### Inverse load calculation of wind turbine support structures - a numerical verification using the comprehensive simulation code FAST

Thomas Pahn, Jason Jonkman, Raimund Rolfes, Amy Robertson
2012 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference20th AIAA/ASME/AHS Adaptive Structures Conference14th AIAA   unpublished
Physically measuring the dynamic responses of wind turbine support structures enables the calculation of the applied loads using an inverse procedure. In this process, inverse means deriving the inputs/forces from the outputs/responses. This paper presents results of a numerical verification of such an inverse load calculation. For this verification, the comprehensive simulation code FAST is used. FAST accounts for the coupled dynamics of wind inflow, aerodynamics, elasticity and turbine
more » ... s. Simulations are run using a 5-MW onshore wind turbine model with a tubular tower. Both the applied loads due to the instantaneous wind field and the resulting system responses are known from the simulations. Using the system responses as inputs to the inverse calculation, the applied loads are calculated, which in this case are the rotor thrust forces. These forces are compared to the rotor thrust forces known from the FAST simulations. The results of these comparisons are presented to assess the accuracy of the inverse calculation. To study the influences of turbine controls, load cases in normal operation between cut-in and rated wind speed, near rated wind speed and between rated and cut-out wind speed are chosen. The presented study shows that the inverse load calculation is capable of computing very good estimates of the rotor thrust. The accuracy of the inverse calculation does not depend on the control activity of the wind turbine. Nomenclature E B = viscous modal damping matrix D = damping matrix i D = modal damping ratio F = Fourier transform of the force vector inv F = inversely calculated load ( ) t f = force vector ( ) f t = force signal 2 f = frequency 0i f = eigenfrequency in Hz ( ) jω H = frequency response function (FRF) matrix ( ) g jω H = generalized FRF matrix i = number of vibration mode M = mass matrix red g M = generalized mass matrix of the reduced system gi m = entry of the generalized mass matrix of the reduced system K = stiffness matrix red g K = generalized stiffness matrix of the reduced system k = stiffness RotThrust = rotor thrust from FAST simulation t = time 0 U = modal matrix ( ) jω Y = Fourier transform of the displacement vector ( ) t y = displacement vector ( ) y t = displacement signal ( ) t y  = velocity vector ( ) t y  = acceleration vector ω = angular frequency 0i ω = eigenfrequency in s -1