37 Development of Simplified Models for Wind Turbine Blades with Application to NREL 5 MW Offshore Research Wind Turbine 399 Fig. 37.6 The pre-calibration (a) and post-calibration (b) mode shape MAC values 5 10 15 20 25 30 0 10 20 30 40 50 60 Model order Flapwise Error Baseline model Beam model 5 10 15 20 25 30 0 10 20 30 40 50 60 Model order Edgewise Error Baseline model Beam model a b Fig. 37.7 The relative approximation error (%) of the baseline FE and beam model for different model orders. The input and output are in the same direction as; (a) flapwise and (b) edgewise. The input is a step function 37.5.2 Model Reduction of Rotor Blade Models At this point, the beam model is calibrated against the baseline model to replicate its behavior in the frequency range from 0.4 to 8 Hz. Since common practice in wind turbine industry is to keep a few low frequency modes of the beam model in aeroelastic codes, for the purpose of entire wind turbine simulation, it remains to apply the mentioned model reduction algorithm to the calibrated beam and baseline models to yield reduced models of far smaller size. To this end, models are imported in MATLAB to assess the predictive power of the reduced updated beam model against the reduced baseline model. Models are clamped at the root and a relative modal damping of 1 % is mapped to all the modes. The reduced-order models of dimension 6–30 by step of two states are computed where the modes have been ranked according to the modal dominancy criterion of (37.15) considering no frequency weighting. The performance of the reduced models is considered using two different load conditions. First, the models are subjected to step excitation inducing first the flapwise bending, and then the edgewise bending to assess the steady state approximation error. Figure 37.7a demonstrates the relative approximation error for different model orders when the blade is subjected with
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