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The Leuven–Heidelberg Kite
Model in a System
Perspective:
optimising with economy
Karin Lindholm, Workshop in Leuven 30th Jan, 2007
[email protected]
my background
• Energy Systems Engineering in Uppsala
(Swe)
• Degree project (~master thesis) in
Heidelberg (Ger)
• Powerkite in a system perspective
contents
1.
Introduction
2.
3.
4.
5.
Initial problem
Solution
Data used
Results
6.
7.
Conclusion
Questions
introduction
• System perspective:
interaction between the outer world and a
realisation of a technical solution
• Crucial: (e.g.) economy
• Optimising according to economic issues
initial problem
• Goal
– minimise costs and maximise income
• Issues
power curve
power
wind speed
ci
wrated
co
initial problem
• Goal
– minimise costs and maximise income
– optimise rated wind speed
• Issues
initial problem
• Goal
• Issues
– choose objective function
– wind data
– estimate costs
– optimisation of each loop during a year but
with the same physical dimensions
solution
• Objective fcn:
– income - costs ?
– O F = P average / € inv
– €inv/kWinst
(cWiP)
solution
• Objective fcn
• Average power output
– Paverage = Pyear = Pyear (Ploop(w), ρ(w))
3
3
– Ploop ~ w → P(w) = P(wrated) * (w / wrated)
power curve
power
wind speed
ci
wrated
co
solution
• Objective fcn
• Yearly average power output
• Free parameters:
– Cable: maximum length and diameter
– Rated wind speed
used data
• 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
used data
• Wind data
• Economic data
– 4-5 categories, sorted by dependency
(area, volume, proportional, (quasi-proportional),
constant)
• Other
quasi-proportional term
cost
power
used data
• 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
used data
• 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
results
• 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
results
• Money
– OF = 1.4kWinst/€inv → 7 1 7 € i n v / k W y e a r
– 381€inv/kWinst
(cWiPoff: 507€inv/kWinst)
conclusion
Thanks
for your
attention
Karin Lindholm, [email protected]
Questions?
Karin Lindholm, [email protected]