Estimating annual energy production of wake mixing control strategies including comparisons to wake steering

Yalla, Gopal R.; Brown, Kenneth; Cheung, Lawrence; Houck, Dan; deVelder, Nathaniel; Jayaraman, Balaji

doi:10.5194/wes-2025-250

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https://doi.org/10.5194/wes-2025-250

Preprints

28 Nov 2025

| 28 Nov 2025

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

Estimating annual energy production of wake mixing control strategies including comparisons to wake steering

Gopal R. Yalla, Kenneth Brown, Lawrence Cheung, Dan Houck, Nathaniel deVelder, and Balaji Jayaraman

Abstract. This study presents an estimation of the annual energy production (AEP) associated with active wake mixing (AWM) control strategies in a wind farm. To achieved this, we first conduct a series of high-fidelity large eddy simulations (LES) of a wind farm for various turbine layouts and control parameters. These simulations extend previous findings from two-turbine studies to a larger array of wind turbines, demonstrating the effectiveness of AWM in enhancing power generation, particularly in geometrically aligned wind farms situated in stable atmospheric boundary layers. The results indicate that while the conventional pulse method leads to the best performance for second-row turbines, the helix method leads to greater improvements in power generation for third-row turbines. Second, a framework for estimating the AEP associated with AWM strategies is developed within the FLOw Redirection and Induction in Steady-state (FLORIS) toolkit, using a new empirical Gaussian wake model. The FLORIS parameters are calibrated to the LES data and an optimization routine is established for determining the optimal use of AWM in a wind farm for maximizing AEP. AEP estimates are provided using Weibull data from the New York Bight for multiple turbine layouts and blade pitching amplitudes. Third, the AEP gains from wake mixing are compared to those from wake steering using the yaw optimization routines in FLORIS. The power performance is similar for both control methods, generally leading to power gains of 1 % to 3 % for the wind conditions where active wake mixing or steering is used, which translates to AEP gains that are mostly less than 1 % for the wind farm and control parameters considered in this study.

Received: 14 Nov 2025 – Discussion started: 28 Nov 2025

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Gopal R. Yalla, Kenneth Brown, Lawrence Cheung, Dan Houck, Nathaniel deVelder, and Balaji Jayaraman

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RC1: 'Comment on wes-2025-250', Anonymous Referee #1, 17 Dec 2025

The manuscript "Estimating annual energy production of wake mixing control strategies including comparisons to wake steering" by Yalla et al. presents a methodology for estimating AEP gains under the application of wake control methods. This methodology is applied to a 3x3 wind farm, where it observes AEP gains of 0.1-0.8%. This is an important contribution to the understanding of wake control strategies and a logical next step in the development of such technologies. Most of the results are presented clearly, and the text is easy to follow. Therefore, the paper should be published in the Journal after considering the following remarks and concerns.
Major comments:
My major concerns revolve around the topic of uncertainty, which, given that the observed AEP gains range in very low values, could ultimately decide between positive and negative AEP gains. I understand that a direct determination of the uncertainty is probably not possible. Therefore, the following aspects should be addressed to at least understand and minimize the uncertainty of the presented results, where possible:

1. The entire study is based on one precursor representing a stable ABL in which AWM is assumed to be particularly effective. However, it appears very unlikely that these stable conditions are representative of the flow conditions throughout the entire year, as they are required for the AEP estimation. Consequently, it must be assumed that in a significant part of the year, AWM actually performs worse than assumed in the calculation, hence the AEP gains would be lower. Related to that, the following questions:

1.1 Does the measurement data from the NY Bight include the atmospheric stability? Can it be justified to assume stable stratification throughout the entire year?

1.2 How would the results change when considering also unstable conditions?

2. Figure 11 validates the tuned FLORIS model with the LES data. Unfortunately, the FLORIS profiles don't match the LES profiles satisfactorily in all cases. For instance, in the second row, at 4D, the wake deficit is almost double as high in the LES as in FLORIS. This might be the reason for the row-averaged power overprediction of FLORIS visible in Fig. 10. This is concerning because the AEP estimates are expected to be very sensitive to these wake profiles, which raises the following questions:

2.1. How do the wake profiles compare in cases with different wind directions?

2.2. How does the standard FLORIS model used for the Baseline control cases compare with the LES? If the match is not better, can the authors explain the source of this mismatch? Maybe from using a Gaussian mean flow model that doesn't account for thermal stratification in a stable ABL?

2.3. The model is trained and validated with the same LES data. Maybe additional LES validation case(s) with unseen wind speeds and wind direction could validate the choice of parameters and estimate the uncertainty coming from the wake model.

3. In lines 332/333, recent studies of synchronizing the helix over multiple rows are used to justify that waked turbines can also apply AWM. However, the cited study from van Vondelen also shows that unfavourable alignment can also reduce the power gains. Therefore, I think a mean flow model would require further adaptation when arguing with synchronization. The question is, therefore, whether the optimizer decides to apply AWM also to mid farm turbines? If yes, it must be assumed that the results are off and consequently increase the uncertainty of the AEP estimates.
=> Considering these points, I would welcome clarification in the title that this is an AEP estimation strategy, but not a generally valid AEP estimate.

Further comments:

4. Line 112 states that the LES domain is 10 km high. Is that really the case, or is a 0 too much? If yes, why? And if yes, what's the inversion layer height and the lapse rate above the free atmosphere? Vertical profiles would help.

5. Line 113/General: Kasper 2025 also uses a 1km high ABL, where a 3x3 wind farm might be representative for the momentum entrainment mechanisms in a larger wind farm. However, it has been shown that more shallow ABLs fundamentally change these mechanisms, leading to global blockage and atmospheric gravity waves. Do the results shown in the manuscript allow for conclusions on a large-scale wind farm subject to deep array effects?

6. Line 60/236: What is the full citation of Frederik et al.(2024)? I was not able to find that publication, but it is where the FLORIS part of the work is based on.

7. Lines 98-100: It is assumed that relative power gains translate from one wind direction to others. What is that assumption based on? Can it be validated?

8. Table 3/Lines176ff.: Helix method is only investigated in one configuration, in which it actually outperforms the Pulse. Why is it then not considered in the other configurations to investigate if it might even lead to larger AEP gains?

9. Fig. 6,7,8, Lines 206ff: I agree there is not a lot of interaction between the turbines visible. At these small wind farms in the given ABL conditions also deep-array effects can probably be neglected. Could the contributions of this paper also be drawn from three turbines with different streamwise and lateral alignments to reduce computational costs?

10. Fig. 11 shows many lines per figure that only differ in terms of very similar colors. Could the FLORIS and LES lines of the same case be plotted in the same color, but with different line styles? If that doesn't help the readability, maybe consider distributing the lines over multiple plots or plotting less downstream distances

11. The manuscript would profit from a more direct comparison between the Wake Steering and AWM results, especially because it is explicitly mentioned in the title. That comparison could focus on realistic scenarios. For instance, it seems unreasonable that any operator will ever apply AWM with 6 ° pitch amplitude, and also turbine spacings of 3D seem rather short. Could the same methodology of Fig. 14 maybe be applied to wake steering and then shown in the same plot as AWM to get a direct comparison?

12. Can wake steering and AWM be combined in the same AEP optimizing routine? Then the AEP would profit from AWM in fully waked conditions and from wake steering in partial wake overlaps. Intuitively, that should further increase the AEP gains.
Minor comments:

-Lines 38-39: The following might be relevant for the underlying physics of wake mixing:

-van der Hoek et al.: "Maximizing wind farm power output with the helix approach: Experimental validation and wake analysis using tomographic particle image velocimetry" (https://doi.org/10.1002/we.2896)

-Coquelet et al.: "Dynamic individual pitch control for wake mitigation: Why does the helix handedness in the wake matter?" (DOI 10.1088/1742-6596/2767/9/092084)

-Gutknecht et al.: "The impact of coherent large-scale vortices generated by helix active wake control on the recovery process of wind turbine wakes" (https://doi.org/10.1063/5.0278687)

-Table 3: I would suggest moving the Pulse with St=0.15 from the bottom of the table up to the cases with the same pitch and wind farm orientation cases to facilitate the comparison of the Power gains with the cases in the same conditions.

-Fig. 5: I recommend plotting different pitch amplitudes in different line styles, to highlight that the lines do not directly compare with each other. This should also be emphasised in the text.

-Line 231: Citation refers to NREL, but the name was recently changed to NLR. Should that be considered here? It might be worth contacting the Editorial board of the Journal for that.

-Line 272: "All of the LES cases were used" sounds like also the helix and pulse 0.15 case were included in the tuning; however, I assume they were not. This might need clarification in the text.

-Line 291: "...does not does..."I guess that's a typo

-Lines 305-315: Description of assumptions feels a bit hard to follow due to quite convoluted sentences. Could these assumptions be outlined in a clearer way?

-How about the loads? (Sorry, I couldn't resist asking that ;-) )

Citation: https://doi.org/10.5194/wes-2025-250-RC1
RC2:
'Comment on wes-2025-250', Anonymous Referee #2, 05 Jan 2026
In the manuscript "Estimating annual energy production of wake mixing control strategies including comparisons to wake steering," the authors quantify the impact on annual energy production (AEP) due to active wake mixing (AWM) and wake steering wind farm control strategies. A suite of high-fidelity large eddy simulations (LES) is used to fit an empirical Gaussian wake model. The empirical model is used to optimize and quantify the AEP gain of AWM and wake steering control at an offshore wind site in the New York Bight. The text is well written, and the methodology is clear. However, the model is not verified against out-of-sample data, raising concerns about the reported values for AEP gain. Furthermore, the influence of atmospheric conditions -- specifically veer and turbulence intensity (TI), which has been highlighted in previous work to have a significant effect on the efficacy of flow control -- is neglected in the modeling framework. Therefore, the degree to which the empirical model provides useful power predictions is uncertain, given that it is used almost ubiquitously to extrapolate across wind farm layouts, control strategies, and inflow conditions. Addressing these concerns would significantly strengthen the conclusions made in the manuscript.

Major comments:
The simulations from Frederik et al. WES (2025b) show that the optimal control strategy is sensitive to the ABL conditions, specifically wind veer and TI. This seems to undermine the central assumption that the relative power gains from AWM are not strongly sensitive to the wind conditions.

The empirical Gaussian model is only evaluated on its calibration data. With many free parameters, it is unsurprising that the empirical model performs well in-sample. However, the same model is used to extrapolate to different wind directions (e.g., partial waking), turbine spacings (including ~3D, where complexity in the near-wake may be significant), wind shear and veer, TI, pulse amplitudes beyond 4 degrees, and cases of wake steering. The results all rely on accurate model extrapolation, but there is no evidence that the model does well out-of-sample. Additional testing cases for model verification are necessary for the results in Section 4 to be trustworthy. Some related questions/comments:
Are the helix and subharmonic pulse (St=0.15) cases used in model calibration?

How is the parameter gamma tuned with only one value of freestream TI in all of the LES data?

There appear to be significant spatial differences between wakes modeled in FLORIS and LES (Figure 10). This causes concerns regarding model extrapolation.

In Figure 4, the variation in power production across the columns of the identically controlled turbines can be quite significant within each control configuration. For example, in the bottom left subfigure (Pulse, A=2 degrees, St=0.3, 6D spacing at 225 degrees), the power gain/loss changes sign in the third row across the columns. Are these physical, or a product of the short averaging time (600 sec)? How does this variation affect the wake model calibration and subsequent results presented in Section 4?

Line 221, Equation 3: What is C? Is it constant or a function of streamwise position? Does the empirical Gaussian model conserve mass and momentum?
Additionally, is Equation 3 a function of x only, or of (x, y, z)?

What effect would including the skewed wake correction (Abkar et al., Energies (2018)) in the Gaussian wake model have on the model results?

Figure 12: The drop in power (or energy production? Please clarify) between all wind conditions and conditions where at least one turbine is actuated is nearly one order of magnitude. However, in the tightest spacings, at least one turbine is actuated upwards of 30% of the time (Figure 13, left). Showing dimensional energy generation binned by operating condition could help explain this further (e.g., amount of energy generation for conditions favoring AWM and without AWM).
Related: In Figure 14, right, it is surprising that the orientation of the wind farm has a relatively small impact on the normalized AEP gain, given how sensitive the benefits to AWM are to the wind direction (shown in Figure 12). Yet the difference between the "worst-case" and "best-case" wind farm orientation only changes the AEP gain by order 0.05%. It may be useful to see how the power gain due to AWM changes with wind direction averaging sector, for example at fixed pulse amplitude.

It may help to show a PDF of power gains due to AWM as a function of turbine spacing distance to explain the non-monotonicity in Figure 12 (conditioned on >0 AWM turbines). The hypothesis stated in the text is that AWM is used more selectively as spacing increases, but that does not necessarily translate to higher power gains when AWM is used.

Previous work has observed the greatest power gain due to wake steering in partial waking, rather than in the fully-waked case (e.g., Tamaro et al. WES 2025). This is not observed in the proposed model (Line 410). If only partial wake conditions are considered, is this observed in the present model as well?

Minor comments (in order as they appear):
Line 040: 1 sentence regarding why previous reduced-order models were not used in this work would be useful.

Line 055 (and more generally): Why is AWM vs wake steering presented as an either/or decision? The general narrative of the paper leans toward "choosing between" wake steering and AWM, rather than the possible synergy between the two strategies. Parts of the introduction, results (specifically Section 4.2), and conclusions could be reworked to provide a more synergistic perspective on flow control strategies for wind farm operation.

Line 082: It would be useful to give an estimation of grid cell size in the rotor region and between turbines. Relatedly, is it necessary to simulate with such high resolution? 1 billion grid cells is a massive computational expense.

Line 090: Please give a rate of surface cooling and roughness for reproducibility. ABL profiles (perhaps in an appendix or reference to other work) would be useful as well. Are these the exact same LES cases as Brown et al. (2025)?

Figure 2, right subfigure: It seems like the turbine numbers (or wind direction) are mislabeled, as the 206.5 degree wind direction should lie between the 180 and 225 degree wind directions. Visually, the plot appears to show more like 160 degrees orientation. Defining the heading angle may help to clarify this.

Figure 3: The important turbine parameters for this study (rated wind speed and dimensions) can simply be put in-text and this figure can be omitted.

Table 3: It is an interesting result that using the pulse method, the 5D spacing with AWM is approximately equal to the 6D spacing with baseline control. This is a saving in footprint area of 30% for the same power output. Perhaps this could be explored further in the text.

Figure 4: The black text on the darkest red squares is difficult to read (consider switching these squares to white text, or outlining the text in white)

Line 189: How are rotor-averaged velocities computed as a function of streamwise position? Possibly related -- Figure 5, top right subfigure: Why is the freestream quantity u/u_baseline approximately 0.33 (and not 1, for example)?

Line 192: Is the higher rotor-averaged velocities behind the third row turbine between the St=0.3 and subharmonic St=0.15 pulse turbines due to wake physics (mixing), or due to the fact that the third row turbine in the subharmonic AWM strategy extracts more power (and imparts a higher thrust)?

Figure 6: What are the colorbar units? Also, the contours show regions of elevated turbulent entrainment behind the first row, but decreased turbulence entrainment further downstream. I would anticipate that this would have detrimental effects downstream if the wind farm extended beyond the third row of turbines.

Figure 7: Differences between subplots are difficult to discern as plotted. Consider showing the difference in u between the baseline case, or remove this figure.

Figure 8: Demarcating the position of the downstream turbine in the right four subfigures would clarify elements of this figure.

Table 4: Please include all default values for variables in Equations 3-5 here (e.g., sigma_{y_0}).

Line 253: Can the W_fact parameter be interpreted simply as an adjustment to C_P?

Figure 13, right: This subfigure seems out of place. Consider omitting altogether and move the main findings to the text (percent of conditions with yaw actuation is invariant of the maximum yaw angle and increases with increased spacing).
Additionally, for all figures with colored lines, the lightest color is difficult to see.

Figure 16: Again, it is difficult to discern differences between contour plots. Consider showing differences in u between baseline and different control methodologies, or omit this figure.

Line 404: Please include the cosine-loss exponent values for thrust and power used in FLORIS.

Line 419: The comparison between "at least one actuated AWM turbine" and "at least one wake steering turbine" is not apples-to-apples because the amount of wake steering is not a binary variable. This should be highlighted in the text. (also in Line 445)

Line 446: The full range of AEP gain due to wake steering (approximately 0.2% to 1.2%) is not reported in the conclusions, while the full range of AEP gain due to AWM is reported (0.1% to 0.4%), which is misleading.

Technical comments (in order as they appear):
Line 069: Section 2.4 is not addressed in this paragraph

Line 092: How are the "rotor averaged shear" and "rotor-averaged veer" computed?

Figure 1, bottom left: radial ticks on the wind speed rose are probably mislabeled.

Table 1: Why do the percentages not add to 100 in the final column or across all combinations of WS/TI conditions?

Line 228: Typo - sigma_{y, z_0} should probably be sigma_{y_0, z_0}.

Some references (e.g., Cheung et al. WES (2024a)) have an out-of-date citation (should be: Cheung, L., Yalla, G., Mohan, P., Hsieh, A., Brown, K., deVelder, N., Houck, D., Henry de Frahan, M. T., Day, M., and Sprague, M.: Modeling the effects of active wake mixing on wake behavior through large-scale coherent structures, Wind Energ. Sci., 10, 1403–1420, https://doi.org/10.5194/wes-10-1403-2025, 2025). Please double-check all references.
Citation: https://doi.org/10.5194/wes-2025-250-RC2

Gopal R. Yalla, Kenneth Brown, Lawrence Cheung, Dan Houck, Nathaniel deVelder, and Balaji Jayaraman

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Short summary

This study examines the increase in annual energy production of a wind farm when using a new control technology designed to re-energize the wind between turbines by enhancing the mixing in the flow behind a turbine. High-fidelity computer simulations are used to create training data for a lower-fidelity model that efficiently predicts wind farm performance. Additionally, the power performance gains are compared to a standard control approach that steers wakes away from downstream turbines.


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