the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Sep 2025
LiDAR-enhanced Closed-Loop Active Helix Approach
Abstract. The Helix approach has shown potential in increasing wind farm power production through enhancing wake mixing. By applying periodic blade pitch signals to upstream turbines, a helical wake is generated, which reduces velocity deficits for downstream turbines and mitigates the wake effect. While promising, the closed-loop implementation of the Helix approach remains largely unexplored, which could enable handling uncertainties and model errors in wind farm applications. This work presents a framework that integrates LiDAR-based wake measurements to enable such closed-loop control. First, a downwind-facing continuous-wave LiDAR is used to extract the hub vortex as the controlled variable. Second, we developed a control algorithm that regulates the hub vortex position in the Helix frame, thereby controlling the helical wake. Simulations in QBlade show that the framework enables a real-time, flow-informed closed-loop wake mixing approach. Compared with the open-loop cases, the framework corrects the shear-induced steady-state wake bias and enables measurement-informed, dynamic pitch adjustments under turbulence. In shear, bias correction increases downstream power but raises structural loads on both turbines; under turbulence, dynamic pitch control delivers a modest farm-level power gain with only minor load increases. These outcomes highlight the promise of flow-informed, closed-loop wake-mixing control and motivate further investigation.
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 paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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RC1: 'Comment on wes-2025-161', Anonymous Referee #1, 13 Oct 2025
In the manuscript "LiDAR-enhanced Closed-Loop Active Helix Approach", the authors demonstrate a control algorithm which uses backward facing lidar to identify the hub vortex motions, and use this information to control the helical wake. This is a very promising line of study, as previous works have only considered the open-loop formulation, and the addition of lidar information opens the door towards many possibilities for optimizing active wake mixing approaches.There are two major items to consider in this manuscript which might strengthen the study and bolster the arguments presented here. First, in section 4.2, it mentions that the main goal of the closed loop algorithm is to "eliminate variations in the helical wake introduced by external wind conditions, generating a more consistent helical wake relative to the uniform wind case." While there are many possible objectives for a closed loop controller, it is unclear if this leads to the best possible outcome in a wind farm context. There may also be external conditions in which this objective cannot be reached, such as in cases with atmospheric stratification or cases with high veer, or where the cost of matching the uniform wind case would actually be detrimental to the upstream/downstream turbine operation (this is alluded to in section 4.4.3 with combined shear and turbulence). The authors could consider what might be alternate objectives to apply, and also discuss the choice of objective more prominently in earlier sections of the manuscript.Secondly, the current study focuses exclusively on applying the control algorithm on variations of one inflow wind speed at 10 m/s. The study also assumes a priori knowledge of the inflow wind speed, as it does not appear to be derived from other control inputs to the turbine. While this simplifies the initial demonstration of the approach, it also introduces several questions. It is currently unclear how much modification of the algorithm is required to handle the more complex problem where the wind speed changes (see comment 9 below), and whether the results of section 4 are similar at other wind speeds. At wind speeds past rated, the turbine blade pitch changes as a function of the wind speed, so it could be worth considering whether the closed loop algorithm can robustly handle those changes.Additional comments1. The current work assumes that the dynamics of the hub vortex is properly resolved in QBlade. However, modeling the dynamics of the wake immediately aft of the hub and nacelle (<1D downstream of the rotor) can be challenging, even for actuator line model or blade-resolved simulations. Are there parameters which control the hub and nacelle properties, such as drag coefficient or nacelle area, in QBlade which might impact the hub vortex dynamics? Providing some additional information on the hub and nacelle model used in QBlade could be helpful for readers.2. In section 3.2.1, the lidar sampling plane is given as encompassing the full rotor plane at a distance of 1D downstream from the rotor. Some additional details on the numerical lidar sampling should be provided, including the sampling frequency, the total number of points sampled, and the spatial distribution of the sampling points.3. Related to the point above, there may be some practical considerations when using backward facing lidars to measure turbine wakes. Recent field measurements of turbine wakes using a continuous wave spinner lidar requires designing specific scan patterns (e.g., the rosette scan pattern in Hsieh et al, https://doi.org/10.1016/j.jweia.2021.104754) with restrictions on revisit times and probe volumes. For a turbine the size of the NREL5MW, the revisit times and the minimum probe volumes may be fairly large (on the order of 10's of meters), and that may reduce the resolution of the measured wake. The authors may wish to comment on some of these practical aspects as they relate to the current study, e.g., would the averaging effect of the lidar sampling impact the helix feature extraction?4. In section 3.3, a delay time of T=11.2 seconds was determined. Assuming that a lidar samples at a distance of 1 rotor diameter for the NREL5MW (126m), this leads to a convection velocity of 11.25 m/s between the rotor plane and the lidar detection plane, which is faster than the mean inflow velocity of 10 m/s. In typical wake cases, we would expect that the convection velocity of wake structures to be about 60-70% of the inflow velocity. Some details on the calibration process would be useful in this regard, as the value of alpha reported here seems to be in conflict with Taylor's hypothesis. Additionally, how sensitive is the control system to the value of alpha?5. In line 297, a missing reference is present (it appears as a question mark "?").6. Section 4.1 mentions that a second turbine is placed 4 rotor diameters from the upstream turbine, due to limits of the simulation quality within QBlade. That streamwise spacing is relatively close, even for offshore turbines, and may miss some dynamics of the helix modes in the farther downstream (see G. Yalla et al, https://wes.copernicus.org/preprints/wes-2025-14/). This study could be strengthened by commenting on how this lidar methodology could apply, or the results might change, with different turbine spacings.7. In table 2, a jet height of 100m is mentioned. Is a low-level jet wind profile being considered in this study?8. Some details on the nominal turbine controls for the NREL5MW, outside of the helix and closed-loop control method discussed in this paper, should be included in section 4.1 or 4.2. For instance, are the blade pitch and rotor speed settings constant, determined by pitch or rotor speed schedules, or set by external control algorithms (e.g., ROSCO https://github.com/NREL/ROSCO)?9. When applied to more realistic scenarios, the inflow wind speed is not constant, which means that the excitation frequency f_e is not constant. How would this situation be handled or incorporated into the current closed loop algorithm, as there may be additional averaging/time delays involved in determining the appropriate excitation frequency and adjusting the closed loop algorithm.Citation: https://doi.org/
10.5194/wes-2025-161-RC1 -
CC1: 'Comment on wes-2025-161', Henrik Asmuth, 20 Oct 2025
The Helix-visualization in Fig. 2 seems to be from Korb et al (2023), https://doi.org/10.1017/jfm.2023.390
Please cite the paper if you use the image.
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2025-161-CC1 -
CC2: 'Reply on CC1', Zekai Chen, 20 Oct 2025
Dear Henry,
Thank you for the commend.
You are right, in one of our blocks, we indeed included an LES simulation of the Helix to illustrate our methodology. You are correct that this figure originates from Korb et al (2023), https://doi.org/10.1017/jfm.2023.390. In the final version, we will either replace it with our own original LES simulation of the Helix or appropriately cite this work.
We sincerely apologize for this oversight. And thanks again for pointing it out.
Kind regards,
Zekai Chen
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2025-161-CC2 -
CC3: 'Reply on CC2', Zekai Chen, 20 Oct 2025
Sorry for my wrong spelling --- it should be "Thank you for the comment."
Disclaimer: this community comment is written by an individual and does not necessarily reflect the opinion of their employer.Citation: https://doi.org/10.5194/wes-2025-161-CC3
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CC3: 'Reply on CC2', Zekai Chen, 20 Oct 2025
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CC2: 'Reply on CC1', Zekai Chen, 20 Oct 2025
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RC2: 'Comment on wes-2025-161', Anonymous Referee #2, 08 Nov 2025
General Comments
Overall, I find this paper to be a very interesting exploration of helical wake improvements using remote sensing measurements. The analysis given is rigorous, with a LiDAR data processing pipeline implemented, and combination of numerous advanced wind turbine control developments such as a helix frame transformation for analyzing the hub position and H-infinity control synthesis.
The analysis provided in this paper is strong. However, there are a few points that could be elaborated/explored further. When analyzing the data in Figure 13, power increases in the downstream wind turbine are highlighted, the “All” section of the bar plot is not mentioned. When looking at this column, there is a 0.4% power increase overall, with an 8-14% increase in blade loads. These load increases relative to the overall power increase are very concerning, and should be addressed in some way to not leave the reader wondering. In addition, no error bars are provided, raising additional concerns since an error margin of >0.4% could be somewhat reasonable.
Overall, there is no inherent problem in Figure 13; rather, there should be more text elaborating the data it is present. This could be done through more body text in the results section, or through more descriptive captions. Throughout the paper, the captions for figures are sparse, leaving a lot of abbreviations and annotations ambiguous. For example, Table 3 does not explicitly define what "WTi" or “Greedy” mean. The meaning of these terms can be assumed based on context, but adding an additional sentence to the caption could help disambiguate these terms.
The idea of using closed-loop control to improve hub wake positioning in shear and turbulent conditions is compelling, but its actual success in industry seems somewhat dubious when comparing the increase in blade loads with the increase in power production. While it would be outside the scope of this paper to do a complete techno-economic analysis on the net benefit despite increased loads, this downside should be discussed in more detail. Even open-loop helical wake generation increases blade loads due to individual blade pitching at each revolution. Therefore, a modest discussion of why closed-loop helical wake generation should be used with or in the place of other methods such as wake steering would increase the impact of this paper. Such a discussion could be placed right before (5) Conclusion.
The Methods used in this paper are very well presented and thorough. For example, the MBC transform and LiDAR modelling methods were very well established. However, there was a lack of discussion of the Internal Model Identification. It is not established clearly why the authors decided to use system identification instead of an analytical physical derivation, or even gray box modeling of unknown system parameters. A brief elaboration on why this design choice was made would be insightful for the reader.
Also, there could be more discussion on how the nonminimum phase zero is limiting the system performance. It seems like the system bandwidth reduction was chosen due to work done in Skogestad and Postlethwaite (2005). However, it is not made clear where the nonminimum phase zero is coming from (e.g., from actuator limitations, or from the helix generation dynamics themselves). This is a very important point to establish, since the nonminimum phase zero is preventing any improvements in hub vortex tracking in turbulent conditions.
Additionally, in future work, it could be good to include a simulation with more than two wind turbines as a potential goal. It would be interesting to see how the balance between energy savings and blade loads changes when the number of turbines is scaled, potentially strengthening the results of this research. In general, the Future Work section of this report is very sparse, and it could be worth elaborating a sentence for each segment of future work provided. For example, “realistic LiDAR integration” is presented, but how that would impact these results and why that is necessary is not explained clearly. There is no mention of the impact of the LiDAR modeling on the results of the study, so the potential impact of this area of future work is not clear.
Small Suggestions (line number(s) given in parentheses)
- (43) citation issue
- (89) WFFC used but not defined earlier, first appeared on (21)
- (79) consider this capitalization: “(Light Detection And Ranging)
- (79) consider replacing “remote method” with “remote sensing method”
- (~105) it could be beneficial to have a figure here illustrating how a MBC transform goes from a nonrotating to fixed frame, if such a figure exists (it is difficult to conceptualize this when only looking at the equation for the linear transformation)
- (115) equation three has V∞, but the following line references U∞
- (183) double check axes labels for Figure 3
- (~225) figure 5 should be placed much higher in the paper. Also, it should be referenced in the text or removed entirely
- (~276) this is a possible run on sentence, and should be reworded
- (297) broken reference
- (325) Equation 16 has a scalar 0.4, but where this scalar comes from is not clearly established
- (356) should be OL3
- (375) should say "section" instead of "chapter"
- (386) the results of Figure 12 seem to demonstrate worse oscillations compared to open loop operation. Consider adding an explanation for why this is the case
- (~400) Figure 13: the bottom row has vertical grid lines, unlike the top two rows
Citation: https://doi.org/10.5194/wes-2025-161-RC2
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