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Abstract
Several methods for aeroelastic modal analysis of a rotating wind
turbine are developed and used to analyse the modal dynamics of
two simplified models and a complex model in isotropic and
anisotropic conditions.
The Coleman transformation is used to enable extraction of the
modal frequencies, damping, and periodic mode shapes of a rotating
wind turbine by describing the rotor degrees of freedom in the
inertial frame. This approach is valid only for an isotropic system.
Anisotropic systems, e.g., with an unbalanced rotor or operating in
wind shear, are treated with the general approaches of Floquet
analysis or Hill's method which do not provide a unique reference
frame for observing the modal frequency, to which any multiple of
the rotor speed can be added. This indeterminacy is resolved by
requiring that the periodic mode shape be as constant as possible in
the inertial frame. The modal frequency is thus identified as the
dominant frequency in the response of a pure excitation of the mode
observed in the inertial frame.
A modal analysis tool based directly on the complex aeroelastic
wind turbine code BHawC is presented. It uses the Coleman
approach in isotropic conditions and the computationally efficient
implicit Floquet analysis in anisotropic conditions. The tool is
validated against system identifications with the partial Floquet
method on the nonlinear BHawC model of a 2.3 MW wind turbine.
System identification results show that nonlinear effects on the
2.3 MW turbine in most cases are small, but indicate that the
controller creates nonlinear damping. In isotropic conditions the
periodic mode shape contains up to three harmonic components, but
in anisotropic conditions it can contain an infinite number of
harmonic components with frequencies that are multiples of the
rotor speed. These harmonics appear in calculated frequency
responses of the turbine. Extreme wind shear changes the modal
damping when the flow is separated due to an interaction between
the periodic mode shape and the local aerodynamic damping
influenced by a periodic variation in angle of attack.
Original language  English 

Place of Publication  Roskilde 

Publisher  Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi 
Number of pages  158 
ISBN (Print)  9788755038486 
Publication status  Published  Mar 2011 
Series  RisøPhD 

Number  66(EN) 
Keywords
 Aeroelastic design methods
 RisøPhD66(EN)
 RisøPhD66
 RisøPhD0066
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 1 Finished

Aeroservoelastisk stabilitetsanalyse og design af vindmøller
Skjoldan, P. F., Hansen, M. H., Thomsen, K., Jensen, J. S., Sergey V., S. & Riziotis, V. A.
01/11/2007 → 02/03/2011
Project: PhD