Motion Control of Pentapod Offshore Wind Turbines under Earthquakes by Tuned Mass Damper
Abstract
:1. Introduction
2. Theories for the Seismic Analysis of OWT
2.1. Seismic Analysis of an Integrated OWT Model
2.2. Integrated Model of OWT for Seismic Analysis
2.3. Load Cases for Seismic Analysis of OWT
3. Structural Responses of the OWT under Seismic Loads
3.1. Dynamic Characteristics of OWT
3.2. Acceleration Responses
- (1)
- Other than the first two natural frequencies of OWT, the higher-order frequency components dominate the tower accelerations under earthquakes, especially for the Northridge seismic wave.
- (2)
- For the nacelle accelerations of the OWT under seismic excitations, the responses are mainly dominated by the first two natural frequencies of the OWT.
- (3)
- Under the El Centro and Taft seismic waves, the fifth natural frequency of the OWT dominates the tower accelerations, as shown in Figure 8a,b.
- (4)
- Figure 8c demonstrates that the higher-order frequency components are stimulated under the Northridge seismic wave, which influence the tower accelerations significantly.
- (5)
- Under the Chichi seismic wave, the influence of the first three natural frequencies of the OWT on the tower accelerations is non-negligible, as shown in Figure 8d.
3.3. Mudline Bending Moment
4. Vibration Control of OWT using TMD
4.1. Governing Equation of Motion of OWT with TMD
4.2. Design of TMDs for OWT under Earthquakes
4.3. Influence of Seismic Waves with Varying PGAs on Vibration Control
4.3.1. Control Effect of TMD on the NAA
4.3.2. Control Effect of TMD on the Mudline Bending Moment
4.4. Influence of the Seismic Excitations on Vibration Control
4.4.1. Control Effect of TMD on NAA under Different Seismic Excitations
4.4.2. Variations in Bending Moments by TMD under Different Seismic Excitations
4.5. Influence of TMD’s Mass Ratio on Vibration Control
4.5.1. Influence of TMD’s Mass Ratio on the Reduction in NAAs
4.5.2. Influence of TMD’s Mass Ratio on the Reduction in Bending Moments
4.6. Influence of TMD’s Location on Vibration Control
4.6.1. Influence of TMD’s Location on the Reduction of NAAs
4.6.2. Influence of TMD’s Location on Reduction in Bending Moments
4.7. Influence of TMD’s Tuning Frequency on Vibration Control
4.7.1. Influence of TMD’s Tuning Frequency on the Reduction in NAAs
4.7.2. Influence of TMD’s Frequency on the Reduction in Bending Moment
5. Conclusions
- (1)
- From the results that the mudline bending moments are influenced by the mode of the rotor blade, the influence of the rotor system on the motion of the support system cannot be neglected in the seismic analysis of OWTs. Thus, it is of necessity to establish the integrated model of the OWT to obtain reasonable structural responses under earthquakes.
- (2)
- For the tower accelerations, the seismic excitations can stimulate higher-order frequency components and it can become the dominant frequency for the structural responses, especially for the seismic waves with abundant frequencies around the natural frequencies of OWTs, such as the Northridge seismic wave.
- (3)
- Using TMD, the influences of the PGA and type of seismic excitation on the control effects of the OWT are investigated. It can be observed that these parameters of the input seismic wave can influence the control effects of TMD remarkably.
- (4)
- The parameters of TMD, such as the tuning frequency and location, are more essentials than the mass ratio in the design of TMD. The higher-order dominant frequencies are proved as the more effective tuning frequencies for reducing the structural responses of the OWT under seismic excitations; e.g., TMD tuned with the second natural frequency of the OWT can achieve more effective control than the TMD tuned with the fundamental frequency.
- (5)
- The locations of TMD installed in nacelle or tower base are validated as the appropriate locations to control the nacelle accelerations and bending moments of the OWT.
- (6)
- The studies prove that the control effects of the TMD can be improved by increasing the mass of the TMD only when an effective tuning frequency and location are adopted.
- (7)
- Limited control effects of TMDs are observed when the structural responses are composed of multi-dominant frequencies, such as the nacelle accelerations and bending moments under the Chichi seismic wave. Additional tuning frequencies or more TMDs may be necessary to achieve significant control effects under such load cases.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Seismic Waves | PGA (g) | State | Winds and Waves | Seismic Direction |
---|---|---|---|---|
El Centro | 0.21 | Parked | - | In F-A direction |
Taft | 0.16 | Parked | - | In F-A direction |
Northridge | 0.13 | Parked | - | In F-A direction |
Chichi | 0.37 | Parked | - | In F-A direction |
Order of the Frequency | Values (Hz) | Note |
---|---|---|
1st OWT | 0.305 | In F-A direction |
1st Flap | 0.690 | First blade collective flap mode |
2nd OWT | 0.742 | In F-A direction |
3rd OWT | 1.544 | |
4rd OWT | 1.824 | |
2nd Flap | 2.029 | Second blade collective flap mode |
5th OWT | 2.521 | In F-A direction |
6th OWT | 3.640 | |
7th OWT | 4.620 |
Maximum Values | Seismic Excitations | |||
---|---|---|---|---|
El Centro | Taft | Northridge | Chichi | |
Peak ground acceleration (PGAs) (m/s2) | 2.06 | 1.57 | 1.27 | 3.63 |
Nacelle acceleration (NAAs) (m/s2) | 1.58 | 0.97 | 0.75 | 2.87 |
DAF of NAA | 0.77 | 0.62 | 0.59 | 0.79 |
Acceleration at the tower top (TTAs) (m/s2) | 4.66 | 2.82 | 6.84 | 7.28 |
DAF of TTA | 2.26 | 1.80 | 5.39 | 2.01 |
Maximum acceleration along the height of the tower (MTAs) (m/s2) | 5.82 | 3.62 | 8.08 | 9.29 |
DAF of MTA | 2.83 | 2.31 | 6.36 | 2.56 |
TMD No. | Optimised Parameters | Parameters of TMD | TMD Location | |||||
---|---|---|---|---|---|---|---|---|
μm (%) | fopt | ζopt | MTMD (kg) | fTMD (Hz) | KTMD (N/m) | CTMD (N/ms−1) | ||
TMD 01 | 1.0 | 0.993 | 0.05 | 14,897 | 0.303 | 52,148 | 2787 | Nacelle |
TMD 02 | 2.0 | 0.985 | 0.07 | 29,795 | 0.300 | 102,769 | 7826 | |
TMD 03 | 3.0 | 0.978 | 0.09 | 44,692 | 0.298 | 151,923 | 14,272 | |
TMD 04 | 1.0 | 0.993 | 0.05 | 14,897 | 0.303 | 52,148 | 2787 | Tower base |
TMD 05 | 2.0 | 0.985 | 0.07 | 29,795 | 0.300 | 102,769 | 7826 | |
TMD 06 | 3.0 | 0.978 | 0.09 | 44,692 | 0.298 | 151,923 | 14,272 | |
TMD 07 | 1.0 | 0.993 | 0.05 | 14,897 | 0.736 | 311,315 | 6810 | Nacelle |
TMD 08 | 2.0 | 0.985 | 0.07 | 29,795 | 0.734 | 613,518 | 19,120 | |
TMD 09 | 3.0 | 0.978 | 0.09 | 44,692 | 0.726 | 906,962 | 34,871 | |
TMD 10 | 1.0 | 0.993 | 0.05 | 14,897 | 0.736 | 311,315 | 6810 | Tower base |
TMD 11 | 2.0 | 0.985 | 0.07 | 29,795 | 0.734 | 613,518 | 19,120 | |
TMD 12 | 3.0 | 0.978 | 0.09 | 44,692 | 0.726 | 906,962 | 34,871 |
Case No. | Seismic excitation | State of OWT | TMD No. |
---|---|---|---|
T1–T12 | El Centro (0.1 g) | Parked | TMD01–12 |
T13–T24 | El Centro (0.15 g) | TMD01–12 | |
T25–T36 | El Centro (0.2 g) | TMD01–12 | |
T37–T48 | El Centro (0.4 g) | TMD01–12 | |
T49–T60 | Taft | TMD01–12 | |
T61–T72 | Northridge | TMD01–12 | |
T73–T84 | Chichi | TMD01–12 |
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Wang, W.; Li, X.; Pan, Z.; Zhao, Z. Motion Control of Pentapod Offshore Wind Turbines under Earthquakes by Tuned Mass Damper. J. Mar. Sci. Eng. 2019, 7, 224. https://doi.org/10.3390/jmse7070224
Wang W, Li X, Pan Z, Zhao Z. Motion Control of Pentapod Offshore Wind Turbines under Earthquakes by Tuned Mass Damper. Journal of Marine Science and Engineering. 2019; 7(7):224. https://doi.org/10.3390/jmse7070224
Chicago/Turabian StyleWang, Wenhua, Xin Li, Zuxing Pan, and Zhixin Zhao. 2019. "Motion Control of Pentapod Offshore Wind Turbines under Earthquakes by Tuned Mass Damper" Journal of Marine Science and Engineering 7, no. 7: 224. https://doi.org/10.3390/jmse7070224