# 9291_c008 - 8 Transient Stability 8.1 8.2 8.3 8.4 8.5...

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8 Transient Stability Kip Moris on Powerte ch Labs, Inc. 8.1 Introduction. ........................................................................ 8 -1 8.2 Basic Theory of Transient Stability. ................................... 8 -1 Swing Equation . Power–Angle Relationship . Equal Area Criterion 8.3 Methods of Analysis of Transient Stability . ...................... 8 -6 Modeling . Analytical Methods . Simulation Studies 8.4 Factors Inﬂuencing Transient Stability. ............................. 8 -8 8.5 Transient Stability Considerations in System Design. ..................................................................... 8 -9 8.6 Transient Stability Considerations in System Operation. ............................................................. 8 -10 8.1 Introduction As discussed in Chapter 7 , power system stability was recognized as a problem as far back as the 1920s at which time the characteristic structure of systems consisted of remote power plants feeding load centers over long distances. These early stability problems, often a result of insufﬁcient synchronizing torque, were the ﬁrst emergence of transient instability. As deﬁned in the previous chapter, t ransient stability is the ability of a power system to remain in synchronism when subjected to large transient disturbances. These disturbances may include faults on transmission elements, loss of load, loss of generation, or loss of system components such as transformers or transmission lines. Although many different forms of power system stability have emerged and become problematic in recent years, transient stability still remains a basic and important consideration in power system design and operation. While it is true that the operation of many power systems are limited by phenomena such as voltage stability or small-signal stability, most systems are prone to transient instability under certain conditions or contingencies and hence the understanding and analysis of transient stability remain fundamental issues. Also, we shall see later in this chapter that transient instability can occur in a very short time-frame (a few seconds) leaving no time for operator intervention to mitigate problems; it is therefore essential to deal with the problem in the design stage or severe operating restrictions may result. In this chapter we discuss the basic principles of transient stability, methods of analysis, control and enhancement, and practical aspects of its inﬂuence on power system design and operation. 8.2 Basic Theory of Transient Stability Most power system engineers are familiar with plots of generator rotor angle ( d ) versus time as shown in Fig. 8.1 . These ‘‘swing curves’’ plotted for a generator subjected to a particular system disturbance show whether a generator rotor angle recovers and oscillates around a new equilibrium point as in trace ‘‘a’’ or ß 2006 by Taylor & Francis Group, LLC.

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whether it increases aperiodically such as in trace ‘‘b.’’ The former case is deemed to be transiently stable, and the latter case transiently unstable. What factors determine whether a machine will be stable or unstable? How can the stability of large power systems be analyzed? If a case is unstable, what can be done to enhance its stability? These are some of the questions we seek to answer in this section.
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9291_c008 - 8 Transient Stability 8.1 8.2 8.3 8.4 8.5...

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