the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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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Status: open (until 02 May 2025)
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RC1: 'Comment on wes-2025-51', Anonymous Referee #1, 17 Apr 2025
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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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