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

Abstract

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 controls. 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. NomenclatureE 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 rad/s -1

Inverse load calculation procedure for offshore wind turbines and application to a 5‐MW wind turbine support structure

“…A third load case with a mean wind speed of 18 m s −1 , at a rotor speed of 12 rpm, confirms the observed characteristics. A description of this load case as well as more information about how the control system influences the inverse calculation are provided in Pahn et al …”

“…A third load case with a mean wind speed of 18 m s À1 , at a rotor speed of 12 rpm, confirms the observed characteristics. A description of this load case as well as more information about how the control system influences the inverse calculation are provided in Pahn et al 25 The summary of results for the land-based simulations makes clear that the inverse calculation approach is able to generate good estimates for the rotor thrust force. Amplifications are observed that are caused by the 3-P excitation and the eigenfrequencies of the rotor blades.…”

Optimization of a dynamic absorber with nonlinear stiffness and damping for the vibration control of a floating offshore wind turbine toy model

“…FOWTs operate over a wide range of wind speeds (typically between 5 and 40 knots) and their operating principle is that the blade speed is essentially constant. In practice, as shown by Pahn et al (2012) in real cases, the tower of a wind turbine is subjected to a thrust force composed of an almost constant term and a periodic force 𝐹 (𝑡) = 𝐴 0 + 𝐴 cos 𝜔𝑡 with 𝜔 = 2𝜋 𝑓 where 𝑓 is the force frequency, which depends mainly on the wind speed variations, the rotation speed and the number of blades of the FOWT. In the various cases considered in this work, most of the dynamic components are below 1 Hz with a maximum amplitude of about 10 kN.…”