DesignandImplementationofEnhanced ArtificialBEEColonyAlgorithmforSingle PhaseShuntActiveFilter
Murugan.M
AssistantProfessor,GovernmentCollegeofEngineering,Bodinayakkanur,marimurugan81@gmail.com
VinodA
AssistantProfessor,GovernmentCollegeofEngineering,Dharmapuri,vinodnash@gmail.com
Abstract:Inthisresearchpaperanewhybridoptimizationapproach,namedEnhancedArtificialBeeColonyAlgorithm (EABC)foridentifyingtheoptimalcontrollergainforsinglephaseShuntActivePowerFilter(SAPF)isproposed.The proposedalgorithmEABC,optimizesthecontrollergainvaluesinordertoimprovethetimedomainspecificationand integralperformancemeasuresofPIcontrollerinSAPF.InthisNovelhybridEABC,amodifiedversionofParticleSwarm optimisation(MPSO)isintegratedwithArtificialBeeColony(ABC)algorithmtoimprovetheoptimisationeffortsofABC andthishybridizationgreatlyimprovestheconvergencecharacteristicsofconventionalABC.ThisnovelhybridABCis appliedforminimizationofvariousIntegralperformancemeasuressuchasIntegralSquareError(ISE),Integralabsolute Errors(IAE)andtimeweightedintegralperformancemeasures.Theproposedoptimisationapproachisimplementedusing MATLABandvariousexperimentationwascarriedouttostudyaboutsteady-stateanddynamicoperatingconditions.The experimentalresultsestablishthattheproposedcontrollerdesignoutperformstheclassicalPI,andABC-PIcontrollerwith improvedsettlingtime,lesspeakovershootofDClinkvoltageandTHDofsourcecurrentwithinalimit.
Keywords:SAPF,ABC,EnhancedABC
I.INTRODUCTION
Theusageofpowerelectronicequipmentinindustries, commercialanddomesticapplicationshaveresultedinhuge currentharmonics.Thisnonlinearloadcausesharmonic propagationoverelectricalnetwork.Thepropagationof generatedharmonicsreducesthesystem‟sefficiency,poor powerfactor,createsadditionalheatinglossesandcause malfunctioningofmanysensitiveequipment‟sthatis connectedtothepowersystem.Toeliminatetheharmonics, passivefilter,activefilterandhybridfilterscanbeused.In commercialandindustrialapplications,thepassivefilters aremostcommonlyusedduetoitssimpledesign,high efficiencyandminimumcostrating.However,thesefilters areveryhugeinsizeanddoesnotfiltersallharmonic frequencies.Thesenumerouslimitationsofpassivefilters singlefrequencytunedfiltersmadetheresearchersto concentrateonactivefilters.Inseriescombinationoffilters. Thefilterhastobedesignedwithmorecurrenthandling capacityasthefilterhastocarrytheloadcurrent.Hencethe
SAPFforharmonicmitigationisgainingitspopularityvery rapidly.TheSAPFextractstheharmoniccurrentandinject backthenegativeharmonicsequenceintotheelectric networkandmakesthesupplycurrenttothesinusoidal shapewithfundamentalfrequency.Inrecentyearstheusage ofpowerelectronicbaseddevicesinthehomeappliances hasincreasedrapidly[1].Hencethisresearchisfocusedon thedesignofsinglephaseshuntactivefilters.
ThesinglephaseSAPFconsistingofavoltagesource inverter.ADClinkcapacitoractastheconstantvoltage sourcetotheinverterandtheinvertergeneratesthenegative sequencecompensationcurrent.Thecompensationcurrentis injectedtothegridatthepointofcommoncoupling.The extractionoftheharmonicsismainlydependingon controllingDClinkcapacitorvoltageataconstantvalue[2]. TomaintaintheDClinkCapacitorVoltagevariouscontrol algorithmswereproposedbytheresearcherssuchas AdaptiveNeuroFuzzyInferenceSystem,FuzzyLogic Controller,NeuralNetworkBasedModelPredictive
Controllers,andModelPredictiveControllers[3].These Controllershavehugecomputationcomplexityandthey involvelotofmathematicalcalculationstopredictthefuture behavioroftheplantandtogeneratecontrolaction.Over thesecontrolalgorithmstheProportionalandIntegrator(PI) controltechniquesverysimpletoimplementandcanbe implementedeasilyandalsothisalgorithmrequiresveryless mathematicalcalculationsfordeterminingthecontrolaction. DuetheseadvantagesthePIcontrolismostwidelyusedin theindustries.Intheliteraturethegainforthecontroller usedintheSAPFwasfoundusingTrialanderrorsearchor mathematicalapproaches[4].Thistrialanderrorand mathematicalapproachdoesn‟talwaysguaranteethe optimalvalue.[5]proposedasystem,thispaperpresentsan effectivefieldprogrammablegatearray(FPGA)-based hardwareimplementationofaparallelkeysearchingsystem forthebrute-forceattackonRC4encryption.Thedesign employsseveralnovelkeyschedulingtechniquesto minimizethetotalnumberofcyclesforeachkeysearchand useson-chipmemoriesoftheFPGAtomaximizethe numberofkeysearchingunitsperchip.
Inveryrecentyearsvariousbioinspiredglobal optimizationtechniqueshavebeenusedtofindoptimal proportionalandintegralgain.SomeofthemareGenetic Algorithm(GA),AntColonyOptimizationtechnique, particleswarmoptimization(PSO),BacterialForaging(BF) technique,GravitationalsearchAdaptiveTabusearchand GeneticAlgorithm,EnhancedBacterialforagingapproach, cuckoosearchalgorithm.InthesealgorithmstheABC optimizationalgorithmisbelievedtoexcellentoptimization capabilitiesandmostlikelytofindaglobalminimumpoint optimizationalgorithmwhencomparetootherevolutionary techniques.Alsoinotheroptimizationtechniquesthereis morenumberofalgorithmparametersthatdirectlyinfluence theperformanceofthealgorithm.InGAifthevalueof Crossoverrateandmutationrateisnotcorrectlysetthenthe qualityoftheresultsbecomeworseandthealgorithmmay evendiverge.Similarly,inACO,thepheromoneevaporation anddepositionrate,Numberofants,numberoftours,hasto besetcorrectlyandthereisnostraightguidanceavailableto selectthevaluesforthesealgorithmparameters.ButinABC thenumberofalgorithmparametersisminimumandthe
optimizationeffortisbetterthanotheroptimization algorithms.Becauseoftheseadvantages,sinceits introductiontheABCisfounditsapplicationinalmostall engineeringfields.InABCalgorithmunconstrained optimizationproblemsyieldsgeneralization[8].However, conventionalABCalgorithmssufferfrompoorconvergence ratebecauseoflessexplorationandexploitation.
Thepaperisorganizedasfollows:Insection2,thebrief literaturereviewandthemajorcontributionoftheresearch ispresented.InSection3theABCbasedControllerdesign forSAPFisdescribed.Insection4thedesignofnovel hybridoptimizationtechniqueisproposedandthecontroller performancesarepresentedtoshowtheeffectivenessofthe proposedcontrollerdesign.Finally,thepaperendswith logicalaconclusioninsection5.
II.LITERATUREREVIEW
ImprovetheconvergencerateofexistingABC,the EnhancedABCalgorithmisproposed.InproposedEABC algorithmanovelmethodbasedontheparticleswarm optimizationisusedtoimprovethequalityofthefood sourceidentifiedbythehoneybees.Somepositiveaspectof proposedEABCisimprovementoflocalsearchby providingguidancebyusingbirdflockingbehavior.The proposedalgorithmEABCisdescribedinthesection3.[6] proposedasystem,LowVoltageDifferentialSignaling (LVDS)isawaytocommunicatedatausingaverylow voltageswing(about350mV)differentiallyovertwoPCB traces.Itdealsabouttheanalysisanddesignofalowpower, lownoiseandhighspeedcomparatorforahighperformance LowVoltageDifferentialSignaling(LVDS)Receiver.The circuitofaConventionalDoubleTailLatchType Comparatorismodifiedforthepurposeoflow-powerand lownoiseoperationeveninsmallsupplyvoltages.The circuitissimulatedwith2VDCsupplyvoltage,350mV 500MHzsinusoidalinputand1GHzclockfrequency.LVDS Receiverusingcomparatorasitssecondstageisdesigned andsimulatedinCadenceVirtuosoAnalogDesign EnvironmentusingGPDK180nm.Bythisdesign,thepower dissipation,delayandnoisecanbereduced.
Themaincontributionofthisresearchoverprevious researchworkarelistedasfollows:
Asingleobjectivefunctionbasedontheintegral performancecriteriacostfunctionisdesignedtofindout theoptimalvaluesofcontrollerfornonlinearSAPF.
AHybridnovelABCalgorithmisproposedtoincrease theconvergencecharacteristicsofconventionalABCby combiningParticleswarmoptimisationisdesigned.
AdetailedanalysisontheproposedEABCPI,ABCPI andConventionalPIcontrollerbasedSAPFisdonein MATLAB/Simulinksystemenvironment.
III.IMPLEMENTATIONOFARTIFICIALBEECOLONY ALGORITHMFOROPTIMALPIGAIN SELECTION
Metaheuristic-populationbasedoptimizationalgorithm ArtificialBeeColony(ABC)isbasedonswarmintelligence. Comparedtootheroptimisationtechniquessuchas simulatedannealing(SA),ACO,GAandDE,theABC algorithmhassimpleimplementationstructurewithless numberofalgorithmparametersandalsoinherent convergenceagility.
Thealgorithmreliesonbeesforagingbehaviourofthe honeybee.Thecolonyconsistsofthreemaingroupofbees namelyemployed,onlookerandscoutbees.Thepopulation sizeofthecolonydecidesthenumberofemployedbeeand otherbees.Halfofthepopulationismadeasemployedbees. Theremainingincludesonlookerbeesandscoutbees.
Numberoffoodsources=10
MaximumIteration=1000
Traillimit=100
Initiallyresettrialcounters.
Step2:Identifyrandomfoodsource.Iftherandomly identifiedfoodsourcevalueishigheror lowerthantheboundconstrainthenthefoodsource isresettledtosatisfytheboundconstraintsof controllerparameters.
Step3:Basedontheobjectivefunctionvalue,theidentified foodsourcesarepassedtofitnessfunctiondetermine it‟sthefitnessvalue.
Step4:EMPLOYEDBEEPHASE
Producemutantsolutionsbasedonfollowing relationship
Whererisarandomnumberbetween0and1,xmin,j isthelowerboundlimitofoptimisationparameterj
InitiallytheEmployeebeesearchestheavailabilityfood,x max,jistheupperboundlimitofoptimisation sourcearoundthefoodsourceintheirmemory,inthe meantimeemployeebeesendthenectarinformationabout theallidentifiedfoodsourcestoonlookerbees.The onlookerbeeswillselectthefoodsourcethathashighnectar valuesfoundedbytheemployedbees,andalsocarryoutthe additionalsearch.Scoutbeesarerequestedtoreplacethe abandonedfoodsourcesbyrandomsearch.
IntheproposedapproachamodelofsinglephaseSAPF isdevelopedinMATLABSimulinkandtheABCis implementedintheMATLABscript.AsABCisiterative theMATLABscriptpassesthefoodsourcestotheSimulink toevaluatethefitnessvalueofthefoodsourceoneachcost functionevaluation.ThedetailedstepsofABCalgorithmfor optimalPIcontrollerdesignaredescribedasfollows:
Step1:Allalgorithmparametersareinitialized
ChoosetheupperandlowerboundforPIcontroller parameters(Kp,Ki)
Colonysize=20
parameterj,“i”isthenumberoffoodsourcesandjis thedimensionoftheoptimisationproblem.Eachfood sourceisevaluatedtofindthefitnessandobjective value.Agreedysearchisappliedbetweensolution“i” andwithitsnewvariant.Ifthemutantsolutionis better,thenreplacethesolution“i”withthemutant andresetthetrialcounterof„i‟andifthesolution„i‟ didnotimprovedthentrialcounterof“i”is incremented.Eachfoodsourceisassignedwitha probabilitythatisproportionaltothequalityandA foodsourcewiththemoreprobabilityisselectedby theemployedbees.
Step5:ONLOOKERBEEPHASE
Calculatethenewsolutionsbasedonthefollowing relationship.Wherejarethenumberofparameters tobeoptimised.
Ifthecontrollerparametersareoutofbound constraintsthemargin,thenthesolutionsoutof boundareshiftedintothemargin.Ifthemutant resultisbetterthanthecurrentsolution,replacethe currentsolutionwithmutant.Findoutthesolution thathasminimumobjectivefunction.Ifthesolution „i‟cannotbeimproved,increaseitstrialcounter.A foodsourceischosenwiththeprobabilitywhichis proportionaltoitsquality.
Step6:SCOUTBEEPHASE
Iftheemployedbeeandonlookerbeecannotable toincreasethefitnessandthesolutionthathas moretrailcountervaluemorethanthe“traillimit” isdroppedandscoutbeeisrequestedtoidentifythe randomfoodsourcetoreplacetheunimprovedfood source.
Step7:RepeatSteps4,5and6togetthebestvaluesfor controllergains.Optimisationcanbeterminatedif maximumnumberofiterationisreached.
Thenumberofparametertobeoptimisedinthe controllerdesignforSAPFistwo.TheProportional gainandintegralgainofthePIcontrollerarethe parametersoftheoptimisationproblem.The objectivefunctionsarevariousintegral performancecriteriaaregiveninthefollowing relationships.
InthisstudytheISEistakenascostfunctionand optimisationiscarriedout.Theresultsofsimulationare discussedintheSimulationResultssection.
1.ImplementationofEnhancedartificialbeecolony algorithmforoptimalPIgainselection
ThedetailedimplementationdetailsofEnhancedABC algorithmarepresentedinthissection.Inconventional ABCalgorithmthescoutbeereplacestheabandonedfood sourcerandomly.Thisrandomreplacementmaynotidentify thegoodfoodsource.Toimprovethesearchingabilityof thescoutbeeanovelapproachisproposedtoguidethe selectionofnewfoodsource.
Fig.1.ABCoptimizationFlowchart
Theproposedguidedapproachusesamodifiedparticle swarmoptimizationmethodwherethesocialandcognitive attractionfactorsareadaptivelychanged.Thepseudocode ofproposedenhancedABCandalgorithmareshownin below.TheflowchartofABCandEABCalgorithmwith optimalPIgainvalueselectionofSAPFisshownin followingFig.1and2.ThealgorithmparametersofABC andenhancedABChavebeengiveninTable1.andTable2 respectively.
Initialvalues
PopulationsizePS 10 Swarmsize20
Particlelength2
Cognitiveattractionfactor1
Socialattractionfactor1
No.ofIterationofPSO20
NumberofCyclesinABC100
TheHybridABChasthefollowingsteps:
StepsforEABCPITuningmethodtoSAPF
Thesteps1-4aresimilartoconventionalABCalgorithm
Step1:AllPITuningparametersareinitialized
Step2:Resettrialcounters
Step3:EmployedBeePhase
Step4:OnlookerBeePhase
Step5:ModifiedScoutBeePhase
InitializethePSOparameterssuchascognitiveattraction C1=1socialattraction,C2=1,velocities.Thepbestsandgbest areinitializedtozero.
Step6:selectthebestfoodsourcefromthecolonyand createanewsolutionparticleneartoit.And evaluatecostofeachindividualparticle.For everyindividual,comparethepbestvaluewithits costfunctionvalue.Ifthevalueofpbestisgreater thanthecurrentfitness,thenassignthecurrent
fitnesstopbest.Thebestfitnessamongthecurrent fitnessvalueisassignedtoglobalbest(gbest).
Step7:repositiontheparticleusingnewvelocity„v‟ofeach individual vj[i+1]=vj[i]+c2*r*(pb-Current_Par)+c2* r*(gb-Cu_sol)
Where,
J=1,2…n,(n-Numberofparticles)
Vj–Velocityofparticlej
C1-Cognitiveattractionfactor
C2–Socialattractionfactor
rand–Randomnumberbetween0and1 Pb–pbestofparticlej
gb–gbestofthegroup
Cu_sol-currentsolution
r-randomnumber
Step8:Applyboundconstrainsonthevelocityupdatevalue vj[i+1]tomaintainintherangeofparticle betweenupperandlowerboundofcontroller parameters
Step9:Updatethepositionofeachindividual new_position[i+1]=persent_position[i]+vj[i+1]
Step10:Ifthenumberofiterationsreachesthemaximumset valuethendothestep11,otherwisegotothestep 7.
Step11:Terminatethevelocityupdateandaddthelatest gbesttothepopulation
Step12:RepeatSteps2,to12untilgetthebestsolutionof controllerparametersandTerminatetheiterativeprocess, whenthereisnoanyfurtherexecutionofiteration. Thisadditionalguidancetothescoutbeeincreasesthe convergencerateandthequalityofthefoodsource identifiedbythescoutbee.
2.SimulationResultsandDiscussions
MATLABsoftwareisusedtosimulateSimulinkmodel ofsinglephaseSAPF.TheerrorbetweenreferenceDCLink voltageandactualDClinkvoltageisusedasaninputsignal forPIcontroller.
ThegainvaluesofthePIcontrollerstatesthevoltage responseanddampingfactor,theminimumvalueofgains forthePIcontrollercanbecalculatedusingEq.3and4.
Fig.3.FoodsourcefromscoutbeeofEABCalgorithm Fromtheplotitisclearthatthegeneratedfoodsource fromscoutbeeofEABCalgorithmisbetterthanthe integralGains,CrepresentsthecapacitanceofDClink capacitor,representsdampingfactor(0.707)and representsangularfrequency.SAPFishighlynonlinear systemandmainlydependsonsystemparametersandload conditions.HencecalculatedPIcontrollerparametersdon‟t meetthesystemrequirementinallconditions.Sointhis proposedworkABCoptimizationisusedtooptimizethe gainvaluesofPIController.TheISEerrorcriterionfunction exhibitslessovershootandfastersettlingtimewhen comparetoIAE,ITAEandITSE.
TheISEerrorcriterionisusedasobjectivefunction“j” foroptimizationisrepresentedbythefollowingequation
conventionalABCalgorithm.Becauseoftheimprovement intheoptimizationeffortsmadebyScoutbeetheproposed EABCconvergessoquicklyattheminimumpoint.
TheStatisticalanalysisofconvergenceplotispresentedin thetable.FromthestatisticalvaluesofEABCsuchaslow
mean,lowminimumvalueitisveryclearthattheproposed algorithmachievesbetterresultsincontrollerdesign.The
WhereristheerrorsignalgeneratedbyacomparatornumericalvaluesofthestatisticalanalysisoftheScoutbee whichisequaltothedifferencebetweenreferenceDClinkfitnesscurveareshowninTable2 voltage
ref time.
Vdcandtisthe
Thissectionpresentsvariousperformanceanalysesof singlephaseSAPFusingdifferentcontrollerdesignmethods suchasconventionalPI,ABCandEnhancedABCbasedPI controllers.TheproposedofflineEABCbasedPIand conventionalalgorithmshavebeenimplementedusing Matlabprogramminglanguage.Insimulationtheminimum objectivefunctionachievedduringeachiterationis monitoredforestimatingtheoptimizationeffortsandalso thequalityofthefoodsourceidentifiedbythescoutbeeis alsomonitored.Theobservedvaluesareplottedinfig.3
TheproposedEABCbasedoptimumcontrollerdesign yieldsbettercontrollerparametervaluesandthisdesign outperformstheconventionaltuningandconventionalABC basedController.ThecorrespondingoptimizedPIgain values(kp,ki)foundtobe0.33and4.29respectively.To
simulatetheharmonicsourceinthesystemasinglephaseH bridgeinverterisconsideredasnonlinearload.Andthis nonlinearloadisconnectedtothesystematthepointof commoncoupling.Beforeturningonthefilter compensationiszeroandtheTHDforthesourcecurrentis 28.47%.AfterturningONthesinglephaseSAPF,the harmonicsareeliminatedto3.53THDandthisiswellbelow thestandardgivenbyIEEEfromsupplycurrent.
Table3PerformanceassessmentofSinglephaseSAPFfor conventionalPI,ABC-PIandEABC-PI.
Sourceresistance&InductanceRs&Ls0.1Ω&1mH SupplyfrequencyF50Hz
DClinkvoltage Vdc200V
DClinkcapacitanceCdc800µF Filterresistance&InductanceRf&Lf0.01Ω&5mH AverageSwitchingFrequencyFsw10kHz
ACsideresistanceRc0.01Ω ACsideinductanceLc1mH DCsideresistanceRLdc28Ω DCsideinductanceLLdc160mH
IV.CONCLUSION
InthismanuscriptanewnovelhybridABCoptimization algorithmisappliedtoPIcontrollerofsinglephaseSAPF hasbeenproposedfornonlinearcontrollerdesignandits performanceisvalidated.Thesimulationandexperimental resultshavebeencarriedoutforthethreecontrolmethods, theConventionalPI,ABC-PIandEABC-PIcontrol methods.Fromtheresultsithasbeenfoundthatproposed hybridEABCcontrolleroutperformstheABCand conventionalPIinallperformanceindicessuchasISE,IAE, ITAE,ITSEandothertimedomainperformancemeasures suchasSettlingtime.
Theconclusionpointsarrivedfromthesimulationstudy arelistedbelow.
1.TheProposedcontrollerdesignEffectively compensatesthecurrentharmonicsandreactive power.
2.TheproposedEABCoptimizedcontroltechnique reducesthesupplycurrentTHDwellbelow5%.
3.SAPFwithEABCoptimizedcontrollerisfoundtobe superiortotheSAPFdesignedbyABCoptimizedPI controllerandconventionalPIcontrollerinall operatingconditions.
4.AgoodcompromisebetweentheTHD,settlingtime andpeakovershootwereobtainedwithISE consideringascostfunctions.
REFERENCES
[1].AtaideMV,PomilioJA.,“Single-phaseshuntactivefilter:Adesign procedureconsideringharmonicsandEMIstandards‟InIndustrial Electronics”,ProceedingsoftheIEEEInternationalSymposium, Vol.2,1997,pp.422-427.
[2].Chatterjee,K.,Fernandes,B.G.,&Dubey,G.K.(1999).An instantaneousreactivevolt-amperecompensatorandharmonic suppressorsystem.IEEETransactionsonPowerElectronics,14(2), 381-392.
[3].Sasaki,H.,&Machida,T.(1971).AnewmethodtoeliminateAC harmoniccurrentsbymagneticfluxcompensation-considerations onbasicdesign.IEEETransactionsonPowerApparatusand Systems,(5),2009-2019.
[4].Zainuri,M.A.A.M.,Radzi,M.A.M.,Soh,A.C.,Mariun,N.,& Rahim,N.A.(2016).DC‐linkcapacitorvoltagecontrolfor single‐phaseshuntactivepowerfilterwithstepsizeerror cancellationinself‐chargingalgorithm.IETPower Electronics,9(2),323-335.
[5].ChristoAnanth,MuthamilJothi.M,M.Priya,V.Manjula,“ParallelRC4 KeySearchingSystemBasedonFPGA”,InternationalJournalof AdvancedResearchinManagement,Architecture,Technologyand Engineering(IJARMATE),Volume2,SpecialIssue13,March 2016,pp:5-12.
[6].ChristoAnanth,BincyPChacko,“AnalysisandDesignofLow VoltageLowNoiseLVDSReceiver”,IOSRJournalofComputer Engineering(IOSR-JCE),Volume9,Issue2,Ver.V(Mar-Apr. 2014),PP10-18.
[7].Patnaik,S.S.,&Panda,A.K.(2013).Real-timeperformance analysisandcomparisonofvariouscontrolschemesforparticle swarmoptimization-basedshuntactivepowerfilters.International JournalofElectricalPower&EnergySystems,52,185-197.
[8].Karaboga,D.,&Ozturk,C.(2011).Anovelclusteringapproach: ArtificialBeeColony(ABC)algorithm.Appliedsoft computing,11(1),652-657.
ControlofElectricalDrives,PowerElectronicsConverter andRenewableEnergySystems.Ihavemoreteaching experiencebothinUG&PGlevelandalsoresearch experience.Ihavepublishedseveralpapersininternational journals.Ihavepresentedmorepapersininternational conferenceproceedingsandseveralpapersinnational conferenceproceedings.Ihaveguidedseveralundergraduate projectsandpostgraduateprojects.
VINODARUNACHALAMis
AssistantProfessoratCollegeofElectronicsand CommunicationEngineering,GovernmentCollegeof Engineering,Dharmapuri.HeholdsMasterofEngineering withspecializationinVLSIDESIGNatAnnaUniversityof TechnologyCoimbatore.Hisresearchareasaremedical imageanalysis,VLSIDESIGN,GeneticAlgorithmsand image/SignalProcessing.HeisamemberofISTE.He publishedmanypaperinreputedjournals.Hecanbe contactedatemail:vinodnash@gmail.com
Dr.M.Murugan,currentlyworkingas anAssistantProfessor,DepartmentofElectricaland ElectronicsEngineering,GovernmentCollegeof Engineering,Bodinayakkanur.Myareaofinterestsare
