Transient Synchronization Stability Analysis and PDC Control of Grid-Following Inverters Based on T–S Fuzzy Model

Synchronization control realized by the phase-locked loop (PLL) is important for grid-following inverters. Synchronization instability leads to inverter oscillation and causes renewable energy disconnection accidents. However, synchronization stability especially the transient stability is difficult to study and improve due to the nonlinear structure and control coupling of PLL. Among all the stability-improving methods, many of them rely on the stability analysis results but not the internal nonlinear mechanism, which causes the methods to have only linear control functions and behave with poor adaptability and portability in applications. This research provides a systematic theory to improve the transient synchronization stability according to the system's nonlinear control mechanism. The method can achieve nonlinear control and behave with higher performance than other methods. First, the Takagi–Sugeno (T–S) fuzzy model is established to convert the nonlinear system into linear subsystems. Then, the linear matrix inequalities (LMIs) are constructed to obtain the Lyapunov function and the transient stability region. Finally, the parallel distributed compensation (PDC) based on the T–S fuzzy theory is investigated and implemented in the PLL to improve synchronization stability. The insights of PDC and the comparison with other methods are explored. The simulation and experiment have verified the theories.