the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A Comparison of Eight Optimization Methods Applied to a Wind Farm Layout Optimization Problem
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
Andrew Ning
Abstract. Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the IEA Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method as well as lists of pros and cons to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by AEP was found using a new sequential allocation method, discreet exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem given that they are applied correctly.
Jared J. Thomas et al.
Status: final response (author comments only)
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RC1: 'Comment on wes-2022-90', Anonymous Referee #1, 23 Jan 2023
In this manuscript, eight different optimization algorithms are used to optimize the layout of wind farms with concave boundaries and discrete regions. The main comments are as follows:
1) The running time and corresponding hardware facilities of each algorithm are suggested to provide.
2) The single wind turbine wake model and wake superposition model should be given.
3) The effect and efficiency of various optimization algorithms need to be analyzed quantitatively, refers to the recent publication:
Yang, Q., Li, H., Li, T., & Zhou, X. (2021). Wind farm layout optimization for levelized cost of energy minimization with combined analytical wake model and hybrid optimization strategy. Energy Conversion and Management, 248, 114778.
Citation: https://doi.org/10.5194/wes-2022-90-RC1 -
AC1: 'Reply on RC1', Jared Thomas, 10 Feb 2023
Note: Numbered statements are from the referee, indented bullets are the author response.
- "The running time and corresponding hardware facilities of each algorithm are suggested to provide"
- The runtime and hardware information is provided in the text, but was intentionally not presented in aggregate form because the widely varying hardware used for each algorithm makes a run-time comparison misleading at best, not to mention the differences due to programming language. Instead of comparing run time, we have compared function call metrics. The information in the function call metrics is arguably more useful than the run-time because the function calls are less dependent on what hardware and language were used.
- "The single wind turbine wake model and wake superposition model should be given."
- Good suggestion. We have included the wake and wake superposition models in the manuscript.
- See lines 176-190 in the revised manuscript excerpt attached.
- "The effect and efficiency of various optimization algorithms need to be analyzed quantitatively, refers to the recent publication: (Yang, Q., Li, H., Li, T., & Zhou, X. (2021). Wind farm layout optimization for levelized cost of energy minimization with combined analytical wake model and hybrid optimization strategy. Energy Conversion and Management, 248, 114778.)"
- It is not clear from the provided citation what efficiency is referred to. We have provided quantitative comparisons between algorithms in terms of function calls, objective results (AEP), and wake-loss. This information provides significant insight into the efficiency of each algorithm (function calls) and efficiency of the resulting layouts (wake loss). The effect of each algorithm is addressed quantitatively through providing the objective results (AEP).
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EC2: 'Reply on AC1', Jonathan Whale, 14 Feb 2023
Dear Authors,
Thank you for responding to the reviewer's comments. We are presently awaiting comments from a second reviewer.
Kind regards
Jonathan Whale
Associate Editor
Citation: https://doi.org/10.5194/wes-2022-90-EC2
- "The running time and corresponding hardware facilities of each algorithm are suggested to provide"
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EC1: 'Reply on RC1', Jonathan Whale, 14 Feb 2023
Hello,
The authors of wes-2022-90 have responded to your comments. Please see their response and the excerpt from the manuscript and comment.
Kind regards
Jonathan Whale
Associate Editor
Citation: https://doi.org/10.5194/wes-2022-90-EC1
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AC1: 'Reply on RC1', Jared Thomas, 10 Feb 2023
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RC2: 'Comment on wes-2022-90', Anonymous Referee #2, 15 Feb 2023
This paper compared the performance of 8 optimization methods for wind farm layout optimization, using a case from the IEA Wind Task 37 with 81 turbines spread in 5 disconnected regions. In general, all methods showed similar performance. The results seem quite interesting and should be valuable for the wind farm optimization field.
The are some places that the reviewer think could be improved, which are listed as follows:
- Minimal distance requirement seems to be a constraint considered, according the descriptions of different methods, but is not mentioned or introduced in the problem formulation description.
- Wake loss (L_w) is defined in Eq. (2) by multiplying 100 to the percentage loss, but in other places, it is always referred to as percentage (%). I can’t seem what is the point of multiplying 100 here.
- According to Fig. 2, it seems that the same Weibull distribution is assumed for all wind direction bins, but this usually is unrealistic, since wind coming from different direction usually have different strength. For a more realistic modelling of wind condition, you could use a joint distribution of wind speed and wind direction, which allows different Weibull distributions in different wind direction sectors, such as the one proposed in: https://doi.org/10.3390/en8043075
- The concave hull is defined with coordinates in lines 243-244. It is better to show it in figure, also there are no numerical axis shown in all the layout/wind farm plots, thus, it is impossible to figure out where is the concave hull located.
- The local search method in the DEBO algorithm is actually very similar to the Random Search (RS) algorithm as proposed in: https://doi.org/10.1016/j.renene.2015.01.005 for wind farm layout optimization, as they both move only one randomly chosen turbine in each iteration. Although DEBO uses discretized grids and RS operates on continuous design space, the basic principle is similar, thus, the reviewer think it may make sense to mention the RS algorithm, and discuss a bit on the similarity and differences.
- d_x and d_y in Eqs. (7-8) are not introduced or explained anywhere.
- In several methods, two stage approaches are applied. It would be nice to present how much improvements can be attribute to different stages. The other aspect is the initial layout, some use randomly generated ones, some use the provided one, some use manually generated good ones. Instead of only compare to the reference layout, i.e., the provided layout, comparison to the used specific initial layout may also be added. So we can have a better idea on how much improvement has been achieved by the algorithm starting from the initial layout.
- Description of the DPA method can be improved, currently, there are purely text and missing some details. But more importantly, the reviewer can’t understand step 4 as stated in lines 627-628, i.e., “using the wind resource information, order the list from highest wind speed to lowest.” If it is onshore wind farm with non-uniform wind resource distribution, such as on complex terrain, I can understand, but for offshore site with uniform wind resource, how do we do this? In this case, every location will have the same ambient inflow wind speed. Better explaination of the algorithm will be need if the readers are to understand the procedure.
- No-free-lunch theorem is mentioned in the discussion section, see line 867-868. I will think the original source of the theorem should also be cited here, i.e.: https://doi.org/10.1109/4235.585893
Citation: https://doi.org/10.5194/wes-2022-90-RC2 -
AC2: 'Reply on RC2', Jared Thomas, 11 Mar 2023
Note: numbered comments and quotations are from the referee, indented bullets contain the author responses.General Comments"This paper compared the performance of 8 optimization methods for wind farm layout optimization, using a case from the IEA Wind Task 37 with 81 turbines spread in 5 disconnected regions. In general, all methods showed similar performance. The results seem quite interesting and should be valuable for the wind farm optimization field."
- Thank you for your review and feedback.
Detailed Comments"The are some places that the reviewer think could be improved, which are listed as follows":- "Minimal distance requirement seems to be a constraint considered, according the descriptions of different methods, but is not mentioned or introduced in the problem formulation description."
- This is a good point. We have referenced another document providing more details on the case study formulation, but agree that providing the constraints explicitly is useful. We have added the objective function, which includes the spacing constraint referred to in the comment
- See lines 195 to 198 in the revised manuscript excerpt attached
- See equation 5 in the revised manuscript excerpt attached
- "Wake loss (L_w) is defined in Eq. (2) by multiplying 100 to the percentage loss, but in other places, it is always referred to as percentage (%). I can’t seem what is the point of multiplying 100 here."
- This is a good point. We added the 100 because of presenting wake loss as a percent later on, but you are right that it is not necessary. We have removed the multiple of 100 from equation (6).
- see line 210 in the revised manuscript excerpt attached
- "According to Fig. 2, it seems that the same Weibull distribution is assumed for all wind direction bins, but this usually is unrealistic, since wind coming from different direction usually have different strength. For a more realistic modelling of wind condition, you could use a joint distribution of wind speed and wind direction, which allows different Weibull distributions in different wind direction sectors, such as the one proposed in: https://doi.org/10.3390/en8043075"
- Thank you for pointing this out. We did use a different wind speed distribution in each direction. We have edited the manuscript to clarify this point.
- See line 203 in the revised manuscript excerpt attached
- See the caption to figure (2) in the revised manuscript excerpt attached
- "The concave hull is defined with coordinates in lines 243-244. It is better to show it in figure, also there are no numerical axis shown in all the layout/wind farm plots, thus, it is impossible to figure out where is the concave hull located."
- Good point. We have added a figure with the concave hull.
- See figure (4) in the revised manuscript excerpt attached
- Note that the boundary points and turbine locations are all provided in the supplemental data repository.
- "The local search method in the DEBO algorithm is actually very similar to the Random Search (RS) algorithm as proposed in: https://doi.org/10.1016/j.renene.2015.01.005 for wind farm layout optimization, as they both move only one randomly chosen turbine in each iteration. Although DEBO uses discretized grids and RS operates on continuous design space, the basic principle is similar, thus, the reviewer think it may make sense to mention the RS algorithm, and discuss a bit on the similarity and differences."
- Thank you for providing the reference. We have added an explanation of the comparison between the two algorithms in the description of the local search part of the DEBO method
- See lines 316 to 328 in the revised manuscript excerpt attached
- "d_x and d_y in Eqs. (7-8) are not introduced or explained anywhere."
- Variables (d_x, d_y) were defined line 330 in the submitted manuscript, we have added more description of these variables to make sure they don’t go unnoticed.
- See lines 337 to 338 in the revised manuscript excerpt attached
- "In several methods, two stage approaches are applied. It would be nice to present how much improvements can be attribute to different stages. The other aspect is the initial layout, some use randomly generated ones, some use the provided one, some use manually generated good ones. Instead of only compare to the reference layout, i.e., the provided layout, comparison to the used specific initial layout may also be added. So we can have a better idea on how much improvement has been achieved by the algorithm starting from the initial layout."
- This information would certainly be interesting. We chose not to provide it because it was only available for some of the algorithms and in different forms for those that did provide the information. Some of the starting layouts used are available in the supplemental data repository for those interested in a deeper dive.
- "Description of the DPA method can be improved, currently, there are purely text and missing some details. But more importantly, the reviewer can’t understand step 4 as stated in lines 627-628, i.e., “using the wind resource information, order the list from highest wind speed to lowest.” If it is onshore wind farm with non-uniform wind resource distribution, such as on complex terrain, I can understand, but for offshore site with uniform wind resource, how do we do this? In this case, every location will have the same ambient inflow wind speed. Better explaination of the algorithm will be need if the readers are to understand the procedure."
- In the DPA algorithm, ordering by wind speed is irrelevant in the case of a uniform wind speed distribution. We have added clarification to this effect.
- see lines 649 to 653 in the revised manuscript excerpt attached
- "No-free-lunch theorem is mentioned in the discussion section, see line 867-868. I will think the original source of the theorem should also be cited here, i.e.: https://doi.org/10.1109/4235.585893"
- Good point. We have included the reference.
- See lines 892 to 895 in the revised manuscript excerpt attached
Jared J. Thomas et al.
Data sets
Data and code repository 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 https://zenodo.org/badge/latestdoi/543173996
Jared J. Thomas et al.
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