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Application of Extended Invariance Principle to Transient Stability Analysis of Asynchronous Generators
KTH, Superseded Departments, Electrical Systems.
KTH, Superseded Departments, Electrical Systems.ORCID iD: 0000-0002-6431-9104
2004 (English)In: Bulk Power System Dynamics and Control - VI, 2004, 513-521 p.Conference paper (Refereed)
Abstract [en]

This paper reports preliminary results of a studyconcerned with the questions related to the transient stabilityof power systems with asynchronous generators. In this studythe asynchronous generators represent a large-scale wind farmconsisting of fixed-speed wind turbines with fixed pitch. Theobjective of the study is to develop a framework for studyingthe transient stability of the asynchronous generators similar tothat of synchronous generators, i.e., an attempt is made to applya Lyapunov/energy function method to the simple power systemwith asynchronous generators.Detailed analysis is performed in order to verify the existenceof a proper Lyapunov function for the system at hand.It was demonstrated analytically that four commonly knownmethods for the construction Lyapunov functions cannot yielda Lyapunov function for the system under consideration, whichindicates that the construction of such a function might be avery difficult mathematical task.A recent development of the theory of nonlinear differentialequations resulted in the discovery of the Extended InvariancePrinciple, which substantially broadens the class of functionsthat can be utilized as Lyapunov functions. The ExtendedInvariance Principle is found capable of constructing an energylikefunction for the power system treated in this paper.Although the Extended Invariance Principle allows a largerclass of functions to be applied for stability studies of powersystems, it comes at the expense of having to perform certainoperations on sets of reals.This paper also addresses the numerical problems inherentin the Extended Invariance Principle by utilizing the methodsof interval arithmetics and, based on the results obtained,presents an extended Lyapunov function for the assessment ofthe transient stability properties of a simple power system.A numerical example is used to illustrate the applicationof Extended Invariance Principle and interval arithmetics forsystem stability analysis of a simplified model of a wind farm.

Place, publisher, year, edition, pages
2004. 513-521 p.
Keyword [en]
Transient stability, direct Lyapunov method, invariance principle, distributed generation, asynchronous generator
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-52839OAI: diva2:467913
Bulk Power System Dynamics and Control - VI, Cortina d’Ampezzo, Italy, August 22-27, 2004
QC 20111221Available from: 2011-12-20 Created: 2011-12-20 Last updated: 2011-12-21Bibliographically approved

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