Articles | Volume 6, issue 5
https://doi.org/10.5194/wes-6-1143-2021
© Author(s) 2021. 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-6-1143-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
09 Sep 2021
Research article |
| 09 Sep 2021
| 09 Sep 2021
Objective and algorithm considerations when optimizing the number and placement of turbines in a wind power plant
National Renewable Energy Laboratory, National Wind Technology Center, Boulder, CO 80303, USA
Owen Roberts
National Renewable Energy Laboratory, National Wind Technology Center, Boulder, CO 80303, USA
Jennifer King
National Renewable Energy Laboratory, National Wind Technology Center, Boulder, CO 80303, USA
Christopher J. Bay
National Renewable Energy Laboratory, National Wind Technology Center, Boulder, CO 80303, 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, Jennifer King, Christopher Bay, and Andrew Ning
Wind Energ. Sci., 7, 433–454, https://doi.org/10.5194/wes-7-433-2022, https://doi.org/10.5194/wes-7-433-2022, 2022
Short summary
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.
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.
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.
Andrew P. J. Stanley, Jennifer King, Christopher Bay, and Andrew Ning
Wind Energ. Sci., 7, 433–454, https://doi.org/10.5194/wes-7-433-2022, https://doi.org/10.5194/wes-7-433-2022, 2022
Short summary
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.
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.
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
Abdelsalam, A. M. and El-Shorbagy, M.: Optimization of wind turbines siting in a wind farm using genetic algorithm based local search, Renew. Energ., 123, 748–755, 2018. a
Abkar, M. and Porté-Agel, F.: Influence of atmospheric stability on wind-turbine wakes: A large-eddy simulation study, Phys. Fluids, 27, https://doi.org/10.1063/1.4913695, 2015. a
Baker, N. F., Stanley, A. P. J., Thomas, J. J., Ning, A., and Dykes, K.: Best Practices for Wake Model and Optimization Algorithm Selection in Wind Farm Layout Optimization, in: AIAA Scitech 2019 Forum, 7–11 January 2019, San Diego, CA, AIAA 2019-0540, https://doi.org/10.2514/6.2019-0540, 2019. a, b, c
Changshui, Z., Guangdong, H., and Jun, W.: A fast algorithm based on the submodular property for optimization of wind turbine positioning, Renew. Energ., 36, 2951–2958, 2011. a
Chen, L. and MacDonald, E.: A system-level cost-of-energy wind farm layout optimization with landowner modeling, Energ. Convers. Manage., 77, 484–494, 2014. a
Chen, Y., Li, H., Jin, K., and Song, Q.: Wind farm layout optimization using genetic algorithm with different hub height wind turbines, Energ. Convers. Manage., 70, 56–65, 2013. a
Crespo, A. and Hernández, J.: Turbulence characteristics in wind-turbine wakes, J. Wind Eng. Ind. Aerod., 61, 71–85, 1996. a
Feng, J. and Shen, W. Z.: Optimization of wind farm layout: a refinement method by random search, in: Proceedings of the 2013 International Conference on aerodynamics of Offshore Wind Energy Systems and wakes (ICOWES 2013), 17–19 June 2013, Lygnby, Denmark, 17–19, 2013. a
Feng, J. and Shen, W. Z.: Solving the wind farm layout optimization problem using random search algorithm, Renew. Energ., 78, 182–192, 2015. a
Fleming, P., Ning, A., Gebraad, P., and Dykes, K.: Wind Plant System Engineering through Optimization of Layout and Yaw Control, Wind Energy, 19, 329–344, https://doi.org/10.1002/we.1836, 2016. a
Gebraad, P., Thomas, J. J., Ning, A., Fleming, P., and Dykes, K.: Maximization of the annual energy production of wind power plants by optimization of layout and yaw-based wake control, Wind Energy, 20, 97–107, 2017. a
Hou, P., Hu, W., Soltani, M., and Chen, Z.: Optimized placement of wind turbines in large-scale offshore wind farm using particle swarm optimization algorithm, IEEE T. Sustain. Energ., 6, 1272–1282, 2015. a
Ituarte-Villarreal, C. M. and Espiritu, J. F.: Optimization of wind turbine placement using a viral based optimization algorithm, Procedia Comput. Sci., 6, 469–474, 2011. a
Katić, I., Højstrup, J., and Jensen, N. O.: A simple model for cluster efficiency, in: EWEA Conference and Exhibition, 6–8 October 1986, 407–410, Rome, Italy, 1986. a
Khanali, M., Ahmadzadegan, S., Omid, M., Nasab, F. K., and Chau, K. W.: Optimizing layout of wind farm turbines using genetic algorithms in Tehran province, Iran, International Journal of Energy and Environmental Engineering, 9, 399–411, 2018. a
Lawrence Berkeley National Laboratory: Wind Technologies Market Report, available at: https://emp.lbl.gov/wind-technologies-market-report/, last access: 31 August 2021. a
Lazard: Lazard's Levelized Cost of Energy Analysis–Version 12.0, https://www.lazard.com/media/450784/lazards-levelized-cost-of-energy-version-120-vfinal.pdf (last acccess: 29 August 2019), 2018. a
Li, W., Özcan, E., and John, R.: Multi-objective evolutionary algorithms and hyper-heuristics for wind farm layout optimisation, Renew. Energ., 105, 473–482, 2017. a
Martins, J. R. R. A. and Ning, A.: Engineering Design Optimization, Cambridge University Press, available at: http://flowlab.groups.et.byu.net/mdobook.pdf (last access: 3 September 2021), 2020. a
Meldrum, J., Nettles-Anderson, S., Heath, G., and Macknick, J.: Life cycle water use for electricity generation: a review and harmonization of literature estimates, Environ. Res. Lett., 8, 015 031, 2013. a
Mittal, A.: Optimization of the layout of large wind farms using a genetic algorithm, PhD thesis, Case Western Reserve University, Cleveland, Ohio, 2010. a
Moorthy, C. B. and Deshmukh, M.: A new approach to optimise placement of wind turbines using particle swarm optimisation, International Journal of Sustainable Energy, 34, 396–405, 2015. a
Niayifar, A. and Porté-Agel, F.: Analytical modeling of wind farms: A new approach for power prediction, Energies, 9, 741, 2016. a
Pérez, B., Mínguez, R., and Guanche, R.: Offshore wind farm layout optimization using mathematical programming techniques, Renew. Energ., 53, 389–399, 2013. a
Pookpunt, S. and Ongsakul, W.: Optimal placement of wind turbines within wind farm using binary particle swarm optimization with time-varying acceleration coefficients, Renew. Energ., 55, 266–276, 2013. a
Previsic, M.: Economic Methodology for the Evaluation of Emerging Renewable Technologies, Re Vision Consulting LLC, Sacramento CA, USA, 2011. a
Razdan, P. and Garrett, P.: Life Cycle Assessment of electricity production from an onshore V136-3.45 MW Wind Plant, Vestas Wind Systems A/S, Aarhus, Denmark, 2017. a
Shakoor, R., Hassan, M. Y., Raheem, A., and Wu, Y.-K.: Wake effect modeling: A review of wind farm layout optimization using Jensen's model, Renew. Sust. Energ. Rev., 58, 1048–1059, 2016. a
Şişbot, S., Turgut, Ö., Tunç, M., and Çamdalı, Ü.: Optimal positioning of wind turbines on Gökçeada using multi-objective genetic algorithm, Wind Energy, 13, 297–306, 2010. a
Stanley, A. P. J.: stanley2020-turbine-number, Zenodo [code], https://doi.org/10.5281/zenodo.5338511, 2021. a
Stanley, A. P. J. and Ning, A.: Coupled wind turbine design and layout optimization with nonhomogeneous wind turbines, Wind Energ. Sci., 4, 99–114, https://doi.org/10.5194/wes-4-99-2019, 2019a. a, b
Stanley, A. P. J. and Ning, A.: Massive simplification of the wind farm layout optimization problem, Wind Energ. Sci., 4, 663–676, https://doi.org/10.5194/wes-4-663-2019, 2019b. a
Stehly, T. J. and Beiter, P. C.: 2018 Cost of Wind Energy Review, Tech. Rep., National Renewable Energy Lab. (NREL), Golden, CO, USA, 2020. a
Thomas, J. J. and Ning, A.: A Method for Reducing Multi-Modality in the Wind Farm Layout Optimization Problem, The Science of Making Torque from Wind, Milano, Italy, J. Phys. Conf. Ser., 1037, 042012, https://doi.org/10.1088/1742-6596/1037/4/042012, 2018. a, b
US Energy Information Administration: Annual energy outlook 2019 with projections to 2050, Department of Energy, Washington DC, 1–83, 2019. a
Vestas: Vestas Sustainability: Life Cycle Assessments, https://www.vestas.com/en/about/sustainability#!lcareports (last access: 20 November 2020), 2020. a
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, İ., Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., and SciPy 1.0 Contributors: SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nat. Methods, 17, 261–272, https://doi.org/10.1038/s41592-019-0686-2, 2020. a
Wiser, R. H. and Bolinger, M.: 2018 wind technologies market report, U.S. Department of Energy (DOE), Washington DC, 2019. a
Wiser, R. H., Bolinger, M., Hoen, B., Millstein, D., Rand, J., Barbose, G. L., Darghouth, N. R., Gorman, W., Jeong, S., Mills, A. D., and Paulos, B.: Wind Technology Data and Trends: Land-Based Focus, 2020 Update, Tech. Rep., Lawrence Berkeley National Lab. (LBNL), Berkeley, CA, USA, 2020. a
Zergane, S., Smaili, A., and Masson, C.: Optimization of wind turbine placement in a wind farm using a new pseudo-random number generation method, Renew. Energ., 125, 166–171, 2018. a
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.
Wind farm layout optimization is an essential part of wind farm design. In this paper, we...
Altmetrics
Final-revised paper
Preprint