Online identification of stability region for large-scale wind farms, Part I: Clustering based piecewise affine impedance modeling

The online assessment of the small-signal stability of wind farms faces challenges in accurately identifying impedance due to the unknown structure and parameters of wind turbine generators. Besides, impedance recalculation is needed under varying operating points. This study proposes a piecewise affine method for impedance modeling and identification under diverse operating points. The piecewise affine impedance is derived through a process that combines offline impedance modeling and online identification. In the offline modeling, the affine impedance is performed in the parameter space of the operating point of the wind turbine generator. A clustering algorithm is employed to optimize the partitioning of the parameter space. In each partition, the impedance is expressed as a first-order explicit function of the complex variable and the operating state variables. Moving to online applications, impedance identification is readily achieved with knowledge of the real-time measured operating point. By locating the operating point in the partitions of the parameter space, the coefficients of the first-order affine models can be determined. Based on the affine first-order impedance of wind turbine generators, the nodal admittance matrix for large-scale wind farms is established with high accuracy. The sensitivity of the dominant eigenvalue is analyzed with respect to the operating point. In validation, the accuracy and efficiency of the piecewise affine impedance model are verified under varying operating points. The online stability and modal analysis based on PWA-identified impedance are validated. A physical experiment is performed to validate the proposed method, which involves impedance data acquisition from frequency scan, offline piecewise affine modeling, online impedance identification, and online stability assessment. • A piecewise affine-based impedance model for wind turbines is proposed.. • The piecewise affine model explicitly maps operating points to wind turbine impedance. • Wind farm nodal admittance matrix is built from piecewise affine WTGs models. • The proposed method can accurately analyze the stability online.