Correction of motion influence for nacelle based lidar systems on floating wind turbines
Abstract. Inflow wind field measurements from nacelle based lidar systems offer great potential for different applications including turbine control, load validation and power performance measurements. On floating wind turbines nacelle based lidar measurements are affected by the dynamic behaviour of the floating foundations. Therefore, effects on lidar wind speed measurements induced by floater dynamics must be well understood. In this work we investigate the influence of floater motions on wind speed measurements from forward looking nacelle based lidar systems mounted on floating offshore wind turbines (FOWT) and suggest approaches for the correction of motion induced effects. We use an analytical model, employing the GUM methodology and a numerical lidar simulation for the quantification of uncertainties. It is found that the uncertainty of lidar wind speed estimates is mainly caused by fore-aft motion of the lidar, resulting from the pitch displacement of the floater. Therefore, the uncertainty is heavily dependent on the amplitude and the frequency of the pitch motion. The bias of 10 min mean wind speed estimates is mainly influenced by the mean pitch angle of the floater and the pitch amplitude.
Further, we discuss the need for motion compensation for different applications of lidar inflow measurements on FOWT and introduce two approaches for the correction of motion induced effects in lidar wind speed measurements. We correct motion induced biases in time averaged lidar wind speed measurements with a model based approach employing the developed analytical model for uncertainty and bias quantification. Testing of the approach with simulated dynamics from two different FOWT concepts shows good results with remaining mean errors below 0.1 ms−1. For the correction of motion induced fluctuation in instantaneous measurements we use a frequency filter to correct fluctuations caused by floater pitch motions for instantaneous measurements. The performance of the correction approach is dependent on the pitch period and amplitude of the FOWT design.
Moritz Johann Gräfe et al.
Status: final response (author comments only)
- RC1: 'Comment on wes-2023-11', Felix Kelberlau, 16 Feb 2023
- RC2: 'Comment on wes-2023-11', Anonymous Referee #2, 24 Feb 2023
- RC3: 'Comment on wes-2023-11', Anonymous Referee #3, 15 Mar 2023
Moritz Johann Gräfe et al.
Moritz Johann Gräfe et al.
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The discussion paper "Correction of motion influence for nacelle[-]based lidar systems on floating wind turbines" submitted by Gräfe et al. introduces two models for analyzing the motion-induced measurement error on wind speed estimates from nacelle-based wind lidars on floating offshore wind turbines. Both models are used to quantify measuerement bias and uncertainty caused by a variety of motion parameters and wind conditions. The paper also describes the results achieved by applying two methods for separate removal of the motion-induced measurement bias and uncertainty. The title of the manuscript clearly reflects the content of the work with regard to motion correction, but it understates the significant amount of work done towards quantification of the measurement error.
The addressed topic is of high relevance to the Wind Energy Science journal because accurate nacelle-based lidar measurements are relevant for power curve measurements and wind turbine pitch control. With its focus on floating offshore wind turbines the paper is of international interest and in particular relevant for regions where wind resources over shallow water are scarce. The paper combines existing methods of lidar simulation with new ideas for how they can be used for nacelle-based wind lidars on floating offshore wind turbines. The conclusions of the work are of high relevance to the scientific and industrial community, in particular the recommendation to not use uncompensated data from pitching nacelle-based wind lidar is important.
The objectives and methods of the study are clearly outlined in the introduction and described in enough detail to make the study reproducible. All assumptions that are made for modelling the lidar measurements are stated explicitely. Though, several of the assumptions made are not or not sufficiently reasoned. They are also not well discussed in terms of their implications to the results. This should be improved in a revised version of the paper.
Many simulation results are presented and briefly discussed. The paper would benefit from a more concise presentation of the most important results and a more in-depth discussion that focuses on the results that are of practical relevance.
Overall, the presentation of the work has a clear structure and is well written. The overall good readability is interrupted by very many minor mistakes regarding missing dashes, commas, and prepositions.
I recommend that publication of the manuscript should be reconsidered after major revisions.
In general, relevant literature has been cited and described. The authors should also include the main findings and limitations of the cited references, so that existing knowledge gaps become clear that motivate the paper. Please explain explicitly why your study extends the existing body of literature.
l 11: The abstract should be improved by making it more concise and result oriented. For example "Further, we discuss the need for motion compensation..." should be replaced by for example "We find that motion compensation is needed if...".
l 71-75: This analysis of an error cause should better be moved to section 3 where it can be put into context that is still missing in the introduction.
l 91: Better include the objectives to be the conclusion of your literature research instead of a short separate subsection.
l 95: A third objective is probably the assessment of the introduced correction methods.
The methodology separated into analytical and numerical modelling is well described. Subsection 2.1 is missing information about time and duration of the campaign, also relevant information about environmental conditions during the campaign are missing (calm or rough sea states...). Some of the notation introduced in 2.2 and 2.3 is incoherent or unclear. Please revise.
l 129: Give a reference to where in the manuscript the lidar is fully described (beam timing, range gates...)
l 145f: This is probably a reasonable simplification but the authors must explain why surge and sway can and should be omitted. Are they small compared to the rigid body motion due to tilt of the floater?
l 148: Variable "a" must be introduced.
l 155: Refer to Figure 2 and introduce x_trans and z_heave
l 165: Please describe: What are the implications of these simplifications on the measurements? Why are they acceptable?
l 167: The "u-component" of the wind vector is often referred to in the manuscript but it is never introduced. The authors should define it in the methods section.
l 172: Mention the specific beam geometry here or refer to where in the manuscript it is given.
l 175: Please include the rotation matrix Rx,y,z (or R(ψ,β,γ)), instead of just mentioning it.
l 180: Briefly describe why volume averaging is omitted (or refer to 2.3 where it is mentioned). Also why is turbulence not needed in the analytical model?
l 208: "surge", "sway" and "heave" have been introduced and should be used for consistency with the rotational DoF.
Eq. 11: What is the index I referring to?
Eq. 12: Index "P" or "p" (Figure 3)
Fig. 3: This figure needs improvements: By definition [xI,yI,zI] are the current positions of the lidar focus points. And [xp,yp,zp] are the positions of focus points after translation. What is the dashed blue vector? If it shall be the translation vector, why does it not connect [xI, yI, zI] and [xp,yp,zp]? Things stay a bit unclear to me.
l 220: Stick to the x,y,z order: "surge, sway and heave".
3 Motion influence in nacelle based lidar measurements
Both 3.3 and 3.4 would benefit from a concise summary of findings like it is given at the end of 3.2. Which parameters are the most critical for uncertainty and bias? What are the ranges of error caused by the different analysed parameters?
l 230: Use subplot labels, e.g., "(a)" to refer to parts of a figure. This accounts for several instances througout the manuscript (e.g., l 341).
l 238: For the frequently occurring wind speed range around 10 m/s, the pitch standard deviation (approx. 0.5deg) is lower than the mean pitch angle (approx. 0.6deg). From this, it is not intuitive that there will be "significant fluctuations in the lidar measurements" while "no large errors in the mean wind speed estimates due to the mean pitch angles are expected". Please explain why you assume stronger influence from the dynamic motion. The authors can do so for example by adding to the plot the translational velocity of the lidar caused by tilt.
Fig. 4 caption: Left: Describe error bars in left plot. What do they show? Right: Which LOS velocity? (Is it arbitrary?). In general, give more information in the captions (here: Data from measurements or simulation?), so that readers who first don't read the text get a better impression.
l 246: Second peak is not visible in the spectrum which ends at 0.5 Hz. Instead, second peak is visible at 0.33 Hz?
l 253: How are uncertainty and bias defined? Maybe refer to the definitions in the appendix.
l 263: The authors should mention that the first analysis presented here is valid only for steady displacement (or very slowly fluctuating motion << 1Hz)
l 263: "of [displacement] in individual DOF"
Fig. 5: Use differentiating text for the subplots in one column (e.g., "Yaw, α=0.0", "Yaw, α=0.1"...). All plots with zero motion but shear show mean reconstructed u velocities < reference wind speed. I understand that this is due to averaging over the rotor plane but it is not intuitive and makes interpretation of the entire figure difficult. Consider normalizing the y-axis to wind speed at zero motion. Or at least add the recontructed wind speed at zero motion to the plots as horizontal lines.
l 270: "stays nearly constant" (roll leads to slightly reduced vertical measurement positions)
l 275: This could be better described with the help of the chosen vertical shear model (Eq. 4): The effect of heave leads to identical sinusoidal variations of the measurement elevation for all four beams. As a result the reconstructed wind speeds in u-direction will show a minor negative bias, i.e, lidar-measured wind speeds will be lower than reference wind speed. This is because the horizontal wind speeds increase slower with increasing height than they decrease with decreasing height. The authors could also give an example to prove the insignificance of this bias in comparison to other biases. Without such a prove the reader might not believe that "no significant bias is introduced by the heave displacement".
l 277 f: It must be clarified that this is true for slow motion relative to the 1Hz scanning pattern of the lidar.
Fig. 6 caption: Describe the value of α.
l 301: Figure 7 shows uncertainties "up to 15%", not "up to 20%"
Fig. 8: Use a),b),c), and d) as titles above the subplots and refer to Table 2 in the caption. Otherwise, it is difficult to get all relevant information and interpret the Figure.
l 324: Isn't it straightforward to show that this relationship is reciprocal: Half the period-> double the translational velocity -> double the uncertainty? The authors can consider using Pitch frequency instead of Pitch period for the horizontal axes in Fig. 8 to show a linear relationship.
l 354: This is 0.5% of the measurement value and would be very significant. In this case the deviations between analytical and numerical solution would need to be explained. From the Figure, it looks like the deviations are actuallz below 0.02m/s.
4 Correction Approaches
l 358-364: Good to summarize but as an improvement, consider to describe the three effects in terms of uncertainty and bias separately. Maybe use a table with DOFs (vertical) and uncertainty and bias (horizontal). Then fill the cells with strong (++,--), low (+,-) and no effect (0).
l 370: "nacelle-based lidar"
l 396: How small are "small time scales"?
l 408: The authors should explain their motivation for not "correcting lidar measurement time series based on the instantaneous turbine tilt angles". Although this would offer a chance correcting for bias and uncertainty at once. What is advantageous about the look-up table plus frequency filtering? What are the drawbacks?
Eq. 13, l 413: "v_correction" is later called "v_corr".
Table 7 caption: Introduce "Hs" and "Tp" here.
l 465-475: Consider removing these three short paragraphs including Figs. 11 and 12. Another parameter study does not add new knowledge and the efficacy of the model-based correction will be shown in Fig. 15. If the authors decide to keep the figures, they should be combined into one
l 482 & 489: Give ME in % here. Relative error is less dependent on WS.
Fig. 13: Adjust both y axes to use the same grid lines: For example:
y left: [-0.4 0.2]
y right: [-6 6]
I recommend showing the relative error.
l 498ff: Consider deleting this paragraph and Fig. 15. It does not contain new ideas or knowledge.
l 505: I agree. Please add: How do the authors assess the remaining motion-induced error? (Why) Is it acceptable?
l 509: Put this into a wider context also considering lidar-specific effects: line-of-sight averaging and cross contamination caused by combining spatially-separated measurement volumes.
Fig. 16 caption: Is wave case 1,2 or 3 shown?
l 512: Which is the natural pitch frequency? Please add the value, if known.
l 516: Why is the MAE of the filtered lidar wind speed estimates slightly higher than the uncorrected value? Also, how do you explain that the remaining error after correction is approximately the same for all cases?
l 541: The authors should discuss what is the effect of including turbulence, volume averaging and the real scanning pattern.
l 561: I agree. Many practical issues like time-synchronization and measurement accuracy are not considered here. Please explain the possible consequences for the application of your method.
l 588: In my opinion the wind shear coefficient should be added to the list of parameters determining the bias.
l 618: At least pitch deflection and velocity in x direction are correlated. Who could this influence the results?
l 633f: What are the implications of this assumption for reconstructed wind vectors in a turbulence wind field?
l 643: What is the measurement plane (the lidar measures along four lines)? Also, it depends on the spatial structure of the turbulent wind field if the samples taken along four beams are representative of the entire measurement plane.
l 4: Words like "well" should be avoided. They usually don't add value to the manuscript. (also "much", l 539)
l 4: The manuscript is missing commas in many instances. For example: "In this work, we investigate..."
l 5: The manuscript is missing dashes in many instances. For example: "...forward-looking nacelle-based lidar systems..." or "...motion-induced effects..."
l 11: The abstract should be written as one paragraph.
l 84: "are calculated"
l 104: "Second," "on an analytical"
l 112: "simulation"
l 119: "Figure" should be capitalized throughout the manuscript. Same for "Equation", "Eq.", and "Table".
l 125: "Ideol's"
l 146: "DOF" instead of "DoF" or vice versa for consistency througout the manuscript.
l 184: "given"
l 194f: "quantify the bias", "as a function"
l 209: "positions are obtained" (plural)
l 212: [xI xI xI]?
l 240f: "as well [as!]" should be replaced by "and" wherever possible.
l 255: "follow[s]" or better "is the same as..."
l 317: "MAE" instead of "MEA"
l 378: "the use [of] nacelle[-]based lidar"
l 393: "maintain the [the] rotor..."
l 396: "measurement[s]"
l 405: "section [3?]"
Table 7: Units [m] and [s] are not written in italics (also l 670).
l 463: "over a[n] averaging"
l 505: "floater[']s"
l 525: "measur[e]ments"
l 536: "measure[me]nts"
l 551: "model [to] calculate"
l 583: "results [uncertainties] derived"
l 611: Rewrite this sentence, or remove "a output".
l 654: "[A]ppe[nd]ix"
l 655: "a[n] parameter"
l 665: "[b]ias"
l 677: "the [the]"
l 683: "minim[a]"