Moritz Diehl

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

ESAT 00.62, January 30, 2007

Moritz Diehl

Overview

What is OPTEC ?

Motivation and Today‘s Program

Moritz Diehl

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

Quarterly and Weekly OPTEC Lecture SeriesQuarterly „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)

„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

Simon Stevin, 1548-1620)

Moritz Diehl

OPTEC Aim

Become a center where mathematical optimization is driven and inspired by engineering demands, andengineering innovation profits from the use of modern optimization techniques.

Kite Wind Power project excellent example forsymbiosis of methods and applications

Moritz Diehl

Overview

What is OPTEC ?

Motivation and Today‘s Program

Moritz Diehl

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

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

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

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

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

KITE-OPT 07, January 30, 2007

Moritz Diehl

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

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

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

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

New Power Generating CycleNew 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

New Power Generating CycleNew 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

Can stack kites, can use on sea

Moritz Diehl

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

Kite Model: State Variables

forces at kite

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:

Moritz Diehl

Kite Model

Control inputs: line length (2nd derivative) roll angle (1st der.) lift coefficient (1st der.)

ODE Model with 12 states and 3 controls

Summarize in form

Moritz Diehl

Periodic Optimization ProblemMaximize mean power production:

by varying line thickness, period duration, controls, subject to periodicity and other constraints:

Moritz Diehl

Generic Periodic Optimal Control Problem

Moritz Diehl

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

Simplified Problem for Illustration of Algorithms

Moritz Diehl

First Approach: Single Shooting

Moritz Diehl

Nonlinear Program (NLP) in Single Shooting

After control discretization, obtain NLP:

Solve with NLP solver, e.g. Sequential Quadratic Programming (SQP)

Moritz Diehl

Sequential Quadratic Programming (SQP)

Moritz Diehl

Toy Problem with One ODE for Illustration

Mildly nonlinear and unstable system.

Moritz Diehl

Single Shooting

Moritz Diehl

Single Shooting: First Iteration

Moritz Diehl

Single Shooting: Second Iteration

Moritz Diehl

Single Shooting: Third Iteration

Moritz Diehl

Single Shooting: 4th Iteration

Moritz Diehl

Single Shooting: 5th Iteration

Moritz Diehl

Single Shooting: 6th Iteration

Moritz Diehl

Single Shooting: 7th Iteration (Solution)

Moritz Diehl

Single Shooting: Pros and Cons

Moritz Diehl

2nd Approach: Direct Multiple Shooting [Bock, Plitt 1981]

Moritz Diehl

Nonlinear Program in Multiple Shooting

Moritz Diehl

SQP for Multiple Shooting

Summarize NLP:

Moritz Diehl

Toy Example: Multiple Shooting Initialization

Moritz Diehl

Multiple Shooting: First Iteration

Moritz Diehl

Multiple Shooting: Second Iteration

Moritz Diehl

Multiple Shooting: 3rd Iteration (already solution!)

Moritz Diehl

Multiple Shooting: 3rd Iteration (already solution!)

Single shooting converged much slower!

Moritz Diehl

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

Crucial Algorithmic Features for Fast NMPCThe MUSCOD Team in Heidelberg

Moritz Diehl

Periodic Problem in Multiple Shooting

Moritz Diehl

Kite Periodicity and Boundary Conditions

Moritz Diehl

Some Kite Parameters

e.g. 10 m x 50 m, like Boeing wing, but much lighter material

standard wind velocity for nominal power of wind turbines

Moritz Diehl

Periodic Optimization ProblemMaximize mean power production:

by varying line thickness, period duration, controls, subject to periodicity and other constraints:

Moritz Diehl

Periodic Optimization Problem SolutionMaximize mean power production:

by varying line thickness, period duration, controls, subject to periodicity and other constraints:

Moritz Diehl

Visualization of Periodic Solution

Moritz Diehl

What about ‚dancing‘ kites ?

Moritz Diehl

Optimization with ‚dancing‘ kites: 14 MW possible

2 x 500 m2 airfoils kevlar line 1500 m, diameter 8 cm wind speed 10 m/s

Moritz Diehl

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

x0

x0

u0

u0

Principle of Model Predictive Control (MPC)

Moritz Diehl

Model Predictive Control When We Drive a Car

Brain predicts and optimizes:e.g. slow down before curve

Always look a bit into the future!

Main challenge for MPC: fast and reliable real-time optimization!

Moritz Diehl

Nonlinear MPC Computation from 1998 to 2006

1998: 5th order distillation model allows sampling times of only 5 minutes [Allgower, Findeisen, 1998]

2001: 206th order distillation model, sampling times of 20 seconds [D. et al. ‚01]

2006: 5th order engine model, sampling times of 10-20 milliseconds [Ferreau et al. ‘06],

5*60*1000 / 20 = 15 000 times faster, due toMoore‘s law + Algorithm Development

Moritz Diehl

Five Provocative Claims

According to speaker’s assessment, the future kite power plants will look as follows:

Kite lines will be far from vertical, kites fly at low angles Lift control will play crucial role Kites will be “pumping” rather than turning a carousel Plants will be built rather on sea than on land Connection to ground by only one line, not two or more

Moritz Diehl

Conclusions

Advanced numerical methods make computation of optimal periodic kite orbits possible

Can generate very cheap wind power, e.g. 5 MW by 500 m2 airfoil Next talks by the Leuven-Heidelberg Kite Team:

• Boris Houska: Robust and open-loop stable kite trajectories• Andreas Ilzhoefer: NMPC and MHE of Power Generating Kites• Karin Lindholm: The Leuven-Heidelberg kite model from a

system perspective

Moritz Diehl

Thank you very much for your attention!

Moritz Diehl

Two events of interest this year

Workshop on NMPC Software and Applications (NMPC-SOFAP), Loughborough, United Kingdom, April 19-20, 2007.

(inv. speakers: Biegler, Findeisen, Kerrigan, Richalet, Schei)

13th Czech-French-German Conference on Optimization (CFG07), Heidelberg, Germany, September 17-21, 2007.

(inv. speakers: Fletcher, Scherer, Trelat, Waechter,...) Traditionally strong in optimal control.