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Definition and Classificationof Power System StabilityAbstractThe problem of defining and classifying powersystem stability has been addressed by several previous CIGREand IEEE Task Force reports. 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 theCIGRE Study Committee 38 and the IEEE Power System DynamicPerformance 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 systematicbasis for its classification, and discuss linkages to related issuessuch as power system reliability and security.Index TermsFrequency stability, Lyapunov stability, oscillatorystability, power system stability, small-signal stability, termsand definitions, transient stability, voltage stability.I. INTRODUCTIONPOWERsystem stability has been recognized as an importantproblem for secure system operation since the 1920s 1, 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, and 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 instabilityhave emerged. For example, voltage stability, frequency stabilityand 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 essential 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 study procedures.The problem of defining and classifying power system stabilityis an old one, and there have been several previous reportson the subject by CIGRE and IEEE Task Forces 47. These,however, do not completely reflect current industry needs, experiences,and understanding. In particular, definitions are notprecise and the classifications do not encompass all practical instabilityscenarios.This report is the result of long deliberations of the Task Forceset up jointly by the CIGRE Study Committee 38 and the IEEEPower System Dynamic Performance Committee. Our objectivesare to: Define power system stability more precisely, 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.II. DEFINITION OF POWER SYSTEM STABILITYIn 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 easily understood and readily applied by powersystem engineering practitioners.A. Proposed DefinitionPower 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 system variables boundedso that practically the entire system remains intact.B. Discussion and ElaborationThe definition applies to an interconnected power system as awhole. Often, however, the stability of a particular generator orgroup of generators is also of interest. A remote generator maylose stability (synchronism) without cascading instability of themain system. Similarly, stability of particular loads or load areasmay be of interest; motors may lose stability (run down and stall)without cascading instability of the main system.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 disturbances 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.The response of the power system to a disturbance may involvemuch of the equipment. Further, devices used to protect individual equipment may respondto variations in system variables and cause tripping of theequipment, thereby weakening 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 preservedi.e., with practically all generators and loads connectedthrough a single contiguous transmission system. Power systems are continually experiencing fluctuationsof small magnitudes. However, for assessing stability whensubjected to a specified disturbance, it is usually valid to assumethat the system is initially in a true steady-state operatingcondition.III. CLASSIFICATION OF POWER SYSTEM STABILITYA 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. Stability is a condition of equilibrium between opposing forces. Dependingon 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 systematic 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 of high dimensionalityand 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 contribute to instabilityand devising methods of improving stable operation, is greatlyfacilitated by classification of stability into appropriate categories8. Classification, therefore, is essential for meaningfulpractical analysis and resolution of power system stabilityproblems. As discussed in Section 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 by 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 overall picture of the power system stabilityproblem, identifying its categories and subcategories. The followingare descriptions of the corresponding forms of stabilityphenomena.B.1 Rotor Angle Stability:Rotor angle stability refers to the ability of synchronous machinesof an interconnected power system to remain in synchronismafter being subjected to a disturbance. It depends on theability to maintain/restore equilibrium between electromagnetictorque and mechanical torque of each synchronous machine inthe system. Instability that may result occurs in the form of increasingangular swings of some generators leading to their lossof synchronism with other generators.B.2 Voltage Stability:Voltage stability refers to the ability of a power system to maintainsteady voltages at all buses in the system after being subjectedto a disturbance from a given initial operating condition.It depends on the ability to maintain/restore equilibrium betweenload demand and load supply from the power system. Instabilitythat may result occurs in the form of a progressive fallor rise of voltages of some buses. A possible outcome of voltageinstability is loss of load in an area, or tripping of transmissionlines and other elements by their protective systems leadingto cascading outages. Loss of synchronism of some generatorsmay result from these outages or from operating conditions thatviolate field current limit 14. B.3 Basis for Distinction between Voltage andRotor Angle Stability: It is important to recognize that the distinction between rotorangle stability and voltage stability is not based on weakcoupling between variations in active power/angle and reactivepower/voltage magnitude. In fact, coupling is strong forstressed conditions and both rotor angle stability and voltagestability are affected by pre-disturbance active power as wellas reactive power flows. Instead, the distinction is based onthe specific set of opposing forces that experience sustainedimbalance and the principal system variable in which theconsequent instability is apparent.B.4 Frequency Stability:Frequency stability refers to the ability of a power system tomaintain steady frequency following a severe system upset resultingin a significant imbalance between generation and load.It depends on the ability to maintain/restore equilibrium betweensystem generation and load, with minimum unintentionalloss of load. Instability that may result occurs in the form of sustainedfrequency swings leading to tripping of generating unitsand/or loads.B.5 Comments on Classification:We have classified power system stability for convenience inidentifying causes of instability, applying suitable analysistools, and developing corrective measures. In any given situation,however, any one form of instability may not occur in itspure form. This is particularly true in highly stressed systemsand for cascading events; as systems fail one form of instabilitymay ultimately lead to another form. However, distinguishingbetween different forms is important for understanding the underlyingcauses of the problem in order to develop appropriatedesign and operating procedures.While classification of power system stability is an effectiveand convenient means to deal with the complexities of theproblem, the overall stability of the system should always bekept in mind. Solutions to stability problems of one categoryshould not be at the expense of another. It is essential to look atall aspects of the stability phenomenon, and at each aspect frommore than one viewpoint.VI. SUMMARYThis report has addressed the issue of stability definition andclassification in power systems from a fundamental viewpointand has examined the practical ramifications of stabilityphenomena in significant detail. A precise definition of powersystem stability that is inclusive of all forms is provided.A salient feature of the report is a systematic classificationof power system stability, and the identification of differentcategories of stability behavior. Linkages between powersystem reliability, security, and stability are also establishedand discussed. The report also includes a rigorous treatmentof definitions and concepts of stability from mathematicsand control theory. This material is provided as backgroundinformation and to establish theoretical connections.REFERENCES1 C. P. Steinmetz, “Power control and stability of electric generating stations,”AIEE Trans., vol. XXXIX, Part II, pp. 12151287, July 1920.2 AIEE Subcommittee on Interconnections and Stability Factors, “Firstreport of power system stability,” AIEE Trans., pp. 5180, 1926.3 G. S. Vassell, “Northeast blackout of 1965,” IEEE Power EngineeringReview, pp. 48, Jan. 1991.4 S. B. Crary, I. Herlitz, and B. 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