Detailed Modeling and Simulation of. Wind Turbines for Certification Purposes.
Load Case Simulations. Certification bodies require manufacturers to simulate ...
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. Fig. 2: Simplified drivetrain
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.
Modeling Principals for Drivetrains
Bearings and Bushings
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 cutout speed must be identified and then determined whether or not critical.
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
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.
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.
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 Fig. 8: 2D Campbell plot
Gear Wheels
Eigen-Energy Plots
Detailed gear wheel elements are used for accurately
At each intersection on the 2D Campbell plot the
simulating meshing frequencies and loading. The
normalized energy of all bodies corresponding to the
require parameters are based upon the ISO 6336. The
eigenmode are plotted (Fig. 9) . If the energy of the
contact locations are calculated analytically. Radial and
body related to the excitation order does not appear, or
angular
only has a low involvement, the resonance can be
misalignments
are
considered
which
is
particularly important for planet stages with floating suns. Profile and flank modifications are required for achieving realistic force distribution.
KOMAI TEKKO Inc.: Wind turbine KWT300
Fig. 5: Contact forces on gear wheel with crowning
ruled out. If, however, this is not the case, than further investigation using 3D Order Analysis is necessary.
Fig. 3: Model for drivetrain resonance analysis
Flexible Bodies
3D Order Analysis
Another common element in drivetrains is the spline
Euler-Bernoulli and Timoshenko theory is used
The time domain results of the run-up analysis, of
coupling. This element is commonly used with planet
for modeling the rotorblades, tower and shafts.
any signal, can be plotted using a 3D Campbell filter
stages in order to allow for the “free” motion of floating
Second order non-linear bending and stiffening
(Fig. 10). This plot is similar to the 2D Campbell plot
suns. A simulation requirement for splines is profile
due to centrifugal forces can be included.
but now includes the amplitude of the signal as the
and flank modification and the ability to allow for radial
More complex structures such as the gearbox
third axis, which enables resonances to be seen as
and angular misalignments.
housing and planet carrier, which have a large
peaks. Particular attention has to be given to
effect on system behavior, can be imported from
damping parameters within the models when
Finite Element software using modal synthesis.
Normalized Energy
Fig. 9: Normalized energy plot
Spline Couplings
Fig. 6: Spline coupling with angular misalignment
Rotational Speed
be investigated for possible resonance for which normalized eigen-energy plots are used.
Fig. 4: Detailed bearing model
Frequency
Fig. 1: Offshore wind turbine simulation model (SWE Uni-Stuttgart)
Fig. 7: Flexible main shaft and planet carrier
investigating the resonance amplitude.
Fig. 10: 3D order analysis
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 bendtwist 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.
Statistics: Blade deflection Flapwise
Statistics: Root Bending Moment
S. Mulski, L. Mauer, SIMPACK AG, www.SIMPACK.com
Fig. 13: Load reduction with higher fidelity modeling
Conclusion
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).
Time
Fig. 11: MBS-CFD coupling (SWE Uni-Stuttgart)
Fig. 12: Rotorblade bend-twist coupling (SWE Uni-Stuttgart)
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.
