Toward stochastic dynamical wake-modeling for wind farms

Low-fidelity analytical models of turbine wakes have traditionally been used to demonstrate the utility of advanced control algorithms in increasing the annual energy production of wind farms. In practice, however, it remains challenging to achieve significant performance improvements using closed-loop strategies that are based on conventional low-fidelity models. This is due to the over-simplified static nature of wake predictions from models that are agnostic to the complex aerodynamic interactions among turbines. To improve the predictive capability of low-fidelity models while remaining amenable to control design, we offer a stochastic dynamical modeling framework for capturing the effect of atmospheric turbulence on the thrust force and power generation as determined by the actuator disk concept. In this approach, we use stochastically forced linear models of the turbulent velocity field to augment the analytically computed wake velocity and achieve consistency with higher-fidelity models in capturing power and thrust force measurements. The power-spectral densities of our stochastic models are identified via convex optimization to ensure statistical consistency while preserving model parsimony.