the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Oct 2024
The optimum range of design axial induction factors for lowest levelized-cost of energy
Abstract. The present work proposes a new fatigue, aerodynamics, and cost-scaled turbine (FACT) blade design methodology. The basis of the FACT blade design is an objective function for change in levelized-cost of energy, ΔLCOE, as a function of design axial induction factor, a, that strikes a balance between increasing (or up-scaling) blade length and annual energy production while accounting for the additional cost and loading changes associated with a longer blade. In the process of developing the ΔLCOE objective function, new insights were gained about changes in capital cost and operations and maintenance cost with rotor up-scaling. As part of the capital cost function development, new engineering approximations for rotor mass are discussed that are suitable for large-diameter offshore wind turbines, which use improved materials technologies and manufacturing processes. Additionally, a detailed operations and maintenance model is developed using available wind farm reliability data. Furthermore, a relationship between turbine failure rate and damage-equivalent loads for failure-prone turbine subsystems is proposed. FACT rotor blade design points are identified using five reference wind turbines with power ratings of 10- to 22-MW as a baseline. Projected LCOE savings with a FACT rotor blade design are on the order of 5 % for an optimum design axial induction factor in the range of a = 0.21 and 0.27, thus falling between the low-induction rotor concept (a = 0.18) and the Betz optimum for maximum CP (a = 0.33).
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RC1: 'Comment on wes-2024-109', Anonymous Referee #1, 30 Oct 2024
The authors propose an interesting study on the impact of induction factor on LCOE for large offshore rotors. The study is significant and there are many interesting takeaways. The manuscript is also clear and well written on first submission. I have some comments for the authors in the attached file
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RC2: 'Comment on wes-2024-109', Anonymous Referee #2, 08 Dec 2024
This manuscript presents an engineering model to calculate the variation of LCOE as a function of the axial induction factor, for the purpose of rotor up-scaling. The topic of rotor design and upscaling are relevant and of interest for the readers of Wind Energy Science. The methodology introduced is insightful and propose a simple and interesting tool to support turbine design. However, the manuscript has critical weaknesses that prevents its publication.
A. The contextualization of the study in the literature is shallow and undermines significantly its relevance. Indeed, the paper highlights only a small subset of the extensive literature on wind turbine design and rotor optimization. The manuscript fails to highlight that both fatigue and LCOE have both been considered in previous works on rotor design. The topics of structural design, ultimate loads or design load cases are not addressed,even though they are often central for this field. The relevance of inverse design methods using a target induction factor is not put in context either. As a result, the authors fail to highlight a relevant and clear research gap in the literature.
B. The methodology behind the ΔLCOE metric presents several limitations:
- There seem to be a major error in the formula for ΔLCOE (see attached file)
- LCOE is a levelized metric, which does not appear in the equations. Did the authors mean to use "cost of energy" instead?
- The proposed engineering model is not validated, which undermines its credibility and the associated results.
C. The text lacks structure, clarity and conciseness. As a result, the details of the methodology and the main message of the work are difficult to understand.
Minor comments:
- Glauerts model is used throughout the paper, but without comments on its validity. There has been several improvements on the model done in the literature and textbooks, which would be relevant to mention.- Eq. 28: The audience of Wind Energy Science is generally familiar with the formula for AEP. Consider removing this equation for conciseness.
- Table 9: The reference designs have not been designed with a target axial induction factor, but with optimization methods. In this context, the precision and relevance of the metric "design a" is questionable.
- Table 3: The numbers in the column "Average" do not correspond to the average of the other columns. The column should be renamed accordingly.
- Figure 2: Can the author confirm that they have the rights to reproduce this figure in a publication? The slides being available online does not mean that they are open-source.
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RC3: 'Comment on wes-2024-109', Anonymous Referee #3, 03 Jan 2025
Dear authors, a few weeks ago the associate editor asked me to provide a third review of your manuscript entitled “The optimum range of design axial induction factors for lowest levelized cost of energy”. I have now found the time to review your document. I found the manuscript well written, and I sincerely appreciate your effort to develop a simpler design methodology for a complex multi-disciplinary problem such as wind turbine design. However, I also find myself fairly well aligned with the comments from reviewer #2. I do think that the manuscript suffers from a number of weaknesses that should be addressed before a publication in the journal of Wind Energy Science. I list here my main comments hoping that you can address them for a successful resubmission.
Literature review is incomplete. Your work immediately brought me back to the literature review that I performed during my PhD studies. Foundational papers like https://doi.org/10.1016/S0167-6105(98)00191-3 should be mentioned, especially because 25 years ago the authors defined a design approach based on first principles that, in some elements, is remarkably similar to what you have defined in your manuscript. Also, I don’t expect you to cite my paper https://doi.org/10.5194/wes-1-71-2016 , but that’s more relevant to your document than other citations that you report, such as for example Canet et al. (2023), which is an excellent paper that has however little to do with the work that you have conducted. After all, the slides that you cite Bottasso, 2019 leverage (and correctly cite) much of my work.
A second major weakness of your manuscript is that the aspects of novelty are not well defined. You write “In line with these efforts, the present work seeks to add to the literature on optimizing wind turbine design with respect to LCOE. The novelty in the present work is the focus on minimizing the LCOE of an up-scaled rotor.” LCOE of upscaled rotors has been addressed for two decades now, at different levels of fidelity. I don’t see novelty in LCOE of upscaling. I do see novelty in other aspects of your work, for example the estimation of OpEx costs, which over the years have often been assumed flat because of limitations in the numerical models.
I found a third major weakness in your approach. You tune your equations leveraging open-source models designed at high aerodynamic performance (axial induction equal or close to 0.33) and you then extrapolate to lower values of axial induction. I see a fundamental issue with this approach. Also, axial induction is a rotor equivalent quantity. Wind turbine rotor designers do look at induction, but focus on its distribution along blade span. While I agree that it can be beneficial to drop axial induction in the outer span of the blade, lowering the overall axial induction of the rotor is hardly a good idea. When you do so, the rotor will operate sub optimally even at very low wind speeds, when loads are low and the value of electricity is high (for value-based metrics see for example https://backend.orbit.dtu.dk/ws/portalfiles/portal/234026713/Beyond_LCOE_New_Assessment_Criteria_for_Evaluating_Wind_Energy_RI.pdf). To limit loads and design larger rotors, isn’t it easier to implement peak thrust shaving logics and pitch the blades close to rated wind speed? This is standard practice in industry. Unfortunately your AEP model is oversimplistic and does not capture this aspect. To overcome these limitations, you may want to adopt more sophisticated models such as the ones implemented in open-source models like NREL's WISDEM (for AEP look here https://github.com/WISDEM/WISDEM/blob/master/wisdem/rotorse/rotor_power.py).
Overall, although I can see how big of an effort went into the preparation of this manuscript, I will not recommend to accept it as is for publication in the journal of Wind Energy Science. Instead, I hope my comments can help the authors rethink their manuscript and resubmit a stronger draft in a not-so-distant future.
Best regardsCitation: https://doi.org/10.5194/wes-2024-109-RC3
Status: closed
-
RC1: 'Comment on wes-2024-109', Anonymous Referee #1, 30 Oct 2024
The authors propose an interesting study on the impact of induction factor on LCOE for large offshore rotors. The study is significant and there are many interesting takeaways. The manuscript is also clear and well written on first submission. I have some comments for the authors in the attached file
-
RC2: 'Comment on wes-2024-109', Anonymous Referee #2, 08 Dec 2024
This manuscript presents an engineering model to calculate the variation of LCOE as a function of the axial induction factor, for the purpose of rotor up-scaling. The topic of rotor design and upscaling are relevant and of interest for the readers of Wind Energy Science. The methodology introduced is insightful and propose a simple and interesting tool to support turbine design. However, the manuscript has critical weaknesses that prevents its publication.
A. The contextualization of the study in the literature is shallow and undermines significantly its relevance. Indeed, the paper highlights only a small subset of the extensive literature on wind turbine design and rotor optimization. The manuscript fails to highlight that both fatigue and LCOE have both been considered in previous works on rotor design. The topics of structural design, ultimate loads or design load cases are not addressed,even though they are often central for this field. The relevance of inverse design methods using a target induction factor is not put in context either. As a result, the authors fail to highlight a relevant and clear research gap in the literature.
B. The methodology behind the ΔLCOE metric presents several limitations:
- There seem to be a major error in the formula for ΔLCOE (see attached file)
- LCOE is a levelized metric, which does not appear in the equations. Did the authors mean to use "cost of energy" instead?
- The proposed engineering model is not validated, which undermines its credibility and the associated results.
C. The text lacks structure, clarity and conciseness. As a result, the details of the methodology and the main message of the work are difficult to understand.
Minor comments:
- Glauerts model is used throughout the paper, but without comments on its validity. There has been several improvements on the model done in the literature and textbooks, which would be relevant to mention.- Eq. 28: The audience of Wind Energy Science is generally familiar with the formula for AEP. Consider removing this equation for conciseness.
- Table 9: The reference designs have not been designed with a target axial induction factor, but with optimization methods. In this context, the precision and relevance of the metric "design a" is questionable.
- Table 3: The numbers in the column "Average" do not correspond to the average of the other columns. The column should be renamed accordingly.
- Figure 2: Can the author confirm that they have the rights to reproduce this figure in a publication? The slides being available online does not mean that they are open-source.
-
RC3: 'Comment on wes-2024-109', Anonymous Referee #3, 03 Jan 2025
Dear authors, a few weeks ago the associate editor asked me to provide a third review of your manuscript entitled “The optimum range of design axial induction factors for lowest levelized cost of energy”. I have now found the time to review your document. I found the manuscript well written, and I sincerely appreciate your effort to develop a simpler design methodology for a complex multi-disciplinary problem such as wind turbine design. However, I also find myself fairly well aligned with the comments from reviewer #2. I do think that the manuscript suffers from a number of weaknesses that should be addressed before a publication in the journal of Wind Energy Science. I list here my main comments hoping that you can address them for a successful resubmission.
Literature review is incomplete. Your work immediately brought me back to the literature review that I performed during my PhD studies. Foundational papers like https://doi.org/10.1016/S0167-6105(98)00191-3 should be mentioned, especially because 25 years ago the authors defined a design approach based on first principles that, in some elements, is remarkably similar to what you have defined in your manuscript. Also, I don’t expect you to cite my paper https://doi.org/10.5194/wes-1-71-2016 , but that’s more relevant to your document than other citations that you report, such as for example Canet et al. (2023), which is an excellent paper that has however little to do with the work that you have conducted. After all, the slides that you cite Bottasso, 2019 leverage (and correctly cite) much of my work.
A second major weakness of your manuscript is that the aspects of novelty are not well defined. You write “In line with these efforts, the present work seeks to add to the literature on optimizing wind turbine design with respect to LCOE. The novelty in the present work is the focus on minimizing the LCOE of an up-scaled rotor.” LCOE of upscaled rotors has been addressed for two decades now, at different levels of fidelity. I don’t see novelty in LCOE of upscaling. I do see novelty in other aspects of your work, for example the estimation of OpEx costs, which over the years have often been assumed flat because of limitations in the numerical models.
I found a third major weakness in your approach. You tune your equations leveraging open-source models designed at high aerodynamic performance (axial induction equal or close to 0.33) and you then extrapolate to lower values of axial induction. I see a fundamental issue with this approach. Also, axial induction is a rotor equivalent quantity. Wind turbine rotor designers do look at induction, but focus on its distribution along blade span. While I agree that it can be beneficial to drop axial induction in the outer span of the blade, lowering the overall axial induction of the rotor is hardly a good idea. When you do so, the rotor will operate sub optimally even at very low wind speeds, when loads are low and the value of electricity is high (for value-based metrics see for example https://backend.orbit.dtu.dk/ws/portalfiles/portal/234026713/Beyond_LCOE_New_Assessment_Criteria_for_Evaluating_Wind_Energy_RI.pdf). To limit loads and design larger rotors, isn’t it easier to implement peak thrust shaving logics and pitch the blades close to rated wind speed? This is standard practice in industry. Unfortunately your AEP model is oversimplistic and does not capture this aspect. To overcome these limitations, you may want to adopt more sophisticated models such as the ones implemented in open-source models like NREL's WISDEM (for AEP look here https://github.com/WISDEM/WISDEM/blob/master/wisdem/rotorse/rotor_power.py).
Overall, although I can see how big of an effort went into the preparation of this manuscript, I will not recommend to accept it as is for publication in the journal of Wind Energy Science. Instead, I hope my comments can help the authors rethink their manuscript and resubmit a stronger draft in a not-so-distant future.
Best regardsCitation: https://doi.org/10.5194/wes-2024-109-RC3
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