A numerical framework for optimal trade-offs between land use and LCOE using efficient, blockage-aware multi-fidelity methods

Frontin, Cory; Allen, Jeff; Bay, Christopher J.; Thomas, Jared; Young, Ethan; Bortolotti, Pietro

doi:https://doi.org/10.5194/wes-2025-103

Preprints

https://doi.org/10.5194/wes-2025-103

Preprints

26 Jun 2025

| 26 Jun 2025

Status: this preprint is currently under review for the journal WES.

A numerical framework for optimal trade-offs between land use and LCOE using efficient, blockage-aware multi-fidelity methods

Cory Frontin, Jeff Allen, Christopher J. Bay, Jared Thomas, Ethan Young, and Pietro Bortolotti

Abstract. This paper introduces a novel approach to efficiently estimate the annual energy production (AEP) of a wind farm. The numerical predictions are generated thanks to a multi-fidelity model that combines a classical low-fidelity wake engineering solver with a mid-fidelity computational fluid dynamic solver. The novel setup is not only faster than conventional approaches but is also capable of estimating the AEP of tightly spaced wind farms. Using this approach, we explore the trade-off between land use and levelized cost of energy (LCOE) for a wind farm made of 25 turbines. The results of this study, which ignore impact the layout sensitivity of fatigue loads and their incumbent effect on costs, quantify the penalty on LCOE performance that can be paid to restrict the land use of a wind farm. The results also exhibit the novel capabilities of our approach for multi-fidelity wind farm design to avoid false optima according to incomplete representations of the relevant physical phenomena.

Received: 07 Jun 2025 – Discussion started: 26 Jun 2025

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Cory Frontin, Jeff Allen, Christopher J. Bay, Jared Thomas, Ethan Young, and Pietro Bortolotti

Status: final response (author comments only)

RC1:
'Comment on wes-2025-103', Anonymous Referee #1, 26 Aug 2025
This manuscript present a multi-fidelity model for aerodynamic analysis of wind farms, with an application to wind farm design with varying requirement for land use. Several interesting ideas are presented. The multi-fidelity method is promising to increase the fidelity of aerodynamic models in wind farm design while keeping the computational costs reasonable. In addition, the study on the impact of land-use limit on the performance metrics of the wind farm is valuable for the community. As such, the topic of this work aligns well with the scope of WES. However, and in the reviewer's opinion, this manuscript cannot be published in its current form due to 2 major weaknesses.

First, the scope is poorly defined. Neither the research question nor the scientific challenge addressed in the work are clearly defined. There are two topics addressed in this work: land-use and multi-fidelity models for wind farm designs, but not enough depth in either one. If the focus of the work is on land-use, one would expect an in-depth review of the drivers of wind farm design and an explanation of how wind farm boundaries are decided. If the focus of the work is on the multi-fidelity models, a comparison of state-of-the-art models with varying fidelity would be expected. The lack of focus in the presented manuscript dilutes its message, and makes it difficult to see its relevance and novelty for the research community.
Second, the presentation of the work is poor and impedes the understanding of the work. There is a lack of structure in the text, with several instance of unnecessary repetition. The language used is verbose and unclear. In particular, the use of emphatic terms ("key issue", "clearly demonstrate", etc.) inflates the impact and importance of the results.

Specific comments and suggestions for improvement are listed below.

Methods and Assumption
Line 17: "A major challenge to achieving this goal is that social and environmental factors are usually harder to pose as straightforward optimization targets. In this work, we take a first step in this direction by studying the trade-off between the levelized cost of energy (LCOE) and land use": This statement is not coherent with work presented in the manuscript. The implementation of a constraint for land use is not difficult, as demonstrated in Eq. (6) with a simple multiplication.

Line 21: "Land-use [...] dictates the likelihood that a wind farm creates and unwanted negative impact" and line 28 "we assume that land use is correlated to the likelihood that a farm intersects with migratory pathways" can the authors provide a reference to support these statements? Land-use does not necessarily lead to negative effects, consider for example the financial compensation received by land owners/farmers.

What is the reasoning behind using a LCOE minimization problem and not an AEP maximization problem? Do the balance of station costs change with a change of wake model fidelity? One would expect that the variation of LCOE shown in Figures 9 and 10 can be explained almost fully by the difference in AEP, with the cost component having a negligible effects on the results.

Line 317: "The results in Fig. 9 demonstrates the necessity of accounting for effects that are not captured by low-fidelity methods" and line 342: "Taken together, these results strongly underscore the importance of incorporating higher-fidelity analyses in optimization". These statements are not backed up by the presented results. What is shown is that models with different fidelity give different results and different performance metrics. Whether or not it is necessary or not to use high fidelity models in design optimization can only be answered if there was a large difference in the optimum (here, the optimal values for L1, L2, theta and phi). It is well known in MDAO applied to wind energy systems that simplified models are used in optimization framework. The performance metrics are then calculated precisely with high-fidelity models.

The use of a grid-based wind farm parametrization limits the impact of the work for wind farm design problems. The results presented do not allow to disentangle the effect of the parametrization and the effect of the high-fidelity model. A discussion on how to generalize the results for other wind farm layout parametrizations would be very interesting.

Line 362: "The framework efficiently combines CFD-based and engineering model estimates of the AEP." and line 363 "2 order of magnitude reduction in the computational effort": the efficiency or computational effort of the proposed approach have not been documented in the manuscript (or it is unclear where this analysis is)

Presentation
The manuscript uses the name of several NREL tools (WindSE, FLORIS) to refer to models with different fidelity. For readers not familiar with these tools, this makes it more difficult to understand the work. In general, the reviewer recommends to refer to the model implemented in the tools (engineering wake model, RANS, etc.) rather than the tools, to make the work relevant for a wider audience.

The XDSM matrix presented in Figure 1 is very relevant in the manuscript, but difficult to read, due to the exclusive use of symbols instead of text.

Equation (5) is introduced, but it seems that all presented results are the solution of Eq. (6).

Some symbols used in the equations are not introduced. See for example the symbols A and A_limit in Eq. (6).

In section 4.1., there is no description nor analysis of the data in Figure 9. The impact of the data follows immediately the introduction of the figure reporting what data is represented. As a result, it is more difficult to understand and follow the reasoning.

In section 3.2, it would be relevant to put the results in perspective with the literature. Furthermore, a comparison between the multi-fidelity, the low-fidelity and high-fidelity models in terms of accuracy and computational effort is missing to really showcase the relevance of the work.

Language
There are repetitions in the manuscript. For example with the blockage effect at lines 44 and 56, and with the multi-fidelity gaussian process at lines 284 and 285.

The following sentences are unclear to the reviewer:
Line 286: "The standard deviation surfaces demonstrate the regions of relative trust for each Gaussian process surface, which are leveraged by the multi-fidelity fitting process."

Line 290: "At the lowest level, the multi-fidelity response and the trivial, power curve Gaussian process response are identical and given by the trivial response in Fig. 6."

Line 302 "At this point, it has been demonstrated that we can approximate blockage-aware AEP using the multi-fidelity solver to capture key features from the high-fidelity solver at significantly reduced cost."

Line 329: "Figure 10 shows the resulting Pareto front that emerges from the optimizer termination points.": the term "optimization termination points" is not standard in the field and a verbose. The terms "optimum" or "solution of the optimization problems" are generally preferred.

Line 324: "These LCOE sub-optimalities": using the term "sub-optimality" is not misleading here, because it suggests that the optimization problem was not solved. The solution of the optimization problem is optimal with regards to the implemented model.
Citation: https://doi.org/10.5194/wes-2025-103-RC1
RC2: 'Comment on wes-2025-103', Anonymous Referee #2, 04 Sep 2025

This study presents a method for combining lower and higher-fidelity methods for annual energy prediction of a wind farm. The new multi-fidelity method promises to optimize land use and LCOE for a given farm layout.
In general, the presentation of the methodology is not clear. An optimization framework is given, but the connection between the steps is not clearly stated. The details of the multi-step method and optimization procedure are not provided in depth. Although it is a major part of the whole study, the computational setup is not presented clearly. The application of the land use optimization is weakly presented, and the results contain contradicting statements, which make the results questionable.
Specific comments:
1. Section 2.1: In this section, the optimization framework is explained, and an XDSM chart is given. It will help to clear this discussion if the basic steps of this procedure, in the order of application, are also given. i.e., what is the starting point, what are the following steps?
2. lines 159-167: In this paragraph, the details of the computational domain set up are given. But it misses some key parameters like the total size of the domain in x-, y-, and z-directions. These values are only stated in the units of boxes and weren't related to lengths such as "D".
As an example, the statement: "Starting from this base mesh, we shifted mesh nodes vertically, such that 65 % of the nodes reside below h_hub + D_rotor (where h_hub is hub height and D_rotor is rotor diameter) to adequately refine the near-ground region."
3. Since the size in the z-direction is not known, it is not possible to judge the distribution of the nodes.
4. Furthermore, this statement suggests refining the near-ground region, but h_hub+D_rotor is above the maximum length of the wind turbine. Please elaborate on this.
5. Similarly, the discussion about "...four levels of nested localized refinements surrounding each turbine..." is also not clear.
Adding a sketch of the computational domain with key lengths would help make this discussion clearer.
6. lines 169-171: the statements "upstream/downstream non-horizontal boundaries" suggest that there exist upstream/downstream horizontal boundaries, which is not true. Simply naming these upstream/downstream boundaries should be sufficient.
7. Figure 3: L_2 is supposed to be parallel to the side of the domain. Also, it would be helpful if the (approximate) flow direction is shown on this sketch (this will also help the discussion in the first paragraph of Section 3.2).
8. The following statements contradict each other:

line 322: "LCOE tends to be higher with the multi-fidelity method than FLORIS predicts"

lines 333-334: "the multi-fidelity minimum LCOE is about 4 % lower than the FLORIS minimum LCOE"
Since the conclusions rely on the second statement, this should be elaborated.
9. lines 335-336: "The multi-fidelity Pareto front suggests that wake and aerodynamic effects have an impact that extends beyond around 20–30 km2 of land use"
It would be better if the lengths in x- and y-directions are given (also) in terms of rotor diameter instead of km^2 (only).
10. Section 4.2.: In the discussion of the results, the necessity of multi-start optimization is stressed. The multi-start optimization is mentioned also earlier in the manuscript, but it is not explained. It would add up to this manuscript if this optimization procedure is briefly explained.

Citation: https://doi.org/10.5194/wes-2025-103-RC2

Cory Frontin, Jeff Allen, Christopher J. Bay, Jared Thomas, Ethan Young, and Pietro Bortolotti

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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.


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