Articles | Volume 10, issue 4
https://doi.org/10.5194/wes-10-827-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-10-827-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Coleman-free aero-elastic stability methods for three- and two-bladed floating wind turbines
Bogdan Pamfil
CORRESPONDING AUTHOR
DTU Wind and Energy Systems, Koppels Allé, Building 403, 2800 Kongens Lyngby, Denmark
Henrik Bredmose
DTU Wind and Energy Systems, Koppels Allé, Building 403, 2800 Kongens Lyngby, Denmark
Taeseong Kim
DTU Wind and Energy Systems, Koppels Allé, Building 403, 2800 Kongens Lyngby, Denmark
Related authors
No articles found.
Paul Veers, Carlo L. Bottasso, Lance Manuel, Jonathan Naughton, Lucy Pao, Joshua Paquette, Amy Robertson, Michael Robinson, Shreyas Ananthan, Thanasis Barlas, Alessandro Bianchini, Henrik Bredmose, Sergio González Horcas, Jonathan Keller, Helge Aagaard Madsen, James Manwell, Patrick Moriarty, Stephen Nolet, and Jennifer Rinker
Wind Energ. Sci., 8, 1071–1131, https://doi.org/10.5194/wes-8-1071-2023, https://doi.org/10.5194/wes-8-1071-2023, 2023
Short summary
Short summary
Critical unknowns in the design, manufacturing, and operation of future wind turbine and wind plant systems are articulated, and key research activities are recommended.
Mohammad Youssef Mahfouz, Climent Molins, Pau Trubat, Sergio Hernández, Fernando Vigara, Antonio Pegalajar-Jurado, Henrik Bredmose, and Mohammad Salari
Wind Energ. Sci., 6, 867–883, https://doi.org/10.5194/wes-6-867-2021, https://doi.org/10.5194/wes-6-867-2021, 2021
Short summary
Short summary
This paper introduces the numerical models of two 15 MW floating offshore wind turbines (FOWTs) WindCrete and Activefloat. WindCrete is a spar floating platform designed by Universitat Politècnica de Catalunya, while Activefloat is a semi-submersible platform designed by Esteyco. The floaters are designed within the Horizon 2020 project COREWIND. Later in the paper, the responses of both models to wind and second-order waves are analysed with an emphasis on the effect of second-order waves.
Freddy J. Madsen, Antonio Pegalajar-Jurado, and Henrik Bredmose
Wind Energ. Sci., 4, 527–547, https://doi.org/10.5194/wes-4-527-2019, https://doi.org/10.5194/wes-4-527-2019, 2019
Short summary
Short summary
This paper presents a comparison study of the simplified model QuLAF (Quick Load Analysis of Floating wind turbines) and FAST for the planar version of various design load cases, in order to investigate how accurate results can be obtained from this simplified model.
The overall analysis shows that QuLAF is generally very good at estimating the bending moment at the tower base and the floater motions, whereas the nacelle acceleration is generally underpredicted.
Antonio Pegalajar-Jurado, Michael Borg, and Henrik Bredmose
Wind Energ. Sci., 3, 693–712, https://doi.org/10.5194/wes-3-693-2018, https://doi.org/10.5194/wes-3-693-2018, 2018
Short summary
Short summary
This paper presents a simplified numerical model to quickly predict motion and loads of floating offshore wind turbines. Hydrodynamic, aerodynamic and mooring loads are extracted from higher-fidelity numerical tools. Without calibration, the model can predict with good accuracy the motions of the system in real wind and wave conditions. Loads at the tower base are estimated with errors between 0.2 % and 11.3 %. The model can simulate between 1300 and 2700 times faster than real time.
Signe Schløer, Laura Garcia Castillo, Morten Fejerskov, Emanuel Stroescu, and Henrik Bredmose
Wind Energ. Sci., 3, 57–73, https://doi.org/10.5194/wes-3-57-2018, https://doi.org/10.5194/wes-3-57-2018, 2018
Short summary
Short summary
A model for quick load analysis is presented. This is a fast model for the calculation of dynamic loads of an offshore wind turbine tower and foundation. The model is compared to the state-of-the-art aeroelastic code. In general, there is good similarity between the two models. This indicates that in the early stage of the design phase a simple dynamic model can be used to make a preliminary design of the foundation and wind turbine tower.
Georg Pirrung, Vasilis Riziotis, Helge Madsen, Morten Hansen, and Taeseong Kim
Wind Energ. Sci., 2, 15–33, https://doi.org/10.5194/wes-2-15-2017, https://doi.org/10.5194/wes-2-15-2017, 2017
Short summary
Short summary
The certification process of a wind turbine requires simulations of a coupled structural and aerodynamic wind turbine model in many different external conditions. Due to the large number of load cases, the complexity of the aerodynamics models has to be limited. In this paper, a simplified vortex method based aerodynamics model is described. It is shown that this model, which is fast enough for use in a certification context, can produce results similar to those of a more complex vortex model.
Related subject area
Thematic area: Dynamics and control | Topic: Dynamics and aeroservoelasticity
Analysis and calibration of optimal power balance rotor-effective wind speed estimation schemes for large-scale wind turbines
Multi-task Learning Long Short-term Memory Model to Emulate Wind Turbine Blade Dynamics
Investigating the interactions between wakes and floating wind turbines using FAST.Farm
Uncertainty quantification of structural blade parameters for the aeroelastic damping of wind turbines: a code-to-code comparison
The rotor as a sensor – observing shear and veer from the operational data of a large wind turbine
Extension of the Langevin power curve analysis by separation per operational state
Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions
A digital twin solution for floating offshore wind turbines validated using a full-scale prototype
Extending the dynamic wake meandering model in HAWC2Farm: a comparison with field measurements at the Lillgrund wind farm
Extreme coherent gusts with direction change – probabilistic model, yaw control, and wind turbine loads
A correction method for large deflections of cantilever beams with a modal approach
A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines
Atindriyo Kusumo Pamososuryo, Fabio Spagnolo, and Sebastiaan Paul Mulders
Wind Energ. Sci., 10, 987–1006, https://doi.org/10.5194/wes-10-987-2025, https://doi.org/10.5194/wes-10-987-2025, 2025
Short summary
Short summary
As wind turbines grow in size, measuring wind speed accurately becomes challenging, impacting their performance. Traditional sensors cannot capture wind variations across large rotor areas. To address this, a new method is developed to estimate wind speed accurately, accounting for these variations. Using mid-fidelity simulations, our approach showed better tracking, better noise resilience, and easy tuning for different turbine sizes.
Shubham Baisthakur and Breiffni Fitzgerald
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-105, https://doi.org/10.5194/wes-2024-105, 2024
Revised manuscript accepted for WES
Short summary
Short summary
Site-specific performance analysis of wind turbines is crucial but computationally prohibitive due to the high cost of evaluating numerical models. To address this, the authors propose a machine learning model combined with dimensionality reduction using Principal Component Analysis and Discrete Cosine Transform, along with a Long Short-Term Memory model, to predict dynamic responses at a fraction of the computational cost.
Lucas Carmo, Jason Jonkman, and Regis Thedin
Wind Energ. Sci., 9, 1827–1847, https://doi.org/10.5194/wes-9-1827-2024, https://doi.org/10.5194/wes-9-1827-2024, 2024
Short summary
Short summary
As floating wind turbines progress to arrays with multiple units, it becomes important to understand how the wake of a floating turbine affects the performance of other units in the array. Due to the compliance of the floating substructure, the wake of a floating wind turbine may behave differently from that of a fixed turbine. In this work, we present an investigation of the mutual interaction between the motions of floating wind turbines and wakes.
Hendrik Verdonck, Oliver Hach, Jelmer D. Polman, Otto Schramm, Claudio Balzani, Sarah Müller, and Johannes Rieke
Wind Energ. Sci., 9, 1747–1763, https://doi.org/10.5194/wes-9-1747-2024, https://doi.org/10.5194/wes-9-1747-2024, 2024
Short summary
Short summary
Aeroelastic stability simulations are needed to guarantee the safety and overall robust design of wind turbines. To increase our confidence in these simulations in the future, the sensitivity of the stability analysis with respect to variability in the structural properties of the wind turbine blades is investigated. Multiple state-of-the-art tools are compared and the study shows that even though the tools predict similar stability behavior, the sensitivity might be significantly different.
Marta Bertelè, Paul J. Meyer, Carlo R. Sucameli, Johannes Fricke, Anna Wegner, Julia Gottschall, and Carlo L. Bottasso
Wind Energ. Sci., 9, 1419–1429, https://doi.org/10.5194/wes-9-1419-2024, https://doi.org/10.5194/wes-9-1419-2024, 2024
Short summary
Short summary
A neural observer is used to estimate shear and veer from the operational data of a large wind turbine equipped with blade load sensors. Comparison with independent measurements from a nearby met mast and profiling lidar demonstrate the ability of the
rotor as a sensorconcept to provide high-quality estimates of these inflow quantities based simply on already available standard operational data.
Christian Wiedemann, Hendrik Bette, Matthias Wächter, Jan A. Freund, Thomas Guhr, and Joachim Peinke
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2024-52, https://doi.org/10.5194/wes-2024-52, 2024
Revised manuscript accepted for WES
Short summary
Short summary
This study utilizes a method to analyze power conversion dynamics across different operational states, addressing non-stationarity with a correlation matrix algorithm. Findings reveal distinct dynamics for each state, emphasizing their impact on system behavior and offering a solution to hysteresis effects in power conversion dynamics.
Kristian Ladefoged Ebbehøj, Philippe Jacques Couturier, Lars Morten Sørensen, and Jon Juel Thomsen
Wind Energ. Sci., 9, 1005–1024, https://doi.org/10.5194/wes-9-1005-2024, https://doi.org/10.5194/wes-9-1005-2024, 2024
Short summary
Short summary
This paper experimentally validates a novel method for characterizing wind turbine dynamics based on vibration measurements. The dynamics of wind turbines can change over short time periods if the operational conditions change. In such cases, conventional methods are inadequate. The validation is performed with a controlled laboratory experiment and a full-scale wind turbine test. More accurate characterization could lead to more efficient wind turbine designs and in turn cheaper wind energy.
Emmanuel Branlard, Jason Jonkman, Cameron Brown, and Jiatian Zhang
Wind Energ. Sci., 9, 1–24, https://doi.org/10.5194/wes-9-1-2024, https://doi.org/10.5194/wes-9-1-2024, 2024
Short summary
Short summary
In this work, we implement, verify, and validate a physics-based digital twin solution applied to a floating offshore wind turbine. The article present methods to obtain reduced-order models of floating wind turbines. The models are used to form a digital twin which combines measurements from the TetraSpar prototype (a full-scale floating offshore wind turbine) to estimate signals that are not typically measured.
Jaime Liew, Tuhfe Göçmen, Alan W. H. Lio, and Gunner Chr. Larsen
Wind Energ. Sci., 8, 1387–1402, https://doi.org/10.5194/wes-8-1387-2023, https://doi.org/10.5194/wes-8-1387-2023, 2023
Short summary
Short summary
We present recent research on dynamically modelling wind farm wakes and integrating these enhancements into the wind farm simulator, HAWC2Farm. The simulation methodology is showcased by recreating dynamic scenarios observed in the Lillgrund offshore wind farm. We successfully recreate scenarios with turning winds, turbine shutdown events, and wake deflection events. The research provides opportunities to better identify wake interactions in wind farms, allowing for more reliable designs.
Ásta Hannesdóttir, David R. Verelst, and Albert M. Urbán
Wind Energ. Sci., 8, 231–245, https://doi.org/10.5194/wes-8-231-2023, https://doi.org/10.5194/wes-8-231-2023, 2023
Short summary
Short summary
In this work we use observations of large coherent fluctuations to define a probabilistic gust model. The gust model provides the joint description of the gust rise time, amplitude, and direction change. We perform load simulations with a coherent gust according to the wind turbine safety standard and with the probabilistic gust model. A comparison of the simulated loads shows that the loads from the probabilistic gust model can be significantly higher due to variability in the gust parameters.
Ozan Gözcü, Emre Barlas, and Suguang Dou
Wind Energ. Sci., 8, 109–124, https://doi.org/10.5194/wes-8-109-2023, https://doi.org/10.5194/wes-8-109-2023, 2023
Short summary
Short summary
This study proposes a fast correction method for modal-based reduced-order models to account for geometric nonlinearities linked to large bending deflections in cantilever beam-like engineering structures. The large deflections cause secondary motions such as axial and torsional motions when the structures go through bending deflections. The method relies on pre-computed correction terms and thus adds negligibly small extra computational cost to the time domain analyses of the dynamic response.
Emmanuel Branlard and Jens Geisler
Wind Energ. Sci., 7, 2351–2371, https://doi.org/10.5194/wes-7-2351-2022, https://doi.org/10.5194/wes-7-2351-2022, 2022
Short summary
Short summary
The article presents a framework to obtain the linear and nonlinear equations of motion of a multibody system including rigid and flexible bodies. The method yields compact symbolic equations of motion. The applications are many, such as time-domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins.
Cited articles
Bauchau, O. and Nikishkov, Y.: An Implicit Floquet Analysis for Rotorcraft Stability Evaluation, J. Amer. Helicopter Soc., 46, 200–209, https://doi.org/10.4050/JAHS.46.200, 2001. a
Bir, G.: Multi-Blade Coordinate Transformation and its Application to Wind Turbine Analysis, in: 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 7–10 January 2008, https://doi.org/10.2514/6.2008-1300, 2008. a
Borg, M., Pegalajar-Jurado, A., Stiesdal, H., Madsen, F., Nielsen, T., Mikkelsen, R., Mirzaei, M., Lomholt, A., and Bredmose, H.: Dynamic response analysis of the TetraSpar floater in waves: Experiment and numerical reproduction, Mar. Struct., 94, 103546, https://doi.org/10.1016/j.marstruc.2023.103546, 2024. a
Bortolotti, P., Chetan, M., Branlard, E., Jonkman, J., Platt, A., Slaughter, D., and Rinker, J.: Wind Turbine Aeroelastic Stability in OpenFAST, J. Phys. Conf. Ser., 2767, 022018, https://doi.org/10.1088/1742-6596/2767/2/022018, 2024. a
Coleman, R., Feingold, A., and for Aeronautics, U. S. N. A. C.: Theory of Self-excited Mechanical Oscillations of Helicopter Rotors with Hinged Blades, NACA R-1351, National Advisory Committee for Aeronautics, https://books.google.dk/books?id=59nAmQEACAAJ (last access: 7 May 2024), 1957. a
CORROSION: ICCP for floating devices, https://www.corrosion.nl/iccp-floating/ (last access: 5 November 2024), 2023. a
Filsoof, O. T., Hansen, M. H., Yde, A., Bøttcher, P., and Zhang, X.: A novel methodology for analyzing modal dynamics of multi-rotor wind turbines, J. Sound Vib., 493, 115810, https://doi.org/10.1016/j.jsv.2020.115810, 2021. a
Floquet, G.: Sur les équations différentielles linéaires à coefficients périodiques, Ann. Sci. Ecole Norm. S., 12, 47–88, https://doi.org/10.24033/asens.220, 1883. a
Frulla, G.: Rigid rotor dynamic stability using Floquet theory, Eur. J. Mech. A-Solid., 19, 139–150, https://doi.org/10.1016/S0997-7538(00)00151-0, 2000. a
Genta, G.: Whirling of unsymmetrical rotors: A finite element approach based on complex co-ordinates, J. Sound Vib., 124, 27–53, https://doi.org/10.1016/S0022-460X(88)81404-4, 1988. a, b
Hansen, M.: Aerodynamics of wind turbines, Earthscan, 3 edn., ISBN 9781138775077, 2015. a
Hansen, M. H.: Aeroelastic stability analysis of wind turbines using an eigenvalue approach, Wind Energy, 7, 133–143, https://doi.org/10.1002/we.116, 2004. a
Hansen, M. H.: Modal dynamics of structures with bladed isotropic rotors and its complexity for two-bladed rotors, Wind Energ. Sci., 1, 271–296, https://doi.org/10.5194/wes-1-271-2016, 2016. a, b, c
Hill, G. W.: On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, 36, 1871–2509, https://doi.org/10.1007/BF02417081, 1886. a
Kim, T., Hansen, A. M., and Branner, K.: Development of an anisotropic beam finite element for composite wind turbine blades in multibody system, Renewable Energy, 59, 172–183, https://doi.org/10.1016/j.renene.2013.03.033, 2013. a
Kim, T., Larsen, T. J., and Yde, A.: Investigation of potential extreme load reduction for a two-bladed upwind turbine with partial pitch, Wind Energy, 18, 1403–1419, https://doi.org/10.1002/we.1766, 2015. a
Lazarus, A. and Thomas, O.: A harmonic-based method for computing the stability of periodic solutions of dynamical systems, CR Mécanique, 338, 510–517, https://doi.org/10.1016/j.crme.2010.07.020, 2010. a
Leishman, J. G., Beddoes, T. S., and Ltd, W. H.: A Generalised Model for Airfoil Unsteady Aerodynamic Behaviour and Dynamic Stall Using the Indicial Method, https://api.semanticscholar.org/CorpusID:126280624 (last access: 10 December 2024), 1986. a
Madsen, H. A., Larsen, T. J., Pirrung, G. R., Li, A., and Zahle, F.: Implementation of the blade element momentum model on a polar grid and its aeroelastic load impact, Wind Energ. Sci., 5, 1–27, https://doi.org/10.5194/wes-5-1-2020, 2020. a
Meng, F., Lio, A., and Riva, R.: Reduced-order modelling of floating offshore wind turbine: Aero-hydro-elastic stability analysis, J. Phys. Conf. Ser., 2767, 062012, https://doi.org/10.1088/1742-6596/2767/6/062012, 2024. a
Offshore Wind Scotland: Floating Wind in Scotland, https://www.offshorewindscotland.org.uk/the-offshore-wind-market-in-scotland/floating-wind-in-scotland/ (last access: 5 November 2024), 2024. a
Pamfil, B., Bredmose, H., and Kim, T.: Floating wind turbine stability and time response analysis with rotating modes, J. Phys. Conf. Ser., 2767, 022057, https://doi.org/10.1088/1742-6596/2767/2/022057, 2024. a, b, c, d
Riva, R., Cacciola, S., and Bottasso, C. L.: Periodic stability analysis of wind turbines operating in turbulent wind conditions, Wind Energ. Sci., 1, 177–203, https://doi.org/10.5194/wes-1-177-2016, 2016. a, b, c
Skjoldan, P.: Modal Dynamics of Wind Turbines with Anisotropic Rotors, in: 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, Orlando, Florida, 5–8 January 2009, https://doi.org/10.2514/6.2009-1036, 2009. a
Skjoldan, P. F.: Aeroelastic modal dynamics of wind turbines including anisotropic effects, PhD thesis, Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi. Risø-PhD No. 66(EN), ISBN 978-87-550-3848-6, https://orbit.dtu.dk/en/publications/aeroelastic-modal-dynamics-of-wind-turbines-including-anisotropic (last access: 17 September 2024), 2011. a, b, c, d, e
Skjoldan, P. F. and Hansen, M. H.: On the similarity of the Coleman and Lyapunov–Floquet transformations for modal analysis of bladed rotor structures, J. Sound Vib., 327, 424–439, https://doi.org/10.1016/j.jsv.2009.07.007, 2009. a, b
Stiesdal Offshore: Tetra Floating offshore foundations, https://www.stiesdal.com/wp-content/uploads/2023/04/32514-Stiesdal-Offshore-brochure.pdf (last access: 5 November 2024), 2023. a
Xu, J. and Gasch, R.: Modale Behandlung linearer periodisch zeitvarianter Bewegungsgleichungen, Arch. Appl. Mech., 65, 178–193, https://doi.org/10.1007/BF00799297, 1995. a
Short summary
A floating wind turbine time domain model, which considers dynamic stall, is used to develop Coleman-free aero-elastic stability analysis methods, namely Hill's and Floquet's. We clarify how the floater tilt is involved in the stability analysis, show damping effects of aerodynamic states, prove that results of both methods agree and can reproduce the forward- and backward-whirling rotor modes in a Coleman-based analysis, and demonstrate that both methods can be applied to a two-bladed rotor.
A floating wind turbine time domain model, which considers dynamic stall, is used to develop...
Altmetrics
Final-revised paper
Preprint