Detailed Modeling and Simulation of Wind Turbines for · PDF fileDetailed Modeling and Simulation of Wind Turbines for Certification Purposes Load Case Simulations ... The simulation

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

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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