新增课文2水轮机数学模型.docx
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新增课文2水轮机数学模型.docx
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新增课文2水轮机数学模型
HydraulicTurbineAndTurbineControlModelsForSystemDynamicStudies
INTRODUCTION
The1973IEEECommitteereportDynamicModelsforSteamandHydroTurbinesinPowerSystemStudies
(1)hasbeenusedwidely.Evenin1973,however,itwasrealizedthatmoreworkneededtobedone.Sincethen,modelingrequirementshaveincreasedgreatlyandmoredetailedmodelshavebeenimplementedintheadvancedsimulationprograms.Theoldermodelswereconsideredadequatefortypicalfirstswingstabilitysimulationscommonintheearly70s.Nowadays,modelsforthefollowingtypesofstudiesarealsoneeded:
●Longertransientstabilityprogramsimulation-uptoandbeyondtensecondsarenowroutine.Inthislongertimeframe,primemoverandprimemoveractioncanaffectresults.
●Lowfrequencyoscillations.
●Islandingandisolatedsystemoperation.
●Systemrestorationfollowingabreak-up.
●Loadrejection.
●Loadacceptance.
●Water-hammerdynamics.
●Pumpstoragegenerationwithcomplexhydraulicstructures.
Otherdevelopmentsrequiringnewmodelsincludethewidespreaduseofelectric-hydraulicspeedcontrolbothinnewconstructionandinmodernizationofolderpowerplants.Itisbettertousemodelsdescribingtheactualequipmentratherthanmakeapproximationstofitexistingmechanicalgovernormodels.Thetremendousincreaseincomputerpowereliminatestheneedforlessdetailedmodels.
Thisreportrecommendshydraulicmodelssuitableforarelativelywiderangeofstudies.Thetwomainsectionsofthereportprovidemodelsfor1)primemoversincludingwatersupplyconduitand2)primemoverspeedcontrols.Thesectiononprimemovermodelsincludesbothlinearandnonlinearcontrols.Non-linearmodelsarerequiredwherespeedandpowerchangesarelarge,suchasinislanding,loadrejection,andsystemrestorationstudies.
TheblockdiagramofFigure1showsthebasicelementsofahydroturbinewithinthepowersystemenvironment.Excludedfromthescopeofthisreportaremodelsforgenerationloadcontrolandelectricalloaddynamics.
Figure1.FunctionalBlockDiagramShowingRelationshipofHydroPrimeMoverSystemandControlstoCompleteSystem
MODELINGOFTURBINECONDUITDYNAMICS
2.1Non-linearModelAssumingaNon-ElasticWaterColumn
TheblockdiagraminFigure2representsthedynamiccharacteristicsofasimplehydraulicturbine,withapehstock,unrestrictedheadandtailrace,andwitheitheraverylargeornosurgetank.
ThepenstockismodeledassuminganincompressiblefluidandarigidconduitoflengthLandcross-sectionA.PenstockheadlosseshlareproportionaltoflowsquaredandfPistheheadlosscoefficient,usuallyignored.
Fromthelawsofmomentum,therateofchangeofflowintheconduitis
Where:
wherehandhlaretheheadattheturbine,andheadlossrespectivelyinperunit,withhbasedefinedasthestaticheadofthewatercolumnabovetheturbine.
Tw,calledwatertimeconstantorwaterstartingtime,isdefinedas:
qbaseischosenastheturbineflowratewithgatesfullyopen(GatepositionG=1)andheadattheturbineequaltohbase.Itshouldbenotedthatthechoiceofbasequantitiesisarbitrary.
Thesystemofbasequantitiesdefinedabovehasthefollowingadvantages:
●Basehead(hbase)iseasilyidentiedasthetotalavailablestatichead(i.e.lakeheadminustailracehead).
●Basegateiseasilyunderstoodasthemaximumgateopening.
Havingestablishedbaseheadandbasegateposition,theturbinecharacteristicsdefinebaseflowthroughtherelationship:
q=f(gate.head)
Theperunitflowratethroughtheturbineisgivenby:
Inanidealturbine,mechanicalpowerisequaltoflowtimesheadwithappropriateconversionfactors.
Thefactthattheturbineisnot100%efficientistakenintoaccountbysubtractingthenoloadflowfromtheactualflowgivingthedifferenceastheeffectiveflowwhich,multipliedbyhead,producesmechanicalpower.Thereisalsoaspeeddeviationdampingeffectwhichisafunctionofgateopening(6).
Perunitturbinepower,Pm,ongeneratorMVAbaseisthusexpressedas:
whereqnlistheperunitno-loadflow,accountingforturbinefixedpowerlosses.Atisaproportionalityfactorandisassumedconstant.ItiscalculatedusingturbineMWratingandgeneratorMVAbase.
wherehristheperunitheadattheturbineatratedflowandqristheperunitflowatratedload.itshouldbenotedthattheperunitgatewouldgenerallybelessthanunityatratedload.
TheparameterAt,definedbyEquation6convertsthegateopeningtoperunitturbinepoweronthevolt-amperebaseofthegeneratorandtakesintoaccounttheturbinegain.Itshouldbenoted,however,thatinsomestabilityprograms,Atisusedtoconverttheactualgatepositiontotheeffectivegateposition,i.e.At=1/(GFL-GNL)asdescribedin(6).Aseparatefactoristhenusedtoconvetthepowerfromtheturbineratedpowerbasetothatofthegeneratorvolt-amperebase.
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