the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On the robustness of a blade loadbased wind speed estimator to dynamic pitch control strategies
Abstract. Current implementations of wind turbine pitch controllers for load alleviation or active wake mixing use limited information about the incoming wind. While these pitch controllers could benefit from broader wind condition awareness, the lack of suitable sensing methods is limiting. Blade loadbased wind speed estimators are an alternative to cup anemometers or LiDARs. In this paper, we wish to verify how robust such estimators are to the control strategy active on the turbine, as it impacts both operating parameters and loads. We use an Extended Kalman Filter (EKF) to estimate incoming wind conditions based on blade outofplane bending moments. The internal model in the EKF relies on the Blade Element Momentum (BEM) theory in which we propose to account for delays between pitch action and blade loads by including dynamic effects. Using LargeEddy Simulations to test the estimator, we show that accounting for the dynamic effects in the BEM formulation is needed to maintain the estimator accuracy when dynamic wake mixing control is active.
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RC1: 'Comment on wes202456', Anonymous Referee #1, 30 May 2024
The submitted article entitled “On the robustness of a blade loadbased wind speed estimator to dynamic pitch control strategies” presents a numerical study on the accuracy of a wind speed estimator based on measurements of blade root bending moments in the presence of different load alleviation and wake mixing control strategies. The estimator is formulated as an Extended Kalman Filter (EKF) and uses Blade Element Momentum (BEM) theory for the statespace model. The static BEM model is modified with a firstorder differential filter to account for dynamic effects in the wake development and the induction of the blades. The article is well written and easy to follow, the methodology is presented comprehensively, and the results are discussed rigorously. The subject of pitch control strategies under wake conditions is also a highly relevant topic and fits the scope of this journal.
Some points could benefit from further clarification:
 The proposed approach of blade loadsbased wind estimation is presented as an alternative to LIDAR measurements. Can you comment on the advantages and disadvantages of each approach? It is mentioned that LIDARs are not widely used commercially due their high capital and operational costs, but the same applies to blade structural health monitoring systems (SHM). Measurements of the blade root bending moments are typically only available for modern offshore wind turbines, which limits the applicability of the proposed approach. Furthermore, there are distinctions in the prediction horizon of wind speeds. LIDARs are able to measure the upstream wind speeds and give the controller several seconds to react to the incoming wind, while blade measurements only provide estimates of current wind speeds.
 The analysis demonstrated that the modification of the BEM model could account for dynamic effects in the aerodynamics such as wake development and blade induction, however, the structural dynamics of the rotor were not considered in this study, since both the EKF estimator and the LES simulations assume a rigid rotor. In reality, the relationship between blade root measurements and wind speeds is also affected by the elastic edge and flapwise bending of the blades. Can you comment on how the structural dynamics would affect the accuracy of the estimator and whether the proposed BEM modification could account for these dynamics? Have you considered numerical studies with aeroelastic software such as OpenFAST or HAWC2 to investigate the effects of the structural dynamics?
 Fig 5,6: the yaxis description seems to be corrupted.
 How are the covariance matrices Q and R of the EKF determined? Was the EKF tuned with respect to Q and R?
Overall, the submitted article is of high quality and I recommend the publication once the above comments have been addressed adequately.
Citation: https://doi.org/10.5194/wes202456RC1 
RC2: 'Comment on wes202456', Anonymous Referee #2, 20 Jun 2024
This is a very wellwritten, clearly explained paper that addresses the accuracy of bladeload based wind speed estimators when pitch control strategies with high pitching frequencies are used. This is a relevant topic because of the interest in using rotorbased wind estimates as part of individual pitch controllers or active wake mixing control strategies. The methodology of evaluating the estimators using highfidelity modeling that is largely independent of the BEM models used in the estimator makes for a robust analysis of estimator accuracy. Finally, the use of a model of the induced velocity dynamics, which has been used for rotor effective wind speed estimators in the past, is a novel contribution to the field of blade loadbased wind speed estimation.
There are no major issues with the paper, but in the list below are several mostly small comments that I believe should be addressed. The main comments include a) describing how the reference wind variables to which the estimates are compared are calculated, b) clarifying why the spatial filtering inherent in the bladeload based estimates could be a significant source of estimation error, since the reference variables should also include spatial filtering, c) providing results in Section 4 for aboverated operation where collective pitch control is active to give a more complete picture of the estimator accuracy and potential need for dynamic BEM models during all pitch control scenarios.
Comments:
 Ln. 33: "Information on the flow conditions, whether explicitly or through blade loads, is not used." This is a little misleading because wake mitigation controllers should at least use measurements/estimates of the wind speed and direction and determine the specific control actions based on whether there are any downstream turbines that would benefit from wake mitigation.
 Section 2.1.2: "Estimation of bladeeffective wind speeds": What is the sampling time/update rate of the EKF bladeeffective wind speed estimator?
 Fig. 1 is missing some characters in the output viarable names on the right side.. Similarly, Figs. 2, 5, 6, 7, and 8 are missing some characters in the axis labels (and for Figs. 5 and 6 the titles as well).
 Ln. 150: "We model the system using the BEM theory": Do you use a specific BEM software, or have you written your own implementation?
 Ln. 179: "r = 2R/3": Can you explain the motivation for assuming the sectoreffective wind speeds represent the wind at this radial location?
 Section 3.2: Please describe how the true values of the estimated variables are determined from the adjunct LES. For example, are sector wind speeds calculated by averaging the longitudinal u component of wind over the sector areas? Is shear determined by fitting to the sector average wind speeds or by finding the bestfit shear over the entire rotor area?
 Ln. 215: What is the time step used?
 Eqs. 1820: Please define "Uref".
 Eqs. 21 and 22: What is the variable alpha_{h,k}? Should this be alpha_{yaw,k} and alpha_{tilt,k}?
 Pg. 9, 1st sentence: "We attribute this to the inherent spatial filtering introduced by the bladeasasensor approach.": Can you explain this in more detail? It seems like the true values of the variables to which the estimates are compared would also include spatial filtering (if they are calculated as the spatial average over the sector areas), so the spatial filtering due to the blade should be beneficial in matching the true rotor effective wind speeds, sector wind speeds, and effective shears.
 Ln. 263: "eventually forcing the wake to displace laterally (see Fig. 3)…": Should this be "laterally and vertically"?
 Ln. 281: Similar to comment 6, how are the reference velocities calculated?
 Ln. 282 and 283: I believe (Fig. 4(b)) and (Fig. 4(c)) in the text should be changed to (Fig. 4(a)) and (Fig. 4(b)). In this case Fig. 4(c) may need to be referenced in the text elsewhere.
 Fig. 4 caption: "used as reference wind speeds to verify it": To verify what? Consider something like "to verify the estimated values".
 Eq. 24: Should "w_{qs}/dt" be changed to "dw_{qs}/dt"?
 Eqs. 2730: This section suggests that the induced velocity filtering time constants are specific to the type of control strategy. Can you comment on how these should be tuned for a turbine that uses IPC some of the time, helix (or another wake mixing control strategy) sometimes, and also collective pitch control for rotor speed regulation? Would you need to be updating the time constants frequently during operation based on the current control mode, or would you use one value that works reasonably well for all cases? Lastly, if only collective pitch control for rotor speed regulation is used, how would you determine the pitching frequency value?
 Section 4.5: If possible, it would be useful to show the accuracy of the bestfit horizontal and vertical shear in addition to the sector wind speeds and rotor effective wind speeds, as in Section 3, because these quantities could be used to inform IPC control strategies.
 Section 4.5 and 4.6: If possible, it would be valuable to show results for an aboverated wind speed (like 14 m/s as in Section 3) in addition to the 9 m/s case. First, IPC for load reduction is more commonly used in aboverated conditions, so it would be useful to show the estimator accuracy with IPC during aboverated operation. Second, because collective pitch control for rotor speed regulation is active in aboverated wind speeds but not in belowrated conditions around 9 m/s, it would be important to understand whether the static BEMbased estimator is sufficient when only collective pitch control is used, or if dynamic BEM is needed in this case too.
 Tables 2 and 3: Can you comment on why the estimation errors are slightly higher when only baseline control is used rather than the more complex IPC and wake mixing controllers?
 Ln. 382: "likely also due to the filtering effect of the bladetosector conversion." Same as comment 10, my understanding is that the reference variables to which the estimates are compared also include spatial filtering. In this case, how would the spatial filtering of the estimator vs. the groundtruth references differ and thus contribute to estimation error?
 Appendix A: Does the BEM model account for the rotor tilt and cone angle? Or is the rotor approximated as being perpendicular to the inflow?
 Algorithm A1: This is a nice presentation of the BEM algorithm. Could you also provide the tolerance value you use?
 Algorithm B1: This algorithm is relatively easy to follow, but a couple variables could be clarified. Could you explain Delta_Theta and just to perfectly clear "n_B"?
Citation: https://doi.org/10.5194/wes202456RC2 
AC1: 'Comment on wes202456  Response to Reviewer Comments', Marion Coquelet, 10 Jul 2024
Dear reviewers,
We wish to thank you for your time, review, and appreciation of the work. We have addressed your comments in the document attached. This document also includes the revised version of the paper in which changes are marked in color. We are thankful for your feedback, as taking your remarks into account has helped us improve the manuscript.
Best regards,
Marion Coquelet and coauthors
Status: closed

RC1: 'Comment on wes202456', Anonymous Referee #1, 30 May 2024
The submitted article entitled “On the robustness of a blade loadbased wind speed estimator to dynamic pitch control strategies” presents a numerical study on the accuracy of a wind speed estimator based on measurements of blade root bending moments in the presence of different load alleviation and wake mixing control strategies. The estimator is formulated as an Extended Kalman Filter (EKF) and uses Blade Element Momentum (BEM) theory for the statespace model. The static BEM model is modified with a firstorder differential filter to account for dynamic effects in the wake development and the induction of the blades. The article is well written and easy to follow, the methodology is presented comprehensively, and the results are discussed rigorously. The subject of pitch control strategies under wake conditions is also a highly relevant topic and fits the scope of this journal.
Some points could benefit from further clarification:
 The proposed approach of blade loadsbased wind estimation is presented as an alternative to LIDAR measurements. Can you comment on the advantages and disadvantages of each approach? It is mentioned that LIDARs are not widely used commercially due their high capital and operational costs, but the same applies to blade structural health monitoring systems (SHM). Measurements of the blade root bending moments are typically only available for modern offshore wind turbines, which limits the applicability of the proposed approach. Furthermore, there are distinctions in the prediction horizon of wind speeds. LIDARs are able to measure the upstream wind speeds and give the controller several seconds to react to the incoming wind, while blade measurements only provide estimates of current wind speeds.
 The analysis demonstrated that the modification of the BEM model could account for dynamic effects in the aerodynamics such as wake development and blade induction, however, the structural dynamics of the rotor were not considered in this study, since both the EKF estimator and the LES simulations assume a rigid rotor. In reality, the relationship between blade root measurements and wind speeds is also affected by the elastic edge and flapwise bending of the blades. Can you comment on how the structural dynamics would affect the accuracy of the estimator and whether the proposed BEM modification could account for these dynamics? Have you considered numerical studies with aeroelastic software such as OpenFAST or HAWC2 to investigate the effects of the structural dynamics?
 Fig 5,6: the yaxis description seems to be corrupted.
 How are the covariance matrices Q and R of the EKF determined? Was the EKF tuned with respect to Q and R?
Overall, the submitted article is of high quality and I recommend the publication once the above comments have been addressed adequately.
Citation: https://doi.org/10.5194/wes202456RC1 
RC2: 'Comment on wes202456', Anonymous Referee #2, 20 Jun 2024
This is a very wellwritten, clearly explained paper that addresses the accuracy of bladeload based wind speed estimators when pitch control strategies with high pitching frequencies are used. This is a relevant topic because of the interest in using rotorbased wind estimates as part of individual pitch controllers or active wake mixing control strategies. The methodology of evaluating the estimators using highfidelity modeling that is largely independent of the BEM models used in the estimator makes for a robust analysis of estimator accuracy. Finally, the use of a model of the induced velocity dynamics, which has been used for rotor effective wind speed estimators in the past, is a novel contribution to the field of blade loadbased wind speed estimation.
There are no major issues with the paper, but in the list below are several mostly small comments that I believe should be addressed. The main comments include a) describing how the reference wind variables to which the estimates are compared are calculated, b) clarifying why the spatial filtering inherent in the bladeload based estimates could be a significant source of estimation error, since the reference variables should also include spatial filtering, c) providing results in Section 4 for aboverated operation where collective pitch control is active to give a more complete picture of the estimator accuracy and potential need for dynamic BEM models during all pitch control scenarios.
Comments:
 Ln. 33: "Information on the flow conditions, whether explicitly or through blade loads, is not used." This is a little misleading because wake mitigation controllers should at least use measurements/estimates of the wind speed and direction and determine the specific control actions based on whether there are any downstream turbines that would benefit from wake mitigation.
 Section 2.1.2: "Estimation of bladeeffective wind speeds": What is the sampling time/update rate of the EKF bladeeffective wind speed estimator?
 Fig. 1 is missing some characters in the output viarable names on the right side.. Similarly, Figs. 2, 5, 6, 7, and 8 are missing some characters in the axis labels (and for Figs. 5 and 6 the titles as well).
 Ln. 150: "We model the system using the BEM theory": Do you use a specific BEM software, or have you written your own implementation?
 Ln. 179: "r = 2R/3": Can you explain the motivation for assuming the sectoreffective wind speeds represent the wind at this radial location?
 Section 3.2: Please describe how the true values of the estimated variables are determined from the adjunct LES. For example, are sector wind speeds calculated by averaging the longitudinal u component of wind over the sector areas? Is shear determined by fitting to the sector average wind speeds or by finding the bestfit shear over the entire rotor area?
 Ln. 215: What is the time step used?
 Eqs. 1820: Please define "Uref".
 Eqs. 21 and 22: What is the variable alpha_{h,k}? Should this be alpha_{yaw,k} and alpha_{tilt,k}?
 Pg. 9, 1st sentence: "We attribute this to the inherent spatial filtering introduced by the bladeasasensor approach.": Can you explain this in more detail? It seems like the true values of the variables to which the estimates are compared would also include spatial filtering (if they are calculated as the spatial average over the sector areas), so the spatial filtering due to the blade should be beneficial in matching the true rotor effective wind speeds, sector wind speeds, and effective shears.
 Ln. 263: "eventually forcing the wake to displace laterally (see Fig. 3)…": Should this be "laterally and vertically"?
 Ln. 281: Similar to comment 6, how are the reference velocities calculated?
 Ln. 282 and 283: I believe (Fig. 4(b)) and (Fig. 4(c)) in the text should be changed to (Fig. 4(a)) and (Fig. 4(b)). In this case Fig. 4(c) may need to be referenced in the text elsewhere.
 Fig. 4 caption: "used as reference wind speeds to verify it": To verify what? Consider something like "to verify the estimated values".
 Eq. 24: Should "w_{qs}/dt" be changed to "dw_{qs}/dt"?
 Eqs. 2730: This section suggests that the induced velocity filtering time constants are specific to the type of control strategy. Can you comment on how these should be tuned for a turbine that uses IPC some of the time, helix (or another wake mixing control strategy) sometimes, and also collective pitch control for rotor speed regulation? Would you need to be updating the time constants frequently during operation based on the current control mode, or would you use one value that works reasonably well for all cases? Lastly, if only collective pitch control for rotor speed regulation is used, how would you determine the pitching frequency value?
 Section 4.5: If possible, it would be useful to show the accuracy of the bestfit horizontal and vertical shear in addition to the sector wind speeds and rotor effective wind speeds, as in Section 3, because these quantities could be used to inform IPC control strategies.
 Section 4.5 and 4.6: If possible, it would be valuable to show results for an aboverated wind speed (like 14 m/s as in Section 3) in addition to the 9 m/s case. First, IPC for load reduction is more commonly used in aboverated conditions, so it would be useful to show the estimator accuracy with IPC during aboverated operation. Second, because collective pitch control for rotor speed regulation is active in aboverated wind speeds but not in belowrated conditions around 9 m/s, it would be important to understand whether the static BEMbased estimator is sufficient when only collective pitch control is used, or if dynamic BEM is needed in this case too.
 Tables 2 and 3: Can you comment on why the estimation errors are slightly higher when only baseline control is used rather than the more complex IPC and wake mixing controllers?
 Ln. 382: "likely also due to the filtering effect of the bladetosector conversion." Same as comment 10, my understanding is that the reference variables to which the estimates are compared also include spatial filtering. In this case, how would the spatial filtering of the estimator vs. the groundtruth references differ and thus contribute to estimation error?
 Appendix A: Does the BEM model account for the rotor tilt and cone angle? Or is the rotor approximated as being perpendicular to the inflow?
 Algorithm A1: This is a nice presentation of the BEM algorithm. Could you also provide the tolerance value you use?
 Algorithm B1: This algorithm is relatively easy to follow, but a couple variables could be clarified. Could you explain Delta_Theta and just to perfectly clear "n_B"?
Citation: https://doi.org/10.5194/wes202456RC2 
AC1: 'Comment on wes202456  Response to Reviewer Comments', Marion Coquelet, 10 Jul 2024
Dear reviewers,
We wish to thank you for your time, review, and appreciation of the work. We have addressed your comments in the document attached. This document also includes the revised version of the paper in which changes are marked in color. We are thankful for your feedback, as taking your remarks into account has helped us improve the manuscript.
Best regards,
Marion Coquelet and coauthors
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