1. Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis Diederik den Dekker September 9 th 2010

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

3. Agenda Introduction Goal of Study Method Results Conclusions & Recommendations 3

4. Introduction

5. Horizontal Axis Wind Turbine 5

6. Wind industry is growing rapidly 6

7. Wind turbines can become a mayor energy source by reducing their costs * U.S. estimate for plants entering service in 2016 7

8. Structural dynamics is the cornerstone of cost reduction 8 Dynamic analysis Optimization Turbine design Behavior prediction Cost Reduction!

9. Linear dynamic formulation Single DoF systemMultiple DoF system 9

10. 10 Linear dynamic formulation

11. No rotations No operational analyses Linear formulation: small body deformations 11

12. 12

13. Floating Frame of Reference (FFR) 13

14. Floating Frame of Reference (FFR) 14

15. Floating Frame of Reference (FFR) 15

16. 16 Floating Frame of Reference (FFR)

17. 17 Non-linear Floating Frame of Reference (FFR)

18. FFR mass matrix 18

19. 36 DoF System in 1 FFR FFR mass matrix 19

20. FFR mass matrix 20 36 DoF System in 1 FFR

21. FFR adds rotational effects to a linear formulation 21 MethodFormulationCharacteristics LinearEfficient FFRRotations

22. Siemens Wind Power uses two tools for structural dynamic analysis BHawC Siemens DS Tool 22

23. BHawCDSRotating DS Simplified Rotating DS Rotations ✓✕✓✓ Model detail CPU Speed ? ? ? 23 Methodologies

24. Goal of Study

25. To what extent can the rotational effects be simplified......for various wind turbine operational analyses......without significantly impacting their dynamic characteristics? 25

26. Method

27. FFR simplification methodology Investigate which DoF to fix 27 Determine fixed position of DoF Fix DoF in equation of motion Simplified equations of motion

28. Investigation into the efficiency and accuracy of simplified models Accuracy and CPU speed Accuracy and CPU speed Verification BHawC model BHawC model Load Cases Output Referenc e model Load Cases Output Simplifie d models Simplifie d models Load Cases Output

29. 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

30. xxxxxxxxxxxx Siemens FFR wind turbine (SFW) model 30

31. Siemens FFR wind turbine (SFW) model 49 DoF 1 FFR xxxxxxxxxxxx

32. Three load cases are used to test the simplifications Steady State Wind Gust Emergency Shut Down 32

33. 33 Steady State: Rotor speed: 16RP M Wind speed:14m/s Extracted power:2.3MW (blade deformation magnified 10x) All units along axes in meters

34. 34 Emergency Shut Down Initial rotor speed: 16RP M Wind speed:14m/s Shut down time:<10s All units along axes in meters

35. Results

36. Deformation DoFRotation DoF Fix Simplification one Simplification two Simplification Three Three simplifications discussed today Reference Model 36

37. Deformation DoFRotation DoF Fix Simplification one Simplification two Simplification Three Three simplifications discussed today Reference Model 37

38. Deformation DoFRotation DoF Fix Simplification one Simplification two Simplification Three Three simplifications discussed today Reference Model 38

39. Deformation DoFRotation DoF Simplification one Simplification two Simplification Three Three simplifications discussed today Reference Model 39

40. Average CPU speed increase per time step* *excluding overhead 40

41. 41 Simplification one Simplification two Simplification Three Reference Model Accuracy: Steady State

42. 42 Simplification one Simplification two Simplification Three Reference Model Accuracy: Steady State

43. 43 Simplification one Simplification two Simplification Three Reference Model Accuracy: Steady State

44. 44 Simplification one Simplification two Simplification Three Reference Model Accuracy: Wind Gust

45. 45 Simplification one Simplification two Simplification Three Reference Model Accuracy: Wind Gust

46. 46 Simplification one Simplification two Simplification Three Reference Model Accuracy: Wind Gust

47. 47 Simplification one Simplification two Simplification Three Reference Model Accuracy: Emergency Shut Down

48. 48 Simplification one Simplification two Simplification Three Reference Model Accuracy: Emergency Shut Down

49. 49 Simplification one Simplification two Simplification Three Reference Model Accuracy: Emergency Shut Down

50. Simplifications often show negligible differences with the reference model maximum relative difference in mean & standard deviation <10%<5%<1% Steady StateThree Wind GustThree Emergency Shut Down TwoOne 50

51. Conclusions & Recommendations

52. 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 52

53. 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

54. Efficient Modeling of Rotational Effects for Wind Turbine Structural Dynamic Analysis Diederik den Dekker September 9 th 2010

55. Quadratic velocity vector to ‘virtual dynamic properties’