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

17

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

22

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

32

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?

51

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)

55

Turbine Blades

• Airfoil: shape that produces lift

• Wind is accelerated over longer top surface creating low pressure (lift)

56

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

64

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

65

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

66

Renewable Portfolio Standards (RPS)

wind and solar, and biomass and …

CA 33% by 2020

67

Low-carbon technologies as least-cost, fast-

deployment, technology options: wind

Production Tax Credit – US

history

69

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

71

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