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This paper presents a feedback/feedforward nonlinear controller for variable-speed wind turbines with doubly fed induction generators. By appropriately adjusting the rotor voltages and the blade pitch angle, the controller simultaneously enables: 1) control of the active power in both the maximum power tracking and power regulation modes; 2) seamless switching between the two modes; and 3) control of the reactive power so that a desirable power factor is maintained. Unlike many existing designs, the controller is developed based on original, nonlinear, electromechanically-coupled models of wind turbines, without attempting approximate linearization. Its development consists of three steps: 1) employ feedback linearization to exactly cancel some of the nonlinearities and perform arbitrary pole placement; 2) design a speed controller that makes the rotor angular velocity track a desired reference whenever possible; and 3) introduce a Lyapunov-like function and present a gradient-based approach for minimizing this function. The effectiveness of the controller is demonstrated through simulation of a wind turbine operating under several scenarios.