Abstract
New concepts of floaters have been developed for multimegawatt wind turbines aiming to reduce the cost of renewable energy generation in deep waters. This paper presents the preliminary design and tuning of a linear quadratic regulator (LQR) for a floating offshore wind turbine (FOWT) constituted of the DTU 10-MW offshore reference wind turbine (RWT) and the CENTEC-TLP tension leg platform (TLP). The goal of the LQR is to improve the performance of the 10-MW CENTEC-TLP FOWT above the rated wind speed using the collective blade pitch actuator within the saturation limits. The LQR design is based on a verified control-oriented FOWT model considering the measurement of surge and pitch floater motions in addition to the rotor speed. Wind and wave disturbances are assumed to be unmeasured. The LQR performance is evaluated for two above-rated operational cases, involving normal and extreme turbulence models combined with relevant sea states. Simulation results show that the designed LQR can yield a reduction of approximately 67% in the rotor speed and power standard deviations compared with a baseline proportional-integral (PI) controller. With the baseline controller, the maximum rotor speed and maximum electrical power are about 15% higher than the rated speed and power, respectively, while this value is reduced to about 6% with the LQR controller. The designed LQR can also yield a TLP pitch reduction of approximately 21%, while keeping the surge amplitude and nacelle axial acceleration below their respective limits.
Similar content being viewed by others
Data availability
Not applicable.
Code availability
Not applicable.
References
C. Bak, F. Zahle, R. Bitsche, T. Kim, A. Yde, L.C. Henriksen, A. Natarajan, M.H. Hansen, Description of the DTU 10 MW reference wind turbine. DTU Wind Energy Report-I-0092. Technical University of Denmark, Roskilde, Denmark (2013)
E. Uzunoglu, C.G. Soares, Hydrodynamic design of a free-float capable tension leg platform for a 10 MW wind turbine. Ocean Eng. 197, 106888 (2020). https://doi.org/10.1016/j.oceaneng.2019.106888
F. Vittori, O. Pires, J. Azcona, E. Uzunoglu, C.G. Soares, R.Z. Rodríguez, A. Souto-Iglesias, Hybrid scaled testing of a 10 MW TLP floating wind turbine using the SiL method to integrate the rotor thrust and moments, in Developments in Renewable Energies Offshore. ed. by C.G. Soares (Taylor & Francis Group, London, 2021), pp.417–423
J. Mas-Soler, E. Uzunoglu, C.G. Soares, G. Bulian, A. Souto-Iglesias, Transportation tests of the CENTEC-TLP concept in waves, in Developments in Renewable Energies Offshore. ed. by C.G. Soares (Taylor & Francis Group, London, 2021), pp.399–407
L.F.A. Tavares, M. Shadman, L.P.F. Assad, C. Silva, L. Landau, S.F. Estefen, Assessment of the offshore wind technical potential for the Brazilian Southeast and South regions. Energy 196, 117097 (2020). https://doi.org/10.1016/j.energy.2020.117097
E.A. Bossanyi, G. Ramtharan, B. Savini, The importance of control in wind turbine design and loading, in Proceedings of the 17th IEEE Mediterranean Conference on Control & Automation, June 24–26, Thessaloniki, Greece (2009). https://doi.org/10.1109/MED.2009.5164721
J.M. Jonkman, Influence of control on the pitch damping of a floating wind turbine. Conference Paper NREL/CP-500-42589. Natl. Renew. Energy Lab. (2008)
T.J. Larsen, T.D. Hanson, A method to avoid negative damped low frequent tower vibrations for a floating, pitch controlled wind turbine: the science of making torque from wind. J. Phys. Conf. Ser. 75(012073), 1–11 (2007). https://doi.org/10.1088/1742-6596/75/1/012073
DNV, Standard DNV-ST-0119: Floating wind turbine structures (2021)
B.D.O. Anderson, J.B. Moore, Optimal Control: Linear Quadratic Methods (Dover, New York, 2007)
IEA; IRENA; UNSD; WORLD BANK, WHO, Tracking SDG 7: the energy progress report (World Bank, Washington, DC, 2022)
O. Bagherieh, R. Nagamune, Gain-scheduling control of a floating offshore wind turbine above rated wind speed. Control Theory Technol. 13(2), 160–172 (2015). https://doi.org/10.1007/s11768-015-4152-0
S. Christiansen, T. Knudsen, T. Bak, Optimal control of a ballast-stabilized floating wind turbine, in Proceedings of IEEE International Symposium on Computer-Aided Control System Design (CACSD), Denver (2011). https://doi.org/10.1109/CACSD.2011.6044574
F. Lemmer, D. Schlipf, P.W. Cheng, Control design methods for floating wind turbines for optimal disturbance rejection: the science of making torque from wind. J. Phys. Conf. Ser. 753(092006), 1–14 (2016). https://doi.org/10.1088/1742-6596/753/9/092006
E. Lindeberg, Optimal control of floating offshore wind turbines. Master of Science Thesis, NTNU, Trondheim (2009)
H. Namik, K. Stol, Individual blade pitch control of a spar-buoy floating wind turbine. IEEE Trans. Cont. Sys. Tech. 22(1), 214–223 (2014). https://doi.org/10.1109/TCST.2013.2251636
L. Pustina, C. Lugni, G. Bernardini, J. Serafini, M. Gennaretti, Control of power generated by a floating offshore wind turbine perturbed by sea waves. Renew. Sustain. Energy Rev. 132, 109984 (2020). https://doi.org/10.1016/j.rser.2020.109984
R.L.C.B. Ramos, Effect of turbulence intensity on the linear quadratic control of spar buoy floating wind turbines. Mar. Syst. Ocean Technol. 16, 84–98 (2021). https://doi.org/10.1007/s40868-021-00098-4
R.L. Ramos, Linear quadratic optimal control of a spar-type floating offshore wind turbine in the presence of turbulent wind and different sea states. J. Mar. Sci. Eng. 6(4), 151 (2018). https://doi.org/10.3390/jmse6040151
G. Betti, M. Farina, G.A. Guagliardi, A. Marzorati, R. Scattolini, Development of a control-oriented model of floating wind turbines. IEEE Trans. Cont. Sys. Tech. 22(1), 69–82 (2014). https://doi.org/10.1109/TCST.2013.2242073
Z. Wu, Y. Li, Platform stabilization and load reduction of floating offshore wind turbines with tension-leg platform using dynamic vibration absorbers. Wind Energy 23(3), 711–730 (2020). https://doi.org/10.1002/we.2453
N.J. Abbas, D.S. Zalkind, L. Pao, A. Wright, A reference open-source controller for fixed and floating offshore wind turbines. Wind Energ. Sci. 7, 53–73 (2022). https://doi.org/10.5194/wes-7-53-2022
A. Fontanella, I. Bayati, M. Belloli, Linear coupled model for floating wind turbine control. Wind Eng. 42(2), 115–127 (2018). https://doi.org/10.1177/0309524X18756970
J.M. Hegseth, E.E. Bachynski, J.R.R.A. Martins, Design optimization of spar floating wind turbines considering different control strategies. J. Phys. Conf. Ser. 1669(012010), 1–11 (2020). https://doi.org/10.1088/1742-6596/1669/1/012010
F. Lemmer, K. Müller, A. Pegalajar-Jurado, M. Borg, H. Bredmose, LIFES50+ D4.1: Simple numerical models for upscaled design. University of Stuttgart, Germany, and DTU Wind Energy, Denmark (2016)
M. Lerch, M. De-Prada-Gil, C. Molins, A simplified model for the dynamic analysis and power generation of a floating offshore wind turbine, in Proceedings of the International Conference on Renewable Energy (ICREN 2018), Barcelona, April 25–27 (2018). https://doi.org/10.1051/e3sconf/20186100001
J. López-Queija, E. Robles, J.I. Llorente, I. Touzon, J. López-Mendia, A simplified modeling approach of floating offshore wind turbines for dynamic simulations. Energies 15(6), 2228 (2022). https://doi.org/10.3390/en15062228
V. Nava, H. Bagbanci, C. Guedes Soares, F. Arena, On the response of a spar floating wind turbine under the occurrence of extreme events, in Proceedings of the ASME 32nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2013), Nantes, June 9–14 (2013). https://doi.org/10.1115/OMAE2013-11140
A. Otter, J. Murphy, V. Pakrashi, A. Robertson, C. Desmond, A review of modelling techniques for floating offshore wind turbines. Wind Energy 25(5), 831–857 (2022). https://doi.org/10.1002/we.2701
J.M. Jonkman, Dynamics modeling and loads analysis of an offshore floating wind turbine. Technical Report NREL/TP-500-41958. Natl. Renew. Energy Lab. (2007)
M.H. Hansen, L.C. Henriksen, Basic DTU Wind Energy Controller. DTU Wind Energy E-0028. Technical University of Denmark, Roskilde, Denmark (2013)
S.K. Chakrabarti, Handbook of Offshore Engineering (Elsevier Science, 2005)
J.M.V. D’andrea, Study of the motions and nacelle accelerations of the Windcrete floating offshore wind turbine according to the IEC 64100-3 procedure. Master’s Thesis in Energy Engineering, Escola Tècnica Superior d’Enginyeria Industrial de Barcelona—UPC, Barcelona (2020)
F. Huijs, R. de Bruijn, F. Savenije, Concept design verification of a semi-submersible floating wind turbine using coupled simulations. Energy Procedia 53, 2–12 (2014). https://doi.org/10.1016/j.egypro.2014.07.210
A.R. Nejad, E.E. Bachynski, T. Moan, Effect of axial acceleration on drivetrain responses in a spar-type floating wind turbine. J. Offshore Mech. Arct. Eng. 141(3), 031901 (2019). https://doi.org/10.1115/1.4041996
M. Taboada, A. Ortega, R. Martín, A. Pombo, J. Moreu, An evaluation of the effect that motions at the nacelle have on the cost of floating offshore wind turbines, in Proceedings of the Offshore Technology Conference, Houston, May 4–7 (2020). https://doi.org/10.4043/30632-MS
B. Fischer, P. Loepelmann, Balancing rotor speed regulation and drive train loads of floating wind turbines: the science of making torque from wind. J. Phys. Conf. Ser. 753(052016), 1–10 (2016). https://doi.org/10.1088/1742-6596/753/5/052016
S. Kanev, T. van Engelen, Wind turbine extreme gust control. Wind Energy 13(1), 18–35 (2010). https://doi.org/10.1002/we.338
M. Shan, Load Reducing Control for Wind Turbines: Load Estimation and Higher Level Controller Tuning Based on Disturbance Spectra and Linear Models (Fraunhofer Verlag, Germany, 2018)
International Electrotechnical Commission (IEC), International Standard IEC 61400-1: wind turbines—Part 1: design requirements. Geneva (2005)
T. Burton, N. Jenkins, E. Bossanyi, D. Sharpe, M. Graham, Wind Energy Handbook (Wiley, 2021)
T.I. Fossen, Handbook of Marine Craft Hydrodynamics and Motion Control (Wiley, 2021)
C.P.M. Curfs, Dynamic behavior of floating wind turbines—a comparison of open water and level ice conditions. Master of Science Thesis in Offshore and Dredging Engineering, Delft University of Technology, Delft (2015)
M. Hall, S. Housner, D. Zalkind, P. Bortolotti, D. Ogden, G. Barter, An open-source frequency-domain model for floating wind turbine design optimization. J. Phys. Conf. Ser. 2265(042020), 1–12 (2022). https://doi.org/10.1088/1742-6596/2265/4/042020
M. Karimirad, T. Moan, A simplified method for coupled analysis of floating offshore wind turbines. Mar. Struct. 27(1), 45–63 (2012). https://doi.org/10.1016/j.marstruc.2012.03.003
P. Bortolotti, H.C. Tarrés, K. Dykes, K. Merz, L. Sethuraman, D. Verelst, F. Zahle, IEA Wind Task 37 on systems engineering in wind energy—WP 2.1 reference wind turbines. Technical Report NREL/TP-5000-73492. Natl. Renew. Energy Lab. (2019)
A. Kurniawan, J. Hals, T. Moan, Assessment of time-domain models for wave energy conversion systems, in Proceedings of the 9th European Wave and Tide Energy Conference, Southampton (2011)
J.M. Jonkman, S. Butterfield, W. Musial, G. Scott, Definition of a 5-MW reference wind turbine for offshore system development. Technical Report NREL/TP-500-38060. Natl. Renew. Energy Lab. (2009)
F.D. Bianchi, H.D. Battista, R.J. Mantz, Wind Turbine Control Systems: Principles, Modeling and Gain Scheduling Design (Springer, London, 2007)
J. Olondriz, I. Elorza, J. Jugo, S. Alonso-Quesada, A. Pujana-Arrese, An advanced control technique for floating offshore wind turbines based on more compact barge platforms. Energies 11(5), 1187 (2018). https://doi.org/10.3390/en11051187
F. Lemmer, Low-order modeling, control design and optimization of floating offshore wind turbines. Doctor of Engineering Sciences Thesis, University of Stuttgart, Germany (2018)
P.A. Fleming, A. Peiffer, D. Schlipf, Wind turbine controller to mitigate structural loads on a floating wind turbine platform, in Proceedings of the ASME 35th International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2016), Busan, Korea, June 19–24 (2016). https://doi.org/10.1115/OMAE2016-54536
J.M. Jonkman, Definition of the floating system for phase IV of OC3. Technical Report NREL/TP-500-47535. Natl. Renew. Energy Lab. (2010)
R.LC.B. Ramos, Controller design for a 10-MW tension leg platform floating offshore wind turbine using linear quadratic regulation, in Proceedings of the SOBENA 29th International Congress on Waterborne Transportation, Shipbuilding and Offshore Constructions (SOBENA 2022), Rio de Janeiro, October 25–27 (2022). https://doi.org/10.17648/sobena-2022-154080
Funding
Not applicable.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author have no competing interest to declare.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper is an expansion of a previous work published in the Proceedings of the 29th SOBENA Congress [54].
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
da Cunha Barroso Ramos, R.L. Linear quadratic regulation for a 10-MW tension leg platform floating offshore wind turbine operating under normal and extreme turbulence model conditions. Mar Syst Ocean Technol (2024). https://doi.org/10.1007/s40868-023-00133-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40868-023-00133-6