Unveiling Inertia Constants by Exploring Mass Distribution in Wind Turbine Blades and Review of the Drive Train Parameters

Round 1

Reviewer 1 Report

The authors have done extensive comparative work in this paper. the paper can be improved by following issues.

1.      Please further clarify the main contributions of this paper.

2.      Please explain the novelty of the methods used in this paper.

3.      The title of this paper should be revised to focus on one issue.

4.      The comparative results should be implemented in the abstract.

5.      Please indicate the future work.

Some long sentences with several clauses are confusing.

Author Response

The authors have done extensive comparative work in this paper.

Thank you, and thank you for your comments. They are quite appropriate and really affect some shortcomings that the previous version had.

the paper can be improved by following issues.

1. Please further clarify the main contributions of this paper.

The following text has been added at the end of the Introduction section.

In summary, the main contributions of this work are to: 

• Select references that provide reliable values of inertia, in kg ・ m2.
• Analyze the influence of the IEC wind class of the turbine, and its material, on the weight of the blade. 

• Provide references with the mass distribution of the blade and validate them by comparing the values of inertia and CoG, provided with those calculated by numerical integration.

• Provide an expression that links the inertia with the position of the CoG, the weight and the length.

• List the references with information on the dynamic constants of the coupling from the turbine to the generator.

• Explain in depth a dimensionless framework to relate magnitudes and parameters with respect to their base references.

2. Please explain the novelty of the methods used in this paper.

At the introduction, starting at new line 110, the following paragraph has been added.

This method of obtaining inertia is novel, and is intended to be the initial stage of a more extensive database to provide reliable data on inertia, unlike inertia data obtained by transient analysis or other non-direct methods.

3. The title of this paper should be revised to focus on one issue.

The new proposed one is: “Unveiling Inertia Constants: Exploring Mass Distribution in Wind Turbine Blades”.

However, I am not sure if it depends on the editor to accept a change in the title. I will propose this new one, and wait for the editor decission.

4. The comparative results should be implemented in the abstract.

The following paragraph has been modified, mainly its final clause.

 [The old paragraph was the following]   In this work, the different bibliographical sources that provide values of blade inertia in kg·m² will be reviewed, and above all, those that provide a distribution of masses along the span of the blade.    

  [The new paragraph is the following] In the present work, the bibliographical sources that provide values of blade inertia in kg·m² are reviewed. A special treatment has been given to those providing the mass distribution along the blade span, for which the provided values of inertia and the position of the center of gravity have been compared with those obtained numerically, showing good matching.

In the following paragraph, the correlation factor has been included.

With this, different reliable relations will be obtained that allow calculating the inertia of the turbine rotor, based on the mass and length of the blade. When the center of gravity is also available, a very correlated expression (r²=0.975) is provided to obtain the inertia.      

5. Please indicate the future work.

In discussion, the following paragraph has been added

The aim of future work is to study in depth the characteristics of the coupling between the hub and the generator, especially in the slow shaft for non direct-drive couplings. This will allow to link the values of stiffness and damping more precisely. The constructive characteristics of squirrel cage, wound rotor and PMSGs will also be studied in order to deduce, in each case, the expressions that link its rated capacity with the rotor weight and, if possible, with its inertia.

Comments on the Quality of English Language

Some long sentences with several clauses are confusing.

We have divided some sentences in two, specifically:

• before “. If the contingency is not serious… ” at new line 39
• before “. It determines the time interval during which an electrical generator…” at new line 48
• at “system. This ensures the stability and resilience of … “ at new line 60
• “kinetic energy. This alleviates the effect of a …” at new line 66
• “generator. It is also mandatory to know the mechanism”, at new line 78
• “under investigation. Therefore, the researcher” at new line 90
• “actual situation. The alternative is to rely on” at new line 92
• “p.u. It also anticipates some issues” at new line 145
• “that considerably reduces” at new line 165
• “gearbox. Its ratio” at new line 176
• “This is true for turbines driving PMSGs” at new line 232

and some other sentences that have been divided by the editing service we have contracted.

Thank you again for your comments.

Reviewer 2 Report

1-      The paper needs language correction

2-     The abstract should follow such a sequence: first, introduce the general research background, then introduce the existing detailed problems, and finally, briefly present the work content and contribution of this paper

3-     Divide the introduction into three subsections: 1) Literature review, 2) Research gap and motivation, and 3) Contribution and paper organization

4-      Write a conclusion at the *end of the article and divide it into three subsections: 1) article contribution, 2) limitations and benefits of the proposed work, and finally 3) the recommended future work of the proposed work

5-      Define all variables used in the equations

6-      Add a reference to the kinetic energy equation

7-      Rearrange the abbreviations alphabetic

8-      Modify reference numbering corresponding to their citation

  The paper needs language correction

Author Response

1-      The paper needs language correction

After addressing the reviewers’ comment, we have contracted a proffesional edition service to correct it.

Previously, we had divided some long sentences in two, to clarify the exposed ideas, specifically:

• before “. If the contingency is not serious… ” at new line 39
• before “. It determines the time interval during which an electrical generator…” at new line 48
• at “system. This ensures the stability and resilience of … “ at new line 60
• “kinetic energy. This alleviates the effect of a …” at new line 66
• “generator. It is also mandatory to know the mechanism”, at new line 78
• “under investigation. Therefore, the researcher” at new line 90
• “actual situation. The alternative is to rely on” at new line 92
• “p.u. It also anticipates some issues” at new line 145
• “that considerably reduces” at new line 165
• “gearbox. Its ratio” at new line 176
• “This is true for turbines driving PMSGs” at new line 232

2-     The abstract should follow such a sequence: first, introduce the general research background, then introduce the existing detailed problems, and finally, briefly present the work content and contribution of this paper.

In fact this was the sequence that we tried to show to the reader, but it is true that probably we failed in clearly distinguishing which sentences correspond to each part. For authors, it is mandatory that the abstract must be written in a single paragraph, which does not help to this purpose. Please also take into account that abstract should not extend beyond 200 words.

We have introduced the text appearing in red in the following paragraph.

[General research background. We would like to include this titles, but it is not allowed by the abstract format]

In studies of dynamic stability and power quality, it is necessary to know the mechanical parameters determining the transient response of wind turbines. Their exact values are not as decisive as the power curve can be, but an unaccurate estimate can distort or even invalidate the simulation results.

[Existing detailed problems]

From a review of the literature, it has been found that, despite their importance, the values of inertia, stiffness and damping are hardly available for any turbine model. Another detected problem is the lack of confidence on the data origin.

[Work content and contribution]

This article aims to solve the issue of the scarcity and unreliability of the data on inertia, and gathers the information found on the remaining mechanical parameters. Available blade inertia values in kg·m² are presented. Special treatment has been given to those providing the mass distribution along the blade span, for which the provided values of inertia have been compared with those obtained numerically, showing good matching.

            With this, different reliable relations are obtained that allow calculating the turbine rotor inertia, based on the mass and length of the blade. When the center of gravity is also available, a very correlated expression (r²=0.975) is provided.

            The even rarer references to the stiffness and damping constant of the drive-train will also be reviewed. In addition, the study includes a revision of gearboxes, generators and blade weight, according to their IEC-class and material.

3-     Divide the introduction into three subsections: 1) Literature review, 2) Research gap and motivation, and 3) Contribution and paper organization

As explained in the template for this journal “The introduction should briefly place the study in a broad context and highlight why it is important. It should define the purpose of the work and its significance. The current state of the research field should be reviewed carefully and key publications cited. Please highlight controversial and diverging hypotheses when necessary. Finally, briefly mention the main aim of the work and highlight the principal conclusions.”

Trying to fit your suggestion and that of the journal, we have divided the introduction in the following subsections:

• Context and purpose of the work.
• Literature review,
• Research gap and motivation.
• Contribution.
• Paper organization.

One paragraph (the one starting by Guillamon in [9]) has been moved to fit this structure.

Please take into account that some of the gaps are exposed immediately after describing a reference, and hence it is difficult to include them in two subsections.

4-      Write a conclusion at the *end of the article and divide it into three subsections: 1) article contribution, 2) limitations and benefits of the proposed work, and finally 3) the recommended future work of the proposed work

As explained in the template for this journal:

\section{Discussion}

Authors should discuss the results and how they can be interpreted from the perspective of previous studies and of the working hypotheses. The findings and their implications should be discussed in the broadest context possible. Future research directions may also be highlighted.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Conclusions}

This section is not mandatory, but can be added to the manuscript if the discussion is unusually long or complex.

In fact this is quite similar to the structure proposed by you. Therefore, I really hope that you do not mind if I keep this content inside the section “Discussion”. In it, and according to your suggestion, we have created the proposed three subsections

4.1. Article contribution

4.2. Limitations and benefits of the proposed work

4.3. Future work

The text of the previous version (after language editing correction) fits well in the subsections 4.1 and 4.2

For the last subsection, we have added the following paragraph

The aim of future work is to study in depth the characteristics of the coupling between the hub and the generator, especially in the slow shaft for non direct-drive couplings. This will allow to link the values of stiffness and damping more precisely. The constructive characteristics of squirrel cage, wound rotor and PMSGs will also be studied in order to deduce, in each case, the expressions that link its rated capacity with the rotor weight and, if possible, with its inertia.

5-      Define all variables used in the equations

At the end of the Introduction, the following text has been added.

“At the end of the paper, a list of abbreviations and variables is included.” This is the place established by the template.

At the end of the paper the list is included.

6-      Add a reference to the kinetic energy equation

Done. The same reference [2] can be used also 

Hence, there is no need of renumbering citations.

This kinetic energy is: 
Ek =1/2 JΩ_G2  (1)
where J is the system inertia and Ω_G is the rotational speed of the electrical generator [2].

7-      Rearrange the abbreviations alphabetic

 Sorry, our fault. Now, with new word abbreviations, it is

AoR Axis of rotation
B Blade
CoG Center of gravity
DD Density distribution
DFIG Doubly-fed induction generator
eq equivalent of m2 and turbine
G Generator
GB Gear Box
GBG Shaft joining gearbox and generator
HGB Shaft joining hub and gearbox
HSS High speed shaft
IG Induction generator
LSS Low speed Shaft
m2 components at the high speed side
P Turbine rated capacity
PMSG Permanent magnet synchronous generator
T Turbine or turbine rotor
W Wind
WT Wind Turbine

8-      Modify reference numbering corresponding to their citation

We do not understand this suggestion. We used the bibliography style provided with the latex template using an external Bibtex file.

In the link https://www.mdpi.com/authors/references

we could read “For LaTeX users we strongly recommend to prepare references with BibTeX”

We also followed the style guide available at

https://mdpi-res.com/data/mdpi_references_guide_v5.pdf

We have checked that this template works in the sense that reference [1] is the first one appearing in the text, reference [2] is the second one appearing in the text, and the same for some other references, and also the last one.

It is true that, e.g. citation to reference [54] appears in page 18, and citation to reference [51] appears in page 19, but this is because of the way in which latex arrange the tables and figures. Since the first reference to table 6 (the one that includes reference [51]) was in subsection 3.3, and the citation to reference [54] was in subsection 5.3, it was a “decission” of Latex, to arrange this citations in this way. Maybe there are some missplacement, but are due to this cause, and we authors have little to do with this. We are sorry for not being being able to address this comment.

Thank you for you comments and your dedication

Reviewer 3 Report

Dear Authors,

The study “Unveiling inertia constants by exploring mass distribution in wind turbine blades and review of the drive train parameters” presents valuable insights into the development of the different bibliographical sources that provide values of blade inertia in kg · m2 by reviewing those.                       

The mechanical characteristics of a wind turbine are essential for understanding its behavior and performance.

The overall structure of the article has sections logically divided. However, the abstract does not provide a concise summary of the research objectives and findings.

The introduction introduces the importance of studying turbine blade inertia and why it matters in the context of wind turbine design and operation.

Methods section provide a foundation for readers to understand the approach taken in the study.

Results section appears to be structured with headings to guide readers through the various results.

The manuscript needs some language editing to improve clarity and readability. There are a few grammatical and typographical errors that should be addressed.

Overall, with some revisions and improvements, this work has the potential to contribute to the understanding of turbine blade inertia and its relationship with geometric parameters.

Author Response

Dear Authors,

The study “Unveiling inertia constants by exploring mass distribution in wind turbine blades and review of the drive train parameters” presents valuable insights into the development of the different bibliographical sources that provide values of blade inertia in kg · m2 by reviewing those.                       

The mechanical characteristics of a wind turbine are essential for understanding its behavior and performance.

Thank you very much for this comment, and thank you for your valuable suggestions.

The overall structure of the article has sections logically divided. However, the abstract does not provide a concise summary of the research objectives and findings.

Yes, it is true that in the 200 words indicated in the mdpi template, it is not possible to provide all motivations and contributions. We have shorten some previous sentences in order to include the following sentences:

“This article aims to solve the issue of the scarcity and unreliability of data on inertia, and gathers the information found on the remaining mechanical parameters.”

And at the end of the abstract

The study also includes a revision of gearboxes, generators, and a blade weight according to their IEC class and material

The introduction introduces the importance of studying turbine blade inertia and why it matters in the context of wind turbine design and operation.

Methods section provide a foundation for readers to understand the approach taken in the study.

Results section appears to be structured with headings to guide readers through the various results.

The manuscript needs some language editing to improve clarity and readability. There are a few grammatical and typographical errors that should be addressed.

After addressing the reviewers’ comment, we have dividide some sentences to clarify the idea that we want to present, specifically:

• before “. If the contingency is not serious… ” at new line 39
• before “. It determines the time interval during which an electrical generator…” at new line 48
• at “system. This ensures the stability and resilience of … “ at new line 60
• “kinetic energy. This alleviates the effect of a …” at new line 66
• “generator. It is also mandatory to know the mechanism”, at new line 78
• “under investigation. Therefore, the researcher” at new line 90
• “actual situation. The alternative is to rely on” at new line 92
• “p.u. It also anticipates some issues” at new line 145
• “that considerably reduces” at new line 165
• “gearbox. Its ratio” at new line 176
• “This is true for turbines driving PMSGs” at new line 232

Finally, we have contracted a proffesional edition service to correct it.

Overall, with some revisions and improvements, this work has the potential to contribute to the understanding of turbine blade inertia and its relationship with geometric parameters.

Thank you for your comments.

Round 2

Reviewer 1 Report

The contributions should be further revised.

Contribution 1, 3 and 5, which are related to references, are not necessary as technical contributions. Thus, they should be deleted.

The other three issues can be regarded as research content, which is what has been done, but not how it was done and what the results are. Thus, it is suggested that the authors please further revise the contributions to make them more technical and theoretical.

Author Response

The contributions should be further revised.

Contribution 1, 3 and 5, which are related to references, are not necessary as technical contributions. Thus, they should be deleted.

In the new version, these paragraphs have been suppressed.

The other three issues can be regarded as research content, which is what has been done, but not how it was done and what the results are. Thus, it is suggested that the authors please further revise the contributions to make them more technical and theoretical.

This part has been rewritten as appears in the following paragraph where the text in red is the result of the modifications done in order to address your comment. The (new) first contribution has been entirely modified to manifest it as a contribution, not a work description. With regard to the second and third contributions, we have tried to incorporate the issues that you suggest. The sentences have not been deeply modified although, in our oppinion, with this modifications the sentences show that the reader will find an expression to accurately estimate the inertia, and a complete formulation for the set of dimensionless variables and parameters involved in the system dynamics.

The theoretical and technical contributions of this paper are to:

• Provide general expressions that allow the weight of the blade to be estimated based not only on its length, but also on the IEC wind class of the turbine and the material of the blade.
• Provide an expression that accurately estimates the blade inertia starting from the position of the CoG, its weight and its length.
• Formulate  in depth a complete dimensionless framework to relate magnitudes and parameters (such as inertia, damping, stiffness and friction) with respect to their base references, valid for systems of three masses and two masses.
  
  

The authors appreciate your time and dedication in the revision of this work.