电力系统安全稳定的最新定义kundur_2004

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1、IEEE TRANSACTIONS ON POWER SYSTEMS,VOL.19,NO.2,MAY 20041387Definition and Classificationof Power System StabilityIEEE/CIGRE Joint Task Force on Stability Terms and DefinitionsPrabha Kundur(Canada,Convener),John Paserba(USA,Secretary),Venkat Ajjarapu(USA),Gran Andersson(Switzerland),Anjan Bose(USA),C

2、laudio Canizares(Canada),Nikos Hatziargyriou(Greece),David Hill(Australia),Alex Stankovic(USA),Carson Taylor(USA),Thierry Van Cutsem(Belgium),and Vijay Vittal(USA)AbstractThe problem of defining and classifying powersystem stability has been addressed by several previous CIGREand IEEE Task Force rep

3、orts.These earlier efforts,however,do not completely reflect current industry needs,experiencesand understanding.In particular,the definitions are not preciseand the classifications do not encompass all practical instabilityscenarios.This report developed by a Task Force,set up jointly by theCIGRESt

4、udyCommittee38andtheIEEEPowerSystemDynamicPerformance Committee,addresses the issue of stability definitionand classification in power systems from a fundamental viewpointand closely examines the practical ramifications.The report aimsto define power system stability more precisely,provide a system-

5、aticbasis foritsclassification,anddiscusslinkagestorelatedissuessuch as power system reliability and security.Index TermsFrequency stability,Lyapunov stability,oscilla-tory stability,power system stability,small-signal stability,termsand definitions,transient stability,voltage stability.I.INTRODUCTI

6、ONPOWERsystemstabilityhasbeenrecognizedasanimportantproblemforsecuresystemoperationsincethe1920s1,2.Many major blackouts caused by power system instability haveillustrated the importance of this phenomenon 3.Historically,transient instability has been the dominant stability problem onmost systems,an

7、d has been the focus of much of the industrysattention concerning system stability.As power systems haveevolved through continuing growth in interconnections,use ofnew technologies and controls,and the increased operation inhighly stressed conditions,different forms of system instabilityhaveemerged.

8、Forexample,voltagestability,frequencystabilityand interarea oscillations have become greater concerns thanin the past.This has created a need to review the definition andclassification of power system stability.A clear understandingof different types of instability and how they are interrelatedis es

9、sential for the satisfactory design and operation of powersystems.As well,consistent use of terminology is requiredfor developing system design and operating criteria,standardanalytical tools,and studyprocedures.The problem of defining and classifying power system sta-bility is an old one,and there

10、have been several previous reportsManuscript received July 8,2003.Digital Object Identifier 10.1109/TPWRS.2004.825981on the subject by CIGRE and IEEE Task Forces 47.These,however,do not completely reflect current industry needs,ex-periences,and understanding.In particular,definitions are notprecise

11、and theclassifications do not encompass all practical in-stability scenarios.ThisreportistheresultoflongdeliberationsoftheTaskForceset up jointly by the CIGRE Study Committee 38 and the IEEEPower System Dynamic Performance Committee.Our objec-tives are to:Define power system stability more precisely

12、,inclusive ofall forms.Provide a systematic basis for classifying power systemstability,identifying and defining different categories,andproviding a broad picture of the phenomena.Discuss linkages to related issues such as power systemreliability and security.Power system stability is similar to the

13、 stability of anydynamic system,and has fundamental mathematical under-pinnings.Precise definitions of stability can be found in theliterature dealing with the rigorous mathematical theory ofstability of dynamic systems.Our intent here is to provide aphysically motivated definition of power system s

14、tability whichin broad terms conforms to precise mathematical definitions.The report is organized as follows.In Section II the def-inition of Power System Stability is provided.A detaileddiscussion and elaboration of the definition are presented.The conformance of this definition with the system the

15、oreticdefinitions is established.Section III provides a detailed classi-ficationofpowersystemstability.InSectionIVofthereporttherelationship between the concepts of power system reliability,security,and stability is discussed.A description of how theseterms have been defined and used in practice is

16、also provided.Finally,in Section V definitions and concepts of stability frommathematics and control theory are reviewed to provide back-ground information concerning stability of dynamic systems ingeneral and to establish theoretical connections.The analytical definitions presented in Section V con

17、stitutea key aspect of the report.They provide the mathematical un-derpinnings and bases for the definitions provided in the earliersections.These details are provided at the end of the report sothat interested readers can examine the finer points and assimi-late the mathematical rigor.0885-8950/04$

18、20.00 2004 IEEE1388IEEE TRANSACTIONS ON POWER SYSTEMS,VOL.19,NO.2,MAY 2004II.DEFINITION OFPOWERSYSTEMSTABILITYIn this section,we provide a formal definition of powersystem stability.The intent is to provide a physically baseddefinition which,while conforming to definitions from systemtheory,is easil

19、y understood and readily applied by powersystem engineering practitioners.A.Proposed Definition Power system stability is the ability of an electric powersystem,for a given initial operating condition,to regain astate of operating equilibrium after being subjected to aphysical disturbance,with most

20、system variables boundedso that practically the entire system remains intact.B.Discussion and ElaborationThe definitionapplies to an interconnectedpower systemas awhole.Often,however,the stability of a particular generator orgroup of generators is also of interest.A remote generator maylose stabilit

21、y(synchronism)without cascading instability of themainsystem.Similarly,stabilityofparticularloadsorloadareasmaybeofinterest;motorsmaylosestability(rundownandstall)without cascading instability of the main system.The power system is a highly nonlinear system that oper-ates ina constantly changing env

22、ironment;loads,generatorout-puts and key operating parameters change continually.Whensubjected to a disturbance,the stability of the system dependson the initial operating condition as well as the nature of thedisturbance.Stability of an electric power system is thus a property of thesystem motion a

23、round an equilibrium set,i.e.,the initial op-erating condition.In an equilibrium set,the various opposingforces that exist in the system are equal instantaneously(as inthe case of equilibrium points)or over a cycle(as in the case ofslow cyclical variations due to continuous small fluctuations inload

24、s or aperiodic attractors).Power systems are subjected to a wide range of disturbances,small and large.Small disturbances in the form of load changesoccur continually;the system must be able to adjust to thechanging conditions and operate satisfactorily.It must alsobe able to survive numerous distur

25、bances of a severe nature,such as a short circuit on a transmission line or loss of a largegenerator.A large disturbance may lead to structural changesdue to the isolation of the faulted elements.At an equilibrium set,a power system may be stable for agiven(large)physical disturbance,and unstable fo

26、r another.Itis impractical and uneconomical to design power systems to bestable for every possible disturbance.The design contingenciesare selectedon the basis theyhavea reasonably high probabilityof occurrence.Hence,large-disturbance stability always referstoaspecifieddisturbancescenario.Astableequ

27、ilibriumsetthushas a finite region of attraction;the larger the region,the morerobust the system with respect to large disturbances.The regionof attraction changes with the operating condition of the powersystem.The response of the power system to a disturbance may in-volve much of the equipment.For

28、 instance,a fault on a crit-ical element followed by its isolation by protective relays willcause variations in power flows,network bus voltages,and ma-chine rotor speeds;the voltage variations will actuate both gen-erator and transmission network voltage regulators;the gener-ator speed variations w

29、ill actuate prime mover governors;andthevoltageand frequencyvariationswill affectthesystem loadstovaryingdegreesdependingontheirindividualcharacteristics.Further,devices used to protect individual equipment may re-spond to variations in system variables and cause tripping of theequipment,thereby wea

30、kening the system and possibly leadingto system instability.If following a disturbance the power system is stable,it willreach a new equilibrium state with the system integrity pre-served i.e.,with practically all generators and loads connectedthrough a single contiguous transmission system.Some gen

31、er-ators and loads may be disconnected by the isolation of faultedelementsorintentionaltrippingtopreservethecontinuityofop-eration of bulk of the system.Interconnected systems,for cer-tain severedisturbances,may also be intentionally split into twoor more“islands”to preserve as much of the generatio

32、n andload as possible.The actions of automatic controls and possiblyhuman operators will eventually restore the system to normalstate.On the other hand,if the system is unstable,it will resultin a run-away or run-down situation;for example,a progres-sive increase in angular separation of generator r

33、otors,or a pro-gressive decrease in bus voltages.An unstable system conditioncould lead to cascading outages and a shutdown of a major por-tion of the power system.Power systems are continually experiencing fluctuationsof small magnitudes.However,for assessing stability whensubjected to a specified

34、disturbance,it is usually valid to as-sume that the system is initially in a true steady-state operatingcondition.C.Conformance With SystemTheoretic DefinitionsIn Section II-A,we have formulated the definition by consid-eringagivenoperatingconditionandthesystembeingsubjectedto a physical disturbance

35、.Under these conditions we requirethe system to either regain a new state of operating equilib-rium or return to the original operating condition(if no topo-logicalchangesoccurredinthesystem).Theserequirementsaredirectly correlated to the system-theoretic definition of asymp-totic stability given in

36、 Section V-C-I.It should be recognizedhere that this definition requires the equilibrium to be(a)stablein the sense of Lyapunov,i.e.,all initial conditions starting ina small spherical neighborhood of radiusresult in the systemtrajectory remaining in a cylinder of radiusfor all time,the initial time

37、 which corresponds to all of the system state vari-ables being bounded,and(b)at timethe system trajec-tory approaches the equilibrium point which corresponds to theequilibrium point being attractive.As a result,one observes thatthe analytical definition directly correlates to the expected be-havior

38、in a physical system.III.CLASSIFICATION OFPOWERSYSTEMSTABILITYA typical modern power system is a high-order multivariableprocess whose dynamic response is influenced by a wide arrayof devices with different characteristics and response rates.Sta-KUNDUR et al.:DEFINITION AND CLASSIFICATION OF POWER S

39、YSTEM STABILITY1389bilityisaconditionofequilibriumbetweenopposingforces.De-pending on the network topology,system operating conditionand the form of disturbance,different sets of opposing forcesmay experience sustained imbalance leading to different formsof instability.In this section,we provide a s

40、ystematic basis forclassification of power system stability.A.Need for ClassificationPower system stability is essentially a single problem;however,the various forms of instabilities that a power systemmay undergo cannot be properly understood and effectivelydealt with by treating it as such.Because

41、 of high dimension-ality and complexity of stability problems,it helps to makesimplifying assumptions to analyze specific types of problemsusing an appropriate degree of detail of system representationand appropriate analytical techniques.Analysis of stability,including identifying key factors that

42、contribute to instabilityand devising methods of improving stable operation,is greatlyfacilitated by classification of stability into appropriate cate-gories 8.Classification,therefore,is essential for meaningfulpractical analysis and resolution of power system stabilityproblems.As discussed in Sect

43、ion V-C-I,such classification isentirely justified theoretically by the concept of partial stability911.B.Categories of StabilityThe classification of power system stability proposed here isbased on the following considerations 8:The physical nature of the resulting mode of instability asindicated b

44、y the main system variable in which instabilitycan be observed.The size of the disturbance considered,which influencesthe method of calculation and prediction of stability.The devices,processes,and the time span that must betaken into consideration in order to assess stability.Fig.1 gives the overal

45、l picture of the power system stabilityproblem,identifying its categories and subcategories.The fol-lowing are descriptions of the corresponding forms of stabilityphenomena.B.1 Rotor Angle Stability:Rotor angle stability refers to the ability of synchronous ma-chines of an interconnected power syste

46、m to remain in synchro-nism after being subjected to a disturbance.It depends on theabilitytomaintain/restoreequilibriumbetweenelectromagnetictorque and mechanical torque of each synchronous machine inthe system.Instability that may result occurs in the form of in-creasing angular swings of some gen

47、erators leading to their lossof synchronism with other generators.The rotor angle stability problem involves the study of theelectromechanical oscillations inherent in power systems.Afundamental factor in this problem is the manner in whichthe power outputs of synchronous machines vary as theirrotor

48、 angles change.Under steady-state conditions,there isequilibrium between the input mechanical torque and theoutput electromagnetic torque of each generator,and the speedremains constant.If the system is perturbed,this equilibriumis upset,resulting in acceleration or deceleration of the rotorsof the

49、machines according to the laws of motion of a rotatingbody.If one generator temporarily runs faster than another,theangular position of its rotor relative to that of the slower ma-chine will advance.The resulting angular difference transferspart of the load from the slow machine to the fast machine,

50、depending on the power-angle relationship.This tends toreduce the speed difference and hence the angular separation.The power-angle relationship is highly nonlinear.Beyond acertain limit,an increase in angular separation is accompaniedby a decrease in power transfer such that the angular separationi

51、s increased further.Instability results if the system cannotabsorb the kinetic energy corresponding to these rotor speeddifferences.For any given situation,the stability of the systemdepends on whether or not the deviations in angular positionsof the rotors result in sufficient restoring torques 8.L

52、oss ofsynchronism can occur between one machine and the rest ofthe system,or between groups of machines,with synchronismmaintained within each group after separating from each other.The change in electromagnetic torque of a synchronousmachine following a perturbation can be resolved into twocomponen

53、ts:Synchronizing torque component,in phase with rotorangle deviation.Damping torque component,in phase with the speed de-viation.Systemstabilitydependsontheexistenceofbothcomponentsof torque for each of the synchronous machines.Lack of suffi-cientsynchronizingtorqueresultsinaperiodicornonoscillatory

54、instability,whereaslackofdampingtorqueresultsinoscillatoryinstability.Forconvenienceinanalysisandforgainingusefulinsightintothe nature of stability problems,it is useful to characterize rotorangle stability in terms of the following two subcategories:Small-disturbance(or small-signal)rotor angle sta

55、bilityis concerned with the ability of the power system to main-tain synchronism under small disturbances.The distur-bances are considered to be sufficiently small that lin-earization of system equations is permissible for purposesof analysis 8,12,13.-Small-disturbance stability depends on the initi

56、al op-erating state of the system.Instability that may resultcan be of two forms:i)increase in rotor angle througha nonoscillatory or aperiodic mode due to lack of syn-chronizing torque,or ii)rotor oscillations of increasingamplitude due to lack of sufficient damping torque.-In todays power systems,

57、small-disturbance rotorangle stability problem is usually associated withinsufficient damping of oscillations.The aperiodicinstability problem has been largely eliminated by useof continuously acting generator voltage regulators;however,this problem can still occur when generatorsoperate with consta

58、nt excitation when subjected to theactions of excitation limiters(field current limiters).1390IEEE TRANSACTIONS ON POWER SYSTEMS,VOL.19,NO.2,MAY 2004Fig.1.Classification of power system stability.-Small-disturbance rotor angle stability problems maybe either local or global in nature.Local problemsi

59、nvolve a small part of the power system,and are usu-ally associated with rotor angle oscillations of a singlepower plant against the rest of the power system.Suchoscillations are called local plant mode oscillations.Stability(damping)of these oscillations depends onthe strength of the transmission s

60、ystem as seen by thepower plant,generator excitation control systems andplant output 8.-Global problems are caused by interactions amonglarge groups of generators and have widespread effects.Theyinvolveoscillationsofagroupofgeneratorsinonearea swinging against a group of generators in anotherarea.Su

61、ch oscillations are called interarea mode oscil-lations.Their characteristics are very complex and sig-nificantly differ from those of local plant mode oscilla-tions.Load characteristics,in particular,have a majoreffect on the stability of interarea modes 8.-The time frame of interest in small-distu

62、rbance sta-bility studies is on the order of 10 to 20 seconds fol-lowing a disturbance.Large-disturbance rotor angle stability or transient sta-bility,as it is commonly referred to,is concerned with theabilityofthepowersystemtomaintainsynchronismwhensubjected to a severe disturbance,such as a short

63、circuiton a transmission line.The resulting system response in-volves large excursions of generator rotor angles and isinfluenced by the nonlinear power-angle relationship.-Transient stability depends on both the initialoperating state of the system and the severity of the dis-turbance.Instability i

64、s usually in the form of aperiodicangular separation due to insufficient synchronizingtorque,manifesting as first swing instability.However,in large power systems,transient instability may notalways occur as first swing instability associated witha single mode;it could be a result of superposition o

65、fa slow interarea swing mode and a local-plant swingmode causing a large excursion of rotor angle beyondthe first swing 8.It could also be a result of nonlineareffects affecting a single mode causing instabilitybeyond the first swing.-The time frame of interest in transient stability studiesis usual

66、ly 3 to 5 seconds following the disturbance.Itmay extend to 1020 seconds for very large systemswith dominant inter-area swings.As identified in Fig.1,small-disturbance rotor angle stabilityas well as transient stability are categorized as short termphenomena.The term dynamic stability also appears in the literature asa class of rotor angle stability.However,it has been used todenote different phenomena by different authors.In the NorthAmericanliterature,ithasbeenusedmostlytodenotesmall-dis-turba