the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Mid-fidelity simulations and comparisons of five techniques for axial induction control of a wind turbine
Abstract. As wind turbines are more frequently placed in arrays, the need to understand and mitigate problems arising from their wakes has increased. When downstream turbines are in the wakes of upstream ones, the downstream turbines produce less power, require more maintenance, and have shorter lifetimes. One wake mitigation technique is known as axial induction control (AIC) and it involves derating (operating suboptimally) upstream turbines such that more energy remains in their wakes for downstream turbines to harvest. While there has been considerable research on this technique, much of it has suffered from a misunderstanding of the most important parameters in optimizing AIC. As such, the research has been largely inconclusive. Herein, we seek to rectify several perceived shortcomings of previous work by using mid-fidelity simulations to compare five different techniques for AIC at three different derate percentages against a baseline case and examining the recovery of the wake. We find that only the case with the lowest derate, 10 %, and using maximum thrust exceeds the baseline when estimating the combined power of the simulated turbine and a virtual turbine five diameters downstream and that it produced 10 % more power. Furthermore, these results help to validate previous work that concluded that the excess energy that is in the wake of a derated turbine will be at the edges of the wake unless the wake can sufficiently recover before the next downstream turbine. Finally, all together this suggests that the precise combination of derate percentage and the method used to derate turbines (i.e., the precise combination of pitch and torque controls), as well as the spacing and arrangement of turbines, must all be considered when optimizing AIC, and that substantial power gains may be possible.
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Interactive discussion
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RC1: 'Comment on wes-2021-122', Anonymous Referee #1, 17 Dec 2021
The paper "Mid-fidelity simulations and comparisons of five techniques for axial induction control of a wind turbine" presents a numerical study of static derating axial induction control of a single wind turbine in view of increasing total power extraction in a virtual downstream turbine. The paper is original and relevant to the wind farm control community. The main highlight of the paper seems to be that only derating at increased thrust setpoints can potentially achieve overall power improvements, and that other techniques are incapable of concentrating energy gains at downstream rotor locations, which is the current state of literature (Annoni 2015). The paper provides some interesting observations, but I feel certain aspects should be further improved to attain scientific standards, especially related to the use of mid-fidelity CACTUS model. More detailed comments are listed below, which I believe could significantly enhance the quality of the paper.
Major comments
1. My main comment relates to the use of mid-fidelity tool CACTUS, and its capability to accurately describe the wake dynamics in response to different turbine setpoints. Based on its description in the paper, I find the overall adequacy of the CACTUS model for the current purpose questionable. More specifically,
a. p.4, L60: The authors mention using a mid-fidelity tool rather than high-fidelity LES for computational cost reasons. However, the computational cost of performing 16 simulations of a single actuator line model at different control setpoints in LES does not seem prohibitive to me. On the other hand, the amount of revolutions required for statistical convergence of the results could significantly increase the LES cost. Could the authors comments on the actual computational cost of CACTUS, and compare it to an estimated LES?
b. The authors comment around L150 that far-wake behavior is subject to 'numerical turbulence'. Is this similar to physical turbulence, or simply noise? If the latter, this would appear to limit its use for modeling wind-turbine interactions. Can this be linked to the spectral analysis in Figure 7 / Section 3.1?
c. Comparison with LES in a prior study showed a discrepancy in wake recovery rates (L170), which would again render CACTUS inappropriate for modeling turbine interactions for control purposes. The authors later mention (L175) that differences can 'likely' be view as bias errors, but I find no convincing justification for this claim. Please clarify.
d. The lack of dissipation is often mentioned as a limiting factor for interpreting CACTUS results (e.g. L157, L221), is this a fundamental limitation of the code? If no, why not include it?
e. The verification section is unconvincing. It consists of an energy balance within the domain, which is more a measure of numerical stability of the code rather than physical realism. The energy residuals of the maxCt cases are far from convergence, with residuals over 50% of total energy at 15 revolutions. The authors mention that additional revolutions will likely improve convergence. Given that the maxCt cases are the most performant cases regarding wake recovery, please explicitly show that this convergence can be attained. Furthermore, Figure 4 does not clearly illustrate positive and negative energy terms to be equal (plot them both as positive to allow visual comparison). Again, the imbalance for maxCt cases is worrying.
g. Considering all comments above, I find the accuracy of CACTUS for the given purpose comes across as relatively weak, and the attempt at verification in my opinion provides no further confidence in the model. Furthermore, literature shows that inlet turbulence strongly affects dynamics of wake recovery, so it is very doubtful that current conclusions can be transfered to turbulent ABL conditions. I thus believe that the authors should stress much more that current results should be interpreted with high caution (throughout the paper, including in the abstract), and that any true physical conclusions can only be formulated after validation in high-fidelity LES and/or wind-tunnel studies. The authors do so to a limited extent around line 175, but given the comments above, I feel this is a much more fundamental flaw of the paper and advise for caution should be formulated stronger.
As a suggestion, it might be feasible to include an LES of at least some cases (baseline, 10maxCt, 1 other 10% derate) in the current paper, as this would significantly strengthen it.
2. The discussion of Fig. 8, with the statement that wake recovery happens more slowly for higher derates, seems quite wishful thinking. The authors themselves point out the exception for maxCt cases, but I'd say that the differences do not seem significant for any of the cases actually.
3. One of the main conclusions is that the wake recovery in the maxCt cases is very different from the other cases. Please relate this to the recent study of wind turbines operating at high thrust coefficients in the following reference: MartínezâTossas, Luis A., et al. "Numerical investigation of wind turbine wakes under high thrust coefficient." Wind Energy (2021).
4. In Figure 17, it is shown that power increase seem to vanish for larger streamwise distances. Can the figure be extended to include larger spacings? Typical turbine spacings in modern farms are well above the 6 rotor diameters shown in this figure.
5. The virtual rotor bending moment analysis in Figure 19 is somewhat misleading and adds little to the overall story. By normalizing with the baseline case, the maxCt appears to lead to significant load enhancement, whereas these high values might not correspond to problematic cases, as the baseline moment is simply very low due to the wake deficit. The load analysis for the bending moment hence simply comes down to a reduced wake deficit (which in itself it the target of the AIC...). The virtual rotor moment analysis can possibly be omitted.
Minor comments
- It would be good to comment on the distinction between static (focus of current paper) and dynamic axial induction control, which has been getting receiving increased attention in recent years, as well as add some references on the latter.
- L96: Reporting a default regularization value at 1e-7 in itself is meaningless, does it have a unit? Either report a unit, or some context for this value, or don't report the exact value at all.
- L122: dynamic viscosity should have a unit
- Figure 3: colormapping preferably in a perceptually uniform, b/w intelligible color (e.g. viridis/parula). If possible, it would be illustrative to explicitly include the contourlines for C_p at 10, 20, and 40% derating (in addition to the equispaced existing contourlines). The purple star appears to operate at higher C_P than the other purple symbols (should all be at 10% derate?).
- Many figures, e.g. 16, 17, non-dimensionalize distances with rotor radius R, whereas the accompanying discussion in the text refers to rotor diameters D. Please be consistent to allow a better direct interpretation between figures and manuscript text.
- Equations (12) and (13) seem to be functions on rotor radial location r through the dependence of C_t and C_q thereon. However, Fig. 19 presents them as single scalar values. should the small r in (12) and (13) be a large R, or is there some implicit radial integration between Eqs. (12) and (13) and Fig. 19? Please clarify.
- Figure 2 is a nice visualization of the FVWM method, but it is not referred to in the text. Please do so in Section 2.
Citation: https://doi.org/10.5194/wes-2021-122-RC1 -
RC2: 'Comment on wes-2021-122', Anonymous Referee #2, 25 Jan 2022
Mid-fidelity simulations and comparisons of five techniques for axial induction control of a wind turbine
Review notes
General
- Agree that this is a topic area in need of a thorough dive such as this as the literature is sometimes contradictory.
- Overall I think paper is well done, it is nicely organized, the figures are clear and instructive, the argument is good, and especially appreciate the way this paper informs on the sometimes contradictory results of past papers and provides a framework to see a harmonized set of results through considering multiple means of implementing axial control
- I think the main opportunity for improvement is to have some consideration, maybe just in the final discussion/conclusions where the authors consider how well these results, which seek to explain static axial induction control, fit with findings on new methods of dynamic axial induction control. I suspect they will fit together well.
Specific
Introduction
- Page 1
- Could it be useful to from the start differentiate AIC from dynamic induction control? I found myself starting out wondering if certain statements applied to both static and dynamic methods
- Page 2
- “This is exemplary of the second shortcoming of previous studies” – This paragraph makes a very good point
Methods
- Page 4
- Sorry if I missed it, has CACTUS been validated against other codes or field data? (note continued reading brings me to this, maybe just mention that is will come later)
- Page 6
- A 27m rotor is small for modern standards, is there a concern these results might not scale to 100m+ rotors? Wake steering for example has been shown to have dependence on rotor size (cf
- Ciri, U., Rotea, M. A., & Leonardi, S. (2018). Effect of the turbine scale on yaw control. Wind Energy, 21(12), 1395–1405. https://doi.org/10.1002/we.2262
- Do you expect AIC to not have this dependence on scale?
- A 27m rotor is small for modern standards, is there a concern these results might not scale to 100m+ rotors? Wake steering for example has been shown to have dependence on rotor size (cf
- Page 8
- Table 1: Agree that this is an interesting set of options to compare
Results
- Figure 8 is very instructive and nicely done, feel free to ignore, but was wondering if:
- The figure was transposed to be taller and less wide, each subfigure could be larger
- Further, rather than the coded label of each subfigure the columns/rows could be labeled with more meaningful “20% derate” // maximum Ct, etc
- (Now I see this is the case in Fig 9, I think it is easier to read like this)
- Page 17
- This sentence is vague: “In particular, we see that vorticity in the maxCt cases decays the fastest and that the maxRR method appears to have the predicted effect.”
- Figure 14: Recommend a solid black line at 0
- In general the results section is well argued and the plots are well done
Discussion
- Page 27
- “The mechanism by which this improvement…” this paragraph provides some helpful contextualization of the results of this paper and more generally.
- A paragraph here considering how the results of this study compare to results from dynamic axial control would fit well. I think the physical explanations of which of these simulations work best will accord well with the studies of how different axial methods (such as cyclic thrust variations or the helix method) are able to increase overall power.
Citation: https://doi.org/10.5194/wes-2021-122-RC2
Interactive discussion
Status: closed
-
RC1: 'Comment on wes-2021-122', Anonymous Referee #1, 17 Dec 2021
The paper "Mid-fidelity simulations and comparisons of five techniques for axial induction control of a wind turbine" presents a numerical study of static derating axial induction control of a single wind turbine in view of increasing total power extraction in a virtual downstream turbine. The paper is original and relevant to the wind farm control community. The main highlight of the paper seems to be that only derating at increased thrust setpoints can potentially achieve overall power improvements, and that other techniques are incapable of concentrating energy gains at downstream rotor locations, which is the current state of literature (Annoni 2015). The paper provides some interesting observations, but I feel certain aspects should be further improved to attain scientific standards, especially related to the use of mid-fidelity CACTUS model. More detailed comments are listed below, which I believe could significantly enhance the quality of the paper.
Major comments
1. My main comment relates to the use of mid-fidelity tool CACTUS, and its capability to accurately describe the wake dynamics in response to different turbine setpoints. Based on its description in the paper, I find the overall adequacy of the CACTUS model for the current purpose questionable. More specifically,
a. p.4, L60: The authors mention using a mid-fidelity tool rather than high-fidelity LES for computational cost reasons. However, the computational cost of performing 16 simulations of a single actuator line model at different control setpoints in LES does not seem prohibitive to me. On the other hand, the amount of revolutions required for statistical convergence of the results could significantly increase the LES cost. Could the authors comments on the actual computational cost of CACTUS, and compare it to an estimated LES?
b. The authors comment around L150 that far-wake behavior is subject to 'numerical turbulence'. Is this similar to physical turbulence, or simply noise? If the latter, this would appear to limit its use for modeling wind-turbine interactions. Can this be linked to the spectral analysis in Figure 7 / Section 3.1?
c. Comparison with LES in a prior study showed a discrepancy in wake recovery rates (L170), which would again render CACTUS inappropriate for modeling turbine interactions for control purposes. The authors later mention (L175) that differences can 'likely' be view as bias errors, but I find no convincing justification for this claim. Please clarify.
d. The lack of dissipation is often mentioned as a limiting factor for interpreting CACTUS results (e.g. L157, L221), is this a fundamental limitation of the code? If no, why not include it?
e. The verification section is unconvincing. It consists of an energy balance within the domain, which is more a measure of numerical stability of the code rather than physical realism. The energy residuals of the maxCt cases are far from convergence, with residuals over 50% of total energy at 15 revolutions. The authors mention that additional revolutions will likely improve convergence. Given that the maxCt cases are the most performant cases regarding wake recovery, please explicitly show that this convergence can be attained. Furthermore, Figure 4 does not clearly illustrate positive and negative energy terms to be equal (plot them both as positive to allow visual comparison). Again, the imbalance for maxCt cases is worrying.
g. Considering all comments above, I find the accuracy of CACTUS for the given purpose comes across as relatively weak, and the attempt at verification in my opinion provides no further confidence in the model. Furthermore, literature shows that inlet turbulence strongly affects dynamics of wake recovery, so it is very doubtful that current conclusions can be transfered to turbulent ABL conditions. I thus believe that the authors should stress much more that current results should be interpreted with high caution (throughout the paper, including in the abstract), and that any true physical conclusions can only be formulated after validation in high-fidelity LES and/or wind-tunnel studies. The authors do so to a limited extent around line 175, but given the comments above, I feel this is a much more fundamental flaw of the paper and advise for caution should be formulated stronger.
As a suggestion, it might be feasible to include an LES of at least some cases (baseline, 10maxCt, 1 other 10% derate) in the current paper, as this would significantly strengthen it.
2. The discussion of Fig. 8, with the statement that wake recovery happens more slowly for higher derates, seems quite wishful thinking. The authors themselves point out the exception for maxCt cases, but I'd say that the differences do not seem significant for any of the cases actually.
3. One of the main conclusions is that the wake recovery in the maxCt cases is very different from the other cases. Please relate this to the recent study of wind turbines operating at high thrust coefficients in the following reference: MartínezâTossas, Luis A., et al. "Numerical investigation of wind turbine wakes under high thrust coefficient." Wind Energy (2021).
4. In Figure 17, it is shown that power increase seem to vanish for larger streamwise distances. Can the figure be extended to include larger spacings? Typical turbine spacings in modern farms are well above the 6 rotor diameters shown in this figure.
5. The virtual rotor bending moment analysis in Figure 19 is somewhat misleading and adds little to the overall story. By normalizing with the baseline case, the maxCt appears to lead to significant load enhancement, whereas these high values might not correspond to problematic cases, as the baseline moment is simply very low due to the wake deficit. The load analysis for the bending moment hence simply comes down to a reduced wake deficit (which in itself it the target of the AIC...). The virtual rotor moment analysis can possibly be omitted.
Minor comments
- It would be good to comment on the distinction between static (focus of current paper) and dynamic axial induction control, which has been getting receiving increased attention in recent years, as well as add some references on the latter.
- L96: Reporting a default regularization value at 1e-7 in itself is meaningless, does it have a unit? Either report a unit, or some context for this value, or don't report the exact value at all.
- L122: dynamic viscosity should have a unit
- Figure 3: colormapping preferably in a perceptually uniform, b/w intelligible color (e.g. viridis/parula). If possible, it would be illustrative to explicitly include the contourlines for C_p at 10, 20, and 40% derating (in addition to the equispaced existing contourlines). The purple star appears to operate at higher C_P than the other purple symbols (should all be at 10% derate?).
- Many figures, e.g. 16, 17, non-dimensionalize distances with rotor radius R, whereas the accompanying discussion in the text refers to rotor diameters D. Please be consistent to allow a better direct interpretation between figures and manuscript text.
- Equations (12) and (13) seem to be functions on rotor radial location r through the dependence of C_t and C_q thereon. However, Fig. 19 presents them as single scalar values. should the small r in (12) and (13) be a large R, or is there some implicit radial integration between Eqs. (12) and (13) and Fig. 19? Please clarify.
- Figure 2 is a nice visualization of the FVWM method, but it is not referred to in the text. Please do so in Section 2.
Citation: https://doi.org/10.5194/wes-2021-122-RC1 -
RC2: 'Comment on wes-2021-122', Anonymous Referee #2, 25 Jan 2022
Mid-fidelity simulations and comparisons of five techniques for axial induction control of a wind turbine
Review notes
General
- Agree that this is a topic area in need of a thorough dive such as this as the literature is sometimes contradictory.
- Overall I think paper is well done, it is nicely organized, the figures are clear and instructive, the argument is good, and especially appreciate the way this paper informs on the sometimes contradictory results of past papers and provides a framework to see a harmonized set of results through considering multiple means of implementing axial control
- I think the main opportunity for improvement is to have some consideration, maybe just in the final discussion/conclusions where the authors consider how well these results, which seek to explain static axial induction control, fit with findings on new methods of dynamic axial induction control. I suspect they will fit together well.
Specific
Introduction
- Page 1
- Could it be useful to from the start differentiate AIC from dynamic induction control? I found myself starting out wondering if certain statements applied to both static and dynamic methods
- Page 2
- “This is exemplary of the second shortcoming of previous studies” – This paragraph makes a very good point
Methods
- Page 4
- Sorry if I missed it, has CACTUS been validated against other codes or field data? (note continued reading brings me to this, maybe just mention that is will come later)
- Page 6
- A 27m rotor is small for modern standards, is there a concern these results might not scale to 100m+ rotors? Wake steering for example has been shown to have dependence on rotor size (cf
- Ciri, U., Rotea, M. A., & Leonardi, S. (2018). Effect of the turbine scale on yaw control. Wind Energy, 21(12), 1395–1405. https://doi.org/10.1002/we.2262
- Do you expect AIC to not have this dependence on scale?
- A 27m rotor is small for modern standards, is there a concern these results might not scale to 100m+ rotors? Wake steering for example has been shown to have dependence on rotor size (cf
- Page 8
- Table 1: Agree that this is an interesting set of options to compare
Results
- Figure 8 is very instructive and nicely done, feel free to ignore, but was wondering if:
- The figure was transposed to be taller and less wide, each subfigure could be larger
- Further, rather than the coded label of each subfigure the columns/rows could be labeled with more meaningful “20% derate” // maximum Ct, etc
- (Now I see this is the case in Fig 9, I think it is easier to read like this)
- Page 17
- This sentence is vague: “In particular, we see that vorticity in the maxCt cases decays the fastest and that the maxRR method appears to have the predicted effect.”
- Figure 14: Recommend a solid black line at 0
- In general the results section is well argued and the plots are well done
Discussion
- Page 27
- “The mechanism by which this improvement…” this paragraph provides some helpful contextualization of the results of this paper and more generally.
- A paragraph here considering how the results of this study compare to results from dynamic axial control would fit well. I think the physical explanations of which of these simulations work best will accord well with the studies of how different axial methods (such as cyclic thrust variations or the helix method) are able to increase overall power.
Citation: https://doi.org/10.5194/wes-2021-122-RC2
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