Region of Attraction Estimation for Power Systems With Multiple Integrated DFIG-Based Wind Turbines

The lack of suitable modeling methods for power systems with multiple doubly-fed induction generator-based wind turbines (DFIGWTs) integrated has left the analytical description of the boundary of the region of attraction (ROA) of such systems largely unexplored. To address this gap, this paper derives an ordinary differential equation (ODE) model for a power system with multiple DFIGWTs integrated. The proposed electromechanical model is validated in a single-machine-infinite-bus (SMIB) power system and a modified 3 machine 9 bus power system with root mean squared errors (RMSEs) of less than 9.5% for trajectory comparisons with the full model, demonstrating that it accurately captures the low-frequency dynamics of the full DFIGWT model. Subsequently, the ODE model is transformed into a polynomial differential-algebraic equation (DAE) model using a nonlinear coordinate transformation. To estimate the ROA, an enhanced expanding interior algorithm (EIA) based on sum of squares (SOS) programming is applied. The feasibility of the proposed model, along with the appropriate conservativeness of the improved EIA, is validated using two test systems that include multiple DFIGWTs and synchronous generators (SGs). By comparison, it is found that the time cost of the improved EIA is reduced by around 17% while maintaining the accuracy. These results demonstrate that the proposed approach has significant practical implications for the integration of wind farms into power systems, and offers an efficient tool for transient stability analysis.