A new approach to wind energy - QualEnergia
Transcript of A new approach to wind energy - QualEnergia
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Comparing Wind Power Performance
Turbine efficiency
P
½ρAU3 Cp =
U
A
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Comparing Wind Power Performance
Turbine efficiency Wind farm power density
P
½ρAU3 Cp =
U
A
PWF
AWF
PD =
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Comparing Wind Power Performance
Turbine efficiency Wind farm power density Cost of electricity
P½ρAU3
Cp =
U
A
PWF
AWFPD =
$¢
kWhLCOE =
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The usual starting point: turbine efficiency
Horizontal-axis wind turbine (HAWT)
Vertical-axis wind turbine (VAWT)
VS.
Comparing Wind Power Performance
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The usual starting point: turbine efficiency What fraction of wind energy flux through the swept area is converted to electricity?
Horizontal-axis wind turbine (HAWT)
Vertical-axis wind turbine (VAWT)
VS.
Comparing Wind Power Performance
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Horizontal-axis wind turbine (HAWT)
Vertical-axis wind turbine (VAWT)
>
Comparing Wind Power Performance
The usual starting point: turbine efficiency What fraction of wind energy flux through the swept area is converted to electricity?
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity?
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2
U0 , A0
U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2
2)
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2
U0 , A0
U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2
2) For steady rotor thrust, U1 = (U0 + U2)/2
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2
U0 , A0
U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2
2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0
2 – U22)
= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2
U0 , A0
U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2
2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0
2 – U22)
= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]
Pmax = 16/27 x (½ρA1U0
3) or 59.3% efficiency (Betz Limit)
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Comparing Wind Power Performance
The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2
U0 , A0
U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2
2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0
2 – U22)
= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]
Pmax = 16/27 x (½ρA1U0
3) or 59.3% efficiency (Betz Limit) Modern HAWTs approach theoretical
maximum efficiency
Is there room for significant improvement? (besides increasing swept area)
netfirms.com
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Comparing Wind Power Performance
Our starting point: wind resource utilization
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Comparing Wind Power Performance
Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?
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Comparing Wind Power Performance
Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?
Frontal kinetic energy flux
Phorz = ½ρAfrontalU3
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Comparing Wind Power Performance
Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?
Frontal kinetic energy flux
Phorz = ½ρAfrontalU3
Planform kinetic energy flux
Pvert ≈ -ρAplanformU <u’w’>
Turbulence velocity fluctuations u’ (streamwise) and w’ (wall-normal) Ensemble average < • >
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The planform kinetic energy flux (ρAplanformU <u’w’>)…
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The planform kinetic energy flux (ρAplanformU <u’w’>)…
1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010)
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The planform kinetic energy flux (ρAplanformU <u’w’>)…
1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance
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The planform kinetic energy flux (ρAplanformU <u’w’>)…
1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance WHY?
• The Betz calculation does not account for wind power in the turbine wake that is extracted by neighboring turbines
leftover
wind power
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The planform kinetic energy flux (ρAplanformU <u’w’>)…
1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance WHY?
• The Betz calculation does not account for wind power in the turbine wake that is extracted by neighboring turbines
• The Betz calculation does not account for wind power that is not extracted in the region between turbines
Cp = 0.5 Cp = 0.5 Cp = 0.5
Cp = 0 Cp = 0
leftover wind
power
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Modelling the planform flux limit
wuUAP planformvert
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Modelling the planform flux limit
wuUAP planformvert
0
2
*ln zdz
Uuwu
Assume log wind profile:
friction velocity, u*
von Karman constant, zero plane displacement, roughness length,
4.0
3/2Hd
10/0 Hz
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Modelling the planform flux limit
wuUAP planformvert
0
2
*ln zdz
Uuwu
Assume log wind profile:
friction velocity, u*
von Karman constant, zero plane displacement, roughness length,
4.0
U
3/2Hd
10/0 Hz
H
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Modelling the planform flux limit
wuUAP planformvert ′′−≈ ρ
( )[ ]
−
==′′−0
2* ln zdz
Uuwu κAssume log wind profile:
friction velocity, u*von Karman constant, zero plane displacement, roughness length,
4.0≈κ
U
H
3/2Hd ≈10/0 Hz ≈
H
Foken 2008
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Modelling the planform flux limit
2
310
2
101
32max
ln
4.0
ln
4.0
UU
HHH
UUPD
A
P
planform
vert
The energy flux through the top of the wind farm is:
wuUAP planformvert
0
2
*ln zdz
Uuwu
Assume log wind profile:
friction velocity, u*
von Karman constant, zero plane displacement, roughness length,
4.0
3/2Hd
10/0 Hz
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Modelling the planform flux limit
2
310
2
101
32max
ln
4.0
ln
4.0
UU
HHH
UUPD
A
P
planform
vert
The energy flux through the top of the wind farm is:
3
max 11.0 UPD
wuUAP planformvert
0
2
*ln zdz
Uuwu
Assume log wind profile:
friction velocity, u*
von Karman constant, zero plane displacement, roughness length,
4.0
3/2Hd
10/0 Hz
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Modelling the planform flux limit
2
310
2
101
32max
ln
4.0
ln
4.0
UU
HHH
UUPD
A
P
planform
vert
The energy flux through the top of the wind farm is:
3
max 11.0 UPD
For ρ = 1.2 kg m-3 and U = 8 m s-1, PDmax = 68 W m-2
wuUAP planformvert
0
2
*ln zdz
Uuwu
Assume log wind profile:
friction velocity, u*
von Karman constant, zero plane displacement, roughness length,
4.0
3/2Hd
10/0 Hz
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How do existing wind farms compare to this upper limit?
DJC Mackay 2010
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How do existing wind farms compare to this upper limit? 2.5 versus 68 W m-2
DJC Mackay 2010
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2.5 versus 68 W m-2
Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit
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2.5 versus 68 W m-2
Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density
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2.5 versus 68 W m-2
Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density
Power Density Calculation PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2
D x S
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2.5 versus 68 W m-2
Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density
Power Density Calculation PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2
D x S Turbine #1 (2.5 MW, 100 m dia.): PD = 2.7 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =2.5 W/m2
For six-diameter average turbine spacing and 30% capacity factor…
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2.5 versus 68 W m-2
Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density
Power Density Calculation PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2
D x S Turbine #1 (2.5 MW, 100 m dia.): PD = 2.7 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =2.5 W/m2
For six-diameter average turbine spacing and 30% capacity factor…
If turbine spacing is reduced to four diameters…
Turbine #1 (2.5 MW, 100 m dia.): PD = 6.0 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =5.7 W/m2
i.e. power density is more than doubled.
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Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement
2.5 versus 68 W m-2
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Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement
d/H
z0/H
Structure spatial density
z 0/H
an
d d
/H
Grimmond and Oke 1999
2.5 versus 68 W m-2
32
101
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Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement
d/H
z0/H
Structure spatial density
z 0/H
an
d d
/H
Grimmond and Oke 1999
2.5 versus 68 W m-2
existing wind farms
32
101
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Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement
d/H
z0/H
Structure spatial density
z 0/H
an
d d
/H
Grimmond and Oke 1999
2.5 versus 68 W m-2
existing wind farms
32
101
Increasing turbine spatial density
Increasing z0 and d
Increasing Pvert
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Additional challenges for conventional wind energy
∙ Structure size, associated design requirements and materials costs
johnrsweet.com
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Paul Anderson
Additional challenges for conventional wind energy
∙ Structure size, associated design requirements and materials costs ∙ Logistics of installation/maintenance
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Google Images
Additional challenges for conventional wind energy
∙ Structure size, associated design requirements and materials costs ∙ Logistics of installation/maintenance ∙ Public acceptance - impact on birds/bats - visual signature - acoustic signature - radar signature
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A new approach: Optimized arrays of smaller vertical-axis wind turbines
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A new approach: Optimized arrays of smaller vertical-axis wind turbines
Power Density Calculation Revisited PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2 D x S
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A new approach: Optimized arrays of smaller vertical-axis wind turbines
Power Density Calculation Revisited PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2 D x S
For six-diameter average turbine spacing and 30% capacity factor…
Windspire Energy VAWT 0.0012 MW, 1.2 m dia.
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A new approach: Optimized arrays of smaller vertical-axis wind turbines
Power Density Calculation Revisited PD = 4 x rated power x capacity factor
π (turbine diameter x turbine spacing) 2 D x S
For six-diameter average turbine spacing and 30% capacity factor…
Windspire Energy VAWT 0.0012 MW, 1.2 m dia.
PD = 8.8 W/m2 3X power density at 1/10 HAWT height!
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What is the optimal arrangement of VAWTs in a wind farm?
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What is the optimal arrangement of VAWTs in a wind farm?
Bio-inspiration: Fish Schooling
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‘Optimal’ fish schooling provides our starting point…
Weihs (1975)
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Triantafyllou et al. (1995)
≈
primary wind
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Potential flow model
1log2
zzizUWVAWT
VAWT complex potential:
uniform flow point vortex (rotation) dipole (blockage)
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Potential flow model
1log2
zzizUWVAWT
VAWT complex potential:
General wind farm complex potential:
uniform flow point vortex (rotation) dipole (blockage)
sum over N VAWTs at locations zn
N
n
nnfarm zzzzizUW0
1log
2
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Potential flow model
1log2
zzizUWVAWT
VAWT complex potential:
General wind farm complex potential:
uniform flow point vortex (rotation) dipole (blockage)
sum over N VAWTs at locations zn
‘Fish school’ wind farm complex potential:
M
m
N
n
nmnmnmnm
M
m
N
n
nmnmnmnmfish
AzAzAzAz
AzAzAzAzizUW
1 1
12
,
11
,
12
,
11
,
1 1
2
,
1
,
2
,
1
,
loglogloglog2
N
n
nnfarm zzzzizUW0
1log
2
where
bcminaaA
bmcinaaA
bcminaaA
bmcinaaA
nm
nm
nm
nm
2422
422
2422
422
2
,
1
,
2
,
1
,
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Potential flow model
2c
b
2a
U
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Whittlesey, Liska, Dabiri (Bioinspiration and Biomimetics, 2010)
Potential flow model
Model predicts order-of-magnitude increase in power density
Ra
ted
Po
wer
Den
sity
(W
m-2
)
2c
b
2a
a = 1.2D, b = 0.4D, c = 2D
U
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Caltech Field Laboratory for Optimized Wind Energy
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Field Study Results Directional dependence of performance at close spacing (1.65 diameters)
• Limited sensitivity to wind direction • Enhanced performance in close proximity
configuration power coefficient
isolated power coefficient Cp
norm =
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Field Study Results Four-diameter downwind spacing required to avoid blockage effects
4D downwind spacing
1.65D downwind spacing
U
configuration power coefficient
isolated power coefficient Cp
norm =
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Field Study Results 6-VAWT array measured over 250 continuous hours
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Field Study Results 6-VAWT array measured over 250 continuous hours
existing wind farms
Planform Kinetic Energy Flux = ρU<u’w’> (W m-2)
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Field Study Results 6-VAWT array measured over 250 continuous hours
existing wind farms
Planform Kinetic Energy Flux = ρU<u’w’> (W m-2)
mean power above cut-in wind speed
mean power, continuous
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Outlook
How do aerodynamic interactions within the VAWT farm determine the overall performance?
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Outlook
How do aerodynamic interactions within the VAWT farm determine the overall performance?
Suppression of vortex shedding by turbine rotation?
Mittal and Kumar, 2003
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Outlook
How do aerodynamic interactions within the VAWT farm determine the overall performance?
How can VAWTs be designed to operate optimally in turbulent, near-ground winds?
≈
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Outlook
How do aerodynamic interactions within the VAWT farm determine the overall performance?
How can VAWTs be designed to operate optimally in turbulent, near-ground winds?
How can we leverage the smaller VAWT size to improve materials costs, O&M, environmental impact, storage, LCOE?
autoanything.com
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Caltech Program in Bio-inspired Wind Energy Field Laboratory (Dabiri) Wind Tunnel Research (Gharib, McKeon) Computational Fluid Dynamics (Colonius) Materials and Manufacturing (Grubbs)
≈ For more info on Field Laboratory:
http://dabiri.caltech.edu/research/wind-energy.html
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Acknowledgments
Robert Whittlesey and Sebastian Liska (graduate students, array modeling)Windspire Energy (turbine-data exchange)
Funding:Gordon and Betty Moore FoundationNational Science Foundation