Basin of attraction analysis in generalized swing equation via dynamical renormalization group approach

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.