Articles | Volume 11, issue 1
https://doi.org/10.5194/wes-11-37-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-11-37-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Introduction to and comparison of deep learning and optimization approaches to analytical wake modeling of a tilted wind turbine
James Cutler
CORRESPONDING AUTHOR
Brigham Young University, Department of Mechanical Engineering, Provo, UT 84602, USA
Christopher Bay
National Renewable Energy Laboratory, National Wind Technology Center, Boulder, CO 80303, USA
Andrew Ning
Brigham Young University, Department of Mechanical Engineering, Provo, UT 84602, USA
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Adam Cardoza and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2026-10, https://doi.org/10.5194/wes-2026-10, 2026
Preprint under review for WES
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New software calculates wind turbine blade design improvements 10 times faster than traditional methods while maintaining accuracy. By combining four advanced mathematical techniques, researchers optimized a blade design to reduce energy costs by 11.4 %, making fatigue-aware design practical for engineering applications.
Cory Frontin, Jeff Allen, Christopher J. Bay, Jared Thomas, Ethan Young, and Pietro Bortolotti
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-103, https://doi.org/10.5194/wes-2025-103, 2025
Revised manuscript under review for WES
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Wind farms produce energy and to do so have to occupy a non-trivial amount of space. Understanding how much energy a proposed wind farm will make (and at what cost) is technically challenging, especially when turbines are packed closely together. Plus, there's a key tradeoff in how much space a farm occupies and how cheap the energy it can produce might be: less space means more costly energy. This work shows an novel way to run computational simulations efficiently to understand that tradeoff.
Regis Thedin, Garrett Barter, Jason Jonkman, Rafael Mudafort, Christopher J. Bay, Kelsey Shaler, and Jasper Kreeft
Wind Energ. Sci., 10, 1033–1053, https://doi.org/10.5194/wes-10-1033-2025, https://doi.org/10.5194/wes-10-1033-2025, 2025
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We investigate asymmetries in terms of power performance and fatigue loading on a five-turbine wind farm subject to wake steering strategies. Both the yaw misalignment angle and the wind direction were varied from negative to positive. We highlight conditions in which fatigue loading is lower while still maintaining good power gains and show that a partial wake is the source of the asymmetries observed. We provide recommendations in terms of yaw misalignment angles for a given wind direction.
Andrew P. J. Stanley, Christopher J. Bay, and Paul Fleming
Wind Energ. Sci., 8, 1341–1350, https://doi.org/10.5194/wes-8-1341-2023, https://doi.org/10.5194/wes-8-1341-2023, 2023
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Better wind farms can be built by simultaneously optimizing turbine locations and control, which is currently impossible or extremely challenging because of the size of the problem. The authors present a method to determine optimal wind farm control as a function of the turbine locations, which enables turbine layout and control to be optimized together by drastically reducing the size of the problem. In an example, a wind farm's performance improves by 0.8 % when optimized with the new method.
Jared J. Thomas, Nicholas F. Baker, Paul Malisani, Erik Quaeghebeur, Sebastian Sanchez Perez-Moreno, John Jasa, Christopher Bay, Federico Tilli, David Bieniek, Nick Robinson, Andrew P. J. Stanley, Wesley Holt, and Andrew Ning
Wind Energ. Sci., 8, 865–891, https://doi.org/10.5194/wes-8-865-2023, https://doi.org/10.5194/wes-8-865-2023, 2023
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This work compares eight optimization algorithms (including gradient-based, gradient-free, and hybrid) on a wind farm optimization problem with 4 discrete regions, concave boundaries, and 81 wind turbines. Algorithms were each run by researchers experienced with that algorithm. Optimized layouts were unique but with similar annual energy production. Common characteristics included tightly-spaced turbines on the outer perimeter and turbines loosely spaced and roughly on a grid in the interior.
Christopher J. Bay, Paul Fleming, Bart Doekemeijer, Jennifer King, Matt Churchfield, and Rafael Mudafort
Wind Energ. Sci., 8, 401–419, https://doi.org/10.5194/wes-8-401-2023, https://doi.org/10.5194/wes-8-401-2023, 2023
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This paper introduces the cumulative-curl wake model that allows for the fast and accurate prediction of wind farm energy production wake interactions. The cumulative-curl model expands several existing wake models to make the simulation of farms more accurate and is implemented in a computationally efficient manner such that it can be used for wind farm layout design and controller development. The model is validated against high-fidelity simulations and data from physical wind farms.
Marco Mangano, Sicheng He, Yingqian Liao, Denis-Gabriel Caprace, Andrew Ning, and Joaquim R. R. A. Martins
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2023-10, https://doi.org/10.5194/wes-2023-10, 2023
Revised manuscript not accepted
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High-fidelity MDO enables more effective system design than conventional approaches. MDO can shorten the wind turbine design cycle and reduce the cost of energy. We present a first-of-its-kind high-fidelity aerostructural optimization study of a turbine rotor using a coupled CFD-CSM solver. We simultaneously improve the rotor aerodynamic efficiency and reduce the mass of a rotor of a 10 MW wind turbine using 100+ design variables. We discuss the results with unprecedented detail.
Michael J. LoCascio, Christopher J. Bay, Majid Bastankhah, Garrett E. Barter, Paul A. Fleming, and Luis A. Martínez-Tossas
Wind Energ. Sci., 7, 1137–1151, https://doi.org/10.5194/wes-7-1137-2022, https://doi.org/10.5194/wes-7-1137-2022, 2022
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This work introduces the FLOW Estimation and Rose Superposition (FLOWERS) wind turbine wake model. This model analytically integrates the wake over wind directions to provide a time-averaged flow field. This new formulation is used to perform layout optimization. The FLOWERS model provides a smooth flow field over an entire wind plant at fraction of the computational cost of the standard numerical integration approach.
Andrew P. J. Stanley, Christopher Bay, Rafael Mudafort, and Paul Fleming
Wind Energ. Sci., 7, 741–757, https://doi.org/10.5194/wes-7-741-2022, https://doi.org/10.5194/wes-7-741-2022, 2022
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In wind plants, turbines can be yawed to steer their wakes away from downstream turbines and achieve an increase in plant power. The yaw angles become expensive to solve for in large farms. This paper presents a new method to solve for the optimal turbine yaw angles in a wind plant. The yaw angles are defined as Boolean variables – each turbine is either yawed or nonyawed. With this formulation, most of the gains from wake steering can be reached with a large reduction in computational expense.
Jared J. Thomas, Christopher J. Bay, Andrew P. J. Stanley, and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2022-4, https://doi.org/10.5194/wes-2022-4, 2022
Revised manuscript not accepted
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We wanted to determine if and how optimization algorithms may be exploiting inaccuracies in the simple models used for wind farm layout optimization. Comparing optimization results from a simple model to large-eddy simulations showed that even a simple model provides enough information for optimizers to find good layouts. However, varying the number of wind directions in the optimization showed that the wind resource discretization can negatively impact the optimization results.
Andrew P. J. Stanley, Jennifer King, Christopher Bay, and Andrew Ning
Wind Energ. Sci., 7, 433–454, https://doi.org/10.5194/wes-7-433-2022, https://doi.org/10.5194/wes-7-433-2022, 2022
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In this paper, we present a computationally inexpensive model to calculate wind turbine blade fatigue caused by waking and partial waking. The model accounts for steady state on the blade, as well as wind turbulence. The model is fast enough to be used in wind farm layout optimization, which has not been possible with more expensive fatigue models in the past. The methods introduced in this paper will allow for farms with increased energy production that maintain turbine structural reliability.
Andrew P. J. Stanley, Owen Roberts, Jennifer King, and Christopher J. Bay
Wind Energ. Sci., 6, 1143–1167, https://doi.org/10.5194/wes-6-1143-2021, https://doi.org/10.5194/wes-6-1143-2021, 2021
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Wind farm layout optimization is an essential part of wind farm design. In this paper, we present different methods to determine the number of turbines in a wind farm, as well as their placement. Also in this paper we explore the effect that the objective function has on the wind farm design and found that wind farm layout is highly sensitive to the objective. The optimal number of turbines can vary greatly, from 15 to 54 for the cases in this paper, depending on the metric that is optimized.
Alayna Farrell, Jennifer King, Caroline Draxl, Rafael Mudafort, Nicholas Hamilton, Christopher J. Bay, Paul Fleming, and Eric Simley
Wind Energ. Sci., 6, 737–758, https://doi.org/10.5194/wes-6-737-2021, https://doi.org/10.5194/wes-6-737-2021, 2021
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Most current wind turbine wake models struggle to accurately simulate spatially variant wind conditions at a low computational cost. In this paper, we present an adaptation of NREL's FLOw Redirection and Induction in Steady State (FLORIS) wake model, which calculates wake losses in a heterogeneous flow field using local weather measurement inputs. Two validation studies are presented where the adapted model consistently outperforms previous versions of FLORIS that simulated uniform flow only.
Jennifer King, Paul Fleming, Ryan King, Luis A. Martínez-Tossas, Christopher J. Bay, Rafael Mudafort, and Eric Simley
Wind Energ. Sci., 6, 701–714, https://doi.org/10.5194/wes-6-701-2021, https://doi.org/10.5194/wes-6-701-2021, 2021
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This paper highlights the secondary effects of wake steering, including yaw-added wake recovery and secondary steering. These effects enhance the value of wake steering especially when applied to a large wind farm. This paper models these secondary effects using an analytical model proposed in the paper. The results of this model are compared with large-eddy simulations for several cases including 2-turbine, 3-turbine, 5-turbine, and 38-turbine cases.
Luis A. Martínez-Tossas, Jennifer King, Eliot Quon, Christopher J. Bay, Rafael Mudafort, Nicholas Hamilton, Michael F. Howland, and Paul A. Fleming
Wind Energ. Sci., 6, 555–570, https://doi.org/10.5194/wes-6-555-2021, https://doi.org/10.5194/wes-6-555-2021, 2021
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In this paper a three-dimensional steady-state solver for flow through a wind farm is developed and validated. The computational cost of the solver is on the order of seconds for large wind farms. The model is validated using high-fidelity simulations and SCADA.
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Short summary
Tilting wind turbines change the airflow behind them, which can lower energy production in wind farms. This research tested both a traditional physics-based model and a deep learning method to predict these effects. While the traditional model improved with added optimization, it struggled with complex wake patterns. The deep learning approach was faster and more accurate, showing potential for better wind farm design and control with reduced computational cost.
Tilting wind turbines change the airflow behind them, which can lower energy production in wind...
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