Preprints
https://doi.org/10.5194/wes-2021-46
https://doi.org/10.5194/wes-2021-46
 
11 Aug 2021
11 Aug 2021
Status: a revised version of this preprint is currently under review for the journal WES.

A symbolic framework for flexible multibody systems applied to horizontal axis wind turbines

Emmanuel Branlard1 and Jens Geisler2 Emmanuel Branlard and Jens Geisler
  • 1National Renewable Energy Laboratory, Golden, CO 80401, USA
  • 2Hochschule Flensburg, University of Applied Sciences, 24943 Flensburg, Germany

Abstract. The article presents a symbolic framework that is used to obtain the linear and non-linear equations of motion of a multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitate the creation and manipulation of models with various levels of fidelity. The symbolic treatment provides analytical gradients and linearized equations of motion. The linear and non-linear equations can be exported to Python code or dedicated software. The application are multiple such as: time-domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, digital twins, etc. In this paper, we describe the method we used to systematically generate the equations of motion of multibody systems. We apply the framework to generate illustrative onshore and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. A Python implementation is provided as an opensource project.

Emmanuel Branlard and Jens Geisler

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2021-46', Anonymous Referee #1, 06 Sep 2021
  • RC2: 'Comment on wes-2021-46', Anonymous Referee #2, 07 Oct 2021
  • CC1: 'Comment on wes-2021-46', Ignacio Romero, 10 Feb 2022
  • AC1: 'Comment on wes-2021-46', Emmanuel Branlard, 14 Mar 2022

Emmanuel Branlard and Jens Geisler

Emmanuel Branlard and Jens Geisler

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The article presents a framework to obtain the linear and non-linear equations of motion of a multibody system including rigid and flexible bodies. The method yields compact symbolic equations of motion. The application are multiple such as: time-domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, digital twins, etc.