Beyond Energy Functions and Numerical Integration: A New Methodology to Determine Transient Stability at the Initial State
Wenhao Wu, Dan Wu, Bin Wang, Jiabing Hu
TL;DR
Problem: traditional transient stability analysis is hindered by the need for sequential time-domain integration and the difficulty of constructing general energy functions. Approach: define a trajectory-dependent indicator $h(t)$, apply a time contraction mapping $\mathcal{M}(t)$ to map $t\in[0,\infty)$ to a finite horizon, and use a near-diagonal Padé approximant to detect a pole, all derived from high-order derivatives via Differential Transformation (DT). Contributions: a rigorous integration-free TSA framework with a pole-detection criterion and DT-based coefficient computation, validated on the Lorenz system, SMIB, and WSCC 9-bus. Significance: enables fast, direct stability verdicts from initial data with potential extension to broad 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.