the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Speeding up large wind farms layout optimization using gradients, parallelization, and a heuristic algorithm for the initial layout
Mads Mølgaard Pedersen
Jens Peter Schøler
Julian Quick
Pierre Réthoré
Abstract. As the use of wind energy expands worldwide, the wind energy industry is considering building larger clusters of turbines. Existing computational methods to design and optimize the layout of wind farms are well suited for mediumsized plants; however, these approaches need to be improved to ensure efficient scaling to large wind farms. This work investigates strategies for covering this gap, focusing on GradientBased (GB) approaches. We investigated the main bottlenecks of the problem, including the computational time per iteration, multistart for GB optimization, and the number of iterations to achieve convergence. The opensource tools PyWake and TOPFARM were used to carry out the numerical experiments. The results show Algorithmic Differentiation (AD) as an effective strategy for reducing the time per iteration. The speedup reached by AD scales linearly with the number of wind turbines, reaching 75 times for a wind farm with 500 wind turbines. However, memory requirements may make AD unfeasible in personal computers or for larger farms. Moreover, flow case parallelization was found to reduce the time per iteration, but the speedup remains roughly constant with the number of wind turbines. Therefore, toplevel parallelization of each multistart was found to be a more efficient approach for GB optimization. The handling of spacing constraints was found to dominate the iteration time for large wind farms. In this study, we ran the optimizations without spacing constraints and observed that all wind turbines were separated by at least 1.4D. The number of iterations until convergence was found to scale linearly with the number of wind turbines by a factor of 2.3, but further investigation is necessary for generalizations. Furthermore, we have found that initializing the layouts using a heuristic approach called SmartStart (SMAST) significantly reduced the number of multistarts during GB optimization. Running only one optimization for a wind farm with 279 turbines initialized with SMAST resulted in a higher final AEP than 5,000 optimizations initialized with random layouts. Finally, estimates for the total time reduction were made assuming the trends found in this work for the time per iteration, number of iterations, and number of multistarts holds for larger wind farms. One optimization of a wind farm with 500 wind turbines combining SMAST, AD, flow case parallelization, and without spacing constraints takes 15.6 h, whereas 5,000 optimizations with random initial layouts, FiniteDifferences, spacing constraints, and toplevel parallelization are expected to take around 300 years.
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Rafael Valotta Rodrigues et al.
Status: final response (author comments only)

RC1: 'Comment on wes202361', Pietro Bortolotti, 04 Aug 2023
The article describes a series of numerical investigations around the layout optimization of very large wind farms. The topic is relevant and not well characterized in literature. The article is well written and deserves publication in the WES journal. I only have a few minor suggestions for improvements and my recommendation is to publish the article once these have been addressed.
 Page 4 line 113: typo, reference is duplicated
 Page 7 line 180: please add "wind farm" to the Horns Rev I
 Page 7 line 191: how off are the AEP values?
 Figure 1b reports a Ct for the IEA 3.4 that is clearly wrong. Not sure where the value comes from, but this file https://github.com/IEAWindTask37/IEA3.4130RWT/blob/master/performance/performance_ccblade.dat might be a better source for Ct
 Figure 2: I don’t understand why 80 turbines are marked in black and others in white
 Page 8 line 203: the sentence seems a little clunky
 Page 10 line 218: what does AEP best mean?
Citation: https://doi.org/10.5194/wes202361RC1 
RC2: 'Comment on wes202361', Anonymous Referee #2, 08 Aug 2023
Overall Thoughts
The authors aim to demonstrate how the cost of parallelization, gradient evaluations, constraint handling, number of iterations, and number of multistarts scale with the number of turbines (to address the feasibility of layout optimization of very large wind farms). The manuscript addresses a practical gap in the literature and the scientific rigor of the work is clear. I recommend the manuscript for publication with minor revisions to the discussion where it is difficult to parse.
Technical Comments
Line 67: Can the need for multiple initial starts be discussed in the introduction? It is a specific issue for gradientbased optimization and is an important background for one of the paper’s objectives.
Table 1: What is the reasoning for choosing ~500 turbines as the “large wind farm” size? Is this the trend in expected wind plant sizes in the coming decades? It is obviously a much larger number of turbines than modern large wind farms of ~100 turbines. I highlight this point because the main conclusions of the article are based on comparing optimization performance on this large ~500 turbine farm, and the results are more modest for the 100300 turbine range.
Line 185: Is this the correct Ct value? It seems extremely high for the rated wind speed. I’m not sure if the results would change much, but I expect that the wake interactions are much larger than they would otherwise be, which may affect convergence. Also, why was a constant Ct value even necessary? Why does the Cp value not need to be constant?
Line 231: Is the minimum spacing between turbines in the optimized layout sensitive to the resolution of the grid spacing in the SMAST initial layout? Is there a resolution of the initial layout that would lead to issues when the spacing constraint is omitted from the problem?
Line 292: Why is “handling” the constraint so expensive compared to the calculation of the relative spacing?
Figure 7: Is the spacing constraint scaling with n_turb^2? That is the rough scaling you would expect from the constraint definition.
Line 300: Does this linear relation hold for the median number of iterations? The median is less susceptible to outliers and is arguably a more useful result for gauging an expected number of iterations.
Table 2: What is the initialization time for the random layouts? For 566 turbines, I expect the time would be nonnegligible to simply satisfy spacing and boundary constraints. Perhaps the factor of time between the two degrees of randomness could be given if the authors wish to put the SMAST initialization in context?
Line 316: Is this tuning always required when using the SMAST algorithm? It seems like there is a nontrivial amount of tuning that would increase development/design time compared with the simple random layout generation.
Figure 9: Why would different levels of randomness in the initial layout result in higher optimal AEP for different sized wind farms? For example, more randomness is resulting in higher optimal AEP for 16 turbines, while practically no randomness is best for the 64 and 279 turbine farms. Is there some numerical issue in the modeling of the small wind farms or in the optimizer that is made up for with more randomization of the initial layout? Are there more local optima for the small farm layout?
Figure 9: Between 2005000 multistarts, there is only an increase in AEP of about 1%. With this lowfidelity wake model for AEP, can you even be confident in this 1% change? The cost of the optimization study increases by a factor of 25 if you insist on getting an extra 1% AEP out of the study, but that may not even be a real improvement if you validated with highfidelity simulations.
Line 337: Why would 0% randomness require any multistarts? If there is no randomness, would you not arrive at the same optimal AEP each time?
Line 358: Why was flow case parallelization done if you argued against it in Section 4.1.2? Is it because you are only doing one SMAST start, and so you can utilize the 32 CPUs on the node without penalty?
Typographical Comments
Line 82: “The CS method typically doubles computation time, as there are two times more bits in each value.” What is meant by the last part of this sentence? Is it that the complex step requires operations with real and imaginary values (as opposed to just real), so the number of floating point operations in the Taylor expansion are roughly doubled?
Eq. 3: The coordinates x and y in this case have the origin at the wind farm center.
Eq. 47: One axis of this parallelogram is assumed to be parallel to the xaxis.
Line 167: I would rearrange this paragraph to avoid confusion. A spacing constraint of 2D was adopted for the initialization of the SMAST algorithm (described in Section 3.4.1) and in the discussion of spacing constraint costs in Section 4.1.3. Then, for all other optimizations, the spacing constraint was dropped because the results show that cost does not scale well with the number of turbines.
Line 182: “The results for the number of iterations and number of multistarts are based on more than 50,000 GBWFLOs, and these were performed with a faster setup, which uses the wind turbine, site, and wake model definitions from the IEA Wind Task 37 case study 1.” Can the flow of these different methods be clarified? Some number of GBWFLOs were performed on the Horns Rev case study to understand the first objectives (time per iteration, parallelization, and constraints), and then an additional 50,000 GBWFLOs were performed on the IEA case study to address the number of iterations and number of multistarts? I just find the wording of the sentence to be confusing.
Line 203: “In this work parallelization is studied, these studies are performed on a computational cluster.” Sentence fragment, consider revising.
Line 218: What does the arrow symbol mean?
Line 242: What is the “th mean”?
Line 249: How do you define convergence here?
Figure 4: How is AEP normalized? Is it the average optimal AEP at 5,000 initial starts?
Figure 5b: The FD line is redundant because the AD and CS lines are in reference to the FD time. I also think “speedup” could be clarified in the caption as in reference to FD.
Figure 9: Can it be clarified that ‘n’ in the legend refers to the number of random initial starts at which SMAST results in higher optimal AEP? Also, the black dashed line is the maximum AEP of the random initial starts (i.e. the final value in Figure 4)?
Line 349: “more realistic [Horns Rev I] setup”
Line 350: “Assuming that the result on number of multistarts for 279 wind turbines is similar for a wind farm with 500 wind turbines.” Sentence fragment, consider revising.
Line 389: What are “wriggles”?
Citation: https://doi.org/10.5194/wes202361RC2
Rafael Valotta Rodrigues et al.
Rafael Valotta Rodrigues et al.
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