Articles | Volume 7, issue 1
https://doi.org/10.5194/wes-7-433-2022
© Author(s) 2022. 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-7-433-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
03 Mar 2022
Research article |
| 03 Mar 2022
| 03 Mar 2022
A model to calculate fatigue damage caused by partial waking during wind farm optimization
currently at: National Wind Technology Center, National Renewable Energy Laboratory, Boulder, CO 80303, USA
formerly at: Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA
Jennifer King
National Wind Technology Center, National Renewable Energy Laboratory, Boulder, CO 80303, USA
Christopher Bay
National Wind Technology Center, National Renewable Energy Laboratory, Boulder, CO 80303, USA
Andrew Ning
Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA
Related authors
Andrew P. J. Stanley, Christopher Bay, Rafael Mudafort, and Paul Fleming
Wind Energ. Sci., 7, 741–757, https://doi.org/10.5194/wes-7-741-2022, https://doi.org/10.5194/wes-7-741-2022, 2022
Short summary
Short summary
In wind plants, turbines can be yawed to steer their wakes away from downstream turbines and achieve an increase in plant power. The yaw angles become expensive to solve for in large farms. This paper presents a new method to solve for the optimal turbine yaw angles in a wind plant. The yaw angles are defined as Boolean variables – each turbine is either yawed or nonyawed. With this formulation, most of the gains from wake steering can be reached with a large reduction in computational expense.
Jared J. Thomas, Christopher J. Bay, Andrew P. J. Stanley, and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2022-4, https://doi.org/10.5194/wes-2022-4, 2022
Revised manuscript not accepted
Short summary
Short summary
We wanted to determine if and how optimization algorithms may be exploiting inaccuracies in the simple models used for wind farm layout optimization. Comparing optimization results from a simple model to large-eddy simulations showed that even a simple model provides enough information for optimizers to find good layouts. However, varying the number of wind directions in the optimization showed that the wind resource discretization can negatively impact the optimization results.
Andrew P. J. Stanley, Owen Roberts, Jennifer King, and Christopher J. Bay
Wind Energ. Sci., 6, 1143–1167, https://doi.org/10.5194/wes-6-1143-2021, https://doi.org/10.5194/wes-6-1143-2021, 2021
Short summary
Short summary
Wind farm layout optimization is an essential part of wind farm design. In this paper, we present different methods to determine the number of turbines in a wind farm, as well as their placement. Also in this paper we explore the effect that the objective function has on the wind farm design and found that wind farm layout is highly sensitive to the objective. The optimal number of turbines can vary greatly, from 15 to 54 for the cases in this paper, depending on the metric that is optimized.
Cory Frontin, Jeff Allen, Christopher J. Bay, Jared Thomas, Ethan Young, and Pietro Bortolotti
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-103, https://doi.org/10.5194/wes-2025-103, 2025
Preprint under review for WES
Short summary
Short summary
Wind farms produce energy and to do so have to occupy a non-trivial amount of space. Understanding how much energy a proposed wind farm will make (and at what cost) is technically challenging, especially when turbines are packed closely together. Plus, there's a key tradeoff in how much space a farm occupies and how cheap the energy it can produce might be: less space means more costly energy. This work shows an novel way to run computational simulations efficiently to understand that tradeoff.
Regis Thedin, Garrett Barter, Jason Jonkman, Rafael Mudafort, Christopher J. Bay, Kelsey Shaler, and Jasper Kreeft
Wind Energ. Sci., 10, 1033–1053, https://doi.org/10.5194/wes-10-1033-2025, https://doi.org/10.5194/wes-10-1033-2025, 2025
Short summary
Short summary
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.
James Cutler, Christopher Bay, and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-172, https://doi.org/10.5194/wes-2024-172, 2025
Revised manuscript accepted for WES
Short summary
Short summary
This study compares two methods for modeling wakes from tilted wind turbines. An optimized analytical model improves accuracy but is limited by assumptions about wake shape. In contrast, a deep learning approach captures complex wake patterns without these constraints, matching high-fidelity simulations with minimal computational effort. The comparison highlights the potential of deep learning to transform wake modeling, offering greater accuracy and efficiency for wind energy optimization.
Mark O'Malley, Hannele Holttinen, Nicolaos Cutululis, Til Kristian Vrana, Jennifer King, Vahan Gevorgian, Xiongfei Wang, Fatemeh Rajaei-Najafabadi, and Andreas Hadjileonidas
Wind Energ. Sci., 9, 2087–2112, https://doi.org/10.5194/wes-9-2087-2024, https://doi.org/10.5194/wes-9-2087-2024, 2024
Short summary
Short summary
The rising share of wind power poses challenges to cost-effective integration while ensuring reliability. Balancing the needs of the power system and contributions of wind power is crucial for long-term value. Research should prioritize wind power advantages over competitors, focussing on internal challenges. Collaboration with other technologies is essential for addressing the fundamental objectives of power systems – maintaining reliable supply–demand balance at the lowest cost.
Andrew P. J. Stanley, Christopher J. Bay, and Paul Fleming
Wind Energ. Sci., 8, 1341–1350, https://doi.org/10.5194/wes-8-1341-2023, https://doi.org/10.5194/wes-8-1341-2023, 2023
Short summary
Short summary
Better wind farms can be built by simultaneously optimizing turbine locations and control, which is currently impossible or extremely challenging because of the size of the problem. The authors present a method to determine optimal wind farm control as a function of the turbine locations, which enables turbine layout and control to be optimized together by drastically reducing the size of the problem. In an example, a wind farm's performance improves by 0.8 % when optimized with the new method.
Jared J. Thomas, Nicholas F. Baker, Paul Malisani, Erik Quaeghebeur, Sebastian Sanchez Perez-Moreno, John Jasa, Christopher Bay, Federico Tilli, David Bieniek, Nick Robinson, Andrew P. J. Stanley, Wesley Holt, and Andrew Ning
Wind Energ. Sci., 8, 865–891, https://doi.org/10.5194/wes-8-865-2023, https://doi.org/10.5194/wes-8-865-2023, 2023
Short summary
Short summary
This work compares eight optimization algorithms (including gradient-based, gradient-free, and hybrid) on a wind farm optimization problem with 4 discrete regions, concave boundaries, and 81 wind turbines. Algorithms were each run by researchers experienced with that algorithm. Optimized layouts were unique but with similar annual energy production. Common characteristics included tightly-spaced turbines on the outer perimeter and turbines loosely spaced and roughly on a grid in the interior.
Christopher J. Bay, Paul Fleming, Bart Doekemeijer, Jennifer King, Matt Churchfield, and Rafael Mudafort
Wind Energ. Sci., 8, 401–419, https://doi.org/10.5194/wes-8-401-2023, https://doi.org/10.5194/wes-8-401-2023, 2023
Short summary
Short summary
This paper introduces the cumulative-curl wake model that allows for the fast and accurate prediction of wind farm energy production wake interactions. The cumulative-curl model expands several existing wake models to make the simulation of farms more accurate and is implemented in a computationally efficient manner such that it can be used for wind farm layout design and controller development. The model is validated against high-fidelity simulations and data from physical wind farms.
Marco Mangano, Sicheng He, Yingqian Liao, Denis-Gabriel Caprace, Andrew Ning, and Joaquim R. R. A. Martins
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2023-10, https://doi.org/10.5194/wes-2023-10, 2023
Revised manuscript not accepted
Short summary
Short summary
High-fidelity MDO enables more effective system design than conventional approaches. MDO can shorten the wind turbine design cycle and reduce the cost of energy. We present a first-of-its-kind high-fidelity aerostructural optimization study of a turbine rotor using a coupled CFD-CSM solver. We simultaneously improve the rotor aerodynamic efficiency and reduce the mass of a rotor of a 10 MW wind turbine using 100+ design variables. We discuss the results with unprecedented detail.
Michael J. LoCascio, Christopher J. Bay, Majid Bastankhah, Garrett E. Barter, Paul A. Fleming, and Luis A. Martínez-Tossas
Wind Energ. Sci., 7, 1137–1151, https://doi.org/10.5194/wes-7-1137-2022, https://doi.org/10.5194/wes-7-1137-2022, 2022
Short summary
Short summary
This work introduces the FLOW Estimation and Rose Superposition (FLOWERS) wind turbine wake model. This model analytically integrates the wake over wind directions to provide a time-averaged flow field. This new formulation is used to perform layout optimization. The FLOWERS model provides a smooth flow field over an entire wind plant at fraction of the computational cost of the standard numerical integration approach.
Andrew P. J. Stanley, Christopher Bay, Rafael Mudafort, and Paul Fleming
Wind Energ. Sci., 7, 741–757, https://doi.org/10.5194/wes-7-741-2022, https://doi.org/10.5194/wes-7-741-2022, 2022
Short summary
Short summary
In wind plants, turbines can be yawed to steer their wakes away from downstream turbines and achieve an increase in plant power. The yaw angles become expensive to solve for in large farms. This paper presents a new method to solve for the optimal turbine yaw angles in a wind plant. The yaw angles are defined as Boolean variables – each turbine is either yawed or nonyawed. With this formulation, most of the gains from wake steering can be reached with a large reduction in computational expense.
Charles Tripp, Darice Guittet, Jennifer King, and Aaron Barker
Wind Energ. Sci., 7, 697–713, https://doi.org/10.5194/wes-7-697-2022, https://doi.org/10.5194/wes-7-697-2022, 2022
Short summary
Short summary
Hybrid solar and wind plant layout optimization is a difficult, complex problem. In this paper, we propose a parameterized approach to wind and solar hybrid power plant layout optimization that greatly reduces problem dimensionality while guaranteeing that the generated layouts have a desirable regular structure. We demonstrate that this layout method that generates high-performance, regular layouts which respect hard constraints (e.g., placement restrictions).
Jared J. Thomas, Christopher J. Bay, Andrew P. J. Stanley, and Andrew Ning
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2022-4, https://doi.org/10.5194/wes-2022-4, 2022
Revised manuscript not accepted
Short summary
Short summary
We wanted to determine if and how optimization algorithms may be exploiting inaccuracies in the simple models used for wind farm layout optimization. Comparing optimization results from a simple model to large-eddy simulations showed that even a simple model provides enough information for optimizers to find good layouts. However, varying the number of wind directions in the optimization showed that the wind resource discretization can negatively impact the optimization results.
Paul Fleming, Michael Sinner, Tom Young, Marine Lannic, Jennifer King, Eric Simley, and Bart Doekemeijer
Wind Energ. Sci., 6, 1521–1531, https://doi.org/10.5194/wes-6-1521-2021, https://doi.org/10.5194/wes-6-1521-2021, 2021
Short summary
Short summary
The paper presents a new validation campaign of wake steering at a commercial wind farm. The campaign uses fixed yaw offset positions, rather than a table of optimal yaw offsets dependent on wind direction, to enable comparison with engineering models of wake steering. Additionally, by applying the same offset in beneficial and detrimental conditions, we are able to collect important data for assessing second-order wake model predictions.
Andrew P. J. Stanley, Owen Roberts, Jennifer King, and Christopher J. Bay
Wind Energ. Sci., 6, 1143–1167, https://doi.org/10.5194/wes-6-1143-2021, https://doi.org/10.5194/wes-6-1143-2021, 2021
Short summary
Short summary
Wind farm layout optimization is an essential part of wind farm design. In this paper, we present different methods to determine the number of turbines in a wind farm, as well as their placement. Also in this paper we explore the effect that the objective function has on the wind farm design and found that wind farm layout is highly sensitive to the objective. The optimal number of turbines can vary greatly, from 15 to 54 for the cases in this paper, depending on the metric that is optimized.
Alayna Farrell, Jennifer King, Caroline Draxl, Rafael Mudafort, Nicholas Hamilton, Christopher J. Bay, Paul Fleming, and Eric Simley
Wind Energ. Sci., 6, 737–758, https://doi.org/10.5194/wes-6-737-2021, https://doi.org/10.5194/wes-6-737-2021, 2021
Short summary
Short summary
Most current wind turbine wake models struggle to accurately simulate spatially variant wind conditions at a low computational cost. In this paper, we present an adaptation of NREL's FLOw Redirection and Induction in Steady State (FLORIS) wake model, which calculates wake losses in a heterogeneous flow field using local weather measurement inputs. Two validation studies are presented where the adapted model consistently outperforms previous versions of FLORIS that simulated uniform flow only.
Jennifer King, Paul Fleming, Ryan King, Luis A. Martínez-Tossas, Christopher J. Bay, Rafael Mudafort, and Eric Simley
Wind Energ. Sci., 6, 701–714, https://doi.org/10.5194/wes-6-701-2021, https://doi.org/10.5194/wes-6-701-2021, 2021
Short summary
Short summary
This paper highlights the secondary effects of wake steering, including yaw-added wake recovery and secondary steering. These effects enhance the value of wake steering especially when applied to a large wind farm. This paper models these secondary effects using an analytical model proposed in the paper. The results of this model are compared with large-eddy simulations for several cases including 2-turbine, 3-turbine, 5-turbine, and 38-turbine cases.
Luis A. Martínez-Tossas, Jennifer King, Eliot Quon, Christopher J. Bay, Rafael Mudafort, Nicholas Hamilton, Michael F. Howland, and Paul A. Fleming
Wind Energ. Sci., 6, 555–570, https://doi.org/10.5194/wes-6-555-2021, https://doi.org/10.5194/wes-6-555-2021, 2021
Short summary
Short summary
In this paper a three-dimensional steady-state solver for flow through a wind farm is developed and validated. The computational cost of the solver is on the order of seconds for large wind farms. The model is validated using high-fidelity simulations and SCADA.
Cited articles
Bastankhah, M. and Porté-Agel, F.:
Experimental and theoretical study of wind turbine wakes in yawed conditions,
J. Fluid Mech.,
806, 506–541, 2016. a
Bernhammer, L. O., van Kuik, G. A., and De Breuker, R.:
Fatigue and extreme load reduction of wind turbine components using smart rotors,
J. Wind Eng. Ind. Aerod.,
154, 84–95, 2016. a
Bossanyi, E. A.:
Individual blade pitch control for load reduction,
Wind Energy,
6, 119–128, 2003. a
Budynas, R. G. and Nisbett, J. K.:
Shigley's mechanical engineering design,
McGraw-Hill Education, New York, NY, USA, 2020. a
Churchfield, M. and Lee, S.:
Wind Turbine Modeling and Simulation-SOWFA, National Renewable Energy Laboratory,
https://www.nrel.gov/wind/nwtc/sowfa.html (last access: 24 February 2022), 2012. a
Churchfield, M., Lee, S., Moriarty, P., Martinez, L., Leonardi, S., Vijayakumar, G., and Brasseur, J.:
A large-eddy simulation of wind-plant aerodynamics,
in: 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Nashville, Tennessee, 9–12 January 2012, p. 537, 2012a. a
Churchfield, M. J., Lee, S., Michalakes, J., and Moriarty, P. J.:
A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics,
J. Turbul., 13, 14, https://doi.org/10.1080/14685248.2012.668191, 2012b. a
Enevoldsen, P. and Xydis, G.:
Examining the trends of 35 years growth of key wind turbine components,
Energy Sustain. Dev.,
50, 18–26, 2019. a
Fleming, P., Gebraad, P., van Wingerden, J.-W., Lee, S., Churchfield, M., Scholbrock, A., Michalakes, J., Johnson, K., and Moriarty, P.:
SOWFA super-controller: A high-fidelity tool for evaluating wind plant control approaches, Tech. rep.,
National Renewable Energy Lab. (NREL), Golden, CO (US), 2013. 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, 2015. a
Gebraad, P. M., Teeuwisse, F., Van Wingerden, J., Fleming, P. A., Ruben, S., Marden, J., and Pao, L.:
Wind plant power optimization through yaw control using a parametric model for wake effects–a CFD simulation study,
Wind Energy,
19, 95–114, 2016. a
Gill, P. E., Murray, W., and Saunders, M. A.:
SNOPT: An SQP algorithm for large-scale constrained optimization,
SIAM Rev.,
47, 99–131, 2005. a
Hayman, G.:
MLife theory manual for version 1.00,
National Renewable Energy Laboratory, Golden, CO, 74, 106, 2012. a
Hu, W., Choi, K., and Cho, H.:
Reliability-based design optimization of wind turbine blades for fatigue life under dynamic wind load uncertainty,
Struct. Multidiscip. O.,
54, 953–970, 2016. a
Hübler, C., Weijtjens, W., Gebhardt, C. G., Rolfes, R., and Devriendt, C.:
Validation of Improved Sampling Concepts for Offshore Wind Turbine Fatigue Design,
Energies,
12, 603, https://doi.org/10.3390/en12040603, 2019. a
Ingersoll, B. and Ning, A.: Efficient incorporation of fatigue damage constraints in wind turbine blade optimization, Wind Energy, 23, 1063–1076, 2020. a
Ishihara, T. and Qian, G.-W.:
A new Gaussian-based analytical wake model for wind turbines considering ambient turbulence intensities and thrust coefficient effects,
J. Wind Eng. Ind. Aerod.,
177, 275–292, 2018. a
Jonkman, B. J. and Buhl Jr, M. L.:
TurbSim user's guide, Tech. rep.,
National Renewable Energy Lab. (NREL), Golden, CO (US), 2006. a
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 Lab. (NREL), Golden, CO (US), 2009. a
Kim, S.-H., Shin, H.-K., Joo, Y.-C., and Kim, K.-H.:
A study of the wake effects on the wind characteristics and fatigue loads for the turbines in a wind farm,
Renew. Energ.,
74, 536–543, 2015. a
Matsuishi, M. and Endo, T.:
Fatigue of metals subjected to varying stress,
Japan Society of Mechanical Engineers, Fukuoka, Japan, 68, 37–40, 1968. a
Mendez Reyes, H., Kanev, S., Doekemeijer, B., and van Wingerden, J.-W.: Validation of a lookup-table approach to modeling turbine fatigue loads in wind farms under active wake control, Wind Energ. Sci., 4, 549–561, https://doi.org/10.5194/wes-4-549-2019, 2019. a
National Renewable Energy Laboratory:
OpenFAST Documentation, National Renewable Energy Laboratory,
https://openfast.readthedocs.io/en/main/ (last access: 24 February 2022), 2017. a
Niayifar, A. and Porté-Agel, F.:
Analytical modeling of wind farms: A new approach for power prediction,
Energies,
9, 741, https://doi.org/10.3390/en9090741, 2016. a
Ning, A.: Using blade element momentum methods with gradient-based design optimization, Struct. Multidiscip. O., 64, 991–1014, 2021. a
Njiri, J. G., Beganovic, N., Do, M. H., and Söffker, D.:
Consideration of lifetime and fatigue load in wind turbine control,
Renew. Energ.,
131, 818–828, 2019. a
Revels, J., Lubin, M., and Papamarkou, T.:
Forward-mode automatic differentiation in Julia,
arXiv [preprint],
arXiv:1607.07892, 2016. a
Stanley, P. J.: pjstanle/loads-journal: wes-published (v1.0.0), Zenodo [code],
https://doi.org/10.5281/zenodo.6285205, 2022. a
Stanley, A. P., King, J., and Ning, A.:
Wind Farm Layout Optimization with Loads Considerations,
J. Phys. Conf. Ser.,
1452, 012072, https://doi.org/10.1088/1742-6596/1452/1/012072, 2020. a
Thomas, J. J. and Ning, A.:
A Method for Reducing Multi-Modality in the Wind Farm Layout Optimization Problem,
J. Phys. Conf. Ser.,
1037, The Science of Making Torque from Wind, Milano, Italy, https://doi.org/10.1088/1742-6596/1037/4/042012, 2018. a
Thomas, J. J. and Stanley, A. P. J.:
FlowFarm.jl, GitHub [code], https://github.com/byuflowlab/FlowFarm.jl,
last access: 25 February 2022. a
Thomas, J. J., Annoni, J., Fleming, P., and Ning, A.:
Comparison of Wind Farm Layout Optimization Results Using a Simple Wake Model and Gradient-Based Optimization to Large-Eddy Simulations,
in: AIAA Scitech 2019 Forum, San Diego, CA, 7–11 January 2019, https://doi.org/10.2514/6.2019-0538, 2019. a
Thomsen, K. and Sørensen, P.:
Fatigue loads for wind turbines operating in wakes,
J. Wind Eng. Ind. Aerod.,
80, 121–136, 1999. a
Veers, P. S.:
Three-dimensional wind simulation, Tech. rep.,
Sandia National Labs., Albuquerque, NM (USA), 1988. a
Wiser, R., Hand, M., Seel, J., and Paulos, B.:
Reducing wind energy costs through increased turbine size: is the sky the limit,
Rev. Berkeley National Laboratory Electricity Markets and Policy Group, https://eta-publications.lbl.gov/sites/default/files/scaling_turbines.pdf (last access: 2 March 2022), 2016. a
Ziegler, L., Gonzalez, E., Rubert, T., Smolka, U., and Melero, J. J.:
Lifetime extension of onshore wind turbines: A review covering Germany, Spain, Denmark, and the UK,
Renew. Sust. Energ. Rev.,
82, 1261–1271, 2018. a
Short summary
In this paper, we present a computationally inexpensive model to calculate wind turbine blade fatigue caused by waking and partial waking. The model accounts for steady state on the blade, as well as wind turbulence. The model is fast enough to be used in wind farm layout optimization, which has not been possible with more expensive fatigue models in the past. The methods introduced in this paper will allow for farms with increased energy production that maintain turbine structural reliability.
In this paper, we present a computationally inexpensive model to calculate wind turbine blade...
Altmetrics
Final-revised paper
Preprint