1. Determining Mechanical Loads for Wind Turbines
Grid
Pitch
Yaw
Rotor Speed
Blades
Tower
Geartrain
Generator
Hub
Lift
Wind
FE Modes
Blade
Determining Mechanical Loads for Wind Turbines
Steve Miller
Technical Marketing, Physical Modeling
MathWorks

2. Key Points
Key Takeaways
Summarize the key points
about this release.
Blade
Efficient development requires the ability to control the tradeoff between model fidelity and simulation speed
Creating reusable models of custom physical elements eliminates redundant work
Access to different modeling approaches lets you include the right amount of detail
FE Modes

3. Agenda Wind turbine system-level model
Modeling the blades and pitch linkage
Adding flexible bodies to the system
Modeling the geartrain
Adding custom mechanical elements
Adding aerodynamics loads

4. Model Blade Pitch Linkage
Problem: Model the blade pitch actuation linkage in the Simulink environment
Solution: Use SimMechanics to model the mechanical linkage

5. Agenda Wind turbine system-level model
Modeling the blades and pitch linkage
Adding flexible bodies to the system
Modeling the geartrain
Adding custom mechanical elements
Adding aerodynamics loads

6. Flexible Bodies in SimMechanics
Lumped parameter approach
Chain of rigid elements connected by spring/dampers
Finite Element Approach
Export eigenmodes from FE program and import into Simulink
Superimpose deflection due to flexibility onto rigid body motion
Rigid Body
FE Software 1 2 3 4
Massless Body
Reaction Force
State-Space Model
Deflection Joint
Deflection Motion
Rigid Body

7. Flexible Blades in SimMechanics
Model:
Problem: Model the blades as flexible cantilevers in the Simulink environment.
Solution: Use SimMechanics to model the flexible body with two approaches (lumped parameter, imported FEA modes).
Massless Body
State-Space Model
Deflection Joint
Rigid Body

8. Agenda Wind turbine system-level model
Modeling the blades and pitch linkage
Adding flexible bodies to the system
Modeling the geartrain
Adding custom mechanical elements
Adding aerodynamics loads

9. Modeling the Geartrain in SimDriveline
Hub Shaft
Generator Shaft
Helical Gear
Helical Gear
Planetary Gear
Problem: Model the geartrain of the wind turbine within the Simulink environment to determine the torque loads.
Solution: Use SimDriveline to model the geartrain.

10. Agenda Wind turbine system-level model
Modeling the blades and pitch linkage
Adding flexible bodies to the system
Modeling the geartrain
Adding custom mechanical elements
Adding aerodynamics loads

11. Creating Custom Models of Physical Components
Torque = -
Problem: Create a new physical modeling component for use in the Simulink environment using this equation.
Solution: Use the Simscape language to model the component.
MATLAB based
Object-oriented
Define implicit equations (DAEs and ODEs)

12. Extend and Create Libraries
Define the physical ports for the Simscape block
Reuse existing physical domains to extend libraries
Define new physical domains

13. Define User Interface
Parameters, default values, units, and dialog box text all defined in the Simscape file (extension .ssc)

14. Simscape Language: MATLAB Based
Use MATLAB functions and expressions for typical physical modeling tasks:
Analyze parameters
Perform preliminary computations
Initialize system variables
Syntax closely follows MATLAB language

15. Create Reusable Components
Equations defined in a text-based language
Based on variables, their time derivatives, parameters, etc.
Define simultaneous equations
Can be DAEs, ODEs, etc.
Assignment not required
Specifying inputs and outputs n ot required
Torque = -
Angular Velocity =

16. Model Components Spanning Additional Physical Domains
Electrical
Electrochemical and electrical
Model components in nearly any physical domain (hydraulic, pneumatic, etc.)

17. Agenda Wind turbine system-level model
Modeling the blades and pitch linkage
Adding flexible bodies to the system
Modeling the geartrain
Adding custom mechanical elements
Adding aerodynamics loads

18. Model the Force of the Wind on the Blades
Single Element Model
Drag
Lift
Model:
Wind
Wind
Moment
Multiple Element Model
Problem: Model the loads on the blades due to the wind and the spinning of the blades
Solution: Use Simulink and Embedded MATLAB to create models at varying levels of detail
Drag
Lift
Wind

19. Modeling the Forces on the Blades: Calculating Lift and Drag
Force on blade depends upon wind speed, direction, and rotor speed
Lift
Drag
Lift = 0.5*v2*Area*ρ*CL
Drag = 0.5*v2*Area*ρ*CD Where CL&CD= f(Angle of Attack, Re,…)
Positive
Pitch Angle (θ)
Rotation Wind = Rotor Speed(ω)*radius
Inflow Angle
= atan
Pure Wind
Rotation Wind
Pure Wind (Vinf) α
Resultant Wind =
Angle of Attack(α)
Inflow Angle -
Pitch Angle

20. Modeling the Forces on the Blades: Segmented Blade Approach
Wind speed varies along the blade
Use Embedded MATLAB to model the force
Rotation Wind

21. Key Points
Key Takeaways
Summarize the key points
about this release.
Blade
Efficient development requires the ability to control the tradeoff between model fidelity and simulation speed
Creating reusable models of custom physical elements eliminates redundant work
Access to different modeling approaches lets you include the right amount of detail
FE Modes

22. Automatically Generating C Code
Model:
Do not use in R2011a P1 P2 Px 10 …
100
Problem: Minimize the simulation time on a parameter sweep to determine controller parameters.
Solution: Use Simulink Coder to create standalone executable.
Standalone Executable
Parameters 1
Parameters 2
Parameters 3
Parameters 4

23. Parameter Sweep using Code Generation
Steps to perform parameter sweep
1) Build standalone executable
2) Generate different parameter sets
3) Run standalone simulation
4) Plot results
Do not use in R2011a
Standalone Executable
>>rtwbuild(Model_Name);
Parameters 1
>>[rtpstruct]= rsimgetrtp(Model_Name);
Parameters 2
Parameters 3
Parameters 4
>>!<model name> -p <parameters>.mat -o <results>.mat

24. Parameter Sweep using Code Generation
Advantages of using standalone executable
Enables rapid simulation with different parameter sets ideal for batch testing or Monte Carlo simulation.
Simulations can be run on different computers, reducing analysis time.
Do not use in R2011a