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The Leuven–Heidelberg Kite Model in a System Perspective: optimising with economy

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

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The Leuven–Heidelberg Kite Model in a System Perspective: optimising with economy

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  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 • Introduction • Initial problem • Solution • Data used • Results • Conclusion • 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 wrated co ci

  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/kWinst (cWiP)

  10. s o l u t i o n • Objective fcn • Average power output • Paverage = Pyear = Pyear (Ploop(w), ρ(w)) • Ploop ~ w3 → P(w) = P(wrated) * (w/ wrated)3

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

  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, wrated: 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

  15. quasi-proportional term cost power

  16. 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) = ckite * A + ccable* V(rmax, dc) + cgenerator * kWinst + + cquasi-prop * fqp(kWi) + ctether* 4 * ft(depth, dt) • Other

  17. u s e d d a t a • Wind data • Economicdata • Other (selection) • cable: 1050m – 1500m, 5.0cm – 7.0cm, • kite: 500m2 • tethering lines: 4 x 20m x 5cm • t: 20s – 23.5s

  18. r e s u l t s • Dimensioning factors • rmax = 1107m • dc = 5.0cm (= min.) • wrated = 8.6m/s (15.9m/s at 511m) • Prated = Ploop = 7.35MW • Pyear,% = 53% → Pyear = 3.9MW • t = 21s

  19. r e s u l t s • Money • OF = 1.4kWinst/€inv → 7 1 7 € i n v / k W y e a r • 381€inv/kWinst (cWiPoff: 507€inv/kWinst)

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

  21. T h a n k sf o r y o u ra t t e n t i o n Karin Lindholm, karin@lungplus.se

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

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