ER100/200 & Public Policy 189/284 Lecture 20 -...
Transcript of ER100/200 & Public Policy 189/284 Lecture 20 -...
Daniel Kammen
November 10, 2015
ER100/200 & Public Policy 189/284
Lecture 20 - Wind Energy
Tuesday: Wind, hydropower and geothermal
Masters, G. (2004) “Wind Power Systems.” Renewable and Efficient Power Systems (Wiley
InterScience: New York), pages 307 – 354 (pages 335-347 are supplemental), 371 – 378.
[ Masters_2004_Wind.pdf]
Zheng, Cheng and Kammen, Daniel (2014) “An Innovation-Focused Roadmap for a Sustainable
Global Photovoltaic Industry,” Energy Policy, 67, 159–169.
The Chinese are obsessed with building large dams (2015) The British Broadcasting Corporation
http://www.bbc.com/future/story/20151014-the-chinese-are-obsessed-with-building-giant-dams
Thursday: Renewable Energy III: Electrochemistry H2 Batteries and Fuel Cells
Masters, G. (2004) “Fuel Cells,” in Renewable and Efficient Power Systems (Wiley InterScience:
New York), pages 206-228. [ Masters_2004_Fuel_Cells.pdf]
Ogden, J. (2006). “High Hopes for Hydrogen”, Scientific American, September, pp. 94-101.
[ Ogden_2006.pdf]
ER200/PP284:
Keith, D. W. and Farrell, A. E. (2003) “Rethinking hydrogen cars”, Science, 301, 315 – 316.
[ Keith_2003.pdf]
Global Wind Resource
Annual global mean wind power at 50m above the surface
Wind dynamics is fluid dynamics
Horns Rev Offshore Wind Farm
Wind turbines in a wind farm ….
Biological inspiration: Fish Schooling
United States Annual Average Wind Power
Basic Calculations: Power Density
• Kinetic Energy (KE) – ½ mV2
• For a constant wind speed v, normal cross sectional area A, and given period of time, t, and air density ρ, – Air mass m = ρAVt
• So,
• KE = ½ ρAtV3
A
v
• Wind power density (per unit area and per second) is:
• Power = ½ ρ V3
Harvestable power scales with the cube of the wind speed
8
time
[ ]
3
22
2
Areaunit
Power
t
KE
t
W =Power
KE =energy kineticin changeWork
: tin time, turbinepast the movesair the
;2
1
2
1
2
1=Energy Kinetic
v
tvvAvtV
mv
airV
rotorair
m
airair
µúû
ùêë
é
úû
ùêë
éD=ú
û
ùêë
é
D=
úú
û
ù
êê
ë
é
÷ø
öçè
æ=÷
ø
öçè
æ=
÷ø
öçè
æ
rr
A
v
Windmill of area A, wind velocity v
Energy in the Air (dervivation)
3
2
1vArotorairr÷
ø
öçè
æ=Power in moving column of air
Harvestable power scales with the cube of the wind speed
Power Density
• The atmosphere approximates an ideal gas
equation in which at the STP (T0 = 288.1K), (P0
= 100.325 Pa),
– ρ0 = 1.225kg/m3
Distribution of wind speed
• The strength of wind varies, and an average value for a given location does not alone indicate the amount of energy a wind turbine could produce there
• To assess the frequency of wind speeds at a particular location, a probability distribution function is often fit to the observed data.
• Different locations will have different wind speed distributions.
• A statistical distribution function is often used to describe the frequency of occurrence of the wind speed – a Weibull or Rayleigh distribution is typically used
• The wind power density is modified by the inclusion of an energy pattern factor (Epf)
• Where Va is the average wind speed
Distribution of Wind Speeds …2
• The amount of wind available at a site may vary from one year to the next, with even larger scale variations over periods of decades or more
• Synoptic Variations– Time scale shorter than a year – seasonal variations
– Associated with passage of weather systems
• Diurnal Variations– Predicable (ish) based on time of the day (depending on location)
– Important for integrating large amounts of wind-power into the grid
• Turbulence– Short-time-scale predictability (minutes or less)
– Significant effect on design and performance of turbines
– Effects quality of power delivered to the grid
– Turbulence intensity is given by I = σ / V, where σ is the standard deviation on the wind speed
Globally Installed wind capacity2014 2004
Wind Power: Quick Summary• Potential: 10X to 40X total US electrical power
– .01X in 2009
• Cost of wind: $.03 – $.07/kWh
– Cost of coal $.02 – $.03 (other fossils are more)
– Cost of solar $.25/kWh• “may reach $.10 by 2020” Photon Consulting
• State with largest existing wind generation– Texas (7.9 GW) – Greatest capacity: Dakotas
• Grid requires upgrade tor scalable wind
• 2012: 51,000 MW, 40,000 turbines
Why wind power integration?
The Danish example
Source: Energinet.dk - EcoGrid
• Approximately 20% of electricity consumption
met by wind power – annual average
• Around 3GW installed wind power capacity
• For a few hours in a year wind power covers the
entire Danish demand
• 50% of electricity consumption to be met by wind
power – annual average
• Around 6GW installed wind power capacity
• Wind power production will often exceed the
Danish demand
2008 2020
14
15
Installed capacity by state
16
Wind Business
• Turbines are now
very big
• Practical issues are
real
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Setting a Tower Base SectionC
on
stru
ctio
n C
ycle
18
Setting the Mid SectionC
on
stru
ctio
n C
ycle
19
An Installed NacelleC
on
stru
ctio
n C
ycle
Paul
Anderson
• Structure size, associated design requirements and materials
costs
• Logistics of installation and maintenance
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Growth in Off-shore Turbines
Wind Turbine Size-Power
Energy Extracting Mechanism
velocity
pressure
pressure
velocity
V∞
Vw
p ∞ p ∞
Vd
p-d
p+d
Actuator disk /
Turbine Blades
Stream tube
Ideal Extractor (Summary)
2
21' vvv
AvP 3
102
1
21
2
2
2
14
1vvvvAP
Due to Albert Betz
• Continuity, energy balance, and force balance across rotor area
• Key Results:
Pmax = 0.59*P(v1)
Mass Flow (More detail)
• Mass flow rate must be the same everywhere
along the tube so,• ρ A∞ V∞ = ρ Ad Vd = ρ Aw Vw (i)
• ∞ refers to conditions far upstream/downstream
• d refers to conditions at the disk
• w refers to conditions in the far wake
• The turbine induces a velocity variation which is
superimposed on the free stream velocity, so:• Vd = V∞(1 – a) (ii)
• Where a is known as the axial flow induction factor, or the
inflow factor
Momentum (More detail)
• The air that passes through the disk undergoes
an overall change in velocity (V∞ - Vw),
• Rate of change of momentum dP• dP= (V∞ - Vw)ρAdVd (iii)
• = overall change in velocity x mass flow rate
• The force causing this change in momentum is
due to pressure difference across turbine so,• (p+
d – p-d)Ad = (V∞ - Vw)ρAdV∞( 1-a) (iv)
Bernoulli’s Equation (More detail)
• Bernoulli’s equation states that, under
steady state conditions, the total energy in
a flow, comprising kinetic energy, static
pressure energy, and gravitational
potential, remains the same provided no
work is done on or by the fluid
• So, for a volume of air, • ½ ρV2 + p + ρgh = constant (v)
Axial Speed Loss (More detail)
• Upstream:• ½ ρ∞V∞
2 + p∞ + ρ∞g h∞ = ½ ρd Vd2 + p+
d + ρdghd (vi)
• Assuming ρ∞ = ρd and h∞ = hd• ½ ρ∞V∞
2 + p∞ = ½ ρd Vd2 + p+
d (vii)
• Similarly downstream• ½ ρ∞V∞
2 + p∞ = ½ ρd Vd2 + p-
d (viii)
• Subtracting,• (p+
d – p-d) = ½ ρ (V∞
2 - Vw2)
• From (iv), • ½ ρ (V∞
2 - Vw2) Ad = (V∞ - Vw)ρAdV∞( 1-a) (ix)
• Vw = (1 -2a)V∞ (x)
Power Coefficient (Summary)
• From earlier, Force F• F = (p+
d – p-d)Ad = 2ρAdV
2∞( 1-a)
• Rate of work done by the force at the turbine = FVd
• Power = FVd = 2ρAdV3
∞( 1-a)2
• Cp (Power Coefficient) = ratio of power harvested to power available in the air
• Cp = (2ρAdV3
∞( 1-a)2 ) / (½ ρAdV3
∞)
• Cp = 4a(1 – a)2
The Betz Limit
• The maximum value of Cp occurs when
dCp/da = 4(1-a)(1-3a) = 0
• Which gives : a = 1/3
• Therefore, CPmax = 16/27 = 0.593
• This is the maximum achievable value of Cp
• No single turbine can exceed this limit
Ideal Extractor Derivation
593.027
16~
112
1
max
1
2
2
1
2
0
p
p
C
v
v
v
v
P
PC
• Irrotational system• No boundary layer or compression flow
• Creeping flow (Re << 1)• Uniform power extraction
• No geometry boundary conditions• Never true!
Distribution of Wind Speeds
• As the energy in the wind varies as the cube of the wind speed, an understanding of wind characteristics is essential for:– Identification of suitable sites
– Predictions of economic viability of wind farm projects
– Wind turbine design and selection
– Effects of electricity distribution networks and consumers
• Temporal and spatial variation in the wind resource is substantial – Latitude / Climate
– Proportion of land and sea
– Size and topography of land mass
– Vegetation (absorption/reflection of light, surface temp, humidity
The Wind Resource•Atmospheric
pressure differences
– Where does the
pressure come from?
• Weight of air in
atmosphere
Area
Force Pressure
~31 km(99% of mass)
• Avg. pressure at sea level
– 101325 Pa (Pascal)
– 1013.25 mb (millibar)
– 29.92 in. Hg (inches of mercury
– 1 atm (atmosphere)
– 14.7 psi (pound per square inch)
Prevailing Winds• Heating and cooling of the air
http://trampleasure.net/science/coriolis/coriolis.png
U. S. Wind Energy Resource Map
Sustained Wind-Energy Density
From: National Renewable Energy Laboratory, public domain, 2009
Mt. Washington, NH
Wind as a fluid (and hydro power)• Pressure differences cause the flow of fluids
(gases and liquids)– pressure is always measured relative to some reference
pressure• Sometimes relative to vacuum absolute
• Sometimes relative to atmospheric pressure
hPB PA
The higher pressure at B will cause fluid to flow out of the tank.
Density of air 1.2041 kg/m3
Density of water, 1000 kg/m3
833 times higher for water
AB Phg P
Fluid density
Acceleration due to gravity
Fluid height
Wind and Water Power - Example•Example:
V = 10 m/s
A = (2 m)2 = 4 m2
Air = 1.2 kg/m3
http://z.about.com/d/gonewengland/1/0/5/C/leaf5.gif
http://enneagon.org/footprint/jpg/dvc01w.jpg
2)()( Power
33
21
AVvelocityareadensity
Remember:
ρwater = 1000 kg/m3 so 833 times more power at
the same velocity
Power Calculation (summary)
• Wind kinetic energy:
• Wind power:
• Electrical power:
– Cb .35 (typically) (<.593 “Betz limit”)
• Max value of
– Ng .75 generator efficiency
– Nt .95 transmission efficiency
2
21 vmE airk
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21 vrP airwind
windtgbgenerated PNNCP
323
1
2
41
1
2
1
2
1
21v
v
v
v
v
v
airdtdE vrP
Wind velocity match Weibull Dist.Weibull Distribution:
Red = Weibull distribution of wind speed over time
Blue = Wind energy (P = dE/dt)
Wind velocity match Weibull Dist.
44
Wind speed distributions (k=2)
391.1
2
1Power averotorair vA
Many wind regimes have wind speed distributions which fall
under a probability distribution called the Rayleigh distribution
(k=2).
(v3)ave=1.91vave3 for winds that have a Rayleigh distribution
V (m/s)
Best fit Rayleigh
distribution
33 91.12
1
2
1Power averotorairaverotorair vAvA
Modern System Components
Where should we put all the stuff?
Situation dependent
• Maintenance requirements• Size
• Wind quality• Budget
Extra:More Cp, or “Why you should choose three
blades too”
Technological Challenges
• Integrating unpredictable energy resources into existing power systems / grids.
• Accurate estimation of wind resources
– Location, location, location!
• Not a commodity, a custom product.
• Scaling up, scaling down…
• Energy storage?
Modern HAWTs
approach
theoretical maximum
efficiency
netfirms.com
Efficiency
Betz Efficiency
Limit
Tip Speed
Ratio
60%
50%
40%
30%
20%
10%
Modern HAWTs
Maximizing Power Production
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?
Modern HAWTs
approach
theoretical maximum
efficiency
Is there room for
fundamental
improvements in
wind energy? netfirms.com
Efficiency
Betz Efficiency
Limit
Tip Speed
Ratio
60%
50%
40%
30%
20%
10%
Modern HAWTs
Maximizing Power Production
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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Wind Classes and ProbabilityNREL Wind Classes at 50m
• Change with height due to Earth’s boundary layer
• Probability
distribution
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Wind velocity (m/s)
Fre
qu
en
cy mean 4m/s
mean 5m/s
mean 6m/s
mean 7m/s
Wind Turbine Configurations
HAWT
VAWT
Boyle, G., Renewable Energy, 2nd ed., Oxford
University Press, 2004
Configuration Tradeoffs• Factors
– Efficiency
• Power produced per unit cost
– Directionality
– Support configuration
– Speed of rotation
– Reliability
– Cost
– Maintainability
Which type is best, HAWT or VAWT?
Common HAWT Construction
Roto
r
• Blades are connected to a hub, which is connected
to a shaft
• Rotational speed will depend on blade geometry,
number of blades, and wind speed (40 to 400
revolutions per minute typical speed range)
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Turbine Blades
• Airfoil: shape that produces lift
• Wind is accelerated over longer top surface creating low pressure (lift)
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Angle of Attack (extra)
• L = lifting force, D = drag, R = resultant force
• Lift force increases with angle of attack until stall occurs
57
Practical Turbine Efficiency• gives an estimate of the turbine performance
),( avgvvf)(vp
3
2
1
)(),()(
avgrotor
avg
avg
vA
vpvvfv
r
hå ×
=
Rated power, Wp
Will come back to this
Variation of windspeed with Height
• Principal effects governing the properties of wind
close to the surface (the boundary layer)
include:
– The strength of the geostrophic wind
– The surface topography / roughness
– Coriolis effects due to the earth’s rotation
– Thermal effects
• Most interesting for us is that the boundary layer
properties are strongly influenced by surface
roughness – therefore site selection is critical
Variation of windspeed with Height
• Taller windmills see higher wind speeds
• Ballpark: doubling the height increases windspeed by 10% and thus increases power density by 30%
• Wind shear formula from NERL (National Renewable Energy Laboratory):
• v(z) = v10(z / 10m)α
• Where v10 is the speed at 10m, α typically around 0.143
• Wind shear formula from the Danish Wind Energy Association:
• v(z) = vref log(z/zo) / log(zref/z0)
• Where z0 is a parameter called the roughness length, vref is the speed at a reference height zref
Variation of windspeed with Height
Type of Terrain Roughness Length z0 (m)
Cities, forests 0.7
suburbs, wooded countryside 0.3
Villages, countryside with trees and hedges 0.1
Open farmland, few trees and buildings 0.03
Flat grassy plains 0.01
Flat desert, rough sea 0.001
Typical Surface Roughness Lengths
(from Wind Energy Handbook, pg 10
Example – Windmill Power
• A windmill has a diameter d = 25m, and a hub height of 32m. The efficiency factor is 50%. What is the power produced by the windmill if the windspeed is 6m/s?
• Power of the wind per m2
• ½ ρv3 = ½ 1.3kg/m3 x (6m/s)3 = 140W/m2
• Power of the windmill = Cp x power per unit area x area
• = 50% x ½ ρv3 x (π/4)d2
• = 50% x 140W/m2 x (π/4)(25m)2
• = 34kW
Windmill Packing Density
• As it extracts energy from the wind, the turbine leaves behind it a wake characterised by reduced wind speeds and increased levels of turbuence
• A turbine operating in the wake of a turbine will produce less energy and suffer greater structural loading
• Rule of thumb is that windmills cannot be spaced closer than 5 times their diameter without losing significant power
Windmill Packing Density
• Power that a windmill can generate per unit land area =
• Power per windmill / land area per windmill
• = (Cp x ½ ρv3 x (π/4)d2) / (5d)2
d
5d
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A simple estimator:
Estimating Annual Energy
Production (AEP)
hrCFPAEP R 8760**
2087.0
D
PvCF R
ave
Where PR is rated power in kW of turbine, and D is
diameter in meters, and a Rayleigh distribution of wind
velocities
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Example (to run through at home)
An Entegrity wind turbine has a blade diameter of 15m and rated output of 65kW. It is to be located in a class 1 wind site (not great!) with an average wind speed of 5.5 m/s.
Estimate the annual energy production, assuming Rayleigh statistics for the wind:
19.0
15
65)/5.5(087.0
2
m
kWsmCF
yrkWhxhrkWAEP /101.18760*19.*65 5
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Renewable Portfolio Standards (RPS)
wind and solar, and biomass and …
CA 33% by 2020
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Low-carbon technologies as least-cost, fast-
deployment, technology options: wind
Production Tax Credit – US
history
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MAKANI (tethered wing)
Turbine at the wing tip
(maximum velocity
SPINNING ROTORS CREATE LIFT TO
FLY
TORQUE ON SHAFT TURNS
GENERATOR
TORQUE
LIFT
WIND
70
POWER GENERATION
ABOVE 10,000 FT. JET STREAM TURBINE FLIES BY
AUTOROTATION
10,000
Ft
Sea
Level
STRATOSPHERE
AUTOROTATION
TROPOSPHERE
POWERED FLIGHT
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Powered Flight to ~ 10,000 Feet, then autorotation
Wind Turbines (just thinking …)
Ocean Monitoring
Wind Energy
Bioinspired Engineering
Jellyfish
UW
AP
L G
LID
ER Soft Robotics
‘Optimal’ fish schooling provides our starting point…
Weihs (1975)
Triantafyllou et al.
(1995)
≈
primary wind