TURBU Offshore

Goal

The integrated assessment of control and aero-elastic stability for modern and future multi-MW turbine requires the availability of tools that combine accurate structural models with the capability of transfer function analysis. Further, the design of especially offshore wind turbines is strongly assisted by fast sensitivity analyses and fast selection of design driving wind and wave conditions. Frequency domain based load calculations use to render the desired computational efficiency. 

TURBU Offshore is a tool that complies with all these demands. It is a software package written in MATLAB for linear modeling and analysis of horizontal axis wind turbines, which may be sited onshore or offshore. TURBU creates elaborate linear time invariant (LTI) models for 3 blade wind turbines.  Both aero-elastic and hydro-elastic interaction is catered. Feedback loops for control can be easily linked to the (open loop) LTI wind turbine model. TURBU also facilitates the combined creation and application of closed loop LTI models. Built-in analysis capability pertains to load calculation, controller evaluation and modal analysis. An impression is given in figure 1.

Model features

TURBU Offshore enables to create a LTI wind turbine model that does and be driven by wind speed variations and waves, or does not

• 3D deformation behavior of foundation by 6 degrees of freedom (DOF);
• bending and torsion of tubular tower (multi-body approach);
• roll, yaw and tilt of nacelle by 6 DOF with control option for yaw;
• variable speed drive train by controllable or viscous-elastic generator torque and gearbox house support torque with DOF for rotor shaft bending and torsion
• bending and torsion of rotor blades (multi-body approach) with flap and lead hinges and pitch servo actuation or direct distributed twist angle control;
• aerodynamic conversion by Blade Element Momentum theory extended with the ECN Dynamic stall model for unsteady profile aerodynamics and the ECN Differential Equation Wake model for dynamic inflow;
• Hydrodynamic conversion based on statistical linearization of Morison’s equation.

Next to the mentioned modeling options, TURBU allows for excluding any DOF and allows including lumped DOF in the tower bottom and blade roots. This enables systematic search for structural properties that cause certain (undesired) observed dynamic behavior.

Figure 2 shows the layout of the wind turbine concerned with the structural model.

Local coordinate systems exist on each element of the multi-body models of the support structure and the rotor blades. Specific structural layout choices as by average yaw, rotor shaft tilt, rotor coning, skew oriented blade axis and blade pre-bend appear as average rotations in the transformation from one local coordinate system to another. This also holds for the average deformation state of the tower and blades and the average pitch angles.

Wind speed variations in axial, tangential and radial direction are allowed for as LTI model input signals on each blade element for load variations. User buttons exist that restrict the wind input signals to axial variations only and/or to only one.

The linear model equations are derived around the average conditions of the wind turbine, which are obtained with solvers for the non-linear BEM equations in the equilibrium and the non-linear average deformation of the rotor blades and tower. The size of the linearized dynamic multi-body blade and tower models can be significantly lowered through boundary constrained modal reduction as per Hurty and Craig & Bampton. A multi-blade transformation as proposed by Coleman & Feingold and a shaft-symmetry transformation are applied for elimination of the azimuth dependency of model coefficients that would arise from the coupling of the tower model to the `rotating models’ of the drive-train and the blades.

Modal Analysis

The computation of aero-hydro-elastic or structural frequencies and damping rates, as well as the simulation and visualization of mode shapes and modal trajectories is provided by built-in MATLAB functions. Mode shapes are shown in extreme positions of the elastic line in the tower and the rotor blades while modal trajectories are shown in time plots and phase/space plots. The modal analysis option includes:

• mode shapes of blade and tower deformation;
• modal trajectories of displacements of the tower top, rotor centre and blade tip and of the centers of element boundaries for the tower and rotor blades ;
• modal trajectories of internal moments in element boundaries for tower and rotor blades;
• model trajectories of setting angle, angle of attack, blade relative wind speed coordinates and aerodynamic profile coefficients for blade elements.

Load calculation

Built-in MATLAB functions allow for simulation of the LTI wind turbine model in the frequency and time domain. The simulations are driven by

• axial component of the (oblique inflowing) rotationally sampled longitudinal turbulence, derived from a space invariant homogeneous wind speed spectrum in a fixed location, combined with a  space invariant coherence function and Taylor’s frozen wave hypothesis for turbulence transport.
• periodic axial wind speed variations by tower shadow, wind shear and the oblique-inflow-induced axial induction variation, and periodic tangential wind speed variations from the transverse and vertical wind velocity component;
• horizontal wave speed and accelerations on each underwater tower element, derived from the water surface elevation spectrum combined with Airy’s theory for underwater wave strength fading and the frequency-wave length relationship for shallow water.
• periodic radial and tangential gravitation variations.

The input power spectra and coherence functions for the wind and waves are computed through selections from a list of provided MATLAB functions, which can be modified by the user. The wind speed signals can be created per blade element or per blade. In the latter case, the blade effective wind speed signals are obtained as weighted averages of the element wind speeds (weight proportional to radius).

Intermediate LTI models are derived from the basic LTI wind turbine model in order to match the model input signals to the above mentioned load driving signal.

The results of the load calculations are the auto power spectral density functions or multiple realizations of the (load) output signals of the LTI wind turbine model. The load signals can be processed into statistical measures like variance, mean and extremes and the fatigue equivalent 1Hz or 1p loads.

Controller evaluation

Built-in MATLAB functions allow for simulation of the LTI wind turbine model in the frequency and time domain similar to that for load calculation. Further, they allow for transfer function analysis through amplitude ratios and phase shifts, which enable systematic review of the controller performance.  Perturbations can be added to the control signals, for example in order to examine the loading effect of planned test signals for system identification experiments.

The here derive intermediate LTI models are better suited for controller evaluation through manipulation with user specific MATLAB code than those derived for load calculation.