The revised manuscript has been greatly improved. I do have some remaining comments that I feel should be addressed, though. The main comments are related to a) including more discussion about how accurate the wind evolution parameters (gamma) used in the analysis are for different TI values, since you are just using a single value of gamma to represent each stability class regardless of the TI, and b) the assumptions made in the lidar spectrum and lidar-REWS cross spectrum equations. Please see responses to the remaining comments below (note: the comment numbers are different than the original numbers). Several new, mostly minor, comments are provided afterwards as well.
1. Reviewer comment 1: Another non-technical general comment is that there are many places in the manuscript where sentences are broken into two sentence fragments. For example, line 192: ”It is clear that a larger coherent eddy structure. . . While the eddy structure is much smaller. . . ”, line 211: ”It can be seen that the turbulence. . . While the variation in the anisotropy. . . ”, line 402: ”To include the turbulence evolution. . . Four-dimensional stochastic turbulence. . . ” I would suggest reviewing the manuscript and combining sentence fragments like these into single sentences.
Author response: Thanks for the your comments. We have reviewed the paper and modified the fragmentary sentences.
Reviewer comment 2: Many of these issues were resolved. However, there are still some incomplete sentences throughout the manuscript. For example, Figure 1 caption "Simulated using the 4D Mann…"; Ln 192: "To include the exponential longitudinal coherence model…"; Ln 357: "Apart from the case that all measurement gates…"; Ln 432: "Because the pitch curve has much higher…"; Ln. 503: "If we do not consider…"; Ln. 522: "Because the turbulence field has a…"
2. Reviewer comment 1: Section 2.3.1: The extended Mann model with evolution clearly shows a dependence on length scale (e.g., Eq. 14). Can you discuss how other wind conditions, such as turbulence intensity, affect the coherence? For example, in Simley and Pao (2015) there is a strong relationship between TI and coherence, but it isn’t clear how this is captured in the extended Mann model.
Author response: Thanks for the your comments. The extended Mann model (space-time tensor) assumes stationary process in time, the turbulence intensity is not affected by the wind evolution. Actually the wind evolution parameter is determined by the parameter ”γ”. So, based on specific situations, one can adjust γ and αε2/3 independently to reach a target turbulence intensity and evolution level.
Reviewer comment 2: I understand that the turbulence intensity isn’t affected by the wind evolution, but I am wondering how the wind evolution parameter gamma in Eq. 15 depends on the turbulence intensity. For example, Simley and Pao (2015) observed a strong relationship between turbulence intensity and the a_x parameter (in Eq. 18). Although Davoust and von Terzi (2016) didn’t observe as strong of a relationship, there may be some dependence of the gamma parameter on TI. See comment #5 also.
3. Reviewer comment 1: Eq. 20: Why is the real number operator needed here? By definition, won’t the coherence be a positive real number? Otherwise, can you explain how coh11 can contain imaginary components?
Author response: Thanks for the your comments. Indeed, the magnitude squared coherence is real and positive. In terms of the least square fitting in Equation (21) (previously 20), we are fitting the co-coherence. We have corrected the equation now and added Equation (10) to explain the definition of co-coherence.
Reviewer comment 2: Can you explain why you are fitting the co-coherence instead of the magnitude squared coherence?
4. Reviewer comment 1: Line 219: ”we use three sets of gamma = 200, 400, and 600 s” Why did you choose these three values?
Author response: Thanks for the question. We have added the reason as: ”The reason for choosing these values for γ is that they result in coherence close to observations in existing literature, as will be discussed later”.
Reviewer comment 2: I have one minor comment, which is to be more specific about which section this will be discussed in "later".
5. Reviewer comment 1: Line 229-231: It is unclear what you mean by ”rarely large ax” and why this suggests you should use gamma = 600 s for the unstable case. More generally, can you discuss in more detail why you chose 600 s to represent the unstable condition (e.g., why not 500 s or 800 s)? Further, can you discuss how accurate the selected gamma values are for the class 1A turbulence intensity used in the simulations? And how would gamma change for different TI values? (e.g., Simley and Pao (2015) observed a strong relationship between TI and coherence).
Author response: Thanks for the question. We use the term ”rarely” according to the probability study by Chen et al. (2020), but we did not write it clearly previously. We chose 600 s because it gives higher ax in the unstable condition than the neutral and stable conditions (in accordance with the LES-based observation by Simley and Pao (2015)). Overall, 600 s is chosen because it gives a reasonable ax value in terms of probability and relative difference with ax from other stability. Now we have modified the sentence to be more clear. Regarding the second question, as explained in the general comment, we have not consider the variation in the TI to emphasize the study on the changes in turbulence length scale. The γ value is independent from the turbulence intensity in the space-time tensor. Also, since the turbulence intensity is adjusted by the parameter αε2/3, which is just a proportional gain. The changes in the αε2/3 will not affect the coherence of velocity components or lidar measurement. In reality, one can design simulations using different γ values to reach the target longitudinal coherence.
Reviewer comment 2: The added discussion helps clarify the choice of gamma = 600 s for the unstable case a lot. Regarding the comment about how accurate these values are for the class 1A turbulence intensity used, I understand that gamma is independent from TI in the model and you are free to use any combination of TI and gamma. But since gamma is an additional free variable, it has to be tuned, as discussed in the manuscript. It therefore could depend on TI (or other variables) in addition to stability. You chose three values of gamma for the three stability classes, but are these choices of gamma valid for all TI values within a certain stability class? It would be insightful if you could discuss how accurate you believe the choices of gamma are for the class 1A TI values you use in the paper and it would help to acknowledge that the three values selected may not be accurate for all TI values (including the class 1A TI used in the paper) if that is the case.
6. Reviewer comment 1: Eq. 31: I think there should be the imaginary number ”i” in front of ”k1Δxi”. Also, as written, because Δxi equals xi, it seems that SRL(k1) won’t contain the phase delays between the measurement points and the rotor because the k1 dependence of the exponent simplifies to exp(i(k1 ∗ x1 − k1 ∗ x1)) = 1. Should Δxi in the equation simply be replaced by xR to model the correct phase delay?
Author response: Thanks for the careful review. The reviewer is correct, the imaginary number ”i” should be included in front of ”k1Δxi”. This has now be added. As for the second question, we added the detailed derivation below: …
Reviewer comment 2: Thanks for providing the derivations. I also see that the equation is nearly identical to the equation presented in Held and Mann, 2019. However, it still isn’t clear why there doesn’t appear to be any phase rotation for the k_1 frequency component due to the time shift between the lidar measurements and the REWS at the rotor plane in Eq. 32, assuming Taylor's hypothesis (i.e., exp(j*k_1*Delta_x)), since the k_1x_i terms cancel out in the equation. Further, if the lidar-estimated REWS contains measurements at different range gates, I would expect the phase differences between the measurements at each range gate and the REWS at the rotor plane to appear in the equation. To better understand Eq. 32, as well as Eq. 29 for S_{LL}(k_1), can you explain the assumptions in the derivations in more detail? For example, is the cross-spectrum in Eq. 32 derived assuming the lidar-estimated REWS is delayed in time according to Taylor's hypothesis so it is in phase with the REWS at the rotor plane? Similarly, when averaging lidar measurements at different range gates (Eq. 28), do you delay the measurements at different range gates in time so they are in phase with the nearest range gate, according to Taylor's hypothesis, before averaging? If not, how is the phase delay between measurements at different range gates accounted for in Eq. 32 (it seems like it is already included in Eq. 29)?
7. Reviewer comment 1: Line 330: ”This also indicates that the filter design is not sensitive to the change in turbulence parameters. . . and a constant filter design is robust.” How does the filter design depend on the wind speed? Do the cutoff frequencies change?
Author response: Thanks for pointing this out, we have removed Table 5 and added Figure 5, which shows the cutoff frequencies as a function of the mean wind speed. We also added the discussions around the line 340 as: ”The cutoff frequencies as a function of mean wind speed are calculated by fitting the GRL and are shown in Figure 5. Firstly, both turbulence models indicate that the cutoff frequencies depend on the mean wind speed linearly. Therefore, the cutoff frequency of the filter can be scheduled based on this linearity”
Reviewer comment 2: When varying the wind speed to determine the cutoff frequencies, are you keeping the TI constant or changing it according to the IEC standard?
8. Reviewer comment 1: Line 546: ”the electricity productions are similar either using LAC or not. . . ” Again, there is a significant drop in power at 14 m/s with LAC. What causes this?
Author response: Thanks for your comment. The reason of the lower mean power at 14m/s has been explained in 42. We now analyzed the reason for power drop at 14m/s in line 582. However, we did not get the reviews opinion that the EP is reduced with LAC. In the plot, the right side y axis is the relative reduction compared to FB-only control. If it is negative value, it means the FFFB gives higher value compared to FB-only control. So the EP is actually increased (very slightly) with LAC. However, since the increment is marginal, our conclusion is that LAC has marginal impact on the EP.
Reviewer comment 2: My mistake. I misinterpreted the meaning of the negative reduction in energy production in the plots.
9. Reviewer comment 1: In many places throughout the manuscript, there are citations without parentheses, for example line 44: ”Mann (1994).” If the reference is actively used as part of the sentence, it is ok to leave the parentheses out, such as lines 46-48. Otherwise, I suggest using parentheses, for example, as is done in line 25.
Author response: Thanks for the careful suggestion. We have went through the paper and corrected relative citations.
Reviewer comment 2: The citations have been improved significantly. There might be a few that still are missing parentheses, however. For example, Ln. 315: "Schlipf et al."
10. Reviewer comment 1: Line 315: ”If a filter with the gain. . . ” This sentence is hard to understand and appears to be incomplete.
Author response: Thanks for pointing this out, this sentence is now rewritten as: ”If a filter is designed to have a gain of GRL(f ), it turns out to be an optimal Wiener filter (Simley and Pao (2013), Wiener et al. (1964)), which results in minimal output variance for a multi-inputs multi-outputs system.”
Reviewer comment 2: The phrase "results in minimal output variance for a multi-inputs multi-outputs system" could use some explanation. What does this mean in the context of the LAC application, and what specific variance does the filter minimize in this application?
New Comments:
1. Ln. 87: Consider providing a little more information about ROSCO here. For example, that it is a reference controller representing an industry standard control system.
2. Ln. 206: "In this work, we emphasize analyzing the impact of turbulence length scale on turbine loads and LAC benefits": Would it be more accurate to say that you are analyzing the impact of turbulence length and the Gamma anisotropy parameter as well, since Gamma is different for the three stability classes?
3. Ln. 220: Please define the quad-coherence
4. Ln. 225: "In their study, a smaller intercept was found for a more stable class. Also, Simley and Pao (2015) studied the turbulence…": It would be worth discussing whether the longitudinal coherence from the modified Mann model also shows different intercepts for different stability classes, even though the Mann model may not explicitly have an intercept parameter like b_x.
5. Figure 2: It would help to state what mean wind speed these spectra are generated for.
6. Section 3.2: I think more details about how the lidar-estimated REWS is formed should be provided here to better understand the spectrum calculations. In particular, how do you combine measurements at different range gates? Do you delay the measurements from the farther range gates according to Taylor's hypothesis so they are in phase with the measurements from the closest range gate before averaging? Or do you average all measurements at the same time? This decision should affect the spectrum equation in Eq. 29.
7. Eq. 28: Is this equation missing a negative sign? According to the angle definitions in Fig. 3, cos(phi) will be negative. If the LOS velocity v_{los,i} is positive, then u_{LL} will be negative as written.
8. Figure 4: Can you list what wind speed these coherence and transfer function curves are generated for?
9. Ln. 403: "M_g = P_{rated}/eta Omega_{gf}": the way this is written, it is unclear whether Omega_{gf} is in the numerator or denominator. This comments applies to line 503 as well.
10. Ln. 412: "lidar-assisted pitch forward signal": Be consistent about "forward" vs. "feedforward" throughout the text.
11. Ln. 419: "where f_c is the cutoff frequency": I think it would help to mention that this is the same cutoff frequency that is discussed in Sect. 3.4.
12. Ln. 420: "The pitch forward signal is then sent to ROSCO after accounting for the pitch actuator delay…": Should the filter delay T_{filter} also be mentioned in this sentence?
13. Ln. 421: "and the half of the time averaging window". Consider clarifying by saying this is "half of the lidar scan time averaging window" or similar.
14. Ln. 425: "…is chosen to be half of the time averaging window". Why is T_{window} set to half the time averaging window? Doesn't the factor of one half already appear in Eq. 40, meaning T_{window} should be the full averaging time window?
15. Ln. 457: "Each 4D turbulence field has a size of 4096 x 11 x 64 x 64 grid points…": Can you mention the time resolution here?
16. Ln. 616: "The electrical power generation is not affected by introducing LAC.": There is a small change, so perhaps "not significantly affected" would be more appropriate.
17. Ln. 669: "also reduces the variation in rotor speed, pitch rate, and electrical power clearly": Why are reductions in pitch rate mentioned here for the Kaimal model, but not on line 664 for the Mann model?
18. Ln. 675: "Overall, we found the benefits of lidar-assisted control by the Kaimal model are slightly different from the results obtained using the Mann model.": Are there any interesting differences to mention here?
New minor comments:
1. Ln. 57: "acting" -> "acts"?
2. Ln. 61: This may be a personal preference, but I think it is helpful to spell out acronyms like "ROSCO" in the body of the text the first time, even if they are defined in the abstract as well.
3. Ln. 63: can you provide references for FAST and OpenFAST?
4. Ln. 67: "tool" -> "tools"?
5. Figure 1 caption: Be consistent on the use of "pulsed lidar" vs. "pulse lidar" throughout the paper.
6. Ln. 71: "value" -> "values"?
7. Ln. 140: "interested" -> "interesting"?
8. Ln. 244: "gives large values of a_x": To make the point more clear, should this say something like "gives unrealistically large values of a_x"?
9. Ln. 380: "propriety" -> "property"?
10. Ln. 501: "even the constant" -> "even though the constant"?
11. Ln. 503: "M_g = P_{rated}/eta omega_{gf}": In section 4.3, the generator speed is written as capital Omega. Should it be the same here?
12. Ln. 511: "less low-frequency rotor speed fluctuation": This is a little confusing. Consider rephrasing as "reduced low-frequency rotor speed fluctuations" or similar.
13. Ln. 521: "RWES" -> "REWS"
14. Ln. 531: "most interested" -> "most interesting"?
15. Ln. 544: "1 p": Usually I see this written with a capital "P"
16. Ln. 556: "statics" -> "statistics" |