Harmonic linearisation of aerodynamic loads in a frequency-domain model of a floating wind turbine

Richard C. Lupton, Robin S. Langley

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


While detailed aero-servo-hydro-elastic simulation codes for modelling floating wind turbines (FWTs) are available, they achieve high accuracy at the expense of calculation speed. For conceptual design and optimisation, fast solutions are needed, and equivalent linearisation techniques combined with frequency-domain analysis offers to capture the complex behaviour of FWTs in fast, approximate models. The main aim of this paper is to apply a harmonic linearisation approach to model the aerodynamic loading within a complete coupled model of a FWT, quantifying its performance, and where accuracy is unsatisfactory, to give insight into the causes. Two linearised models are derived from a coupled nonlinear aero-hydro-servo-elastic model, using the OC3-Hywind FWT as a test case: the typical tangent linearisation derived by numerical perturbation of the nonlinear model and the harmonic linearisation yielding improved representation of the aerodynamic loads. Comparisons against nonlinear time-domain simulations from Bladed show that it is possible to create a frequency-domain model of a FWT, including a flexible structure, aeroelastic rotor loads and the effect of the control system, with reasonable accuracy. The biggest source of errors is the presence of additional harmonics caused by nonlinear interactions between loads at different frequencies, rather than inaccurate linearisation of the magnitudes of forces. The computational cost of the harmonic linearisation implemented varies, but in most cases is ∼10× slower than the tangent linearisation and ∼100× faster than the time domain solution.

Original languageEnglish
Pages (from-to)833-856
Number of pages24
JournalWind Energy
Issue number8
Early online date21 Dec 2020
Publication statusPublished - 16 Jul 2021

Bibliographical note

Funding Information:
This work was funded by an EPSRC doctoral training award (ref. 1089390) and supported by GL Garrad Hassan. We would like to thank the three anonymous reviewers for their helpful comments.

Publisher Copyright:
© 2020 The Authors. Wind Energy published by John Wiley & Sons Ltd

Copyright 2020 Elsevier B.V., All rights reserved.


  • aerodynamic loads
  • equivalent linearisation
  • floating wind turbine
  • frequency-domain modelling
  • harmonic linearisation
  • nonlinearity

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment


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