ElectricPowerSystemsResearch142(2017)9–11
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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
Distribution network reconfiguration using a genetic algorithm with varying population size
Morad Abdelaziz
DepartmentofElectricalandComputerEngineering,UniversitéLaval,Québec,Canada
a r t i c l e i n f o
Articlehistory:
Received29February2016 Receivedinrevisedform2May2016 Accepted21August2016
Keywords:
Distributionnetwork Feederreconfiguration Geneticalgorithms Populationsize
a b s t r a c t
Geneticalgorithm(GA)hasbeenshowntobeaneffectivewaytosolvethecomplexcombinatorial,and constrainednon-linearmixedintegeroptimizationproblemofdistributionnetworkreconfiguration.
ExtensiveworkhasbeendoneintheliteraturetoefficientlyapplyGAtothereconfigurationproblem.
Nonetheless,todate,allthepreviousworkinthisareahavepresupposedthattheGApopulationsize shouldremainconstantthroughouttheevolutionofthesearchprocess.Inthispaper,weproposethe applicationofageneticalgorithmwithvariablepopulationsize(GAVAPS)tothereconfigurationproblem.
Wedemonstratethatallowingthepopulationsizetoadaptivelygrowandshrinkaccordingtothestatus oftheGAsearchcanallowforamoreefficientsolution,comparedtostandardgeneticalgorithm.
©2016ElsevierB.V.Allrightsreserved.
1. Introduction
Distributionnetworkreconfigurationistheprocessofchang- ingthetopologicalstructureofdistributionfeedersbyupdating theopen/closestatusofthenetworksectionalizesandtieswitches.
Reconfigurationisaneffectivewaytoimprovetheperformanceof powerdistributionnetworks.Byupdatingtheswitchesopen/close status,adistributionnetworkreconfigurationalgorithmchanges the topological structure of distribution feeders in a way that optimizesthesystemperformancewhilesatisfyingitsoperational constraints.Giventhenonlinearcharacteristicsofthedistribution systemconstraints,aswellasthelargenumberofsystemswitch- ingelements,thedistributionnetworkreconfigurationproblemis acomplex,nonlinearandconstrainedmixed-integeroptimization problemwhereintegervariablesrepresentthesystemswitches andcontinuousvariablesrepresentthedistributionnetwork.The complexnatureofthedistributionnetworkreconfigurationprob- lem,makesitprohibitivetoadoptmostoftheexactoptimization methodstosolveit[1].Ontheotherhand,heuristictechniques havebeenshowntobeparticularlysuitabletohandlethecom- plexoptimizationproblemofdistributionsystemreconfiguration.
Inparticular,extensiveworkhasbeendonetoefficientlyapply geneticalgorithm (GA) to thereconfiguration problem(see for instance[1–4]andreferencestherein). Nonetheless,todate,all the previous work in this area have presupposed that the GA populationsizeshouldremainconstantthroughouttheevolution
E-mailaddress:[email protected]
ofthesearchprocess.Inthispaper,weproposetheapplicationof ageneticalgorithmwithvariablepopulationsize(GAVAPS)tothe reconfigurationproblem.Wedemonstratethatallowingthepopu- lationsizetoadaptivelygrowandshrinkaccordingtothestatusof theGAsearchcanallowforamoreefficientsolution,comparedto standardgeneticalgorithm(SGA)thatmaintainsaconstantpopu- lationsize.
2. DistributionnetworkreconfigurationbyGAVAPS
ThetheoryofGAVAPS wasoriginallyintroducedtothefield of Evolutionary Computationsin [5]. Reference[5] presented a non-elitistGAVAPStomaximizenon-linearmulti-modalmathe- maticalfunctions.Inthispaper,webuildontheworkin[5]and proposeanelitistGAVAPStosolvethepowerdistributionnetwork reconfiguration problem. The proposed GAVAPS searches for a solutiontothereconfigurationproblemusinga populationthat evolves through successivegenerations. Each individual in the populationrepresentsapossiblesolutionandistermeda“chro- mosome”.Achromosomeiscodedasageneticstringcontaining thelocationsofopenswitchesinthepowerdistributionnetwork.
Eachchromosomeisassignedalifetimeparameteratitscreation.
Ateach generation,anoffspring populationis createdfromthe currentpopulationusinggeneticselection,mutationandcrossover operators.Chromosomesinthecurrentpopulation,whoseage(i.e., thenumberofgenerationsthechromosomehasbeenalive)does notexceedtheirlifetimeparameter,arepassedtothenextgen- erationalongwiththeoffspringpopulation.Chromosomeswhose ageexceedtheirlifetimeparameterdieandleavethegeneticpool.
http://dx.doi.org/10.1016/j.epsr.2016.08.026 0378-7796/©2016ElsevierB.V.Allrightsreserved.
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V0=1.05 p.u.
Fig.1.Distributiontestsystem[6],(Vbase=12.66kVandSbase=10MVA).
Thegenerationssucceedoneanotheruntilthesearchconverges oramaximumnumberoffitnessfunctionevaluationsisattained.
TheimplementationproceduresoftheproposedGAVAPSpro- cesscanbegivenasfollows;atgenerationt;Step1:determinethe sizeoftheoffspringpopulationNoffspringas
Noffspring(t)=max(round(N(t)∗),˛) (1)
whereN(t)isthesizeofthepopulationatgenerationt,isthe reproductionrateparameter,and˛istheelitecountparameter.
Step2:thefirst˛chromosomes intheoffspringpopulationwill betheelitechildrenselecteddirectlyfromthecurrentpopulation basedontheirfitnessvalues.Step3:ifNoffspring(t)>˛,thesubse- quentˇchromosomesintheoffspringpopulationwillbecrossover children,
ˇ(t)=round((Noffspring(t)−˛)∗) (2) andisacrossoverfractionparameter.Similarly,theremaining chromosomeswillbemutationchildren;
(t)=Noffspring(t)−˛−ˇ(t) (3)
Eachchromosomeinthecurrentpopulationcanbechosento parentcrossoverandmutationchildrenwithequalprobabilityand irrespectiveofitsfitnessvalue.Step4:foreachofthegenerated crossoverandmutationchildrendeterminethefitnessvalue(based onthesystempowerlosses)and feasibility(basedonthecon- straintssatisfaction)bysolvingtheloadflowproblem.Amutation orcrossoverchildisincludedintheoffspringpopulation,onlyif itpassesthefeasibilitytests.Otherwise,therespectivecrossover ormutationoperatorisrepeatedtogenerateafeasiblealternative.
Step5:selectivepressureisappliedthroughthechromosomelife- timeparameter.Thelifetimeparameterforeachchromosomecin theoffspringpopulationiscalculatedaccordingto
Lifetime(c)=min
MinLT+fitness(c)
AvgFit ,MaxLT
(4) whereMinLTandMaxLTaretheminimumandmaximumallowable lifetimeparameters,=0.5(MaxLT−MinLT),fitness(c)isthefitness ofthecthchromosomeintheoffspringpopulationandAvgFitis theaveragefitnessvalueofthecurrentpopulation.Step6:increase theageofeachchromosomeinthecurrentpopulationbyone.Step 7:formthepopulationforgenerationt+1tocompromisetheoff- springpopulationaswellasallthechromosomesinthecurrent populationtwhose agedidnotexceedtheirlifetimeparameter andthatarenotpresentintheoffspringpopulation.
Table1
ComparisonofSGAandGAVAPSresults.
Initialpopulationsize 10 15 20 25 30
Averagenumberofpowerflows
SGA 435 591 787 901 1114
GAVAPS 310 333 383 385 427
3. Testandresults
TheproposedGAVAPSforpowerdistributionnetworkrecon- figuration wastested onthewell-known Baran reconfiguration testsystem,showninFig.1.Inthiswork,weinvestigateasingle- objective loss reduction problem formulation. However, other possibleformulationsmaybereadilyadoptedwiththeproposed GAVAPS.Theperformanceoftheproposedapproachhasbeencom- paredtoSGA.Inordertoallowforanobjectivecomparison,theGA parameters,codificationaswellasgeneticmutationandcrossover operatorswereidenticalforbothSGAandGAVAPS.Mutationand crossoveroperatorssimilartotheonespresentedin[3]and[1], respectively,havebeenadoptedinthiswork.Ontheotherhand, thegeneticselectionoperator,whichrepresentsoneofthemain differencesbetweentheproposedGAVAPSandSGA, wasdiffer- ent.WhileinGAVAPSalltheindividualsinthecurrentpopulation haveequalprobabilitytoparentmutationandcrossoverchildren (i.e.,irrespectiveoftheirfitness),inSGAtheselectionofparentsis basedonthefitnessvalue(i.e.,individualsofhigherfitnesshave higherprobabilityofbeingselectedasparentsformutationand crossoverchildren).Initialpopulationsizesof10,15,20,25and30 weretestedwithbothSGAandGAVAPS.IncaseofSGA,thesizeof initialpopulationremainedconstantthroughouttheevolutionof theGAsearch.InthecaseofGAVAPS,areproductionrateof0.4, aminimumandmaximumlifetimeparametersof1and7,respec- tively,wereappliedandthepopulationsizeevolvedthroughthe searchprocess.Acrossoverfractionof0.8andanelitecountof2 wereappliedforbothSGAandGAVAPS.Populationswereinitial- izedatrandom,and50independentrunswereperformedoneach initialpopulationsize.Thenumberofpowerflowsrequiredwere averagedoverthese50runsgivingthereportedresults.Thebest solutionpresents114.271kWlosses,withthefollowingbranches open:7, 12,31, 35and 37. Table1shows theaveragenumber ofpowerflowevaluationsrequiredineachcasestudiedtoreach thebestconfiguration.TheresultsinTable1demonstratethatthe adoptionofavariablepopulationsizecansignificantlydecreasethe computationalcostofthereconfigurationalgorithmandallowfor abetterexplorationofthesolutionspaceaswellaslesssuscep- tibilitytotheinitialpopulationsize.Hereitisworthmentioning thattheapplicationofGAVAPStotheelectricdistributionnetwork
M.Abdelaziz/ElectricPowerSystemsResearch142(2017)9–11 11
Table2
Comparisonwithpreviouslypublishedalgorithms.
Algorithm ProposedGAVAPS Reference[7] Reference[8] Reference[4] Reference[9] Reference[10] Reference[11]
Averagenumberofpowerflowevaluationrequired 310 450 705 525 1600 640 433
reconfigurationproblemisnotlimitedtotheGAprocesspresented inSection2.Advancedencodingandcodificationalgorithmspre- viouslyadoptedwithSGA(seeforinstance[1–4])canbereadily adoptedwithGAVAPS.Table2presentsacomparisonofthenum- berofpowerflowevaluationsrequiredbytheproposedGAVAPS withthoserequiredbyothertechniquesavailableintheliterature.
4. Conclusion
Existingliteratureinvestigatingdistributionnetworkreconfig- urationusingGAhaveallpresupposedthattheGApopulationsize shouldremainconstantthroughouttheevolutionofthesearchpro- cess.Inthispaper,weamendthispresuppositionandproposean alternativeapproachthatallowsthepopulationsizetochangesize adaptivelythroughtheprogressinggenerationsbasedonthesearch status. It is demonstrated that a GAof varying populationsize canyieldlowercomputationalcostsinsolvingthereconfiguration problem.
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