1© 2011 The MathWorks, Inc.

Determining Mechanical Loadsfor Wind Turbines

Steve Miller

Technical Marketing, Physical Modeling

MathWorks

FEMode

s

Blade

http://www.mathworks.com/physical-modeling/

Grid

Pitch

Yaw

RotorSpeed

Blades

Tower

Geartrain GeneratorHub

Lift

Wind

2

Key Points

Efficient development requiresthe ability to control the tradeoffbetween 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

FEMode

s

Blade

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 PitchLinkage

Problem: Model the blade pitch actuation linkage in the Simulink environment

Solution: Use SimMechanics to model the mechanical linkage

Model:

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

DeflectionJoint

DeflectionJoint

State-SpaceModel

MasslessBody

MasslessBody

ReactionForce

ReactionForce

DeflectionMotion

RigidBody

RigidBody

RigidBody

RigidBody

RigidBody

Rigid Body

1 2

3 4

FESoftwar

e

7

Flexible Blades in SimMechanics

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).

Model:

Rigid Body

State-SpaceModel

DeflectionJoint

MasslessBody

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

Problem: Model the geartrain of the wind turbine within the Simulink environment to determine the torque loads.

Solution: Use SimDriveline to model the geartrain.

Model:

PlanetaryGear

HelicalGear

HelicalGear

HubShaft

GeneratorShaft

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

Problem: Create a new physicalmodeling component for use in the Simulink environment using this equation.

Solution: Use the Simscape language to model the component.

Model:

MATLAB basedObject-orientedDefine implicit equations (DAEs and ODEs)

Torque = - 2k

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

Torque = -Angular Velocity =

2k

dt

d

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

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 ofthe Wind on the Blades

Problem: Model the loads onthe 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

Model:

Lift

Drag

Wind

Single Element Model

Multiple Element Model

LiftDrag

Wind

Wind

Moment

19

Modeling the Forces on the Blades:Calculating Lift and Drag

Force on blade depends upon wind speed, direction, and rotor speed

Pure Wind(Vinf)

Rotation Wind = Rotor Speed(ω)*radius

PositivePitch Angle (θ)

ResultantWind

= atanPure Wind

Rotation WindInflow Angle

Lift = 0.5*v2*Area*ρ*CL

Drag = 0.5*v2*Area*ρ*CD

Where CL&CD= f(Angle of Attack, Re,…)

Lift

Drag

α

=Angle of Attack(α)

InflowAngle

- 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

RotationWind

21

Key Points

Efficient development requiresthe ability to control the tradeoffbetween 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

FEMode

s

Blade