Use of mixed coordinates in modeling wind turbines including tubular tower

Ayman Nada,Ali Al-Shahrani

doi:10.5194/ms-10-35-2019

Ayman Nada, Ali Al-Shahrani

Open Access

https://doi.org/10.5194/ms-10-35-2019

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Journal: Mechanical Sciences	Publication Date: Jan 10, 2019
Citations: 2	License type: CC BY 4.0

Affiliation: Benha University, Jazan University

Abstract

Abstract. This paper studies the effect of the tower dynamics upon the wind turbine model by using mixed sets of rigid and/or nodal and/or modal coordinates within multibody system dynamics approach. The nodal model exhibits excellent numerical properties, especially in the case where the rotation of the rotor-blade is extremely high, and therefore, the geometric stiffness effect can not be ignored. However, the use of nodal models to describe the flexibility of large multibody systems produces huge size of coordinates and may consume massive computational time in simulation. On the other side, the dynamics of the tower as well as other components of wind turbine remain exhibit small deformations and can be modeled using Cartesian and/or reduced set of modal coordinates. The paper examines a method of using mixed sets of different coordinates in the same model, although there are differences in the scale and the physical interpretation. The equations of motion of the wind-turbine model is presented based on the floating frame of reference formulation. The mixed coordinates vector consists of three sets: Cartesian coordinates set to present the rigid body motion (nacelle and rotor bodies), elastic nodal coordinates for rotating blades, and reduced-order modal coordinates for low speed components and those that deflect by simple motion shapes (circular Tower). Experimental validation has been carried out successfully, and consequently, the proposed model can be utilized for design process, identification and health monitoring aspects.

Highlights

Computational modeling of wind turbines is an important tool in design and control of these dynamic systems
It is can be considered that wind turbines are the real and most important application of flexible multibody dynamics, see Fig. 1
The Floating Frame of Reference (FFR) formulation, which uses a set of Cartesian, orientational and elastic coordinates, in which the deformation of the body with respect to its local frame is described using finite deformations and rotations, more details are presented in Nikravesh and Lin (2005), Nada et al (2009, 2010) and Wu and Tiso (2014)

Summary

Introduction

Computational modeling of wind turbines is an important tool in design and control of these dynamic systems. Once the rotor speed reaches the first natural frequency of blade structure, the use of linear form gives wrong solution, and the nonlinear term (geometric stiffness term) should be included in the FFR model In this case, the elastic coordinates must be utilized in the model construction (Nada et al, 2010). This paper examines how to calculate the deformation gradient and the resulting strain on the body of the tower in cylindrical coordinates, and selecting the minimum number of modal coordinates that can be used in the tower model This investigation proposes FFR model of wind turbines using three sets of coordinates: Cartesian coordinates plus the Euler parameters to present the rigid body motion (Nacelle and rotor bodies). The paper examines the effectiveness of the proposed FFR formulation in modeling small-size wind turbines as well as the effect of the tower dynamics on the rotor speed

Dynamics of multibody system

FFR Based Nodal Coordinates

FFR Based Modal Coordinates

Multibody mixed coordinates model

Numerical and experimental study

Conclusions