1. The Leuven–Heidelberg Kite Model in a System Perspective: optimising with economy Karin Lindholm, Workshop in Leuven 30th Jan, 2007 karin@lungplus.se

2. m y b a c k g r o u n d Energy Systems Engineering in Uppsala (Swe) Degree project (~master thesis) in Heidelberg (Ger) Powerkite in a system perspective

3. c o n t e n t s 1.Introduction 2.Initial problem 3.Solution 4.Data used 5.Results 6.Conclusion 7.Questions

4. i n t r o d u c t i o n System perspective: interaction between the outer world and a realisation of a technical solution Crucial: (e.g.) economy Optimising according to economic issues

5. i n i t i a l p r o b l e m Goal –minimise costs and maximise income Issues

6. p o w e r c u r v e power wind speed ci w rated co

7. i n i t i a l p r o b l e m Goal –minimise costs and maximise income –optimise rated wind speed Issues

8. i n i t i a l p r o b l e m Goal Issues –choose objective function –wind data –estimate costs –optimisation of each loop during a year but with the same physical dimensions

9. s o l u t i o n Objective fcn: –income - costs ? – O F = P a v e r a g e / € i n v –€ inv /kW inst (cWiP)

10. s o l u t i o n Objective fcn Average power output –P average = P year = P year ( P loop ( w ), ρ( w ) ) –P loop ~ w 3 → P( w ) = P( w rated ) * (w / w rated ) 3

11. p o w e r c u r v e power wind speed ci w rated co

12. s o l u t i o n Objective fcn Yearly average power output Free parameters: –Cable: maximum length and diameter –Rated wind speed

13. u s e d d a t a Wind data –wind shear model ref height 10m, roughness length 0.1 –ci = 2.5, co = 25.0, w rated : 4.5 – 25.0 –Weibull distribution (2 param.) α = 1.708,β =8.426 Economic data Other

14. u s e d d a t a Wind data Economic data –4-5 categories, sorted by dependency (area, volume, proportional, (quasi-proportional), constant) Other

16. power cost quasi-proportional term

18. u s e d d a t a Wind data Economic data –4-5 categories, sorted by dependency (area, volume, proportional, (quasi-proportional), constant) –denominator(OF) = c kite * A + c cable * V( r max, dc ) + c generator * kW inst + + c quasi-prop * f qp (kW i ) + c tether * 4 * f t ( depth, dt ) Other

19. u s e d d a t a Wind data Economic data Other (selection) –cable: 1050m – 1500m, 5.0cm – 7.0cm, –kite: 500m 2 –tethering lines: 4 x 20m x 5cm –t: 20s – 23.5s

20. r e s u l t s Dimensioning factors –r max = 1107m –dc = 5.0cm (= min.) –w rated = 8.6m/s (15.9m/s at 511m) –P rated = P loop = 7.35MW –P year,% = 53% → P year = 3.9MW –t = 21s

21. r e s u l t s Money –OF = 1.4kW inst /€ inv → 7 1 7 € i n v / k W y e a r –381€ inv /kW inst (cWiP off : 507€ inv /kW inst )

22. c o n c l u s i o n

23. T h a n k s f o r y o u r a t t e n t i o n Karin Lindholm, karin@lungplus.se

24. Q u e s t i o n s ? Karin Lindholm, karin@lungplus.se