Interaction Large-Signal Stability Analysis of M3C and GFM/GFL Hybrid Control Strategies Converters Based on the Novel Fuzzy Tensor Space Method

This article proposes a novel fuzzy tensor space method to analyze the interaction large-signal stability of modular multilevel matrix converter and grid-forming/following (GFM/GFL) hybrid control strategy converters. By addressing the challenges of high-order, strong nonlinearity, and multi-frequency coupling in the system's dynamic model, the complexity is reduced from exponential to constant levels using sector nonlinearity theory. It is achieved by optimizing the original membership function set into a linearly independent fuzzy tensor basis. In addition, leveraging the physical significance of the fuzzy tensor space reduces the mapping area for solving the Lyapunov functional problem, effectively lowering the conservatism. Furthermore, the stability analysis results obtained from this method offer a better balance of complexity and accuracy compared to traditional TS fuzzy theory. Based on the improved method, the complex coupling stability mechanism caused by the interaction of multiple power electronic devices and control strategies can be analyzed quickly and accurately. In particular, these results are used to study the impact of different configurations of GFM/GFL converters under various disturbance conditions, as well as the interaction stability mechanism of different configuration ratios combined with grid strength. Finally, the validity of these results is confirmed through theoretical and experimental verification.