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Highlights

Harmonic linearisation gives a 2–4x reduction in error in aerodynamic loads.

Torque and pitch controller behaviour is linearised well, away from rated wind speed.

Interactions between torque and pitch controllers at rated are harder to linearise.

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.

Keywords

Wind energy

Aerodynamic loads

Frequency-domain modelling

Harmonic linearisation

Equivalent linearisation

Non-linearity

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