Regions of Attraction Approximation Using Individual Invariance

TL;DR

This paper introduces a novel theorem based on individual invariance to simplify the approximation of regions of attraction in nonlinear systems, with applications to power system transient stability analysis.

Contribution

It develops a new theoretical framework using individual invariance for more efficient regions of attraction approximation and demonstrates its effectiveness on power system stability problems.

Findings

The theorem accurately estimates regions of attraction in nonlinear systems.

The proposed algorithm successfully identifies critical clearing times in power systems.

Applications on standard power system models validate the approach's practicality.

Abstract

Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an artificial system. The theoretical foundation is provided for a theorem in individual invariance to relate regions of attraction of artificial systems to the original vector field's region of attraction which leads to significant simplification in approximating regions of attraction. Several second order examples are used to demonstrate the effectiveness of this theorem. It is also proposed to use this theorem for the transient stability problem in power systems where an algorithm is presented to identify the critical clearing time through sequences of function evaluations. The algorithm is successfully applied on the 3-machine 9-bus system as well as the IEEE 39-bus New England system giving accurate and realistic estimations of the critical clearing time.