Abstract

Offshore wind turbines (OWTs) are subjected to multi-hazards of wind, wave, and seismic loads, and excessive vibrations may occur in the support structure. To effectively alleviate these vibrations, an active tuned mass damper (TMD) is considered to be installed in the nacelle in this study. Based on Euler–Lagrange's equations, the OWT with an active TMD is modeled by a multi-modal model incorporating the structural dynamics, seismic, hydrodynamic, and aerodynamic loads as well as the active control system. The active TMD is regulated using the linear quadratic regulator controller. In this study, the dynamic responses of the uncontrolled monopile OWT are initially examined, followed by a comparison of the dynamic responses of the controlled monopile OWT. Moreover, the performance of the active structural control strategy is evaluated as the weighting matrices and optimal TMD parameters are varied. According to the results of the study, it indicates that seismic load significantly excites the fundamental vibration modes of the support structure, resulting in a notable increase in the nacelle's fore-aft displacements. Both the designed passive and active TMDs effectively reduce these vibrations, with the active TMD providing superior vibration control performance. The vibration suppression performance of the passive TMD is severely reduced when the stiffness parameter deviates significantly from the optimal value, whereas the active TMD can effectively compensate for this drawback.

References

1.
Asareh
,
M. A.
,
Schonberg
,
W.
, and
Volz
,
J.
,
2016
, “
Effects of Seismic and Aerodynamic Load Interaction on Structural Dynamic Response of Multi-Megawatt Utility Scale Horizontal Axis Wind Turbines
,”
Renew. Energy
,
86
, pp.
49
58
.
2.
Asareh
,
M. A.
,
Prowell
,
I.
,
Volz
,
J.
, and
Schonberg
,
W.
,
2016
, “
A Computational Platform for Considering the Effects of Aerodynamic and Seismic Load Combination for Utility Scale Horizontal Axis Wind Turbines
,”
Earthquake Eng. Eng. Vib.
,
15
(
1
), pp.
91
102
.
3.
Yang
,
Y.
,
Ye
,
K.
,
Li
,
C.
,
Michailides
,
C.
, and
Zhang
,
W.
,
2018
, “
Dynamic Behavior of Wind Turbines Influenced by Aerodynamic Damping and Earthquake Intensity
,”
Wind Energy
,
21
(
5
), pp.
303
319
.
4.
Yang
,
Y.
,
Bashir
,
M.
,
Li
,
C.
, and
Wang
,
J.
,
2019
, “
Analysis of Seismic Behaviour of an Offshore Wind Turbine With a Flexible Foundation
,”
Ocean Eng.
,
178
, pp.
215
228
.
5.
Xi
,
R.
,
Xu
,
C.
,
Du
,
X.
,
El Naggar
,
M. H.
,
Wang
,
P.
,
Liu
,
L.
, and
Zhai
,
E.
,
2022
, “
Framework for Dynamic Response Analysis of Monopile Supported Offshore Wind Turbine Excited by Combined Wind-Wave-Earthquake Loading
,”
Ocean Eng.
,
247
, p.
110743
.
6.
Liu
,
Y.
,
Li
,
X.
,
Shi
,
W.
,
Wang
,
W.
, and
Jiang
,
Z.
,
2024
, “
Vibration Control of a Monopile Offshore Wind Turbines Under Recorded Seismic Waves
,”
Renew. Energy
,
226
, p.
120455
.
7.
Wani
,
Z. R.
,
Tantray
,
M.
,
Farsangi
,
E. N.
,
Nikitas
,
N.
,
Noori
,
M.
,
Samali
,
B.
, and
Yang
,
T. Y.
,
2022
, “
A Critical Review on Control Strategies for Structural Vibration Control
,”
Annu. Rev. Control
,
54
, pp.
103
124
.
8.
Xie
,
F.
, and
Aly
,
A. M.
,
2020
, “
Structural Control and Vibration Issues in Wind Turbines: A Review
,”
Eng. Struct.
,
210
, p.
110087
.
9.
Zuo
,
H.
,
Bi
,
K.
, and
Hao
,
H.
,
2020
, “
A State-of-the-Art Review on the Vibration Mitigation of Wind Turbines
,”
Renew. Sustain. Energy Rev.
,
121
, p.
109710
.
10.
Murtagh
,
P. J.
,
Ghosh
,
A.
,
Basu
,
B.
, and
Broderick
,
B. M.
,
2008
, “
Passive Control of Wind Turbine Vibrations Including Blade/Tower Interaction and Rotationally Sampled Turbulence
,”
Wind Energy
,
11
(
4
), pp.
305
317
.
11.
Stewart
,
G. M.
, and
Lackner
,
M. A.
,
2014
, “
The Impact of Passive Tuned Mass Dampers and Wind–Wave Misalignment on Offshore Wind Turbine Loads
,”
Eng. Struct.
,
73
, pp.
54
61
.
12.
Wang
,
W.
,
Li
,
X.
,
Zhao
,
H.
,
Wang
,
B.
, and
Li
,
Y.
,
2020
, “
Vibration Control of a Pentapod Offshore Wind Turbine Under Combined Seismic Wind and Wave Loads Using Multiple Tuned Mass Damper
,”
Appl. Ocean Res.
,
103
, p.
102254
.
13.
Zuo
,
H.
,
Bi
,
K.
, and
Hao
,
H.
,
2017
, “
Using Multiple Tuned Mass Dampers to Control Offshore Wind Turbine Vibrations Under Multiple Hazards
,”
Eng. Struct.
,
141
, pp.
303
315
.
14.
Yang
,
Y.
,
Bashir
,
M.
,
Li
,
C.
,
Michailides
,
C.
, and
Wang
,
J.
,
2020
, “
Mitigation of Coupled Wind-Wave-Earthquake Responses of a 10 MW Fixed-Bottom Offshore Wind Turbine
,”
Renew. Energy
,
157
, pp.
1171
1184
.
15.
Colwell
,
S.
, and
Basu
,
B.
,
2009
, “
Tuned Liquid Column Dampers in Offshore Wind Turbines for Structural Control
,”
Eng. Struct.
,
31
(
2
), pp.
358
368
.
16.
Chen
,
J.
,
Liu
,
Y.
, and
Bai
,
X.
,
2015
, “
Shaking Table Test and Numerical Analysis of Offshore Wind Turbine Tower Systems Controlled by TLCD
,”
Earthquake Eng. Eng. Vib.
,
14
(
1
), pp.
55
75
.
17.
Hemmati
,
A.
,
Oterkus
,
E.
, and
Barltrop
,
N.
,
2019
, “
Fragility Reduction of Offshore Wind Turbines Using Tuned Liquid Column Dampers
,”
Soil Dyn. Earthquake Eng.
,
125
, p.
105705
.
18.
Sun
,
C.
, and
Jahangiri
,
V.
,
2018
, “
Bi-Directional Vibration Control of Offshore Wind Turbines Using a 3D Pendulum Tuned Mass Damper
,”
Mech. Syst. Signal Process
,
105
, pp.
338
360
.
19.
Sun
,
C.
, and
Jahangiri
,
V.
,
2019
, “
Fatigue Damage Mitigation of Offshore Wind Turbines Under Real Wind and Wave Conditions
,”
Eng. Struct.
,
178
, pp.
472
483
.
20.
Sun
,
C.
,
Jahangiri
,
V.
, and
Sun
,
H.
,
2019
, “
Performance of a 3D Pendulum Tuned Mass Damper in Offshore Wind Turbines Under Multiple Hazards and System Variations
,”
Smart Struct. Syst.
,
24
(
1
), pp.
53
65
.
21.
Jahangiri
,
V.
,
Sun
,
C.
, and
Kong
,
F.
,
2021
, “
Study on a 3D Pounding Pendulum TMD for Mitigating Bi-Directional Vibration of Offshore Wind Turbines
,”
Eng. Struct.
,
241
, p.
112383
.
22.
Liu
,
G.
,
Lei
,
Z.
, and
Wang
,
H.
,
2022
, “
Investigation and Optimization of a Pre-Stressed Tuned Mass Damper for Wind Turbine Tower
,”
Struct. Control Health Monit.
,
29
(
3
), p.
e2894
.
23.
Liu
,
G.
,
Lei
,
Z.
,
Law
,
S. S.
, and
Yang
,
Q.
,
2023
, “
The Nonlinear Behavior of Prestressed Tuned Mass Damper for Vibration Control of Wind Turbine Towers
,”
Nonlinear Dyn.
,
111
(
12
), pp.
10939
10955
.
24.
Lei
,
Z.
,
Liu
,
G.
, and
Wen
,
M.
,
2023
, “
Vibration Attenuation for Offshore Wind Turbine by a 3D Prestressed Tuned Mass Damper Considering the Variable Pitch and Yaw Behaviors
,”
Ocean Eng.
,
281
, p.
114741
.
25.
Lei
,
Z.
,
Liu
,
G.
,
Zhang
,
X.
,
Yang
,
Q.
, and
Law
,
S. S.
,
2023
, “
Three-Dimensional Prestressed Tuned Mass Damper for Passive Vibration Control of Coupled Multiple DOFs Offshore Wind Turbine
,”
Struct. Control Health Monit.
,
2023
, p.
8897653
.
26.
Lei
,
Z.
,
Liu
,
G.
,
Cong
,
Y.
, and
Tang
,
W.
,
2024
, “
Research on Fatigue Damage Mitigation of Offshore Wind Turbines by a Bi-Directional PSTMD Under Stochastic Wind-Wave Actions
,”
Eng. Struct.
,
301
, p.
117275
.
27.
Liu
,
X.
,
Xu
,
J.
,
He
,
G.
, and
Chen
,
C.
,
2022
, “
Lateral Vibration Mitigation of Monopile Offshore Wind Turbines With a Spring Pendulum Pounding Tuned Mass Damper
,”
Ocean Eng.
,
266
, p.
112954
.
28.
Ding
,
H.
,
Zhang
,
Z.
,
Wang
,
J.
,
Zhang
,
J.
, and
Altay
,
O.
,
2024
, “
Multiscale Fluid–Structure Coupled Real-Time Hybrid Simulation of Monopile Wind Turbines With Vibration Control Devices
,”
Mech. Syst. Signal Process
,
215
, p.
111439
.
29.
Ding
,
H.
,
Chen
,
Y.-N.
,
Wang
,
J.-T.
, and
Altay
,
O.
,
2022
, “
Numerical Analysis of Passive Toroidal Tuned Liquid Column Dampers for the Vibration Control of Monopile Wind Turbines Using FVM and FEM
,”
Ocean Eng.
,
247
, p.
110637
.
30.
Ding
,
H.
,
Wang
,
W.
,
Liu
,
J.-F.
,
Wang
,
J.-T.
,
Le
,
Z.-J.
,
Zhang
,
J.
, and
Yu
,
G.-M.
,
2023
, “
On the Size Effects of Toroidal Tuned Liquid Column Dampers for Mitigating Wind-and Wave-Induced Vibrations of Monopile Wind Turbines
,”
Ocean Eng.
,
273
, p.
113988
.
31.
Ding
,
H.
,
Altay
,
O.
, and
Wang
,
J.-T.
,
2023
, “
Lateral Vibration Control of Monopile Supported Offshore Wind Turbines With Toroidal Tuned Liquid Column Dampers
,”
Eng. Struct.
,
286
, p.
116107
.
32.
Buckley
,
T.
,
Watson
,
P.
,
Cahill
,
P.
,
Jaksic
,
V.
, and
Pakrashi
,
V.
,
2018
, “
Mitigating the Structural Vibrations of Wind Turbines Using Tuned Liquid Column Damper Considering Soil-Structure Interaction
,”
Renew. Energy
,
120
, pp.
322
341
.
33.
Arrigan
,
J.
,
Pakrashi
,
V.
,
Basu
,
B.
, and
Nagarajaiah
,
S.
,
2011
, “
Control of Flapwise Vibrations in Wind Turbine Blades Using Semi-Active Tuned Mass Dampers
,”
Struct. Control Health Monit.
,
18
(
8
), pp.
840
851
.
34.
Chen
,
J.
,
Yuan
,
C.
,
Li
,
J.
, and
Xu
,
Q.
,
2015
, “
Semi-Active Fuzzy Control of Edgewise Vibrations in Wind Turbine Blades Under Extreme Wind
,”
J. Wind Eng. Ind. Aerodyn.
,
147
, pp.
251
261
.
35.
Sun
,
C.
,
2018
, “
Mitigation of Offshore Wind Turbine Responses Under Wind and Wave Loading: Considering Soil Effects and Damage
,”
Struct. Control Health Monit.
,
25
(
3
), p.
e2117
.
36.
Sun
,
C.
,
2018
, “
Semi-Active Control of Monopile Offshore Wind Turbines Under Multi-Hazards
,”
Mech. Syst. Signal Process
,
99
, pp.
285
305
.
37.
Hemmati
,
A.
, and
Oterkus
,
E.
,
2018
, “
Semi-Active Structural Control of Offshore Wind Turbines Considering Damage Development
,”
J. Mar. Sci. Eng.
,
6
(
3
), p.
102
.
38.
Jiang
,
J.
,
Dong
,
X.
,
Lian
,
J.
, and
Jia
,
Y.
,
2024
, “
Research on Semi-Active Vibration Reduction of Offshore Wind Turbine Structure Combined Eddy Current Theory With Tuned Mass Dampers
,”
Renew. Energy
,
234
, p.
121185
.
39.
Staino
,
A.
,
Basu
,
B.
, and
Nielsen
,
S. R. K.
,
2012
, “
Actuator Control of Edgewise Vibrations in Wind Turbine Blades
,”
J. Sound Vib.
,
331
(
6
), pp.
1233
1256
.
40.
Fitzgerald
,
B.
,
Sarkar
,
S.
, and
Staino
,
A.
,
2018
, “
Improved Reliability of Wind Turbine Towers With Active Tuned Mass Dampers (ATMDs)
,”
J. Sound Vib.
,
419
, pp.
103
122
.
41.
Fitzgerald
,
B.
, and
Basu
,
B.
,
2016
, “
Structural Control of Wind Turbines With Soil Structure Interaction Included
,”
Eng. Struct.
,
111
, pp.
131
151
.
42.
Jonkman
,
J.
, and
Musial
,
W.
,
2010
, “
Offshore Code Comparison Collaboration (OC3) for IEA Wind Task 23 Offshore Wind Technology and Deployment
,”
National Renewable Energy Laboratory
,
Golden, CO
.
43.
Jonkman J
,
M.
,
Butterfield
,
S.
,
Musial
,
W.
, and
Scott
,
G.
,
2009
, “
Definition of a 5-MW Reference Wind Turbine for Offshore System Development
,” NREL/TP-500-38060,
National Renewable Energy Laboratory
,
Golden, CO
.
44.
Bir
,
G.
,
2013
, “
Blades and Towers Modal Analysis Code (BModes): Verification of Blade Modal Analysis Capability
,”
American Institute of Aeronautics & Astronautics Inc.
,
New York
.
45.
Sun
,
C.
, and
Jahangiri
,
V.
,
2017
, “
Mitigation of Offshore Wind Turbines Under Wind and Wave Loading
,”
The 13th Americas Conference on Wind Engineering (13ACWE)
,
Gainesville, FL
,
May 21–24
.
46.
Li
,
C.
,
Hao
,
H.
,
Li
,
H.
, and
Bi
,
K.
,
2015
, “
Theoretical Modeling and Numerical Simulation of Seismic Motions at Seafloor
,”
Soil Dyn. Earthquake Eng.
,
77
, pp.
220
225
.
47.
Chiou
,
B.
,
Darragh
,
R.
,
Gregor
,
N.
, and
Silva
,
W.
,
2008
, “
NGA Project Strong-Motion Database
,”
Earthquake Spectra
,
24
(
1
), pp.
23
44
.
48.
Fitzgerald
,
B.
,
Basu
,
B.
, and
Nielsen
,
S. R. K.
,
2013
, “
Active Tuned Mass Dampers for Control of In-Plane Vibrations of Wind Turbine Blades
,”
Struct. Control Health Monit.
,
20
(
12
), pp.
1377
1396
.
49.
Fitzgerald
,
B.
, and
Basu
,
B.
,
2014
, “
Cable Connected Active Tuned Mass Dampers for Control of In-Plane Vibrations of Wind Turbine Blades
,”
J. Sound Vib.
,
333
(
23
), pp.
5980
6004
.
50.
Den Hartog
,
J. P.
,
1985
,
Mechanical Vibrations
,
Courier Corporation
,
North Chelmsford, MA
.
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