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The KEBA model Axel Kleidon and Lee Miller1
The Kinetic Energy Budget of the Atmosphere (KEBA) approach:
Estimating wind power potentials that account for the kinetic energy removal by wind turbines
Axel KleidonMax-Planck-Institute for Biogeochemistry
Jena, Germany
Lee M MillerAtmospheric and Environmental Research
Lexington, MA, USA
The KEBA model Axel Kleidon and Lee Miller
Motivation
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2
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0 5 10 15 20 25 30
LandElectricity generation
Wind speeds
Installed Capacity (Wi m-2)
Gen
erat
ion
(We
m-2
) Wind S
peeds (m s
-1)
Modified after:Miller and Kleidon (2016) PNAS https://www.pnas.org/content/113/48/13570
From:Volker et al. (2017) ERL
https://iopscience.iop.org/article/10.1088/1748-9326/aa5d86
Atmospheric model simulations show that turbine yields decline as wind energy use expands in scale because of wind speed reductions
How can these yield reductions due to interactions with the atmosphere be accounted for?
The KEBA model Axel Kleidon and Lee Miller
The KEBA Model
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Downward influxof kinetic energyJin,v = ρ Cd vin3
Horizontalinflux of
kinetic energyJin,h = ρ/2 vin3
heig
ht H
width W
length L
TurbulentdissipationDfric = ρ Cd v3
Energy extraction by wind turbines
(electricity yield Pel,tot+ wake dissipation Dwake)
Horizontaloutflux of
kinetic energyJout,h = ρ/2 v3
Effectivevelocity v
Budgeting the kinetic energy of the lower atmosphere yields analytic expressions to predict wind speed and yield reductions
v = f1/3red ⋅ vin
Pel,tot = fred ⋅ N ⋅ Pel,iso
KEBA equations yields a reduction
factor fred, reducing the yield compared to
an isolated turbine
H: height of the well-mixed
boundary layer
The KEBA model Axel Kleidon and Lee Miller
The KEBA Model
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The KEBA equations are implemented in an Excel spreadsheet, including:wind forcingatmospheric characteristics turbine characteristicsscenario specifications yield estimates (yellow)
The KEBA model Axel Kleidon and Lee Miller
Testing KEBA
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Region ARegion BRegion C
Pow
er (k
W)
0
500
1000
1500
2000
Freq
uenc
y
0
0.05
0.10
0.15
0.20
CD
F
0
0.5
1.0
Wind speed (m s-1)0 10 20 30
WRF simulations from: Volker et al (2017), ERL https://iopscience.iop.org/article/10.1088/1748-9326/aa5d86
Input: Wind climate, atmospheric characteristics,
power curve, scenarios
Output: Electricity yields, wind speed
reduction, energy fluxes
KEBA implemented as Excel spreadsheet
Downward influxof kinetic energyJin,v = ρ Cd vin3
Horizontalinflux of
kinetic energyJin,h = ρ/2 vin3
heig
ht H
width W
length L
TurbulentdissipationDfric = ρ Cd v3
Energy extraction by wind turbines
(electricity yield Pel,tot+ wake dissipation Dwake)
Horizontaloutflux of
kinetic energyJout,h = ρ/2 v3
Effectivevelocity v
KEBA model
Wind forcing from 3 Regions: Central US, North sea,
Strait of Magellan
Winds
Powercurve
Scenarios:3 spacings (W, I, N)4 sizes (S, M, L, XL),
ranging from L = 5-340 km
2 MWturbine
The KEBA model Axel Kleidon and Lee Miller
Energy Yields
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Region ARegion BRegion C1:1 line Larger
farms
Smallerfarms
Yiel
d (T
Wh
a-1)
KEBA
10−1
1
101
102
103
104
Yield (TWh a-1)Volker et al (2017)
10−1 1 101 102 103 104
Largerfarms
Smallerfarms
KEBA = 6.40 + 1.02 * WRFn = 36; r2=0.822
Red
uctio
n in
yie
ld (%
)KE
BA
−80
−60
−40
−20
0
Reduction in yield (%)Volker et al (2017)
−80 −60 −40 −20 0
KEBA estimates compare very well to WRF-based estimates of Volker et al. (2017) across a set of sensitivities
Absolute yields(open circles: no wind reductions)
Relative reductions (compared to no wind reductions)
The KEBA model Axel Kleidon and Lee Miller
Interpreting KE Budgets
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W I N W I N W I N W I N
KE influx (vertical)KE influx (horizontal)KE outflux (horizontal)
Frictional dissipationWake dissipationYield
W I N W I N W I N W I N
Con
tribu
tion
(%)
(Reg
ions
B a
nd C
)
0
50
100
Con
tribu
tion
(%)
(Reg
ion
A)
0
50
100
Small Medium Large X-Large
KEBA implemented as Excel spreadsheet
Downward influxof kinetic energyJin,v = ρ Cd vin3
Horizontalinflux of
kinetic energyJin,h = ρ/2 vin3
heig
ht H
width W
length L
TurbulentdissipationDfric = ρ Cd v3
Energy extraction by wind turbines
(electricity yield Pel,tot+ wake dissipation Dwake)
Horizontaloutflux of
kinetic energyJout,h = ρ/2 v3
Effectivevelocity v
Diagnosed kinetic energy (KE) fluxes show that yields (yellow) of large wind farms ( > 100 km) get close to how much wind energy enters the box (blue). Hence, wind speeds and yields per turbine are reduced.
Energy fluxes (left) have the same color as arrows in the KEBA diagram (below)
The KEBA model Axel Kleidon and Lee Miller
Larger Scales = Less Wind Energy
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WideIntermediateNarrow
SmallMedium
LargeX-Large
Ener
gy fl
ux (W
m-2
)
0
2
4
6
8
10
Cap
acity
fact
or (%
)
0
20
40
60
Red
uctio
n fa
ctor
f red
0
0.2
0.4
0.6
0.8
1.0
Downwind length L (km)0 100 200 300 400
dominated by horizontal flow of KE
dominated by vertical mixing of KE
When downwind length of wind farms increases, the horizontal inflow of kinetic energy becomes less important, while the vertical mixing becomes more important.
Hence, at larger scales, the wind energy yields converge from initially large ( > 1 W m-2) to a low limit of < 1 W m-2 per surface area.KEBA implemented
as Excel spreadsheet
Downward influxof kinetic energyJin,v = ρ Cd vin3
Horizontalinflux of
kinetic energyJin,h = ρ/2 vin3
heig
ht H
width W
length L
TurbulentdissipationDfric = ρ Cd v3
Energy extraction by wind turbines
(electricity yield Pel,tot+ wake dissipation Dwake)
Horizontaloutflux of
kinetic energyJout,h = ρ/2 v3
Effectivevelocity v
large-scalelimit
singleturbine
The KEBA model Axel Kleidon and Lee Miller
Summary
The Kinetic Energy Budget of the Atmosphere (KEBA): A physics-based method to account for wind speed and yield reductions in large wind farmsWorks very well compared to WRF simulationsProvides explanations why wind energy potentials decline to < 1 W m-2 at large, downwind scales L > 100 km
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KEBA Spreadsheet available on MPG Data Repositoryhttps://edmond.mpdl.mpg.de/imeji/collection/ctvrVzG7CpKsqBB?q=
Application to German Offshore wind energy potentialshttps://www.agora-energiewende.de/projekte/offshore-wind-potenzial/
More Information:
Contact:
@akleidon
www.earthsystem.org
Manuscript has been submitted