationandthemain feeder.

TheIMIandICVareobtainedbyusingKirchhoff’svoltagelaw andgettingthemeshequations.Fromtheseequations,simplerules areformulatedtoformthismatrixandthisvectorbyinspection.

ThediagraminFig.2illustrateshowthepositive,negativeand zerosequencecircuitsareconnectedtothemeshequationsinorder tobewritten.InthisdiagramthereareN+MgenerationPV,where

NisthenumberofthegenerationPVbeforethefaultandMisthe numberofthegenerationPVafterthefault.

In Fig. 2 the positive sequence impedances, the positive sequencevoltagesand thepositive sequencecurrentsthathave subscripts in uppercase letters, indicate the voltages, currents and impedances that appear from the substation to the fault point.Moreover,thepositivesequenceimpedances,thepositive sequencevoltagesand thepositive sequencecurrentsthathave subscriptswithlowercaseletters,indicatethevoltages,currents andimpedancesofthecircuitthatturnupontheothersideofthe faultpoint(rightpartofFig.2).

Theequivalentimpedance(ZEQ)istheassociationofthe

neg-ativesequenceimpedance(Z−)andzerosequenceimpedanceZ0,

whichvaluedependsonthetypeoffault.E.g.:

LLfault

Thezerosequencenetworkisopen.Thus:

ZEQ=Z− (7)

LGfault

Thisimpliesthatthesequencenetworksmustbeconnectedin series.Therefore:

ZEQ=(Z−)+(Z0) (8)

LLGfault

The negative sequence network is in parallel with the zero sequencenetwork.Then:

ZEQ= ₍(Z−)(Z0)

Z−)+(Z0) (9)

LLLfault

Thecurrentsarebalancedandonlythepositivesequence net-workisoperating.Therefore:

ZEQ=0 (10)

TherulesforformingtheIMIandICVareappliedtothereduced systemandtheyarethefollowing:

A.IMI

A1.Thediagonalelements(indexii):

(A11)Elementwithindex11–Sumoftheimpedancesofthe mainfeederfromthesubstationtothefault,withopposite sign.

(A12)Elementwithindex22–alwaysnull.

(A13)Otherelementswithindicesii:Ifthebranchconnected tonodej=i−1hasaPV generation,thentheelementwill haveanunitvalue.However,ifthebranchconnectedtonode

j=i−1hasnoPVgeneration,thentheelementwillbenull. A2.Off-diagonalelements(indexij):

(A21)Elementwithindex12isequal−1.

(A22)Elementwithindex21:Sumoftheimpedancesofthe mainfeeder fromthesubstationtothefaultadded tothe equivalentimpedance,withoppositesign.

(A23) Other elementswith indices i1: (f1) PV generation sourcesbeforethefault:Sumoftheimpedancesofthemain feeder,afteritsrespectivegenerationPV,fromthesubstation tothefaultaddedtotheequivalentimpedance,with oppo-sitesign;(f2)PVgenerationsourcesafterthefault:Equivalent impedancewithoppositesign.

(A24)Otherelementswithindicesij:null. B.ICV

B1.Element11:−1+PVbefore(impedancesofthemainfeeder

fromthegenerationsourceitothefault)×generationsource currenti].

B2. Element 21: −1+PVbefore(impedances of the main

feeder fromthe generation source ito the fault+equivalent impedance)×generationsourcecurrenti]+PVafter(equivalent

impedance)×generationsourcecurrentk].

B3. Elements 3 ... (3+N−1), 1 (they are related with power generation PV before the fault), where N is the number of the generation PV before the fault: (Sum of the impedances from generation source i to the fault+equivalent impedance)×generation source current

i+PVbefore(impedancesofthemainfeeder fromthe

genera-tionsourcejtothefault+equivalentimpedance)×generation sourcecurrentj]+PVafter(equivalentimpedance)×generation

sourcecurrentk].

Read data

Form the classical impedance matrices

Calculate initial post-fault positive sequence voltages

Accumulate positive sequence impedances

Solve the linear system

Print results Form the IMI and the ICV

Calculate |Ipost-fault(+) |

Pcalculated - P0<=Tol or Iter>Itermax |Ipost-fault(+) |<=|Imax-inverter |

Yes No

Yes

Calculate fault currents Iter=Iter+1

Iter=0

No

Ipost-fault(+)=|Ipost-fault(+) |* (cosØ+jsinØ)

Ipost-fault(+)=|Imax-inverter |* (cosØ+jsinØ)

Fig.3.Basicflowchartoftheproposedmethod.

where:PVbeforeisasumrelatedwithpowergenerationPV

beforeofthefault;PVafterisasumrelatedwithpower

gener-ationPVafterofthefault.

Takeforexample,adistributionsystemwhichconsidersthree generationsPVofthesubstationsideandthreegenerationsPV afterthefaultpoint.Inthisexample,thelinediagramisthesame asinFig.2byremovingthedashedlines.Themeshequations allowtowritethefollowinglinearsystemofequations:





























−(ZA+ZB+ZC+ZD) −1 0 0 0 0 0 0

−(ZA+ZB+ZC+ZD+ZEQ) 0 0 0 0 0 0 0

−(ZB+ZC+ZD+ZEQ) 0 1 0 0 0 0 0

−(ZC+ZD+ZEQ) 0 0 1 0 0 0 0

−(ZD+ZEQ) 0 0 0 1 0 0 0

−ZEQ 0 0 0 0 1 0 0

−ZEQ 0 0 0 0 0 1 0

−ZEQ 0 0 0 0 0 0 1

























































Vf+

VPV

VPV1

VPV2

Vpv

Vpv1

Vpv2

























































−1+(ZB+ZC+ZD)IPV+(ZC+ZD)IPV1+(ZD)IPV2

−1+(ZB+ZC+ZD+ZEQ)IPV+(ZC+ZD+ZEQ)IPV1+(ZD+ZEQ)IPV2+ZEQ(Ipv+Ipv1+Ipv2)

(ZPV+ZB+ZC+ZD+ZEQ)IPV+(ZC+ZD+ZEQ)IPV1+(ZD+ZEQ)IPV2+ZEQ(Ipv+Ipv1+Ipv2)

(ZC+ZD+ZEQ)IPV+(ZPV1+ZC+ZD+ZEQ)IPV1+(ZD+ZEQ)IPV2+ZEQ(Ipv+Ipv1+Ipv2)

(ZD+ZEQ)IPV+(ZD+ZEQ)IPV1+(ZPV2+ZD+ZEQ)IPV2+ZEQ(Ipv+Ipv1+Ipv2)

(Za+Zpv+Zb+ZEQ)Ipv+(Zb+Zc+ZEQ)Ipv1+(Zc+ZEQ)Ipv2+ZEQ(IPV+IPV1+IPV2)

(Zb+Zc+ZEQ)Ipv+(Zb+Zc+ZEQ+Zpv1)Ipv1+(Zc+ZEQ)Ipv2+ZEQ(IPV+IPV1+IPV2)

(Zc+ZEQ)Ipv+(Zc+ZEQ)Ipv1+(Zc+ZEQ+Zpv2)Ipv2+ZEQ(IPV+IPV1+IPV2)





























TheIMIandtheICVareusedtosolvealinearsystemof equa-tionswherethefollowingpost-faultvariables are:current in substation,thevoltageatthefaultpointandvoltagesinthePV grid-connectednodes.

Fig.3presentsthebasicflowchartoftheproposedmethod. ThecalculatedactivepowerisgivenbyEq.(11).

Pcalculated=3.Vpost-fault(+).Ipost-fault(∗ +).Sbase (11)

InbasicflowchartP0isthespecifiedactivepowerforPV gener-ation(MW).

Fig.4.Smalldistributionsystem.

AccordingtoFig.2,thecalculatedfaultcurrentisgivenbyEq.

(8).

IF=I1+IPV+IPV1+IPV2+···+Ipv2+Ipv1+Ipv (12)

C.Simulationofasmallsystem

Inthisparticularitem,wewillgiveanumericalexampleto illustratetheIMICVfaultanalysismethod.

Consider the distribution system shown in Fig. 4. The three-phase short-circuit power and single-phase short-circuit power of the bus 1 are respectively: 4808∠−80◦_{MVA and}

4109∠−80◦_{MVA. The two transformers are delta-grounded}

wye and their data are: T23−138/11.95kV–15MVA−8.68%. T45−11.95/0.22kV-500kVA−5%. The data

distribu-tion lines are: L12: Zpositive=0.1902+j0.4808ohms/km,

Zzero=0.4414+j1.7452ohms/km, distribution line length=

10km, L34: Zpositive=0.1903+j0, 3922ohms/km,

Zzero=0.4359+j1.8540ohms/km,distributionlinelength=0.8km.

Faultphase-earthoccursonbus3(PhaseA),calculate:(1)Thefault current,(2)ThecurrentcontributionofthePVgenerator.

TheinjectedpowerofthePVgeneratoris500kW.The distribu-tionsystembaseis100MVA.

Thecalculationsfollowthebasicflowchart.Thenomenclature isthesameasinFig.2.

1.Calculationofimpedancematrixelements(pu)

Z33positive=0.0136+0.6244i

Z53positive=0.0136+0.6244i

Z33zero=0.0+0.5787i Z53zero=0.0+0.0i

2.Calculationof theinitialpost-fault positive sequencevoltage (pu).

AccordingtoEq.(4):

v

2(Z3,3)+Z30,3+3(0)

3.Accumulationofpositivesequenceimpedances

ZA=0.0136+0.6244i Za=0.1066+10.2197i

4.IMIandICVcalculation

IMI=





−0.1202−10.8441i −1 0 −0.2404−31.6882i 0 0 −0.2268−31.0638i 0 1





ICV=





−0.9995+0.0776i

−0.9991+0.2359i

0.0009+0.2359i





5.Iterativeprocess Tolerance=0.00001pu

Convergenceiterationnumbers=3

IF=0.0316∠−89.3829◦ pu Ipv=0.0051∠−0.1988

◦

pu

4. Validatingtheproposedmethod

Faultcurrentscalculationisakeyfactorindeterminingthetap settingsoftheprotectionrelaysformanypracticalapplications.

The commercial software Simultaneous Fault Analysis (ANAFAS), developed by the Electric Energy Researches Cen-ter (CEPEL) – Brazil, wasused just for verification of the fault currentscalculation.

Thisstudywasperformedontheregionaldistributionsystem thatconsistsofathree-phaseradialdistributionfeederwithurban andruralbranches.ThetestfeederusedwascalledLOC-36andits dataarestatedinAppendix.Thisfeederislocatedinthe distribu-tionsystemoftheEnergyCompanyofCeara–Brazil.LOC-36has 36buses,35branchesanditsthree-phaseshort-circuitpoweris 505.59∠59.10◦_{MVA.Thetransformersubstationisdelta-grounded}

wyeandtheirdataare:69/13.8kV–6%inthesystembase.The single-linediagramofthefeederLOC-36isshowedinFig.5.

Thesimulatedsolarplantswerebasedonphotovoltaicpanels SX120Umodel(manufacturersolarPB).

TheintegrationofPVgenerationunitsaregivenasfollows:330 unitsofgeneratorPVwereinstalledinbus4;110unitsof gen-eratorPVwereinstalledinbus13and990unitsofgeneratorPV wereinstalledinbus19,totalingrespectively,0.957MW(PF=1), 0.319MW (PF=1) and 2.817MW (PF=0.92 inductive) of rated power.Thecomputerusedinthesesimulations,isaDELLcomputer withIntel(R)Core(TM)[email protected],Memory(RAM)

Fig.5.FeederLOC-36diagram.

Fig.6.Overheadlinespacings.

Table1

Faultcurrentresults–bus23.

Faulttype PhasecurrentabsolutevalueANAFAS(pu) PhasecurrentabsolutevalueIMICV(pu)

IA IB IC IA IB IC

LGA 0.590 0 0 0.5915 0 0

LGB 0 0.590 0 0 0.5915 0

LGC 0 0 0.590 0 0 0.5915

LLAB 0.811 0.811 0 0.8166 0.8166 0

LLBC 0 0.811 0.811 0 0.8166 0.8166

LLAC 0.811 0 0.811 0.8166 0 0.8166

LLGAB 0.772 0.901 0 0.7764 0.9076 0

LLGBC 0 0.772 0.901 0 0.7764 0.9076

LLGAC 0.901 0 0.772 0.9076 0 0.7764

Table2

Faultcurrentspercenterrors.

Faulttype Abs(error)(%)

LG 0.25

LL 0.69

LLG 0.57and0.73

LLL 0.67

Table3

FaultcurrentsofthePVgenerations.

Faulttype–bus PVcurrentabsolute value(pu)ANAFAS

PVcurrentabsolute value(pu)IMICV

LG–4 0.010 0.0100

LG–13 0.003 0.0034

LG–19 0.034 0.0337

LL–4 0.011 0.0109

LL–13 0.004 0.0040

LL–19 0.039 0.0393

LLG–4 0.011 0.0111

LLG–13 0.004 0.0042

LLG–19 0.041 0.0411

LLL–4 0.013 0.0128

LLL–13 0.005 0.0055

LLL–19 0.055 0.0547

Table4

NumberofiterationsforIMICVconvergenceandCPUtime.

Faulttype Iterationsnumber Totalexecutiontime(s)

LG 4 0.0049

LL 4 0.0048

LLG 5 0.0060

LLL 4 0.0049

8GBand64-bitsOS.TheIMICVfaultanalysismethodwaswrittenin MATLABcode.Afterwards,theresultsobtainedfromANAFASand IMICVwerecompared.

Table1showsacomparisonofthefaultcurrentsonbus23of thefeederLOC-36inbothprogramsdescribedabove.Table2shows thepercenterrorsobtained,respectively,withANAFASandwith theIMICV.

AccordingtoTables 1and 2 theresultsfromIMICV andthe resultsfromANAFAScanbeseentobemuchcloser.Thelargest erroris0.73%.

Table3illustratestheresultsof thefaultcurrentsof thePV generationslocatedonbuses4,13and19.TheresultsofANAFAS softwarereportonlythreedecimaldigits.Oneunderstandsthen thattheresultsfromIMICVandtheresultsfromANAFASalsocan beseentobemuchcloser.Therefore,theIMICVproposedmethod canbeconsideredasvalidated.

Table4presentstheconvergenceiterationnumbersforIMICV andtotal executiontime. Here,thevalueofthespecified toler-ancewas0.00001pu.Furthermore,thelargestiteration number occurredforLLG.Nevertheless,thenumberofiterationsfor conver-gencemadebyANAFASisnotaccessibleinitsresultsfile.Finally, thetotalexecutiontimeoftheIMICVshowsthatthistoolis appro-priatefortheelectricpowerindustryreal-timefaultanalysis.

5. Conclusion

AnovelIMICVfaultanalysismethodisdevelopedinthispaper. Theproposedmethodcanbeusedtosimulateradialdistribution systemwithmultiplePV grid-connected inverters and,also for real-time fault analysis. The numerical results were compared withresultsoftheprofessionalsoftwareANAFASandtheproposed method was validated. Computer simulations show that the

proposed method is efficient, accurate and easy to program. Therefore,thenewmethodcanbeausefultool fortheelectric powerindustry.

Appendix.

DatafromthefeederLOC-36areshownbelow.

CONDUCTORDATAandLENGTHOFTHEDISTRIBUTIONLINES.

Size/stranding/material From To Linelength feet

R(/mile) GMR feet

266,800/26/7//ACSR 1 2 197 0.385 0.0217

266,800/26/7//ACSR 2 3 656 0.385 0.0217

4/ 6/1 /ACSR

3 4 3083 2.57 0.00437

266,800/26/7//ACSR 3 5 2230 0.385 0.0217

266,800/26/7//ACSR 5 6 525 0.385 0.0217

1/0

ACSR

6 7 3149 1.12 0.00446

4/ 6/1 /ACSR

7 8 5871 2.57 0.00437

4/ 6/1 /ACSR

8 9 1476 2.57 0.00437

4/ 6/1 /ACSR

8 10 2624 2.57 0.00437

4/ 6/1 /ACSR

10 11 1148 2.57 0.00437

4/ 6/1 /ACSR

10 12 2788 2.57 0.00437

4/ 6/1 /ACSR

12 13 2427 2.57 0.00437

266,800/26/7//ACSR 6 14 164 0.385 0.0217

1/0 ACSR

14 15 426 1.12 0.00446

1/0 ACSR

15 16 1148 1.12 0.00446

1/0 ACSR

16 17 492 1.12 0.00446

1/0 ACSR

17 18 262 1.12 0.00446

1/0 ACSR

18 19 230 1.12 0.00446

266,800/26/7//ACSR 14 20 1640 0.385 0.0217

95/ COPPER

20 21 7675 0.356 0.01506

1/0 ACSR

20 22 2493 1.12 0.00446

1/0 ACSR

22 23 886 1.12 0.00446

1/0 ACSR

23 24 394 1.12 0.00446

4/ 6/1 /ACSR

24 25 2624 2.57 0.00437

4/ 6/1 /ACSR

25 26 754 2.57 0.00437

25/ AA

24 27 3542 1,429 0.00794

25/ AA

27 28 5904 1,429 0.00794

25/ AA

28 29 394 1,429 0.00794

25/ AA

29 30 853 1,429 0.00794

25/ AA

30 31 3608 1,429 0.00794

25/ AA

Appendix(Continued)

Size/stranding/material From To Linelength feet

R(/mile) GMR feet

25/ AA

32 33 3772 1,429 0.00794

25/ AA

33 34 787 1,429 0.00794

25/ AA

34 35 2952 1,429 0.00794

25/ AA

35 36 2296 1,429 0.00794

Fig.6showsthespacingdistancesamongphaseconductorsused foroverheaddistributionlines.

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