Beyond Energy Functions and Numerical Integration: A New Methodology to Determine Transient Stability at the Initial State

TL;DR

This paper introduces a new, direct methodology for transient stability analysis that avoids traditional energy functions and numerical integration, using a trajectory-dependent indicator and high-order derivatives for efficient stability prediction.

Contribution

The paper proposes a novel approach that transforms transient stability analysis into a pole-placement detection problem using high-order derivatives and rational function approximation.

Findings

Method provides direct stability prediction without numerical integration.

Numerical validation confirms efficiency and accuracy on benchmark systems.

Establishes a new general methodology for nonlinear dynamical systems.

Abstract

This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability indicator function to distinguish the system's destiny. To overcome the difficulty in analyzing the asymptotic behavior at infinite time, a strategic time contraction mapping is then applied. This allows TSA to be recast as a pole-placement detection problem for the indicator function. By leveraging high-order derivatives at the initial state, a rational function approximation is derived, yielding a mathematically direct and computationally efficient prediction. Numerical validations on benchmark systems demonstrate that the method not only provides a direct mathematical shortcut for TSA in power systems but also establishes a promising new methodology for evaluating the transient stability of a broad class of nonlinear dynamical systems.