Preprints
https://doi.org/10.5194/wes-2024-6
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2024-6
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
23 Jan 2024
| 23 Jan 2024
Status: a revised version of this preprint was accepted for the journal WES and is expected to appear here in due course.
Load assessment of a wind farm considering negative and positive yaw misalignment for wake steering
Abstract. Wake steering strategies are employed to increase the overall power production of wind farms by deflecting wakes of upstream turbines away from downstream ones. The gain in net power comes at the expense of increased fatigue loads experienced by downstream turbines. In this work we investigate performance and fatigue loading characteristics of a small farm consisting of five aligned IEA Wind 15-MW wind turbines. A parametric study is performed where, for every wind direction from -20 to 20 degrees, the yaw misalignment angle varies from -25 to 25 degrees. This setup allowed us to investigate asymmetries and identify optimal conditions for a given wind direction. In general, we found that positive yaw configurations are preferred and that yaw configurations that result in attractive power gains (25 % or more when compared to a baseline no-yaw scenario) come with significant increase in fatigue loading (we used standard deviation and damage-equivalent load (DEL) of the blade-root, low-speed shaft, and tower-base moments as proxies for fatigue load). We found that for any given positive wind inflow angle, yaw angles between -2.5 and 15 degrees yield power gains of 10–20 % over a no-yaw baseline, and positive yaw is preferred because of lower fatigue loadings. For any given negative wind inflow angles, positive yaw also results in lower magnitudes of standard deviation and DEL for the channels investigated. A small power loss of up to 2 % is observed for some positive yaw angles under negative wind directions (as compared symmetric negative yaw and positive wind cases), but gains in terms of loads exceed 25 % and may be enough to justify a positive yaw configuration under negative winds as well. We show that such behavior can be explained by partial waking and the direction of rotation of the rotor.
How to cite. Thedin, R., Barter, G., Jonkman, J., Mudafort, R., Bay, C. J., Shaler, K., and Kreeft, J.: Load assessment of a wind farm considering negative and positive yaw misalignment for wake steering, Wind Energ. Sci. Discuss. [preprint], https://doi.org/10.5194/wes-2024-6, in review, 2024.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
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Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
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RC1: 'Comment on wes-2024-6', Anonymous Referee #1, 26 Apr 2024
In the paper “Load assessment of a wind farm considering negative and positive yaw misalignment for wake steering,” the Authors present a parametric study on the effect of yaw misalignment on power production and loads for an array of turbines under different wind directions. The study is based on an engineering model calibrated with a set of large eddy simulations under different yaw misalignments and one wind direction for which the five turbines in the array are aligned.
The topic is of interest to the community and the paper presents a large and valuable dataset on yaw misalignment/wind direction configuration. Nevertheless, there are some points, which I think should be addressed before publication in WES. I list below my main points.
Major points:
- Definition of “power gain” and “baseline case.” For their analysis, the Authors take as the baseline the case of zero degree wind direction (for which the wind turbines are all aligned) and evaluate power differences with respect to this case. I think it is misleading to call these differences “power gains.” The zero-degree wind direction is the worst case scenario for the array considered and using it as a baseline overestimate the effect of yaw control. It appears to me that these “power gains” on the order of 30%-40% are due to a very underperforming baseline, and not an actual measure of yaw control effectiveness. I believe the appropriate baseline should be, for each wind direction, the case gamma=0 (no misalignment). I understand the Authors may want a unique reference to normalize the data (perhaps the rated power?), but the discussion should be adjusted accordingly to avoid misunderstandings.
- Related to the previous point, the Authors claim that the “bottom right quadrant” contains “attractive” operational conditions. I am not sure I completely agree. For instance, estimating from figure 12, for the case at 10deg wind direction, it seems there is not much percentage difference between the highlighted point gamma=7.5 and gamma=0. I do not think it would be attractive or beneficial to incur in the potentially increased fatigue loading due to yaw misalignment for a slight increase in power production. This is a known limitation of yaw control as previous studies in the literature have proposed methods to identify ‘clusters’ or ‘partitions’ within the wind farm where yaw control might be beneficial based on some performance metric (e.g. Kanev, 2020 Renew. Energy.; Bernardoni et al. 2021 J. Renew. Sust. Energy). To a certain extent, it seems that the scenario (wind turbine array and wind conditions) considered by the Authors is overall not very amenable to yaw optimization, because even in the worst-case direction (0° deg) the power improvement for different gammas is very mild (at least judging from the contours in fig. 12).
- Some of the differences analyzed are quite small (2-4%) and appear to be of the same order of magnitude of the difference between the FAST model and the LES (Figure 8). Are these differences statistically significant? Have the Authors considered to perform a few additional LES to validate the model results (e.g. for one or some of the conditions they highlight through the paper)? I understand the computational cost is significant, but this is an important point to validate the discussion, since based on Figure 8 the model-LES discrepancy seems to increase with yaw misalignment.
- In addition, the calibration in Section 3 only reports metrics for the mean power production, what is the difference for the other load ‘channels’ analyzed in Sections 4 and 5? Why using the wake position for model calibration instead of the metrics used for the analysis and discussion?
- In the methodology description, Section 2.4, line 136, the Authors report that a “surface roughness” of 0.75m was used for the LES. I assume this refers to the aerodynamic roughness length in the classic log-law velocity profile (“z_0”). In such case, this seems an uncommonly very large value for “z_0,” and I am concerned about how realistic are the inflow conditions considered in the study and the consequent wake evolution in the array.
Minor points:
- The Authors often refers to the “symmetry” of the results, or some trends as being “monotonic.” As essentially all the quantities of interest are functions of two variables (yaw and wind direction), it may be ambiguous at time to follow what symmetry or monotonicity are the Authors referring to. I suggest to specify throughout the manuscript what variable is analyzed, e.g. “monotonic with respect to the wind direction.”
- Figure 4, panel (e): perhaps the x-axis of the figure should be centered around 0deg?
- Table 2 and 3: perhaps units are missing in Table 2? Have the Authors considered summarizing the results in one table only? I was expecting the selected value when reading table 2 and the discussion of the calibration process.
- Section 5: the Authors mention that some “quadrants” are not of interest because are not increasing power production, however they could provide useful information if interpreting the angle “gamma” as an unwanted misalignment (instead of an intentional yaw control effect).
- Page 21, line 371: “as well with the exceptions”?- line 396: should this be analogous the scenario (b) instead of (a)?
Citation: https://doi.org/10.5194/wes-2024-6-RC1 - AC1: 'Reply on RC2', Regis Thedin, 24 Jul 2024
-
RC2: 'Comment on wes-2024-6', Anonymous Referee #2, 01 May 2024
The paper addresses a very important aspect of wind farm flow control through wake steering by including the effect of the steering direction on turbine power production and loads. Overall, the paper is well written, and the scientific quality is high. However a few points could be better elaborated upon to improve understanding.
- Figure 1, It is not clear what the red label ‘direction of pos alpha’ signifies. While alpha is described later in the text, it should be defined here already with its first use.
- Line 92, it would be beneficial to state the wall time of the LES simulation here to get some context of computational cost.
- Line 104, why was alpha varied in increments of 2 degrees? Was a sensitivity analysis conducted regarding the minimal increment? Would the results be different if it was 1 degree, 0.5 degree?
- Same comment for the yaw angle. Increments of 2.5 degrees seem arbitrary. A reader would benefit from knowing why these increments were chosen.
- Line 113 seems grammatically incorrect, the structure could be improved.
- Figure 2, most of the legend items for the different wind directions are very difficult to tell apart from each other in this figure. It is also not clear what the high res and low res legend items are referring to, as they have not been introduced in the text yet.
- Line 120, while it is reasonable to select a single wind speed, the choice of 8.6 m/s again seem arbitrary. Additionally, a comment on whether choosing other below rated wind speeds could have an impact on the analysis presented.
- Line 135, what was the resolution of the LES simulation? Is the resolution sufficient to capture the turbine performance (represented using actuator line model) accurately?
- Line 136, a surface roughness of 0.75m seems exceedingly high. Earlier on in the text, the authors cite the Massachusetts waters development as the motivation for the turbine spacing, indicating offshore application for this. The chosen surface roughness does not well represent offshore conditions, and is possibly too high even to represent onshore conditions. This could significantly affect the wind inflow conditions, the resulting wake recovery and the overall conclusions.
- A citation for the DEL methodology should be included
- Line 220, are both wake centerline error and power error metrics used in the minimization or just one? It’s a bit unclear. Were any steps taken to avoid local minima or overfitting during the minimization? More information on how the minimization was carried out could be included.
- Figure 11 is too small and can be increased in size to improve readability.
- Figures 16, 17, 18 for the load channels, the fore aft tower loads and combined together. Same is done for the blade flapwise and edgewise blade root bending moments. Including an additional plot showing the impact on the individual load components would be valuable to see the impact of control. The plot labels are also too small and barely legible.
Citation: https://doi.org/10.5194/wes-2024-6-RC2 - AC1: 'Reply on RC2', Regis Thedin, 24 Jul 2024
Status: closed
Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor
| : Report abuse
-
RC1: 'Comment on wes-2024-6', Anonymous Referee #1, 26 Apr 2024
In the paper “Load assessment of a wind farm considering negative and positive yaw misalignment for wake steering,” the Authors present a parametric study on the effect of yaw misalignment on power production and loads for an array of turbines under different wind directions. The study is based on an engineering model calibrated with a set of large eddy simulations under different yaw misalignments and one wind direction for which the five turbines in the array are aligned.
The topic is of interest to the community and the paper presents a large and valuable dataset on yaw misalignment/wind direction configuration. Nevertheless, there are some points, which I think should be addressed before publication in WES. I list below my main points.
Major points:
- Definition of “power gain” and “baseline case.” For their analysis, the Authors take as the baseline the case of zero degree wind direction (for which the wind turbines are all aligned) and evaluate power differences with respect to this case. I think it is misleading to call these differences “power gains.” The zero-degree wind direction is the worst case scenario for the array considered and using it as a baseline overestimate the effect of yaw control. It appears to me that these “power gains” on the order of 30%-40% are due to a very underperforming baseline, and not an actual measure of yaw control effectiveness. I believe the appropriate baseline should be, for each wind direction, the case gamma=0 (no misalignment). I understand the Authors may want a unique reference to normalize the data (perhaps the rated power?), but the discussion should be adjusted accordingly to avoid misunderstandings.
- Related to the previous point, the Authors claim that the “bottom right quadrant” contains “attractive” operational conditions. I am not sure I completely agree. For instance, estimating from figure 12, for the case at 10deg wind direction, it seems there is not much percentage difference between the highlighted point gamma=7.5 and gamma=0. I do not think it would be attractive or beneficial to incur in the potentially increased fatigue loading due to yaw misalignment for a slight increase in power production. This is a known limitation of yaw control as previous studies in the literature have proposed methods to identify ‘clusters’ or ‘partitions’ within the wind farm where yaw control might be beneficial based on some performance metric (e.g. Kanev, 2020 Renew. Energy.; Bernardoni et al. 2021 J. Renew. Sust. Energy). To a certain extent, it seems that the scenario (wind turbine array and wind conditions) considered by the Authors is overall not very amenable to yaw optimization, because even in the worst-case direction (0° deg) the power improvement for different gammas is very mild (at least judging from the contours in fig. 12).
- Some of the differences analyzed are quite small (2-4%) and appear to be of the same order of magnitude of the difference between the FAST model and the LES (Figure 8). Are these differences statistically significant? Have the Authors considered to perform a few additional LES to validate the model results (e.g. for one or some of the conditions they highlight through the paper)? I understand the computational cost is significant, but this is an important point to validate the discussion, since based on Figure 8 the model-LES discrepancy seems to increase with yaw misalignment.
- In addition, the calibration in Section 3 only reports metrics for the mean power production, what is the difference for the other load ‘channels’ analyzed in Sections 4 and 5? Why using the wake position for model calibration instead of the metrics used for the analysis and discussion?
- In the methodology description, Section 2.4, line 136, the Authors report that a “surface roughness” of 0.75m was used for the LES. I assume this refers to the aerodynamic roughness length in the classic log-law velocity profile (“z_0”). In such case, this seems an uncommonly very large value for “z_0,” and I am concerned about how realistic are the inflow conditions considered in the study and the consequent wake evolution in the array.
Minor points:
- The Authors often refers to the “symmetry” of the results, or some trends as being “monotonic.” As essentially all the quantities of interest are functions of two variables (yaw and wind direction), it may be ambiguous at time to follow what symmetry or monotonicity are the Authors referring to. I suggest to specify throughout the manuscript what variable is analyzed, e.g. “monotonic with respect to the wind direction.”
- Figure 4, panel (e): perhaps the x-axis of the figure should be centered around 0deg?
- Table 2 and 3: perhaps units are missing in Table 2? Have the Authors considered summarizing the results in one table only? I was expecting the selected value when reading table 2 and the discussion of the calibration process.
- Section 5: the Authors mention that some “quadrants” are not of interest because are not increasing power production, however they could provide useful information if interpreting the angle “gamma” as an unwanted misalignment (instead of an intentional yaw control effect).
- Page 21, line 371: “as well with the exceptions”?- line 396: should this be analogous the scenario (b) instead of (a)?
Citation: https://doi.org/10.5194/wes-2024-6-RC1 - AC1: 'Reply on RC2', Regis Thedin, 24 Jul 2024
-
RC2: 'Comment on wes-2024-6', Anonymous Referee #2, 01 May 2024
The paper addresses a very important aspect of wind farm flow control through wake steering by including the effect of the steering direction on turbine power production and loads. Overall, the paper is well written, and the scientific quality is high. However a few points could be better elaborated upon to improve understanding.
- Figure 1, It is not clear what the red label ‘direction of pos alpha’ signifies. While alpha is described later in the text, it should be defined here already with its first use.
- Line 92, it would be beneficial to state the wall time of the LES simulation here to get some context of computational cost.
- Line 104, why was alpha varied in increments of 2 degrees? Was a sensitivity analysis conducted regarding the minimal increment? Would the results be different if it was 1 degree, 0.5 degree?
- Same comment for the yaw angle. Increments of 2.5 degrees seem arbitrary. A reader would benefit from knowing why these increments were chosen.
- Line 113 seems grammatically incorrect, the structure could be improved.
- Figure 2, most of the legend items for the different wind directions are very difficult to tell apart from each other in this figure. It is also not clear what the high res and low res legend items are referring to, as they have not been introduced in the text yet.
- Line 120, while it is reasonable to select a single wind speed, the choice of 8.6 m/s again seem arbitrary. Additionally, a comment on whether choosing other below rated wind speeds could have an impact on the analysis presented.
- Line 135, what was the resolution of the LES simulation? Is the resolution sufficient to capture the turbine performance (represented using actuator line model) accurately?
- Line 136, a surface roughness of 0.75m seems exceedingly high. Earlier on in the text, the authors cite the Massachusetts waters development as the motivation for the turbine spacing, indicating offshore application for this. The chosen surface roughness does not well represent offshore conditions, and is possibly too high even to represent onshore conditions. This could significantly affect the wind inflow conditions, the resulting wake recovery and the overall conclusions.
- A citation for the DEL methodology should be included
- Line 220, are both wake centerline error and power error metrics used in the minimization or just one? It’s a bit unclear. Were any steps taken to avoid local minima or overfitting during the minimization? More information on how the minimization was carried out could be included.
- Figure 11 is too small and can be increased in size to improve readability.
- Figures 16, 17, 18 for the load channels, the fore aft tower loads and combined together. Same is done for the blade flapwise and edgewise blade root bending moments. Including an additional plot showing the impact on the individual load components would be valuable to see the impact of control. The plot labels are also too small and barely legible.
Citation: https://doi.org/10.5194/wes-2024-6-RC2 - AC1: 'Reply on RC2', Regis Thedin, 24 Jul 2024
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Latest update: 20 Nov 2024
National Renewable Energy Laboratory, Golden, CO, USA
Garrett Barter
National Renewable Energy Laboratory, Golden, CO, USA
Jason Jonkman
National Renewable Energy Laboratory, Golden, CO, USA
Rafael Mudafort
National Renewable Energy Laboratory, Golden, CO, USA
Christopher J. Bay
National Renewable Energy Laboratory, Golden, CO, USA
Kelsey Shaler
Shell International Exploration and Production, Houston, TX, USA
Jasper Kreeft
Shell Global Solutions International B.V., The Hague, Netherlands
Short summary
This work investigates asymmetries in terms of power performance and fatigue loading on a 5-turbine wind farm subject to wake steering strategies. Both the yaw misalignment angle and the wind direction were varied from negative to positive. We highlight conditions in which fatigue loading is lower while still maintenance good power gains and show that partial wake is the source of the asymmetries observed. We provide recommendations in terms of yaw misalignment angles for a given wind direction.
This work investigates asymmetries in terms of power performance and fatigue loading on a...
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