9291_c009 - 9 Small Signal Stability and Power System...

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9 Small Signal Stability and Power System Oscillations John Paserba Mitsubishi Electric Power Products, Inc. Juan Sanchez-Gasca GE Energy Prabha Kundur University of Toronto Einar Larsen GE Energy Charles Concordia Consultant 9.1 Nature of Power System Oscillations . ............................... 9 -1 Historical Perspective . Power System Oscillations Classified by Interaction Characteristics . Conceptual Description of Power System Oscillations . Summar y on the Nature of Power System Oscillations 9.2 Criteria for Damping . ......................................................... 9 -7 9.3 Study Procedure . ................................................................. 9 -7 9.4 Mitigation of Power System Oscillations. ......................... 9 -9 Siting . Control Objectives . Closed-Loop Control Design . Input Signal Selection . Input-Signal Filtering . Control Algorithm . Gain Selection . Control Output Limits . Performance Evaluation . Adverse Side Effects . Higher-Order Terms for Small-Signal Analysis 9.5 Higher-Order Terms for Small-Signal Analysis. ............. 9 -13 9.6 Summary. ........................................................................... 9 -14 9.1 Nature of Power System Oscillations 9.1.1 Historical Perspective Damping of oscillations has been recognized as important in electric power system operations from the beginning. Before there were any power systems, oscillations in automatic speed controls (governors) initiated an analysis by J.C. Maxwell (speed controls were found necessary for the successful operation of the first steam engines). Apart from the immediate application of Maxwell’s analysis, it also had a lasting influence as at least one of the stimulants to the development of very useful and widely used method by E.J. Routh in 1883, which enables one to determine theoretically the stability of a high-order dynamic system without having to know the roots of its equations (Maxwell analyzed only a second-order system). Oscillations among generators appeared as soon as AC generators were operated in parallel. These oscillations were not unexpected, and in fact, were predicted from the concept of the power vs. phase- angle curve gradient interacting with the electric generator rotary inertia, forming an equivalent mass- and-spring system. With a continually varying load and some slight differences in the design and loading of the generators, oscillations tended to be continually excited. In the case of hydrogenerators, in particular, there was very little damping, and so amortisseurs (damper windings) were installed, at first as an option. (There was concern about the increased short-circuit current and some people had to be persuaded to accept them (Crary and Duncan, 1941).) It is of interest to note that although the only ß 2006 by Taylor & Francis Group, LLC.
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significant source of actual negative damping here was the turbine speed governor (Concordia, 1969), the practical ‘‘cure’’ was found elsewhere. Two points were evident then and are still valid today. First, automatic control is practically the only source of negative damping, and second, although it is obviously desirable to identify the sources of negative damping, the most effective and economical place to add damping may lie elsewhere.
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9291_c009 - 9 Small Signal Stability and Power System...

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