Some decentralized optimization and control algorithms for the control of wind farms

This is a preliminary study of decentralized algorithms that can be applied to wind farm controls. Traditionally, wind farm control is comprised of the wind farm level control and the wind turbine level control. The wind farm level control is a centralized controller that takes the demands from the grid and generates operating points for each wind turbine within the wind farm. The wind turbine level control then generates the optimal control for each turbine to match the operating point. Unfortunately, this traditional control scheme does not constitute the optimal operation of a wind farm due to it???s disregard at either level of control for the interactions between wind turbines in the wind farm . Consequently, a different two level control scheme is proposed in this thesis. This control scheme is shown to be a decentralized controller in that each wind turbine has the ability to both generate its own operating point and calculate its own optimal control. Through the communication of the wind turbines with each other, the interactions between the wind turbines are incorporated into both levels of control. The generation of the operating point is posed as a stochastic resource allocation problem that takes into account the stochastic wind and other wind farm characteristics. We develop a stochastic algorithm based on network dynamic system theory to solve the resource allocation problem. We show that the algorithm converges to the solution of the resource allocation problem almost surely. The calculation of each wind turbine???s optimal control is formulated as an Linear Quadratic Regulator (LQR) optimization problem with a equality constraint. We develop an algorithm that is based on the Tatonnement process in Economics to solve the LQR problem. We first consider the performance of the algorithm in a dynamically decoupled system and show that the algorithm solves the LQR problem. We then consider the performance of the algorithm in a dynamically coupled system and discuss the difference between the two cases