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Improved linearised models of wind turbine aerodynamics and control system dynamics using harmonic linearisation

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  • Lupton, Richard C.
  • Langley, Robin S.

Abstract

Where non-linearities are not too strong, linearised frequency-domain approaches offer fast calculations, which can be valuable for preliminary design of wind turbine blades, foundations and floating platforms. But the aerodynamic and control system behaviour of a wind turbine is noticeably non-linear. Here we show for the first time that the technique of harmonic linearisation can reduce error in the approximation of aerodynamic and control system non-linearities, compared to the more common tangent linearisation. After deriving the linearised models, comparing linearised results to non-linear simulations for the NREL 5 MW turbine shows that: (1) harmonic linearisation captures aero-elastic effects and non-linearity in aerodynamic forces, giving a 2–4x reduction in error compared to the tangent linearisation; (2) harmonic linearisation can capture non-linear wake dynamics; and (3) the torque and pitch controller behaviour can be approximated with good results away from the rated wind speed but with some challenges when the two controllers interact. Further improvements in the linearised model of the control system have been identified. By improving the accuracy of linearised models, harmonic linearisation is a promising means to extend the applicability of frequency-domain approaches for initial design and optimisation of wind turbines.

Suggested Citation

  • Lupton, Richard C. & Langley, Robin S., 2019. "Improved linearised models of wind turbine aerodynamics and control system dynamics using harmonic linearisation," Renewable Energy, Elsevier, vol. 135(C), pages 148-162.
    • Handle: RePEc:eee:renene:v:135:y:2019:i:c:p:148-162
    DOI: 10.1016/j.renene.2018.11.067
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    1. Lupton, Richard C. & Langley, Robin S., 2019. "Complex but negligible: Non-linearity of the inertial coupling between the platform and blades of floating wind turbines," Renewable Energy, Elsevier, vol. 134(C), pages 710-726.
    2. Lupton, R.C. & Langley, R.S., 2017. "Scaling of slow-drift motion with platform size and its importance for floating wind turbines," Renewable Energy, Elsevier, vol. 101(C), pages 1013-1020.
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    Cited by:

    1. Dali, Ali & Abdelmalek, Samir & Bakdi, Azzeddine & Bettayeb, Maamar, 2021. "A new robust control scheme: Application for MPP tracking of a PMSG-based variable-speed wind turbine," Renewable Energy, Elsevier, vol. 172(C), pages 1021-1034.

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    1. Lupton, Richard C. & Langley, Robin S., 2019. "Complex but negligible: Non-linearity of the inertial coupling between the platform and blades of floating wind turbines," Renewable Energy, Elsevier, vol. 134(C), pages 710-726.

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