Yawing effects in wind power plants: stochastic wake modeling and control

The success of model-based closed-loop yaw control strategies relies on the accuracy of models that are used to estimate the spatio-temporal attributes of wakes behind wind turbines. We utilize a stochastic dynamical modeling framework to develop reduced-order models of wind farm turbulence that capture the effects of yaw misalignment due to control or atmospheric variability on turbine wakes and their interactions. In this approach, stochastically forced linear models of the turbulent velocity field are used to augment analytical descriptions of the wake velocity provided by low-fidelity engineering wake models. The power-spectral densities of the stochastic models are identified via convex optimization to ensure statistical consistency with high-fidelity large-eddy simulations while preserving model parsimony. We first demonstrate the utility of our approach in capturing turbulence intensity variations at the hub-height of turbines that are yawed against the inflow velocity field impinging on the wind farm. We then extend our two-dimensional (2D) models of hub-height velocity to three-dimensional (3D) wind field models that account for the dynamics of the normal velocity and can thus capture complex attributes of yawed wind turbine wakes such as their rotation and curl. Our results in training 2D and 3D stochastic linear models provide insight into the significance of sparse field measurements in reproducing the statistical signature of wind farm turbulence and demonstrate the robustness of our modeling approach to atmospheric uncertainties and yaw misalignment effects. In the final part of this thesis, we use actuator disc concepts to demonstrate the utility of infinite-horizon stopping in optimizing the yaw angles of wind turbines for constrained maximum power production.