the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Wind Vane Correction during Yaw Misalignment for Horizontal Axis Wind Turbines
Andreas Rott
Leo Höning
Paul Hulsmann
Laura J. Lukassen
Christof Moldenhauer
Martin Kühn
Abstract. This paper investigates the accuracy of wind direction measurements for horizontal axis wind turbines and its impact on yaw control. The yaw controller is crucial for aligning the rotor with the wind direction and optimizing energy extraction. Wind direction is conventionally measured by one or two wind vanes located on the nacelle, but the proximity of the rotor can interfere with these measurements. The authors show that the conventional corrections, including lowpass filters and calibrated offset correction, are not adequate to account for a systematic overestimation of the wind direction deviation caused by the rotor misalignment. This measurement error can lead to an overcorrection of the yaw controller, and thus, to an oscillating yaw behaviour, even if the wind direction is relatively steady. The authors present a theoretical basis and methods for quantifying the wind vane measurement error and validate their findings using computational fluid dynamics simulations and operational data from two commercial wind turbines. Additionally, the authors propose a correction function that improves the wind vane measurements and demonstrate its effectiveness in two free field experiments. Overall, the paper provides new insights into the accuracy of wind direction measurements and proposes solutions to improve the yaw control for horizontal axis wind turbines.
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Andreas Rott et al.
Status: final response (author comments only)

CC1: 'Comment on wes202353', Johannes Schreiber, 04 Jul 2023
Dear authors,
thank you for this very interesting and important work, I really enjoyed reading it.
So far, the nacelle anemometry of misalinged turbines is not well enough understood and this work and the presented methods are definetly a very usefull contribution to that field, especially in the context of wake steering wind farm control.
While reading your work, a few minor comments and questions came to my mind, that I would like to share below with the authors.
 Line 161: "...the influence of the thrust of the rotor on the wind vane on the wind turbine, ..." I understand what is meant, but maybe it can be rephrased to improve readability.
 Line 235: "The yaw control ensures that the yaw angle after the yaw manoeuvre corresponds to the measured wind direction before the yaw". Is this valid for every yaw controller? If a yaw controller yaws until the (filtered) releative wind direction becomes zero, the approach may not work as intended. I imagine that larger turbines, with low yaw speed implement such a control.
 Figure 8/Line 400: You mention within the discussion that a nonlinearity between the shown variables is likley. Maybe you could include binned mean values (or similar) within Figures 7 and 8. That could help visualizing the nonlinearity especially for larger misalignments (which are indeed very important operation modes in wake steering).
 Table 1/A: Is it possible to add uncertainties to the yaw actuations and distances? Maybe the "bootstrapping" method (see Simley, 2021) could be used.
 Table 1/B: Is the "yaw distance per 10 min" equivalent to the maybe more commonly used actuator duty cycle (ADC)? If so, you might consider mentioning or using it.
See for example:
S. Kanev, “Dynamic wake steering and its impact on wind farm power production and yaw actuator duty,” Renewable Energy, vol. 146, pp. 9–15, Feb. 2020, doi: 10.1016/j.renene.2019.06.122.
F. Campagnolo, R. Weber, J. Schreiber, and C. L. Bottasso, “Wind tunnel testing of wake steering with dynamic wind direction changes,” Wind Energ. Sci., vol. 5, no. 4, pp. 1273–1295, Oct. 2020, doi: 10.5194/wes512732020.  Table 1/C: Within the text you report also the effet of power increase, you could add those values to Table 1 as well. Also, an uncertainty quantification (see comment Table 1/A) may be helpful.
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/wes202353CC1 
RC1: 'Comment on wes202353', Anonymous Referee #1, 05 Jul 2023
The authors presented a study on the coupling between the wind direction measurement error by a wind vane in the wake of the rotor and the yaw misalignment apllied on the turbine. They found that the yaw misalignment measurement error of the wind vane is overestimated and apply a transfer function to correct this error. The coefficient of this transfer function are computed from CFD simulation and SCADA measurements crossed with metmast measurement on a real wind farm. This transfer function allows to have a better estimation of both the wind direction and the yaw misalignment. Eventually, this corrected measurement of wind direction is applied to a yaw controller of a real wind farm, and it is observed that this correction allows to signficantly reduce the yaw actuator activity and slightly increase the production of the wind farm.
The authors made a relevant critic of their article in the "Discussion" section, emphasizing the strengths and weaknesses of their work, and giving relevant perspectives of their work.
The article is generally wellwritten and relevant, a last proofreading of the article might be necessary, as several typos could have been spotted during the reading.
Citation: https://doi.org/10.5194/wes202353RC1 
RC2: 'Comment on wes202353', Anonymous Referee #2, 10 Jul 2023
The authors present a correction function that improves the quality of the wind measurements used to ensure an optimal alignment of the wind turbine. The topic is relevant and the manuscript is well writen. However, readability could be improved by making shorter paragraphs or using resoucers such as bullet lists or writting the key words in bold. Some other suggestions are
 L5: to account for should be substituted by to correct
 L15: In order to provide full context on the relevance of the problem, it might be interesting to explain with more detail why the alignment is one of the key parameters.
 L4952: Questions can be phased in a way that makes them more understandable.
 L104: It might be interesting to point out that the proposed transfer function is static. Has a dynamic transfer function been considered? Why was that idea discarded?
 L111: Rephrase: Wind vane data therefore normally already includes a correction for this offset.
 L145: How does the uncertainty in the measurement of the met mast affect the results?
 L190: A comma is missing somewhere in the sentence
 L212: a comma is missing after as aleardy mentioned.
 L220: shown instead of show.
 L276: A comma is missing.
Citation: https://doi.org/10.5194/wes202353RC2 
AC1: 'Comment on wes202353', Andreas Rott, 25 Aug 2023
We want to thank everyone for their constructive feedback.
In the following section, we address each of your comments and suggestions individually. Corresponding revisions of the manuscript will be referred to.
Referee 1
Thank you for the concise feedback. We have proofread our manuscript again and corrected typos to the best of our ability.
Referee 2
Thank you for the comments, which we will address in the following. Here we will paraphrase your feedback, preceded by RC2, and then give our answer, preceded by AC.RC21:
use "correct" in L5 instead of "to account for"
AC1:
doneRC22:
(L15) explain in more detail, why the alignment is a crucial parameter.
AC2:
We have added the following sentence to emphasize the importance of the alignment of the rotor to the wind direction.
"Only if the turbine is oriented into the wind, it can reach its maximum possible power coefficient. Even with relatively small misalignment, its conversion of the kinetic energy in the wind into electricity is impaired. In addition, this imposes more uneven forces on the blades, which can result in increased fatigue loads. In certain situations, intentional misalignment of the turbine can be used to manipulate the wake so that downstream turbines are less affected. We refer to this approach as Active Wake Deflection and will discuss it briefly below. However, even for this particular mode of operation, it is therefore essential to accurately estimate the alignment of the wind turbine. The standard procedure to determine the alignment involves using one or two wind vanes to detect deviations from the wind direction and adjust the yaw angle of the turbine through an active yaw manoeuvre accordingly."RC23:
(L4952) Phrase the questions in a more understandable wayAC3:
1. Is there a systematic error in wind vane readings when utilityscale wind turbines are not aligned with the wind direction, and how can this error be described?
2. Can the inaccuracies in wind vane measurements be corrected using operational data, both with and without external reference measurements?
3. What impact does correcting the wind vane during yaw misalignment have on the overall performance of a wind turbine?RC24:
(L104) Why was a static transfer function used and not a dynamic transfer function?AC4:
As far as we understand this question, a dynamic transfer function could consider the time dependence of the wind direction misalignment or the inclusion of additional parameters. For example, that the correction factor is not constant, but depends on wind direction change rate, its integrated mean, or other parameter. Examples comprise the wind speed, the atmospheric stability (TI, MoninObukhov length, wind shear, veer), the absolute wind direction in case of complex terrain, or the operation mode of the turbine (normal operation / curtailed operation).
Such parameters could potentially have an influence on the correction factor and are therefore worth additional investigations.
However, we chose to make the transfer function as straightforward as possible while still obtaining convincing results in the fullscale experiment, mainly for two reasons:
First, we believe that the most important parameter affecting the corrections factor is the thrust coefficient, which is relatively constant in the partial load range. We filtered for wind speeds and found that the estimated correction factor did not change significantly over the partial load range. For wind speeds greater than the rated wind speed and where the thrust coefficient decreases, the correction factor approaches a value of 1. Unfortunately, the amount of usable measurement data for these situations was too small to obtain statistically valid results.
The second reason is that each new parameter adds another dimension of complexity and requires thorough investigation and sufficient data, in some cases, extra measurement devices, for example, in the case of atmospheric stability). To be able and allowed to implement the transfer function into the wind turbine controller, the function needed to be simple and convincing.
After our initial results have shown promising benefits for wind turbine operation, we hope that other manufacturers will feel encouraged to integrate similar or even more complex transfer functions into their turbines’ control system and make the effort to test them.RC25:
Rephrase L111AC5:
We reformulated the clause:
"As a result, wind vane data typically incorporates an adjustment to account for this deviation. Consequently, our subsequent analysis focusses on the correction factor $c$, with the offset factor $b$ being set to 0 degrees."RC26:
What is the impact of uncertainty in the measurement of the met mast on the results?AC6:
The uncertainty in the measurement of the met mast means that we do not have a true reference for the wind direction. This complicates the analyses because we cannot simply estimate the uncertainty of the wind vane by comparing with a reference value. The cause of measurement errors in the correlation of both systems cannot clearly be identified between the two measurement systems and consists most likely of errors in both systems. As we explained in the paragraph about the ODR, standard statistical tools like ordinary linear regression lead to false results since these require having an undisturbed value (predictor, which is commonly plotted on the xaxis) and a response variable (on the yaxis, which can have uncertainty). In our case, both variables have uncertainties, so neither is the undisturbed predictor for the other. The undisturbed wind direction, which is unknown, is the predictor variable for both.
Fortunately, methods like ODR still allow us to identify correlations between the two variables. And since we can assume that the uncertainty in the measurement of the met mast is independent of the yaw angle of the turbine, we can use them to characterize the influence of the yaw angle on the measurement of the wind vane. To strengthen this argument, we included the results of the CFD Simulation, where we know the true wind direction and see the same behaviour of a potential wind vane. Therefore, we conclude that using the met mast measurements is valid.
RC27 to 10:
Missing commas and typosAC7 to 10:
We corrected the corresponding passages.
Community Comment 1
Dear Johannes Schreiber,Thank you very much for taking the time and effort to review the preprint and provide your extremely valuable and helpful comments. In the following, we will address your comments individually.
CC11:
Improve readability of L161AC1:
We have rewritten the sentence in the following way:
“In order to determine the influence of the rotor's thrust on the wind vane of the wind turbine, only situations in which the wind turbine was operated in the partial load range and without curtailment were considered for the comparison of the measured values.”CC12:
"The yaw control ensures that the yaw angle after the yaw manoeuvre corresponds to the measured wind direction before the yaw" Is this valid for every yaw controller? If a yaw controller yaws until the (filtered) relative wind direction becomes zero, the approach may not work as intended. I imagine that larger turbines, with low yaw speed implement such a control.AC2:
First, we would like to clarify how this is to be understood here: The filtered wind vane measurement before the yaw manoeuvre is used to trigger a yaw manoeuvre and determine the new target angle of the nacelle. The measurements during the yaw manoeuvre are NOT used; only after the yaw manoeuvre the measurements are recorded again and filtered for triggering the next yaw manoeuvre.
If the controller also uses the measurements during the yaw process in the filter, then the system would overshoot to set the filtered value to zero. (We assume this is meant in the second part of the question, so we agree with that). In control engineering terms, the yaw controller would thus be a pure Icontroller (Integral, without proportional (P) or derivative (D) parts). It would, of course, be possible to create a complete PID controller that theoretically would not overshoot, but it has proven best only to use strongly filtered values of the wind vane since the individual measurements fluctuate very strongly, which would make it very difficult to balance the P and D portion in the controller.
For precisely this reason, the target value is determined before the yawing process, and the measurements are discarded during yawing.
It is challenging to say whether all yaw controllers work on precisely this principle, as wind turbine manufacturers commonly do not share yaw control algorithms. To the best of our knowledge, this is how it works in all the turbines we have dealt with. This reactive behaviour of the yaw control thus implicitly assumes a persistence model for the wind direction, which is a logical assumption given the lack of better alternatives. Therefore, the research on proactive yaw controllers is fascinating and can utilize information gathered upstream. (See Sengers, B. A. M., Rott, A., Simley, E., Sinner, M., Steinfeld, G., and Kuehn, M.: Increased power gains from wake steering control using preview wind direction information, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes202359, in review, 2023.)CC13:
Maybe include binned mean values to show a possible nonlinear dependency between the wind direction deviation reference and wind direction deviation measured by the wind vane.AC3:
We agree that investigating nonlinearity is exciting research, which can be necessary for active wake deflection.
In the context of this paper, we decided against it because the focus here is on standard operation, and the linear modelling of the relationship between wind direction deviation and the wind vane measurement seems sufficient for this operation. We did not want to complicate the paper or make it even longer unnecessarily, and more data with intentional misalignment should be investigated for an investigation with due diligence.
However, we like to use this discussion to present a few more thoughts/suggestions that we have made on this topic:
Aggregating the data in Fig. 7 and Fig. 8 by binning and thus investigating the correlation sounds logical and was one of our first approaches. However, this leads to the same problem as with linear regression. The mapping of the wind direction deviation measured by the wind vane to the xaxis and the wind direction deviation measured by the met mast to the yaxis is arbitrary and can be swapped freely since both measurements have uncertainties, and thus neither is a valid predictor of the other.
As with linear regression, binning implicitly assumes no measurement uncertainty on the binned value. If we apply binning to the xaxis, we get a different result than if we swap the axes or use binning to the yaxis. Therefore, the validity of the binned mean values is questionable.
A reasonable method for investigating the linear or nonlinear relationship would be the principal component analysis or the Proper Orthogonal Decomposition. Here, the data are projected onto a vector space that maps the variances sorted by size. The number of dimensions of the new vector space does not change, so two dimensions remain. The first dimension (principal component/mode) represents the largest variances within the scatterplot. This forms a straight line through the scatterplot, minimising the squared orthogonal distances to the scatter points.The ODR line, which we have determined, fulfils exactly this property and is, therefore, the first principal component / the first mode. This method shows, first, only a linear relation and, in fact, the strongest one. To analyse a possible nonlinear relationship, the second dimension of the new vector space can be examined, i.e., the residual or error that remains in the ODR. The total error will yield a distribution with a mean of 0 (this is the case by definition). But in the case of a pure linear correlation, the error should be randomly distributed over the entire measurable range of the ODR line and have no discernible structure. In the case of a nonlinear correlation, this should be recognisable if we consider, for example, now binned mean values of the residual over the ODR straight line.
For modelling the nonlinear relationship, we have come up with a model that makes sense, but more data with larger misalignments will be needed for a thorough investigation that proves the advantages of this model over the linear model. We have briefly outlined the model in the appendix of this discussion [Draft of nonlinear wind vane correction model].CC14:
Uncertainties to the yaw actuation and distances?AC4:
The number of average actuations is simply calculated by dividing the total number of actuations within the period by the duration, extrapolated to 10 min. Different methods could be used to get an idea of the distribution, but their results vary slightly. For example, divide the time series into 10 min sections and look at the number of yaw manoeuvres in each interval. The average value of these data also corresponds to the average value given here. The fluctuation is notable here for the interpretation since this data basis permits only whole numbers. It would make more sense to look at the distribution of the number of yaw manoeuvres in 10 min for each day or, for example, for all four hours. This might show further correlations between, e.g., atmospheric stability, turbulence intensity, and the number of yaw manoeuvres.
The bootstrapping method is beneficial for calculating the standard error of the mean when only small amounts of data are available.
CC15:
Is yaw distance per 10 min equivalent to the more commonly used actuator duty cycle (ADC)AC5:
The Actuator Duty Cycle (ADC) and the Yaw Distance per 10 min specified here are very. Due to the inertia of the nacelle the rotational speed of the nacelle is not constant during acceleration and deceleration, and therefore the yaw distance does not correlate 100 % with the duration of the yaw manoeuvre and thus not with the ADC. (Small yaw manoeuvres take more time per degree of turn, relatively speaking.)But this is a useful hint, which has been added to the script as the following paragraph in Chapter 3.3.1:
“The yaw distance, in general, is closely related to the actuator duty cycle (ADC) of the yaw controller. The BARD5.0 turbine yaws at an average rotational speed of about $0.75^\circ$ per second, so the average yaw distance per 10 min of $13.66^\circ$ for normal operation takes approximately 18.21 seconds, which means that the yaw motor is active about $3\,\%$ of the time. Due to the inertia of the nacelle, the rotation speed is not entirely constant; therefore, this conversion is only an approximation. Thus, in this evaluation, we only use the average yaw distance per 10 min and not additionally the ADC.”
Andreas Rott et al.
Andreas Rott et al.
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