A Control-Oriented Dynamic Model for Wakes in Wind Plants

In this paper, we present a novel control-oriented model for predicting wake effects in wind plants, called the FLOw Redirection and Induction Dynamics (FLORIDyn) model. The model predicts the wake locations and the effective flow velocities at each turbine, and the resulting turbine electrical energy productions, as a function of the control degrees of freedom of the turbines (the axial induction and the yaw angle of the different rotors). The model is an extension of a previously presented static model (FLORIS). It includes the dynamic wake propagation effects that cause time delays between control setting changes and the response of downstream turbines. These delays are associated with a mass of air in the wake taking some time to travel from one turbine to the next, and the delays are dependent on the spatially-and time-varying state of the wake. The extended model has a state-space structure combined with a nonlinear feedback term. While including the control-relevant dynamics of the wind plant, it still has a relatively small amount of parameters, and the computational complexity of the model is small enough such that it has the potential to be used for dynamic optimization of the control reference signals for improved wind plant control.