Aeroelastic Modelling of Wind Turbines a report by Spyros G Voutsinas Department of Mechanical Engineering, National Technical University of Athens
Motivation and Context
Wind turbines have considerably advanced over the last 20 years and at present, modern wind turbines have rotor diameters larger than 100 m and are designed to deliver multi-megawatt power for a lifetime of more than 20 years. One of the main drivers of this quick development has been the early definition of safety and reliability standards and their subsequent continuous improvement. The actual process, as detailed in the International Electrotechnical Commission (IEC)-61400 Standard,1 contains the assessment of the design based on estimated loads, reproducing the complete lifetime of a wind turbine. This task is carried out by means of simulation models in which aeroelastic modelling plays a central role.
When referring to aeroelastic modelling of wind turbines, it is important to keep in mind the specific requirements set by the standard as regards the variety of operating conditions and the modelling context of the wind turbine and its components, as well as the extent of these simulations. The list of the so-called ‘design load cases’ (DLC) includes normal operating conditions covering the entire range of wind speeds and normal starts and stops, as well as cases of fault occurrence. The list is quite long, while certain load cases involve several separate 10 minute simulations for each wind speed, resulting in a total number of simulations which is so large that it is practically impossible to avoid simplifying assumptions. Following the progress in aeroelastic modelling over time, there is a clear tendency to remove as many simplifications as possible, provided that the penalty in computational cost is affordable. Therefore, it is expected that there will be a continuous upgrading of comprehensive aeroelastic models by incorporating knowledge and advanced modelling from the research sector. The aim of the present article is to set the general context in which aeroelastic models of varying complexity can be formulated and consider some of the more detailed modelling strategies currently available.
Formulation of the Dynamic Equations
In aeroelastic modelling, wind turbines are considered as multi-component electromechanical systems operating in dynamic equilibrium. The obvious choice has the blades as main components; the drivetrain which contains the gearbox and the generator as sub-components; and the tower.2
Other less conventional components
can also be defined, as, for example, the control system or even the wind flow and the hydrodynamic system. In these cases, aeroelastic models become servo- or hydro-servo-aero-elastic models.3
In order to formulate the corresponding dynamic equations, a suitable approach is defined by the so-called multi-component or multi-body approach in which each component is first considered separately. Depending on the type of component, appropriate models are used that describe their dynamic equilibrium. For example, the main components are modelled as deformable bodies by means of
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a structural model; the wind flow is described by an aerodynamic model; the control system by the control equations, etc. Each separate model will describe the behaviour of the component it refers to. Thus the structural model is formulated with respect to elastic displacements and rotations; the aerodynamic model is formulated with respect to velocities and pressures; the control system is described with respect to the control parameters, etc. All of these quantities constitute the set of the unknown degrees of freedom that together describe the behaviour of the complete system. The components are then coupled by means of appropriately defined contact conditions that establish kinematic and dynamic continuity corresponding to the necessary boundary conditions for each of the separate models used in the first stage.
At solid–solid contacts one of the connected components is selected to define the position and velocity of the contact point, while all others contribute their loads. This is the case at the rotor hub where the blades are connected to the drivetrain and at the top of the tower. Extra rigid-body motions, such as blade rotation, blade pitch or yaw, are added at the contact points which are often linked to the control system.
Fluid–structure interactions can be defined similarly. Of course, in this case, the contact is no longer concentrated; however, the principle remains the same. For example, over the wetted area, the solid component provides the position and velocity of the contact surface while the fluid provides the loading. Note that in general, the coupling conditions are formulated with respect to the unknown degrees of freedom.
External excitation is mainly due to the wind inflow but can also include other effects such as: sea waves and currents in the case of offshore wind turbines; earthquakes in certain cases; and excitation from the electrical grid. Wind inflow is input into the aerodynamic model; sea waves and currents are input into the hydrodynamic system; gravity and earthquake acceleration are input into the structural model; and finally electrical grid excitation is input into the generator sub-model.
By compiling the equations of all components and the corresponding contact conditions and adding the external excitations, the final set of dynamic equations of the complete system is obtained in the following usual MCK form:
Mq + Cq + Kq = Q (1)
where q denotes the vector of the degrees of freedom of the system, M, C and K denote the mass, damping and stiffness operators (matrices) and Q the vector of external excitation. The above form implies that the system is linear, which is misleading since M, C, K
© TOUCH BRIEFINGS 2012
Wind
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