An Analytical Solution for Transient Stability Analysis of Power Systems Based on Renormalization Group Approach

To clarify the intrinsic mechanism of transient stability, a transient stability analysis method for power systems based on the renormalization group (RG) approach is proposed to derive an analytical solution to the swing equation. Initially, the swing equation is reformulated into a polynomial matrix form using Taylor series expansion, providing a foundation for analytical computation. Subsequently, a perturbation method is applied to obtain an approximate analytical solution to the swing equation. However, perturbation methods often introduce secular terms, which grow unbounded over time, limiting the validity of the solution for long-term analysis. To address this issue, the RG method is employed to eliminate secular terms, leading to a renormalized closed-form solution of the swing equation. The practical effectiveness of the proposed method is demonstrated through case studies on a single-machine infinite-bus (SMIB) system and an IEEE 4-machine 11-bus system. This approach enhances the accuracy of modeling power system dynamics and provides an efficient tool for transient stability evaluation in complex systems.