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Detailed Modeling and Simulation of
Wind Turbines for Certification Purposes
Load Case Simulations
Certification bodies require manufacturers to simulate entire wind turbine systems subject to specific wind and operating
conditions. The simulation results are used for the initial dimensioning of components and certification purposes.
How detailed are standard models?
Simplified Multi-Body Simulation (MBS) models, generally up to 28 degrees of freedom (DOF) are used (Fig. 1). These models
consider only the first four eigenfrequencies of the rotorblades, two in the flapwise and edgewise directions. The eigenfrequencies
of which usually lie below 5 Hz for 1 MW turbines and above. Similarly, only the first two bending modes of the tower are
considered. Aerodynamics are simulated using the Blade Element Momentum (BEM) theory which is based on the quasi-static
change of air momentum passing through the entire rotor area. The drivetrain is generally modeled as two lumped inertias, rotor
and generator side, connected by a torsional spring (Fig. 2). Rudimentary control systems are used to control the rotorblade pitch
angles, nacelle yaw angle and electrical connection to the grid.
What do the standard models not consider?
Higher frequency bending and torsional modes of the blades and tower are not included. Internal mechanical components of the
drivetrain, azimuth and pitch systems are also neglected. Resonances are often the primary cause of malfunctions due to fatigue
and over loading but are almost completely ignored within the initial load case simulations.
What are the advantages of more detailed models?
Using higher fidelity models results in a better understanding and optimization of resonances and component loads within the
complete turbine system, not only for mechanical components but also for aerodynamics and control strategies. Cost optimization
is possible through minimized material use and reduced maintenance.
Conclusion
Standard MBS models are used for carrying out load simulations. Certification and
dimensioning of components is based upon the results of these simulations. Resonance
analysis of models, with detailed drivetrain components, are also carried out for certification
purposes. By considering further detail in the mechanical, electrical, aerodynamic and control
models, a significant reduction of loads can be achieved which enables saving of weight and
therefore manufacturing costs.
Minimizing and eliminating resonances is essential for achieving a lifespan of twenty years.
Since testing is extremely limited due to accessibility and weather conditions, a high
emphasis must be placed upon simulations with detailed models.
Modeling Principals for Drivetrains
The GL Guideline for the Certification of Wind Turbines (2010) requires manufacturers to
perform a Drivetrain Resonance Analysis. All potential resonances between cut-in and cut-
out speed must be identified and then determined whether or not critical.
The MBS models include all components from the rotor through to the generator. The
generator forces are applied using a simple non-linear torque function dependent upon
rotational velocity. Detailed elements are used to model the gear wheels, bushings and
bearings. The rotor blades, shafts, planet carriers and couplings are modeled as flexible
bodies.
Statistics: Blade deflection Flapwise Statistics: Root Bending Moment
S. Mulski, L. Mauer, SIMPACK AG, www.SIMPACK.com
Higher Fidelity Wind Turbine Models
Higher accuracy and confidence in the results of the simulations can be achieved by additional modeling
detail. Including pre-bend and pre-sweep, along with higher frequencies of the rotorblades, has an
important influence on system behavior. Particularly the bend-twist coupling of the rotorblades becomes
increasingly important with increasing turbine size. For the IEC Ultimate Load Case 1.3 differences can
be seen between using basic rotorblade modeling, which do not include twist, and advanced with bend-
twist coupling (Fig. 12).
Potential Flow (Lifting Line Free Wake Vortex) is a processing time efficient method which also enables
individual pitch and larger yaw angles to be computed, as opposed to using BEM method with empirically
based correction factors. For extreme load conditions, such as sudden wind gust with change of direction,
using methods other the BEM theory can be advantageous. Full CFD-MBS coupling is generally not used
commercially due to the required computation time (Fig. 11). As always, when increasing modeling fidelity,
a trade-off between simulation times and accuracy must be made.
Further detail and frequency content can be included within most mechanical components. Since all
drivetrain components are coupled by the bedplate, including the flexibility thereof may be necessary in
order to achieve accurate loads. Detailed mechanics and hydraulics, when necessary, can also be
included for more accurate resonance analysis and in order to obtain internal loadings.
Interfaces to MATLAB and Simulink are often used to achieve fidelity above what is attainable with
standard interfaces to wind turbine controller DLLs. Not only are detailed generator and inverter models
used, with more refined turbine control strategies, but also the electrical coupling between turbines is
often considered. Paying particular attentions to control when connecting to the grid or dealing with Low
Voltage Ride Through (LVRT) can also lead to reduced loads (Fig. 13).
Fig. 1: Offshore wind turbine simulation model (SWE Uni-Stuttgart)
Fig. 2: Simplified drivetrain
Fig. 3: Model for drivetrain
resonance analysis
Fig. 12: Rotorblade bend-twist coupling (SWE Uni-Stuttgart)
Fig. 11: MBS-CFD coupling (SWE Uni-Stuttgart)
Fig. 13: Load reduction with higher fidelity modeling
Time
Gear Wheels
Detailed gear wheel elements are used for accurately
simulating meshing frequencies and loading. The
require parameters are based upon the ISO 6336. The
contact locations are calculated analytically. Radial and
angular misalignments are considered which is
particularly important for planet stages with floating
suns. Profile and flank modifications are required for
achieving realistic force distribution. Fig. 5: Contact forces on gear wheel
with crowning
Bearings and Bushings
Simple linear stiffness and damping coefficients under nominal
loading conditions can be used. Full 6x6 stiffness and damping
matrices which consider the cross-coupled terms can also be
included within the model. The internal dynamics of bushings
can be considered by using frequency dependent force
elements which are calibrated in a pre-curve-fitting step.
Specific bearing codes from suppliers are also commonly used.
Detailed MBS models (Fig. 4), which consider the individual
roller–race contacts, are not generally used for system
simulation due to required simulation times. Fig. 4: Detailed bearing model
Flexible Bodies
Euler-Bernoulli and Timoshenko theory is used
for modeling the rotorblades, tower and shafts.
Second order non-linear bending and stiffening
due to centrifugal forces can be included.
More complex structures such as the gearbox
housing and planet carrier, which have a large
effect on system behavior, can be imported from
Finite Element software using modal synthesis. Fig. 7: Flexible main shaft and planet carrier
Eigen-Energy Plots
At each intersection on the 2D Campbell plot the
normalized energy of all bodies corresponding to the
eigenmode are plotted (Fig. 9) . If the energy of the
body related to the excitation order does not appear, or
only has a low involvement, the resonance can be
ruled out. If, however, this is not the case, than further
investigation using 3D Order Analysis is necessary. Normalized Energy
Fig. 9: Normalized energy plot
2D Campbell Plot
Once the drivetrain model is complete a run-up
simulation is preformed and the eigenfrequencies up to
several hundred Hertz are plotted over rotational speed
(Fig. 8. red dots). All possible excitation orders (diagonal
lines), which correspond to rotational velocities and gear
pair meshing frequencies, are entered. The lower
harmonics of the excitation orders are also entered. All
intersections between cut-in and cut-out speed need to
be investigated for possible resonance for which
normalized eigen-energy plots are used. Fig. 8: 2D Campbell plot
Rotational Speed
Fre
qu
en
cy
Spline Couplings
Another common element in drivetrains is the spline
coupling. This element is commonly used with planet
stages in order to allow for the “free” motion of floating
suns. A simulation requirement for splines is profile
and flank modification and the ability to allow for radial
and angular misalignments.
Fig. 6: Spline coupling with angular
misalignment
3D Order Analysis
The time domain results of the run-up analysis, of
any signal, can be plotted using a 3D Campbell filter
(Fig. 10). This plot is similar to the 2D Campbell plot
but now includes the amplitude of the signal as the
third axis, which enables resonances to be seen as
peaks. Particular attention has to be given to
damping parameters within the models when
investigating the resonance amplitude. Fig. 10: 3D order analysis
KOMAI TEKKO Inc.: Wind turbine KWT300