the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 May 2025
A robust active power control algorithm to maximize wind farm power tracking margins in waked conditions
Abstract. We present an active wind farm power control (APC) algorithm that operates wind turbines to maximize their power availability and robustly track a reference power signal in the presence of turbulent wind lulls. The operational setpoints of the wind turbines are optimized with an augmented version of FLORIS that combines induction control with wake steering to deflect low-momentum wakes and increase power margins. The algorithm also features a proportional-integral closed loop inspired by the literature to correct potential errors deriving from the offline calculation of the setpoints.
First, we demonstrate the methodology in steady-state conditions, showing how the availability of power is increased by mitigating wake interactions. We observe that the methodology is particularly effective in conditions of strong wake impingement, occurring in scenarios of high power demand and for particular wind farm layouts. Later, considering two wind farm layouts, we compare the performance of the algorithm to three state-of-the-art reference APC formulations in unsteady scenarios using large-eddy simulations coupled with the actuator line method (LES-ALM). We show that the occurrence and treatment of local, temporary instances of power unavailability (saturations) dramatically affect power tracking accuracy. The proposed method yields superior power tracking due to the increased power margins that limit the occurrence of saturation events. Additionally, we show that this performance is achieved with reduced structural fatigue.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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RC1: 'Comment on wes-2025-66', Anonymous Referee #1, 23 May 2025
This manuscript introduces a robust active power control (APC) algorithm for wind farms, aiming to maximize power availability and accurately track reference power signals amidst turbulent wind lulls. The algorithm optimizes turbine operational setpoints using an augmented version of FLORIS, with induction control and wake steering to increase power margins. It incorporates a proportional-integral closed loop for real-time error correction. The results, based on steady-state and unsteady scenarios via large-eddy simulations (LES), demonstrate that it is possible to significantly enhances power tracking by reducing saturation events. The proposed approach seems to be particularly effective under strong wake impingement and high power demand conditions.
Overall the manuscript is well written and well organised, with convincing results. It should also be noted that the authors are clearly highlighting the limitations of their approach. The conclusion and outlook section is providing an excellent summary of the work. I am definitely in favor of a publication and only have few comments for the authors to address:
1-The introduction is possibly missing few words about recent AI-based methods such as Reinforcement Learning for the optimization of the performance of wind farms.
2-The authors should provide the main findings from their two previous studies (mentioned line 77-79), and explain why and how the method needed to be improved.
3-Can the authors expend a bit on the tracking error mentioned line 97. Is it important?
4-The proposed approach is based on the offline optimization of the control setpoints that, once stored in look-up tables, are interpolated at runtime. Would there be an advantage in doing this process online, especially for unseen scenarios?
5-I think the authors should have a small discussion about the type of optimizations that are suitable for wind farm problems. They are using gradient-based optimization but recently, several papers have been published with different approaches.
6-It would be good to add a sentence to justify the use of the Gauss Curl Hybrid wake model (I guess it is because it is a very accurate wake model).
7-The authors states that “Another limitation of the unsteady results is the use of rigid wind turbine models in the simulations. If, on the one hand, this is not expected to play a major role in the behavior of wakes”. I would expect aeroelastic effects to have significant effects on the behavior of turbine wakes, and hence of any optimization. Can the authors add some references to back up their claim?
8-How many optimization were performed in section 2.5 and what was the overall cost?
9-What is the rational for using the Jensen model in section 2.6?
10-Why is it necessary to add a zero-mean white noise to improve the robustness of the gains in section 2.6?
11-Would it be possible to add few lines to describe the in-house LES code used for this work?
12-Figure 7 is not really discussed.
13-Is it realistic (representative of real conditions) to have TI % above 25% in figure 11 in the wake of the third turbine?
14-Would it be possible to discuss about the yaw/pitch angles for each turbine (with respect to the wind direction in section 3)? I would expect to always have a zero yaw angles for turbine 3 (as there is no turbine downstream), a rather large yaw angle for the first turbine and a rather small yaw angle for the second one. It would be interesting to discuss any correlation with the reference power demand signal.
15-I have a question regarding the fatigue analysis. What is the main cause of fatigue? The turbulence level experienced by the turbine (which seems to be the case here) or the wind speed (which is higher for the first turbine than for the third turbine)? Also, would a turbine experience more fatigue when yawed than when in greedy mode? As an interested reader, I would find a bit more explanation extremely helpful in this section of the manuscript.
Citation: https://doi.org/10.5194/wes-2025-66-RC1 -
RC2: 'Comment on wes-2025-66', Anonymous Referee #2, 30 May 2025
Review of manuscript: A robust active power control algorithm to maximize wind farm power tracking margins in waked conditionsThis study presents a closed-loop, active power control (APC) algorithm for wind farm operation to track a reference power signal that maximizes power reserves. The algorithm incorporates a combination of yaw and induction control, leveraging recent advancements in aerodynamic rotor modeling, to model the curtailment of a yaw-misaligned wind turbine. The proposed APC method is compared with three reference APC formulations which only use induction control, and large eddy simulations are used to test the controller against a standard test signal reference power. The combination of yaw and induction control increases the ability of the wind farm to track a reference power demand signal, especially at relatively high power demands. Overall, the manuscript includes promising results and valuable contributions to the wind farm control community. However, the reference controllers chosen make it very difficult to determine which novelty is leading to a reduction of error in power tracking. Furthermore, there are questions about the numerical setup and robustness of the results. Specific comments are listed below.Major comments:
- There are several key scientific questions that this study includes, but does not effectively separate. The first is the effect of wake steering on APC, which has been explored in previous studies (c.f. Boersma, et al. (2019), Starke et al. (2023, 2024)). The second is an open-loop versus closed-loop formulation (c.f., van Wingerden et al. (2017), Vali et al. (2019), Starke et al. (2023)). The third is the effect of the advances in aerodynamic rotor modeling. Using the reference APC algorithms proposed in the manuscript, it is not clear which of these aspects contribute to, say, improvements in power tracking observed in the CL+MR versus OL algorithms, because the two algorithms differ in these three major ways. To be specific, here are several sub-comments:
- Is the enhanced rotor aerodynamic modeling important to the CL+MR approach, or does a tuned cosine model suffice? After all, the closed-loop control benefits from being model-agnostic, as the authors note. Adding a "cosine model" yaw APC as a reference would help to elucidate the importance of aerodynamic modeling.
- Only the CL+MR strategy uses yaw control. The comparison in Sec. 3.3 to the OL algorithm is therefore more of a comparison between induction control versus induction + yaw control, and should be highlighted as such.
- An OL induction + yaw algorithm would be a valuable reference strategy for comparison in the unsteady simulations.
- For all open-loop offline optimizations, is the cost function to maximize the minimum reserve? This is unclear for the induction-only control scenario, Sect. 2.2.
- Throughout the study, the blade pitch angle is used as an analog for the curtailment (below rated conditions). However, in yaw misalignment, the yaw and blade pitch both lead to curtailment. Therefore, the analogy between blade pitch and curtailment used throughout the paper breaks down for the CL+MR control algorithm.
- Why is the inflow upstream of the leading turbine non-uniform in the LES simulations (Figure 10)? Please check the numerical setup.
- In the unsteady results, the dynamic response of the wind turbines is averaged over, resulting in ill-posed averaging because the conditions are not quasi-steady. This raises concerns as to whether the turbulent fluctuations from the mean velocity shown in the TI plot (Figure 11) are mainly from ABL turbulence or from the reference power signal used. Furthermore, the turbulence intensity is surprisingly high in the wake of the induction controlled turbines, which may be related. Please elaborate on the discussion in Lines 304-305, and what results are "expected".
- The 1000-second analysis window (~17 minutes) for LES data is very short. Including two or three instantiations of the analysis window for the key algorithms (CL+MR versus CL, for example) would improve the robustness of the results.
- Please give further details on the turbine controller used for the different control algorithms, including the greedy control. It is unclear why the variance of the greedy control power in Figures 12 and 13 is much higher than the open loop control, for example.
- The fatigue analysis and the load balancing controller (CL+LB) raise many questions. For example, if the goal of the CL+LB controller is to equalize the structural loading between the turbines in the wind farm, Figures 21-24 do not show whether this is successfully accomplished. The increased DELs for the CL+LB and decreased DELs for the CL+MR seem to be the stand-out results in Sect. 3.4.3, but the analysis and figures provided do not explain why. Rather than including the CL+LB algorithm as a reference, I recommend the other reference control algorithms (mentioned above) to better complement the study. Otherwise, perform a more comprehensive analysis of the findings to identify the sources of fatigue, relation to the controller operation and saturation, cost function sensitivity analysis, etc.
Minor comments (sorted by line number):- Line 90: Especially in the model formulation section, a section road map paragraph would be particularly useful for navigating Sec. 2.
- Line 105: Throughout the manuscript, "maximizes the minimum power reserve" is used synonymously with "maximizes the minimum power ratio" (e.g. Line 116), "maximizes the smallest power margin" (e.g. Line 214), and "maximizes the minimum local available power" (e.g. Line 402). The different nomenclature to describe the same strategy adds unnecessary confusion to the manuscript. Additionally, the text on Line 116 seems incorrect as it is inconsistent with Equation (1), which is to 'minimize the maximum power ratio'.
- Line 115: Clearly explain how the dependence of the power coefficient CP on the yaw misalignment angle is separate from the additional factor ηP such that the power loss due to yaw/tilt is not double-counted.
- Line 163: When all turbines are close to saturation, the wind farm power should be maximized. Therefore, it seems like all turbines should ideally operate in 'power boost' mode rather than 'greedy mode', particularly because on Line 124 it is noted that "power boosting [is] a limiting case of the proposed APC formulation."
- Line 185: Which wake superposition method is used in FLORIS?
- Figure 3: Are the black lines level sets of ε? Please clarify.
- Line 234: What is ΔL,i and how is it computed/normalized?
- Line 247: How does the closed-loop update time (0.01 sec or 100 Hz) compare with other literature? And how does the closed-loop update time affect the LES time step?
- Line 276: Is Pgreedy defined using a wake model? Please clarify how this quantity is computed, and if it is time-varying.
- Line 348: There are no error bars in Figures 16 or 17 - what is the text referring to?
Technical comments (sorted by line number):- Line 33: This paragraph (and several others throughout the manuscript) is very short and should be merged with the following paragraph.
- Line 113: In the unnumbered equation immediately following, "arg max" should be "max"
- Line 238: What is the dimensional diameter D?
- Line 239: Clarify how "rotor overlap" is defined (e.g., at hub height)
- Line 276: Please define Ψ.
- Figures 12 and 13: The light gray shading (greedy control) is difficult to see, especially in print.
- Figures 13 and 14: Why does the x-axis not begin at 200 seconds?
- Figures 16 and 17: What is the horizontal black line?
- Figures 19 and 20: "All values are normalized by the wind turbine rated power" -> "Tracking error values are normalized..." (the x-axis is normalized differently).
- Line 523 and in several other locations in the references: DOI links are incorrect
References:Boersma, S., Doekemeijer, B. M., Keviczky, T., & van Wingerden, J. W. (2019). Stochastic Model Predictive Control: Uncertainty impact on wind farm power tracking. 2019 American Control Conference (ACC), 4167–4172.Starke, G. M., Meneveau, C., King, J., & Gayme, D. F. (2023). Yaw-Augmented Control for Wind Farm Power Tracking. 2023 American Control Conference (ACC), 184–191.Starke, G. M., Meneveau, C., King, J. R., & Gayme, D. F. (2024). A dynamic model of wind turbine yaw for active farm control. Wind Energy, 27(11), 1302–1318.
Vali, M., Petrović, V., Steinfeld, G., Y. Pao, L., & Kühn, M. (2019). An active power control approach for wake-induced load alleviation in a fully developed wind farm boundary layer. Wind Energy Science, 4(1), 139–161.
van Wingerden, J.-W., Pao, L., Aho, J., & Fleming, P. (2017). Active Power Control of Waked Wind Farms. IFAC-PapersOnLine, 50(1), 4484–4491.Citation: https://doi.org/10.5194/wes-2025-66-RC2 - There are several key scientific questions that this study includes, but does not effectively separate. The first is the effect of wake steering on APC, which has been explored in previous studies (c.f. Boersma, et al. (2019), Starke et al. (2023, 2024)). The second is an open-loop versus closed-loop formulation (c.f., van Wingerden et al. (2017), Vali et al. (2019), Starke et al. (2023)). The third is the effect of the advances in aerodynamic rotor modeling. Using the reference APC algorithms proposed in the manuscript, it is not clear which of these aspects contribute to, say, improvements in power tracking observed in the CL+MR versus OL algorithms, because the two algorithms differ in these three major ways. To be specific, here are several sub-comments:
Data sets
Software and data Simone Tamaro et al. https://doi.org/10.5281/zenodo.14716525
Video supplement
Video of one simulation Simone Tamaro et al. https://youtu.be/dS_FrPhw3EM
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