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)
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”
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 10 3 – 10 5 km 2 • Turbine density 0 . 25 – 16 km − 2
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
Consequence 20 km 2 Current: the offshore wind farm Horns Rev I 8 MW i km -2 � has a annual power density of up-to 3.98 W m -2 � 10 4 - 10 5 km 2 ∼ Dogger Bank � � Future: very large wind farms would have a power production per area of 25% compared to Horns Rev I
Experimental set-up of WRF 3 turbine spacings 2 WF schemes 4 wind farm sizes • Small (Horns Rev I) • 5.25 D 0 • WRF-WF Fitsch et al.2012 • Medium (London Array) 7 D 0 • • Large (Dogger Bank) • 10.5 D 0 • EWP Volker et al.2015 • Very large (Iowa) Number of 2 MW turbines Small Medium Large Very Large Wide (10.5 D 0 ) 6 × 6 22 × 22 202 × 202 402 × 402 Intermediate (7 D 0 ) 9 × 9 33 × 33 303 × 303 603 × 603 Narrow (5.25 D 0 ) 12 × 12 44 × 44 404 × 404 804 × 804 Volker et al.: Prospects for generating electricity by large onshore and offshore wind farms Environ. Res. Lett. 2017
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) Region B (sea) Region C (sea) Moderate winds Strong winds Very strong winds Great Plains North Sea Strait of Magellan b a c 0.20 0.20 0.20 Region A Region B Region C 0.15 0.15 0.15 Frequency Frequency Frequency 0.10 0.10 0.10 0.05 0.05 0.05 0.00 0.00 0.00 0 10 20 30 0 10 20 30 0 10 20 30 � m s − 1 � � m s − 1 � � m s − 1 � U U U
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 Region A EWP Region B WRF-WF 12 Region C 10 U h ( ms − 1 ) 8 6 4 0 50 100 150 Distance (km) • Offshore there is less mixing and equilibrium is reached much later • Equilibrium wind speed remains higher with better wind conditions
Actual vs Reference PD for very large wind farms 12 Adams and Keith (Great Plains) Region A 11 10 9 Parametrisatrion Approach EWP 8 Wm − 2 � WRF-WF 7 6 � 5 APD 4 3 2 1Wm − 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Wm − 2 � � RPD • In the Great Plains also 1 W m -2 (differences are due to parametrisation)
Actual vs Reference PD for very large wind farms 12 Adams and Keith (Great Plains) Region A 11 Region B 10 9 Parametrisatrion Approach EWP 8 Wm − 2 � WRF-WF 7 6 � 5 APD 4 3 2Wm − 2 2 1Wm − 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Wm − 2 � � RPD • In the Great Plains also 1 W m -2 (differences are due to parametrisation)
Actual vs Reference PD for very large wind farms 12 Adams and Keith (Great Plains) Region A 11 Region B 10 Region C 9 Parametrisatrion Approach EWP 8 Wm − 2 � WRF-WF 7 6 � 5 APD 4 3 . 5Wm − 2 3 2Wm − 2 2 1Wm − 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Wm − 2 � � RPD • 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
Wind farm efficiency (APD/RPD) Region A 100 75 Efficiency ( % ) 50 25 0 10 2 10 3 10 4 10 5 Wind farm area 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
Wind farm efficiency (APD/RPD) Region A Region B 100 100 75 75 Efficiency ( % ) Efficiency ( % ) 50 50 25 25 0 0 10 2 10 3 10 4 10 5 10 2 10 3 10 4 10 5 Wind farm area Wind farm area 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
Wind farm efficiency (APD/RPD) Region A Region B Region C 100 100 100 75 75 75 Efficiency ( % ) Efficiency ( % ) Efficiency ( % ) 50 50 50 25 25 25 0 0 0 10 2 10 3 10 4 10 5 10 2 10 3 10 4 10 5 10 2 10 3 10 4 10 5 Wind farm area Wind farm area Wind farm area 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
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
(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 km 2 ) in 2 wind farms? Separation in km: S00 S10 S20 S30 WF1 WF2 WF1 WF2 . . . Density 1 with 9145 turbines: Density 2 with 12802 turbines: - S00 5.0 W m -2 7.0 W m -2 - S00 - S10 6.0 W m -2 8.4 W m -2 - S10 - S20 7.5 W m -2 - S20 10.5 W m -2 - S30 10 W m -2 - S30 14.0 W m -2
Wind speed reduction for different WF spacings Hub-height wind speed 9.0 8.5 U h ( ms − 1 ) 8.0 7.5 S00 7.0 6.5 0 25 50 75 Distance (km) Highest efficiency is a balance between: • wind speed reduction in the wind farms f (turbine density) • wind speed recovery between the wind farms
Wind speed reduction for different WF spacings Hub-height wind speed 9.0 8.5 U h ( ms − 1 ) 8.0 7.5 S00 7.0 S10 6.5 0 25 50 75 Distance (km) Highest efficiency is a balance between: • wind speed reduction in the wind farms f (turbine density) • wind speed recovery between the wind farms
Wind speed reduction for different WF spacings Hub-height wind speed 9.0 8.5 U h ( ms − 1 ) 8.0 7.5 S00 7.0 S10 S20 6.5 0 25 50 75 Distance (km) Highest efficiency is a balance between: • wind speed reduction in the wind farms f (turbine density) • wind speed recovery between the wind farms
Wind speed reduction for different WF spacings Hub-height wind speed 9.0 8.5 U h ( ms − 1 ) 8.0 7.5 S00 7.0 S10 S20 S30 6.5 0 25 50 75 Distance (km) Question: • Can the overall wind farm cluster efficiency be higher by separating wind farms?
Efficiency of WF1 and WF2 Region B (blue) and Region C (green) Efficiency of up-stream WF1 Power reduction of down-stream WF2 1.00 Density 1 Density 1 Density 2 0.8 Density 2 APD WF2/WF1 ( % ) 0.95 Efficiency ( % ) 0.7 0.90 0.6 0.85 0 10 20 30 0 10 20 30 Wind Farm separation (km) Wind Farm separation (km) • The efficiency decreases with • The power reduction for the 2 increasing turbine density attached wind farms is up-to 20% • In region B the efficiency is always • The power reduction does not lower than 70%, because the wind converge to 1! farm size is too large
Overall efficiency for the 1st case Region B Region C Single WF 0.70 Single WF Tot. cluster Tot. cluster 0.80 0.65 Effciency ( % ) Effciency ( % ) 0.75 0.60 0.55 0.70 0.50 0.65 0.45 0 10 20 30 0 10 20 30 Wind Farm separation (km) Wind Farm separation (km) • 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
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