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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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

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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

akleidon@bgc-jena.mpg.de@

www.earthsystem.org

Manuscript has been submitted