1. REDUCTION OF TEETER ANGLE EXCURSIONS FOR A TWO-BLADED DOWNWIND ROTOR USING CYCLIC PITCH CONTROL Torben Juul Larsen, Helge Aagaard Madsen, Kenneth Thomsen, Flemming Rasmussen Risø, National Laboratory Technical University of Denmark EWEC 2007,7.-10. May, Milano

2. 2 Outline The 2-bladed turbine The simulation platform – HAWC2 The teeter mechanism  3 influence The cyclic pitch control The control alternative – teeter velocity proportional control - and the combination Results Conclusion

3. 3 The 2-bladed turbine Data based on 3-bladed fictive turbine used in IEA annex 23 benchmark. 3 blades replaced by 2 with same radius and solidity. Downwind configuration. Tilt angle included – no cone angle.

4. 4 Scaling laws for blade scaling Aerodynamic layout: Radius constant 61.5 m Chord and height x 1.5 (constant solidity) Structural layout scale parameters Constant material stress Aerodynamic loads Structural layout - results The material thickness Cross sectional area – and mass Bending stiffness Torsion stiffness

5. 5 The simulation platform HAWC2 Structural model based on a multibody formulation. The turbine structure is modeled as a number of bodies interconnected by joints. Each body include its own coordinate system, hence large rotations are accounted for by a proper subdivision of bodies. Within a body small deflections and rotations are assumed. Forces are placed on the structure in the deflected state, which is essential for pitch loads of the blades.

6. 6 The simulation platform HAWC2 The aerodynamic model is based on Blade Element Momentum. Extended to handle dynamic inflow, dynamic stall, skew inflow, shear effects on the induction and effects of large deflections. For downwind turbines a jet model for the tower shadow deficit is used. This deficit changes location according to the turbulence.

7. 7 The teeter bearing A special bearing that allows for flapwise rotation of the rotor.

8. 8 The delta 3 angle An angle of the teeter bearing axis that enables a direct coupling between teeter and pitch With this defintion of the teeter angle, the change in pitch related to teeter angle is:

9. 9 Gyroscopic motion Basic knowledge of gyroscopic motion is essential for the understanding of two-bladed teetering rotors. A disc spinning with constant speed will turn 90° after the load impact.

10. 10 The basic teeter motion The teeter motion can traditionally be seen in two ways 1. From the shaft in a rotating frame of reference. (classical approach) The centrifugal force is a stiffness term of teeter motion. It can be shown that this system has an eigenfrequency of 1P. A delta 3 coupling will change this natural frequency – but does it reduce the teeter angles? Aerodynamic forces change the damping of the system.

11. 11 Basic teeter motion - continued 2. From outside in a fixed frame of reference. The rotor spins in a plane not perpendicular to the shaft. In this plane a kind of cyclic pitch occurs. This cyclic pitch has a maximum at 90 degrees before the teeter maximum. Another way of observing the system:

12. 12 Basic teeter motion – linear shear case Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom

13. 13 Delta 3 coupling – example 8m/s Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom

14. 14 Delta 3 coupling – example 20m/s Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom

15. 15 Finding the teeter plane - decoupled around two axes Front view Side view z x z y

16. 16 A PI-regulator on each axis is aplied And the phase shift of β=90° is included in the transformation to pitch angles. Servo delays can also be included in this angle PI 0 0 z x

17. 17 Filters need to be included too PI 0 2P 1P 0

18. 18 Cyclic pitch example – linear shear case Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom

19. 19 Alternative control using teeter velocity proportional pitch Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom

20. 20 Different qualities for the approaches. 20m/s with turbulence Collective pitch: A large deterministic 1P content present. Cyclic pitch: The determistic 1P content removed. Velocity proportional pitch: General load reduction, but 1P content still present. The combination of cyclic and velocity proportional pitch joins the advantages.

21. 21 Operational loads 4-25m/s – statistics – IEA61400 class IA

22. 22 Operational loads 4-25m/s - statistics

23. 23 Operational loads – 20 years of operation mColCycVelCyc+Vel Blade 1 flap121.00 1.01 Blade 1 edge121.001.01 1.02 Blade 1 torsion81.000.99 1.00 Tower top tilt51.001.01 Tower top side51.000.981.000.99 Tower top yaw51.00 Tower bottom tilt51.000.991.000.99 Tower bottom side51.000.97 Tower bottom yaw51.00

24. 24 Conclusion Cyclic pitch can be used to limit teeter excursions without causing extra loads If a direct coupling between teeter velocity and blade pitch can be done this is a very simple and efficient way to limit teeter excursions. A coupling between cyclic pitch and velocity proportional pitch is possible and gives very good result. A reduction of 52% teeter angle excursion is possible – IEC 61400-1 class IA operational loads. Delta 3 coupling in the teeter bearing does not reduce teeter angle excursion (for this size of turbine) but induce extra loads. This does not seem to be a a good approach for a modern large scale turbine!