wind farm e ciency assessed by wrf with a statistical

Wind farm efficiency assessed by WRFwith a statistical-dynamical approach

P.J.H. Volker, A.N. Hahmann, J. Badger,

and H. Sørensen

DTU Wind Energy (Risø Campus)

1

Motivation

Adams and Keith, Environ Res Lett, 2013

“The results suggest that the maximum energy thatcan be extracted by turbine arrays at these scales isabout 1 W m-2”

Miller et al., Proc Natl Acad Sci, 2015

“. . . expanding wind farms to large scales willlimit generation rates, thereby constraining meanlarge-scale generation rates to about 1 W m-2 evenin windy regions”

2

Method of Adams and Keith 2013

They use the WRF model to simulate:• Actual Power Density (APD) (wake effects with wind farm parametrisation)• Reference Power Density (RPD) (no wake effects)

Simulations over the Great plains in winter/summer 2006

The Power Density (PD) in function of

• Wind farm size 103 – 105 km2

• Turbine density 0.25 – 16 km−2

3

Result of Adams and Keith 2013

Actual (wakes) versus Reference or expected (no wakes) Power Density (PD)

APD/RPD is the degree to which the turbine drag reduces the wind speed

It seemed that the APD converges to around 1 W m-2

4

Consequence

Current: the 20 km2 offshore wind farm Horns Rev I(8 MWi km-2

)has a annual power density of up-to 3.98 W m-2

Future: very large(104- 105 km2 ∼ Dogger Bank

)wind farms would

have a power production per area of 25% compared to Horns Rev I

5

Experimental set-up of WRF

4 wind farm sizes

• Small (Horns Rev I)

• Medium (London Array)

• Large (Dogger Bank)

• Very large (Iowa)

3 turbine spacings

• 5.25 D0

• 7 D0

• 10.5 D0

2 WF schemes

• WRF-WFFitsch et al.2012

• EWPVolker et al.2015

Number of 2 MW turbines

Small Medium Large Very Large

Wide (10.5 D0) 6 × 6 22 × 22 202 × 202 402 × 402

Intermediate (7 D0) 9 × 9 33 × 33 303 × 303 603 × 603

Narrow (5.25 D0) 12 × 12 44 × 44 404 × 404 804 × 804

Volker et al.: Prospects for generating electricity by large onshore andoffshore wind farms Environ. Res. Lett. 2017

6

Wind Conditions

For each wind farm we simulated a range of idealised case experimentsbetween the turbine cut-in and cut-out wind speed.

From the set of simulations we define 3 wind conditions

Region A (land)Moderate windsGreat Plains

Region B (sea)Strong windsNorth Sea

Region C (sea)Very strong windsStrait of Magellan

Region A

0.00

0.05

0.10

0.15

0.20

0 10 20 30U

(ms−1

)

Freq

uenc

y

Region B

0.00

0.05

0.10

0.15

0.20

0 10 20 30U

(ms−1

)

Freq

uenc

y

Region C

0.00

0.05

0.10

0.15

0.20

0 10 20 30U

(ms−1

)

Freq

uenc

y

a b c

7

Wind speed reduction in very large wind farms

At equilibrium wind speed a balance between the dragforce f(Ct, U) and turbulent influx of momentum

EWPWRF-WF

Region ARegion BRegion C

4

6

8

10

12

0 50 100 150Distance (km)

Uh(

ms−

1 )

• Offshore there is less mixing and equilibrium is reached much later

• Equilibrium wind speed remains higher with better wind conditions

8

Actual vs Reference PD for very large wind farms

1Wm−2

Adams and Keith (Great Plains)

Parametrisatrion ApproachEWPWRF-WF

Region A

0123456789

101112

0 1 2 3 4 5 6 7 8 9 10 11 12RPD

(Wm−2

)

APD

( Wm

−2)

• In the Great Plains also 1 W m-2 (differences are due to parametrisation)

9


1Wm−2

2Wm−2



Region ARegion B

0123456789

101112

0 1 2 3 4 5 6 7 8 9 10 11 12RPD

(Wm−2

)

APD

( Wm

−2)

• In the Great Plains also 1 W m-2 (differences are due to parametrisation)

10


1Wm−2

2Wm−2

3.5Wm−2



Region ARegion BRegion C

0123456789

101112

0 1 2 3 4 5 6 7 8 9 10 11 12RPD

(Wm−2

)

APD

( Wm

−2)

• In the Great Plains also 1 W m-2 (differences are due to parametrisation)• However: In regions with very strong winds the APD is around 3.5 W m-2

⇒ The APD is not limited, but depends strongly on wind (and roughness) conditions

11

Wind farm efficiency (APD/RPD)

0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

Region A

– Typeset by FoilTEX – 1

Region A: A Very large wind farm (160.000 turbines) produces 700 TWh

Region B: A cluster of nine medium wind farms (total 9.801 turbines) 77 TWh

Region C: A small wind farm 1 TWh (50% more than Horns Rev I). A verylarge wind farm would produce 1.7 PWh

12


0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

Region A Region B





13


0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

0

25

50

75

100

102 103 104 105

Wind farm area

Effi

cien

cy(%

)

Region A Region B Region C





14

Conclusion

Power Density

• The power density is not limited to 1 W m−2 as previously assumed

• Instead it depends also for very large wind farms on the local

up-stream wind and surface conditions

Wind farm efficiency/production

• In onshore regions with moderate wind conditions very large wind

farms can significantly contribute to the electricity production

• Offshore, clusters of smaller wind farms are more efficient

• However, in regions with very strong winds very large wind farms

become also efficient

15

(II) Efficiency of a wind farm cluster in 2 regions

Can the overall cluster efficiency be improved by separating the same number ofturbines on fixed area (3658 km2) in 2 wind farms?

Separation in km:

S00 S10 S20 S30

WF1 WF2 WF1 WF2 . . .

Density 1 with 9145 turbines:

- S00 5.0 W m-2

- S10 6.0 W m-2

- S20 7.5 W m-2

- S30 10 W m-2

Density 2 with 12802 turbines:

- S00 7.0 W m-2

- S10 8.4 W m-2

- S20 10.5 W m-2

- S30 14.0 W m-2

16

Wind speed reduction for different WF spacings

S00

6.5

7.0

7.5

8.0

8.5

9.0


Uh(

ms−

1 )

Hub-height wind speed

Highest efficiency is a balance between:

• wind speed reduction in the wind farms f (turbine density)

• wind speed recovery between the wind farms

17


S00S10

6.5

7.0

7.5

8.0

8.5

9.0


Uh(

ms−

1 )





18


S00S10S20

6.5

7.0

7.5

8.0

8.5

9.0


Uh(

ms−

1 )





19


S00S10S20S306.5

7.0

7.5

8.0

8.5

9.0


Uh(

ms−

1 )


Question:

• Can the overall wind farm cluster efficiency be higher by separating wind farms?

20

Efficiency of WF1 and WF2

Region B (blue) and Region C (green)

Density 1Density 2

0.6

0.7

0.8

0 10 20 30Wind Farm separation (km)

Effi

cien

cy(%

)

Efficiency of up-stream WF1

Density 1Density 2

0.85

0.90

0.95

1.00


APD

WF2

/WF1

(%)

Power reduction of down-stream WF2

• The efficiency decreases withincreasing turbine density

• In region B the efficiency is alwayslower than 70%, because the windfarm size is too large

• The power reduction for the 2attached wind farms is up-to 20%

• The power reduction does notconverge to 1!

21

Overall efficiency for the 1st case

Single WFTot. cluster

0.45

0.50

0.55

0.60

0.65

0.70


Eff

cien

cy(%

)

Region BSingle WFTot. cluster

0.65

0.70

0.75

0.80


Eff

cien

cy(%

)

Region C

• The chosen wind farm is to large for the Region B wind conditions,since the efficiency is relatively low

• In the experiments with the lower installed capacity a wind farmseparation could improve the efficiency

22

wind farm e ciency assessed by wrf with a statistical

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