Analysis of Frequency Regulation Capability and Fatigue Loads of Wind Turbine Based on Over-Speed Control
Round 1
Reviewer 1 Report
l.12 1. Introduction
l.213 use rather term ''simulated WT'' than ''tested WT'', if you work was done virtual
l.270 Is there also any benefits of frequency control? If so you should mention them in the Conclusions.
Author Response
Response to Reviewers’ comments
Dear Reviewers:
Thank you for your comments concerning our manuscript entitled “Analysis of frequency regulation capability and fatigue loads of wind turbine based on over-speed control” (ID: # electronics-2299552). We appreciate for your warm work earnestly. Your comments have greatly helped us improve the quality of our paper. We have re-examined and revised the manuscript again and we hope to get approval. Revised portions are marked in this paper. Please refer to the attachment for specific modifications.
The main corrections in the paper and the responses to the reviewer comments are as flowing:
Reviewer #1:
Comment 1.
l.12 1. Introduction
Authors’ response 1: Thank you for your comment. We have rewritten the introduction。
Line 13 in Page 1:
- Introduction
In recent years, the role of wind turbines (WTs) in the primary frequency regulation of power systems has garnered increased attention [1–4]. Over-speed control is one of the most commonly used primary frequency regulation methods, as it can improve the frequency stability of power systems with high renewable energy penetration [5–9]. However, the frequency regulation capability and fatigue loads of WTs under over-speed control have been seldom analyzed. The aforementioned analysis can provide guidance for the primary frequency regulation of WTs to enhance system frequency stability and prolong their service life.
While over-speed control is a widely used primary frequency regulation method, most research has only focused on the performance of the system frequency [10], neglecting the WT’s response characteristics and stability margin under different wind speeds, de-loading factors, and frequency regulation gains. However, recent studies have highlighted the impact of frequency regulation on fatigue loads, which can accelerate the aging process of the mechanical system due to the high rates of change of torque and power [11,12]. Moreover, field tests have shown that different control methods have significant differences in their impact on fatigue loads [13], and simulation models have been used to examine the trend of fatigue load changes under different control parameters [14]. These studies indicate that under frequency response, the fatigue load on the low-speed shaft and tower increases, with a greater increase in fatigue load as the frequency response parameter becomes larger [15,16]. In addition, the impact of inertial response on low-speed shaft and tower has been evaluated using the power spectral density of system frequency and generator torque [17]. Results indicate that the fatigue load on the low-speed shaft may increase by over 200% under frequency response. One study analyzed the energy transmission path under frequency response using small signal modeling, which showed that the increase in fatigue load is mainly caused by the fluctuation of generator torque under frequency response [18]. However, most of these studies have only focused on the influence of control parameters on fatigue load, neglecting the impact of other factors such as wind speed. Therefore, clarifying the frequency regulation capability of WTs under different states is crucial to determine the frequency regulation gain range and guide the establishment of frequency regulation methods to improve system frequency stability. Additionally, understanding the mechanism of the impact of fatigue load is essential to prolong the service life of WTs and improve their frequency regulation performance.
This paper aims to investigate the frequency regulation capability and fatigue load of WT. The research focuses on addressing the following issues: 1) the establishment of a small-signal model of WT with different generator torque control based on over-speed control, 2) the analysis of the stability margin of the closed-loop control system, 3) the analysis of the response characteristics of the system, and 4) the analysis of the fatigue loads of WT caused by frequency response.
The main contributions of this study are as follows: 1. The establishment of a small signal model of WT with different generator torque control based on over-speed control. 2. The analysis of the stability margin of the closed-loop control system to calculate the range of optimal frequency regulation gain. 3. The analysis of the response characteristics to investigate the effect of wind speed, de-loading factor, and frequency regulation gain on the system frequency. 4. The analysis of the fatigue loads of WT experienced by the drive train, tower, and blade caused by over-speed control.
Another limitation is that the study mainly focuses on the fatigue loads of the low-speed shaft, tower, and blades, while other components of the wind turbine, such as the gearbox and bearings, are not considered. In addition, the study only analyzes the impact of frequency response on WT fatigue loads, and other factors, such as wind shear and turbulence, are not taken into account. Furthermore, the study assumes a linear relationship between the control gain and the system response, which may not always hold in practice. Finally, the study only considers the impact of frequency regulation on the WT itself and does not take into account the impact on the power grid or the interaction between the WT and the power grid.
The paper is organized as follows. Section II introduces the WT control and over-speed control. Section III describes the establishment of WT’s small signal models. Section IV and V analyze the frequency regulation capability and fatigue loads based on over-speed control, respectively. Conclusions are described in Section VI.
Comment 2.
l.213 use rather term ''simulated WT'' than ''tested WT'', if you work was done virtual
Authors’ response 2: The corresponding description has been improved.
Line 244 in Page 12: The parameters of the simulated WT can be found in Table 2.
Comment 3.
l.270 Is there also any benefits of frequency control? If so you should mention them in the Conclusions.
Authors’ response 3: The corresponding description has been improved.
Line 327 in Page 19:
- Conclusions and Discussions
The frequency response of wind turbines is expected to play a crucial role in the future development of power systems, as it can significantly enhance the frequency stability of these systems. For instance, droop control can reduce the maximum frequency deviation, while inertia control can lower the rate of system frequency change.
We tried our best to improve the manuscript and made some changes in the manuscript. Furthermore, we enlisted the help of language professionals to edit and refine the language used in our article. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in revised paper. Once again, thank you very much for your comments and suggestions.
Sincerely,
Yufeng Guo
Reviewer 2 Report
Authors have tried to address the issue of frequency regulation in high wind speed conditions when the likelihood of fluctuations in frequency needs to be controlled. The small signal model and its analysis, as used by the authors, is a strategy in the right direction. Some observations are as under.
1. Authors may wish to list the study's limitations in a separate section, preferably at the start.
2. The bode's plots are interesting. Can authors create a zoom-out of the lines at their point of intersection? This can be put as an insert.
3. Authors have taken a fixed wind turbine and air conditions to do the analysis. Can the authors state somewhere in the work how a change in these values (Table 1) will impact the results? Are these expected or unexpected using the strategy employed?
4. Can authors include a statement towards the end if or not this work was funded?
Author Response
Response to Reviewers’ comments
Dear Reviewers:
Thank you for your comments concerning our manuscript entitled “Analysis of frequency regulation capability and fatigue loads of wind turbine based on over-speed control” (ID: # electronics-2299552). We appreciate for your warm work earnestly. Your comments have greatly helped us improve the quality of our paper. We have re-examined and revised the manuscript again and we hope to get approval. Revised portions are marked in this paper. Please refer to the attachment for specific modifications.
The main corrections in the paper and the responses to the reviewer comments are as flowing:
Reviewer #2:
Authors have tried to address the issue of frequency regulation in high wind speed conditions when the likelihood of fluctuations in frequency needs to be controlled. The small signal model and its analysis, as used by the authors, is a strategy in the right direction. Some observations are as under.
Comment 1.
Authors may wish to list the study's limitations in a separate section, preferably at the start.
Authors’ response 1: Thank you for your comment. The corresponding description has been improved.
Line 58 in Page 2: Another limitation is that the study mainly focuses on the fatigue loads of the low-speed shaft, tower, and blades, while other components of the wind turbine, such as the gearbox and bearings, are not considered. In addition, the study only analyzes the impact of frequency response on WT fatigue loads, and other factors, such as wind shear and turbulence, are not taken into account. Furthermore, the study assumes a linear relationship between the control gain and the system response, which may not always hold in practice. Finally, the study only considers the impact of frequency regulation on the WT itself and does not take into account the impact on the power grid or the interaction between the WT and the power grid.
Comment 2.
The bode's plots are interesting. Can authors create a zoom-out of the lines at their point of intersection? This can be put as an insert.
Authors’ response 2: The corresponding description has been improved.
Line 207 in Page 10: The Bode diagrams of ∆f/∆PLoad under different wind speeds (S1 is 0 or 1) are shown in Fig.12 and Fig.14, with Fig.13 and Fig.15 showing partial enlargements of Fig.12 and Fig.14, respectively.
Page 14: Fig.19 represents a partial enlargement of the Fig.18.
Line 275 in Page 14: It can be seen from Fig.23 that the ∆Ft would increase with a larger kFR below rated wind speed, where Fig.24 is the Partial enlargement of the Fig.23.
Comment 3.
Authors have taken a fixed wind turbine and air conditions to do the analysis. Can the authors state somewhere in the work how a change in these values (Table 1) will impact the results? Are these expected or unexpected using the strategy employed?
Authors’ response 3: The corresponding description has been improved.
Line 303 in Page 18:
4.4. The impact of WT parameters on fatigue load under frequency response
With the development of technology and changes in market demand, the design parameters and operating environment of WT are constantly changing. Therefore, it is necessary to analyze the impact of changes in WT size and operating environment on the fatigue load of WT under frequency response. As wind turbines grow in size, the inertia of the wind rotor tends to increase in tandem. This is due to the increased weight and inertia of the rotor as it expands in size, as well as the need for manufacturers to reinforce the wind rotor structure with additional materials and thickness for enhanced stability and reliability. Consequently, this section will primarily examine how the increase in rotor and generator inertia impacts the fatigue load.
The graph depicted in Fig. 32 illustrates the impact of frequency response on LSS as the inertia constant of the rotor and generator increases below the rated wind speed. The resonant frequency of LSS decreases as the inertia constant rises. Below the resonant frequency of LSS, the influence of frequency response on LSS increases with the inertia constant, while above the resonant frequency, this influence decreases with the inertia constant. The same trend is observed in the influence of frequency response on LSS above the rated wind speed, as shown in Fig. 33. It is important to note that the frequency band of the system fluctuation is typically smaller than the resonant frequency of LSS, meaning that overall, the influence of frequency response on LSS increases with an increase in the inertia constant. Thus, as the rated capacity of the WT grows, the influence of frequency response on LSS will increase. Meanwhile, changes in air density will have no impact. The impact of frequency response on the generator and tower, however, remains relatively constant with changes in the inertia constant, and the results are not displayed.
Comment 4.
Can authors include a statement towards the end if or not this work was funded?
Authors’ response 4: The corresponding description has been improved.
Line 351 in Page 20:
Funding: This work is funded by State Grid Corporation of China. This work was supported by Science and technology projects managed by the headquarters of State Grid Corporation of China under Grant 5108-202299259A-1-0-ZB.
We tried our best to improve the manuscript and made some changes in the manuscript. Furthermore, we enlisted the help of language professionals to edit and refine the language used in our article. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in revised paper. Once again, thank you very much for your comments and suggestions.
Sincerely,
Yufeng Guo
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The work done by the authors are with more mathematical modelling which is good part in this paper.
The following are the points where the authors should incorporate in this paper.
1. Introduction part must be explained more with recent papers.
2. Express about equation 9, 10 and 11 clearly in the content.
3. The analysis of the proposed work must be shown in a comparative table.
The paper can be accepted with the above minor changes.
Author Response
Response to Reviewers’ comments
Dear Reviewers:
Thank you for your comments concerning our manuscript entitled “Analysis of frequency regulation capability and fatigue loads of wind turbine based on over-speed control” (ID: # electronics-2299552). We appreciate for your warm work earnestly. Your comments have greatly helped us improve the quality of our paper. We have re-examined and revised the manuscript again and we hope to get approval. Revised portions are marked in this paper. Please refer to the attachment for specific modifications.
The main corrections in the paper and the responses to the reviewer comments are as flowing:
Reviewer #3:
The work done by the authors are with more mathematical modelling which is good part in this paper.
The following are the points where the authors should incorporate in this paper.
Comment 1.
- Introduction part must be explained more with recent papers.
Authors’ response 1: Thank you for your comment. We have rewritten the introduction.
Line 13 in Page 1:
- Introduction
In recent years, the role of wind turbines (WTs) in the primary frequency regulation of power systems has garnered increased attention [1–4]. Over-speed control is one of the most commonly used primary frequency regulation methods, as it can improve the frequency stability of power systems with high renewable energy penetration [5–9]. However, the frequency regulation capability and fatigue loads of WTs under over-speed control have been seldom analyzed. The aforementioned analysis can provide guidance for the primary frequency regulation of WTs to enhance system frequency stability and prolong their service life.
While over-speed control is a widely used primary frequency regulation method, most research has only focused on the performance of the system frequency [10], neglecting the WT’s response characteristics and stability margin under different wind speeds, de-loading factors, and frequency regulation gains. However, recent studies have highlighted the impact of frequency regulation on fatigue loads, which can accelerate the aging process of the mechanical system due to the high rates of change of torque and power [11,12]. Moreover, field tests have shown that different control methods have significant differences in their impact on fatigue loads [13], and simulation models have been used to examine the trend of fatigue load changes under different control parameters [14]. These studies indicate that under frequency response, the fatigue load on the low-speed shaft and tower increases, with a greater increase in fatigue load as the frequency response parameter becomes larger [15,16]. In addition, the impact of inertial response on low-speed shaft and tower has been evaluated using the power spectral density of system frequency and generator torque [17]. Results indicate that the fatigue load on the low-speed shaft may increase by over 200% under frequency response. One study analyzed the energy transmission path under frequency response using small signal modeling, which showed that the increase in fatigue load is mainly caused by the fluctuation of generator torque under frequency response [18]. However, most of these studies have only focused on the influence of control parameters on fatigue load, neglecting the impact of other factors such as wind speed. Therefore, clarifying the frequency regulation capability of WTs under different states is crucial to determine the frequency regulation gain range and guide the establishment of frequency regulation methods to improve system frequency stability. Additionally, understanding the mechanism of the impact of fatigue load is essential to prolong the service life of WTs and improve their frequency regulation performance.
This paper aims to investigate the frequency regulation capability and fatigue load of WT. The research focuses on addressing the following issues: 1) the establishment of a small-signal model of WT with different generator torque control based on over-speed control, 2) the analysis of the stability margin of the closed-loop control system, 3) the analysis of the response characteristics of the system, and 4) the analysis of the fatigue loads of WT caused by frequency response.
The main contributions of this study are as follows: 1. The establishment of a small signal model of WT with different generator torque control based on over-speed control. 2. The analysis of the stability margin of the closed-loop control system to calculate the range of optimal frequency regulation gain. 3. The analysis of the response characteristics to investigate the effect of wind speed, de-loading factor, and frequency regulation gain on the system frequency. 4. The analysis of the fatigue loads of WT experienced by the drive train, tower, and blade caused by over-speed control.
Another limitation is that the study mainly focuses on the fatigue loads of the low-speed shaft, tower, and blades, while other components of the wind turbine, such as the gearbox and bearings, are not considered. In addition, the study only analyzes the impact of frequency response on WT fatigue loads, and other factors, such as wind shear and turbulence, are not taken into account. Furthermore, the study assumes a linear relationship between the control gain and the system response, which may not always hold in practice. Finally, the study only considers the impact of frequency regulation on the WT itself and does not take into account the impact on the power grid or the interaction between the WT and the power grid.
The paper is organized as follows. Section II introduces the WT control and over-speed control. Section III describes the establishment of WT’s small signal models. Section IV and V analyze the frequency regulation capability and fatigue loads based on over-speed control, respectively. Conclusions are described in Section VI.
[1] Cheng, Y.; Azizipanah-Abarghooee, R.; Azizi, S.; Ding, L.; Terzija, V. Smart frequency control in low inertia energy systems based on frequency response techniques: A review. Applied Energy 2020, 279, 115798.
[2] Yao, Q.; Li, S.; He, J.; Cai, W.; Hu, Y. New design of a wind farm frequency control considering output uncertainty and fatigue suppression. Energy Reports 2023, 9, 1436–1446.
[3] Guan, M. Scheduled Power Control and Autonomous Energy Control of Grid-Connected Energy Storage System (ESS) With Virtual Synchronous Generator and Primary Frequency Regulation Capabilities. IEEE Transactions on Power Systems 2022, 37, 942–954.
[4] Björk, J.; Pombo, D.V.; Johansson, K.H. Variable-Speed Wind Turbine Control Designed for Coordinated Fast Frequency Reserves. IEEE Transactions on Power Systems 2022, 37, 1471–1481.
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Comment 2.
Express about equation 9, 10 and 11 clearly in the content.
Authors’ response 2: The corresponding description has been improved.
Line 114 in Page 5:
Comment 3.
The analysis of the proposed work must be shown in a comparative table.
Authors’ response 3: The corresponding description has been improved.
We tried our best to improve the manuscript and made some changes in the manuscript. Furthermore, we enlisted the help of language professionals to edit and refine the language used in our article. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in revised paper. Once again, thank you very much for your comments and suggestions.
Sincerely,
Yufeng Guo
Author Response File: 
Author Response.docx
