Equivalence of Three Quadratic Approximation Methods of Stability Boundaries of Nonlinear Dynamic Systems

Author

Chen, Lei ; Min, Yong

Author_Institution

Dept. of Electr. Eng., Tsinghua Univ., Beijing, China

Volume

55

Issue

5

fYear

2010

fDate

5/1/2010 12:00:00 AM

Firstpage

1258

Lastpage

1262

Abstract

Approximation of stable manifolds of unstable equilibrium points is a key problem in stability region estimation of nonlinear dynamic systems. Different quadratic approximation methods have been proposed in past literature. Then what is their relationship and which has better performance are of concern. The mathematical equivalence of three quadratic approximation methods is proved in this note. Their computation burdens of numerical implementation are compared, and the one with the least computation time is recommended for application.

Keywords

approximation theory; boundary-elements methods; nonlinear dynamical systems; quadratic programming; stability; nonlinear dynamic system stability boundaries; quadratic approximation methods; stability region estimation; Approximation methods; Eigenvalues and eigenfunctions; Manifolds; Nonlinear dynamical systems; Nonlinear systems; Power engineering and energy; Power engineering computing; Power system dynamics; Power system stability; Power system transients; Taylor series; Nonlinear systems; quadratic approximation; stability of NL systems; stable manifold;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2042765

Filename

5409607