| 09 Jan 2026
Large eddy simulation of airborne wind energy systems flying in turbulent wind using model predictive control
Abstract. Wind energy is foreseen to be a cornerstone of the future energy mix, with a total capacity projected to increase drastically in the coming decades. To this end, the size of horizontal‑axis wind turbines is continuously increasing, which poses significant structural challenges and requires increasing material resources. Those challenges have triggered interest in alternative technologies. Airborne wind energy (AWE) shows great potential and has recently gained a great deal of interest. However, the implementation of airborne wind energy systems (AWES) is in its infancy, and the only existing systems operate isolated. For AWES to take an active part in wind energy, their operation in turbulent environments must be further studied, and wind farms must also be considered. This work proposes a framework based on computational fluid dynamics for studying AWES in ambient turbulent wind and wakes, as will be encountered when arranged in farms. The present work focuses on ground-gen rigid-wing AWES. The framework relies on a large eddy simulation flow solver, in which the kites are represented using a model based on an actuator line for the main wing with its ailerons, and complemented with models for the tail control surfaces (rudder and elevator). The flow solver is coupled, via a two-way coupling, to a control module based on model-predictive control, to follow optimal trajectories. The framework is presented in some detail and is then used to investigate the MegAWES aircraft, a MW-scale AWES of 42.5 m wingspan, here flying four-loop trajectories. The first part of the investigation focuses on a single system. Its ability to fly in a turbulent wind is demonstrated and analyzed, and its wake is also characterized. It is demonstrated that the controlled kite can handle the turbulent wind. The deviation from its reference trajectory is less than 15 % of the wingspan. In the second part, a tandem configuration is considered, with the same foor-loop trajectory for each kite. It is found that there is a configuration where the second kite, even fully aligned with the first one, can fly in unperturbed flow (other than the turbulence of the wind). A second case is investigated where the second kite is forced to fly in the wake from the first one. It is found that the wake produced by the first kite does not compromise the trajectory tracking of the second kite. However, the second kite feels the velocity deficit and its power production is reduced by 6 %.
GENERAL COMMENTS
This is an interesting and well-written paper, relevant to the airborne wind energy community. The authors develop a framework to simulate multiple ground-gen AWES with LES, while running a Model Predictive Controller. With this tool, they simulate a system from the literature and analyze the performances of two systems, where the second system is operated to avoid or to encounter the wake of the first system. The results show that the second system can be operated such that it almost entirely avoids the wake of the first, producing higher power.
I have minor reviews and a few suggestions for further analyses, which could be incorporated here or in future works.
SUGGESTED ADDITIONAL ANALYSES
It would be nice to have a deeper explanation of how the aerodynamic force contributes to the reduction of wind speed for a Ground-gen AWES. Indeed, the wing is moving downstream, because of the reel-out, and generates an aerodynamic force. From the force of the lifting line and its velocity you should be able to reconstruct the work done on the fluid from the AWES. Note that this work should be directly comparable with the power available at the ground station, taking in account the work done by the tether drag, the change in kinetic energy of the AWES and the exchange of potential gravitational energy. These two last quantities are conservative, so that after a full periodic cycle there should be a balance between the aerodynamic work and the electric energy. It would be nice to have some insights on the work done on the fluid from the AWES, which can hardly be reconstructed by the plots given in the paper because of the reel-out speed and of the kite attitude. This could provide a more detailed explanation on the skewed reduction in wind speed.
DETAILED REVIEW
Line n. 1) Given that the journal is Wind Energy Science, I think it is not necessary to start the abstract with 7 lines of introduction. I would reduce it to max 2 lines.
30) Please cite the original paper from Loyd
55) please use the same tense in all the manuscript. This should be proposes
121) A comment on Sect. 2.3 is missing
Eq6) It is not clear from the text why the non-dimensional coordinate s should be in front of the parenthesis. I believe it is because this expression comes from a moment equation: The moment at the ground station generated by the distributed drag (you right-hand-side times l) should be equal to the moment generated by the concentrated drag with the kite (you left-hand-side times l). It would be nice to have a brief explanation of this type, so that it is clear why s appears in the expression
211) remove “of which”
219) the citation should go inside the parenthesis ()
229) even if the meaning of r and e is understandable (elevator and rudder), you could write it out, so there is no doubt
235) Are the commas supposed to be multiplication signs? If yes, add the effective lift slope coefficient symbol in front for clarity
245) is the chord-wise length of the aileron equal to 60% of the wing chord? that seems a lot compared to the wing drawing in the appendix.
265) This should be a vector with square brackets. The \hat{omega} should be highlighted with \boldsymbol, in accord to the WES guidelines. Moreover, I would also add the dependence of the control inputs u on the time t.
299) maybe refer to x_0 as x(t=0)? and eq 13d consequently.
330) repetition of “the”
334) Can you give a reference for the mollification width? It is still Trigaux et al (2024a)?
Fig 13 to 22) there is some text missing in the figures, for example in Fig13 a “B” in the legend and a “v” in the fig b y-label are missing. Please makes sure the figures are well-rendered in the manuscript.
Fig 14) here it seems that the wake is being partially deflected towards the ground a few D after the 4th loop of the trajectory. That makes sense because the aerodynamic force has a vertical component. It would be nice to add a comment on this and maybe to reproduce Fig 14b for different distances downstream.
An additional point on the discussion at line 445 might be that the kite fly the lower part of the loop always at the same altitude (probably because of some constraints in the MPC), while the altitude of the top part changes during the reel-out. This means that the loads are distributed over a larger swept area and thus lower induction can be found. However, I’m not sure if this effect is negligible. Other considerations might come from the suggested analyses.
465) I don’t really understand the meaning of the term “2^e”. Could you write it out? If it just stands for “second”, then you could use “ 2’ ” or “2^\circ” or “II”.
481) please write it out that the free stream velocity is 11m/s: “.. is estimated to be approximatively equal to the free-stream velocity of 11 m/s”
495) if you refer here to Fig. 23, then you should explain it better. I think here you refer to Fig. 23 (a) and (b), where the in-phase cases are shown. Then please refer just to these two images, I tried to understand the figs (c) and (d), and the realized the explanation was at line 516.
543) I don’t really understand this sentence. An influence of -6% in power production is somehow relevant and it is caused by the reduction in wind speed. Since the controller is in-the-loop you might not see it in flight speed. To clarify this aspect, you could add the numerical values of the period T_p of the various solutions somewhere in Sect. 5.2.2 (all plots show the normalized time, so we don’t know the actual value of T_p). In alternative, you could also show a plot of the time evolution of the flight speed. For example, in Fig. 20b you show that the case phase-shifted has lower values of power, but it seems that it has the same flight speed as the loops have the same length.