Small-signal model and dynamic analysis of variable speed induction machine wind farms

A unified, modular, small-signal dynamic model for an induction machine-based wind farm is presented. The proposed model can represent an arbitrary number of fixed-speed, partially variable-speed (doubly fed) and variable-speed induction machine-based wind units in a wind farm. The model represents the dynamics of (i) each wind turbine-generator electromechanical system, (ii) each converter system and the corresponding controls and (iii) the host electrical grid, within the subsynchronous frequency range (0.1?60 Hz). In contrast to the widely used state-space formulation, the proposed approach is based on developing electrical and mechanical transfer-function matrices to formulate the overall system as a multivariable feedback system. Thus, it provides significant flexibility to represent a large number of wind units and their controllers, identical or nonidentical, within a wind farm. Based on the developed model, a frequency response-based method is also introduced, as an alternative to the eigen analysis approach, for small-signal subsynchronous dynamic analysis of the wind farm and its host electrical grid. The proposed method provides a new performance robustness criterion for performance evaluation and also a design tool based on the `size? of the system transfer-function matrix. The concept of induced norm is adopted here as a measure of matrix size. As an example, applications of the model and the analysis approach to a twounit wind farm is presented and the results are validated based on time-domain simulation studies in the PSCAD/ EMTDC environment.