The paper has been improved greatly. It now contains stronger motivation for the work, clearer explanations of the methods, and an improved summary of the results. Given that this is a long paper and there were many changes made to it, I do have many mostly minor comments that I believe should be addressed for the final version.
Comments on Author Responses:
18. Pg. 8, ln. 193-194: There is also a 4-beam Windar CW lidar, and the grid configuration pattern is based on the SWE pulsed lidar. Can you explain why you classified these scan patterns as pulsed and CW, respectively? Furthermore, since you are only modeling a single measurement range, it is unclear how you model CW and pulsed lidars any differently in you simulations. Can you explain this further? Lastly, you are giving up additional measurement points (and therefore potentially wind eld reconstruction accuracy) by only using a single range for the pulsed lidars. Why didn't you use multiple range gates?
AR: We have removed the paragraph describing the currently available nacelle lidars. The previous classification between CW and PL lidar was only made to reference the existing type of nacelle lidars. Still, it did not influence the simulation results, as we mainly simulate the probe volume effects by a pre defined weighting function. The reason for using a single range is conditional on the fact that we use DWM model-based elds as target elds. Indeed, the DWM model predicts quasisteady wake deficits, which are computed according to a specified downstream distance. These deficits are meandered transversely, advected in stream-wise direction with the mean wind speed using Taylor's assumption, and superimposed on random turbulence eld realizations (we have now described that in detail in Sect. 3.2). As the DWM model does not simulate turbulence evolution, we cannot simulate multiple range gates. This analysis would be suitable using an LES-based wake field. Another aspect to consider when using multiple ranges is that the wake recovers and expands with farther downstream distances; therefore, the wake field characteristics observed further upstream of the rotor may be considerably different from those approaching the turbine rotor.
"As the DWM model does not simulate turbulence evolution, we cannot simulate multiple range gates": The simplification to one range is fine for the paper. But it would still be possible to simulate multiple ranges without wind evolution. This is done frequently when assessing lidar-assisted control. It just adds an additional assumption about the wind field.
Also, since many readers will be familiar with pulsed and CW lidars, please discuss the assumptions used in the paper (e.g., that you are modeling a pulsed lidar at one range, a CW lidar, or that your model is not specific to one type of lidar).
20. Pg. 8, ln. 204: "A probe volume with an extension of 30 m in the LOS direction is assumed" Can you provide some references for how you chose 30 m for pulsed and CW lidars? Furthermore, how is the probe volume extension defined? For example, the std. dev. of Gaussian weighting function?
AR: We have added that the probe volume length is here defined as the standard deviation of the Gaussian weighting function, and added references. The probe volume length of 30 m does not identify a specific lidar system, but it is an estimate that is comparable with the current CW lidar technology measuring at distances beyond 120 m [2]. Further, we conduct a sensitivity analysis by varying the probe volume lengths in Sect. 4.3.2, to analyze how these lengths influence the accuracy in power and load predictions.
"but it is an estimate that is comparable with the current CW lidar technology measuring at distances beyond 120 m [2]": This is a reasonable simplification, but I would provide an explanation like this in the paper. Further, a 30 m probe length is commonly used to model pulsed lidars, so that might be a better justification to use. For example, 30 m is used as the full-width-at-half-maximum probe volume in:
Schlipf, D. Lidar-Assisted Control Concepts for Wind Turbines. Ph.D. Thesis, University of Stuttgart, Stuttgart, Germany, 2016.
23. Pg. 10, ln. 226: What do you mean by `The u-velocity fluctuations are recovered from the target wake fields?'
AR: We have rephrased to: `Only the u-velocity fluctuations are reconstructed from the target wake fields.'
Consider "…are reconstructed from the lidar measurements of the target wake fields."
25. Eq. 10: I'm confused about how K_def,lidar is dened. From Fig. 1, K_def is presented as a scaling factor applied to the ambient wind field (= 1, when wake losses are not present). But here, it appears to be defined as the normalized deficit (= 0, when wake losses are not present). Can you clarify this and make sure the definitions of K_def are consistent?
AR: That's correct, we now define K_def as the normalized deficit (= 0, when wake losses are not present) and keep this definition consistently.
This is clear now in Sect. 3.4.2. However, the definitions of U_def and K_def in Eqs. 13+14 do not appear to be consistent with the definitions in Fig. 2 and Eq. 6. I.e., in Eqs. 13+14, U_def and K_def are defined as 0 outside of the wake deficit region. But in Fig. 2 and Eq. 6 it appears they both equal 1 outside of the wake region.
30. Fig. 7: On the left plot showing U_eff/U_amb, can you explain why the ratio converges to 0.93 at high wind speeds? As wind speed increases, the turbine thrust should keep decreasing causing wake losses to continue to decrease, so I would expect the ratio to approach 1.
AR: It does not converge to 1 because although the trust coefficient decreases for higher wind speeds, the ambient turbulence is relatively low, and therefore the wake field does not fully recover at a distance of 5D, which is the one analyzed in this study. The ratio U_eff/U_amb will converge to 1 for higher ambient turbulence or farther downstream distances due to the increased turbulence mixing. We have now described that in the paper.
The lower turbulence at higher wind speeds does explain part of why the wake would not recover as much as expected by 22 m/s. However, since the ratio plateaus at ~0.93 for several wind speed bins, it seems like something else is happening. Is U_amb treated as the mean freestream wind speed at hub height? If that is the case, then maybe even in freestream conditions, U_eff will be ~0.93*U_amb because of wind shear.
34. Pg. 21, ln. 469: "It should be noted that the structural resonance occurring at low wind speeds, which excites the tower can potentially affect the correlation results." Can you discuss why this resonance appears? Could it be removed by improving the controller tuning?
AR: It appears because of the structural design of the DTU 10 MW, which is a reference (theoretical) turbine model. At low wind speeds (thus low RPM), the 3P rotational frequency (0.3{0.48 Hz) excites the eigenfrequency of the tower ( 0.25 Hz). Considering that the wake induces unbalanced load distribution on the rotor, which in turn amplifies the rotor harmonics (1P, 2P, and 3P), this results in structural resonance. Besides that, we also observe that the bending moment of the tower bottom for large turbines is highly driven by the 3P frequency, as also shown in Fig. 13 (where the imprint of the turbulence wind is almost non-existence). Some internal work at DTU has been conducted to reduce the resonance, and the controller utilized in this work should be optimized to reduce resonance effects, which are still present and amplified under wake conditions. Future studies that evaluate these lidar-based reconstruction approaches can be conducted with different wind turbine designs that do not experience these resonances.
A sentence about the cause of the controller resonance would be insightful in the paper.
Additional Comments:
1. Ln. 55: "Further, to accurately reconstruct wake meandering time series, it is essential to ensure accurate power and load predictions in a load validation analysis"? This seems to make more sense the other way around: "to accurately predict power and loads in a load validation analysis, it is essential to accurately reconstruct wake meandering time series." Is this correct?
2. Lns. 74-77: Would "monitoring wind turbine performance" make more sense as "condition monitoring of wind turbines"? Additionally, brief examples of how lidar-based power and load validation under wakes would improve the listed application areas would be appreciated.
3. Fig. 2: In the middle plot, k_mt appears to be 1 outside of the wake deficit region. But if this represents wake-added turbulence, should k_mt be zero outside of the wake region?
4. Ln. 197: "… scales the residual field of a Mann-generated turbulence field". What is the TI or std. dev. of the turbulence field. I.e., if k_mt is used to scale the turbulence, then what is the baseline turbulence level that it is scaling?
5. Lns. 221-222: "from fitting the free-stream observed turbulence velocity spectra with the Mann model with the use of pre-computed look-up-tables". It isn’t clear how look-up-tables would be used for this.
6. Lns. 226-228: Similarly, what is the std. dev. of the u^prime_j time series?
7. Eq. 9: How are the elevation and azimuth angle defined? If azimuth is defined as the azimuth angle in the rotor plane (similar to azimuth angle of a blade), it is hard to see why the cos(theta) appears in the estimate of u_lidar.
8. Lns. 275-279: Since Gaussian weighting functions are typically used to model pulsed lidars and Lorentzian functions are used to model CW lidars, I would mention this point in the paper.
9. Section 3.4: Is it correct that the high-frequency wake added turbulence is not explicitly included in the 2 wake field reconstruction methods? I wasn't sure while reading the section, so it might be good to highlight this point.
10. Ln. 290: "set A and set B": It might be good to remind the reader that set A is used for the target fields.
11. Ln. 309: The constraint set is hard to understand. For example, what is the dimension of H? Should "r" be "r_i" in the defintion of H, if the constraint is for a specific location? Finally, if each constraint is a measured time series, then should c_i be written as c_i(t)? And is M the number of points in the scan pattern?
12. Ln. 377: "The normalized RMSE indicates if the lidar-reconstructed fields are unbiased compared…" How would RMSE indicate the bias? The mean error would indicate bias, whereas RMSE could be caused by variability in the error.
13. Ln. 415: "These effects are not fully recovered in the reconstructed fields, mainly due to the lidar probe volume…" Also because the method fits the lidar measurements to a standard Mann turbulence field, without the small-scale wake-added turbulence being explicitly included.
14. Ln. 540: "underpredicted by Delta_R ~ 2-3%". Based on Fig. 12 the bias can be up to 6%.
15. Ln. 554: Is it accurate to call the power time series the "Power_mean" time series? Mean would suggest the mean over the 10-minute period, but you are looking at the full time series, correct?
16. Lns. 606-608: "This indicates that when L is low,…" In addition, the turbulence structure sizes become small relative to the lidar probe volume, causing the lidar measurements to average out more of the turbulence.
Minor Comments:
1. Ln. 73: "power and load" -> "power and loads"
2. Ln. 451: "2 m/s" -> "2 m/s bin width"? Also, consider adding "respectively" at the end of the sentence.
3. Ln. 491: "40-60% estimates" -> "40-60% accuracy"?
4. Ln. 537: "fictitious biases" -> "fictitious lack of biases"? |