Dynamic Programming Framework for Wind Power Maximization

The contribution of this paper is the formulation of the wind farm power maximization problem as a multi-stage dynamic programming problem. This formulation is made possible by introducing a state-space model to describe the evolution of the wind velocity profile as a function of the free-stream wind velocity and the wind turbine control variables. This state-space model is coupled with a multi-stage utility function that quantifies the power to be maximized. The benefits of this approach include: a simple algorithm to determine the turbine optimal controls, as a feedback function of the wind farm state, and a rigorous, yet simple, method to calculate the limit of performance for wind farm power maximization. A one-dimensional cascade of wind turbines is used to illustrate the approach. Also given is an analytical expression for the maximum power that can be extracted from the one-dimensional cascade, which parallels the well-known Betz limit for a single turbine.