the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Apr 2025
Synchronized Helix Wake Mixing Control
Abstract. Wind farm control optimizes wind turbines collectively, implying that some turbines operate suboptimally to benefit others, resulting in a farm-level performance increase. This study presents a novel control strategy to optimize wind farm performance by synchronizing the wake dynamics of multiple turbines using an Extended Kalman Filter (EKF)-based phase estimator in a Helix control framework. The proposed method influences downstream turbine wake dynamics by accurately estimating the phase shift of the upstream periodic Helix wake and applying it to its downstream control actions with additional phase offsets. The estimator integrates a dynamic Blade Element Momentum model to improve wind speed estimation accuracy under dynamic conditions. The results, validated through turbulent large-eddy simulations in a three-turbine array, demonstrate that the EKF-based estimator reliably tracks the phase of the incoming Helix wake, with slight offsets attributed to model discrepancies. When integrated with the closed-loop synchronization controller, significant power enhancement with respect to the single-turbine Helix can be attained (up to +10 % on the third turbine), depending on the chosen phase offset. Flow analysis reveals that the optimal phase offset sustains the natural Helix oscillation throughout the array, whereas the worst phase offset creates destructive interference with the incoming wake, which appears to negatively impact wake recovery.
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-2025-51', Anonymous Referee #1, 17 Apr 2025
The reviewer strongly believes that the paper presents insights into synchronized Helix wake mixing control. The results appear original and well written.
Page 1, Lines 15–20 (Introduction): When citing Manwell et al. (2010) and Barthelmie et al. (2009), clarify whether the 20% drop applies to onshore or offshore farms—or both—as atmospheric stability differs markedly between environments.
Page 2, Lines 30–35 (Introduction): The comparison between DIC and Helix (lower tower loads vs. higher gains) lacks quantitative value.
Page 2, Lines 46: The phrase “deeper arrays” is used without definition. Indicate the number of turbine rows or array dimensions to which “deeper” refers (e.g., > 5 rows).
Page 4, Figure 1 Caption: The caption omits key LES conditions (Reynolds number, TSR, inflow laminar vs. turbulent). Please add “TSR, Re number” to the caption for reproducibility.
Page 6, Lines 124: You state that ωᵣ±ωₑ yields the effective rotating‐frame frequency. A brief note on potential aliasing when ωₑ approaches ωᵣ (say when ωₑ ≈ 0.9 ωᵣ) would alert practitioners to choose safe Strouhal ranges as explained in Equation 2.
Page 7, Equation (11): Please confirm if random wall model for uuK as described is applicable for oscillatory models.
Page 14, Algorithm 1, Step 1: which states that “Identify the frequency band of interest”. It will be helpful to state or refresh the reader, or which criteria are being considered.
Page 14, Lines 305: In Equation (22), amplitude A is reused from upstream, but pitch rate constraints can vary downstream. Please comment on how actuator saturation is handled.
Section 4.4 – Figure 13, The Gaussian Process fit effectively interpolates power gains, but the manuscript does not specify the kernel choice, hyperparameter tuning method, or the confidence‐interval level (e.g., 95%). Including these details (perhaps in a brief footnote) would allow other researchers to reproduce the interpolation for better judgment.
General comments:
Authors should consider scaling down the scope of the manuscript or splitting into two papers, as it becomes hard to follow at some point. The manuscript tackles estimation theory, control design, high‑fidelity LES validation, fatigue assessment, and flow‑recovery analysis all in one paper, which makes it difficult to follow the core contributions.
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RC2: 'Comment on wes-2025-51', Anonymous Referee #2, 22 May 2025
The paper is well written, the subject is interesting and the results appear rather robust. However, some important details about the flow setting, the choice of some relevant parameters and some important measures are missing or unclear, hindering the reliability and interpretation of the results. Please consider the following detailed comments.
Section 2.2
Concerning the approxiamation of the Jacobian by central differences, it is stated that the choice of dn requires balancing truncation and round-off errors. I imagine that this balancing has been done in the calibration of the algorithm, and it is definitely worth to show the results of this calibration in the paper, or justify in more detail the choice of dn (which is indeed not specified).Section 2.5
Figure 5: the cut-off frequency appears too low, since it completely cuts off the strong peak at frequency 0.3, which is definitely not noise. I strongly suggest increasing it to 0.4 at least, and comparing the results.
Section 3.1
Is it not clear whether the tower is taken into account, and how. Also, the domain and boundary conditions are defined only for the precursor simulation. It is not clear why the grid is refined upstream of the first turbine (usually it is refined in correspondence with the turbines). The sampling time of the y-z planes for the inflow boundary is not specified. The Coriolis frequency is also not provided, nor the tip speed ratio. All in all, the computational setting is obscure, and needs more details, as well as validation of the results.
Section 3.3.1
The procedure for the wind velocity data is unclear. It is claimed that the wind speed along the sampling lines are averaged over time, but averaging over time along fixed lines would smooth out the dynamics. I guess it is a phase average instead of a time average? Please discuss this point in detail.
Section 4.1
Figure 9: Why the phase shifts are very smooth for the ground truth and very jagged for the estimation? It appears counter-intuitive, since estimation employs a filter to isolate the noise. It might be interesting here to see what changes by increasing the cut-off frequency (see question above)
Section 4.2Table 3: For the 180° case, the phase errors on Utilt and Uyaw are very high, but the coherence is very high. This is rather counter-intuitive and deserves further analysis.
Section 4.4
With respect to which case the increase/loss of overall power production are evaluated? I guess the comparison is made between the synchronized case and the BL Helix case, although this is not clearly stated. Anyhow, for the "optimal" case, a power gain of 10% on the third turbine is registered, at the cost of a power loss of 5% on the second. This appears to suggest that: i) with only two turbines, the synchronization leads to a power loss; ii) if the synchronization would be applied also on the third turbine, its power loss would decrease as well, leading to a power decrease. I think these points should be discussed in detail, to make the conclusions about power increase much more realistic.
Section 4.5
There is no mention of the Coriolis effect on the wake, so I am not sure whether this effect is taken into account also in the turbine simulation, or only on the precursor one. It is also not clear whether the inflow velocity profile has a veer at the hub height or not. Showing the time-average and rms of the inflow velocity profiles can be useful here, as well as discussing the effect of the veer on the wake (see for instance Manganelli et al. "The effect of Coriolis force on the coherent structures in the wake of a 5MW wind turbine" 2025), which should in fact deform the helix.
Citation: https://doi.org/10.5194/wes-2025-51-RC2
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