Articles | Volume 11, issue 6
https://doi.org/10.5194/wes-11-2229-2026
© 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-11-2229-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Graph neural operator for wind farm wake flow
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Frederik Peder Weilmann Rasmussen
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Julian Quick
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Pierre-Elouan Réthoré
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
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Jens Peter Schøler, Frederik Peder Weilmann Rasmussen, M. Paul van der Laan, Alfredo Peña, and Pierre-Elouan Réthoré
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2026-54, https://doi.org/10.5194/wes-2026-54, 2026
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As offshore wind farms are built closer together, predicting how they affect each other becomes critical. We compared two AI approaches for this task, training both on cheap approximate data before refining them with expensive high-accuracy simulations. One predicts wake boundaries better, while the other estimates wind speeds more accurately, offering complementary tools for future wind farm design.
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Wind turbines create wakes, with lower speeds that reduce downstream power. Optimizing turbine placement requires accounting for these reductions. We compared a neural network trained on CFD simulations against engineering wake models across various farm sizes. The neural network predicted flow most accurately but was slower. Surprisingly, a simple TurbOPark model produced layouts with higher validated energy output, suggesting that accuracy is not the only important metric for such models.
Rafael Valotta Rodrigues, Mads Mølgaard Pedersen, Jens Peter Schøler, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 321–341, https://doi.org/10.5194/wes-9-321-2024, https://doi.org/10.5194/wes-9-321-2024, 2024
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The use of wind energy has been growing over the last few decades, and further increase is predicted. As the wind energy industry is starting to consider larger wind farms, the existing numerical methods for analysis of small and medium wind farms need to be improved. In this article, we have explored different strategies to tackle the problem in a feasible and timely way. The final product is a set of recommendations when carrying out trade-off analysis on large wind farms.
Julia Steiner, Emily Louise Hodgson, Maarten Paul van der Laan, Leonardo Alcayaga, Mads Pedersen, Søren Juhl Andersen, Gunner Larsen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 11, 1679–1703, https://doi.org/10.5194/wes-11-1679-2026, https://doi.org/10.5194/wes-11-1679-2026, 2026
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Wake steering is a promising strategy for wind farm optimization, but its success hinges on accurate wake models. We assess models of varying fidelity for a 22 MW reference turbine, comparing single- and two-turbine cases against large-eddy simulations. All models reproduced qualitative trends for power and loads (if applicable), but quantitative agreement varied, and in general the error increased with increasing yaw angle.
Jens Peter Schøler, Frederik Peder Weilmann Rasmussen, M. Paul van der Laan, Alfredo Peña, and Pierre-Elouan Réthoré
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2026-54, https://doi.org/10.5194/wes-2026-54, 2026
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As offshore wind farms are built closer together, predicting how they affect each other becomes critical. We compared two AI approaches for this task, training both on cheap approximate data before refining them with expensive high-accuracy simulations. One predicts wake boundaries better, while the other estimates wind speeds more accurately, offering complementary tools for future wind farm design.
Nicola Bodini, Patrick Moriarty, Regis Thedin, Paula Doubrawa, Cristina Archer, Myra Blaylock, Carlo Bottasso, Bruno Carmo, Lawrence Cheung, Camille Dubreuil, Rogier Floors, Thomas Herges, Daniel Houck, Ali Kanjari, Colleen M. Kaul, Christopher Kelley, Ru LI, Julie K. Lundquist, Desirae Major, Anh Kiet Nguyen, Mike Optis, Luan R. C. Parada, Alfredo Peña, Julian Quick, David Ricarte, William C. Radünz, Raj K. Rai, Oscar Garcia Santiago, Jonas Schulte, Knut S. Seim, M. Paul van der Laan, Kisorthman Vimalakanthan, and Adam Wise
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2026-34, https://doi.org/10.5194/wes-2026-34, 2026
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Predicting wind farm energy production is challenging because wind patterns are complex. We tested 16 different models against real data from a major field experiment to see which worked best. Surprisingly, the most expensive and detailed models were not always more accurate than simpler ones. We found that feeding models better weather data was the most effective way to improve accuracy. These results help the industry choose the right tools for designing more efficient wind farms.
Jens Peter Schøler, Ernestas Simutis, M. Paul van der Laan, Julian Quick, and Pierre-Elouan Réthoré
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Wind turbines create wakes, with lower speeds that reduce downstream power. Optimizing turbine placement requires accounting for these reductions. We compared a neural network trained on CFD simulations against engineering wake models across various farm sizes. The neural network predicted flow most accurately but was slower. Surprisingly, a simple TurbOPark model produced layouts with higher validated energy output, suggesting that accuracy is not the only important metric for such models.
Julian Quick, Edward Hart, Marcus Binder Nilsen, Rasmus Sode Lund, Jaime Liew, Piinshin Huang, Pierre-Elouan Rethore, Jonathan Keller, Wooyong Song, and Yi Guo
Wind Energ. Sci., 11, 493–507, https://doi.org/10.5194/wes-11-493-2026, https://doi.org/10.5194/wes-11-493-2026, 2026
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Wind turbine main bearings often fail prematurely, creating costly maintenance challenges. This study examined how wake effects – where upstream turbines create disturbed airflow that impacts downstream turbines – affect bearing lifespans. Using computer simulations, we found that wake effects reduce bearing life by 16 % on average. The direction of wake impact matters significantly due to interactions between wind forces and gravity, informing better wind turbine and farm design strategies.
Maarten Paul van der Laan, Alexander Meyer Forsting, and Pierre-Elouan Réthoré
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-287, https://doi.org/10.5194/wes-2025-287, 2026
Revised manuscript under review for WES
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Wind turbine interaction can lead to energy losses. This article introduces a fast open source wind turbine interaction model that can be used to design energy efficient wind farms including effects of atmospheric turbulence and temperature. The model can inherit the accuracy of a higher fidelity model while being about five orders of magnitude faster. However, the model is an order of magnitude slower than analytic wind turbine interaction models, and more research is needed to reduce it.
Thuy-Hai Nguyen, Julian Quick, Pierre-Elouan Réthoré, Jean-François Toubeau, Emmanuel De Jaeger, and François Vallée
Wind Energ. Sci., 10, 1661–1680, https://doi.org/10.5194/wes-10-1661-2025, https://doi.org/10.5194/wes-10-1661-2025, 2025
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Current offshore wind farms have been designed to maximize their production of electricity at all times and not to keep a reserve of power in case of unexpected events on the grid. We present a new formulation for designing wind farms to maximize revenues from both energy and reserve markets. We apply it to a real-life wind farm and show that profits are expected to increase in a significant way for wind farms designed and operated for reserve, with less energy supplied.
Charbel Assaad, Juan Pablo Murcia Leon, Julian Quick, Tuhfe Göçmen, Sami Ghazouani, and Kaushik Das
Wind Energ. Sci., 10, 559–578, https://doi.org/10.5194/wes-10-559-2025, https://doi.org/10.5194/wes-10-559-2025, 2025
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This research develops a new method for assessing hybrid power plant (HPP) profitability, combining wind and battery systems. It addresses the need for an efficient, accurate, and comprehensive operational model by approximating a state-of-the-art energy management system (EMS) for spot market power bidding using machine learning. The approach significantly reduces computational demands while maintaining high accuracy. It thus opens new possibilities in terms of optimizing the design of HPPs.
Jens Visbech, Tuhfe Göçmen, Özge Sinem Özçakmak, Alexander Meyer Forsting, Ásta Hannesdóttir, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 1811–1826, https://doi.org/10.5194/wes-9-1811-2024, https://doi.org/10.5194/wes-9-1811-2024, 2024
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Leading-edge erosion (LEE) can impact wind turbine aerodynamics and wind farm efficiency. This study couples LEE prediction, aerodynamic loss modeling, and wind farm flow modeling to show that LEE's effects on wake dynamics can affect overall energy production. Without preventive initiatives, the effects of LEE increase over time, resulting in significant annual energy production (AEP) loss.
Yuriy Marykovskiy, Thomas Clark, Justin Day, Marcus Wiens, Charles Henderson, Julian Quick, Imad Abdallah, Anna Maria Sempreviva, Jean-Paul Calbimonte, Eleni Chatzi, and Sarah Barber
Wind Energ. Sci., 9, 883–917, https://doi.org/10.5194/wes-9-883-2024, https://doi.org/10.5194/wes-9-883-2024, 2024
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This paper delves into the crucial task of transforming raw data into actionable knowledge which can be used by advanced artificial intelligence systems – a challenge that spans various domains, industries, and scientific fields amid their digital transformation journey. This article underscores the significance of cross-industry collaboration and learning, drawing insights from sectors leading in digitalisation, and provides strategic guidance for further development in this area.
Javier Criado Risco, Rafael Valotta Rodrigues, Mikkel Friis-Møller, Julian Quick, Mads Mølgaard Pedersen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 585–600, https://doi.org/10.5194/wes-9-585-2024, https://doi.org/10.5194/wes-9-585-2024, 2024
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Wind energy developers frequently have to face some spatial restrictions at the time of designing a new wind farm due to different reasons, such as the existence of protected natural areas around the wind farm location, fishing routes, and the presence of buildings. Wind farm design has to account for these restricted areas, but sometimes this is not straightforward to achieve. We have developed a methodology that allows for different inclusion and exclusion areas in the optimization framework.
Rafael Valotta Rodrigues, Mads Mølgaard Pedersen, Jens Peter Schøler, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 9, 321–341, https://doi.org/10.5194/wes-9-321-2024, https://doi.org/10.5194/wes-9-321-2024, 2024
Short summary
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The use of wind energy has been growing over the last few decades, and further increase is predicted. As the wind energy industry is starting to consider larger wind farms, the existing numerical methods for analysis of small and medium wind farms need to be improved. In this article, we have explored different strategies to tackle the problem in a feasible and timely way. The final product is a set of recommendations when carrying out trade-off analysis on large wind farms.
Julian Quick, Pierre-Elouan Rethore, Mads Mølgaard Pedersen, Rafael Valotta Rodrigues, and Mikkel Friis-Møller
Wind Energ. Sci., 8, 1235–1250, https://doi.org/10.5194/wes-8-1235-2023, https://doi.org/10.5194/wes-8-1235-2023, 2023
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Wind turbine positions are often optimized to avoid wake losses. These losses depend on atmospheric conditions, such as the wind speed and direction. The typical optimization scheme involves discretizing the atmospheric inputs, then considering every possible set of these discretized inputs in every optimization iteration. This work presents stochastic gradient descent (SGD) as an alternative, which randomly samples the atmospheric conditions during every optimization iteration.
Andrew Clifton, Sarah Barber, Andrew Bray, Peter Enevoldsen, Jason Fields, Anna Maria Sempreviva, Lindy Williams, Julian Quick, Mike Purdue, Philip Totaro, and Yu Ding
Wind Energ. Sci., 8, 947–974, https://doi.org/10.5194/wes-8-947-2023, https://doi.org/10.5194/wes-8-947-2023, 2023
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Wind energy creates huge amounts of data, which can be used to improve plant design, raise efficiency, reduce operating costs, and ease integration. These all contribute to cheaper and more predictable energy from wind. But realising the value of data requires a digital transformation that brings
grand challengesaround data, culture, and coopetition. This paper describes how the wind energy industry could work with R&D organisations, funding agencies, and others to overcome them.
Maarten Paul van der Laan, Oscar García-Santiago, Mark Kelly, Alexander Meyer Forsting, Camille Dubreuil-Boisclair, Knut Sponheim Seim, Marc Imberger, Alfredo Peña, Niels Nørmark Sørensen, and Pierre-Elouan Réthoré
Wind Energ. Sci., 8, 819–848, https://doi.org/10.5194/wes-8-819-2023, https://doi.org/10.5194/wes-8-819-2023, 2023
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Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses. In this work, an efficient numerical method is presented that can be used to estimate these energy losses. The novel method is verified with higher-fidelity numerical models and validated with measurements of an existing wind farm cluster.
Camilla Marie Nyborg, Andreas Fischer, Pierre-Elouan Réthoré, and Ju Feng
Wind Energ. Sci., 8, 255–276, https://doi.org/10.5194/wes-8-255-2023, https://doi.org/10.5194/wes-8-255-2023, 2023
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Our article presents a way of optimizing the wind farm operation by keeping the emitted noise level below a defined limit while maximizing the power output. This is done by switching between noise reducing operational modes. The method has been developed by using two different noise models, one more advanced than the other, to study the advantages of each model. Furthermore, the optimization method is applied to different wind farm cases.
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.
Jana Fischereit, Kurt Schaldemose Hansen, Xiaoli Guo Larsén, Maarten Paul van der Laan, Pierre-Elouan Réthoré, and Juan Pablo Murcia Leon
Wind Energ. Sci., 7, 1069–1091, https://doi.org/10.5194/wes-7-1069-2022, https://doi.org/10.5194/wes-7-1069-2022, 2022
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Wind turbines extract kinetic energy from the flow to create electricity. This induces a wake of reduced wind speed downstream of a turbine and consequently downstream of a wind farm. Different types of numerical models have been developed to calculate this effect. In this study, we compared models of different complexity, together with measurements over two wind farms. We found that higher-fidelity models perform better and the considered rapid models cannot fully capture the wake effect.
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Short summary
We propose a machine learning model that represents wind turbines as nodes in a graph, learning how they interact to predict the wind speed at any location on a farm. Trained on thousands of simulated farms, it captures complex wake interactions across varying layouts and sizes at low computational cost, supporting faster neighboring farm wake assessment.
We propose a machine learning model that represents wind turbines as nodes in a graph, learning...
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