The modeling and control design for a grid- connected wind-energy converter system including a matrix converter are presented. A nonlinear model is developed including equations of mechanical aerodynamic conversion, drive train, matrix converter, and squirrel-cage induction generator. The model is linearized, and the steady-state and transient responses of the small-signal model are evaluated and compared with the nonlinear system. A controller is developed to track the desired active and reactive powers delivered to the grid. Zero steady-state error is achieved using integral action with state- feedback control designed using LQ optimization. Simulations show that the system outputs follow the references with zero steady-state errors.
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Barakati et al. (2007) studied this question.