A Familie of Simplified Aerodynamic Models for Wind Turbine Controller Design and Analysis
Creators: name: Geisler, Jens
Publisher: name: Zenodo
Year: 2021
Subjects: controller design
simplified aerodynamics
aerodynamic damping
blade modes
kalman filter
wind turbine

description: This is a sister presentation to the also submitted talk on “Symbolic Flexible Multibody Models for Wind Turbine Controller Design and Analysis”. Both talks could stand alone but they share a common goal. The next generation of wind turbine digital technologies requires versatile aero-servo-elastic models, of various levels of fidelity, and suitable for a wide range of applications (Lemmer, 2018). Typically, applications such as controller design, state observers or digital-twins require these models to be computationally efficient and in some cases an analytical representation is also desirable, e.g. in order to derive gradients or sensitivity matrices (Loew et al., 2018 or Verschueren et al., 2018). For the aerodynamic model this means that the solution of the dynamic blade element momentum equations must be simplified, usually by regarding only rotor averaged steady-state solutions form a pre-computed 2D look-up-table for the power (cp) and thrust (ct) coefficient. But this approach neglects the influence of structural motion of the tower and blades, aka. aerodynamic damping (Chen et al., 2020). Further, the rotor averaged approach is not viable when the excitation forces for flexible blades are required (Xi et al., 2020). <br> To address these issues, we propose an approach that allows to assemble an aerodynamic model from different pre-computed look-up-tables. Thus, any scalar force and moment such as rotor torque, hub center thrust, and blade modal excitation forces can be modeled. All these forces may include any variation of a steady-state part and parts that result from one specific shape of apparent wind speed variation along the blade such as modal deformations or wind shear (Xiong et al., 2010). This approach is computationally efficient, differentiable up to the degree of the splines used in the look-up-tables, and it is modular and can be adapted to many different model configurations. Firstly the classical rotor averaged torque and thrust are derived (Ning, 2014). Here, the influence of tower fore-aft motion is included in its fully non-linear form. The second part explains how modal forces that act on a specific blade mode can be derived from blade section-wise steady-state solutions of the blade element momentum equations. The third part shows how any of the steady-state forces can be extended by first order approximations to include the effect relative wind speed variations with a certain distribution shape along the blade. The equations show the influence of blade modal motions but the same approach could be used to derive the effect of wind shear or tower top pitching or tower side-side motion. It is expected that the effect of blade twisting could be considered in a similar way. <br> In the presentation, we will describe the derivation of the different aspects of the proposed model. We will compare our results with OpenFAST simulations for different models, and we will present how this model can be applied to various research projects. The code for this project is available at: https://github.com/jgeisler0303/CCBlade-M References:<br> Chen, C., Duffour, P., &amp; Fromme, P. (2020). Modelling wind turbine tower-rotor interaction through an aerodynamic damping matrix. Journal of Sound and Vibration, 489, 115667. https://doi.org/10.1016/j.jsv.2020.115667 Henriksen, L. C., Hansen, M. H., &amp; Poulsen, N. K. (2012). Beyond the cp-curve in model-based control of wind turbines, In EWEA 2012-European Wind Energy Conference &amp; Exhibition. European Wind Energy Association (EWEA). Lemmer, F. (2018). Low-order modeling, controller design and optimization of floating offshore wind turbines (Dissertation). Universitt Stuttgart. Liu, X., Lu, C., Li, G., Godbole, A., &amp; Chen, Y. (2017). Effects of aerodynamic damping on the tower load of offshore horizontal axis wind turbines. Applied Energy, 204, 1101-1114. https://doi.org/10.1016/j.apenergy.2017.05.024 Loew, S., &amp; Obradovic, D. (2018). Real-time Implementation of Nonlinear Model Predictive Control for Mechatronic Systems Using a Hybrid Model, In 2018 IEEE 14th International Conference on Automation Science and Engineering (CASE). https://doi.org/10.1109/COASE.2018.8560359 Ning, S. A. (2014). A simple solution method for the blade element momentum equations with guaranteed convergence. Wind Energy, 17 (9), 1327-1345. https:/doi.org/10.1002/we.1636 Verschueren, R., Frison, G., Kouzoupis, D., van Duijkeren, N., Zanelli, A., Quirynen, R., &amp; Diehl, M. (2018). Towards a modular software package for embedded optimization [6th IFAC Conference on Nonlinear Model Predictive Control NMPC 2018]. IFAC-PapersOnLine, 51 (20), 374-380. https://doi.org/10.1016/j.ifacol.2018.11.062 Xi, R., Wang, P., Du, X., Xu, K., Xu, C., &amp; Jia, J. (2020). A semi-analytical model of aerodynamic damping for horizontal axis wind turbines and its applications. Ocean Engineering, 214, 107861. https://doi.org/10.1016/j.oceaneng.2020.107861 Xiong, L., Xianmin, Z., Gangqiang, L., Yan, C., &amp; Zhiquan, Y. (2010). Dynamic Response Analysis of the Rotating Blade of Horizontal Axis Wind Turbine. Wind Engineering, 34 (5), 543-559. https://doi.org/10.1260/0309-524X.34.5.543