Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis

Diederik den Dekker September 9th 2010

U.S. President Obama visits Siemens rotor blade plant in the U.S. state of Iowa, april 28th, 2010

Agenda

Introduction

Goal of Study

Method

Results

Conclusions & Recommendations

3

Introduction

Horizontal Axis Wind Turbine

5

Wind industry is growing rapidly

6

Wind turbines can become a mayor energy source by

reducing their costs

* U.S. estimate for plants entering service in 2016

7

Structural dynamics is the cornerstone of cost

reduction

8

Dynamic analysisDynamic analysis

OptimizationOptimizationTurbine designTurbine design

Behavior predictionBehavior prediction

Cost Reduction!Cost Reduction!

Linear dynamic formulation

m&&x + kx=F

Single DoF system Multiple DoF system

m1

x1

Fm2k1 k2

x2

m1 0

0 m2

⎡

⎣⎢⎢

⎤

⎦⎥⎥

&&x1

&&x2

⎡

⎣⎢⎢

⎤

⎦⎥⎥+

k1 −k2

−k2 k2

⎡

⎣⎢⎢

⎤

⎦⎥⎥

x1

x2

⎡

⎣⎢⎢

⎤

⎦⎥⎥=

0

F

⎡

⎣⎢⎢

⎤

⎦⎥⎥ M&&x + Kx=F

x

k

Fm

9

m ff&&q f + K ffqf = Qe( ) f

x1

x2

x3

10

Linear dynamic formulation

No rotations

No operational analyses

Linear formulation: small body deformationsx1

x2

11

x1

x2

12

x1

x2

′x1

′x2

Floating Frame of Reference (FFR)

13

x1

x2

&&q fm ff K ff q f Qe( ) f+ =

′x1

′x2

Floating Frame of Reference (FFR)

14

&&qr&&q f

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

0 00 K ff

⎡

⎣⎢⎢

⎤

⎦⎥⎥

qrq f

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Qe( )r

Qe( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

+ =

x1

x2

′x1

′x2

Floating Frame of Reference (FFR)

15

&&qr&&q f

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

0 00 K ff

⎡

⎣⎢⎢

⎤

⎦⎥⎥

qrq f

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Qe( )r

Qe( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Qv( )r

Qv( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

+ = +

x1

x2

′x1

′x2

16

Floating Frame of Reference (FFR)

&&qr&&q f

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

0 00 K ff

⎡

⎣⎢⎢

⎤

⎦⎥⎥

qrq f

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Qe( )r

Qe( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Qv( )r

Qv( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

+ = +

x1

x2

′x1

′x2

17

Non-linear

Floating Frame of Reference (FFR)

FFR mass matrix

18

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

36 DoF System in 1 FFR

FFR mass matrix

QuickTime™ and aH.264 decompressor

are needed to see this picture.

mrr qr ,q f( ) mrf qr ,qf( )

mrfT qr ,qf( ) mff

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

19

FFR mass matrix mrr qr ,q f( ) mrf qr ,qf( )

mrfT qr ,qf( ) mff

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

20

36 DoF System in 1 FFR

FFR adds rotational effects to a linear

formulation

m ff&&q f + K ffqf = Qe( ) f

21

Method

FormulationCharacteristic

s

Linear Efficient

FFR Rotations

&&qr&&q f

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

0 00 K ff

⎡

⎣⎢⎢

⎤

⎦⎥⎥

qrq f

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Qe( )r

Qe( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Qv( )r

Qv( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

+ = +

Siemens Wind Power uses two tools for structural

dynamic analysisBHawCSiemens DS Tool

22

BHawC DS Rotating DSSimplified

Rotating DS

Rotations ✓ ✕ ✓ ✓

Model detail

CPU Speed ? ? ?23

Methodologies

Goal of Study

To what extent can the rotational effects be simplified...

...for various wind turbine operational analyses...

...without significantly impacting their dynamic characteristics?

25

Method

FFR simplification methodology

&&qr&&q f

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

mrr mrf

mrfT m ff

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

0 00 K ff

⎡

⎣⎢⎢

⎤

⎦⎥⎥

qrq f

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Qe( )r

Qe( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Qv( )r

Qv( ) f

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

+ = +

M qr ,q f( )&&q+ Kq=Qe &qr , &qf ,qr ,qf( ) +Qv &qr , &qf ,qr ,qf( )

Investigate which DoF to fixInvestigate which DoF to fix

27

Determine fixed position of DoFDetermine fixed position of DoF

Fix DoF in equation of motionFix DoF in equation of motion

Simplified equations of motion Simplified equations of motion

M&&q + Kq=Qe +Qv( )

Investigation into the efficiency and accuracy of

simplified models

Accuracy and

CPU speed

Accuracy and

CPU speedVerificationVerification

BHawC model

BHawC model

Load CasesLoad Cases

OutputOutput

Reference

model

Reference

model

Load CasesLoad Cases

OutputOutput

Simplified

models

Simplified

models

Load CasesLoad Cases

OutputOutput

Siemens SWT-2.3-93

Nominal power: 2.3 MW

Rotor diameter: 93m

Operating wind speed: 4 - 25m/s

Rotor speed: 6 - 16RPM

Turbines in operation: 1,374

29

xxxx

xx

X3

X2X1

X3

X2X1

X2iX1

i

X3i

X1i

X3i

X2i

Siemens FFR wind turbine (SFW)model

30

Siemens FFR wind turbine (SFW)model

• 49 DoF

• 1 FFR

xxxx

xx

X3

X2X1

X3

X2X1

X2iX1

i

X3i

X1i

X3i

X2i

Three load cases are used to test the simplifications

Steady State

Wind Gust

Emergency Shut Down

32

33

Steady State:

Rotor speed:

16RPM

Wind speed:

14m/s

Extracted power:2.3MW

(blade deformation magnified 10x)

All units along axes in meters

34

Emergency Shut Down

Initial rotor speed:

16RPM

Wind speed:

14m/s

Shut down time: <10s

QuickTime™ and aH.264 decompressor

are needed to see this picture.

All units along axes in meters

Results

Deformation DoF Rotation DoF

Fix Fix

ϕθψ q f

Simplificationone

Simplificationtwo

Simplification

Three

Three simplifications discussed today

ReferenceModel

36

Deformation DoF Rotation DoF

Fix Fix Fix

ϕθψ q f

Simplificationone

Simplificationtwo

Simplification

Three

Three simplifications discussed today

ReferenceModel

37

Deformation DoF Rotation DoF

Fix Fix Fix Fix

ϕθψ q f

Simplificationone

Simplificationtwo

Simplification

Three

Three simplifications discussed today

ReferenceModel

38

Deformation DoF Rotation DoF

ϕθψ q f

Simplificationone

Simplificationtwo

Simplification

Three

Three simplifications discussed today

ReferenceModel

39

Average CPU speed increase

per time step*

*excluding overhead40

41

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Steady State

42

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Steady State

43

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Steady State

44

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Wind Gust

45

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Wind Gust

46

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Wind Gust

47

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Emergency Shut Down

48

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Emergency Shut Down

49

Simplificationone

Simplificationtwo

Simplification

ThreeReference

Model

Accuracy: Emergency Shut Down

Simplifications often show negligible differences with

the reference modelmaximum relative difference in mean & standard deviation

<10% <5% <1%

Steady State Three Three Three

Wind Gust Three Three Three

EmergencyShut Down

Two One One

50

Conclusions & Recommendations

Main conclusions

• Simplifications prove that rotational effects can be simplified for dynamic wind turbine models at minimal accuracy loss:

• The SFW model’s CPU speed can be increased up to 140 times in steady cases

• The SFW model’s CPU speed can be increased up to 5 times in transient cases.

• Complete `linearization’ is not possible when external forces are defined in different axes w.r.t. the body they act on 5

2

Main recommendations

• Apply FFR and its simplififcations to the Siemens DSTool

• Investigate simplified FFR applied to models of other wind turbine types

• Investigate simplified FFR for other applications with (‘axisymmetric’) rotating bodies

53

Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis

Diederik den Dekker September 9th 2010

Quadratic velocity vector to ‘virtual dynamic

properties’

Quadratic velocity vector to ‘virtual dynamic

properties’

Qv =Cvij &q+ K v

ijq+ Fvij

Mij&&q +Cv&q+ K + K v( )q=Qe + Fv( )