As renewable energy integration continues to accelerate, transient stability challenges in modern power systems have become increasingly pronounced, particularly due to the systems’ inherent high-dimensional nonlinear dynamics. Developing a reliable and efficient method for assessing transient stability and the associated basin of attraction remains a critical yet unresolved challenge. This study focuses on the precise estimation of the basin-of-attraction boundary in phase-locked loop based voltage source converter systems, which can be described by a generalized swing equation. To address this problem, a higher-order Taylor expansion renormalization approach is proposed. This method enables the construction of a highly accurate approximation of the stable manifold that serves as the basin-of-attraction boundary, offering substantial improvements over conventional linear and second-order local approximations. The reliability and effectiveness of the proposed approach are rigorously validated through simulations under various fault scenarios in the transient stability assessment. The proposed method provides a robust tool for analyzing transient stability in modern power systems and offers new insights into the stability characterization of other nonlinear dynamical systems.
Zhou et al. (Wed,) studied this question.