The key control problems associated with variable speed wind turbines are maximization of extracted energy when operating below the rated wind speed, and power and speed regulation when operating above the rated wind speed. In this paper, we develop a nonlinear systems framework to address these problems. The framework is used to visualize and analyze the equilibria of the wind turbine as its operating regimes and controllers change. For both below rated and above rated wind speeds, we adopt nonlinear controllers, analyze the stability property of the resulting equilibria, and establish the criterion for switching between control regimes. Further, the regions of attraction of the resulting equilibria are determined, and the existence of a common region of attraction, which allows stable switching between operating regimes, is shown. The control input maintains continuity at the point of switching. We next provide a method for blade pitch modulation to control rotor speed at high wind speeds. Through Lyapunov stability analysis, we prove stability of the equilibria in the presence of the two independently functioning torque- and pitch-control feedback loops. Simulation results are presented and the controller is compared with existing works from the literature.

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