Transient Stability Analysis of Grid Forming-Grid Following Paralleled System Using Improved Sum-of-Squares Programming

This paper investigates the transient stability of the grid-forming and grid-following (GFM-GFL) paralleled system based on the Lyapunov direct method. To achieve this goal, an improved sum-of-squares (SOS) programming method is proposed to construct the low-conservativeness Lyapunov function for the GFM-GFL paralleled system. The proposed method simplifies the conventional SOS constraints and enables adaptive tuning of SOS parameters according to the conservativeness of the domain of attraction (DOA). Compared with existing numerical Lyapunov methods, the proposed method achieves faster computation and lower conservativeness, thus enabling more precise evaluation of the transient stability. Furthermore, the influence of system parameters on the transient stability of the GFM-GFL paralleled system is quantitatively analyzed using the volume of DOA as a metric. Finally, the effectiveness of the proposed method is verified through comparative studies.