Under severe faults on the grid side

the wind turbine grid-connected system exhibits nonlinear characteristics and control switching throughout the fault process

posing significant challenges to transient stability analysis. To address this

this paper proposes a Multi-geometric-center Sum-of-squares Iterative (MSI) method for accurately estimating the transient stability domain (TSD) of PLL- synchronized wind power systems. Firstly

a transient synchronization model

compatible with various control strategies and capable of addressing the dynamics of current recovery

is proposed for the wind power system throughout all fault stages. Next

to further quantify the transient stability

multiple Lyapunov functions are constructed. The nonlinear transient synchronization model is equivalently recast into a sum-of-squares model

thereby overcoming the challenge of satisfying the non-negative conditions of constructing Lyapunov functions. Furthermore

to achieve a more accurate solution of the proposed model

the MSI method is presented. Multiple shifted shape functions are constructed and iteratively updated

with their geometric centers adjusted

to obtain TSD boundaries from different directions. Finally

the proposed analysis and method are validated through rigorous simulation results and case studies.