PDE-Based Modeling and Control for Power Generation Management of Wind Farms

This paper introduces a partial differential equation (PDE) based modeling paradigm for wind farms. The PDE model governs the evolution of a function that represents the distribution of the wind turbines over a range of pitch angles, yaw angles, and wind speeds. The PDE model is embedded into a hierarchical control architecture, in which the central (top) level controller uses the feedback of the individual pitch and yaw angles of the turbines in the farm and synthesizes universal changes in pitch and yaw angles such that the cumulative power generated by the farm tracks a desired power generation trajectory. The controller ensures good tracking performance while satisfying the constraints of the pitch and yaw actuator dynamics. The control design is performed on the PDE model using a framework that includes dynamic inversion, model predictive control and linear matrix inequalities.