Abstract: [Objectives] To address the overly conservative estimation of the attraction domain for direct-drive permanent magnet synchronous generator (D-PMSG) systems using existing methods, a transient stability analysis method based on the sum-of-squares (SOS) optimization algorithm is proposed, aiming to reduce this conservativeness. [Methods] First, based on Lyapunov stability theory and the theoretical framework for optimal estimation of the attraction domain, the S-procedure theorem is introduced to construct an SOS optimization model incorporating semi-definite constraints. This model is then solved to obtain the globally optimal Lyapunov function, thereby accurately estimating the system’s attraction domain. Subsequently, by adjusting key parameters such as wind turbine parameters, fault duration, fault severity, and wind speed variations, the system operating point is analyzed to determine whether it resides within the attraction domain estimated by the SOS optimization algorithm. This analysis provides a basis for evaluating the transient stability of the D-PMSG system. Finally, the effectiveness of the proposed method is verified based on the MATLAB/Simulink time-domain simulation platform. [Results] The proposed method significantly reduces the conservativeness in estimating the attraction domain of the D-PMSG system. It can not only effectively determine the transient stability of the system, but also reliably quantify the impact degree of various key parameters on the system’s transient stability. [Conclusions] The proposed method effectively addresses the issue of overly conservative estimation of the attraction domain for D-PMSG systems, providing a more accurate theoretical basis and a more practical evaluation tool for analyzing the transient stability of such systems.

Key words: renewable energy, wind power generation, direct-drive permanent magnet synchronous generator (D-PMSG), sum-of-squares optimization, transient stability, Lyapunov function, semi-definite constraints, attraction domain