Wind Power: Wind Power: Optimization at All LevelsOptimization at All Levels

Jaime CarbonellJaime Carbonell

www.cs.cmu.edu/~jgcwww.cs.cmu.edu/~jgc

11-September-200911-September-2009

Wind Turbines (that work)Wind Turbines (that work)

HAWT: Horizontal Axis VAWT: Vertical Axis

Wind Turbines (flights of Wind Turbines (flights of fancy)fancy)

Wind Power FactoidsWind Power Factoids Potential: Potential: 10X to 40X total US electrical power10X to 40X total US electrical power

.01X in 2009.01X in 2009 Cost of wind: Cost of wind: $.02 – $.06/kWh$.02 – $.06/kWh

Cost of coal $.02 – $.03 (other fossils are more)Cost of coal $.02 – $.03 (other fossils are more) Cost of solar $.25/kWh – Photon Consulting Cost of solar $.25/kWh – Photon Consulting

““may reach $.10 by 2010” Photon Consultingmay reach $.10 by 2010” Photon Consulting

State with largest existing wind generationState with largest existing wind generation Texas (7.9 MW) – Greatest capacity: DakotasTexas (7.9 MW) – Greatest capacity: Dakotas

Wind farm construction is semi recession proofWind farm construction is semi recession proof Duke Energy to build wind farm in Wyoming – Reuters Sept 1, 2009Duke Energy to build wind farm in Wyoming – Reuters Sept 1, 2009 Government accelerating R&D, keeping tax creditsGovernment accelerating R&D, keeping tax credits

Grid requires upgrade to support scalable Grid requires upgrade to support scalable wind wind 

Top Wind Power ProducersTop Wind Power Producersin TWh for Q2 2008in TWh for Q2 2008

CountryCountry Wind TWhWind TWh Total TWhTotal TWh % Wind% Wind

GermanyGermany 4040 585585 7%7%

USAUSA 3535 4,1804,180 < 1%< 1%

SpainSpain 2929 304304 10%10%

IndiaIndia 1515 727727 2%2%

DenmarkDenmark 99 4545 20%20%

Sustained Wind-Energy Sustained Wind-Energy DensityDensity

From: National Renewable Energy Laboratory, public domain, 2009

Yet Another Wind MapYet Another Wind Map

US Wind Farms in 2006US Wind Farms in 2006

Inside a Wind TurbineInside a Wind Turbine

GE Wind Energy's 3.6 megawatt wind turbine

From Wikipedia

Power CalculationPower Calculation

Wind kinetic energy:Wind kinetic energy: Wind power: Wind power:

Electrical power:Electrical power: CCb b .35 (<.593 “Betz limit”) .35 (<.593 “Betz limit”)

Max value of Max value of

NNg g .75 generator efficiency .75 generator efficiency

NNt t .95 transmission efficiency .95 transmission efficiency

221 vmE airk

3221 vrP airwind

windtgbgenerated PNNCP

3231

241

1

2

1

2

1

21 vv

vv

vv

airdtdE vrP

Wind v & E match Weibull Wind v & E match Weibull Dist.Dist.

Weibull Distribution:Weibull Distribution:

Red Red = = WeibullWeibull distribution of wind speed over distribution of wind speed over timetime

BlueBlue = = Wind energyWind energy (P = dE/dt) (P = dE/dt)

kxkxkkW exp),( )1(

Data from Lee Ranch, Colorado wind farm

Optimization OpportunitiesOptimization Opportunities Site selection Site selection

Altitude, wind strength, constancy, grid access, …Altitude, wind strength, constancy, grid access, … Turbine selectionTurbine selection

Design (HAWTs vs VAWTs), vendor, size, quantity,Design (HAWTs vs VAWTs), vendor, size, quantity, Turbine Height: “7Turbine Height: “7thth root law” root law”

Greater precision for local conditionsGreater precision for local conditions Local topography (hills, ridges, …) Local topography (hills, ridges, …)

Turbulence caused by other turbinesTurbulence caused by other turbines Prevailing wind strengths, direction, variancePrevailing wind strengths, direction, variance Ground stability (support massive turbines)Ground stability (support massive turbines)

Grid upgrades: extensions, surge capacity, …Grid upgrades: extensions, surge capacity, … Non-power constraints/preferencesNon-power constraints/preferences

Environmental (birds, aesthetics, power lines, …)Environmental (birds, aesthetics, power lines, …) Cause radar clutter (e.g. near airports, air bases)Cause radar clutter (e.g. near airports, air bases)

ggh

ggh

hgh

vv PPPg

h 43.07 3

7

World’s Largest Wind Turbine (7+Megawatts, 400+ feet tall)

Oops...Oops... What’s wrong with this picture?What’s wrong with this picture?

• Proximity of turbines

• Orientation w.r.t. prevaling winds

• Ignoring local topography

• …

Near Palm Springs, CA

Economic OptimizationEconomic Optimization

$1M-3M/MW capacity$1M-3M/MW capacity $3M-20M/turbine$3M-20M/turbine QuestionsQuestions

Economy of scale?Economy of scale? NPV & longevity?NPV & longevity? Interest rate?Interest rate? Operational costs?Operational costs?

Price of ElectricityPrice of Electricity 8% improvement in 25B invested = $2B8% improvement in 25B invested = $2B Price of storage vs upgrade of grid transmission Price of storage vs upgrade of grid transmission

vs bothvs both

Penultimate Optimization Penultimate Optimization ChallengeChallenge

Objective FunctionObjective Function Construction: cost, time, risk, capacity, …Construction: cost, time, risk, capacity, … Grid: access & upgrade cost,Grid: access & upgrade cost, Operation: cost/year, longevity, Operation: cost/year, longevity, Risks: price/year of electricity, demand, reliability, …Risks: price/year of electricity, demand, reliability, …

ConstraintsConstraints Grid: Ave & surge capacity, max power storage, …Grid: Ave & surge capacity, max power storage, … Physical: area, height, topography, atmospherics, …Physical: area, height, topography, atmospherics, … Financial: capital raising, timing, NPV discounts, …Financial: capital raising, timing, NPV discounts, … Regulatory: environmental, permits, safety, …Regulatory: environmental, permits, safety, … Supply chain: availability & timing of turbines, …Supply chain: availability & timing of turbines, …

Energy StorageEnergy Storage

Compressed-air storage Surprisingly viable Efficiency ~50%

Pumped hydroelectric Cheap & scalable Efficiency < 50%

Advanced battery Cost prohibitive

Flywheel arrays (unviable) Superconducting capacitors (missing

technology)

Compressed-Air Storage Compressed-Air Storage SystemSystem

Wind farm:PWF = 2 PT (4000 MW)

Spacing = 50 D2

vrated = 1.4 vavg Transmission:PT = 2000 MW

Comp Gen

PC = 0.85 PT (1700 MW)

Underground storage

Wind resource:k = 3, vavg = 9.6 m/s,

Pwind = 550 W/m2 (Class 5)hA = 5 hrs.

Eo/Ei = 1.30

PG = 0.50 PT

(1000 MW)

hS = 10 hrs.(at PC)

1

0 1

CF = 81%CF = 81%CF = 76%CF = 76%

CF = 68%CF = 68%CF = 72%CF = 72%

Slope ~ 1.7

0.5

0.5

1.5

1.5

Optimization To DateOptimization To Date

Turbine blade designTurbine blade design Huge literatureHuge literature

GeneratorsGenerators Already near optimalAlready near optimal

Wind farm layoutWind farm layout Mostly offshoreMostly offshore Integer programmingInteger programming

TopographyTopography Multi-siteMulti-site + Transmission+ Transmission + Storage+ Storage

new new challengchallengee

Need Wind DataNeed Wind Data Prevalent Direction, Speed, seasonalityPrevalent Direction, Speed, seasonality Measurement tower position & duration Measurement tower position & duration

optimization too…optimization too…

US Investment in Wind US Investment in Wind PowerPower

2008 Investment: $16.4B 2008 Investment: $16.4B (private + (private + public)public)

Total since 1980: $45+BTotal since 1980: $45+B Estimate for 2009-2018: $300B-$700BEstimate for 2009-2018: $300B-$700B

Optimization can have a huge Optimization can have a huge impactimpact

San Goronio Pass, CA

Trusted Third PartyTrusted Third Party

Wind power industry now generates studies Wind power industry now generates studies for public utilities for public utilities Every industry provider (Vestas, GE, Siemens, Every industry provider (Vestas, GE, Siemens,

…) shows their wind-generators are the best …) shows their wind-generators are the best no true comparison, no site/context sensitivity.no true comparison, no site/context sensitivity.

No global optimization across designs, etc.No global optimization across designs, etc. Modeling, optimization, assessment is Modeling, optimization, assessment is

complex, requires expertisecomplex, requires expertise Room for a non-profit expertise pool and modelsRoom for a non-profit expertise pool and models Track evolving technologiesTrack evolving technologies

ReferencesReferences Schmidt, Michael, Schmidt, Michael, “The Economic Optimization of Wind The Economic Optimization of Wind

Turbine Design” MS Thesis, Georgia Tech, Mech E. Nov, Turbine Design” MS Thesis, Georgia Tech, Mech E. Nov, 2007.2007.

Donovan, S. “Wind Farm Optimization” University of Donovan, S. “Wind Farm Optimization” University of Auckland Report, 2005.Auckland Report, 2005.

Elikinton, C. N. “Offshore Wind Farm Layout Optimization”, Elikinton, C. N. “Offshore Wind Farm Layout Optimization”, PhD Dissertation, UMass, 2007.PhD Dissertation, UMass, 2007.

Lackner MA, Elkinton CN. An Analytical Framework for Lackner MA, Elkinton CN. An Analytical Framework for Offshore Wind Farm Layout Optimization. Offshore Wind Farm Layout Optimization. Wind Engineering Wind Engineering 2007; 2007; 3131: 17-31. : 17-31.

Elkinton CN, Manwell JF, McGowan JG. Optimization Elkinton CN, Manwell JF, McGowan JG. Optimization Algorithms for Offshore Wind Farm Micrositing, Algorithms for Offshore Wind Farm Micrositing, Proc. Proc. WINDPOWER 2007 Conference and ExhibitionWINDPOWER 2007 Conference and Exhibition, American American Wind Energy Association, Los Angeles, CA, 2007. Wind Energy Association, Los Angeles, CA, 2007.

Zaaijer, M.B. et al, “Optimization Through Conceptial Zaaijer, M.B. et al, “Optimization Through Conceptial Varation of a Baseline Wind Farm”, Delft University of Varation of a Baseline Wind Farm”, Delft University of Technology Report, 2004.Technology Report, 2004.

First First Wind Energy Optimization Summit, Wind Energy Optimization Summit, Hamburg, Feb 2009.Hamburg, Feb 2009.

THANK YOU!THANK YOU!

Supplementary MaterialSupplementary Material

US Electrical Power in 2008 US Electrical Power in 2008

Other (4.1%) = Biomass (2%) + Wind (1%) + Solar + Geothermal + …

A Second Opinion…A Second Opinion…

Power Class

Wind Power(W/m2)

Speed*(m/s)

    

1 <200 <5.6

2 200-300 5.6-6.4

3 300-400 6.4-7.0

4 400-500 7.0-7.5

5 500-600 7.5-8.0

6 600-800 8.0-8.8

7 >800 >8.8

From Battelle Wind Energy Resource Atlas

Viable Class 3 or above

Good Class 4 or above