Use of mixed coordinates in modeling wind turbines including tubular tower

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.

Effectiveness of Using Mixed Coordinates in Modeling Wind Turbines

This paper presents the effectiveness of using mixed, nodal and/or modal coordinates in modeling wind turbines. The paper shows that the nodal model exhibits excellent numerical properties, especially in the case of highly rotations. In the case where the rotation of the rotor-blade is extremely high, the geometric stiffness effect must be taken into account, and therefore, the nonlinear stiffness terms should be included within the model. On the other side, the dynamics of the tower as well as other components can be modeled using a set of modal coordinates. The paper shows a method of utilizing experimental modal coordinates for low speed components and those that deflected by simple motion shapes. The wind-turbine model based on the floating frame of reference formulation and by using the suggested mixed coordinates can be utilized for design process, identification and health monitoring aspects.

A Symbolic Approach to the Multibody Modeling of Road Vehicles

This paper introduces MBSymba, an object-oriented language for the modeling of multibody systems and the automatic generation of equations of motion in symbolic form. MBSymba has built upon the general-purpose computer algebra software Maple and it is freely available for teaching and research purposes. With MBSymba, objects such as points, vectors, rigid bodies, forces and torques, and the relationships among them may be defined and manipulated both at high and low levels. Absolute, relative or mixed coordinates may be used, as well as combination of infinitesimal and noninfinitesimal variables. Once the system has been modeled, Lagrange’s and/or Newton’s equations can be derived in a quasi-automatic way, either in an inertial or noninertial reference frame. Equations can be automatically converted into Matlab, C/C++ or Fortan code to produce stand alone, numerically optimized simulation code. MBSymba is particularly suited for the modeling of ground, water or air vehicles; therefore, the mathematical model of a passenger car with trailer is illustrated as a case study. Time domain simulations, steady state analysis and stability results are also presented.