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Wind farm efficiency assessed by WRF with a statistical-dynamical - - PowerPoint PPT Presentation

Jul 18, 2023 162 likes •387 views

Wind farm efficiency assessed by WRF with a statistical-dynamical approach P.J.H. Volker, A.N. Hahmann, J. Badger, and H. Srensen DTU Wind Energy (Ris Campus) Motivation Adams and Keith, Environ Res Lett , 2013 The results suggest that

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SLIDE 1

Wind farm efficiency assessed by WRF with a statistical-dynamical approach

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

DTU Wind Energy (Risø Campus)

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SLIDE 2

Motivation

Adams and Keith, Environ Res Lett, 2013 “The results suggest that the maximum energy that can be extracted by turbine arrays at these scales is about 1 W m-2” Miller et al., Proc Natl Acad Sci, 2015 “. . . expanding wind farms to large scales will limit generation rates, thereby constraining mean large-scale generation rates to about 1 W m-2 even in windy regions”

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SLIDE 3

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
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SLIDE 4

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

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SLIDE 5

Consequence

Current: the 20 km2

  • ffshore

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

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SLIDE 6

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-WF

Fitsch et al.2012

  • EWP

Volker 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 and

  • ffshore wind farms Environ. Res. Lett. 2017
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SLIDE 7

Wind Conditions

For each wind farm we simulated a range of idealised case experiments between the turbine cut-in and cut-out wind speed. From the set of simulations we define 3 wind conditions Region A (land) Moderate winds Great Plains Region B (sea) Strong winds North Sea Region C (sea) Very strong winds Strait of Magellan

Region A

0.00 0.05 0.10 0.15 0.20 10 20 30 U

  • m s−1

Frequency

Region B

0.00 0.05 0.10 0.15 0.20 10 20 30 U

  • m s−1

Frequency

Region C

0.00 0.05 0.10 0.15 0.20 10 20 30 U

  • m s−1

Frequency

a b c

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SLIDE 8

Wind speed reduction in very large wind farms

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

EWP WRF-WF Region A Region B Region C

4 6 8 10 12 50 100 150 Distance (km) Uh(ms−1)

  • Offshore there is less mixing and equilibrium is reached much later
  • Equilibrium wind speed remains higher with better wind conditions
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SLIDE 9

Actual vs Reference PD for very large wind farms

1Wm−2 Adams and Keith (Great Plains) Parametrisatrion Approach EWP WRF-WF Region A

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

  • Wm−2

APD

  • Wm−2
  • In the Great Plains also 1 W m-2 (differences are due to parametrisation)
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SLIDE 10

Actual vs Reference PD for very large wind farms

1Wm−2 2Wm−2 Adams and Keith (Great Plains) Parametrisatrion Approach EWP WRF-WF Region A Region B

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

  • Wm−2

APD

  • Wm−2
  • In the Great Plains also 1 W m-2 (differences are due to parametrisation)
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Actual vs Reference PD for very large wind farms

1Wm−2 2Wm−2 3.5Wm−2 Adams and Keith (Great Plains) Parametrisatrion Approach EWP WRF-WF Region A Region B Region C

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

  • 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

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SLIDE 12

Wind farm efficiency (APD/RPD)

25 50 75 100 102 103 104 105 Wind farm area Efficiency (%)

Region A

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 very large wind farm would produce 1.7 PWh

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SLIDE 13

Wind farm efficiency (APD/RPD)

25 50 75 100 102 103 104 105 Wind farm area Efficiency (%) 25 50 75 100 102 103 104 105 Wind farm area Efficiency (%)

Region A Region B

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 very large wind farm would produce 1.7 PWh

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SLIDE 14

Wind farm efficiency (APD/RPD)

25 50 75 100 102 103 104 105 Wind farm area Efficiency (%) 25 50 75 100 102 103 104 105 Wind farm area Efficiency (%) 25 50 75 100 102 103 104 105 Wind farm area Efficiency (%)

Region A Region B Region C

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 very large wind farm would produce 1.7 PWh

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SLIDE 15

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

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

Can the overall cluster efficiency be improved by separating the same number of turbines 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
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SLIDE 17

Wind speed reduction for different WF spacings

S00

6.5 7.0 7.5 8.0 8.5 9.0 25 50 75 Distance (km) 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
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SLIDE 18

Wind speed reduction for different WF spacings

S00 S10

6.5 7.0 7.5 8.0 8.5 9.0 25 50 75 Distance (km) 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
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SLIDE 19

Wind speed reduction for different WF spacings

S00 S10 S20

6.5 7.0 7.5 8.0 8.5 9.0 25 50 75 Distance (km) 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
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SLIDE 20

Wind speed reduction for different WF spacings

S00 S10 S20 S30

6.5 7.0 7.5 8.0 8.5 9.0 25 50 75 Distance (km) Uh(ms−1)

Hub-height wind speed

Question:

  • Can the overall wind farm cluster efficiency be higher by separating wind farms?
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SLIDE 21

Efficiency of WF1 and WF2

Region B (blue) and Region C (green)

Density 1 Density 2

0.6 0.7 0.8 10 20 30 Wind Farm separation (km) Efficiency (%)

Efficiency of up-stream WF1

Density 1 Density 2

0.85 0.90 0.95 1.00 10 20 30 Wind Farm separation (km) APD WF2/WF1 (%)

Power reduction of down-stream WF2

  • The efficiency decreases with

increasing turbine density

  • In region B the efficiency is always

lower than 70%, because the wind farm size is too large

  • The power reduction for the 2

attached wind farms is up-to 20%

  • The power reduction does not

converge to 1!

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SLIDE 22

Overall efficiency for the 1st case

Single WF

  • Tot. cluster

0.45 0.50 0.55 0.60 0.65 0.70 10 20 30 Wind Farm separation (km) Effciency (%)

Region B

Single WF

  • Tot. cluster

0.65 0.70 0.75 0.80 10 20 30 Wind Farm separation (km) Effciency (%)

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 farm

separation could improve the efficiency