Calculating Domain of Attraction Boundary of Power Systems Based on the Gentlest Ascent Dynamics

TL;DR

This paper introduces a novel numerical approach using gentlest ascent dynamics and stable manifold algorithms to accurately compute the domain of attraction boundary in power systems, aiding transient stability analysis.

Contribution

It develops a new computational framework for identifying the DOA boundary by constructing unstable critical elements and their stable manifolds, with theoretical validation.

Findings

Algorithms accurately capture the geometric structure of the DOA boundary.

Numerical experiments validate the effectiveness and accuracy of the proposed methods.

The approach provides a new numerical tool for transient stability analysis in power systems.

Abstract

The power system, a fundamental public utility, is increasingly important due to growing global electricity demand. Recent large-scale blackouts (e.g., Iberian Peninsula, UK) have raised concerns about transient stability under impact faults. Transient stability is determined by post-disturbance synchronizing capability of synchronous generators, formulated as identifying the domain of attraction (DOA) boundary of the asymptotically stable equilibrium. Using a benchmark model of synchronous-generator-dominated power systems, this report employs a gentlest ascent dynamics (GAD) method for 1-saddle points, an adjoint operator method for periodic orbits, and stable manifold algorithms to compute the DOA boundary. These algorithms transform DOA boundary determination into constructing unstable critical elements (saddle points and periodic orbits) and their stable manifolds. Theoretically, under certain assumptions we prove that the DOA boundary is the closure of the union of stable manifolds of index-1 critical elements, and establish a stability theory for a perturbed GAD system. Numerical experiments on two-machine and three-machine systems (with only saddle points or with periodic orbits) validate the effectiveness and accuracy. Results show the algorithms accurately capture the geometric structure of the DOA boundary, providing a new numerical tool for transient stability analysis.