Articles | Volume 9, issue 7
https://doi.org/10.5194/wes-9-1547-2024
© Author(s) 2024. 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-9-1547-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On the power and control of a misaligned rotor – beyond the cosine law
Simone Tamaro
Wind Energy Institute, Technical University of Munich, 85748 Garching bei München, Germany
Filippo Campagnolo
Wind Energy Institute, Technical University of Munich, 85748 Garching bei München, Germany
Wind Energy Institute, Technical University of Munich, 85748 Garching bei München, Germany
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Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-66, https://doi.org/10.5194/wes-2025-66, 2025
Preprint under review for WES
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We proposed a new method for active power control that uniquely combines induction control with wake steering to maximize power tracking margins. Our methodology results in significantly improved robustness against wind fluctuations and fatigue loading when compared to the state of the art.
Emmanouil M. Nanos, Carlo L. Bottasso, Simone Tamaro, Dimitris I. Manolas, and Vasilis A. Riziotis
Wind Energ. Sci., 7, 1641–1660, https://doi.org/10.5194/wes-7-1641-2022, https://doi.org/10.5194/wes-7-1641-2022, 2022
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A novel way of wind farm control is presented where the wake is deflected vertically to reduce interactions with downstream turbines. This is achieved by moving ballast in a floating offshore platform in order to pitch the support structure and thereby tilt the wind turbine rotor disk. The study considers the effects of this new form of wake control on the aerodynamics of the steering and wake-affected turbines, on the structure, and on the ballast motion system.
Abhinav Anand and Carlo L. Bottasso
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-101, https://doi.org/10.5194/wes-2025-101, 2025
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We formulate a controller for wind turbines that has three main characteristics. First, it optimizes profit by balancing revenue from power generation with cost. Second, cost includes the effects of cyclic fatigue that, departing from most of the existing literature on control, is rigorously accounted for by an exact cycle counting on receding horizons. Third, it uses a model capable of learning and improving its performance based on measured or synthetic data.
Hadi Hoghooghi and Carlo L. Bottasso
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-98, https://doi.org/10.5194/wes-2025-98, 2025
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We formulate and demonstrate a new digital shadow (i.e. a virtual copy) for wind turbines. The digital shadow is designed in order to be capable of mirroring the response of the machine even in complex inflow conditions. Results from field measurements illustrate the ability of the shadow to estimate loads with good accuracy, even with minimal tuning.
Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso
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We proposed a new method for active power control that uniquely combines induction control with wake steering to maximize power tracking margins. Our methodology results in significantly improved robustness against wind fluctuations and fatigue loading when compared to the state of the art.
Andre Thommessen, Abhinav Anand, Christoph M. Hackl, and Carlo L. Bottasso
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-72, https://doi.org/10.5194/wes-2025-72, 2025
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We present a method to forecast inertia that accounts for wake effects in a wind farm. The approach is based on mapping forecasted site conditions to each single wind turbine in the farm through a wake model. The resulting inflow conditions are used to predict the inertia that the wind farm can provide to the grid, taking the wind turbine control strategies and operational limits into account.
Abhinav Anand, Robert Braunbehrens, Adrien Guilloré, and Carlo L. Bottasso
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-67, https://doi.org/10.5194/wes-2025-67, 2025
Revised manuscript has not been submitted
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We present a new method for wind farm control, based on the optimization of an economic cost function that accounts for revenue from power production and cost due to operation and maintenance. The new formulation also includes constraints to ensure a desired lifetime duration. The application to relevant scenarios shows consistently improved profit when compared to alternative formulations from the recent literature.
Marta Bertelè, Paul J. Meyer, Carlo R. Sucameli, Johannes Fricke, Anna Wegner, Julia Gottschall, and Carlo L. Bottasso
Wind Energ. Sci., 9, 1419–1429, https://doi.org/10.5194/wes-9-1419-2024, https://doi.org/10.5194/wes-9-1419-2024, 2024
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A neural observer is used to estimate shear and veer from the operational data of a large wind turbine equipped with blade load sensors. Comparison with independent measurements from a nearby met mast and profiling lidar demonstrate the ability of the
rotor as a sensorconcept to provide high-quality estimates of these inflow quantities based simply on already available standard operational data.
Jenna Iori, Carlo Luigi Bottasso, and Michael Kenneth McWilliam
Wind Energ. Sci., 9, 1289–1304, https://doi.org/10.5194/wes-9-1289-2024, https://doi.org/10.5194/wes-9-1289-2024, 2024
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The controller of a wind turbine has an important role in regulating power production and avoiding structural failure. However, it is often designed after the rest of the turbine, and thus its potential is not fully exploited. An alternative is to design the structure and the controller simultaneously. This work develops a method to identify if a given turbine design can benefit from this new simultaneous design process. For example, a higher and cheaper turbine tower can be built this way.
Franz V. Mühle, Florian M. Heckmeier, Filippo Campagnolo, and Christian Breitsamter
Wind Energ. Sci., 9, 1251–1271, https://doi.org/10.5194/wes-9-1251-2024, https://doi.org/10.5194/wes-9-1251-2024, 2024
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Wind turbines influence each other, and these wake effects limit the power production of downstream turbines. Controlling turbines collectively and not individually can limit such effects. We experimentally investigate a control strategy increasing mixing in the wake. We want to see the potential of this so-called Helix control for power optimization and understand the flow physics. Our study shows that the control technique leads to clearly faster wake recovery and thus higher power production.
Paul Veers, Carlo L. Bottasso, Lance Manuel, Jonathan Naughton, Lucy Pao, Joshua Paquette, Amy Robertson, Michael Robinson, Shreyas Ananthan, Thanasis Barlas, Alessandro Bianchini, Henrik Bredmose, Sergio González Horcas, Jonathan Keller, Helge Aagaard Madsen, James Manwell, Patrick Moriarty, Stephen Nolet, and Jennifer Rinker
Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, https://doi.org/10.5194/wes-8-1071-2023, 2023
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Critical unknowns in the design, manufacturing, and operation of future wind turbine and wind plant systems are articulated, and key research activities are recommended.
Helena Canet, Adrien Guilloré, and Carlo L. Bottasso
Wind Energ. Sci., 8, 1029–1047, https://doi.org/10.5194/wes-8-1029-2023, https://doi.org/10.5194/wes-8-1029-2023, 2023
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We propose a new approach to design that aims at optimal trade-offs between economic and environmental goals. New environmental metrics are defined, which quantify impacts in terms of CO2-equivalent emissions produced by the turbine over its entire life cycle. For some typical onshore installations in Germany, results indicate that a 1 % increase in the cost of energy can buy about a 5 % decrease in environmental impacts: a small loss for the individual can lead to larger gains for society.
Robert Braunbehrens, Andreas Vad, and Carlo L. Bottasso
Wind Energ. Sci., 8, 691–723, https://doi.org/10.5194/wes-8-691-2023, https://doi.org/10.5194/wes-8-691-2023, 2023
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The paper presents a new method in which wind turbines in a wind farm act as local sensors, in this way detecting the flow that develops within the power plant. Through this technique, we are able to identify effects on the flow generated by the plant itself and by the orography of the terrain. The new method not only delivers a flow model of much improved quality but can also help in understanding phenomena that drive the farm performance.
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).
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.
Emmanouil M. Nanos, Carlo L. Bottasso, Simone Tamaro, Dimitris I. Manolas, and Vasilis A. Riziotis
Wind Energ. Sci., 7, 1641–1660, https://doi.org/10.5194/wes-7-1641-2022, https://doi.org/10.5194/wes-7-1641-2022, 2022
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A novel way of wind farm control is presented where the wake is deflected vertically to reduce interactions with downstream turbines. This is achieved by moving ballast in a floating offshore platform in order to pitch the support structure and thereby tilt the wind turbine rotor disk. The study considers the effects of this new form of wake control on the aerodynamics of the steering and wake-affected turbines, on the structure, and on the ballast motion system.
Stefan Loew and Carlo L. Bottasso
Wind Energ. Sci., 7, 1605–1625, https://doi.org/10.5194/wes-7-1605-2022, https://doi.org/10.5194/wes-7-1605-2022, 2022
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This publication presents methods to improve the awareness and control of material fatigue for wind turbines. This is achieved by enhancing a sophisticated control algorithm which utilizes wind prediction information from a laser measurement device. The simulation results indicate that the novel algorithm significantly improves the economic performance of a wind turbine. This benefit is particularly high for situations when the prediction quality is low or the prediction time frame is short.
Emmanouil M. Nanos, Carlo L. Bottasso, Filippo Campagnolo, Franz Mühle, Stefano Letizia, G. Valerio Iungo, and Mario A. Rotea
Wind Energ. Sci., 7, 1263–1287, https://doi.org/10.5194/wes-7-1263-2022, https://doi.org/10.5194/wes-7-1263-2022, 2022
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The paper describes the design of a scaled wind turbine in detail, for studying wakes and wake control applications in the known, controllable and repeatable conditions of a wind tunnel. The scaled model is characterized by conducting experiments in two wind tunnels, in different conditions, using different measurement equipment. Results are also compared to predictions obtained with models of various fidelity. The analysis indicates that the model fully satisfies the initial requirements.
Helena Canet, Stefan Loew, and Carlo L. Bottasso
Wind Energ. Sci., 6, 1325–1340, https://doi.org/10.5194/wes-6-1325-2021, https://doi.org/10.5194/wes-6-1325-2021, 2021
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Lidar-assisted control (LAC) is used to redesign the rotor and tower of three turbines, differing in terms of wind class, size, and power rating. The load reductions enabled by LAC are used to save
mass, increase hub height, or extend lifetime. The first two strategies yield reductions in the cost of energy only for the tower of the largest machine, while more interesting benefits are obtained for lifetime extension.
Chengyu Wang, Filippo Campagnolo, Helena Canet, Daniel J. Barreiro, and Carlo L. Bottasso
Wind Energ. Sci., 6, 961–981, https://doi.org/10.5194/wes-6-961-2021, https://doi.org/10.5194/wes-6-961-2021, 2021
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This paper quantifies the fidelity of the wakes generated by a small (1 m diameter) scaled wind turbine model operated in a large boundary layer wind tunnel. A detailed scaling analysis accompanied by large-eddy simulations shows that these wakes are very realistic scaled versions of the ones generated by the parent full-scale wind turbine in the field.
Marta Bertelè, Carlo L. Bottasso, and Johannes Schreiber
Wind Energ. Sci., 6, 759–775, https://doi.org/10.5194/wes-6-759-2021, https://doi.org/10.5194/wes-6-759-2021, 2021
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A previously published wind sensing method is applied to an experimental dataset obtained from a 3.5 MW turbine and a nearby hub-tall met mast. The method uses blade load harmonics to estimate rotor-equivalent shears and wind directions at the rotor disk. Results indicate the good quality of the estimated shear, both in terms of 10 min averages and of resolved time histories, and a reasonable accuracy in the estimation of the yaw misalignment.
Helena Canet, Pietro Bortolotti, and Carlo L. Bottasso
Wind Energ. Sci., 6, 601–626, https://doi.org/10.5194/wes-6-601-2021, https://doi.org/10.5194/wes-6-601-2021, 2021
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The paper analyzes in detail the problem of scaling, considering both the steady-state and transient response cases, including the effects of aerodynamics, elasticity, inertia, gravity, and actuation. After a general theoretical analysis of the problem, the article considers two alternative ways of designing a scaled rotor. The two methods are then applied to the scaling of a 10 MW turbine of 180 m in diameter down to three different sizes (54, 27, and 2.8 m).
Bart M. Doekemeijer, Stefan Kern, Sivateja Maturu, Stoyan Kanev, Bastian Salbert, Johannes Schreiber, Filippo Campagnolo, Carlo L. Bottasso, Simone Schuler, Friedrich Wilts, Thomas Neumann, Giancarlo Potenza, Fabio Calabretta, Federico Fioretti, and Jan-Willem van Wingerden
Wind Energ. Sci., 6, 159–176, https://doi.org/10.5194/wes-6-159-2021, https://doi.org/10.5194/wes-6-159-2021, 2021
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This article presents the results of a field experiment investigating wake steering on an onshore wind farm. The measurements show that wake steering leads to increases in power production of up to 35 % for two-turbine interactions and up to 16 % for three-turbine interactions. However, losses in power production are seen for various regions of wind directions. The results suggest that further research is necessary before wake steering will consistently lead to energy gains in wind farms.
Chengyu Wang, Filippo Campagnolo, and Carlo L. Bottasso
Wind Energ. Sci., 5, 1537–1550, https://doi.org/10.5194/wes-5-1537-2020, https://doi.org/10.5194/wes-5-1537-2020, 2020
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A new method is described to identify the aerodynamic characteristics of blade airfoils directly from operational data of the turbine. Improving on a previously published approach, the present method is based on a new maximum likelihood formulation that includes errors both in the outputs and the inputs. The method is demonstrated on the identification of the polars of small-scale turbines for wind tunnel testing.
Filippo Campagnolo, Robin Weber, Johannes Schreiber, and Carlo L. Bottasso
Wind Energ. Sci., 5, 1273–1295, https://doi.org/10.5194/wes-5-1273-2020, https://doi.org/10.5194/wes-5-1273-2020, 2020
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The performance of an open-loop wake-steering controller is investigated with a new wind tunnel experiment. Three scaled wind turbines are placed on a large turntable and exposed to a turbulent inflow, resulting in dynamically varying wake interactions. The study highlights the importance of using a robust formulation and plant flow models of appropriate fidelity and the existence of possible margins for improvement by the use of dynamic controllers.
Cited articles
Abramowitz, M., Stegun, I. A., and Romer, R. H.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Am. J. Phys., 56, 958–958, https://doi.org/10.1119/1.15378, 1988. a
Bak, C., Zahle, F., Bitsche, R., Kim, T., Yde, A., Henriksen, L. C., Natarajan, A., and Hansen, M.: Description of the DTU 10 MW reference wind turbine, Tech. Rep. I-0092 5, DTU Wind Energy, https://backend.orbit.dtu.dk/ws/portalfiles/portal/55645274/The_DTU_10MW_Reference_Turbine_Christian_Bak.pdf (last access: 12 July 2024), 2013. a, b
Bartl, J., Mühle, F., Schottler, J., Sætran, L., Peinke, J., Adaramola, M., and Hölling, M.: Wind tunnel experiments on wind turbine wakes in yaw: effects of inflow turbulence and shear, Wind Energ. Sci., 3, 329–343, https://doi.org/10.5194/wes-3-329-2018, 2018. a
Bortolotti, P., Tarres, H. C., Dykes, K. L., Merz, K., Sethuraman, L., Verelst, D., and Zahle, F.: IEA Wind TCP Task 37: Systems Engineering in Wind Energy – WP2.1 Reference Wind Turbines, Tech. rep., NREL – National Renewable Energy Lab., https://doi.org/10.2172/1529216, 2019. a, b, c, d
Bottasso, C., Croce, A., Nam, Y., and Riboldi, C.: Power curve tracking in the presence of a tip speed constraint, Renew. Energy, 40, 1–12, https://doi.org/10.1016/j.renene.2011.07.045, 2012. a, b
Bottasso, C. L. and Campagnolo, F.: Wind Tunnel Testing of Wind Turbines and Farms, in: Handbook of Wind Energy Aerodynamics, edited by: Stoevesandt, B., Schepers, G., Fuglsang, P., and Sun, Y., Springer International Publishing, Cham, 1077–1126, ISBN 978-3-030-31307-4, https://doi.org/10.1007/978-3-030-31307-4_54, 2022. a, b, c, d
Bottasso, C. L., Campagnolo, F., and Petrović, V.: Wind tunnel testing of scaled wind turbine models: Beyond aerodynamics, J. Wind Eng. Indust. Aerodynam., 127, 11–28, https://doi.org/10.1016/j.jweia.2014.01.009, 2014. a, b
Burton, T., Jenkins, N., Sharpe, D., and Bossanyi, E.: Wind Energy Handbook, John Wiley & Sons, Ltd, ISBN 9780470699751, https://doi.org/10.1002/9781119992714, 2011. a, b, c
Campagnolo, F., Petrović, V., Schreiber, J., Nanos, E. M., Croce, A., and Bottasso, C. L.: Wind tunnel testing of a closed-loop wake deflection controller for wind farm power maximization, J. Phys.: Conf. Ser., 753, 032006, https://doi.org/10.1088/1742-6596/753/3/032006, 2016. a, b
Campagnolo, F., Weber, R., Schreiber, J., and Bottasso, C. L.: Wind tunnel testing of wake steering with dynamic wind direction changes, Wind Energ. Sci., 5, 1273–1295, https://doi.org/10.5194/wes-5-1273-2020, 2020. a, b, c, d
Campagnolo, F., Tamaro, S., Mühle, F., and Bottasso, C. L.: Wind Tunnel Testing of Combined Derating and Wake Steering, IFAC-PapersOnLine, 56, 8400–8405, https://doi.org/10.1016/j.ifacol.2023.10.1034, 2023. a, b, c
Coleman, R. P., Feingold, A. M., and Stempin, C. W.: Evaluation of the Induced-Velocity Field of an Idealized Helicopter Rotor, Wartime report, National Advisory Committee for Aeronautics, Langley Memorial Aeronautical Laboratory, https://apps.dtic.mil/sti/pdfs/ADA801123.pdf (last access: 12 July 2024), 1945. a
Cossu, C.: Wake redirection at higher axial induction, Wind Energ. Sci., 6, 377–388, https://doi.org/10.5194/wes-6-377-2021, 2021a. a, b, c, d
Cossu, C.: Evaluation of tilt control for wind-turbine arrays in the atmospheric boundary layer, Wind Energ. Sci., 6, 663–675, https://doi.org/10.5194/wes-6-663-2021, 2021b. a, b
Dahlberg, J. and Montgomerie, B.: Research program of the Utgrunden demonstration offshore wind farm, final report part 2, wake effects and other loads, Technical report 02-17, Swedish Defense Research Agency (FOI), Kista, Sweden, 2005. a
Doekemeijer, B. M., Kern, S., Maturu, S., Kanev, S., Salbert, B., Schreiber, J., Campagnolo, F., Bottasso, C. L., Schuler, S., Wilts, F., Neumann, T., Potenza, G., Calabretta, F., Fioretti, F., and van Wingerden, J.-W.: Field experiment for open-loop yaw-based wake steering at a commercial onshore wind farm in Italy, Wind Energ. Sci., 6, 159–176, https://doi.org/10.5194/wes-6-159-2021, 2021. a
Draper, M., Guggeri, A., López, B., Díaz, A., Campagnolo, F., and Usera, G.: A Large Eddy Simulation framework to assess wind farm power maximization strategies: Validation of maximization by yawing, J. Phys.: Conf. Ser., 1037, 072051, https://doi.org/10.1088/1742-6596/1037/7/072051, 2018. a, b
Fleming, P., Gebraad, P. M., Lee, S., van Wingerden, J.-W., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P., and Moriarty, P.: Simulation comparison of wake mitigation control strategies for a two-turbine case, Wind Energy, 18, 2135–2143, https://doi.org/10.1002/we.1810, 2015. a, b, c
Fleming, P., Annoni, J., Shah, J. J., Wang, L., Ananthan, S., Zhang, Z., Hutchings, K., Wang, P., Chen, W., and Chen, L.: Field test of wake steering at an offshore wind farm, Wind Energ. Sci., 2, 229–239, https://doi.org/10.5194/wes-2-229-2017, 2017. a
Fleming, P., Annoni, J., Churchfield, M., Martinez-Tossas, L. A., Gruchalla, K., Lawson, M., and Moriarty, P.: A simulation study demonstrating the importance of large-scale trailing vortices in wake steering, Wind Energ. Sci., 3, 243–255, https://doi.org/10.5194/wes-3-243-2018, 2018. a
Fleming, P., King, J., Dykes, K., Simley, E., Roadman, J., Scholbrock, A., Murphy, P., Lundquist, J. K., Moriarty, P., Fleming, K., van Dam, J., Bay, C., Mudafort, R., Lopez, H., Skopek, J., Scott, M., Ryan, B., Guernsey, C., and Brake, D.: Initial results from a field campaign of wake steering applied at a commercial wind farm – Part 1, Wind Energ. Sci., 4, 273–285, https://doi.org/10.5194/wes-4-273-2019, 2019. a
Fleming, P. A., Gebraad, P. M., Lee, S., van Wingerden, J.-W., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P., and Moriarty, P.: Evaluating techniques for redirecting turbine wakes using SOWFA, Renew. Energy, 70, 211–218, https://doi.org/10.1016/j.renene.2014.02.015, 2014. a
Gao, F. and Han, L.: Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Comput. Optimiz. Appl., 51, 259–277, https://doi.org/10.1007/s10589-010-9329-3, 2012. a
Gebraad, P. M. O., Teeuwisse, F. W., van Wingerden, J. W., Fleming, P. A., Ruben, S. D., Marden, J. R., and Pao, L. Y.: Wind plant power optimization through yaw control using a parametric model for wake effects – a CFD simulation study, Wind Energy, 19, 95–114, https://doi.org/10.1002/we.1822, 2016. a
Hansen, M.: Aerodynamics of wind turbines: Third edition, Routledge, ISBN 9781315769981, https://doi.org/10.4324/9781315769981, 2015. a, b, c, d
Howland, M. F., González, C. M., Martínez, J. J. P., Quesada, J. B., Larrañaga, F. P., Yadav, N. K., Chawla, J. S., and Dabiri, J. O.: Influence of atmospheric conditions on the power production of utility-scale wind turbines in yaw misalignment, J. Renew. Sustain. Energ., 12, 063307, https://doi.org/10.1063/5.0023746, 2020. a, b
Hulsman, P., Sucameli, C., Petrović, V., Rott, A., Gerds, A., and Kühn, M.: Turbine power loss during yaw-misaligned free field tests at different atmospheric conditions, J. Phys.: Conf. Ser., 2265, 032074, https://doi.org/10.1088/1742-6596/2265/3/032074, 2022. a
Jiménez, A., Crespo, A., and Migoya, E.: Application of a LES technique to characterize the wake deflection of a wind turbine in yaw, Wind Energy, 13, 559–572, https://doi.org/10.1002/we.380, 2010. a, b, c
Jonkman, J., Butterfield, S., Musial, W., and Scott, G.: Definition of a 5-MW Reference Wind Turbine for Offshore System Development, Tech. rep., National Renewable Energy Laboratory, https://doi.org/10.2172/947422, 2009. a, b, c
Juangarcia, D. A., Eguinoa, I., and Knudsen, T.: Derating a single wind farm turbine for reducing its wake and fatigue, J. Phys. Conf. Ser., 1037, 032039, https://doi.org/10.1088/1742-6596/1037/3/032039, 2018. a, b, c
Katz, J. and Plotkin, A.: Low-Speed Aerodynamics, in: Cambridge Aerospace Series, 2nd Edn., Cambridge University Press, https://doi.org/10.1017/CBO9780511810329, 2001. a
King, J., Fleming, P., King, R., Martínez-Tossas, L. A., Bay, C. J., Mudafort, R., and Simley, E.: Control-oriented model for secondary effects of wake steering, Wind Energ. Sci., 6, 701–714, https://doi.org/10.5194/wes-6-701-2021, 2021. a
Krogstad, P.-A. and Adaramola, M. S.: Performance and near wake measurements of a model horizontal axis wind turbine, Wind Energy, 15, 743–756, https://doi.org/10.1002/we.502, 2012. a
Leloudas, G., Zhu, W. J., Sørensen, J. N., Shen, W. Z., and Hjort, S.: Prediction and Reduction of Noise from a 2.3 MW Wind Turbine, J. Phys.: Conf. Ser., 75, 012083, https://doi.org/10.1088/1742-6596/75/1/012083, 2007. a
Liew, J., Urbán, A. M., and Andersen, S. J.: Analytical model for the power–yaw sensitivity of wind turbines operating in full wake, Wind Energ. Sci., 5, 427–437, https://doi.org/10.5194/wes-5-427-2020, 2020. a, b, c
Marelli, S. and Sudret, B.: UQLab: A Framework for Uncertainty Quantification in Matlab, in: The 2nd International Conference on Vulnerability and Risk Analysis and Management (ICVRAM 2014), American Society of Civil Engineers, 2554–2563, https://doi.org/10.1061/9780784413609.257, 2014. a
Martínez-Tossas, L. A. and Meneveau, C.: Filtered lifting line theory and application to the actuator line model, J. Fluid Mech., 863, 269–292, https://doi.org/10.1017/jfm.2018.994, 2019. a
Martínez-Tossas, L. A., King, J., Quon, E., Bay, C. J., Mudafort, R., Hamilton, N., Howland, M. F., and Fleming, P. A.: The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows, Wind Energ. Sci., 6, 555—570, https://doi.org/10.5194/wes-6-555-2021, 2021. a
Medici, D.: Experimental studies of wind turbine wakes : power optimisation and meandering, PhD thesis, Royal Institute of Technology, Stockholm, Sweden, https://www.mech.kth.se/thesis/2006/phd/phd_2006_davide_medici.pdf (last access: 12 July 2024), 2005. a
Meyer Forsting, A., van der Laan, M., and Troldborg, N.: The induction zone/factor and sheared inflow: A linear connection?, J. Phys.: Conf. Ser., 1037, 072031, https://doi.org/10.1088/1742-6596/1037/7/072031, 2018. a
Meyers, J., Bottasso, C., Dykes, K., Fleming, P., Gebraad, P., Giebel, G., Göçmen, T., and van Wingerden, J.-W.: Wind farm flow control: prospects and challenges, Wind Energ. Sci., 7, 2271–2306, https://doi.org/10.5194/wes-7-2271-2022, 2022. a, b, c
MKS Instruments Inc.: 226A Baratron Differential Capacitance Manometer, https://www.mks.com/ (last access: 12 July 2024), 2022. a
Nanos, E. M., Bottasso, C. L., Tamaro, S., Manolas, D. I., and Riziotis, V. A.: Vertical wake deflection for floating wind turbines by differential ballast control, Wind Energ. Sci., 7, 1641–1660, https://doi.org/10.5194/wes-7-1641-2022, 2022. a, b
NREL: AeroDyn Users Guide and Theory Manual, https://github.com/OpenFAST/OpenFAST/blob/main/docs/source/user/aerodyn/index.rst (last access: 19 March 2023), 2023a. a
NREL: OpenFAST, https://github.com/openfast (last access: 19 March 2023), 2023c. a
Pedersen, M. M., van der Laan, P., Friis-Møller, M., Rinker, J., and Réthoré, P.-E.: DTUWindEnergy/PyWake: PyWake, Zenodo [code], https://doi.org/10.5281/zenodo.2562662, 2019. a, b
Pitt, D. M. and Peters, D. A.: Theoretical prediction of dynamic inflow derivatives, Vertica, 5, 1981. a
Schottler, J., Hölling, A., Peinke, J., and Hölling, M.: Brief communication: On the influence of vertical wind shear on the combined power output of two model wind turbines in yaw, Wind Energ. Sci., 2, 439–442, https://doi.org/10.5194/wes-2-439-2017, 2017. a
Shapiro, C. R., Gayme, D. F., and Meneveau, C.: Modelling yawed wind turbine wakes: a lifting line approach, J. Fluid Mech., 841, R1, https://doi.org/10.1017/jfm.2018.75, 2018. a
Simley, E., Fleming, P., Girard, N., Alloin, L., Godefroy, E., and Duc, T.: Results from a wake-steering experiment at a commercial wind plant: investigating the wind speed dependence of wake-steering performance, Wind Energ. Sci., 6, 1427–1453, https://doi.org/10.5194/wes-6-1427-2021, 2021. a
Tamaro, S., Campagnolo, F., and Bottasso, C. L.: On the power and control of a misaligned rotor – Beyond the cosine law, Zenodo [source code and data set], https://doi.org/10.5281/zenodo.10974493, 2024a. a, b, c
Tamaro, S., Campagnolo, F., and Bottasso, C. L.: On the power and control of a misaligned rotor – Beyond the cosine law, Binder [source code and data set for Figs. 2, 5, 6, 21, and 22], https://tinyurl.com/btcl-figs (last access: 12 July 2024), 2024b. a
Tietjens, O. and Prandtl, L.: Applied Hydro- and Aeromechanics: Based on Lectures of L. Prandtl, in: no. Bd. 2 in Applied hydro- and aeromechanics: based on lectures of L. Prandtl, Dover Publications, ISBN 9780486603759, https://books.google.de/books?id=Ds-bd0zAwIYC (last access: 12 July 2024), 1957. a
Troldborg, N., Sørensen, J. N., and Mikkelsen, R.: Actuator Line Simulation of Wake of Wind Turbine Operating in Turbulent Inflow, J. Phys.: Conf. Ser., 75, 012063, https://doi.org/10.1088/1742-6596/75/1/012063, 2007. a
Wang, C., Wang, J., Campagnolo, F., Carraón, D. B., and Bottasso, C. L.: Validation of large-eddy simulation of scaled waked wind turbines in different yaw misalignment conditions, J. Phys.: Conf. Ser., 1037, 062007, https://doi.org/10.1088/1742-6596/1037/6/062007, 2018. a
Wang, C., Campagnolo, F., Canet, H., Barreiro, D. J., and Bottasso, C. L.: How realistic are the wakes of scaled wind turbine models?, Wind Energ. Sci., 6, 961–981, https://doi.org/10.5194/wes-6-961-2021, 2021. a, b, c
Wang, J., Wang, C., Campagnolo, F., and Bottasso, C. L.: Wake behavior and control: comparison of LES simulations and wind tunnel measurements, Wind Energ. Sci., 4, 71–88, https://doi.org/10.5194/wes-4-71-2019, 2019. a
Zalkind, D., Nicotra, M., and Pao, L.: Constrained power reference control for wind turbines, Wind Energy, 25, 914–934, https://doi.org/10.1002/we.2705, 2022. a, b
Short summary
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.
We develop a new simple model to predict power losses incurred by a wind turbine when it yaws...
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