Stochastic dynamical modeling of wake turbulence in wind farms

Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In practice, however, it remains challenging to correctly estimate the flow and achieve significant performance gains using controllers that are based on such 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. We use stochastically forced linearized NS equations to model a turbulent velocity field that complements the analytically computed static wake velocity. This enables us to achieve consistency with the predictions of higher-fidelity models in capturing power and thrust force measurements. The model is also capable of predicting the turbulence intensities both in the presence and absence of yaw misalignment. The power-spectral densities of our stochastic models are identified via convex optimization to ensure consistency with partially available velocity statistics or power and thrust force measurements. Our results provide insight into the significance of sparse field measurements in recovering the statistical signature of the flow using stochastic linear models.