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This paper presents a graph‐based dynamic yaw model to predict the dynamic response of the hub‐height velocities and the power of a wind farm to a change in yaw. The model builds on previous work where the turbines define the nodes of the graph and the edges represent the interactions between turbines. Advances associated with the dynamic yaw model include a novel analytical description of the deformation of wind turbine wakes under yaw to represent the velocity deficits and a more accurate representation of the interturbine travel time of wakes. The accuracy of the model is improved by coupling it with time‐ and space‐dependent estimates of the wind farm inflow based on real‐time data from the wind farm. The model is validated both statically and dynamically using large‐eddy simulations. An application of the model is presented that incorporates the model into an optimal control loop to control the farm power output.

 

We employ a recently introduced structured input–output analysis (SIOA) approach to analyse streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds-number ( $Re$ ) low-bulk Richardson number ( $Ri_b$ ) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent–laminar layers commonly observed in the high- $Re$ high- $Ri_b$ intermittent regime. An SIOA across a range of $Ri_b$ and $Re$ values suggests that the classical Miles–Howard stability criterion ( $Ri_b\leq 1/4$ ) is associated with a change in the most amplified flow structures when the Prandtl number is close to one ( $Pr\approx 1$ ). However, for $Pr\ll 1$ , the most amplified flow structures are determined by the product $PrRi_b$ . For $Pr\gg 1$ , SIOA identifies another quasi-horizontal flow structure that we show is principally associated with density perturbations. We further demonstrate the dominance of this density-associated flow structure in the high $Pr$ limit by constructing analytical scaling arguments for the amplification in terms of $Re$ and $Pr$ under the assumptions of unstratified flow (with $Ri_b=0$ ) and streamwise invariance. 

The dynamics of the turbulent atmospheric boundary layer play a fundamental role in wind farm energy production, governing the velocity field that enters the farm as well as the turbulent mixing that regenerates energy for extraction at downstream rows. Understanding the dynamic interactions among turbines, wind farms, and the atmospheric boundary layer can therefore be beneficial in improving the efficiency of wind farm control approaches. Anticipated increases in the sizes of new wind farms to meet renewable energy targets will increase the importance of exploiting this understanding to advance wind farm control capabilities. This review discusses approaches for modeling and estimation of the wind farm flow field that have exploited such knowledge in closed-loop control, to varying degrees. We focus on power tracking as an example application that will be of critical importance as wind farms transition into their anticipated role as major suppliers of electricity. The discussion highlights the benefits of including the dynamics of the flow field in control and points to critical shortcomings of the current approaches. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

Input–output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that this forcing is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured-singular-value-based approach that preserves certain input–output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis, experiments and direct numerical simulation (DNS) of transitional channel flows. Application of this method to transitional plane Couette and plane Poiseuille flows leads to not only the identification of the streamwise coherent structures predicted through traditional input–output approaches, but also the characterization of the oblique flow structures as those requiring the least energy to induce transition, in agreement with DNS studies, and nonlinear optimal perturbation analysis. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large channel size. The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with weakening of the lift-up mechanism, which is known to dominate the linear operator. Capturing this key nonlinear effect enables the prediction of a wider range of known transitional flow structures within the analytical input–output modelling paradigm.