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Definition and Classification?of Power System Stability
Abstract—The problem of defining and classifying power?system stability has been addressed by several previous CIGRE?and IEEE Task Force reports. These earlier efforts, however,?do not completely reflect current industry needs, experiences?and understanding. In particular, the definitions are not precise?and the classifications do not encompass all practical instability?scenarios.?
This report developed by a Task Force, set up jointly by the?CIGRE Study Committee 38 and the IEEE Power System Dynamic?Performance Committee, addresses the issue of stability definition?and classification in power systems from a fundamental viewpoint?and closely examines the practical ramifications. The report aims?to define power system stability more precisely, provide a systematic?basis for its classification, and discuss linkages to related issues?such as power system reliability and security.?Index Terms—Frequency stability, Lyapunov stability, oscillatory?stability, power system stability, small-signal stability, terms?and definitions, transient stability, voltage stability.?
I. INTRODUCTION?
POWERsystem stability has been recognized as an important?problem for secure system operation since the 1920s [1], [2].?Many major blackouts caused by power system instability have?illustrated the importance of this phenomenon [3]. Historically,?transient instability has been the dominant stability problem on?most systems, and has been the focus of much of the industry’s?attention concerning system stability. As power systems have?evolved through continuing growth in interconnections, use of?new technologies and controls, and the increased operation in?highly stressed conditions, different forms of system instability?have emerged. For example, voltage stability, frequency stability?and interarea oscillations have become greater concerns than?in the past. This has created a need to review the definition and?classification of power system stability. A clear understanding?of different types of instability and how they are interrelated?is essential for the satisfactory design and operation of power?systems. As well, consistent use of terminology is required?for developing system design and operating criteria, standard?analytical tools, and study procedures.?
The problem of defining and classifying power system stability?is an old one, and there have been several previous reports?on the subject by CIGRE and IEEE Task Forces [4]–[7]. These,?however, do not completely reflect current industry needs, experiences,?and understanding. In particular, definitions are not?precise and the classifications do not encompass all practical instability?scenarios.
?This report is the result of long deliberations of the Task Force?set up jointly by the CIGRE Study Committee 38 and the IEEE?Power System Dynamic Performance Committee. Our objectives?are to:
?? Define power system stability more precisely, inclusive of?all forms.
?? Provide a systematic basis for classifying power system?stability, identifying and defining different categories, and?providing a broad picture of the phenomena.?
? Discuss linkages to related issues such as power system?reliability and security.?
II. DEFINITION OF POWER SYSTEM STABILITY?
In this section, we provide a formal definition of power?system stability. The intent is to provide a physically based?definition which, while conforming to definitions from system?theory, is easily understood and readily applied by power?system engineering practitioners.
A. Proposed Definition
Power system stability is the ability of an electric power?system, for a given initial operating condition, to regain a?state of operating equilibrium after being subjected to a?physical disturbance, with most system variables bounded?so that practically the entire system remains intact.?
B. Discussion and Elaboration?
The definition applies to an interconnected power system as a?whole. Often, however, the stability of a particular generator or?group of generators is also of interest. A remote generator may?lose stability (synchronism) without cascading instability of the?main system. Similarly, stability of particular loads or load areas?may 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 changes?occur continually; the system must be able to adjust to the?changing conditions and operate satisfactorily. It must also?be able to survive numerous disturbances of a severe nature,?such as a short circuit on a transmission line or loss of a large?generator. A large disturbance may lead to structural changes?due to the isolation of the faulted elements.?
The response of the power system to a disturbance may involve?much of the equipment. Further, devices used to protect individual equipment may respond?to variations in system variables and cause tripping of the?equipment, thereby weakening the system and possibly leading?to system instability.
?If following a disturbance the power system is stable, it will?reach a new equilibrium state with the system integrity preserved?i.e., with practically all generators and loads connected?through a single contiguous transmission system.
Power systems are continually experiencing fluctuations?of small magnitudes. However, for assessing stability when?subjected to a specified disturbance, it is usually valid to assume?that the system is initially in a true steady-state operating?condition.?
III. CLASSIFICATION OF POWER SYSTEM STABILITY?
A typical modern power system is a high-order multivariable?process whose dynamic response is influenced by a wide array?of devices with different characteristics and response rates. Stability is a condition of equilibrium between opposing forces. Depending?on the network topology, system operating condition?and the form of disturbance, different sets of opposing forces?may experience sustained imbalance leading to different forms?of instability. In this section, we provide a systematic basis for?classification of power system stability.
?A. Need for Classification?
Power system stability is essentially a single problem;?however, the various forms of instabilities that a power system?may undergo cannot be properly understood and effectively?dealt with by treating it as such. Because of high dimensionality?and complexity of stability problems, it helps to make?simplifying assumptions to analyze specific types of problems?using an appropriate degree of detail of system representation?and appropriate analytical techniques. Analysis of stability,?including identifying key factors that contribute to instability?and devising methods of improving stable operation, is greatly?facilitated by classification of stability into appropriate categories?[8]. Classification, therefore, is essential for meaningful?practical analysis and resolution of power system stability?problems. As discussed in Section V-C-I, such classification is?entirely justified theoretically by the concept of partial stability?[9]–[11].?
B. Categories of Stability?
The classification of power system stability proposed here is?based on the following considerations [8]:
?? The physical nature of the resulting mode of instability as?indicated by the main system variable in which instability?can be observed.?
? The size of the disturbance considered, which influences?the method of calculation and prediction of stability.?
? The devices, processes, and the time span that must be?taken into consideration in order to assess stability.?
Fig. 1 gives the overall picture of the power system stability?problem, identifying its categories and subcategories. The following?are descriptions of the corresponding forms of stability?phenomena.?
B.1 Rotor Angle Stability:?Rotor angle stability refers to the ability of synchronous machines?of an interconnected power system to remain in synchronism?after being subjected to a disturbance. It depends on the?ability to maintain/restore equilibrium between electromagnetic?torque and mechanical torque of each synchronous machine in?the system. Instability that may result occurs in the form of increasing?angular swings of some generators leading to their loss?of synchronism with other generators.
?B.2 Voltage Stability:?Voltage stability refers to the ability of a power system to maintain?steady voltages at all buses in the system after being subjected?to a disturbance from a given initial operating condition.?It depends on the ability to maintain/restore equilibrium between?load demand and load supply from the power system. Instability?that may result occurs in the form of a progressive fall?or rise of voltages of some buses. A possible outcome of voltage?instability is loss of load in an area, or tripping of transmission?lines and other elements by their protective systems leading?to cascading outages. Loss of synchronism of some generators?may result from these outages or from operating conditions that?violate field current limit [14].?
B.3 Basis for Distinction between Voltage and?Rotor Angle Stability: It is important to recognize that the distinction between rotor?angle stability and voltage stability is not based on weak?coupling between variations in active power/angle and reactive?power/voltage magnitude. In fact, coupling is strong for?stressed conditions and both rotor angle stability and voltage?stability are affected by pre-disturbance active power as well?as reactive power flows. Instead, the distinction is based on?the specific set of opposing forces that experience sustained?imbalance and the principal system variable in which the?consequent instability is apparent.?
B.4 Frequency Stability:?Frequency stability refers to the ability of a power system to?maintain steady frequency following a severe system upset resulting?in a significant imbalance between generation and load.?It depends on the ability to maintain/restore equilibrium between?system generation and load, with minimum unintentional?loss of load. Instability that may result occurs in the form of sustained?frequency swings leading to tripping of generating units?and/or loads.
B.5 Comments on Classification:?We have classified power system stability for convenience in?identifying causes of instability, applying suitable analysis?tools, and developing corrective measures. In any given situation,?however, any one form of instability may not occur in its?pure form. This is particularly true in highly stressed systems?and for cascading events; as systems fail one form of instability?may ultimately lead to another form. However, distinguishing?between different forms is important for understanding the underlying?causes of the problem in order to develop appropriate?design and operating procedures.?
While classification of power system stability is an effective?and convenient means to deal with the complexities of the?problem, the overall stability of the system should always be?kept in mind. Solutions to stability problems of one category?should not be at the expense of another. It is essential to look at?all aspects of the stability phenomenon, and at each aspect from?more than one viewpoint.?
VI. SUMMARY
?This report has addressed the issue of stability definition and?classification in power systems from a fundamental viewpoint?and has examined the practical ramifications of stability?phenomena in significant detail. A precise definition of power?system stability that is inclusive of all forms is provided.?
A salient feature of the report is a systematic classification?of power system stability, and the identification of different?categories of stability behavior. Linkages between power?system reliability, security, and stability are also established?and discussed. The report also includes a rigorous treatment?of definitions and concepts of stability from mathematics?and control theory. This material is provided as background?information and to establish theoretical connections.
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