Design of an optimal SMES for automatic generation control of two-area thermal power system using Cuckoo search algorithm

Availableonlineatwww.sciencedirect.com

ScienceDirect

JournalofElectricalSystemsandInformationTechnology2(2015)1–13

Design

of

an

optimal

SMES

for

automatic

generation

control

of

two-area

thermal

power

system

using

Cuckoo

search

algorithm

Sabita

Chaine

,

M.

Tripathy

DepartmentofElectricalEngineering,VeerSurendraSaiUniversityofTechnology,Burla,Odisha768018,India

Availableonline14March2015

Abstract

Thisworkpresentsamethodology adoptedinorder to tunethe controller parametersofsuperconducting magneticenergy

storage(SMES)systeminthe automaticgenerationcontrol(AGC)ofatwo-areathermalpowersystem.Thegainsofintegral

controllersofAGCloop,proportionalcontrollerofSMESloopandgainsofthecurrentfeedbackloopoftheinductorinSMES

areoptimizedsimultaneouslyinordertoachieveadesiredperformance.Recentlyproposedintelligenttechniquebasedalgorithm

knownasCuckoosearchalgorithm(CSA)isappliedforoptimization.Sensitivityandrobustnessofthetunedgainstestedatdifferent

operatingconditionsprovetheeffectivenessoffastactingenergystoragedeviceslikeSMESindampingoutoscillationsinpower

systemwhentheircontrollersareproperlytuned.

©2015ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC

BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Superconductingmagneticenergystorage(SMES);Integralcontroller;Automaticgenerationcontrol(AGC);Cuckoosearchalgorithm (CSA)

1. Introduction

Itisawellknownfactthat,anymismatchbetweengenerationandloadinaninterconnectedpowersystemcauses instabilitythatdeterioratesthesystemdynamicperformancesdisturbingtheequilibriumofrealpowerofthesystem, whichinturnaffectsthesystemfrequency.Inthisregard,thepurposeofAGCistodevelopacontrolsystemwhich shouldbeabletomaintainthesystemfrequencyandtielinerealpowerflowingbetweendifferentcontrolareasattheir respectivespecifiednominalvalueswhenthesystemissubjectedtoloadvariations.

Withaviewtoachievetheaboveobjective,oneimportantreviewworkinthefieldofAGChastriedto compre-hensivelydiscussvariouscontrolstrategiesadoptedtilltoday(IbraheemandKothari,2005).Effectsofthemechanical governor,electricgovernor,asinglestagereheatturbineandatwo-stagereheatturbine,onthedynamicresponseshave beenexploredbyNandaetal.(2006).Someotherworkshaveformulatedtheprobleminthedomainofoptimizationand

∗_{Correspondingauthor.}

E-mailaddresses:[email protected](S.Chaine),[email protected](M.Tripathy). PeerreviewundertheresponsibilityofElectronicsResearchInstitute(ERI).

http://dx.doi.org/10.1016/j.jesit.2015.03.001

2314-7172/©2015ElectronicsResearchInstitute(ERI).ProductionandhostingbyElsevierB.V.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

triedtoinvestigateintotheapplicationofbothconventional(Malleshametal.,2010)aswellasheuristicoptimization techniques(Ghoshal,2004).

Besidesthemethodofgaintuningthroughoptimization,researchworkshavealsotriedtoexaminetheefficacies ofotherpowerelectronicsbased devicesinthe familyofflexibleACtransmissionsystems (FACTs)(Bhatt etal., 2010),todampoutoscillationsinthefrequencyandtie-linepowerexchanges.Fast-actingenergystoragedevicesuch asSMESsystemhasalsobeenfound(Banerjeeetal.,1990;Tripathyetal.,1992)tointroducerequireddampingin theseoscillations.

Thisworkaimsatobtainingan optimalcontrollerfor SMESinatwo-areapowersystem(Elgerd,2005) which shouldexhibitrobustnessinitsperformanceforavaryingoperating conditionsandparametersofthesystem.Two mostimportantissuesmentionedbelow,whichdecidetheeffectivenessofanysuchtunedcontroller,areemphasized whileformulatingandsolvingtheproblem.Theyare

(i) Thenatureofdesignedobjectivefunction. (ii) Theefficiencyofoptimizationmethod.

Objectivefunctionsare suitably designedfrombothtimedomainandfrequencydomainperspectives andafter optimizationtheirrelativeperformancesaretestedwhensubjectedtoperturbations.Inordertooptimizetheproblem, recentlyproposednature-inspiredmetaheuristicalgorithmsknownasCuckoosearch(CS)(YangandDeb,2009)have beenutilized.

Thepaperisorganizedasfollows.Section2 illustratesthesystemmodel,anditsmaincomponents.InSection 3,abriefoverviewonSMESanditsproposedcontrolstrategyispresented.Section4discussesaboutthedifferent objectivefunctionswhichareoptimizedtomaximizetheperformanceoftheSMESinAGCdomain.Abriefoverview oftheintelligenttechniquebasedoptimizationalgorithmCSiselaboratedinSection5.Thesimulationandresults, obtainedfollowingseveraltestsrelatedtotheperformanceoftunedSMES,areexplainedandanalyzedinSection6. Attheend,conclusionsarepresentedinSection7.

2. AGCintwo-areathermalpowersystemwithSMES

ManyproblemsinAGC,particularlyrelatedonlytotheautomaticloadfrequencycontrol(ALFC)partofAGCwithin twointerconnectedareasofpowersystem,haveutilizedawidelyacceptedmodel(Elgerd,2005)inordertoexaminethe responseofpowersystemtowardsseveralfactorsincludingchangesinsystemparameter,modelparameters,operating condition,gainsof controllers,etc.Fig.1 depictsthe outlineof thismodel,wheretheblocksof transferfunctions representingthe governor system,steam reheats turbines,regulation droopR, frequencybiasconstant,β,etc. are connected.Theareacontrolerror(ACE)isdefinedbycombiningΔfandΔPTieasdepictedinEqs.(1)and(2),which arewidelyused:

e1(t)=ACE1=β1f1+PTie (1)

e2(t)=ACE2=β2f2−P_Tie (2)

2.1. TheroleofSMESintheproblemofAGC

ThepresenceofSMESinthecontroloffrequencyinanAGCframeworkprovidesrapidrecoveryintherequirement ofdeficitorsurplusrealpower,byderivingthesamefromalargeinductororreactor.Aspertheneedofthepower system,thepowerdeliveredorrecoveredfromthereactorcanbecontrolledbysuitablydesignedcontrollerdedicated fortheSMES.Adetailedoverviewbehindthefundamentalphysicsandsomeelementarymodellingissuesshallbe coveredinSection3.

3. Superconductingmagneticenergystorage(SMES)system:briefdiscussion

AsdepictedinFig.2,theSMESsystemhasaDCmagneticcoilthatisconnectedtotheACgridthroughapower conversionsystem(PCS)whichincludestwonumbersofconvertersforinversionandrectificationpurposes.

Fig.1.Two-areainterconnectedpowersystemwithSMESunitconsideringGRC.

The control of the operation of SMES duringits charging, discharging, andsteady state mode and the power modulatingdynamicoscillatoryperiodareachievedbytheapplicationofadequatepositiveornegativevoltagetothe inductor,through thecontrol offiring angle ofthe converterbridges.Fig.3 illustratesthetransferfunctionmodel representationoftheSMEScontrolscheme,wheretheACEmaybegiventotheproportionalblock(KSMES)toderive

theincrementalchangeinconvertervoltage(Ed),asexplainedinEq.(3).Inordertoachievequickrestorationof inductorcurrent(Id)afteranypossiblechangeinloaddemandinthesystem,theincrementalIdissensedandused asanegativefeedbacksignalintheSMEScontrolloop(Banerjeeetal.,1990):

Edi= 1 1+sTdci

[KSMES(βifi+Pij)−KId_iId_i] (3)

SMES P ΔΔ

Π

I

I

++

ΔΔ

E

Δ

−

Σ

Σ

+

+

K

sT

1

1

+

K

Fig.3.TransferfunctionmodelofSMESunits.

InEq.(3),Tdcistheconvertertimedelayins;KSMESisthegainoftheSMEScontrolloopforACEsignalinkV/unit

ACE,KIdisthegainoftheinductorcurrentdeviationfeedbackloopinkV/kA.

Sincetheamountofstoredenergyisfinite,theinductorcurrentfalls.ThedeviationintheinductorcurrentIdis expressedasfollowsinEq.(4):

Id= Ed

PL (4)

wherePisthedifferentialoperatorwithrespecttotime.ThedeviationintheinductorpowerflowPSMESisgivenby

theexpressionasfollowsinEq.(5):

PSMES=Id0·Ed+Ed·Id (5)

TheinductorisinitiallychargedtoitsratedcurrentId0byapplyingasmallpositivevoltage.Oncethecurrenthas

attainedtheratedvalue,itisheldconstantbyreducingthevoltageideallytozerosincethecoilissuperconducting. However,averysmallvoltagemayberequiredtoovercomethecommutatingresistance.

4. Theformulationoftheproblemandobjectivefunctions

Astheproblemisplannedtobeformulatedinanoptimizationframework,suitabledesignofobjectivefunctionis tantamounttotheefficacyofoverallcontrolperformance.Hence,differentobjectivefunctions,i.e.,J1andJ2,integral

oftimemultipleofabsoluteerror(ITAE)andintegraloftimemultipleofsquareoferrors(ITSE)arediscussed: J1=ITAE=

_tsim

0

t[|(f1)|+|(f2)|+|(PTie)|]·dt (6)

Intheaboveequation,tsimisthetimerangeofsimulation:

J2=ITSE=

_tsim

0

t[(f1)2+(f2)2+(P_Tie)2]·dt (7)

ThevaluesofITSE,settlingtime(Ts)ofbothareafrequencydeviations(f1andf2)andPTiealongwiththe minimumdampingratiosamongallthesystemeigenvaluesarecombinedtoformulatethethirdobjectivefunctionJ3

asgivenbelowinEq.(8):

J3=ω1(ITSE)+ω2(1/X)+ω3(Ts) (8) ω1,ω2andω3aretheweighingfactorssuitablychosen.x=minimumdampingratio(MDR)amongalltheeigenvalues

ofthesystem.Ts=settlingtime;T_s=T_sf

1 +Tsf2 +TsPTie.TsPTie,Tsf1,Tsf2.Settlingtimeoftielinepowerdeviation, frequencydeviationinarea1and2.

5. Cuckoosearchalgorithm:anoverview

CSAisanevolutionaryalgorithmthatisinspiredbythebroodparasitismfoundinthebreedingbehaviourofsome commonlyfoundspeciesofCuckoos.Moreover,thealgorithmalsoincorporatesintoitsstructurethemathematical modelofthebehaviourofLévyflightfoundinsomebirdsandfruitflies(YangandDeb,2009).

IntheevolutionstrategyofCSA,animportantmethodologyofchoosingarandomdirectiontogeneratethestep

lengthisdonewiththehelpofanalgorithmknownasMantegnaalgorithm.Theaboveprocessguaranteesastable

symmetricLévydistribution(Yang,2010).

5.1. Cuckoosearchalgorithm:theprogrammingmethodology

Asfarasapplyingthealgorithmisconcerned,threesimplifyingassumptionsdescribedbelowhavebeenusedin thiswork.

(i) Eachcuckoolaysoneeggatatimewhichitdumpsinarandomlyselectednest(n). (ii) Thebestnestshavingbetterqualityeggsareretainedforsubsequentgenerations.

(iii) Keepingthetotalnumbersofhostnestsasconstant,anegglaidbyacuckoocouldbedetectedbythehostbird withaprobability(Pa)of0.1.

Basedonthesethreerules,thebasicstepsoftheCSAareprovidedintheflowchartshowninFig.4.

6. Simulationandresults

TheAGCsystemmodeldevelopedinMATLAB/SIMULINKisusedtoobtaindynamicresponseforastepload perturbation. The integral controller parameter (KI) for the main AGCloop, SMES gainparameter (KSMES) and

feedbackgain(KId)inSMEScontrollooparetobeobtainedseparatelybyoptimizingthethreedifferentobjective functions.ForthepurposeofoptimizationCuckoosearchalgorithmisapplied.

TwonumbersofSMESeachhavingcapacitiesof30MJareincorporatedinboththeareas.Theactualandperunit valueofSMESdevicearegiveninAppendixA.

Moreover,inordertotakeintoaccountthesmallesttimeconstantsassociatedwithSMES,time-domainanalysisof thecontinuoussystemisperformedwithatimestepof0.01swithappropriatechoiceofsamplingtimeintervalsfor thecontrollers.

6.1. CSAtunedcontrollerparameters(KI,KSMES,KId)

Foroptimizingtheobjectivefunctionseachoftheparametersarerandomlyinitializedinsuitablerangesandthe parametersevolvethroughsuccessivegenerationgivingtheoptimumresultsattheend.Thevaluesofallthecontroller parametersareobtainedseparatelybyoptimizingtheobjectivefunctionsJ1,J2andJ3withthehelpofCSAinthree

differentrunsofthealgorithm.Itistobenotedthat theobjectivefunctionsaredependentonthetimedomainand eigenvaluebasedperformanceindices(PFIs),whichareevaluatedattheendofsimulationtimeof30s.AllthesePFIs arealsoevaluatedforthecasewhennoneoftheeitherareasisoperatingwithSMES.Theoptimizedvaluesofthe abovementionedcontrollerparametersobtainedseparatelybyoptimizingthethreeobjectivefunctionsareelucidated inTable1.

6.2. Controllerperformanceevaluationfromoptimizationresults

BesidesthePFIsdefinedandusedintheformulationoftheobjectivefunctions,twootherPFIs,i.e.,integralsquare error(ISE)andintegralabsoluteerror(IAE)arealsoevaluatedandcomparedforeachsetofoptimizedcontrollers. ThesePFIsareenumeratedinTable2.Fromtheresults,itisclearthatwiththeproposedalgorithmthesystemmodes shiftmoreinthelefthalfofS-plane,whichenhancesthesystemstability.Minimumdampingratio(MDR)ofsystem among allthe systemeigenvalues, obtained separatelyfor all the objective functionsoptimizedwith CS are also

Table1

Theoptimizedvaluesofcontrollerparameterswiththethreeobjectivefunctions. Objectivefunction/controller

parameters

Controllerparameters Optimizedvalueof objectivefunction SMESloopgain

(KSMES)

Inductorcurrent feedbackgain(KId)

Integralgain(KI)

DifferentobjectivefunctionstunedinCSAwithSMES

J1 _85.8402 20.1975 5.0464 0.0423

J2 _91.9804 1.7957 3.4621 2.5732e−004

J3 _99.1703 14.3716 4.7118 14.8430

J3tunedinPSOwithSMES 96.0970 19.2532 4.9322 17.0554

J3tunedinCSAwithout SMES

0 0 0.4986 76.3698

Table2

SeveralPFIsandMDRamongalltheeigenvaluesofthesystemusingCSAbasedondifferentobjectivefunctionsJ1,J2,andJ3withandwithout SMES.

Performanceindices DifferentobjectivefunctionswithSMES J3withoutSMES

J1 J2 J3

ISE 3.5351e−004 2.8043e−004 3.1536e−004 0.0017 ITSE 4.2914e−004 2.5732e−004 3.5042e−004 0.0031

IAE 0.0312 0.0365 0.0324 0.1252 ITAE 0.0423 0.0758 0.0484 0.4510 Ts(s) Δf1 10.3500 10.3500 4.9000 25.4900 Δf2 11.5400 11.5400 4.3400 26.5800 ΔPTie 9.3400 9.3400 3.9800 23.9800 MDR 0.6227 0.6561 0.6954 0.0098 Eigenvalues −12.5000 −26.0324 −3.1790+3.9950i −3.1790−3.9950i −12.5000 −26.4451 −3.4691+3.9902i −3.4691−3.9902i −12.5000 −24.2947 −3.8294+3.9570i −3.8294−3.9570i −3.3333 −12.5000 −0.0250+2.5572i −0.0250−2.5572i

illustrated.Thesettlingofdeviationsisveryfast,around5sinobjectivefunctionJ3anddampingratioalsoimproved

ascomparedtootherobjectivefunctionsinTable2.

6.3. ComparisonofCSAwithparticleswarmoptimization(PSO)

AcomparisonisalsosoughtinthisworkbetweenCSAandthewidelyacceptedoptimizationtechniquePSOin termsoftheperformanceobtainedbytherespectivecontrollerswhenthegainsofthesameareobtainedbyoptimizing theobjectivefunctionJ3.AsdepictedinFigs.5–7,whichshowboththeareas’frequencyandtielinepowerdeviations

for0.01SLPinthe1starea,CSAtunedcontrollerhasprovidedbetterdampingcomparedtotheonetunedbyPSO.

Table3

ComparisonofseveralPFIsandMDRofthesystemwithcontrollerstunedwithCSAandPSObasedonobjectivefunctionJ3.

Performanceindices ISE ITSE Ts MDR

Δf1 Δf2 ΔPTie

CSAtunedJ3 3.1536e−004 3.5042e−004 4.9000 4.3400 3.9800 0.6954 PSOtunedJ3 3.3400e−004 3.8993e−004 5.7300 5.1300 5.1800 0.6787

0 5 10 15 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 PSO CSA Time in sec Fre quenc y deviation Δ f1 (p .u. )

Fig.5. Changeinfrequencyof1stareafor1%loadchangein1starea.

0 5 10 15 -0.01 -0.005 0 0.005 0.01 0.015 Time in sec PSO CSA Frequency deviation f 2 Δ

Fig.6. Changeinfrequencyof2ndareafor1%loadchangein1starea.

0 5 10 15 -4 -2 0 2 4x 10 -3 PSO CSA Time in sec

Tie-line Power Deviation (p.u.)

0 5 10 15 20 25 30 -0.03 -0.02 -0.01 0 0.01 Time in sec With SMES Without SMES Frequency Deviation f1 (p.u.) Δ

Fig.8.Changeinfrequencyof1stareafor1%loadchangein1starea.

0 5 10 15 20 25 30 -0.03 -0.02 -0.01 0 0.01 Time in sec With SMES Without SMES Frequency Deviation f2 (p.u.)

Δ

Fig.9.Changeinfrequencyof2ndareafor1%loadchangein1starea.

0 5 10 15 20 25 30 -8 -6 -4 -2 0 2x 10 -3 Time in sec With SMES Without SMES

Tie-line Power Deviation (p.u.)

0 5 10 15 20 25 30 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 Frequency Deviation f1 Time in sec Δ

Fig.11.Changeinfrequencyof1stareaduetoloadvariationin1st,2ndandbothareas.

0 5 10 15 20 25 30 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 1% load in 2nd 1% load in 1st area 1% load in both areas Time in sec Frequency deviation f2 (p.u.) Δ

Fig.12.Changeinfrequencyof2ndareaduetoloadvariationin1st,2ndandbothareas.

0 5 10 15 20 25 30 -4 -2 0 2 4x 10 -3

Tie-line Power Deviation (p.u.)

Time in sec

Table4

Sensitivityanalysis.

Parametervariation %change PerformanceindexITSE Settlingtime MDR

f1 f2 PTie T12 +50 2.0071e−004 10.6400 11.4500 9.6500 0.5020 +25 2.2153e−004 10.6100 11.5900 9.6400 0.5681 −25 3.1676e−004 10.4900 11.9900 9.3700 0.6828 −50 4.0349e−004 10.5300 12.5100 8.9500 0.7364 Tg +50 3.2611e−004 11.9300 11.9300 9.4800 0.6954 +25 2.8919e−004 10.7500 11.9300 9.6200 0.6954 −25 2.3025e−004 10.4500 11.6400 9.5000 0.6954 −50 2.0743e−004 10.8900 11.8500 9.8400 0.6954 Tr +50 4.0266e−004 13.3000 14.5500 14.1400 0.6954 +25 3.2122e−004 12.1700 13.4500 12.1900 0.6954 −25 2.0633e−004 7.4000 8.3100 3.5500 0.6954 −50 1.5441e−004 4.6900 4.7700 3.7900 0.6954 Kr +50 1.8588e−004 3.8300 4.3100 3.4500 0.6954 +25 2.1237e−004 8.5600 9.5300 4.5300 0.6954 −25 3.5564e−004 10.8200 11.9800 11.9000 0.6954 −50 5.8164e−004 19.5000 20.2500 12.2500 0.6954 Tt +50 4.1800e−004 10.7400 11.8300 9.0600 0.6954 +25 3.3124e−004 10.6500 11.8100 9.4500 0.6954 −25 1.9742e−004 10.5600 11.7400 9.5400 0.6954 −50 1.4947e−004 10.8600 12.0100 9.6200 0.6954 Loadingcondition +50 1.5537e−004 10.8000 11.9800 9.6900 0.6006 +25 1.5261e−004 10.8400 12.0100 9.6700 0.6194 −25 1.4640e−004 12.4900 12.4900 10.0200 0.7234 −50 1.4685e−004 11.4100 12.5300 10.0300 0.8035 H +50 2.7482e−004 10.4300 11.6100 9.2800 0.5994 +25 2.6620e−004 10.4400 11.6300 9.3700 0.6187 −25 2.5164e−004 10.7800 11.9700 9.8500 0.7240 −50 2.5466e−004 10.8600 12.0100 10.0200 0.8041

Moreover,lookingattheseveralperformanceindicesgiveninTable3,itcanbeseenthatwithCSAoptimizedcontroller, theperformancesparticularlythesettlingtimesarebettercomparedtothoseobtainedwithPSO.

6.4. Controllerperformanceevaluationfordifferentdisturbancesandchangesinparameters

6.4.1. Steploadincreaseinarea1

TheIntegralandSMEScontrollerparametersaresetatthevaluesobtainedbyoptimizingobjectivefunctionJ3.The

optimalvaluefortheintegralgainKIfoundinbothcaseswithoutandwithSMESisgiveninTable1.Thefirstcontrol areaissubjectedtoaSLPof1%fromitsnominalvalueattimet=0.Dynamicresponseoffrequencydeviations(Δf1

andΔf2)ofboththecontrolareasandthedeviationintielinepower(ΔPTie)obtainedforthisperturbationisdepicted inFigs.8–10.Fromthefiguresitcanbewitnessedthat,thefrequencyandtielinepoweroscillationsareseentosettle around25swithoutSMES,whereasthesamevaluereducesto5swiththeSMESoperating.Thevaluesofover-shoot, under-shootandMDRhavealsoimprovedpredominantlyasenumeratedinTable2.

6.4.2. Steploadincreaseinbotharea1and2

BoththecontrolareasaresubjectedtoSLPof1%eachfromtheirnominalvaluesasitwasdoneintheprevioustwo cases.Dynamicresponseoffrequencydeviations(Δf1andΔf2)andthedeviationintielinepower(ΔPTie)obtained forthisperturbationsaredepictedinFigs.11–13.FromFigs.11and12,itcanbeseenthattheboththeareafrequency deviationsbecomemorewhenloadsinbothofthemareincreasedsimultaneously.Moreover,itcanbenoticedfrom Fig.13that,whenboththeareasaresubjectedtosamesteploadperturbation,frequencydeviationsinboththeareas

haveincreased,butnooscillationisnoticedintielinepowerdeviationasequaldisturbancesgiventotwoequalarea havingsameinertiawouldnotrequireanyexchangethroughtieline.

6.4.3. Sensitivityanalysiswithvariationinparameter

TostudytherobustnessoftheproposedcontrollersobtainedbyoptimizingJ3variationsinthesystemparameters

andoperatingconditionsaredeliberatelyintroduced.Fortestingthecontrollerperformancewithparametervariations, severalnumbersoftimeconstantsrelatedtothegoverningsystem(Tg),turbines(Tt),thesynchronizingpowercoefficient (T12),reheater(Tr)arevariedintherangeof−50%to+50%fromtheirrespectivenominalvaluesinseparateeventsof perturbationcases.Similarvariationsinthevaluesofreheatergain(Kr)andinertiaconstant(H)havealsonotdisturbed theoscillationskeepingthemstable.

Moreover,thenumericalvaluesofITSE,frequencydeviationsofboththeareasandthetielinepowerdeviations obtainedwithvariationsinsystemparametersandoperatingconditions are listedinTable4.Thevalues obtained corroboratetherobustnessoftheproposedcontrollerformodifiedparametersandoperatingconditions.

7. Conclusion

Inthiswork,observedthateffectivelytunedcontrollergainsofSMESalongwiththoseofthepowersystemenable thelatertooperateinamorestablemannercomparedtothecasewhennoSMESwerepresent.Itwasfoundthat, besidestheefficiencyofCSAoptimizationalgorithm,suitabledesignoftheobjectivefunctionalsoplaysanimportant roleinobtainingarobustdesignofdifferentcontrollersinacoordinatedmanner.However,anypossiblemodification ofthealgorithmeitherthroughtheprocessofhybridizationwithothersimilarevolutionaryalgorithms,orbyaltering thebasicprocessformultiobjectiveoptimizationproblemsmayresultinimprovingitsefficiency.

AppendixA.

A.1. SMIBdata

Totalratedareacapacity(Pr)=2000MW,f=60Hz,R1=R2=2.4(Hz/p.u.MW),Tt1=Tt2=0.3s.

Tr1=Tr2=10s,Tg1=Tg2=0.08s,Tp1=Tp2=20s(Tp=(2H/fD)),Kp1=Kp2=120Hz/p.u.MW(Kp=(1/D))

Di=PDi/fi=8.33×10−

3

p.u.MW/Hz,Kr1=Kr2=0.5,β1=β2=0.425,T12=0.0867s.

A.2. SMESsystemdata

Tdc1=Tdc2=0.03s,SB=basepower=2000MW,assumingbasevalueofEd=10kVandId=200kA. Baseimpedance(ZBase)=0.05,L1=L2=2.65H(absolutevalue)=19,970p.u.

TheinitialcurrentId0=4.5kA=0.02p.u.(seecurrentbase).

A.3. PSOparameters

Numberofparticles=20,C1=1.2,C2=1.2,momentofinertia=0.9.

Maximumnumberofstep=20,dimensionoftheproblem=3.

References

Banerjee,S.,Chatterjee,J.K.,Tripathy,S.C.,1990.Applicationofmagneticenergystorageunitasloadfrequencystabilizer.IEEETrans.Energy Convers.5(1),46–51.

Bhatt,P.,Ghoshal,S.P.,Roy,R.,2010.Loadfrequencystabilizationbycoordinatedcontrolofthyristorcontrolledphaseshiftersandsuperconducting magneticenergystorageforthreetypesofinterconnectedtwo-areapowersystems.Electr.PowerEnergySyst.32(10),1111–1124.

Elgerd,O.I.,2005.ElectricEnergySystemsTheory:AnIntroduction,2nded.,25threprint.McGraw-Hill.

Ghoshal,S.P.,2004.OptimizationsofPIDgainsbyparticleswarmoptimizationsinfuzzybasedautomaticgenerationcontrol.Electr.PowerSyst. Res.72,203–212.

Ibraheem,P.K.,Kothari,D.P.,2005.Recentphilosophiesofautomaticgenerationcontrolstrategiesinpowersystems.IEEETrans.PowerSyst.20 (1),346–357.

Mallesham,G.,Mishra,S.,Jha,A.N.,2010.OptimizationofcontrolparametersinAGCofmicrogridusinggradientdescentmethod.In:16th NationalPowerSystemsConference,pp.37–42.

Nanda,J.,Mangla,A.,Suri,S.,2006.Somenewfindingsonautomaticgenerationcontrolofaninterconnectedhydrothermalsystemwithconventional controllers.IEEETrans.EnergyConvers.21(1),87–194.

Tripathy,S.C.,Balasubramania,R.,Chanramohanan,N.P.S.,1992.Adaptiveautomaticgenerationcontrolwithsuperconductingmagneticenergy storageinpowersystem.IEEETrans.EnergyConvers.7(3),434–441.

Yang,X.S.,Deb,S.,2009.CuckoosearchviaLévyflights.In:Proc.ofWorldCongressonNature&BiologicallyInspiredComputing(NaBIC 2009),India.IEEEPublications,USA.

Yang,X.S.,2010.Nature-InspiredMetaheuristicAlgorithms,2nded.LuniverPress.

Mrs.SabitaChainereceivedtheB.E.fromGovernmentCollegeofEngineering,Keonjhar,Odisha,Indiaintheyear 2005andM.Tech.degreefromtheBijuPattnaikUniversityofTechnology,Rourkela,Odisha,Indiaintheyear2011. SheiscurrentlypursuingthePh.D.degreeintheDepartmentofElectricalEngineering,VeerSurendraSaiUniversityof Technology,Burla,Odisha,India.Hercurrentresearchinterestsincludepowersystemoperationandcontrol.

Dr.ManishTripathyreceivedtheB.E.degreefromN.I.T.(FormerlyRegionalEngineeringCollege),Rourkela,India, in1991,andworkedinIndustryforfiveyearsbeforecompletingM.E.fromV.S.S.U.T.(formerlyUniversityCollegeof Engineering),Burlaintheyear2001.HecompletedPh.D.fromIndianInstituteofTechnology,Delhi,Indiaintheyear 2009.HehasbeenafacultyintheDepartmentofElectricalEngineeringatV.S.S.U.T.,Burlaindifferentcapacities,as Lecturerduring2006–2010andasaReadersince2010.Hisfieldofinterestisapplicationofintelligenttechniquestopower systemoperationandcontrolandwindenergyconversionsystems.