This paper presents a wind plant modeling and optimization tool that enables the maximization of wind plant annual energy production (AEP) using yaw-based wake steering control and layout changes. The tool is an extension of a wake engineering model describing the steady-state effects of yaw on wake velocity profiles and power productions of wind turbines in a wind plant. To make predictions of a wind plant's AEP, necessary extensions of the original wake model include coupling it with a detailed rotor model and a control policy for turbine blade pitch and rotor speed. This enables the prediction of power production with wake effects throughout a range of wind speeds. We use the tool to perform an example optimization study on a wind plant based on the Princess Amalia Wind Park. In this case study, combined optimization of layout and wake steering control increases AEP by 5%. The power gains from wake steering control are highest for region 1.5 inflow wind speeds, and they continue to be present to some extent for the above-rated inflow wind speeds. The results show that layout optimization and wake steering are complementary because significant AEP improvements can be achieved with wake steering in a wind plant layout that is already optimized to reduce wake losses.

This paper presents the results of two case studies regarding the wind farm layout optimization problem. We asked members of the computational optimization and wind communities to take part in the studies that we designed. Nine individuals participated. Case study 1 considered variations in optimization strategies for a given simple Gaussian wake model. Participants were provided with a wake model that outputs annual energy production (AEP) for an input set of wind turbine locations. Participants used an optimization method of their choosing to find an optimal wind farm layout. Case study 2 looked at trade-offs in performance resulting from variation in both physics model and optimization strategy. For case study 2, participants calculated AEP using a wake model of their choice while also using their chosen optimization method. Participants then used their wake model to calculate the AEP of all other participants' optimized layouts. Results for case study 1 show that the best optimal wind farm layouts in this study were achieved by participants who used gradient-based optimization methods. A front-runner emerged with the Sparse Nonlinear OPTimizer plus Wake Expansion Continuation (SNOPT+WEC) optimization method, which consistently discovered the highest submitted AEP. For case study 2, two participants found a similar layout that was judged to be superior by all five participants. It is unclear if the better solution resulted from an improved optimization process, or a wake model that was more amenable to optimization.

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The FLOw Redirection and Induction in Steady-state (FLORIS) model, a parametric wind turbine wake model that predicts steady state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This paper provides details on the recent changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing the FLORIS model to more reliably find better solutions to wind farm optimization problems. Keywords FLORIS, optimization, wake model, WFLOP, wind farm, wind turbine wakes ξ init Angle from the wind direction to the wake center line of the FLORIS model, deg. ξ init Added FLORIS model parameter defining a constant addition to ξ init , deg.

The models used during wind farm layout optimization use simplifying assumptions that can alter the design space. Some characteristics of the simple models may negatively influence the resulting layouts. In this paper, we perform wind farm layout optimization using a simple wake model and compare the resulting improvements to large-eddy simulation (LES) results to confirm that the layout was actually improved. We begin by describing the models used, including changes specific for use with gradient-based optimization. We then compare our models' output to previously published model and LES results. Using the models described, we performed gradient-based wind farm layout optimization using exact gradients. Power production for the original and optimized layouts were recalculated using LES. The model and LES results were then compared. The simple models predicted an improvement in annual energy production (AEP) of 7.4%, while the LES reported an AEP improvement of 9.9%. We concluded that the improvements found by optimizing with the simple models are not just an artifact of the model characteristics, but are real improvements.