Availableonlineatwww.sciencedirect.com
Journal of Applied Research and Technology
www.jart.ccadet.unam.mx JournalofAppliedResearchandTechnology15(2017)152–166
Original
ACS algorithm tuned ANFIS-based controller for LFC in deregulated environment
Ramesh Kumar Selvaraju
∗, Ganapathy Somaskandan
AnnamalaiUniversity,Chidambaram,India Received25May2016;accepted23January2017
Availableonline31March2017
Abstract
Inthispaper,anartificialcooperativesearch(ACS)algorithmtunedadaptivenetwork-basedfuzzyinferencesystem(ANFIS)controllerfor optimalgaintuningofloadfrequencycontrol(LFC)operationinderegulatedscenariohasbeenoffered.Theconventionalcontrollersforload frequencycontroloperationarehavingfixedgainvaluesintendedfornominaloperatingconditionsofthepowersystemandtheydonotafford effectiveandefficientperformanceoveralargerangeofoperatingscenariosinthederegulatedenvironment.Toprogressthesystemperformanceto itsnearoptimumforallprobableoperatingcircumstancesofthepowersystem,thecontrollergainshavetobecomputedfortheequivalentoperating conditionsbyusingtherestructuredparameters.Forthisintention,acontrollerbasedonanadaptivenetwork-basedfuzzyinferencesystemseems tobethemostexcellentandvaluablepreference.TheANFISistrainedbyoff-linedataobtainedusinganewoptimizationtechnique,artificial cooperativesearchoptimizationalgorithmandthecorrespondinggainsareupdatedinreal-timeasperthechangingoperatingconditions.ACSisa swarmintelligencealgorithmdevelopedforsolvingnumericaloptimizationproblems.TheswarmintelligencephilosophybehindACSalgorithm isbasedonthemigrationoftwoartificialsuperorganismsastheybiologicallyinteracttoachievetheglobalminimumvaluepertainingtothe problem.ToexhibitthecompetenceandrobustnessoftheprojectedACSalgorithmtunedANFIScontroller,thecontrollerhasbeenimplemented onatwo-areatwo-unitinterconnectedderegulatedpowersystemhavingonereheatunitandonenon-reheatunitineacharea.Thesimulationresults exhibittheabilityofthedesignedACSalgorithmtunedANFIScontrollerforonlineLFCoperationinderegulatedenvironment.
©2017UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccessarticleunder theCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Adaptivenetwork-basedfuzzyinferencesystem;Artificialcooperativesearchalgorithm;Deregulatedpowersystem;Loadfrequencycontrol
1. Introduction
Modern power systems are huge,interconnected andvery compositeinnature.Theselargeinterconnectedpowersystems arecomposedof manynumberofcontrolareashavingcoher- entgroupofgenerators.Allthecontrolareasareinterconnected bythetie-lines,whichareused forenergy exchangebetween theareasandenableinter-areabackingduringuncharacteristic conditions(Talaq&Al-Basri,1999).Forqualityandtrustworthy powersupplytotheconsumers,itisvitaltoupholdthefrequency andtie-linedeviationswithintheprearrangedvalueofthepower
∗Correspondingauthor.
E-mail addresses: [email protected], [email protected] (R.K.Selvaraju).
PeerReviewundertheresponsibilityofUniversidadNacionalAutónomade México.
system(Masiala,Ghribi,&Kaddouri,2004).Lately,alloverthe world,theconfigurationofconventionalelectricpowerutilities areinachangeoverstatefromverticalintegratedconfiguration toderegulatedconfiguration.Inderegulatedstructure,theelec- tricpowerutilitiesaresplitintothreeseparatecontrolcompanies asGENCO,theGeneratingCompany,DISCO,theDistribution CompanyandTRANSCO,theTransmissionCompanyrespec- tively.Thepurposeofallthethreeutilitiesarecontrolledbya separateindependentoperatorcalledasanIndependentSystem Operator (ISO).Forreliableoperation,the ISOhasanumber of ancillary services,loadfrequencycontrol beingoneof the important ancillary services (Bekhouche,2002; Rakhshani&
Sadeh,2010a,2010b).
During lastdecade, manytechniquesandapproacheshave beenprojectedfordesignofLFCcontrollers(Jain,Chakrabarti,
& Singh, 2013; Lakshmi, Fathima, & Muthu, 2016; Pandey, Mohanty,&Kishor,2013;Shayeghi,Shayanfar,&Jalili,2009).
http://dx.doi.org/10.1016/j.jart.2017.01.010
1665-6423/©2017UniversidadNacionalAutónomadeMéxico,CentrodeCienciasAplicadasyDesarrolloTecnológico.Thisisanopenaccessarticleunderthe CCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Fig.1.Two-areaLFCblockdiagraminderegulatedpowerstructure.
Mostof the controller designsare based onthe conventional approach.Theconventionalcontrollersarefixedgaincontrollers being designed for nominal operating conditions. Such type of controller designs does not integrate the different operat- ing conditions of the operating power system and does not revisetheparametersforcomputingtheirgainvalues.So,these controllers cannotafford enhanced performance(Hosseini &
Etemadi,2008).Toovercometheabovementioneddrawbacks andtoimprovethesystemperformance,thedesignofanANFIS- basedcontrollergainsaddedsignificance.
In recent years, different artificial intelligence techniques andswarmintelligencetechniqueshavebeenimplementedfor obtainingoptimalsolution forLFC controllersinderegulated environment(Anilkumar&Venkataramana,2012).Inthispaper, a new artificial cooperative search algorithm tuned adaptive
network-basedfuzzyinferencesystem(ANFIS)controllerfor optimalgaintuningofloadfrequencycontrol(LFC)indereg- ulatedscenariohasbeenofferedtoprovidebetterperformance.
Theartificialcooperativesearchalgorithmisanewoptimization algorithm designed for solving complex optimization prob- lems. As the structure of ACS algorithm is simpler than the structuresofotherartificialintelligencealgorithms,itiseasily programmableandnotablyfasterthantheotheralgorithms.For purposesofexaminingthesuccessofACSalgorithminsolving numericaloptimizationproblems,91benchmarkproblemsthat havedifferentspecificationsweretestedbyCivicioglu(2013).
ThesuccessofACSalgorithminsolvingthebenchmarkprob- lemswascomparedtothesuccessesobtainedbyPSO,SADE, CLPSO,BBO,CMA-ES,CKandDSAalgorithms.Theresults obtainedintheanalysisdemonstratethatthesuccessachieved
Fig.2.StructureofadaptiveANFISnetwork.
Table1
ACStunedoptimalintegralgainvaluesfordifferentoperatingconditions.
Trainingpatterns Systemoperatingparameters ACSalgorithmtunedoptimalintegralgainvalues
Tps T12 β
1 10 0.145 0.125 0.980715
2 10 0.145 0.275 0.476667
3 10 0.145 0.425 0.317016
4 10 0.345 0.125 0.814559
5 10 0.345 0.275 0.406147
6 10 0.345 0.425 0.274288
7 10 0.545 0.125 0.806068
8 10 0.545 0.275 0.411567
9 10 0.545 0.425 0.278225
10 20 0.145 0.125 1.986164
11 20 0.145 0.275 1.272081
12 20 0.145 0.425 0.805527
13 20 0.345 0.125 1.342520
14 20 0.345 0.275 0.797469
15 20 0.345 0.425 0.564495
16 20 0.545 0.125 1.213173
17 20 0.545 0.275 0.727705
18 20 0.545 0.425 0.526443
19 30 0.145 0.125 1.566895
20 30 0.145 0.275 1.622808
21 30 0.145 0.425 1.062214
22 30 0.345 0.125 1.190938
23 30 0.345 0.275 0.876175
24 30 0.345 0.425 0.671788
25 30 0.545 0.125 1.161970
26 30 0.545 0.275 0.791438
27 30 0.545 0.425 0.616596
Table2
OptimalKivaluesobtainedusingANFISandACSAforaSampleTestData.
Technique Tps T12 β OptimalKi Objectivevalue
ACSalgorithm 15 0.245 0.125 1.4050 179.6226
ANFIS 15 0.245 0.125 1.4611 179.6450
0 5 10 15 20 25 30 –0.4
–0.3 –0.2 –0.1 0 0.1 0.2 0.3
Time in seconds ΔF 1 in Hz
ACSA ANFIS
Fig.3.Frequencydeviationinarea-1.
0 5 10 15 20 25 30
–0.2 –0.15 –0.1 –0.05 0 0.05
Time in seconds ΔF 2 in Hz
ACSA ANFIS
Fig.4.Frequencydeviationinarea-2.
0 5 10 15 20 25 30
–0.04 –0.03 –0.02 –0.01 0 0.01 0.02
Time in seconds ΔP tie in p.u. MW
ACSA ANFIS
Fig.5.Tie-linepowerdeviation.
byACSalgorithminsolvingnumericaloptimizationproblems isbetterincomparisontotheothercomputationalintelligence algorithmsused inthispaper.HenceACSalgorithmhasbeen preferredforthispaper.TheACSalgorithmisusedforobtain- ingtheoff-line training data.TheperformanceofACS tuned ANFIS controlleris comparedwith the performanceof ACS tunedcontrollerbasedonintegralsquareerrorcriteria.
2. Powersystemmodel
Thepowersystemmodelinderegulatedenvironmentconsists of theGENCOsandDISCOswhichhaveavarietyofcombi- nation ofbilateralcontractsamongthem.Thebilateralpower transfercontractsamongtheGENCOsandDISCOscanbereal- izedinactualfactbyusingDISCOParticipationMatrix(DPM).
0 5 10 15 20 25 30 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time in seconds P G1 in p.u. MW
ACSA ANFIS
Fig.6.PowergenerationofGENCO-1.
0 5 10 15 20 25 30
0 0.02 0.04 0.06 0.08 0.1 0.12
Time in seconds P G2 in p.u. MW
ACSA ANFIS
Fig.7.PowergenerationofGENCO-2.
0 5 10 15 20 25 30
–0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
Time in seconds P G3 in p.u. MW
ACSA ANFIS
Fig.8.PowergenerationofGENCO-3.
TheDPMprovidestheparticularsofthecontractswhichexist betweentheGENCOandDISCO.Thenumberofrowspresent inDPMhastobeequaltothenumberofGENCOsandthenum- berofcolumnspresentinDPMhastobethesametothenumber ofDISCOsinthederegulatedenvironment.EachentryofDPM representsafractionofthetotalloadpowercontractbetweena DISCOandGENCOinthederegulatedpowersystem.Thetotal
sumofalltheentriesofDPMcolumnisunity(Donde,Pai,&
Hiskens,2001).
Σicpfij =1 (1)
Theprojectedderegulatedsystemisatwo-areasystemwith twoGENCOsandtwoDISCOsineacharea.Theblockdiagram ofLFCmodelinderegulatedscenarioisgiveninFigure1.The
0 5 10 15 20 25 30 –0.04
–0.035 –0.03 –0.025 –0.02 –0.015 –0.01 –0.005 0 0.005 0.01
Time in seconds P G4 in p.u. MW
ACSA ANFIS
Fig.9.PowergenerationofGENCO-4.
0 5 10 15 20 25 30
–0.4 –0.35 –0.3 –0.25 –0.2 –0.15 –0.1 –0.05 0 0.05 0.1
Time in seconds ΔF 1 in Hz
ACSA ANFIS
Fig.10.Frequencydeviationinarea-1.
0 5 10 15 20 25 30
–0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3
Time in seconds ΔF 2 in Hz
ACSA ANFIS
Fig.11.Frequencydeviationinarea-2.
0 5 10 15 20 25 30 –0.02
–0.01 0 0.01 0.02 0.03 0.04 0.05
Time in seconds ΔP tie in p.u. MW
ACSA ANFIS
Fig.12.Tie-linepowerdeviation.
0 5 10 15 20 25 30
0 0.05 0.1 0.15 0.2 0.25
Time in seconds P G1 in p.u. MW
ACSA ANFIS
Fig.13.PowergenerationofGENCO-1.
0 5 10 15 20 25 30
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Time in seconds P G2 in p.u. MW
ACSA ANFIS
Fig.14.PowergenerationofGENCO-2.
resultantDPMmatrixcanbeexpressedasgivenbelow,where
‘cpf’representsthecontractparticipationfactor.
DPM=
⎡
⎢⎢
⎢⎢
⎣
cpf11 cpf12
cpf21 cpf22
cpf13 cpf14
cpf23 cpf24
cpf31 cpf32
cpf41 cpf42
cpf33 cpf34
cpf43 cpf44
⎤
⎥⎥
⎥⎥
⎦
In DPM,theoffdiagonalentriessymbolizethedemand of DISCO in one area with the GENCO in another area. The expressionfor scheduledtieline powerflowbetweenthetwo interconnectedareasisgivenby
ΔPtie 1−2,scheduled
=(DemandofDISCOsinareaIIfromGENCOsinareaE)
−(DemandofDISCOsinareaIfromGENCOsinareaII)
0 5 10 15 20 25 30 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Time in seconds P G3 in p.u. MW
ACSA ANFIS
Fig.15.PowergenerationofGENCO-3.
0 5 10 15 20 25 30
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Time in seconds PG4 in p.u. MW
ACSA ANFIS
Fig.16.PowergenerationofGENCO-4.
0 10 20 30 40 50 60 70 80
–0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01 0 0.01
Time in seconds P tie Scheduled in p.u. MW
ACSA ANFIS
Fig.17.Scheduledtie-linepowerdeviation.
Theoffdiagonal blocksof theDPM aresubstitutedinthe aboveexpressionforthescheduledtie-linepowerflowasgiven below
ΔPtie 1−2,scheduled
=[(cpf13+cpf23)ΔPL3+(cpf14+cpf24)ΔPL4]
−[(cpf31+cpf41)ΔPL1+(cpf32+cpf42)ΔPL2]
Thegeneralizedexpressionforscheduledtie-linepowerflow canbewrittenas
ΔPtie scheduled =
2 i=1
4 j=3
cpfijΔPLj−
4 i=3
2 j=1
cpfijΔPLj (2)
TheoptimalvaluesofcontrollergainsfortheLFCofdereg- ulatedpowersystemarecalculatedusingIntegralSquareError
0 5 10 15 20 25 30 –0.7
–0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2
Time in seconds ΔF 1 in Hz
ACSA ANFIS
Fig.18.Frequencydeviationinarea-1.
0 5 10 15 20 25 30
–0.35 –0.3 –0.25 –0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15
Time in seconds ΔF 2 in Hz
ACSA ANFIS
Fig.19.Frequencydeviationinarea-2.
0 5 10 15 20 25 30
–0.03 –0.02 –0.01 0 0.01 0.02 0.03 0.04 0.05
Time in seconds ΔP tie in p.u. MW
ACSA ANFIS
Fig.20.Tie-linepowerdeviation.
criterion. Theobjective functionJforISE istaken as(Bhatt, Roy,&Ghoshal,2010).
J=
(Δf12+Δf22+ΔPtie2 1−2)dt (3)
3. IntegralgainoptimizationusingACSalgorithm
Artificial cooperative search algorithm (ACS) is a swarm intelligencealgorithmdevelopedforsolvingcomplexnumeri- caloptimizationproblems(Civicioglu,2013).Ageneticcontact naturallyprevailsbetweendiverselivingthingsinnaturalworld.
The livingkind concerned ingenetic contacttries toachieve
0 5 10 15 20 25 30 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Time in seconds P G1 in p.u. MW
ACSA ANFIS
Fig.21.PowergenerationofGENCO-1.
0 5 10 15 20 25 30
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Time in seconds P G2 in p.u. MW
ACSA ANFIS
Fig.22.PowergenerationofGENCO-2.
0 5 10 15 20 25 30
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Time in seconds P G3 in p.u. MW
ACSA ANFIS
Fig.23.PowergenerationofGENCO-3.
mutual benefits from the natural interaction. The habitation thoughtinACSalgorithmrepresentsthesearchspaceconcept thatbelongstotheassociatedproblem.
In ACS algorithm, a superorganism consisting of arbi- trary solutions of the associated problem corresponds to an artificial superorganism migrating to more fruitful feeding areas. ACS algorithm contains two superorganisms; αand β
that have artificial sub-superorganisms equal to the dimen- sionofthepopulation(N).Thedimensionoftheproblem(D) is equal to the number of individuals within the associated sub-superorganisms. In ACS algorithm,α andβ superorgan- isms are used for the finding of artificial Predator and Prey sub-superorganisms.ThePredatorsub-superorganismsinACS algorithmcanfollowthePreysub-superorganismsforaperiod
0 5 10 15 20 25 30 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Time in seconds P G4 in p.u. MW
ACSA ANFIS
Fig.24.PowergenerationofGENCO-4.
Table3
Comparisontableofthesystemperformanceparameters.
Controllerdescription/timedomainspecifications ControllerdesignedusingACSA ControllerdesignedusingANFIS
F1 F2 Ptie F1 F2 Ptie
Scenario-1
os 0.19 0.035 0.018 0.19 0.038 0.0184
us −0.34 −0.17 −0.37 −0.34 −0.17 −0.37
ts 9.82 15.52 16.32 9.82 15.52 16.32
Scenario-2
os 0.095 0.24 0.05 0.095 0.24 0.05
us −0.39 −0.3 −0.018 −0.39 −0.3 −0.018
ts 10.32 12.54 13.12 10.32 12.54 13.12
Scenario-3
os 0.14 0.148 0.05 0.14 0.148 0.05
us −0.64 −0.32 −0.028 −0.64 −0.32 −0.028
ts 11.42 12.35 15.38 11.42 12.35 15.38
oftimewhiletheymigratetowardsglobalminimumoftheprob- lem.Whenthe iterativecalculationprocessofACSalgorithm thatisnamedasco-evolutionprocessisconsidered,itcanbeseen thatthetwosuperorganismslookingfortheglobalminimumof therelatedproblem,establishmutualaid-basedbiologicalcon- tactbetweeneachother.InACSalgorithm,theinitialvaluesof theindividualsofithsub-superorganismofα(i.e.,α(i,j))and β(i.e.,β (i,j))aredefinedbyusing(4)and(5);
αi,j,g=0=rand·(upj−lowj)+lowj (4)
βi,j,g=0=rand·(upj−lowj)+lowj (5)
wherei=1,2,3,...,N,j=1,2,3,...,Dandg=0,1,2,3,...,max cycle.The‘g’valuedenotesthegenerationnumberexpressing theco-evolutionlevelcontainingtheassociatedsuperorganisms.
The rand shows arandom numberchosen from the uniform distributionwithU∼[01].Theupjandlowjaretheupperand lower limits of search space for jth dimension of the related problem.Thefitnessvaluesarecomputedbyusing(6)and(7);
0 10 20 30 40 50 60 70 80
–0.08 –0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01 0
Time in seconds P tie Scheduled in p.u. MW
ACSA ANFIS
Fig.25.Scheduledtie-linepowerdeviation.
Thefitnessvalueisobtainedasfollows:
Fitness function= 1 1+J
whereJistheobjectivefunction,i.e.,integralsquareerrorgiven by(3).
yi;α=f(αi) (6)
yi;β=f(βi) (7)
Thebiologicalinteractionlocation,X,betweenPredatorand Preysub-superorganismsismodelledusingEq.(8);
X=Predator+R(Prey−Predator) (8)
whereRisthescalefactorthatcontrolsthespeedofbiological contact.The probabilisticcharacter of ACS algorithmcauses the super-organism that is determined as the predator to be changedineachgeneration.Therefore,ACSalgorithmprovides a cooperative/co-evolution process for both of the superor- ganisms.The proposedalgorithm hasbeen implementedwith iterationcountasthestoppingcriteria.ThepseudocodeofACS algorithmisprovidedin(Civicioglu,2013).
ForLoadFrequencyControlinaderegulatedenvironment using ACS algorithm, to begin with, the random generated biologicalcontactposition X,i.e., theintegral controller gain value,isusedtocalculatefitnessvalueusingtheobjectivefunc- tion, J. For each iteration, the sub-superorganism (α and β) valuesare obtained using (4) and(5). Thepredator andprey sub-superorganismsaredeterminedineachgenerationbyusing α and β superorganisms. The biological contact position X, betweenpredatorandpreyisupdatedusing(8).Theobjective functionJiscalculatedforeachsetofXusing(3).Theprocess isrepeateduntiloptimalintegralgain,correspondingtoglobal minimumobjectivefunctionvalueisobtained.Iterationcount istakenasthestoppingcriteria.Fortheproposedproblem,the maximumiterationcounthasbeenassumedas30.
4. Adaptivenetwork-basedfuzzyinferencesystem
Theadaptivenetwork-basedfuzzyinferencesystem(ANFIS) servesas afundamentalfor constructing asetof fuzzy rules withappropriate membershipfunctionstogeneratethe prear- rangedinput–outputpairs(Jang,1993;Lee,1990).Varioustypes offuzzyruleshavebeenprojectedintheearlierperiod(Jang, 1993;Kumar&Vani,2014;Mosaad&Salem,2014;Rao,2012).
Adaptivenetworksareevolving, dynamicnetworks, inwhich thetopologychangesindependenceofthedynamicstateofthe nodes,whilethe dynamicsof the statedepends onthe topol- ogy.Theoutputdependsonthe parameterpertainingtothese nodesandtheerrorvaluesareminimizedbasedontheparameter changesgivenbythelearningrules.ANFISisthefuzzylogic- basedmodelthatgraspsthelearningabilitiesofANNtoimprove theintelligentsystem’sperformanceusingaformerknowledge.
Usingagiveninput/outputdataset,ANFISconstructsafuzzy inferencesystemwhose membershipfunction parametersare tunedusingback-propagationalgorithmincombinationwitha least-squarestypeofmethod.Thisallowsthefuzzysystemto
learnandmodel fromthesedata.Thesetechniquesprovide a methodforthefuzzymodellingproceduretolearninformation aboutadataset,inordertocomputethemembershipfunction parametersthatbestallowtheassociatedfuzzyinferencesys- temtotrackthegiveninput/outputdataasshowninFigure2.
Thislearningmethodworkslikewisetothatofneuralnetworks (Rajkumar, Ramachandaramurthy,Yong, & Chia,2011). The ANFISsystemhasnolimitationsexceptthenetworkshouldbe feed forwardtype. Due tothisminimal restriction, the adap- tivenetworkapplication hasnobounds.AnANFIScontroller inMATLABSimulinkisusedtoprovidefastdampingcontrol forLFCoperation.
Theperformanceofthefixedgaincontrollerdeteriorateswith changeinsystemoperatingconditions.Tohavepreferredsystem performance,itisessentialtotakeintoaccounttheperformance ofthesystemoveranextensiverangeofoperatingconditions.In thispaper,powersystemtimeconstantTps,synchronizingpower coefficientT12 andfrequencybiassettingβwhichcorrespond tothesystemoperatingconditionhavebeenusedasinputtothe ANFISnetwork.Threenumbersoffuzzymembershipfunctions havebeenused.Twenty sevendifferentfuzzyruleshavebeen framedforthiscontroller.Itusesabellshapedfuzzymembership function.Twentysevennumbersoftrainingsampleshavebeen used.Thepatternfortraining aregeneratedfor diversevalues ofsystemparametersTps,T12andβ.Ifthenumbersoftraining patternsarelarge,thenetworktrainingprocesswillbeveryslow (Farzi,2012;Jainetal.,2013).Toovercomethisdrawback,only twentysevendifferentcombinationsofsystemparametershave been used.The calculatedintegral gainvaluesforthe twenty seven different powersystemoperating condition patterns by usingACSalgorithmaretabulatedinTable1asfollows.
5. Resultsanddiscussion
Thetwo-areainterconnectedderegulatedpowersystemwith onereheatand onenon-reheatunit ineach area as shownin Figure 1 is used to reveal the effectiveness of the projected ANFISapproach.Thesystemparametersfortheproposedpower systemmodelare givenin(Dondeetal.,2001;Ganapathy&
Velusami, 2010)respectively. The followingparametervaria- tions,showninTable2are consideredfor simulationandthe corresponding optimalintegral gainvalues obtained by ACS algorithmandACStunedANFISaregivenbelow.Thesimula- tionresultsfordifferentderegulatedcontractsarealsoshown.
Veryslenderdegradationofoscillatoryprocessisobservedwith ANFIS,asanticipated,duetothefactthatANFISusesonlythree distinctsignalsnamelysystemtimeconstantTps,synchroniz- ingpowercoefficientT12andfrequencybiassettingβ,whereas ACS controllerusesfullstatefeedback(Djukanovic,Calovic, Vesovic,&Sobajic,1997).
5.1. Scenario1
In thisscenario,allthe GENCOstakepartequallyinLFC operation. Theparticipationfactorsare assumedtobe identi- calasgiven:apf1=apf2=apf3=apf4=0.5.Inthisscenario,the variation inload is assumed to takeplace onlyin area-1,so
0 5 10 15 20 25 30 179.62
179.64 179.66 179.68 179.7 179.72 179.74 179.76 179.78 179.8 179.82
Iteration
ObjVal
Fig.26.Iterationcountversusobjectivevalue.
onlyDISCO-1andDISCO-2claimtheload.Theperunitload demandofDISCO-1andDISCO-2areassumedtobe0.1p.u.
MW.Thereforeforthiscase,theentriesinDiscoParticipation Matrixbecomemodifiedasgivenbelow.
DPM=
⎡
⎢⎢
⎢⎣
0.5 0.5 0.5 0.5
0 0 0 0 0 0
0 0
0 0 0 0
⎤
⎥⎥
⎥⎦
ThegeneratedpowerofeachGENCO(PMi)isexpressed intermsofContractParticipationFactor(cpf)andloaddemand ofDISCOs(PLj)asgivenbelow
ΔPMi=
j
cpfijΔPLj (9)
Forthiscase,
ΔPM1=0.1 p.u MW, ΔPM2=0.1 p.u MW, ΔPM3=0 p.u MW and ΔPM4=0 p.u MW
The simulation results for this scenario-1 are given in (Figs.3–9).
5.2. Scenario2
Inthisscenario,alltheDISCOsinthesystemhavecontract withGENCOsinanyotherareaaspertheDPM.EachDISCO isassumedtoclaim0.1p.u.MWpowerfromtheGENCOs.The areaparticipationfactorsareassumedasapf1=0.75,apf2=0.25, apf3=0.5, apf4=0.5. Therefore the DPM becomes as shown below
DPM=
⎡
⎢⎢
⎢⎣
0.5 0.25 0.2 0.25
0 0.3
0 0
0 0.25 0.3 0.25
1 0.7
0 0
⎤
⎥⎥
⎥⎦
Thescheduledtie-linepowerfromarea1toarea2iscalcu- latedfromthevaluesoftheoffdiagonalelementsoftheDPM
usingthefollowingexpression,
ΔPtie scheduled=
2 i=1
4 j=3
cpfijΔPLj−
4 i=3
2 j=1
cpfijΔPLj
=(cpf13+cpf23)ΔPL3+(cpf14
+cpf24)ΔPL4−(cpf31+cpf41) ΔPL1
−(cpf32+cpf42) ΔPL2=(0+0)0.1 +(0.3+0)0.1−(0+0.3)0.1
−(0.25+0.25)0.1
=−0.05 p.u MW (10)
The power generation of GENCOs (PMi) are calculated using(9)
ΔPM1=0.105 p.u MW, ΔPM2=0.045 p.u MW, ΔPM3=0.195 p.u MW and
ΔPM4=0.055 p.u MW
The simulation results for this scenario-2 are given in (Figs.10–17).
5.3. Scenario3
In this case, the existing contract is violated by DISCO 1 by demanding 0.1p.u. MW overload power thanits actual contracted power. The additionaluncontracted power will be providedbytheGENCOsthatareinthesameareaoftheDISCO whichviolatesthecontractthatisGENCO1andGENCO2.The totalload inarea1 is equaltothe sum ofload of DISCO1, loadofDISCO2andtheuncontractedload,whichisequalto 0.3p.u.MW.Similarlytheloadinarea2isequaltothesumof theloadsofDISCO3andDISCO4whichis0.2p.u.MW.The DPM issameasinscenario2.Theallocationofuncontracted loadamongtheGENCOsisdeterminedbytheareaparticipation
factor.Thesimulationresultsforthiscontractviolationscenario aregivenin(Figs.18–25).
TheareafrequencydeviationsaremeasuredinHz,tie-line powerdeviations aremeasured inp.u. MW andsettling time in seconds. Table 3 shows the comparison table of the sys- temperformanceparameters.Inscenario-1,thepeakfrequency overshoot in area-1 with controller designed using ACSA is 0.19Hz, whichisalmostidentical tothefrequencyovershoot in area-1 with controller designed using ANFIS. The peak frequencyovershoots in area-2 and tie-line power deviations withcontrollerdesignedusingACSAare0.35Hzand0.018Hz respectively.Thepeakfrequencyovershootsinarea-2andtie- linepowerdeviationswithcontrollerdesignedusingANFISis also0.035Hzand0.018p.u.MWrespectively.Theovershootfor tie-linepowerdeviationswithbothACSAdesignedcontroller andANFIScontrollerisapproximately0.018Hz.Similarly,the settling timefor area frequencydeviation and tie-line power deviations using ACSA designed controller and ANFIS con- trollerisalmostidentical.Thispatternofperformanceexistsin scenario-2andscenario-3also.TheANFIScontrollerresponses aresimilartotheresponsesofACSAdesignedcontroller.This increasestheoverallefficiencyofANFIScontrollerforonline application.
Thesimulationoutcomesmake knownthatthe ACStuned ANFIScontrollerresponsesarealmostmatchingtheresponses ofACStunedcontrollerresponses.Inspectionoftheobjective functionvaluesrevealsthattheobjectivefunctionvaluesareto someextentequalwhen anANFIScontrollerisusedas com- paredtotheACScontroller.Theiterationgraphi.e.,Figure26 showsthattheACSalgorithmtakesalmost15iterationsforcon- vergencewhichtakesapproximately30s.TheANFIScontroller takesonlyafractionofasecond.Thisindicatesthesuperiorper- formanceofACStunedANFIScontrolleranditsadaptability foronlineapplications.
6. Conclusion
Inthispaper,anewartificialcooperativesearch(ACS)algo- rithm tuned adaptive network-based fuzzy inference system (ANFIS)controllerfor optimalgaintuningof LFC operation inderegulatedscenariohasbeenproductivelyimplementedand testedonatwo-areainterconnectedpowersysteminderegulated scenarioforawiderangeofoperatingconditions.Theartificial cooperativesearchalgorithmisusedfortuningtheconventional controller integral gain values and also the integral gains at differentoperatingconditionsforANFIStraining.Ithasbeen observedthattheresponsesofthesystemusingACStunedcon- trollerandACSalgorithmtunedadaptivenetwork-basedfuzzy inferencesystem controller are almost identical. The ANFIS trackstheoperatingconditionandusestheupdatedparameters tocomputetheintegralgain.Thetimetakenfortuningismore incase of ACS tuned controller but, the response of ANFIS controller for different operating conditions is instantaneous.
Thismakes theACS algorithmtunedadaptivenetwork-based fuzzyinferencesystemcontrollermoresuitedfor onlineLFC operation in deregulated scenario than the other controllers.
It has been obtained from the simulation results that the
ANFIS-basedcontrollerandtheACStunedcontrollerarecom- parable for any given operating condition. Furthermore, it has been noted that ANFIS eliminates the need for switch- ing betweenindividual controllers as the operating condition changestherebymakingthemovementfromoneoperatingpoint toanothersmootherandautomatic.
Conflictofinterest
Theauthorshavenoconflictsofinteresttodeclare.
References
Anilkumar,T.,&Venkataramana,N.(2012).Areviewoncontrolstrategiesfor LFCinderegulatedscenario.i-Manager’sJournalonCircuits&Systems, 1(1),27.
Bekhouche,N.(2002).Automaticgenerationcontrolbeforeandafterderegu- lation.InProceedingsoftheAnnualSoutheasternSymposiumonSystem Theory,IEEE(pp.321–323).
Bhatt,P.,Roy,R.,&Ghoshal,S.P.(2010).OptimizedmultiareaAGCsimulation inrestructuredpowersystems.InternationalJournalofElectricalPower&
EnergySystems,32(4),311–322.
Civicioglu,P.(2013).Artificialcooperativesearchalgorithmfornumericalopti- mizationproblems.InformationSciences,229,58–76.
Djukanovic,M.B.,Calovic,M.S.,Vesovic,B.V.,&Sobajic,D.J.(1997).
Neuro-fuzzy controller of lowhead hydropower plantsusing adaptive- network based fuzzy inference system. IEEE Transactions on Energy Conversion,12(4),375–381.
Donde,V.,Pai,M.A.,&Hiskens,I.A.(2001).Simulationandoptimizationin anAGCsystemafterderegulation.IEEETransactionsonPowerSystems, 16(3),481–489.
Farzi,S.(2012).Trainingoffuzzyneuralnetworksviaquantum-behavedparticle swarmoptimizationandrivalpenalizedcompetitivelearning.TheInterna- tionalArabJournalofInformationTechnology,9(4),306–313.
Ganapathy,S.,&Velusami,S.(2010).MOEAbaseddesignofdecentralized controllersforLFCofinterconnectedpowersystemswithnonlinearities, AC–DCparalleltie-linesandSMESunits.EnergyConversionandManage- ment,51(5),873–880.
Hosseini,S.H.,&Etemadi,A.H.(2008).Adaptiveneuro-fuzzyinferencesystem basedautomaticgenerationcontrol.ElectricPowerSystemsResearch,78(7), 1230–1239.
Jain,S.K.,Chakrabarti,S.,&Singh,S.N.(2013).Reviewofloadfrequency controlmethods,Part-I:Introductionandpre-deregulationscenario,CARE 2013.InInternationalConferenceonControl,Automation,Roboticsand EmbeddedSystems,Proceedings,IEEE(pp.1–5).
Jang,J.S.(1993).ANFIS:Adaptive-network-basedfuzzyinference system.
IEEETransactionsonSystems,Man,andCybernetics,23(3),665–685.
Kumar,T.B.,&Vani,M.U.(2014).Loadfrequencycontrolintwoareapower systemusingANFIS.ComputerEngineeringandIntelligentSystems,5, 27–35.
Lakshmi,D.,Fathima,A.P.,&Muthu,R.(2016).Simulationofthetwo-area deregulatedpowersystemusingparticleswarmoptimization.International JournalonElectricalEngineeringandInformatics,8(1),93.
Lee,C.C.(1990).Fuzzylogicincontrolsystems:Fuzzylogiccontroller.I.IEEE TransactionsonSystems,Man,andCybernetics,20(2),404–418.
Masiala,M.,Ghribi,M.,&Kaddouri,A.(2004).Anadaptivefuzzycontroller gainschedulingforpowersystemload-frequencycontrol.InIndustrialTech- nology,2004.IEEEICIT’04.2004IEEEInternationalConferenceon(Vol.
3),IEEE(pp.1515–1520).
Mosaad,M.I.,&Salem,F.(2014).LFCbasedadaptivePIDcontrollerusing ANNandANFIStechniques.JournalofElectricalSystemsandInformation Technology,1(3),212–222.
Pandey,S.K.,Mohanty,S.R.,&Kishor,N.(2013).Aliteraturesurveyon load-frequencycontrolforconventionalanddistributiongenerationpower systems.RenewableandSustainableEnergyReviews,25,318–334.
Rajkumar,R.K.,Ramachandaramurthy,V.K.,Yong,B.L.,&Chia,D.B.(2011).
Techno-economicaloptimizationofhybridpv/wind/batterysystemusing Neuro-Fuzzy.Energy,36(8),5148–5153.
Rakhshani,E.,&Sadeh,J.(2010a).Reduced-orderobservercontrolfortwo- areaLFCsystemafterderegulation.ControlandIntelligentSystems,38(4), 185.
Rakhshani,E.,&Sadeh,J.(2010b).Practicalviewpointsonloadfrequency controlprobleminaderegulatedpowersystem.EnergyConversionand Management,51(6),1148–1156.
Rao,C.S.(2012).AdaptiveNeuroFuzzybasedLoadFrequencyControlofmulti areasystemunderopenmarketscenario.In2012InternationalConference onAdvancesinEngineering,ScienceandManagement(ICAESM),IEEE (pp.5–10).
Shayeghi,H.A.S.H.,Shayanfar,H.A.,&Jalili,A.(2009).Loadfrequency controlstrategies:Astate-of-the-artsurveyfortheresearcher.EnergyCon- versionandManagement,50(2),344–353.
Talaq,J.,&Al-Basri,F.(1999).Adaptivefuzzygainschedulingforloadfre- quencycontrol.IEEETransactionsonPowerSystems,14(1),145–150.
