Extreme coherent gusts with direction change – probabilistic model, yaw control and wind turbine loads
 DTU Wind Energy Dept., Technical University of Denmark, Roskilde, Denmark
 DTU Wind Energy Dept., Technical University of Denmark, Roskilde, Denmark
Abstract. Observations of large coherent fluctuations from a decade of measurements are used to define a probabilistic model of coherent gusts with direction change. The gust model provides the joint description of the gust rise time, amplitude and directional changes with a 50year return period. In conjunction with the gust model, a yaw controller is presented in this study to investigate the load implications of the joint gust variables. These loads are compared with the design load case of the extreme coherent gust with direction change (ECD) from the IEC 614001 Ed.4 wind turbine safety standard. Within the5 framework of the gust model we find the return period of the ECD to be approximately 460 years. From the simulations we find that for gusts with a relatively long rise time the blade root flapwise bending moment, for example, can be reduced by including the considered yaw controller. From the extreme load comparison of the ECD and the modeled gusts we see that by including the variability in the gust parameters the load values from the modelled gusts are between 20 % and 74 % higher than the IEC gusts.
Ásta Hannesdóttir et al.
Status: final response (author comments only)

RC1: 'Comment on wes202238', Anonymous Referee #1, 18 Jul 2022
Overall comments:
 The manuscript presents results from a probabilistic model of a dataset consisting of 92 measurements of wind conditions meeting the authors’ definition of a coherent gust. The probabilistic model uses the Nataf model to create a trivariate distribution of the data in terms of rise time, direction change, and amplitude change of the gust and ISORM is used to calculate environmental surfaces (i.e., combinations of these three variables with a common mean return period). The coherent wind gusts associated with the 50yr environmental surface are then analyzed using a model of the DTU 10MW wind turbine in HAWC2 and the results are presented in terms of several crosssectional demands on the tower and blades of the turbine. Simulations are implemented with and without a yaw controller. Results are compared with demands calculated following the definition of a coherent gust in IEC 614001.
 The authors present a clear and interesting analysis of an influential load case in the design of wind turbines. Their interpretation of the analysis provides useful insight and I enjoyed reading the manuscript. I have a few recommendations to increase clarity and accuracy, but otherwise recommend this paper for publication.
Specific comments:
 Line 6, the 460 year return period is written as if this is a general finding. Please revise to clarify that this return period is specific to a particular dataset at a particular location following a particular methodology.
 Line 16, DLCs not DLC’s
 Line 18, pls replace the wording “which is the target reliability level in wind turbine design.” with something like “which is the intended recurrence period of the environmental conditions prescribed by the IEC Standard.” The target reliability level depends on load and resistance factors in addition to the intended recurrence period of the environmental conditions of the DLC.
 Lines 6168, while the authors refer to a previous study for the detection and characterization of the coherent gusts within their dataset, it would be helpful to provide a sentence or two here describing the criteria for an event to be categorized as a gust and the way in which the three variables are calculated for each event. In particular, please provide brief information on the spatial criteria for classification as a gust and the time average used to calculate the wind speed.
 Lines 6869, how are the wind speeds Ua and Ub averaged in time and in space? I imagine this is described comprehensively in the authors’ previous work, but it would help to provide some brief information here.
 Section 3.1, the discussion on IFORM and ISORM needs revision. On Line 88, the statement that IFORM has been shown to underestimate the exceedance probability by an order of magnitude needs conditioning, as this is not a statement that is generally true. Can the authors elaborate what they are talking about? When multiple variables are being modeled probabilistically, there are many, equally legitimate, ways to determine exceedance probabilities and recurrence periods for combinations of these variables, so I am having trouble understanding what the authors mean when they say the exceedance probability is underestimated – underestimated compared to what?
 On Line 90, the authors refer to Equation (7) to distinguish between IFORM and ISORM, however this equation, which defines a sphere with radius beta in standard normal space, is used for both IFORM and for ISORM. The difference between the methods is in how the sphere is used to define the space of variables for which probability is calculated. In IFORM, the space is defined by a plane tangent to the sphere. In ISORM, which is a new method to me, I believe the space is defined as all points outside of the sphere. Can the authors explain more clearly the differences between IFORM and ISORM given that both require use of Equation (7)?
 On Line 91, the authors refer to an exact solution for the return period using ISORM. Perhaps I am not understanding the authors’ intent here, but I don’t understand the idea of an exact solution for calculating a return period for combinations of three variables. Since multiple variables cannot be ranked unambiguously, there are many ways to calculate exceedance probability/return periods for combinations of these variables. IFORM is one way. ISORM is another way. I don’t think it’s appropriate to call either one exact. They are just different. Are the authors saying that environmental surfaces using ISORM lead to more accurate calculations of probability of structural failure? If so, this should be clarified. And, even still, calling the result generally exact is too strong of a statement since this could only be true for a specific and simple idealization of the loading given the environmental variables.
 Section 3.1.2, suggest editing the section title to emphasize IEC, e.g. “the IEC ECD” instead of “the ECD”
 The result on Line 160 should be emphasized as being calculated for one specific site using one specific methodology.
 Line 232, bending not binding.
 Line 251, at this point the meaning of “load channels” was not clear to me. I eventually figured it out after seeing Table 2. It could be helpful to define this term earlier.
 Line 257, pitch not pith.
 Line 271, as I was thinking about the results for TT_yaw, I was curious how much of the loading is inertial as the yaw controller accelerates the rotor. On a related note, does the yawing of the spinning rotor during an ECD cause a significant gyrotorque? This may be outside of scope, but, it my opinion, it would be interesting to provide some discussion on the influence of inertial loading compared to aerodynamic loading for this condition
 Table 2, suggest dropping a couple of significant figures from the reported moments.
 AC1: 'Reply on RC1', Ásta Hannesdóttir, 12 Sep 2022

RC2: 'Comment on wes202238', Anonymous Referee #2, 16 Nov 2022
General comments:
This paper is both relevant and well written and it contains material relevant for important discussion on how to improve modeling related to gust events. It contains a study on the actual wind conditions that is close to a ECD event as well as a consequence study of the measured windconditions simplified in to a parametric study of standardized IEC gust of the ECD type with variation in the parameters wind speed, wind direction and rise time.
The first part of the study that relates to the measured wind event is in general very good. Only minor remarks to this part to enhance the clarity. Eg how is it ensured that the selected wind events are related to a situations like an ECD, where the increased wind speed and wind direction stay on this new plateau for substantial amount of time? How is it ensured that the wind structure is coherent over a area covering a multi MW wind turbine? Perhaps this is covered in a prior reference, but it could be made more clear to the reader.
It is also surprising that gusts with rise time down to 5s is included in this stude, as it is based on a previous study (Hannesdottir and Kelly, 2019) where the fastest gust seen for this site is 9s. How can this be? is this an artifact of the ISORM approach or can such fast events be justified as a coherent gust opposite being part of turbulence?
The second part of the paper addressing the consequence study of the chosen distribution of gust parameters is quite clear, and a public available turbine model with controller is used. It is nice that a public available turbine model is used as it makes it possible for other to reproduce the results. However, to conclude that the results found is what is expected from using an inductrial controller is not clear at all and the author should be cautious about concluding anything general from this analysis. From the time series shown in the appendix, it appears as the controller is highly sensitive to rapid changes in wind speed as well as highly sensitive to yaw errors which is understandable as there are nothing done in the controller to ensure low loads in such extreme situations. At most, conclusions from the consequence studies can be seen as indicative and not representative of the reponse of all wind turbines.
Specific comments:
 Are the measured gust mainly related to the western or eastern sector. Is is mainly onshore ore offshore/near shore conditions that result in the measured gusts. Is there a difference in gusts from East or West?
 p.3 line 60. Is there a relation between start wind speed rise [m/s] and wind direction error as used in the standard, or how is it on this site?
 p.3 line 66. "from a variety of phenomena" like what? Can you give examples to the reader?
 How are the wind measurements done? Height of measurement, number of points, single or multiple metmast? Does a rise time of 5 seconds still correspond to a coherent gust with a spatial size of +100m?
 How is it ensured that eg the wind direction is "permanent" and not just a temporary gust returning at a low value after short time? Same question for the delta wind speed.
 How is it ensured that gust structures are large enough to quality for a coherent structure for a multiMW turbine?
 It is stated that 92 gusts have been detected. How is it ensured that there is enough points?
 p.5 line 115. What is IDF?
 p.6 line 132. it is unclear how the correlation coefficients rho_ij calculated?
 p.6 line 137. How is U derived?
 p6 line 138. Is equation 12 to be understood as a dot product?
 p.7 Figure 2. It is quite difficult to see any quanticative results of these plot. In the right plot is appears as not data a present for a delta u<10m/s, whereas the left plot show the majority of points below 10m/s. Perhaps the points can be placed in Figure 3 with colors representing the rise time.
 p.7 line 156. Why is the rise time negative here?
 p.8 eq(17) Why is this shown as a dot product?
 p 10. It would be nice if eg the tower top resulting bending moment was included as well.
 p 10. Line232. "binding" > "bending"
 p11. line 246. "may be seen". Can it be seen or can it not be seen? Please choose.
 p 11. Fig 5 Please write in captions what sensor is seen in the plot and or make it more clear from the individual figures
 p 12. Fig 6 Please write in captions what sensor is seen in the plot and or make it more clear from the individual figures
 p 16. Line 315. Are you sure the accuracy to the BEM model in HAWC2 decrease with yaw error? otherwise the work "may" should be included beween "(BEM)" and "decrease"
 p16. Line 316. Is is fine to reflect on the model accuracy, but as I read the paper, I am more concerned about the uncertainty in the simple turbine power controller than the aerodynamics.
 Appendix A. Figure A1 Please include wind speed and wind direction for clarity.
 Appendix A. Figure A1. What is the difference between the dottet and the solid lines?
 Appendix A. Figure A1. Gust parameters are written in the figure title, but it is unclear what the numbers represents.
 Appendix A. Figure A2. See comments related to figure A1
 AC2: 'Reply on RC2', Ásta Hannesdóttir, 28 Nov 2022
Ásta Hannesdóttir et al.
Ásta Hannesdóttir et al.
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