POWER SYSTEM DYNAMICS AND STABILITY

1 IPOWERSYSTEMDYNAMICSANDSTABILITYP eter W. Sauerand M. A. PaiDepartment of Electricaland ComputerEngineeringTheUniversity of Illinoisat Urbana-Champaign1406W. ,IL 61801iiCopyrightc 1997(updated2006), theproperty of andis notto be sold,reproduced,or .. Interest..62 ..203 ..614 ..865 .. Stator/NetworkTransients.. (Flux-Decay) Model.. 1176 .. Stator/NetworkTransients.. {Decay Model.. niteBus.. 1527 erential-AlgebraicModel.. statoralgebraicequations.. cationof theTwo-AxisModel.. (FullModel).. : POWER -BalanceForm.. Method .. :Current-BalanceForm.. model.. 2118 .. ModelA.. ModelB.. ects.. ectof loading.. ectofKA.. ectof type of load.}

2 SystemStabilizers.. K6 constants [78,88].. systemstabilizerdesign.. 2709 .. 'sMethod.. (PEBS).. nite-bussystem.. single-machinein .. E( ) anditsusein (BCU)Method .. 313A .. 327 Bibliography333 CONTENTSixxCONTENTSPREFACET heneedforpower systemdynamicanalysishasgrownsigni cantlyinrecent duelargelyto thedesireto utilizetransmissionnetworksformore beenstudiedforyearsin a long-termplanninganddesignenvironment,th ereis a recognizedneedto performthisanalysisin a weeklyor even devotedtodynamicmodelingandsimulationasi t relatestosuch a need,combiningtheoreticalaswellaspractic alinformationforuseas a textforformalinstructionor forreferenceby textforformalinstruction,thisbookassumes a backgroundinelectromechanics,machines,an dpower , thetextwouldnormallybe usedin a graduatecoursein hasbeendesignedforusein a one-semester( fteen-week)

3 , mosttraditionalmachineandpower systemanalysisbooksandattemptsto follow theindustrystandardsso thata tran-sitionto moredetailandpracticalapplicationis dividedinto two to 6 give anin-troductionto electromagnetictransient analysisanda systematicderivationof rigorousexplanationof modelorigins,development, andsimpli givento thecon-ceptof reduced-ordermodelingusingintegralmanifo ldsas a rmbasisforunderstandingthederivationsand limitationsof a mathematicalintroductionto thistechniqueof to 9 utilizethesedynamicmodelsforsimulationan dstability givento thecalculationof initialconditionsandthealternative analysisis presentedin a sequentialxixiiPREFACE manner,concludingwiththedesignof POWER analysisis formulatedusingenergyfunctionmethods withanem-phasisontheessentialsof thepotentialenergyboundarysurfaceandthec ontrollingunstableequilibriumpoint notclaimto be a completecollectionof allmodelsandsimulationtechniques,butseek sto providea basicunderstandingof moredetailedandaccuratemodelsexistin theliterature,a majorgoalof thisbookis toexplainhow individualcomponent modelsareinterfacedfora systemstudy.

4 Ourobjective is toprovidea rmtheoreticalfoundationforpower systemdynamicanalysistoserve as a startingpoint fordeeper explorationof complexphenomenaandapplicationsin electricpower have so many peopleto acknowledgefortheirassistancein ourcareersandlives thatwe willlimitourlistto sixpeoplewhohave hada directimpacton theUniversity of Illinoispower programandthepreparationof thisbook:StanHelm,forhisdevotionto thepower areaof electricalengineeringforoversixty years;GeorgeSwenson,forhisleadershipin strengtheningthepowerareain thedepartment; MacVanValkenburg,forhisfatherlywisdomand guidance;DavidGrainger,forhis nancialsupportof thepower program;PetarKokotovic,forhisinspiration andenergeticdiscussions;andKarenChitwood , yearsof collaborationat theUniversity of Illinois,we have strivedto maintaina healthy balancebetweeneducationandre-search.

5 We thanktheUniversity , systemshave evolved fromtheoriginalcentralgeneratingstationc on-ceptto a modernhighlyinterconnectedsystemwithimpr ovedtechnologiesa ectingeach partof thesystemseparately. Thetechniquesforanalysisofpower systemshave beena ectedmostdrasticallyby thematurity of otherdisciplineswithinelectricalengineer ing,thefoundationsof theanalysisareoftenhiddenin assumptionsandmeth-ods thathave resultedfromyearsof ,we have a hostof techniquesandmodelsmixedwiththeartof powerengineeringand,at theotherextreme,we have sophisticatedcontrolsystemsrequiringrigo roussystemtheory. It is necessaryto strike a balancebetweenthesetwo extremesso thisbookis to seeksuch a middlegroundin theareaof modelingandsimulationliesintheneedto capture(withminimalsizeandcomplexity) the\phenomenaofinterest.

6 "Thesephenomenamustbe understood beforee ective simulationcanbe POWER systemdynamicsandstability is clearlyanex-tremelybroadtopicwitha longhistoryandvolumesof ways to divideandcategorizethissubjectforbothedu cationandresearch. Whilea substantialamount of informationaboutthedynamicbehaviorof POWER systemscanbe gainedthroughexperienceworkingwithandtes tingindividualpiecesof equipment, thecomplexproblemsandoper-atingpractices of largeinterconnectedsystemscanbe betterunderstood if12 CHAPTER1. INTRODUCTION thisexperienceis coupledwitha as transient networkanalyzershave a valuein providinga physicalfeel-ingforthedynamicresponseof POWER systems,buttheyarelimitedto smallsizesandarenot exibleenoughto a placein thestudyof systemdynamics,capability and exibility have thestudyof POWER systemdynam-icsandstability [1].

7 DeMelloclassi eddynamicprocessesinto threecategories:1. Electricalmachineandsystemdynamics2. Systemgoverningandgenerationcontrol3. Prime-mover energysupplydynamicsandcontrolIn thesamereference,C. ConcordiaandR. P. Schulzclassifydynamicstudiesaccordingto fourconcepts:1. Thetimeof thesystemcondition:past,present, or future2. Thetimerangeof thestudy:microsecondthroughhourlyrespons e3. Thenatureof thesystemunderstudy:newstation,newline, Thetechnicalscope of thestudy:faultanalysis,loadshedding,sub- synchronousresonance, theseclassi cationssharea commonthread:Theyemphasizethatthesystemi s notin steadystateandthatmany modelsforvariouscom-ponents mustbe usedin varyingdegreesof detailtoallow e cient rsthalfof thisbookis thus devotedto thesubjectof modeling,andthesecondhalfis devotedtotheuseof anexhaustivetreatment.

8 Rather,fundamentalconceptsarepresentedas a foundationforprobingdeeper into thevastnumber of important andinterestingdynamicphenomenain POWER of a POWER systemcanbe representedin a block-diagramformat,asshownin , iFuelSourceFurnace&BoilerTurbineGenerato rNetworkLoadsEnergyControlCenterP, :Systemdynamicstructureresentationdoes notshow allof thecomplexdynamicinteractionbetweencompo nents andtheircontrols,it serves to broadlydescribe , therehasbeena majordivisioninto themechanicalandelectricalsubsystemsas notabsolute,however,sincetheelectricalsi declearlycontainscomponents withmechan-icaldynamics(tap-changing-und er-load(TCUL)transformers,motorloads,etc .)andthemechanicalsideclearlycontainscom ponents withelectricaldy-namics(auxiliarymotordr ives,processcontrols,etc.)

9 Furthermore,bothsidesarecoupledthroughth emonitoringandcontrolfunctionsof classi cationof dynamicphenomenais theirnaturaltimerangeof typicalclassi cationis shownin similarconceptis presentedin [6].Thistime-rangeclassi cationis important becauseof itsimpactoncomponent shouldbeintuitivelyobviousthatit is notnecessaryto solve thecomplextransmissionlinewave equationsto investigatetheimpactof a changein minda statement madeearlierthat\thesystemis notin steadystate."Evidently, dependingonthenatureof thedynamic4 CHAPTER1. INTRODUCTIONL ightning PropagationSwitching SurgesStator Transients andSubsynchronous ResonanceTransientStabilityGovernor and LoadFrequency ControlBoiler and Long-Term Dynamics10 710 510 (sec) :Timerangesof dynamicphenomenadisturbance,portionsof thepower systemcanbe consideredin \quasi-steadystate.

10 "Thisratherambiguoustermwillbe explainedfullyin thecontextoftime-scalemodeling[2]. cationsof dynamicphenomenaillustratethepotentialco mplexity of even smallor POWER systemdynamicsandstability arecompoundedim-menselyby thecurrent sizeof generalsystemstructureis shownin notnecessarilycom-monto interconnectedsystemsthroughouttheworld, it represents a typicalNorthAmericansystemandserves to illustratetheconceptof a \large-scalesystem."If we speculateaboutthepossiblesizeof a singleinterconnectedsystemcontainingnine coordinatingcouncils,fourpoolsper 20 GeneratorsPool2 10 CompaniesCoordinatingCouncil 3 5 PoolsInternational9 :Systemorganizationalstructurecouncil,si xcompaniesper pool,andtengeneratorsper company, thetotalpossiblenumber of (138{765kV)thentypicallyconsistsof over 10, ,thecurrent demandin theninecoordinatingcouncilswithintheNort hAmericanElectricReliability Council(NERC)exceeds500,000MW[3].}