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1 st International Workshop on Modelling and Optimization of Power Generating Kites KITE-OPT 07

1 st International Workshop on Modelling and Optimization of Power Generating Kites KITE-OPT 07. Moritz Diehl Optimization in Engineering Center (OPTEC), K.U. Leuven and Boris Houska, Andreas Ilzhoefer IWR, University of Heidelberg Co-sponsored by OPTEC, ICCoS.

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1 st International Workshop on Modelling and Optimization of Power Generating Kites KITE-OPT 07

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  1. 1st International Workshop on Modelling and Optimization of Power Generating KitesKITE-OPT 07 Moritz Diehl Optimization in Engineering Center (OPTEC), K.U. Leuven and Boris Houska, Andreas Ilzhoefer IWR, University of Heidelberg Co-sponsored by OPTEC, ICCoS Moritz Diehl ESAT 00.62, January 30, 2007

  2. Overview • What is OPTEC ? • Motivation and Today‘s Program Moritz Diehl

  3. What is OPTEC? Founded as “Center of Excellence: Optimization in Engineering“ (12 centers of this type at K.U. Leuven) Five year project with 500.000 Euro per year, from 2005 to 2010 Promoted by four engineering departments, in order to connect OPTIMIZATION METHODS AND APPLICATIONS: • CHEM - Chemical Engineering • CS - Computer Science • ESAT - Electrical Engineering • MECH - Mechanical Engineering New positions: • 4-6 PhD, 2-4 Postdoc • new professorship (at ESAT) for „Principal Investigator“ (M.D.) Moritz Diehl

  4. Quarterly and Weekly OPTEC Lecture Series • Quarterly „Simon Stevin Lecture on Optimization in Engineering“: • Dec. 6: Larry Biegler, CMU Pittsburgh (past) • Mar. XX: Julio Banga, Varga, Spain (tentative) • July XX: Steven Wright, Wisconsin • Oct 26: Manfred Morari, ETH Zurich • Dec XX: David Mayne, Imperial, London (tentative) Simon Stevin, 1548-1620) • „K.U. Leuven Seminar on Optimization in Engineering“ : • Jan. 31: Mario Milanese (Torino): MPC of semi-active damping • Feb. 8: Philippe Toint (Namur): large scale optimization methods • Feb. 22: Peter Kuehl (Heidelberg): Robust optimal feedback control • March 1: Yurii Nesterov (UCL)/ Florian Jarre (Duesseldorf): new optimization algorithms Moritz Diehl

  5. OPTEC Aim Become a center where • mathematical optimization is driven and inspired by engineering demands, and • engineering innovation profits from the use of modern optimization techniques. Kite Wind Power project excellent example for symbiosis of methods and applications Moritz Diehl

  6. Overview • What is OPTEC ? • Motivation and Today‘s Program Moritz Diehl

  7. Conventional Wind Turbines • Due to high speed, wing tips are most efficient part of wing • High torques at wings and mast limit size and height of wind turbines • But best winds are in high altitudes! Could we construct a wind turbine with only wing tips and generator? Moritz Diehl

  8. Conventional Wind Turbines • Due to high speed, wing tips are most efficient part of wing • High torques at wings and mast limit size and height of wind turbines • But best winds are in high altitudes! Could we construct a wind turbine with only wing tips and generator? Moritz Diehl

  9. Kite Wind Power [Loyd 1980, Ockels 1996, Ippolito/Milanese 2004, D. 2006,...] • use kites with high lift-to-drag-ratio • use strong lines, but no mast and basement • automatic control keeps kites flying • Allows to exploit the strong winds in high altitudes But how could a generator be driven? Three teams give different answers... Moritz Diehl

  10. Today‘s Schedule (ESAT, 00.62) • 9:00 Welcome (M. Diehl) • 9:10 Keynote W. Ockels: The Laddermill Project • 10:00 Coffee Break • 10:30 Delft Presentation (B. Lansdorp, A. Podgaets, J. Breukels, R. Ruiterkamp) • 11:10 Keynote M. Milanese: The KiteGen Project • 12:00 Lunch (The Lodge) • 14:00 M. Diehl: Optimal Control of Kites • 14:45 B. Houska: Robustly Stable Orbits • 15:15 A. Ilzhoefer: Predictive Control of Kites • 15:45 Coffee Break • 16:15 K. Lindholm; A System Perspective • 16:45 Discussion on Future Plans • 18:00 End Moritz Diehl

  11. The Leuven-Heidelberg Approach to Optimization of Power Generating Kites Moritz Diehl Optimization in Engineering Center (OPTEC) K.U. Leuven, Belgium joint work with Boris Houska, Andreas Ilzhoefer, Karin Lindholm Moritz Diehl KITE-OPT 07, January 30, 2007

  12. Organisation of the Talk • Basic Idea • Kite Modelling • Periodic Optimization Problem Formulation • Numerical Methods for Optimal Control • Nonlinear Model Predictive Control • Five Provocative Claims Moritz Diehl

  13. Conventional Wind Turbines • Wing tips move 8-10 times faster than true wind • Due to high speed, wing tips are most efficient part of wing • High torques at wings and mast limit size and height of wind turbines Could we construct a wind turbine with only wing tips and generator? Moritz Diehl

  14. Conventional Wind Turbines • Wing tips move 8-10 times faster than true wind • Due to high speed, wing tips are most efficient part of wing • High torques at wings and mast limit size and height of wind turbines Could we construct a wind turbine with only wing tips and generator? Moritz Diehl

  15. Crosswind Kite Power (Loyd 1980) • use kite with high lift-to-drag-ratio • use strong line, but no mast and basement • automatic control keeps kites looping But where could a generator be driven? Moritz Diehl

  16. New Power Generating Cycle New cycle consists of two phases: • Power generation phase: • add slow downwind motion by prolonging line (1/3 of wind speed) • generator at ground produces power due to large pulling force • Retraction phase: • change kite‘s angle of attack to reduce pulling force • pull back line Cycle produces same power as (hypothetical) turbine of same size! Moritz Diehl

  17. New Power Generating Cycle New cycle consists of two phases: • Power generation phase: • add slow downwind motion by prolonging line (1/3 of wind speed) • generator at ground produces power due to large pulling force • Retraction phase: • change kite‘s angle of attack to reduce pulling force • pull back line Cycle produces same average power as wind turbine of same wing size, but much larger units possible (independently patented by Ockels, Ippolito/Milanese, D.) Moritz Diehl

  18. Can stack kites, can use on sea Moritz Diehl

  19. Organisation of the Talk • Basic Idea • Kite Modelling • Periodic Optimization Problem Formulation • Numerical Methods for Optimal Control • Nonlinear Model Predictive Control • Five Provocative Claims Moritz Diehl

  20. Kite Model: State Variables Kite position in polar coordinates: Cable elasticity: distinguish true and nominal cable lengths and Velocities are also states, changed by forces at kite and cable Control roll angle and lift: Power = cable force x velocity: forces at kite Moritz Diehl

  21. Kite Model Summarize in form ODE Model with 12 states and 3 controls Control inputs: • line length (2nd derivative) • roll angle (1st der.) • lift coefficient (1st der.) Moritz Diehl

  22. Periodic Optimization Problem Maximize mean power production: by varying line thickness, period duration, controls, subject to periodicity and other constraints: Moritz Diehl

  23. Generic Periodic Optimal Control Problem Moritz Diehl

  24. Organisation of the Talk • Basic Idea • Kite Modelling • Periodic Optimization Problem Formulation • Numerical Methods for Optimal Control • Nonlinear Model Predictive Control • Five Provocative Claims Moritz Diehl

  25. Simplified Problem for Illustration of Algorithms Moritz Diehl

  26. First Approach: Single Shooting Moritz Diehl

  27. Nonlinear Program (NLP) in Single Shooting • After control discretization, obtain NLP: • Solve with NLP solver, e.g. Sequential Quadratic Programming (SQP) Moritz Diehl

  28. Sequential Quadratic Programming (SQP) Moritz Diehl

  29. Toy Problem with One ODE for Illustration Mildly nonlinear and unstable system. Moritz Diehl

  30. Single Shooting Moritz Diehl

  31. Single Shooting: First Iteration Moritz Diehl

  32. Single Shooting: Second Iteration Moritz Diehl

  33. Single Shooting: Third Iteration Moritz Diehl

  34. Single Shooting: 4th Iteration Moritz Diehl

  35. Single Shooting: 5th Iteration Moritz Diehl

  36. Single Shooting: 6th Iteration Moritz Diehl

  37. Single Shooting: 7th Iteration (Solution) Moritz Diehl

  38. Single Shooting: Pros and Cons Moritz Diehl

  39. 2nd Approach: Direct Multiple Shooting [Bock, Plitt 1981] Moritz Diehl

  40. Nonlinear Program in Multiple Shooting Moritz Diehl

  41. SQP for Multiple Shooting Summarize NLP: Moritz Diehl

  42. Toy Example: Multiple Shooting Initialization Moritz Diehl

  43. Multiple Shooting: First Iteration Moritz Diehl

  44. Multiple Shooting: Second Iteration Moritz Diehl

  45. Multiple Shooting: 3rd Iteration (already solution!) Moritz Diehl

  46. Multiple Shooting: 3rd Iteration (already solution!) Single shooting converged much slower! Moritz Diehl

  47. Multiple Shooting: Pros and Cons Optimal control package MUSCOD-II (C/C++/Fortran) for large ODE/DAE models continuously developed in Heidelberg and Leuven (Leineweber, Schäfer, Diehl, Sager, Albersmeyer, Potschka, ..., 1999 - ) Moritz Diehl

  48. The MUSCOD Team in Heidelberg Crucial Algorithmic Features for Fast NMPC Moritz Diehl

  49. Periodic Problem in Multiple Shooting Moritz Diehl

  50. Kite Periodicity and Boundary Conditions Moritz Diehl

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