Articles | Volume 10, issue 8
https://doi.org/10.5194/wes-10-1637-2025
© Author(s) 2025. 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-10-1637-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
14 Aug 2025
Research article |
| 14 Aug 2025
| 14 Aug 2025
Integer programming for optimal yaw control of wind farms
Felix Bestehorn
TU Braunschweig, Institute for Mathematical Optimization, Universitätsplatz 2, 38106 Braunschweig, Germany
now at: Carl Zeiss SMT GmbH, Rudolf-Eber-Straße 2, 73447 Oberkochen, Germany
Florian Bürgel
CORRESPONDING AUTHOR
TU Braunschweig, Institute for Mathematical Optimization, Universitätsplatz 2, 38106 Braunschweig, Germany
Christian Kirches
TU Braunschweig, Institute for Mathematical Optimization, Universitätsplatz 2, 38106 Braunschweig, Germany
Sebastian Stiller
TU Braunschweig, Institute for Mathematical Optimization, Universitätsplatz 2, 38106 Braunschweig, Germany
Andreas M. Tillmann
TU Braunschweig, Institute for Mathematical Optimization, Universitätsplatz 2, 38106 Braunschweig, Germany
now at: TU Clausthal, Institute of Mathematics, Erzstraße 1, 38678 Clausthal-Zellerfeld, Germany
Related authors
No articles found.
Florian Bürgel, Robert Scholz, Christian Kirches, and Sebastian Stiller
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2023-2, https://doi.org/10.5194/wes-2023-2, 2023
Revised manuscript not accepted
Short summary
Short summary
Wind turbines are an important electric power source. Usually, they are organized in wind farms. Thereby, each wind turbine causes a so-called wake with a reduced wind speed. This can influence following wind turbines and is an opportunity to optimize the operation of each wind turbine. A wind gust usually makes the tower oscillate. We control a wind turbine in a way such that the following turbine significantly less oscillates. Thereby, we also paid attention to the power of the wind turbines.
Related subject area
Thematic area: Dynamics and control | Topic: Wind farm control
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Marcus Becker, Maxime Lejeune, Philippe Chatelain, Dries Allaerts, Rafael Mudafort, and Jan-Willem van Wingerden
Wind Energ. Sci., 10, 1055–1075, https://doi.org/10.5194/wes-10-1055-2025, https://doi.org/10.5194/wes-10-1055-2025, 2025
Short summary
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Established turbine wake models are steady-state. This paper presents an open-source dynamic wake modeling framework that complements established steady-state wake models with dynamics. It is advantageous over steady-state wake models to describe wind farm power and energy over shorter periods. The model enables researchers to investigate the effectiveness of wind farm flow control strategies. This leads to a better utilization of wind farms and allows them to be used to their fullest extent.
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.
Stijn Ally, Timothy Verstraeten, Pieter-Jan Daems, Ann Nowé, and Jan Helsen
Wind Energ. Sci., 10, 779–812, https://doi.org/10.5194/wes-10-779-2025, https://doi.org/10.5194/wes-10-779-2025, 2025
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Wind farms are crucial for a sustainable energy future. However, their power can fluctuate significantly due to changing weather conditions, which complexly affect their power generation. This paper presents a novel machine-learning-based method to enhance wind farm power predictions, enabling improved power scheduling, trading and grid balancing. This makes wind power more valuable and easier to integrate into the energy system.
Joeri A. Frederik, Eric Simley, Kenneth A. Brown, Gopal R. Yalla, Lawrence C. Cheung, and Paul A. Fleming
Wind Energ. Sci., 10, 755–777, https://doi.org/10.5194/wes-10-755-2025, https://doi.org/10.5194/wes-10-755-2025, 2025
Short summary
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In this paper, we present results from advanced computer simulations to determine the effects of applying different control strategies to a small wind farm. We show that when there is variability in wind direction over height, steering the wake of a turbine away from other turbines is the most effective strategy. When this variability is not present, actively changing the pitch angle of the blades to increase turbulence in the wake could be more effective.
Aemilius Adrianus Wilhelmus van Vondelen, Marion Coquelet, Sachin Tejwant Navalkar, and Jan-Willem van Wingerden
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-51, https://doi.org/10.5194/wes-2025-51, 2025
Revised manuscript under review for WES
Short summary
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Wind farms suffer energy losses due to wake effects between turbines. We present a new control strategy that synchronizes turbine wakes to enhance power output. By estimating and aligning the phase shifts of periodic wake structures using an advanced filtering method, downstream turbines recover more energy. Simulations show up to 10 % increased power at the third turbine. These results offer a promising path to improving wind farm efficiency while mixing wakes.
Piotr Fojcik, Edward Hart, and Emil Hedevang
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-17, https://doi.org/10.5194/wes-2025-17, 2025
Revised manuscript accepted for WES
Short summary
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Increasing the efficiency of wind farms can be achieved via reducing the impact of wakes: flow regions with lower wind speed occurring downwind from turbines. This work describes training and validation of a novel method for estimation of the wake effects impacting a turbine. The results show that for most tested wind conditions, the developed model is capable of robust detection of wake presence, and accurate characterisation of its properties. Further validation and improvements are planned.
Gopal R. Yalla, Kenneth Brown, Lawrence Cheung, Dan Houck, Nathaniel deVelder, and Nicholas Hamilton
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-14, https://doi.org/10.5194/wes-2025-14, 2025
Revised manuscript under review for WES
Short summary
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When wind reaches the first set of turbines in a wind farm, energy is extracted, reducing the energy available for downstream turbines. This study examines emerging technologies aimed at re-energizing the wind between turbines in a wind farm to improve overall power production. Optimizing these technologies depends on understanding complex features of the atmosphere and the wakes behind turbines, which is accomplished using high fidelity computer simulations and data analysis techniques.
Manuel Alejandro Zúñiga Inestroza, Paul Hulsman, Vlaho Petrović, and Martin Kühn
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-171, https://doi.org/10.5194/wes-2024-171, 2025
Revised manuscript under review for WES
Short summary
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Wake effects cause power losses that degrade wind farm efficiency. This paper presents a wind tunnel investigation of dynamic induction control (DIC), a strategy to mitigate wake losses by improving turbine-flow interactions. WindScanner lidar measurements are used to explore the wake development of model turbines in response to DIC. Our results demonstrate consistent benefits and adaptability under realistic inflow conditions, highlighting DIC’s potential to increase wind farm power production.
Peter Bachant, Peter Ireland, Brian Burrows, Chi Qiao, James Duncan, Danian Zheng, and Mohit Dua
Wind Energ. Sci., 9, 2235–2259, https://doi.org/10.5194/wes-9-2235-2024, https://doi.org/10.5194/wes-9-2235-2024, 2024
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Intentional misalignment of upstream turbines in wind plants in order to steer wakes away from downstream turbines has been a topic of research interest for years but has not yet achieved widespread commercial adoption. We deploy one such wake steering system to a utility-scale wind plant and then create a model to predict plant behavior and enable successful control. We apply calibrations to a physics-based model and use machine learning to correct its outputs to improve predictive capability.
Matteo Baricchio, Pieter M. O. Gebraad, and Jan-Willem van Wingerden
Wind Energ. Sci., 9, 2113–2132, https://doi.org/10.5194/wes-9-2113-2024, https://doi.org/10.5194/wes-9-2113-2024, 2024
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Wake steering can be integrated into wind farm layout optimization through a co-design approach. This study estimates the potential of this method for a wide range of realistic conditions, adopting a tailored genetic algorithm and novel geometric yaw relations. A gain in the annual energy yield between 0.3 % and 0.4 % is obtained for a 16-tubrine farm, and a multi-objective implementation is used to limit loss in the case that wake steering is not used during farm operation.
Elie Kadoche, Pascal Bianchi, Florence Carton, Philippe Ciblat, and Damien Ernst
Wind Energ. Sci., 9, 1577–1594, https://doi.org/10.5194/wes-9-1577-2024, https://doi.org/10.5194/wes-9-1577-2024, 2024
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This work proposes a new wind farm controller based on wind predictions and conducts a synthetic sensitivity analysis of wake steering and the variations of the wind direction. For wind turbines that can rotate from −15 to 15° every 10 min, if the wind direction changes by more than 7.34° every 10 min, it is important to consider future wind data in a steady-state yaw control optimization.
Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso
Wind Energ. Sci., 9, 1547–1575, https://doi.org/10.5194/wes-9-1547-2024, https://doi.org/10.5194/wes-9-1547-2024, 2024
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We develop a new simple model to predict power losses incurred by a wind turbine when it yaws out of the wind. The model reveals the effects of a number of rotor design parameters and how the turbine is governed when it yaws. The model exhibits an excellent agreement with large eddy simulations and wind tunnel measurements. We showcase the capabilities of the model by deriving the power-optimal yaw strategy for a single turbine and for a cluster of wake-interacting turbines.
Maarten J. van den Broek, Marcus Becker, Benjamin Sanderse, and Jan-Willem van Wingerden
Wind Energ. Sci., 9, 721–740, https://doi.org/10.5194/wes-9-721-2024, https://doi.org/10.5194/wes-9-721-2024, 2024
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Wind turbine wakes negatively affect wind farm performance as they impinge on downstream rotors. Wake steering reduces these losses by redirecting wakes using yaw misalignment of the upstream rotor. We develop a novel control strategy based on model predictions to implement wake steering under time-varying conditions. The controller is tested in a high-fidelity simulation environment and improves wind farm power output compared to a state-of-the-art reference controller.
Eric Simley, Dev Millstein, Seongeun Jeong, and Paul Fleming
Wind Energ. Sci., 9, 219–234, https://doi.org/10.5194/wes-9-219-2024, https://doi.org/10.5194/wes-9-219-2024, 2024
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Wake steering is a wind farm control technology in which turbines are misaligned with the wind to deflect their wakes away from downstream turbines, increasing total power production. In this paper, we use a wind farm control model and historical electricity prices to assess the potential increase in market value from wake steering for 15 US wind plants. For most plants, we find that the relative increase in revenue from wake steering exceeds the relative increase in energy production.
Nick Janssens and Johan Meyers
Wind Energ. Sci., 9, 65–95, https://doi.org/10.5194/wes-9-65-2024, https://doi.org/10.5194/wes-9-65-2024, 2024
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Proper wind farm control may vastly contribute to Europe's plan to go carbon neutral. However, current strategies don't account for turbine–wake interactions affecting power extraction. High-fidelity models (e.g., LES) are needed to accurately model this but are considered too slow in practice. By coarsening the resolution, we were able to design an efficient LES-based controller with real-time potential. This may allow us to bridge the gap towards practical wind farm control in the near future.
Filippo Gori, Sylvain Laizet, and Andrew Wynn
Wind Energ. Sci., 8, 1425–1451, https://doi.org/10.5194/wes-8-1425-2023, https://doi.org/10.5194/wes-8-1425-2023, 2023
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Wake steering is a promising strategy to increase the power output of modern wind farms by mitigating the negative effects of aerodynamic interaction among turbines. As farm layouts grow in size to meet renewable targets, the complexity of wake steering optimisation increases too. With the objective of enabling robust and predictable wake steering solutions, this study investigates the sensitivity of wake steering optimisation for three different farm layouts with increasing complexity levels.
Daniel van den Berg, Delphine de Tavernier, and Jan-Willem van Wingerden
Wind Energ. Sci., 8, 849–864, https://doi.org/10.5194/wes-8-849-2023, https://doi.org/10.5194/wes-8-849-2023, 2023
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Wind turbines placed in farms interact with their wake, lowering the power production of the wind farm. This can be mitigated using so-called wake mixing techniques. This work investigates the coupling between the pulse wake mixing technique and the motion of floating wind turbines using the pulse. Frequency response experiments and time domain simulations show that extra movement is undesired and that the
optimalexcitation frequency is heavily platform dependent.
Balthazar Arnoldus Maria Sengers, Gerald Steinfeld, Paul Hulsman, and Martin Kühn
Wind Energ. Sci., 8, 747–770, https://doi.org/10.5194/wes-8-747-2023, https://doi.org/10.5194/wes-8-747-2023, 2023
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The optimal misalignment angles for wake steering are determined using wake models. Although mostly analytical, data-driven models have recently shown promising results. This study validates a previously proposed data-driven model with results from a field experiment using lidar measurements. In a comparison with a state-of-the-art analytical model, it shows systematically more accurate estimates of the available power. Also when using only commonly available input data, it gives good results.
Johan Meyers, Carlo Bottasso, Katherine Dykes, Paul Fleming, Pieter Gebraad, Gregor Giebel, Tuhfe Göçmen, and Jan-Willem van Wingerden
Wind Energ. Sci., 7, 2271–2306, https://doi.org/10.5194/wes-7-2271-2022, https://doi.org/10.5194/wes-7-2271-2022, 2022
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We provide a comprehensive overview of the state of the art and the outstanding challenges in wind farm flow control, thus identifying the key research areas that could further enable commercial uptake and success. To this end, we have structured the discussion on challenges and opportunities into four main areas: (1) insight into control flow physics, (2) algorithms and AI, (3) validation and industry implementation, and (4) integrating control with system design
(co-design).
Mou Lin and Fernando Porté-Agel
Wind Energ. Sci., 7, 2215–2230, https://doi.org/10.5194/wes-7-2215-2022, https://doi.org/10.5194/wes-7-2215-2022, 2022
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Large-eddy simulation (LES) is a widely used method to study wind turbine flow. To save computational resources, the turbine-inducing forces in LES are often modelled by parametrisations. We validate three widely used turbine parametrisations in LES in different yaw and offset configurations with wind tunnel measurements, and we find that, in comparison with other parametrisations, the blade element actuator disk model strikes a good balance of accuracy and computational cost.
Konstanze Kölle, Tuhfe Göçmen, Irene Eguinoa, Leonardo Andrés Alcayaga Román, Maria Aparicio-Sanchez, Ju Feng, Johan Meyers, Vasilis Pettas, and Ishaan Sood
Wind Energ. Sci., 7, 2181–2200, https://doi.org/10.5194/wes-7-2181-2022, https://doi.org/10.5194/wes-7-2181-2022, 2022
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The paper studies wind farm flow control (WFFC) in simulations with variable electricity prices. The results indicate that considering the electricity price in the operational strategy can be beneficial with respect to the gained income compared to focusing on the power gain only. Moreover, revenue maximization by balancing power production and structural load reduction is demonstrated at the example of a single wind turbine.
Marcus Becker, Bastian Ritter, Bart Doekemeijer, Daan van der Hoek, Ulrich Konigorski, Dries Allaerts, and Jan-Willem van Wingerden
Wind Energ. Sci., 7, 2163–2179, https://doi.org/10.5194/wes-7-2163-2022, https://doi.org/10.5194/wes-7-2163-2022, 2022
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In this paper we present a revised dynamic control-oriented wind farm model. The model can simulate turbine wake behaviour in heterogeneous and changing wind conditions at a very low computational cost. It utilizes a three-dimensional turbine wake model which also allows capturing vertical wind speed differences. The model could be used to maximise the power generation of with farms, even during events like a wind direction change. It is publicly available and open for further development.
Julian Quick, Ryan N. King, Garrett Barter, and Peter E. Hamlington
Wind Energ. Sci., 7, 1941–1955, https://doi.org/10.5194/wes-7-1941-2022, https://doi.org/10.5194/wes-7-1941-2022, 2022
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Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of alignment with the incoming wind, thereby steering wakes away from downstream turbines. Trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present an optimization approach for efficiently exploring the trade-offs between power and loading during wake steering.
Florian Pöschke and Horst Schulte
Wind Energ. Sci., 7, 1593–1604, https://doi.org/10.5194/wes-7-1593-2022, https://doi.org/10.5194/wes-7-1593-2022, 2022
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The paper compares two different strategies for wind turbine control when following a power command. A model-based control scheme for a 5 MW wind turbine is designed, and a comparison in terms of the mechanical loading and the attainable power dynamics is drawn based on simulation studies. Reduced-order models suitable for integration into an upper-level control design are discussed. The dependence of the turbine behavior on the chosen strategy is illustrated and analyzed.
Balthazar Arnoldus Maria Sengers, Matthias Zech, Pim Jacobs, Gerald Steinfeld, and Martin Kühn
Wind Energ. Sci., 7, 1455–1470, https://doi.org/10.5194/wes-7-1455-2022, https://doi.org/10.5194/wes-7-1455-2022, 2022
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Wake steering aims to redirect the wake away from a downstream turbine. This study explores the potential of a data-driven surrogate model whose equations can be interpreted physically. It estimates wake characteristics from measurable input variables by utilizing a simple linear model. The model shows encouraging results in estimating available power in the far wake, with significant improvements over currently used analytical models in conditions where wake steering is deemed most effective.
Daan van der Hoek, Joeri Frederik, Ming Huang, Fulvio Scarano, Carlos Simao Ferreira, and Jan-Willem van Wingerden
Wind Energ. Sci., 7, 1305–1320, https://doi.org/10.5194/wes-7-1305-2022, https://doi.org/10.5194/wes-7-1305-2022, 2022
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The paper presents a wind tunnel experiment where dynamic induction control was implemented on a small-scale turbine. By periodically changing the pitch angle of the blades, the low-velocity turbine wake is perturbed, and hence it recovers at a faster rate. Small particles were released in the flow and subsequently recorded with a set of high-speed cameras. This allowed us to reconstruct the flow behind the turbine and investigate the effect of dynamic induction control on the wake.
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Short summary
Wind turbines organized in wind farms are an important electric power source. Thereby, each wind turbine causes a so-called wake with a reduced wind speed. This can influence wind turbines that follow and is an opportunity to optimize the operation of the complete wind farm; i.e., we steer the wakes to increase the total power output of the wind farm. In order to do this efficiently, we exploit repetitive structures within a wind farm.
Wind turbines organized in wind farms are an important electric power source. Thereby, each wind...
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