Applicationof Artificial Neural Networksfor Voltage Stability Evaluation of Power Systems
By
~Salish.C.vallabhan,B.Tech.
A thesissubmitted to theSchoolof Graduate Studiesinpartialfulfillmentof the requirements
forthedegreeof Masterof Engineering.
Facultyof EngineeringandAppliedScience MemorialUniversityofNewfoundland
August,1995.
St.Jchn's Newfoundland Canada
1...1
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Abstract
Voltageinstabilityhasemergedas oneofthe mostimportant areasof concernto modem power utilities.Once associatedwithweak powersystemsandlongtransmissionlines,voltage instability problemsare now acutelyfelt inhighlydevelopednetworks.This isbecausemany utilities are leading theirbulk transmissionnetworks to their maximum capacity toavoidthe enormousc.tpitalcosts of building new lines.In recentyears, voltageinstabilityhas been responsiblefor severalsystem collapsesin Europe,AsiaandNorth America.
Voltageinstabilityisconcernedwith the ability ofapowersystem to maintainacceptable voltage al allbuses in the systemundernormalloadingconditionsand afterbeingsubjectedto a disturbance.Asystem entersa state of voltage instability when a disturbance,increaseinload demand,or changeinsystem conditioncauses aprogressiveand uncontrollabledeclineinvoltage.
Themain reasoncausingvoltage instabilityisthe inability of thepowersystemto meet the demand for reactivepower. The other factorscontributingto voltage instability are generatorreactive power/voltage controllimits,load characteristics, characteristics ofstaticvarcompensators. and action of on load transformertapchangers.
Thestudy ofvoltage instabilityhasbecomean importantarea of researchinthefieldof power systemcngineering. The main thrustof researchhas been toarrive at an accurateand reliable indicator ofthe proximity of asystem to voltage collapse. Such an indicator wouldbeuseful10 utilities in operating theirsystems with maximumeconomy and security.However.forsuch voltagestabilityindices tobetrulyuseful toutilitiesfrom an operationsPoint ofview. they should beimplementeden-lineinthe Energy ManagementSystem(EMS). The Energy Management Systemhas become a very importanttoolinmodempower system controland operationand has versatile capabilitiesfor powersystem control.analysisand monitoring.The major hurdlein the on-lineimplementationofvoltagestabilityindicesin anEMS wouldbetheheavy computational costsinvolvedintermsof time,memory and hardwarecosts. Thisisbecause most mcthodsfor voltagestability ..nalysisneed repeatedsolutionsof powerflowsand associatedcalculations.Thus, foron-lineapplications.thereis aneed for tools which can quickly idcntifypotentiallydangerous conditionsand providetheoperator with guidanceto steer thesystem fromvoltage collapse,Also.
inviewofthelarge size of modempowernetworks,itis importantthatthememory requirements of thecomputationaltoolsbeas lowas possible.
In recentyears,therehasbeen considerableinterestinthe applicationofArtificialNeural Networks(ANN)10 powersystem problems.ArtificialNeural Networks havethe abilityto identifyand classifycomplexrelationships,which arenonlinear andresultfromlargemathematical models.The main featureof an ANNis the ability to achievecomplicatedinput-outputmappings through a learningprocess,withoulexplicitprogramming.OnceanANNhasbeentrained,it can classify new data muchfasterthan wouldbepossibleby solving the model analyticaJly.ANNs have the potentialto play an importantroleinEnergy Management Systemsby providingsystem operatorswithafast andreliableindicationoflhe voltagestabilityof a powersystem.
This thesis presentstheapplicationof ANNs for evaluationof powersystemvoltage instability.Two popularvoltagestability indicesare studiedand simulationsare carriedouton the IEEE 24Bus system andthe 39Bus New Englandsystem.The effectof contingenciesonthe voltage stability of the abovetwosystems was investigated.ANN models were designed to evaluatethevoltagestabilityindicesusingthe systemparametersavailablefrom theEMSas inputs. Forthe energy marginbased voltagestabilityindex, separate ANN modelswere usedfor each contingency.However, for theload margin index,a singleANN modelwhich takesinto account the networktopology,wasusedto evaluatethevoltage stability.ThissingleANN model is able10 evaluatethe voltagestability of a system undernormaloperatingcondition(i.e.,al1linesinservice) and also inthe eventof a line outage. Simulation resultsare presentedonthe applicationof the above indices toboth powersystems.Theperformanceof the ANNmodels arepresented, which comparesthe predicted accuracyto the expectedvalue.The thesisalso proposes a scheme for integrating the ANNbased systemintothe EMSenvirorunent.
iii
Acknowledgments
Iwould like:toexpressmysioeeregratitude andappretialionfortheinvaluable helpand guida.'1CCgiventomebyDr.BenjaminJc:yaswya duringallstagesoh mswork.Mythanksarealso duetoDr.Jcyasury a,theFacultyofEngineering andApplied ScienceandtheSchoolof Graduate Studiesforthefinancialsupportprovided10me duringtheCOIlI'SCof myM.Eng.progr.un.
I acknowledgetheassistancereceivedfromfaculty membcn,fellow graduatestudentsand otherstaff oftheFaculty of Engineeringand AppliedScience.
Finally, Iexpressmysincere gratitude to myfamily for theirencouragement,supportand understanding, withoutwhichthisworkwouldnothave beenpossible.
iv
Contents
Abstract
Ackn owledg ment Contents ListofFigures List
or
Tables List ofSymbolsIntr od uct ion andliteraturesurvey onvolta ge collapsephe nomena 1.1lmroduction
1.1 ThePhenomenonof VnltsgeInstability
I.Ll TheMegawatt-rotorangleand Megavar-VoltageInteraction 1.2 Voltage Stability.Static or Dynamic?
1.3TraditionalMethodsof VoltageStabilityAnalysis 1.3.1 P·VCurves
1.3.2 Q.VCurves
1.4 Recent Incidents of VoltageCollapse 1.4.1 Voltage Collapse onFrench System 1.4.2 Voltage Collapseon SwedishSystem 1.4.3 Voltage CoJlapse onJapanese System
1.5 BriefHistory of Research inthe fieldof Voltage Instability 1.6 Currently AvailableMethods forEvaluating Voltage Instability 1.6.1 Glavitch'sM ethod
Ix xl xlii
10 11 12
13
14 15 IS
I.S.2 Minimum SingularValueMethod 16
1.6 .3 Energy FunctionAnalysis Methods 17
1.7 Applicationof Artificial NeuralNetworks 19
1.8 Significance of Artificial NeuralNetworks in Modem Power SystemControl 20
1.9 The EnergyManagement System 20
1.10 AimoftheThesis 21
L11 Organizationof(he Thesis 22
ApplicationoiArtifi cialNeuralNetworks 10PowerSystems 2.1 Introduction
2.2 ArtificialNeuralNetworks 2.2.1 Models of a Neuron 2.2.2 Types of Activation Functions 2.2.3 NetworkArchitectures 2.2.4 Neural Network Algorithms
2.3 Back PropagationAlgorithm 2.4 Important Issues inapplying Bac k Propagation 2.4.1 Leam.ingRate
2.4.2 Mo mentu m 2.4.3 StoppingCriteria 2.4.4 Initialization 2.4.5 Generaliza tion 2.4.6 Size of Training set
vi
23 23 23 25 26 28 31 32 36 37 37 37 38 38 38
2.5 SelectedApplicationsto PowerSystems 39
2.5.1 TransientStability 39
2.5.2 NeuralNetworkApproach10 evaluateCCT 40
2.6 LoadForecasting 41
2.6.1 NeuralNetworkApproachto Load Forecasting 41
2.7 ContingencyScreening 42
2.8 Alarm ProcessingandFaultDiagnosis 42
2.8.1 Neural NetworkApproachtoFaultDiagnosis 43
Energy Fundlon Methodsfor Evaluallon ofVoltageStability 45
3.\ Introduction 45
3.2 Overviewof EnergyFunctionMethods 45
3.2.1 ApplicationofEnergyMethodto TransientStability 45
3.2.2 Applicationof EnergyMethodsto VollageStability 47
3.3 Low VoltagePower How Solutions
"
3.3.1 LowVoltageSolutionsfor sample5 BusSystem 53
3.4 EnergyMargin Computation 59
3.5 Effectof ContingenciesonEnergyMargin 65
3.6 Summary 68
ArtificialNeural Networks forEvalua tion ofVoltageStability 69
4.1 Introduction 69
4.2 Selectionofthe ANNAlgorithm 70
vii
4.3 Selectionof the InputParameters 71
4.4 TrainingoftheNeural Network 72
4.5 Test Results 74
4.6 ANNModelsconsideringsystemcontingencies 76
4.7 ApplicationinanEMS environment 79
4.8 Summary 81
Application of Load MarginMethod for Evaluati ngVoltage Stab ility 82
5.1 Introduction 82
5.2 Computationof NearestInstabilityPoint 83
5.3 BasicTheoryfordeterminationof shortestdistanceto instability 83
5.4 GeneralDescriptionof the Procedure 88
5.5 Applicationtothe39Bus New EnglandPowerSystem 89
5.6 Effectof Contingencieson Load Margin of 24 Bus System 92
5.7 Summary 96
ArtificlalNeura lNetworks forEvaluationofLoad Margins 97
6.1 Introduction 97
6.2 SelectionofANNAlgorithm 98
6.3 Selectionof inputParameters 98
6.4 Trainingof theNeuralNetwork 99
6.5 Test Results for the39Bus New EnglandPowerSystem 99 6.6 M'N Modelstoevaluate effectof ContingenciesonLoadMargin 102
6.7 Summary 108
viii
Conclwlo ns
7.1 Contributionsof thisresearch 7.2 Suggestionsfor future work
References
110 110 112
113
List or Figures
1.1 Simplemodelfor t:alculation of real and reactivepowertransmission 1.2 Simpleradialsystem
1.3 SampleP -V Curve 1.4 SampleQ.V Curve 2.1Nonlinearmodelof aneuron 2.2Thresholdfunction
2.3 Sigmoidfunction
2.4 Feedforwardnetworkwithasinglelayer 2.$Multilayernetworktopology 2.6 AsimplerecurrentnetWork
2.7 TypicalArchitectureof a threelayerbackpropagationneuralnetwork 3.1IlIwt:rationof theEqualAreaCriterionconcept
3.2Illustration oftheenergywellconcept
J.JSample5buspowersystem 3.4 Single linediagramofsampletwobussystem 3.SVariationofEnergyMarginwithloading for2bussystem.
3.6VariationofEnergyMarginwithloadingforS bussystem 3.7 24 BusPowersystem consideredforstudy 3.8Variation ofEnergyMarginwithloadfor24BusSystem ].9 ComparisonofEnergyMarginwithline 7-21 out andwithnooutage
ix
10 26 21 28 29 30 30 34
46 48 S3 60 60 61 62 6S 66
3.11Comparison of Energy Margin with line 8·21 out and with no outage 67
4.1 NeuralNetwork Performance Evaluation 75
4.2 Comparison of percentagepredictionerror for two tolerances 76 4.3 NeuralNetwork Performanceconsideringoutage of line 7·21 77 4.4 NeuralNetwork Performanceconsideringoutage of line 6-19 78 4.5 NeuralNetwork Performanceconsideringoutage of line I -
s
outeged 78 4.6NeuralNetwork Performanceconsideringoutage of line 2 ·4 outaged 79 4.7 Blockdiagram for intcgratingANN based voltage stability monitor into EMS 815.1 Asimpleradial system 85
5.2 Singular surface S in the p.Q plane 87
5.3 39 Bus New England PowerSystem 90
5.4 Plot ofLaad Margin in M.W.against LoadingFactor, K 91
5.5 lEEE 24 Bus ReliabilityTest System 93
6.1 Performance Evaluation of Neural Network 101
6.2 Neural Network PerformanceEvaluation 102
6.3Neural NetworkPerformance Evaluation for line 1 - 5 outaged lOS 6.4 Neural NetworkPerformanceEvaluation forlineI - 3 outaged lOS 6.5 Neural Network PerformanceEvaluation for line 2-
e
outeged 106 6.6 NeuralNetworkPerformanceEvaluation for line 2 ·4 outaged 106 6.7 Neural Network PerformanceEvaluation for line 7 - 8 outaged 107 6.8 Neural NetworkPerformanceEvaluation for no line outage. 107List oCTables
2.1 Comparativeperformance of differentANNalgorithms 3.1Loadflowsolutions for Sbussystem
3.2Startingvalues cfvoltages for5bussystem 3.3 Low voltage solutioncorrespondingto0 0 a I 3,4Lowvoltagesolutioncorresponding to 0 0 I 0 3,5Low voltagesolutioncorrespondingto0 0 I 1 3.6Low voltagesolutioncorresponding 100 I 00 3.7 Low voltage solutioncorresponding to 0 I 0 I 3.8Lowvoltagesolutioncorrespondingto 0 1 I 0 3.9Lowvoltage solutioncorresponding to 0 I I I 3.10 Variationof nwnberof rootswith increaseinload 3.11Load flowsolutionfor5 bussystem for K"'4.5 3.12StartingvaluesforK
=
4.5for 5 bussystem 3.13Low voltagesolutionfor 5 bus systemfor K= 4.5 3.14Base CaseLoadflew resultsfor 24Bus system 3.15Onelowvoltagesolutionfor24 Bussy~tembasecase 4.1 Table showinginputparametersforonesetofinputtrainin'jdata 4.2Important designparameters for Neural Network 5.1Calculationof shortestdistanceto instabilityforsystemin Fig. S.l 5.l LoadflowresultsforIEEE 24 Bus Reliability Test System32 54 54 55 56 56 56 57 57 57 58 58 59 59 63 64 74 75 S7 94
5.3loadings ofl inesselectedforoutageinIEEE24BusSystem 5.4Variationof toadmarginwithlineoutageforbasecase load 6.1Onesetof inputtrainingdata
6.2Importantdesign parametersforNeuralNetwork 6.3Table showingonesetofinputtrainingdataforline 1-5outaged 6.4 ImportantdesignparametersforANNmodelconsideringcontingencies
xii
95 95 '00 100 103 104
Nomenclatura:
:InternalVQ!tage behindthe synchronousreactance V : Voltageatabus
5 :MachineangleorPower angle Power factorangle M InertiaConstant
Speedofthegenerator PL: Active poweratload bus QL:Reactivepoweratload bus Po:Active powergeneration at generationbus Qo : Reactivepowergenerationatgenerationbus Vpv: VoltageatPV(VoltageControlled) bus Dg : Elementsof the Bus AdmittanceMatrix 0,
Vi Voltage at the stableoperatingpoint
VU :Voltageat the unstablecquilibriwnpointor low voltagesolution PV : VoltageControlledbus
Systemstatcvector Parameter vector Line Current Apparentpower
xiii
X: SystemReactance Z:SystemImpedance el: Realpanof voltageatbus I
Imaginarypart of voltageatbus I f" : NeuralNetworkoutputfunction
Wj! :Weightofconnectionbetweenhiddenlayer and inputlayer WkJ: Weightofconnectionbetween output layer and hiddenlayer
Learningrateoftheneuralnetwork 0pk· Error at a singleoutputunit
Chapter 1
Introduction and Literature Survey on Voltage Collapse Phenomenon
1.0Introdudion
Traditionally,the primaryconcernof powersystemdesigners and plannershas been ensuring rotorangle (synchronous) stabilityand thermalloadingcapabilities.Tilltheearly eighties, whenenvironmental issues cametothe forefront.the expansionofthe transmission anddistributionnetworkwas dictated Iltrgelybytheloaddemand.Generation, transmissionanddistribution facilitieswere plannedand installeddependingon theload growth. Theonlyconstraintsystemplannersfaced was tomaintain anglestability.Thefew blackouts thattook placewere attributedto transientstabilityproblems.Thearrival offast protective relaysandcircuit breakers have helpedin part toalleviatethis problem.The transmission anddistributionnetwork continuedtoexpand10 meet the load growthlimited onlybythe utilities' financial constraints.The"normal"operationofapowersystemwas definedbyitsabilityto maintainanglestability.
However,this scenario startedto changeby theearlyeighties.Ahost of newissues cameup which have combined to completelyalter thewaypower systems havebeen plannedanddesigned. Theforemostamongthesewas thegeneraleconomicdepression whichcharacterisedallmajoreconomiesoftheworld.Utilities nolongerhadtheresources to buildnew facilitieseitherforgeneration, transmission or distribution. Another major development wastheheightened awarenessof environmentalissues.Environmentalissues became the centrestage of anydevelopmental activity.All new developments,beit constructionof anew generationplantorconstructionofa newtransmissionline, were examinedfor theirenvironmental impact. Naturally,this resultedina severecurtailmentof anynew construction of facility, whichinnormal coursewouldhave beenapproved.The problem was twofold.Ontheonehand,utilitieswerestrapped forfunds and evenif they
could findfunds foressentialprojects. long delays becamethe order of thedaydue to complicated approval procedure s.How ever, all through thisperiod,therewas no appreciable declinein theloadgrowth. Thus.the scenarioin the eighties wasthatof increasingload and very little expansion ofthefacilitiesthat existed .Utilitie swere faced with the taskof squeezingthe maximum possib lepower through theexisting netw orks.
Thesenewdevelopments broughtin their wake,a new set ofpowersystempro blemswhich had not beenseriouslythoughtofor studie dbefore.
1.1 The Phenomenon of Voltag eStability
Asa result oftheabove mentione d situatio n,systemplannersand designerswere nowbeing increasinglyfaced with a new problem:Howto maintain thevolta geprofileu thetransmission anddistributionlevelsto acceptab levalues?
1.1.1The MegaWatt . rotor angle and MegaVar .Voltage InteractIo n Ithasbeen longrecognizedthatthe reis a strongcouplingbetwee n MegaW att (MW) androtor angleand MegaVar (MVAR) and thevo ltageII).Inother words.theavailab ility of MW is dictatedbythe machineangle which intum isdeci dedbytheinput totheprime movers .Onthe otherhand. voltage is relatedto the MYARavailabilityatthatpoint. In figure 1.1, E.,is the sendingendvoltage,Xisthereactance ofthe transmissio n line,E,.is the volt age at thereceivingend and
a
isthe power angleor machine angle.r isthe current throughthelineandSr isthe powerinMVA.Therelationshipbetweenac tivepower, reactive power.sendingend voltage.receivingendvolta ge,systemangleandsystem reactanceis as givenby theequations below.~
E,LB jX E,L O
Fig.1.1Simple modelforcalculation of realand reactiv epower transmission
Therela tionshipcanbederived asfoll ows:
Sr= P,+jQr= E, I' (1.1)
=Er(Elcosli+~~.Sln5-Etf (1.2)
Pr+jQ =¥slna+jE,Er C:'~li -E~ (1.3 )
Pr=¥ Sln li=p....s.inO (1.4)
Or=E!E!t~li-E; (1.5)
VoJragein stability canbeascribed tothe lackof VAR support needed10maintain the voltageprofileat thespecitiedvalu e.Since voltage collapseoccursunder heavy loading condition s ,it maybeworth whiletoexploretheeffectoflargeload angle on reacti vepowe r transmission .From the above equationfor reactivepower (eqn 1.5),it may be seenthatas the load angleinc reasesthereactivepowerbecomesnegative end thetransmission line becomes adrain on the receivingendsystem.Thus, asthe realpower transferincreasesthe reactive powerrequiredfro mbothsending and receiv ingendsystemwillincrease, andat veryheavy loadings,morethan oneunitMV AR willberequiredforeach additio nal MW transmitted.Animportantreasonwhyreactivepowertransfershouldbeminimised is the heavy react ivelos sesincurred.Since reactive10 55Ispro por tionalto12X!the reactivelosses Increaseinanon-linearcu rrentsquaredrelatio n.Ifinan already heavil yloadedsystem.
thereis aloss ofaline,the lossesintheremaininglines maybecome very high and the voltageproblemmay worsen.Thus,itmaybeseenthat thereactive power aVai lability is one ofthekey aspectsof voltagestability.
Reference[I]defi nesvoltage stabilityandvoltagecollapseasfoll ows:
A powersyslemata givenoperatingslateandsubject/0agivtndistu rbance is vol/age srableifvo/tages nearloadsapproac hpit disturbanceequilibriumvalues.
Apowersystem ata give"operating5/Qre andsubjecttoagivendistu rbanctundergoes vo/ragecollapseifpostdisturbanceequilibrium valuesarebelowQcceptabLeI~ls.
Thus. voltagecollapseisanextremefo rm ofvo ltageinstability.Asopposedto angle instability. themain dynamicsinvolvedin voltage co llapseistheload dynamics . Hence voltagestabilityhasalsobeencalledloadstab ility{2].Duringtheperiodofvoltagedecay.
otherdynamicsno lessimportantcome intoplay.Thesearegene ratorexc itationcontr ol, on loadtapchangers (OLTCs).staticVatcompe nsator(SVC)controls,thermoslatcon trolled loadsetc.Sincealltheabove controlshavea lo ngerres ponsetime(of theorderofse conds).
the dynamics aretermed asslowdynamics.Typically. theresponsetime may rangefrom 1(),20sec ondstothe orderof severalminutes.Wewillnowexaminehowvoltagestability candevelopinasimpleradial systemand showhowthe variouscontrolslistedabove contributeto voltageinstability.
L.T .C RES.LOAD GEN.TQTRIP
I
INDUSTRI ALLOA D
Fig.1.2Simple radialsyste m.
PRIMARY CAPACIT ORS
-e ~
L.T.C !NOL.LOAD
Considerthe radialsystemsho wninFigure1.2. whichconsistsof a generatorfeedingthree differenttypes ofdistri bution systemsthroughahe avilyloadedtransmissionline.
The threedifferenttypes of loads are
I) Type I isdome sticloadwhichismostlyheatingandlightingloadandisrelatively hig hpower factor load. Thistypeof loadlendstodropwithdropin voltage.
2) Type 2isanindustrial loadon a loadlap changer(LTC).Mostof the industrialload com prises of inductionmotorsandhenceis[ow power fac toranddoesnotvary much'-'l.I.::' voltage.
3) Type 3isan industrialload noton LTC.
Inthisheavily loaded systemoperatingnearitsvoltage stability limit, a small increasein load(active orreactive), a loss ofgenerationorshunt compensation, adropin send ingend voltageetc.can bringin voltageinstability.Assumingthatone ofthe above mentionedchangeshappen.andtbe receivingendvoltagefalls.several mechanismscome intoplay.Sinceresidentialloadsan:voltagedependent, theactive and reactiveloadsdrops with dropinvoltage. The industrial activeandreactiveloads dominatedby induction motors cbangeonly bya smallamount. Thus,theoverall effectmaybethestabilisatio nof volta geat avalueslightly les s than the ratedvalue.Thenextactionisoperation of distributiontransformertapchangersto restoredistributionvoltages.Theresidentialactive loadwillincrease while theindustrialreactiveloadwilldecrease.The increasingresidential loadwill outweighthe decreasein reactive loadcausingthe transformerprimaryvoltage to faJ!further.Theincreasedprimaryreactive losseswillfurther drop thetransformer prim ary voltage.Inthisscenari o, tlteOLTCs ( on loadtap changer)maybeclosetotheirlimi ts, primaryvolta geat around90%and distributionvoltagesbelownormal.Asvoltagesensitive controlledloads(reside ntial)ereepback towardfull power.primaryand second aryvoltages will dropfurther.TheType3 industrialloads,l.e.•withoutOLTCswillbeexposedto the reducedvolta gelevels.Thisgreatly inc reases thestalling of inductionmoto rs (stal ling occurswhen loadtorque is greater thandevelopedtorque).Whenamotorstalls. itwill drawincreasing reactivecurrent.bringingdown thevoltage onlhebus.Thisresultsina
"cascade"stal lingof other inductionmotors tesulting inalocalisedvoltagecoll apse.Since
most largeinductionmotorsarecontrolledbymagnetically heldcomactcrs. the voltage collapsewouldcausemost motorsto dropoff from thesystem,ThisIO£S ofload will cause the voltageto recover.However,the recoveredvoltagewillagainresult inthe comactor closingand mo torstallingand anothercollapse,Thus. thisloss and recovery of theloadcan causealternatecollapseandrecoveryof voltage.Theeffectof automaticvoltageregulation (AVR)maybeexplainedasfollows:Asthe voltagedrops theAVRsteps in and increases the reactivege neration.This increasesthe fieldcurrentandwhenthe currentlimit is reached, theexcitationlimiterscome into play andthe voltagesareallowedto drop. Ne arby generators may pickupthe reactiveload,but thismaylast onlyfor a few minutesifthey tooreachtheirexcitation limits.
Thus.fromthe abovediscussion it is clear that voltagestabilityis essentially"slow"
dynamicsand is affectedbythe nature and type ofload. transformertapchangeraction, generatorAVRcontroletc.
To summarise.the variousimportant factors contributing to longtermvoltage instab ility
Stressedpowersystem,l.e.,highactiveandreactiveloadingdue to excessiveload arlinez transtormeroutages.
2) inadequatefastreactivepower resourcesavailablelocally,aggravated by actionof fieldcurre ntlimitersof generators.
J) loadresponseat low voltages.
4) tapchanger'sresponsetodistribution voltagemagnitudeandprop uploads as primary voltagescontinue to fall.
l.1.VoltageStablllty·StaticorDynamic?
Theabovescenariowhich describeshow a voltagecollapsecanevolveina syste m showsthat the timeframe foracollapse 10occurcan beofthe order ofminutes dependi ng onthe responseofthevariouscontrolsinvolved.Traditionally, dynamicanalysisas applied to anglestability has limiteditselfto thegeneratordynamicsduringthe transient phase of theorderof milliseconds.However,the timeframe for voltagestabilityismuch largerand
thecomputatioarequlreeeau,if thegener.alorcrjfWllicsa«10betaken into accountfor such• longperiodoftime.wouldbeprohibitive.Inviewof thelongertimeframeinvo lved.
voltagestabilityhasOftCIIbeenviewedas a steadystaleproblem suitablefor staticanalysis.
Also.since amajocfactorillvoltage inst4lbi.lityistheavailability ofreactive power.the problemisidealfor powerflow anaJysis.Thestaticapproochcan offeran insightintothe phenomena andcan indeed givean approximate, yetacceptablesolutionwhic his comPJlationallymuc hsimplercomparedtothed)'namic approach.However. sincethe effectof loaddependencyonvoltage is ofprimeimportanceinvoltagestability; itis desirablethatthestaticloadflow approachbemodifiedsuitablyto incorporatethe vo ltage dependency onload. This"quasi static" modelcan give areasonableaccuracy without a correspondingincreaseincomputation requirement.Thus,itmaybeseenthatthere isa tradeoffinvol ved inbothapproaches.andsince engineeringsolutions shouldbepracti cal andeconomicaland not necessarilyideal.thestatic approachis widely usedbymost utilitiestoday.Thetraditionalmethodsof voltagestabilityanalysisarediscussedbel ow.
1..3 T...dlUonaf MethodsorVoltageStabilityAnalJ'S1s
As mentionedearlier.the'slatic' or powerflowapproachhasbeen the mainstay of voltagestab ility analysis.Thetwopopularmethods whichmake useoftheloadflow approachfor vo lta.ge stabilityanaJysisare(1)PVCUIYeS(2)QVcurves
1..3.1P VCu m':5
Ithasbeen sho wninReferences[3-4]lhatif!hereceivingend voltageVisplotted against theactive powerP,theresultingcurveis a parabola Curvesare obtainedfor differentvaluesof power factor.PVcurves canbeeasilygeneratedfromtheloadflowby slowly increasi ngtheloadindiscrete stepsandnoti ng the corresponding changes involtage.
It is observedthatas theloadincreasestheparabolic curvedropsdown,reachesa 'nose' pointandthen turnsback towardtheorigin.Thismethod can give thesteadystateload ing limitswhicharerelated10voltagestability.A samplePVcurve isshowninfigure1.3 and canbeinterpre tedasbelow:
I) Inthetop halfofthe curve.thevoltageV decreases asthereceivingend powerS increases.Theslopeof the curveis negativein thisregion.
2) Theapexor nose pointis the pointat which theslopereversesdirection.TheX co- ordinate ofthis powerrepresentsthe maximumpowerthatcan theoreticallybe delivered tothe load.
3) Themaximum powerthatcanbedeliveredtotheload is afunctionofthe receiving endvoltage and seriesexternal impedancebetweenthe sendingendand the load point.It isequal to V1.j4Z·.whereVIisthevoltageof thesendingend. and Zisthe line impedance.
4) jfthe load demandwereto increasebeyondthe maximumtransferlimit.the amount of actual loadwhich canbesuppliedaswellas thereceivingend voltagewillboth decrease.Inother words.beyondthe nosepoint,theability\0supplyadditional loadis nonexistent.
Thus. the tophal f ofthe curvecan bereferredtoasthestable regionandthebottom part as the unstableregion. Thus. it isreasonabletosay thatforeveryload.thetophalf of thecurve representsthe highvoltage orfeasiblesolution.and thebottomhalf thelow voltage or fictitious solutio n. One ofthe majorproblemsin generating the PV curveisthat the load flowsimulationwilldiverge nearthenosepoint.This isduetothefact thatunderheavy loading conditio nstheJacobian tendstowardsingula rity andtheloadflow solutionsare no longer reliable.Therefore,specialprogramsare required\0overcomethis problem.
v
p ---+
Fig.1.3Sample PVCurve
1.3.2 Q V Curves
Theprocedurefor obtainingtheQVCUIVeSis similarto thatfor P Vcurvesoutlined above.The curvesare ob tained by a series ofpower flow simulations.QVcurvesplot voltageata busagainstthe reactive powerat the samebus.Inthe QVcurve.voltageison theXaxisand lhereactivepowerQontheYaxis(Fig.1.4).The main advantagesorov curvesareasfollows:
" Since voltage securityis closelyrelated to the availabilityofreactivepower,the Q V curve gives thereactivepower margin atthelestbus.Thereactivepowermargin is the MVARdistance from Iheoperatingpoint tothe bottomofthecurve.
"Thecharacteristicsofbusshuntreactivecompensationcanbeplotted directly on the Q V curve.1be operatingpointislheintersection ofthe Q V characteristicandthe reactive compensationcharacteristic.
Thus.QV curves whichalsoprovideseveralme ansof detenniningtheproximityof anoperatingpoint tovoltagecollapse havebecomequite popularwithutilities in analysing voltagestability[5].
Q
Rg.1.4 SampleQVcurves
IAReuntIndden ts of Volta; 1Collapo;e[1)
TIlerecent interestinthephenomenonof voltagecollapsehasbeentriggeredby severalincidentsof massivepowerfailuresin severalpowersystemsthroughouttheworld.
1bese incidentsprovedthatthelhseatof voltagecoUaps,ewasindeedvet)'realandcould DOl beignored. ThefactworthnotingislhaI: all tbeseincidents took place nocinweak and isolatedsystems,butinwelldevelopedandmature systems. A numberoftrendsinsystem design andplanning haveconlributed10this situatiOll.Power systemshavebecomeIlllXe complex andarebeingoperatedcloser to their capabilitylimitsdueto economicand environmentalreasons,asdiscussedearlier.Thesituatio niscomplicaltdfurtherbydelays in buildingnew transmissionfacilities. Whilethesetrendshavecontri buted to angle instabilityalso.it is clearfrom a studyof recent incidentsof system failure thatitis voilage instability thatisthemajorfactorinthesefailures.
10
1.4.1 VollageCollapseonFrtnehSystem
l>eftmber19,1978
TheFrench systemisa c1ow:ly meshedandinterconnected nationalgrid comprising ofboth 400KVand220 KVtransmissioncircuits.Onthemorningof December19.a cold snapresulledinarapidloadrise of4600MWbetween7AMand8AM.The resulting increase in powertransferfrom easternparts totheParis metroareakd10continuous voltagedeteriorationoverthe next26minutes.Atapprcxirnetcly8.20 AM.thevoltage on the400 KV system stabilisedatabout 350 KV.Within6minutes.the heavilyloaded 400 KY feederwas trippedby the actionof overloadrelays.Thisintumted tooverloadtripping of other400KV and220KVlines.Widespreadvoltageoscillations spread overthe entire Frenchsystem andwidespreadislanding ofthesystemtookplace.
January12,1987
This failure affected the wholewesternpartof!heFrenchsystem.Inthis incident.threeout offourthcnnaJunits ofa majorgeneratingstationtripped andoperatorscalled forgas turbioes10 startup.However.before the gaslurbinescouldcome online.thefourthunit trippedonfieldcverccrrem.Subsequently.nine gener.lotingunitsinanothermajor generatingstation aJso tripped.Thevoltageon\he400KVsystem stabilizedatlesslhan 300KY.
Thefu'S!.incident.i.e..on December19.1978.wasassociatedwithrapidloadincrease, whichintum causedextremely high activeand reactive powerlosses.Itis characterizedas aslow phenomena.thedurationof the incident beingnearlyhalfanhour.
Thesecond incident is characterizedas relatively fasl. II wasinlneted bysudden unforeseen lossof generatingunits.The responseofload and OLTCstothe resulting low voltage contnbutedtofunhervoltagedeteriorationandcollapse.
II
Cerreeuv eActionlaklEn
EOF(E1ectricite'deFrance) plans10use onlinecomputalionofvoltagccollapseproxi~ty index.inviewoftheprn~iveandslow 'Vollagedeterioration.which will allowoperators to takecorrectivemeasures.Also,studies havebeeninitialed to improve co-ordination betweenautomaticvoltageregulation.fieldcurrentlimitationsand protections.Automatic OLTCblockingbasedona regionallow voltage criterionisbeingimplementedonthe Frenchsystem.Automaticloadsheddingis alsobeinglookedinto.
1.4.2 Voltage Collapseon SwedishSystem December 17,1983
In theSwedishsystem.mosoflhegenerating plantsarelocatedin thenorth and the majorloadcentresin the south.Thehydroplantsinthenorth areconnected tothe load area.'!
inthe south by seven 400KVtransmissionlines. Alllinesareseriesandshunt compensated. Beforetbecollapse.thetotalload including losseswas18.000MW.t.e.iless thanthepeakload.Thevoltages.onthenetworkwere stable between400and405KV and systemfrequencywasclosetoSOHLThevoltagecollapsewas Initia tedbythefailureofan isolatoron a400KVswitchgearatasubstationwestofStockholm.Thissubstationfeeds the220 KV networkintheStockholmarea.Asa result. two outof seven 400 KV transmissionlineswhich bring power from north to southtripped.This resulted inhigh loading oftheremaining fivenorth-southtransmissionlines as wellasa220 KVline throughStockholm.Approximately8secondsaftertheinitialgroundfault, two220KV linestrippeddue10overloading.Afterthistrippingloadstarted to restore dueto transfonner loadtapchangeraction.ApproximatelySOseconds after theinitialIault, another 400KV linetrippedonoverload.Theremaining 400KV linesbecameheavilyloadedandacascade tripping ofalltheselines betweennorthernand southernSwedentookplace.Thelossof the EHV ticlines isolatedsouthernSweden from thehydroplanlsin thenorth.Becauseofthe massive power deficitinthesouth, oJlgenerators inSouthwere trippedonoverloador underfrequency,
12
CerrecuveMeasurestaken
Anumberof researchprojectshave beeninitiatedbytheSwedish Power Boardafter the aboveincidents.A co-ordinatedcontrolstrategyfortransfonner load tapchangers.shunt reactors.shuntcapacitorsand otherequipmentgeneratingreactivepower in thesystemhas been designed.Also.sinceoverloadtrippingof transmissiontriggered thecollapse.the overloadcharacteristics ofthe relayswere also investigated.Itwas concludedthattheoffset mho characteristicofdistancerelaysprotectinglonglines would havetobemodified.
Automaticblocking.of OLTCswas also investigated.
1.4.3Voltag e Collapseat TokyoanJuly 23,1987
OnJuly23.1981.Tokyoexperiencedunusually hot weatherwithrecordhigh temperaturesof36°C to3~C.Thedemand increasedat a rate of400 MWf minutefar higherthat theestimatedlevel.The voltageonthe 500KVsystemgraduallydroppedto 460 KV,About13:19. the voltagecontinuedto drop and reached310KV(0 .14 p.u.).These substetlons were trippedbyoperationof protectiverelays.Itwas foundthat theactionof OLTCscontributedinamajor wayin acceleratingthe collapse,Thus a combinationof heavy.unexpected loadandthe responseoftap changersandloads contributedin amajor way towards this collapse.One ofthehearteningaspectsof the Tokyo collapsewasthat utilities and academicsin Japan started seriousresearchinto thevariouscontributingfactors towardsvoltage collapse.
Correctivemeasurestaken
Inviewof the Tokyocollapse.anumber ofmeasureswereproposed.Theseinclude constructionof anew 1000 MWgenerationfacility.newshunt compensation equipment.
upgradingofdemandforecasts.sophisticatedcontrols for OLTCs.Also. power purchases fromneighbouring utilitieswouldbeencouraged.
13
1.5 BrierHi~toryor Researth in the Oeldor VoltageInstability
As discussedearlier,thestaticor powerflow approach is a widelyused and establishedmethod for voltage stabilityanalysis.Though the past ten yearshas seenalot of workinthis field,some earlierresearchersalsohad contributedagreatdealonestablishing asolid foundation. It was Venikov etal.•whoin 1975 showed thatthere isindeed a close connection between aload flowand steadystatestability (6]. They provedthaithe change ofsign of the Jacobian of theloadlow equation isan indicator of theonset ofinstability.
Thisworkwouldbemadeuse ofby futureresearchers.In1978.one ofttl<lrtf'St papers on voltagecollapse waspublished by Lachs[71.Heanalysed ingreatdetailthe effectof heavy systemloading andcorrespondingreactivelosses, transfonner tap changing.generator reactivecapabilityetc.This wasprobablythefirstpaper whichmadeuse of the PV curveto showthe relationbetweensystem loading and voltage collapse.Thispaper is valuablein that for the first time anoverall viewof thevarious mechanisms contributing to voltage collapsewas taken.In1981. Tamura and IwamotofolloweduponVenikov eta1.'swork and proposeda methodto detenninemultipleload flow solutions [8].Theyproposedtheuse of optimum multipliers oracceleratorstothe Newlon-Raphsonmethod.Thismethodalso wouldbemade use of byfuture researchers.In1982,Abe et.aJ.showedthat loadflow can indeed beused fortheanalysisof voltageinstability [9].They also proposedamodelfor tapchangerandalso theeffectoftapchangeroperationon load models.In1983,Tamura et.nl.showedthe relationship between vo ltageinstability and multipleloadflow solutions (WJ. Theauthorsshowedthatasthe system gets more heavily loaded,the number of solutionsdecreaseandat veryhighloadings,a pairof'IeI)' close solutions areobtained.
Theyalsoproposed a voltagestability criterionbased onchange of sign oftheJacobian and the numberof close solutions.Thisaspectwasnotinvestigated furtheruntil recently.In 1983,Palmeret.al.argued from a utilities pointof viewtheimportanceof reactivepower despatchingformaintainingpowersystemvoltagesecurity (llJ. They also proposeda method forschedulingreactiveequipmentduringnonnal and post contingencysituations.
Thus, we secthatfrom themidseventies totheeighties, an understandingof thevoltage stabilityphenomena and the relationofthesteady stateload flow tovoltagestability had
14
been developed.However,itwas not until1986.that a comprehensive ind ex forevaluating thevoltagestability ofasystem was proposed.This andthecurrentlyavailablemethods will be discussedin the next section.
1.6 Cu rre ntlyAvaila bleMethodsforEva luati ng Voltag eStability
There are anumber of methods availableforevaluating voltagestabilityfrom a static (loadflow)point of view.However.the most popularand widelyused ones are :
I) Glavitch'sMethod 2) MinimumSingularValueMethod 3)Energyfunction Method.
1.6.1Gla vit ch 'sMethod
In1986.Kessel and Glavitchpropo sed thefirst voltagestability index[12].This method providesa meansto assess voltagestability without actually comp uting the operatingpoint where thecollapse takes place.Glaviteh's method is essentiallybased on a staticor load flow mode.Inthismethod.theload flow program is run several times and various parameters used to computevoltage stabilityare taken from this.Thismethod is originallyderived from a two bus networkwhereone ofthe buses is the slackandtheother is aPQbus.A stabilityindicator~is derived which variesbetweenzero andone and which characterisestheexistence ofa voltagesolution. The index essentiallyrelatesthecomplex powerS;, elementsof bus admittancematrix Viiand voltage Vjin the relation
(1.6)
Foramultibus system, the indexhas tobe calculatedforeach bus.Themaximum value (closest to one) is anindicato r of the proximityto powerflow divergence.The important condition for stabilitytobeguaranteed isL;<I.The indicatorL;isa quantitativemeas ure fortheestimation of thedistanceof the actualstareof the system tothe stabilitylimit.The local indicatOrI..;permitsthedeterminationofthosenodes from which acoll apse maytake
15
place.Thepattern of indicatorsis quiteinformative of the behaviourof the system,in that allnodes belongingtothe same critical area show a similardevelopmentofthe stability indicator. Experience has shownthata threshold of 0.2canbe appliedtothe critical indicator.Ifthe indicatorof thepartic ular node exceeds this value, the area around this node is critical. When1..;of a singlenode ora group of nodes exceeds the value of0.2,the situationbecomes critical. Clusteringof indicators means the fonna tionof an area of similarbehaviour.When theclusterseparatesfromanothercluster,the area hasastrong te ndency to separatefrom thestableareavoltage wise,
Thus,the stability ind icator1.;is ableto characterise the load flow solution andthe potential of the systemto become unstable.This is bound to the load flow modeland the assumption of a PQ node,Themodel does not reflect any dynamic behaviour.Theindicator 4is a very strong signal of the dangerous situation, The evaluation(If1.;is also quite simple sinceallrequiredpar ametersareavailablefrom theloadflow solution.
1.6.2MinimumSin gu la r Valu eMethod
As farback in 1975,venlkovetal.16Jhad shown thatitis theJacobian of theload flow equation that characterisesthestead ystatestability limits andthereforeeigenvalues of the Jacobian mayhave a directbearing on any bifurcation of theequilibriumstate,Many subseque ntresearchers havenoted the singularityof theJacobian duringa voltage collapse.
In1988, Tiranuehiter. al.proposed a globalvoltage stabilityindex based on theminimum singularvalueof theJacobian[l3 ).One ofthe most importantaspects to be examinedwhen deriving corrective control measures is the question"how closeistheJacobianto being slnguler?". Tiranue hitctel.showed thata measure of thenearness of amatrixAto sing ularityis its minimumsingularval ue.Hence.the minimum singular valuecan givea measure of the nearnessto instability orin otherwords, a'distance' to collapse.Ifthe minimumsingularvalueis plottedagainst real power,it is seen that the minimum singular value is very sensitiveto change inloadnear the steady staleboundary.Oncdisadvan tage (Ifthis method.as pointed out by theauthors themse lves,isthelarge CPU limerequiredfor thecomputationof the minimumsingularvaluefor large systems.Themoreimportantuse
16
of this index istherelation it provides for control.If var compensationeither through shunt capacitors ofexcitation control is available, this indexprovides the answerto the problem ofhowto distributethe resourcesthroughoutthe system for maximumbenefit.
At aboutthesame time,Lof,ArnborgandAndersonproposeda similarindex,albeit withsome modifications(l4).They contended that the minimumsingular value ofasuh matrixG.of the Jacobian J canbeused, whereG.describestheeffectonthe voltage magnitude of change inreactivepowerinjectionin thenetwork. This matrix OJis essentially asubmatrix of theJacobianJwithsome modifications. They showed thatthe minimumsingularvalue ofO.isamorereliablestaticvoltagestabilityindex.It isshown thatthepowerflowJacobian becomessingularwhen thematrixOJbecomessingular.When the minimumsingularvalue oftheJacobian J andthesub matrix G.areplotted againstthe activepower. it isseenthat it couldbecome difficulttouse theminimum singularvalue of theJacobianJ todeterminehowfar the conditionsof the systemare deterioratedwhenthe load isincreased.The minimumsingularvalue ofJcouldbedependentonstatic angle stabilityproblems atfirstand hencecouldbefairlyconstantbefore itsuddenly startsto decreasemuchmore rapidlywhen voltageproblemsbecome more dominant.Lofet.al.
contend that the use of thematrix J is appropriatefor theconstruction of astaticstability indexwhen the cause of instabilitycouldbe either angleorvoltage problems.The minimum singularvalue of matrixGJis a betterbasisfora staticvoltagestabilityindexforplanning and systemstudies.
1.6.3 EnergyFunction AnalystsMethods
Energy functions havelong been used inpowersystem angle stabilityand arenow wellestablished{1~J.They are consideredareliablemeansof obtaining the criticalclearing time: in large powersystems.Asmentionedearlier,Tamura et.aI.hadshownthe relationshipbetweenmultipleloadflow solutionsandvoltageinstability.They showed that though a powerflow may havea numberof solutions.onlyonesolution is an'operable' solutionorstableequilibriumpoint.The othersolutionsareunstableequilibrium points.
These solutionsarealso called low voltagesolutions.Tamurashowed thatas the load 17
increases, the number of lowvoltage solutions decrease until near the pointof collapsea pairof closesolutio ns are obtained.TheJacobian atthisstage approaches singularity. De Marco and Overbye[16· 18Jdefined anenergy function (similar to the Lyapunovfunction), whichrelatesthe system busvoltagemagnitudesand phaseangleswith thepropertythat the operablesolution definesalocal minimum of this energy. Theenergy function shows the energy differencebetweenthe operablesolution and thelow volta gesolution.Asthe system loadincreases andthesystem movestowards collapse.it isseen thatthe energydifference decreases and becomes zero at the poimof collapse.Theenergydifferencebetween thehigh voltage andlow voltage solutio ncangive an indicationofthesyste ms vulnerabilityto voltage collapse.Animportant aspect of the energyfunctionmethod is that itshows how load varia tions can pushthesyste m intoinstability[16-181. YARlimitsongenerators can also be incorporated in this function.sincetheene rgy functionisessentially based on the loadflow solution.Theplot ofenergy measureagainstloadisavaluableindicatorofthe proximity of thesystem to collapse.Theonlycomputation requirementisthedetennination of thelowvoltagesolutions, which for large networks maybetimeconsumi ng. This approachindeedshowspromise of becoming a valuable indexifcertain otherparameters like effectof transfonner tap changer, voltage dependency of loadsetc.aretakeninto account.
As incidentsof voltageinstability becomemorecommon andsystems continueto beloaded closer 10 their stability limits,it becomesimperativethatsystemope ratorsbe provided with tools thetcanidentifypotentially dangeroussituationsleadingtovoltage collapse.Voltagestabilityindicesare valuable andpowerfultools forsystem operators in evaluating the voltage stabilityof apowersystem. However,it shouldbenoted that ifa voltage stabilityindexisto be reallyuseful, itshould be implemented on • linein an Energy ManagementSystem (EMS).This will allow system operatorsto continuouslymon itorthe voltage stability indexof a powersystem andswiftlyreact toany conditionsthat may trigger avoltage collapse. But,the on-line implemen tationofa voltage stability index. presents manychallenges.theprincipalamongthembeingthecomputational burden imposedon the EMS. Thisis because mostof the voltage stability indicesare computationintensiveand for
18
powersystems of realisticsize,thecomputationalburdenmayuse uprneehofthecapability of lheEMS.
1.7 App licationor ArtifldalNruralNeh 'orks
Asindicated earlier, perhapsthe roes important aspect ofapractical voltage stability index isthecomputation.effort andhencethespeedofcomputationinvolved.This isbecause forthelarge,reallifepowersystemswiththousandsofbuses. computation speed becomes a criticalfactorwhen an on line calculationofthestabilityindex is requiredThis on-line response isimportant so that the operators can takecorrectivestepsifanabnormal situationis encounteredandsteerthesystemawayfrom collapse.All themethodslisted above arecomputationallyintensive,when largesystems are considered.Itthenbecomes necessarytolookatotheralternative approaches to minimisecomputationalburden and responsetime.Artificialneural networkshave wide interestintlK. fieldofpower engineeringandapplicationshave beenreportedfromalmostallfieldsof powerengineering 121-23J.TheartificialneuralnetworkIsessentially a pattern recognitiontool.Itcanbe tnlined torecognisecomplex.nonlinear relationshipsbetween anumber ofdiffm:nt parameters.TberesponsetimeofatrainedAA'NisextremelyfMt, since there areno complucomputations involved.Thus,insituations whereaswiftresponse:isrequired.asin thecase of powersystem voltagestabilityindex,anANNbasedapproachcan provean enrecnvealternativetothecomputationally intensivealculation of the index.1beaccuracy oftheANN"spredictionswhile depending Il'rgelyonthequalityof training. hasprovedto bequiteacceptable for otherpowersystem applicationlikeload forecasting,dynamic securityanalysisandtransientstability.
1.8.Slgnlfltanceof Artificial NeuralNetworksIn Modem PowerSystemControl Themodempowersystemhasbecomeverycomplexandoperatesundera great deal of constraints.Ontheonehand,the gent-i':.!.economicdepression hasforcedmany utilities to cutbackon theirexpansionandmodernisationplans.but on the otherhand there lsno noticeabledecline inloadgrowth.Also,the consumerdemandfor efficiency and
19
reliabilityhas never been higher.Environmental and ecological factors have also contributedto makingthe expansionof power systems a time consumingprocess. Thus, throughthenineties and beyond,thescenarioforpower system plannersand designers is grim:they haveto maintainvery highstandards of systemreliabilityandefficiencywith fewerresourcesto doit.
1.9The EnergyMsns r:;emenlSystem
The complexityand size ofthemodem power systemhas given riseto a number of problems.These problemscansignificanUy affectsystemsecurityand efficiency,two of the most important aspectsof modem powersystems.One of the mostimportant tools forthe power system designer and operatorin maintaining a high level of system security is the EnergyManagementSystem(EMS).TheEMSis anupgradedversionoftheSupervisory Control andData Acquisition(SCADA)systems which have beenin service for quite a long time.In additionto performingroutinecontrol functions of SCADA. theEMShas enhancedcapabilitiesforon-linemonitoringofthe powersystemandperforming such tasks as unit commitmentand generationscheduling,optimalpower flow,contingencyanalysis, securityassessment.energyexchangebetweenutilities, stateestimation.load forecasting etc.Thus. it can be seenthat the EMS is a veryimportant aspect of modempowersystem controland operation.Thelinking of protection.control and other devicesthrough a local data communications networkhas enabled thecontrolof entire substationsfroma central host computer.The EMShasmade possiblethe analysis. controland operationoflarge powersystemsfrom a central locationand dramaticallyimprovedthe efficiency.reliability andco-ordinatedoperationof modempowersystems.
1.10 Aim ort heThesis
Oneof the major stumblingblocksto on-linecontrol of powersystemsthroughan EMS isthe heavy computationalburdenimposed by most power system analysissoftware.
Thus. computationspeed, whichintum depends on the computerhardwarespecifications. is the decidingfactor, whichdetermines the on-lineimplementation of power system
20
functions.Theinitialinvestmentsrequired for sophisticated computingequipment areso high thatin mos t cases,utilitiesarenotable to afford them. This prompted researchersto lookat alternativesto raw computing power.Asdescribed intheprevious section.ANNs hold out considerable promise asamediumforon-line implementationofmanyEMS functionssuchastransientstabilityand voltagestability analysis.TIle response of atrained ANNtoaninputisextremelyfast. and the memoryrequirement ofanANNbasedsystemis considerably lowerthanthat of aconventionalsequentialprogram.Also.sincepower systemconditionsarearesult ofsystemloadingswhichforma pattern.the pattern recognitionabilityofANNswouldbea valuable 1001in identifying the systemloading condition swhichcan leadtoabnonnal systemoperation.AnANNbased systemwouldnot require additionaldata acquisitionequipment andtherefore.the overall benefitsboth froma standpointof computing speed, and economywouldbeconsiderable.An ANN based system inconjunctionwithan expertIfuzzylogicsystem, willresult in the goal of an intelligent contro lcentre.whichC'\J\resultin increased reliability,economyandefficiency of operation.
TIllsworkexplores the applicationof ANNsfor assessment ofvoltagestabilityof power systems. Simulations areperfonned on standardlest powersystemsfortwodifferent voltage stabilityindices.andresultsarepresented ontheaccuracy of thepredictionsofthe ANN basedsystemfor both theindices.Anatte mpt has alsobeen madeto map the network topology in terms ofaneuraJnetwork.
1.11Thesis Organisation
Thisthesis consistsofsevenchapters.Chapter two presentsanoverviewof artificial neural networks andtheir applicatio ns to powersystems.Chapterthreepresentstheenergy function basedvoltagestability indexand simulationresultson twobus.five bus and twenty four bus powersystems.Chapter four presentsanartificialneuralnetworkbased energymargin voltagestabilityindicator.Chapter five includesdescriptionof the load margin basedvoltagestability index andalso simulation results ontheNew England39bus systemandalsotheIEEE 24 bussystem. Chaptersixpresentsartificialneural net work
2\
basedmodelsfocthe39 bus systemandalsothe: 24busSysICm, one withlineoutagesand theother without,Tbechapleralsoproposesan ANN model whichtalcesinto eccocntthe:
networktopology.Chapter seven concludestbe thesiswith somesuggestionsfor further researchinthisarea.
22
Chapter 2
Application of Ar tificial Neural Networks to Power Systems
2.1 Introduction
Artificial Neural Networks have aroused wideinterest indifferent branches of engineering.Thisis because artificial neural networks(ANNs) have several properties thatmake them attractive toolsin engineeringapplications.The importantproperties are parallel distributed processing,high computalionrates, faulttolerance, and adaptive capability.The areas in whichANNsare widelyappliedincludecontrolsystems,robotics, and recentlyin power system engineering. Thischapter presentsthebasic conceptsof ANNsand their applicationto powersystemengineering.
2.2 ArllndalNeura lNetworks
Anartificialneuralnetwork can be definedas ahighlyconnected array of elementary processorsor neurons(19-20J. Neurons are linked with otherneuronswith interconnectsanalogoustothe biologicalsynapse. Thishighly connected array of elementary processorsdefines the systemhardware.
Several neural network algorithms havebeen proposed.which haveenabled researchers to apply neural networks to a widerange of engineering problems. The neural network derivesitscomputingpowerthrough,first,its massivelyparalleldistributed structureand, second, its ability10 learnand therefore generalize. Generalizationrefersto the neuralnetwork producing reasonableoutputsfor inputs not encountered during training.Theuse ofneural networks offersthefoHewingusefulpropcnies and capabilities:
23
I.Nonlinearity :A neuron is basically a nonlineardevice.Consequently. a neural network.made up of a numberof neurons is itself nonlinear.Nonlinearity is ahighly usefulproperty,panicularly,if the system generating the inputitself is nonlinear.
2.Input-Output Mapping:The neuralnetworkcanbetrained to recognize me hidden relationshipbetweenthe input and output. The relationship between the input parameters andtheoutput(s)maybenonlinear innature.
3.Adaptivity: Neural Networks have a built-incapabilityto adapt theirsynaptic weights to changes in the sorrounding environment.In particular.aneural network trained to operate in a specific environment canbeeasilyretrained to deal with minorchanges in theoperatingenvironmentconditions.Examplesof adaptiveneuralnetworks are the ARTl.and ART2algorithms.
4.FaultTolerance:A neuralnetwork,implementedin hardware form,has the potential tobeinherentlyfaulttolerant inthe sense that its performanceis degraded gracefully underadverse operatingconditions.For example. if a neuron or its connecting links are damaged.recallofa stored patternisimpaired in quality.However, owingto the distributednature ofinformation in the network.the damage has to be extensive before the overallresponseofthe systemis degraded seriously.
5.VLSI tmplernentability:The massively parallel natureof the reural networkmakesit potentiallyfast for the computationof certain tasks.This same feature makes the neural networkideallysuited forimplementation using VLSItechniques.The particular virtue of VLSI is that it provides a meansof capturing trulycomplex behaviourin a highly heirarchial fashion whichmakesit possible to usc a neuralnetwork as a tool for real time applications involving pauem recognition. signalprocessing and control.
6. UniformityofAnalysis and Design:Basically.neuralnetworksenjoyuniversality as infonnationprocessors. This isbecause the same notation isused in all the domains involvingthe applicationof neural networks.This feature manifestsitself indifferent ways:
Neurons. in one fonn or another,representan ingredientcommonto all neural networks
24
b. This commonality makesitpossibleto sharetheoriesandleami ngalgorithms in differentapplicatio ns ofneural netwo rks.
c. Modularnetw orkscan be builtthroughaseer-cessintegrationof modules.
Though theadvantagesofne ural netw orkaremany andvaried. it doeshave some serious Iimhatanon s,whenapplied torealwo rldsituations, Themost serious limit ation of anartifici al neural networksuucrureseems tobethelackoftools or guidelinesto arrive atanoptimumneural architecture . Thesize andthe numberof layersvary with applicationandarriving atanoptimumarchitec ture is oftenbasedontheusers experience andintuiti on,Ano ther serio us draw back withANNsolutionsis thepossibilityoflocal minima solutions,Presently, thereisno conclusivewayoftestingifthe networkhas indeedsettled downto a global minimum. This wouldbeespeciallytrue forcomplex problemswherethe remay existcomp lex hypc rsurfaceswiththe associated possib ility of manylocal minima.
2.2.1 Models of a Neuron
Aneuron isaninforma tionprocessing unit thatis fundamen tal to the operationof a neuralnetwork.There arethreebasic elem entsofthene uronmode l,as described below:
I. A setofsynapses orco nnectinglinks,each of which is characterize d byaweightor strengthof itsown, Specifically,a signal xJ at theinputof synapsejconnected to neuron kismultip liedby thesynapticweightWkj'
2,An adderforsummi ng the inputsignals,weightedbytherespective synapsesofthe neuron.The operatio nsdescri bed he re constitutea linearcombiner.
3.An activationfunctionforlimitingtheamplitudeofthe outputofaneuron, Inmathe ma tical terms , we maydescr ibe a neuronkby writing thefollowing pairs of equations:
(2.1)
""d
25
whereXI. X 2, Xp arcthe inputsignals;wei ,Wu,. • Wkparethe synapticweightsof neuronk,Ukisthe linearcombineroutput,9kis thethreshold,cpisthe activation functionand Yk is the output signalof the neuron.
Figure2.1showstho:modelof a neuron.Inthefigure,x istheinput,w is the connection weight,I isthe summingjunction.
e
is thethreshold.cp is theactivation functionandy.the output.
" ~
cp, Activation function
x
Fig.2.1Non linearmodelofa neuron.
2.2.2Types ofactlva rlcn functions
Theactivationfunction.denotedbycp.definestheoutput ofaneuron interms of theactivitylevelatits input.Wecan identifytwo basictypes ofactivation cuuctions: I.Thresholdfunctions:For thistypeofactivation function.wehave
q>(v)=II ifv~0 10 ifvs0
Correspondingly. the output of neuronkemploying such a threshold functionis expressed
Yk '"II ifvk~0 { 0 ifv.<0
26
whereVkis the internal activitylevel ofthe neuron; that is,
Vk=
, fwkJXJ-O, .,
Figure2.2illustrates the thresholdfunction.
Fig.2.2Thresholdfunction
(2.3)
2. SigmoidFunction: Thesigmoid functionisbyfarthe mostcommon formof activationfunctionusedintheconstruction of artificial neuralnetworks.Itis defined asa strictlyincreasingfunctionthatexhibits smoothnessand asymptoticproperties. An exampleofthesigmoidis thelogistic function,definedby
lPk= I+exp~-av) (2.4)
where a isthe slope parameter ofthe sigmoidfunction.By varying the parametera, we obtainsigmoidfunctions of differentslopes.Inthe limit.as the stope parameter approaches infinity,thesigmoidfunction becomessimplya thresholdfunction.Whereas a thresholdfunctionassumesa valueof 0 orI,thesigmoidfunctionassumes a continuousrange of values from0toI.Figure2.3shows theS shapedsigmoidfunction.
27
Fig. 2.3 Sigmoid Function
2.2.3Network Arch itect ures
The manner inwhich theneurons are structuredis intimately linked with the learningalgorithmused10trainthenetwork.Ingeneral.there arefour types of network architectures[19]:
1. Single-La yer Feed-forwardNelwor ks
Alayered neural network is a network of neuronsorganized inthefonn oflayers.
In thesimplestform of alayered network,we just have an inputlayer of sourcenodes that projects onto anoutputlayer of neurons butnot vice versa.Inother words, this networkis strictlyof the feedforwardtype. Such a networkis called a single layer network,referring to the outputlayer of computationalnodes(neurons).Inotherwords.we do not count the inputlayerof sourcenodes,because no computation is perfonned there.
Figure2.4illustrates the structureofasimplesinglelayernetworkconsisting of the input layerandlhe output layer.
28
Inputlayer Outputlayer
Fig. 2.4 Feedforw ardnetwo rkwitha single layer
2.Multilayerfeedrorward networks
The second clas s offeed forward neuralnetwork distinguishesitselfbyth e presence of oneor morehiddenlayers,whose computation nodes are correspo nding ly called hiddenneu rons or hiddenunits.Thefunctio nofhid den neuronsistointervene betweentheexte rn alinput andthenetwork output.Byaddingone ormore hidden layers.
the netw o rk is ab leto ex tract higherorder statistic s.forthenetwork acquiresa glob al perspecti vedesp i teits localconnecti vitybyvirtueof the extrasetof syna pticcon nections andthe extra dimensionofneural interactions.The abilityof hiddenneurons toextrac t complex nonlinearpatte rns isparticularlyvaluablewhenthesizeof the inpu t layer is large.Thesource layers of the input layerof thenetwork supply respectiveelementsof theactiv ation pattern (in putvector) which constitu tetheinput signal sappliedtothe neurons in thesecond layer(i.e.• the firsthidden layer) .Theoutput ofthe second layerare usedas inputs for the third layer.andsoon fortherest of the network .Thesetof output signals of the neu rons in the output (final)Jayercon stitutestheoveral lresponseofthe network to the ac tivation patternsuppliedbytheinput layer.
Figure 2.5 illustrates a sim ple multilayernetwork.consistingof an inp u t layer.a hidden layer andanoutputlayer.
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Input laye r HiddenLayer Outputlayer
Fig.2.S.Simp le multila yer network topology.
3. RecurrenlNetworks
Arecurren t neuralnetworkdistinguishes itself fromafeedforward neural network in thatit hasatleastonefe edbackloop.Forexample.a recurren t network mayconsist of asinglelayer of neurons witheach neuron fee ding itsoutput signalbackto theinputs of all theotherneurons. A recurrentnetworkmayalsobeof the muhilayeredtype.with feedbackconnections orig i nating from both thehidde nunits and theoutput units.Figure 2.6 illustrate s a si m plerecurrentnetwork cons isting of an input layer.anoutput layer and afeedback toop.
feedback loop
6~o=J
Input layer Outputlayer
Fig.2.6 Asimple recurrentnetwork.
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4. Lattice Structure
A lattice consists of a one dimensional, two dimensional or higher dimensional array of neurons witha corresponding set of source nodes that supply the input signals to thearray; the dimension of the lattice refers to the number of the dimensions of the space in which the graph lies.Alattice neural network is really a feedforward network withthe output neurons arranged in rows and columns.
2.2.4NeuralNetwork Algori thms
The most important property of a neural network is itsability to 'learn',Learning maybe definedas a process by which the free parameters of a neural network are adapted through a continuingprocess of stimulation by theenviro nment in which the network is embedded.Thetwo main types of learning algorithms are supervised learning and unsupervisedleaming.Supervised learning is performed under the supervisionof an external'teacher'. Unsupervised learning isperformedin aself organised mannerin that no external teacher is required to instructsynaptic changes in the network.A popular example of supervised learningis the error back propagation algorithm, while the KohonenNetwork isngood exampleof the unsupervised learning,Table 2.1 below gives comparison of the features of different neural network algorithms [19].
In table 2,1below,the following abbreviations are used:
BPN:Back Propagation Network BAM:Bi-Directional Associative Memory CPN:Counter Propagation Network SOM:Self Organizing Map STN:Spatio Temporal Network ART:Adaptive Resonance Theory
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Table2.1Compara tiveperformanceof differe ntANNalgorithms
Type or Trainin g Ce nain ity Typ< ofDomain Ability of Purpose
ANN time to reach input inp u t report ;r
glo bal panem pattern mismatch
minimum occurs
BPN Modera te No Analng Spa Ual No General
BAM Low No Digital Sp atial No General
Hopfi eld Low No Digital Spa t ial No Gene ral
CPN Low No Digital Spatial No General
SOM Moderate No Analog Spatial No General
STN Moderate No Analog Tem poral No Speech
ART Low Possible Analog Spa llal Yes General
Bolt z mann High No DigItal Spatial No General
Z.3 BackPropagatio nAlgorilhm
Thedevelopmentof the back propagation(HP)algorithmre presentsa landmarkin neuralnetworksinthatitprovides a computational lyefficientmethodfor thetrainingof multilaye rpercepucns.Thebasic ideaof back propagationwasfirstproposedbyWe rbos in 1974(21]andsubsequentlypopularisedby Rume lhart et.al, [22J.
Backp ropagationisone ofthe mostpopular algorithmsin use today.This ispanly duetoIts simplicity,andapplica bility10 a widevariety of engineeringprob lems. Back propagationis ideal for complexpatternmatchin gproble ms.The basic wo rkingofthe algori thmcanbesummarizedas follows.The networklearnsapredefinedsetofinput- outputexamplepairsby using atwopha se propagate-adaptcycle.Afteraninp utpatt ern hasbeenapplie dasastim ulus to thefirstlayer of network units, itispropagated through each up perlaye r untilanoutputis generated.Thiscutput isthen compared tothe desire d output.and anerror signalis co mputed for each output unit. Theerror signalsarethe n
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trans mittedbackwardformtheoutput layer toeach node inthe intermediate layerthat contributeddirectlyto the output.However,eac h unitin the intermediate layer receives onl ya portio nof thetotalerrorsignal.roughlybased on the relativecontri b ution the unit made to theoriginaloutput.This processrepeats,layerbylayer,until eachnode inthe network hasreceived an errorsignal thatdescribesits relativecontribution to thetotal error.Basedontheerror signalreceive d.connect ionweightsarethenupda ted byeach unittocausethe netwo rk to convergetow arda statethatallowsallthetrain ingpatternsto be encoded.
Thesignifican ceofthe processis that,asthenetworktrains, the nodes inthe intermediate layersorganizethemselve s such thai diffe rentnodeslearnto recognize diffe rent featuresof thetotalinput space,Aftertraining,whenpresentedwithanarbitrary inpu tpattern that isno isy orInco mplete, the units inme hiddenlaye rsof thenetwork will respondwithan active outputif the new inputcontainsa patternth at resemb lethefe a ture theinidvidualunitsle arnedtorecognizeduring training. Conversely,thehiddenlayer unitshave atendencyto inhib ittheiroutputsif theinput patterndoesnot containthe feature thallhey were trainedto recogniz e .
Asthe signals propagate throughthe diffe rent layers of the networ k . the activity pattern presen tat each uppcrlayer canbethough tofasapatternwith featuresthatcan be reco gn izedby units in the subseq uentlayer. The output patte·....nerated can betho u ght ofas~featuremapthat prov idesan indicationof thepresence orabsenceof many different feature comb inationsatthe input.Thetotal effec tof thisbehavio uristhat tbe BPNprovides an effecti vemeansof allowinga computersystemto examine dan pattens thatmaybein completeor noisy .andtorecognize subtlepatternsfro m thepartial input
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L M Fig. 2.7TypicalArchitectureofa three layerbackpropagationneuralnetwork
Figure2.7showsthetypicalarchitectureof a threelayer BPnetwork.Theinputlayerhas unitsfrom(1•...•••.i.; N);the hiddenlayer has (1 j , L)units. the output layerhas(I, k M)units,The inputuni tsdisuibutethe valuesto thehidden layerunits.The netinputto thej-thhiddenunitis
(2.5)
wherew~isthe weighton theconnectionfromthei-fh input unit, ande~is a biasterm.
This termis aweight onaconnec tion thathasitsinputvaluealwaysequaltoI.Theuse of the bias term islargely optional.The'h'superscriptrefers to quantitiesonthehidde n
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layer.Assumingthat theactivation ofthis node is equaltothenetinput; then,theoutput of this node is
(2.6 )
wheref represents the functionadopted.egosigmoidal.gaussian.linear etc.
Theequatio n s for the output nodes are
net;'
=±, w :Jipj + O:
I·'
(2.7 )(2.8 ) opk.=J:(net~ )
where thesuperscri pt'0' refersto quantitiesontheoutputlayer.
The errorat asingle outputunit isdefinedtobe5p.;=(ypk- opt).wherethe subscript'p'refers to thep-th training vector,and'k'refersto thek-th output unit.Inthis case,Y~kisthe desired v.Jue.and opkisthe actualoutput fromthe k-thunit
The variousste psinvol vedin the backpropagationalgorithmaresummarized below.
Applytheinpu tvector,x~'"(:t~h:t~J, '•••. .• ..•xpNitotheinputunits 2. Calcu latethenet-input values to the hidden layerunits:
nelpjh =t.W~Xpl+O~ (2.9)
3. Calcu la tetheoutputsfromthehidden layer:
ipi =fJ(nethpJ) (2.10)
4. Movetotheoutputlayer.Calculatethenet- input valuestoeach unit:
S. Calcu la teIhe outputs:
Opk
=
fkO(netpko)35
(2.11)
(2.12)
