Articles | Volume 11, issue 8
https://doi.org/10.5194/wes-11-2845-2026
© 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-11-2845-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Validation of RANS-calibrated engineering models and ANN-based surrogate for wind farm flow simulation and layout optimization
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Ernestas Simutis
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
M. Paul van der Laan
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Julian Quick
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
DTU Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
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Jens Peter Schøler, Frederik Peder Weilmann Rasmussen, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 11, 2229–2256, https://doi.org/10.5194/wes-11-2229-2026, https://doi.org/10.5194/wes-11-2229-2026, 2026
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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.
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.
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.
Maarten Paul van der Laan, Alexander Meyer Forsting, and Pierre-Elouan Réthoré
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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 5 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.
Jens Peter Schøler, Frederik Peder Weilmann Rasmussen, Julian Quick, and Pierre-Elouan Réthoré
Wind Energ. Sci., 11, 2229–2256, https://doi.org/10.5194/wes-11-2229-2026, https://doi.org/10.5194/wes-11-2229-2026, 2026
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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.
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.
Maarten Paul van der Laan and Simon Watson
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2026-59, https://doi.org/10.5194/wes-2026-59, 2026
Revised manuscript under review for WES
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A theoretical limit for the energy extraction of offshore wind farms has been suggested by Simão Ferreira et al. (2026) based on a simple model of an infinite wind farm and an ad hoc method to correct the model for application to finite wind farms. In this work, we discuss a number of concerns and we conclude that the limit proposed in Simão Ferreira et al. (2026) is not a theoretical limit but a model limit that is strongly dependent on the ad hoc finite wind farm correction.
Oscar García-Santiago, Jake Badger, Andrea N. Hahmann, Patrick J. H. Volker, Søren Ott, M. Paul van der Laan, and Mark Kelly
EGUsphere, https://doi.org/10.5194/egusphere-2026-2144, https://doi.org/10.5194/egusphere-2026-2144, 2026
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We improve how weather models represent the turbulence generated by wind turbines within and behind wind farms. Rather than adding this turbulence only at grid squares with turbine locations, the new method transports it through the wake as it moves downwind. Tests against high-resolution simulations of an idealised wind farm showed better agreement in wake turbulence and more accurate reductions in wind speed, providing a more realistic picture of wake effects across the wind farm.
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
Revised manuscript accepted for WES
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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
Revised manuscript under review for WES
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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.
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.
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.
Mads Baungaard, Takafumi Nishino, and Maarten Paul van der Laan
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-50, https://doi.org/10.5194/wes-2025-50, 2025
Manuscript not accepted for further review
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A systematic comparison between 2D and 3D Reynolds-averaged Navier-Stokes simulations of wind farm flows have been conducted. It is found that the 2D simulations are, at least, two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases considered. The large computational speed-ups and sensible results makes 2D simulations a promising option in the low- to mid-fidelity range.
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.
Maarten Paul van der Laan, Mark Kelly, Mads Baungaard, Antariksh Dicholkar, and Emily Louise Hodgson
Wind Energ. Sci., 9, 1985–2000, https://doi.org/10.5194/wes-9-1985-2024, https://doi.org/10.5194/wes-9-1985-2024, 2024
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Wind turbines are increasing in size and operate more frequently above the atmospheric surface layer, which requires improved inflow models for numerical simulations of turbine interaction. In this work, a novel steady-state model of the atmospheric boundary layer (ABL) is introduced. Numerical wind turbine flow simulations subjected to shallow and tall ABLs are conducted, and the proposed model shows improved performance compared to other state-of-the-art steady-state models.
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.
Mark Kelly and Maarten Paul van der Laan
Wind Energ. Sci., 8, 975–998, https://doi.org/10.5194/wes-8-975-2023, https://doi.org/10.5194/wes-8-975-2023, 2023
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The turning of the wind with height, which is known as veer, can affect wind turbine performance. Thus far meteorology has only given idealized descriptions of veer, which has not yet been related in a way readily usable for wind energy. Here we derive equations for veer in terms of meteorological quantities and provide practically usable forms in terms of measurable shear (change in wind speed with height). Flow simulations and measurements at turbine heights support these developments.
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.
Maarten Paul van der Laan, Mads Baungaard, and Mark Kelly
Wind Energ. Sci., 8, 247–254, https://doi.org/10.5194/wes-8-247-2023, https://doi.org/10.5194/wes-8-247-2023, 2023
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Understanding wind turbine wake recovery is important to mitigate energy losses in wind farms. Wake recovery is often assumed or explained to be dependent on the first-order derivative of velocity. In this work we show that wind turbine wakes recover mainly due to the second-order derivative of the velocity, which transport momentum from the freestream towards the wake center. The wake recovery mechanisms and results of a high-fidelity numerical simulation are illustrated using a simple model.
Mads Baungaard, Stefan Wallin, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 1975–2002, https://doi.org/10.5194/wes-7-1975-2022, https://doi.org/10.5194/wes-7-1975-2022, 2022
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Wind turbine wakes in the neutral atmospheric surface layer are simulated with Reynolds-averaged Navier–Stokes (RANS) using an explicit algebraic Reynolds stress model. Contrary to standard two-equation turbulence models, it can predict turbulence anisotropy and complex physical phenomena like secondary motions. For the cases considered, it improves Reynolds stress, turbulence intensity, and velocity deficit predictions, although a more top-hat-shaped profile is observed for the latter.
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.
Tuhfe Göçmen, Filippo Campagnolo, Thomas Duc, Irene Eguinoa, Søren Juhl Andersen, Vlaho Petrović, Lejla Imširović, Robert Braunbehrens, Jaime Liew, Mads Baungaard, Maarten Paul van der Laan, Guowei Qian, Maria Aparicio-Sanchez, Rubén González-Lope, Vinit V. Dighe, Marcus Becker, Maarten J. van den Broek, Jan-Willem van Wingerden, Adam Stock, Matthew Cole, Renzo Ruisi, Ervin Bossanyi, Niklas Requate, Simon Strnad, Jonas Schmidt, Lukas Vollmer, Ishaan Sood, and Johan Meyers
Wind Energ. Sci., 7, 1791–1825, https://doi.org/10.5194/wes-7-1791-2022, https://doi.org/10.5194/wes-7-1791-2022, 2022
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The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of wind farm flow control benefits. Here we present the first part of the benchmark results for three blind tests with large-scale rotors and 11 participating models in total, via direct power comparisons at the turbines as well as the observed or estimated power gain at the wind farm level under wake steering control strategy.
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.
Mads Baungaard, Maarten Paul van der Laan, and Mark Kelly
Wind Energ. Sci., 7, 783–800, https://doi.org/10.5194/wes-7-783-2022, https://doi.org/10.5194/wes-7-783-2022, 2022
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Wind turbine wakes are dependent on the atmospheric conditions, and it is therefore important to be able to simulate in various different atmospheric conditions. This paper concerns the specific case of an unstable atmospheric surface layer, which is the lower part of the typical daytime atmospheric boundary layer. A simple flow model is suggested and tested for a range of single-wake scenarios, and it shows promising results for velocity deficit predictions.
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Short summary
Wind turbines create wakes, which reduce downstream power. Optimizing turbine placement requires accounting for these reductions. We compared a neural network trained on numerical 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.
Wind turbines create wakes, which reduce downstream power. Optimizing turbine placement requires...
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