Motivated by the vast potential of wind power as a renewable energy source and the reliability issues arising from its integration into a power system, this dissertation designs and analyzes a novel, diverse collection of controllers, which significantly enhance the capability and performance of variable-speed wind turbines and large-scale wind farms.

In the dissertation, we consider a number of key problems and pressing issues in the area and develop, for each of them, a solution based on systems and control theory as well as optimization methods. More specifically, we first devise a nonlinear controller using feedback linearization and a gradient-based approach, which enables wind turbines with doubly fed induction generators to jointly control their active and reactive powers in both the maximum power tracking and power regulation modes. We also extend the controller by incorporating bias estimation and exploiting timescale separation, so that it can cope with turbines with uncertainties, and evaluate our controller via simulations with realistic wind profiles, demonstrating its effectiveness.

Building upon single turbine controllers by other researchers and by us, we next turn to the emerging problem of wind farm power control, in which there is a lack of models that appropriately simplify the complex overall wind farm dynamics. To fill this void, we use system identification approaches to construct a structurally simple, approximate wind turbine control system (WTCS) model, which attempts to mimic the complex active and reactive power dynamics of generic analytical and empirical WTCS models. Through extensive validation, we show that the approximate model is accurate and versatile, capable of closely imitating several WTCS models from the literature and from real data.

Based on the approximate model, we subsequently develop a centralized wind farm controller, which makes the wind farm power output accurately and smoothly track a desired reference from the power grid operator. The wind farm controller is made up of a model predictive controller on the outer loop, which uses various forecasts and feedbacks to iteratively plan the desired power trajectories for optimal tracking, and an adaptive controller on the inner loop, which uses estimated wind speed characteristics to adaptively tune the controller gains for optimal smoothness. We also carry out a series of simulations, which illustrate the salient features of our wind farm controller.

Finally, we study how a wind turbine equipped with a maximum power tracking controller and a proportional inertia response controller may affect the power system frequency from a control standpoint, including the resulting system equilibria, pole-zero locations, and stability properties.