Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics

R. Qi, D. Cook, W. Kliemann, Vijay Vittal

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

In this paper we consider the visualization of the behavior of high-dimensional dynamical systems by computing the approximated stable manifolds around fixed points using the normal form technique and the energy function method, respectively. By using an effective graphic package called XGobi, we show the high-dimensional invariant manifolds of fixed points of the dynamical system obtained in two different ways, i.e., the normal form method and the energy function method. XGobi allows us to compare different approximations of the invariant manifolds in all dimensions of the system in the same picture, and to analyze the behavior of actual system trajectories in the neighborhood of the fixed point. By viewing in all dimensions, global structural characteristics of the system can be easily detected.

Original languageEnglish (US)
Pages (from-to)175-195
Number of pages21
JournalJournal of Nonlinear Science
Volume10
Issue number2
StatePublished - Mar 2000
Externally publishedYes

Fingerprint

Stable Manifold
System Dynamics
Power System
Dynamical systems
Visualization
Fixed point
Invariant Manifolds
Energy Function
dynamical systems
Normal Form
High-dimensional
Dynamical system
Global Dimension
Trajectories
trajectories
Trajectory
energy
Computing
Approximation
approximation

Keywords

  • Dynamical system
  • Nonlinear
  • Normal form
  • Visualization
  • XGobi

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics. / Qi, R.; Cook, D.; Kliemann, W.; Vittal, Vijay.

In: Journal of Nonlinear Science, Vol. 10, No. 2, 03.2000, p. 175-195.

Research output: Contribution to journalArticle

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