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An Application of Immersion and Invariance to a Class of Differential Algebraic Systems

  • N. S. ManjarekarEmail author
  • Ravi N. Banavar
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Electrical power systems are naturally described by nonlinear differential-algebraic equations (DAEs). The dynamics of the dynamical components in the system such as the synchronous generators are given by the set of differential equations, while various network constraints such as power balance equations at different nodes are expressed by a set of algebraic equations. In this chapter we extend the I&I methodology to a class of differential algebraic systems, without the need for solving for the nonlinear algebraic equations explicitly.

Keywords

Algebraic Constraint Differential Algebraic System Target Dynamic Short Circuit Fault Operating Equilibrium 
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References

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    J.A. Acosta, R. Ortega, A. Astolfi, I. Sarras, A constructive solution for stabilization via immersion and invariance: the cart and pendulum system. Automatica 44(9), 2352–2357 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
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    N.S. Manjarekar, R.N. Banavar, R. Ortega, Nonlinear Control Synthesis for Asymptotic Stabilization of the Swing Equation using a Controllable Series Capacitor via Immersion and Invariance. in IEEE Conference on Decision and Control, (Cancun, Mexico, pp. 2493–2498, 2008)Google Scholar
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    A.R. Bergen, D.J. Hill, A structure preserving model for power system stability analysis. IEEE Transaction on Power Apparatus and Systems vol. PAS- 100, pp. 25–35, January 1981Google Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Interdisciplinary Programme in Systems and Control EngineeringIndian Institute of TechnologyPowai, MumbaiIndia

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