Study of Torsional Vibration Bifurcation Characteristics of Direct-Drive Wind Turbine Shaft System

Round 1

Reviewer 1 Report

As for Figure4-9, it seems that the results themselves are quite rational. On the other hand, the changes of some results are relatively quite small. So, importance of the changes and the trend is difficult to judge.

That is, the changes is less than 0.1% to the absolute value while the significant digit of the given parameters are sometimes 1 or 2 (i.e. Cm, Ce, Cz, or elements of matrices H2, P etc.)

It should be discuss the sensitivity and allowable range in engineering sense of the results. 

Author Response

Response to comment: It should be discuss the sensitivity and allowable range in engineering sense of the results.

Response: We have made correction according to the Reviewer’s comments. Unify the valid numbers of each matrix parameter and set them to 4. The valid numbers of graphs and tables are set to 3. According to the sensitivity results, combined with the actual engineering practice, set the value of sensitivity is less than 0.1, the degree of influence of parameters on the system can be negligible.

Author Response File: Author Response.docx

Reviewer 2 Report

A file has been uploaded, with "major reviews", although the article as is has to be rejected.

Comments for author File: Comments.pdf

Author Response

1. Response to comment: The mathematical part should be better explained.

Response: A list of symbols has been added after the model introduction in Figure 1, and some unreasonable explanations in the mathematical part have been modified.

 

2. Response to comment: The “compute instances” shows a very limited discussion on a particular data set.

Response: We are very sorry for our oversight and have revised the conclusions regarding the graphs in Figure 2 and Figure 3.

 

3. Response to comment: The parametric effect analysis lack experimental or other authors’ values.

Response: In this article, the purpose of parameter effect analysis is to analyze whether the effect of each parameter on R_i is positive feedback, which needs to be combined with sensitivity analysis in order to obtain the effective regulation of each parameter on system stability. Therefore, the parametric effect analysis can be regarded as a step of the sensitivity analysis.

 

4. Response to comment: The sensitivity analysis, in what point is it calculated?

Response: The formulas for the sensitivity analysis were referred to those in section 3.4 of the literature [12]. and the value of each control parameter was set to the minimum value of the range of values taken for the analysis of the parametric effects adjusted by +20% to analyze the degree of impact on R_i.

 

5. Response to comment: List of symbols (nomenclature) is mandatory for an article at Journal Quality Standards.

Response: A list of symbols has been added and explained.

 

6. Response to comment: The part computes instances that should be renamed.

Response: We have modified some of the unreasonable descriptions in the calculation examples.

 

7. Response to comment: There is a mistake in the parameter naming in the parametric effect analysis.

Response: We are very sorry for our incorrect writing, and the incorrect description of the parameter name in the parameter effect analysis has been corrected.

 

8. Response to comment: Some other people around the world have worked on this particular topic and their results could be mentioned here.

Response: As the Reviewer suggested that we have added some essays by other scholars around the world on the topics covered in this article as references.

Author Response File: Author Response.docx

Reviewer 3 Report

The Study of Torsional Vibration Bifurcation Characteristics of Direct-drive Wind Turbine Shaft System is potentially interesting, however, there are some issues that should be addressed by the authors:

1. The Introduction" sections can be made much more impressive by highlighting your contributions.

2. The contribution of the study should be explained simply and clearly. The authors should further enlarge the Introduction with current work about advanced stability analysis techniques to improve the research background, for example, Analysis of torsional vibration characteristics and time delay feedback control of semi-direct drive cutting transmission system in shearer, Robust Model Predictive Control Paradigm for Automatic Voltage Regulators against Uncertainty Based on Optimization Algorithms; Optimal design of non‐fragile PID controller ‏‏.

3. Clarify how you handle the constraints of the model during the analysis.

4. Clarify the practical implementation of the dynamics model

5. Clarify how you adjust the parameters of the proposed optimization techniques.

6.Increase the quality of the figures

7. Conclusion section should be rearranged. According to the topic of the paper, the authors may propose some interesting problems as future work in the conclusion.

This study may be proposed for publication if it is addressed in the specified problems.

Author Response

1. Response to comment: The Introduction" sections can be made much more impressive by highlighting your contributions.

Response: Replace the contribution in the introduction with the following: This article establishes a kinetic model of the shaft system torsional vibration for direct-drive wind turbine with the phenomenon of unstable shaft system torsional vibration. Based on the Routh-Hurwitz stability theorem, we analyze the range of values of control parameters when the system is stable and the bifurcation phenomenon occurs, reveal the stability domain of the system through the Lyapunov stability theorem, and obtain the action law of parameters on system stability in the torsional vibration system by sensitivity analysis. It provides a reference for the structural design of direct-drive permanent magnet wind turbine.

 

2. Response to comment: The contribution of the study should be explained simply and clearly.

Response: We have made correction according to the Reviewer’s comments. Add the research background of the wind turbine stability study in the “introduction”.

 

3. Response to comment: Clarify how you handle the constraints of the model during the analysis.

Response: According to the definition of the root, the value of  in equation (12) must be greater than or equal to zero. Since the value of each parameter is positive, the value of T must be constrained to be greater than or equal to the value of Tm/Je in the process of system analysis. Similarly, the value of  in Equation (17) is constrained to be greater than or equal to zero.

 

4. Response to comment: Clarify the practical implementation of the dynamics model.

Response: The values of each parameter of a certain type of wind turbine are substituted into the dynamics model of shaft system torsional vibration for system stability analysis. The value of T_m/J_e is calculated to obtain T≥ T_m/J_e according to the definition of the root sign, and furthermore the range of values of the bifurcation parameter T is obtained. Determine another range of values of the bifurcation parameter T according to equation (2.8) and verify the stability of the system at the equilibrium point when calculating T for a subset of the two ranges of values. At the stable equilibrium point, the stability domain of the sought parameters of the system is calculated by substituting the T value.

 

5. Response to comment: Clarify how you adjust the parameters of the proposed optimization techniques.

Response: According to the analysis of the effective regulation and sensitivity of the system parameters, the value of R_i can be adjusted by adjusting the rotor inertia of the generator J_e or the stiffness coefficient K_z of the drive shaft to achieve the control of system stability. When the value of R_i needs to be increased, the value of J_e can be adjusted to increase or decrease the value of K_z, where the value of J_e is more effective. The opposite is also true.

 

6. Response to comment: Increase the quality of the figures.

Response: The quality of the graphics in the article has been replaced.

 

7. Response to comment:  Conclusion section should be rearranged.

Response: This article obtains a range of values for the control parameters when the torsional vibration system is stable and when bifurcation phenomena occur, and the conclusion is supplemented at the end with an analysis of the characteristics of the system when bifurcation phenomena occur at the equilibrium point and how to control them as future work.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors have not corrected what it was explained in the first round. Moreover, it seems that their corrections can be done in less than one week. Something does not fits. A new file with almost the same corrections to be introduced has been uploaded.

Comments for author File: Comments.pdf

Author Response

1. Response to comment: The introduction is really short and it lacks some better problem focusing. Then, the article includes two parts and conclusions, namely: mathematical development, results with parametric analysis and discussion.

Response: The introduction has been revised, and the position of the parametric analysis and sensitivity analysis has been adjusted to make the structure of the paper more reasonable.

 

2. Response to comment:The mathematical part should be better explained. And a list of symbols to follow the equations in a proper way should be mandatory.

Response: Some mathematical parts that need further explanation have been supplemented and a full list of symbols has been added.

 

3. Response to comment: Parametric effects analysis lacks experimental or other authors' values.

Response: Corresponding studies were added as references to the parametric effects analysis.

 

4. Response to comment: The sensitivity analysis, in what point is it calculated?

Response:The sensitivity analysis is related to the value of each design parameter and the bifurcation parameter, and is independent of the value of the equilibrium point. Equation (21) obtains the range of values of the bifurcation parameter T when the system is stable, and Ri is calculated by taking a point within the range of T. Since each design parameter is adjusted by +20%, the value △x/x is equivalent to 20%·x, correspondingly, △R_i/ R_i is equivalent to ((R_i)_1.2x - (R_i)_x) / (R_i)x, and further system sensitivity can be obtained.

 

5. Response to comment: Figure 2 and 3 could be removed..

Response: We fully agree with you that Figures 2 and 3, which have little to do with the full text, have been removed.

 

6. Response to comment: All the graphs should be improved in their lay-out.

Response: All chart formats have been modified and unified.

 

7. Response to comment: Figs. 6 to 9 could be better displayed. And what is (pu) as unit in the Fig. 8?

Response: Improvements have been made to the colors and types of graphics in Figures 6 through 9. Figure 8 (pu) is the standard value, which is a numerical marking method commonly used in power system analysis and engineering calculations, representing the relative values of each physical quantity and parameter, which is dimensionless in this article.

 

8. Response to comment: Some other people around the world have worked on this particular topic and their results could be mentioned here.

Response: As the Reviewer suggested that we have added some essays by other scholars around the world on the topics covered in this article as references.

Author Response File: Author Response.docx

Reviewer 3 Report

no comments

Author Response

Dear Reviewer:

Thanks very much for your kind work. On behalf of my co-authors, we would like to express our great appreciation to editor and reviewers.

Thank you and best regards.

Yours sincerely,

Rongjie Wu

 

Author Response File: Author Response.docx