The Largest Estimated Domain of Attraction and Its Applications for Transient Stability Analysis of PLL Synchronization in Weak-Grid-Connected VSCs

This paper mainly focuses on transient stability issue of phase-locked-loop synchronization (PLL-Syn) in a weak-grid connected VSC (WG-VSC) system. First, the linear matrix inequality (LMI) optimization method has been applied to construct the largest estimated domain of attraction (LEDA) of the WG-VSC system for the first time. Compared with the frequently-used methods such as direct energy function method, Takagi-Sugeno (TS) method and Sum-of-Square Programming (SOS) method, the proposed method has the lowest conservation in constructing LEDA. Second, to ensure transient stability of PLL-Syn in severe faults, the concept of the feasible region of active/reactive current reference is proposed. Furthermore, based on the LEDA obtained by LMI optimization method, a simple algorithm to obtain this feasible region is presented. And, the influence of typical parameters on this feasible region is analyzed. Third, for transient instability scenarios, a simple variable step size iterative algorithm has been proposed to search the estimated critical action time with the derived LEDA. Moreover, two associated emergency control methods including adjusting the current reference values back to the feasible region and clearing grid fault have been considered to verify the estimated critical action time. Time-domain simulation results based on detailed switching model in PSCAD/EMTDC have been provided to verify the above theoretical analysis.