the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Jul 2025
Joint Yaw-Induction Control Optimization for Wind Farms
Abstract. Wind farm flow control has demonstrated significant potential to increase wind farm power and energy production. Two commonly used methods are wake steering, which entails yaw misaligning individual turbines to deflect wakes laterally, and induction control, which typically modifies the thrust coefficients of individual wind turbines to reduce wake deficits. These two control approaches are often studied and utilized independently. This study investigates the combination of both of these strategies, termed joint yaw-induction control. By synergistically controlling wind turbine yaw angles and thrust levels, increased wind power can be achieved compared to either induction or yaw control in isolation. This research leverages the Unified Momentum Model to capitalize on the interplay between the yaw misalignment and the thrust coefficient of a turbine rotor on the power and wake velocities generated by the wind turbine. The Unified Momentum Model is integrated with blade element modeling to yield a blade element momentum model that both predicts the power and forces on wind turbines with arbitrary input of yaw, pitch, and tip speed ratio, and also predicts the initial wake velocities needed for far-wake models. Forward-mode automatic differentiation is integrated into the rotor and wake model to efficiently optimize control strategies using gradient-based optimization. Using the fast-running wind farm model, which is a coupling between the Unified Momentum Model and a Gaussian far-wake model, we demonstrate that joint yaw-induction control outperforms individual yaw or thrust control strategies, leading to significant increases in power production. First using a two-turbine test case, we show that the Unified Momentum Model reliably predicts the dependence of the freestream turbine power on its yaw and thrust coefficient compared to 210 independent large eddy simulations of wind turbines in a conventionally neutral atmospheric boundary layer. However, larger discrepancies result from the wake model, particularly in yawed conditions. The leading turbine control strategy that maximizes the combined power of the two turbines entails yaw misalignment and a thrust coefficient larger than Betz-optimal. Next, a 25-turbine wind farm case study highlights the benefits of integrated rotor and wake modeling but indicates that improvements in fast-running, gradient-compatible wake models are required to realize the potential benefits of joint yaw-induction control. The findings underscore the importance of modeling interdependencies between yaw and induction control to inform effective optimization strategies.
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Status: final response (author comments only)
- RC1: 'Comment on wes-2025-90', Anonymous Referee #1, 28 Jul 2025
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RC2: 'Comment on wes-2025-90', Anonymous Referee #2, 11 Sep 2025
The work is potentially interesting and presents a study on the optimization of the joint control of axial induction and yaw misalignment in order to maximize the power, for wind speeds below the rated value, of a cluster of 2 machines and of a wind farm of 25 turbines. The purpose of the article should be to show that a simultaneous variation in thrust and yaw can lead to greater benefits in terms of power boosting than classic wake steering implemented solely through misalignment of the upstream machines.Â
To this end, engineering models are introduced. The first allows the prediction, without relying on the tuning of many parameters, of the power losses induced by misalignment when the thrust (and therefore the induction) is both lower and higher than the optimal value predicted by the classic 1D moment theory. Specifically, the proposed model is innovative because it allows the performance of the machine to be modeled in conditions of axial induction greater than 1/3 without using empirical formulations. The second model estimates the flow distribution in the wind farm, thanks to submodels capable of estimating the speed and position of the far wake, rather than superimposing multiple wakes. Finally, an LES model is introduced, used as a plant.
The study has significant limitations that undermine its scientific rigor, validity, and relevance of the results produced. As highlighted by the authors, the engineering model significantly underestimates the power gains, with respect to LES predictions, when the machines are misaligned (whether or not the thrust is also changed). Similarly, it slightly overestimates the power gains obtained by controlling thrust alone. The authors objectively acknowledge the reasons for this, which are related to the shortcomings of the wind farm model used. In fact, this model does not capture the dependence between the thrust at which a machine operates and the speed at which its shed wake recovers. Similarly, physical phenomena such as the curled shape of the wake shed by a misaligned machine, rather than secondary steering, are not properly captured. In my opinion, these deficiencies not only have an impact on the results from a quantitative point of view, but also from a qualitative point of view. The authors argue that joint yaw and thrust control can bring greater benefits than yaw control alone. This statement is supported by the findings obtained with the engineering modeling, but is not confirmed by the LES results. Similarly, it is argued that thrust control is most advantageous in full-wake conditions and for distances between machines of 5-6 diameters. This statement is again based on the predictions of a flawed engineering model that are not supported by the high-fidelity simulations conducted by the authors (as well as by the results presented in other publications). While it is acceptable that deficiencies in modeling may produce results that are quantitatively different from those highlighted by the high-fidelity plant model, I do not consider qualitative differences to be acceptable. In fact, I wonder what value this article brings if the results predicted by the engineering models proposed here do not correspond, even qualitatively, to the predictions of the high-fidelity model used as a plant.
In my opinion, in order to consider publishing this work, it is necessary to review the engineering modeling to make it more accurate, with results that are similar to those of the high-fidelity model in all possible operating conditions, i.e., not only for the baseline scenario (as done by the authors). This can be done either by modifying the proposed model or by using other models available to the general public. In the recent past, many wind farm models (e.g., FLORIS, PyWake) have been developed and made available as open source. These models capture the physical phenomena not modeled by the model adopted in this work.
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Additional comments
Eq 19: Is N the number of blades? In the following, N is also the number of turbines in the farm. Given the many variables introduced throughout the paper, a nomenclature section would be of help.
Lines 215-217: I'm confused. Lines 182-183 state that the algorithm (i.e., eqs 8 to 17) is iterated until convergence on a_n and a'. I clearly see the iteration on a_n: Eq. 17 uses CT as input to compute a_n, which is then used in Eqs. 8 and 9 to compute axial and tangential velocity. I can't see, however, the iteration on a'. It could be done with Eq. 20, but the authors state it's not. The authors should clarify this point.
Line 241: The wind farm model used by the authors doesn't account for the effect of axial thrust on the wake recovery/spreading parameter k_w, which is well described by the authors in lines 466-469. Indeed, k_w only depends on the local turbulence at the rotor, but not on the thrust coefficient of the turbine. This capability is of fundamental importance to capture the benefit of over-induction, whose handling is the fundamental motivation for the development of the Unified Momentum Model, on the wake recovery (see Cossu, 2021). Its lack severely affects the accuracy of the results presented by the authors.
Line 393: When thrust control is active, the results show that the axial induction should be decreased, as shown by the Ct and Ct' in Figs 3b and 3d, as well as by the pitch in Fig 3e. It has been proven, in many publications based on simulations or even wind tunnel testing, that a reduction of the thrust/induction is not beneficial for a cluster of 2 aligned machines spaced 5-6D, as in this case. The advantage of a lower wake deficit in the near wake is indeed offset by a slower wake recovery, as also highlighted by the authors in lines 466-469. I expect the results found by the authors are due to the lack of modeling of these physical aspects in their wind farm model.
Fig 3a: When I first saw this plot, I got confused by a farm Cp of 0.52 for no-waked conditions, as I expected the farm Cp to be the sum of the "Cps" of the first and second turbines. I would suggest moving forward the definition of the farm Cp, which is provided quite a while after this plot and the text describing it (line 447).
General comment on section 4.4.1: it looks quite similar, in terms of scope and outcome, to section 5.2 of Tamaro et al (2024) (https://wes.copernicus.org/articles/9/1547/2024/). The differences, indeed, are in the used models: Unified Momentum with or without BEM + MITWindFarm for this work, a new proposed Momentum/BEM-based analytical model + FLORIS in the work of Tamaro et al (2024). The trend of Figs. 3f (TSR) for the joint control is quite close to the trends of Fig. 22 of Tamaro et al (2024). However, the trend of Fig. 3e (pitch) for the joint control differs substantially: in this paper, pitch angles higher and lower than those with No Control are expected in almost full-wake conditions and partial-wake conditions, respectively. The exact opposite is reported in Tamaro et al (2024). It would be valuable if the authors could comment on this. Specifically, discuss whether this is due to the model used for predicting the power losses in the yawed/derated wind turbine or to the far-wake model.
Lines 425-428: The difference between yaw control and joint control is only visible for a very small range of wind direction: probably only between -1 and +1 degrees, i.e., in the condition of full-wake interaction. As wind farms are designed to minimize the occurrences of this condition, I Â wonder what the benefit of using the joint control could be, in terms of AEP boosting, with respect to yaw control in a real scenario characterized by a standard "wind rose".
Lines 494-502: I appreciate the idea of comparing the performance of the model proposed by the authors with the performance predicted by the classic cosine model. However, I think it is incorrect to use an exponent of 3 for the cosine model. There is a great amount of scientific evidence (dozens of publications) that an exponent of 3 overestimates the effect of power losses due to yaw misalignment in wind speeds below the rated speed. The comparison should therefore be made using, for example, an exponent equal to 1.9. This is partially done: the optimal values of Ct' and yaw mis. are indicated for this exponent, but not the gain expected from the LES data. The discussion of the results (comparison of power losses on the upstream machine and gains on the downstream machine) should be carried out using the results obtained with an exponent of 1.9, rather than 3.
Line 527: What about the wind speed? Should the reader assume that it was set constant and equal to the hub height wind speed of the LES? Please be more specificLine 560-564: It's extremely difficult to see the trends described in the text by looking at Fig. 8b-e. Probably, a plot reporting the control action with respect to wind direction (with 6 lines, one per machine) would be better.
Figure 9: It's almost impossible to distinguish between the points based on their color. The figures could be clearer if the points associated with different yaw angles were shown with different markers and using colors that differ more
Citation: https://doi.org/10.5194/wes-2025-90-RC2
Model code and software
MITWindfarm 1.0.0 Jaime Liew, Ilan M. L. Upfal, Kirby S. Heck, Michael F. Howland https://doi.org/10.5281/zenodo.15367720
MITRotor 0.1.1 Jaime Liew, Ilan M. L. Upfal https://github.com/Howland-Lab/MITRotor
Dualitic Jaime Liew https://github.com/jaimeliew1/Dualitic
Unified Momentum Model 0.3.0 Jaime Liew, Kirby S. Heck, Michael F. Howland https://doi.org/10.5281/zenodo.10524066
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This research article describes the use of the Unified Momentum model to predict optimized wind farm performance using both yaw (wake steering) and thrust (induction) as means of actuation. These optimizations are verified against large eddy simulations with actuator disks (LES-AD). A simple two-turbine case supports the assertion that modulating both yaw and thrust will provide power gains above those from yaw alone. However, a 25-turbine case fails to show significant benefit from actuating thrust in addition to yaw, indicating that the present model would likely not be effective for optimizing a real-world wind farm. Nevertheless, the study makes a good argument for further investigation of so-called joint control.
Major comments:
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