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

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.