Wind Power:
Optimization at All Levels
Jaime Carbonell
www.cs.cmu.edu/~jgc
11-September-2009
Wind Turbines (that work)
HAWT: Horizontal Axis
VAWT: Vertical Axis
Wind Turbines (flights of fancy)
Wind Power Factoids
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Potential: 10X to 40X total US electrical power

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.01X in 2009
Cost of wind: $.02 – $.06/kWh

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Cost of coal $.02 – $.03 (other fossils are more)
Cost of solar $.25/kWh – Photon Consulting
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State with largest existing wind generation
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“may reach $.10 by 2010” Photon Consulting
Texas (7.9 MW) – Greatest capacity: Dakotas
Wind farm construction is semi recession proof
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Duke Energy to build wind farm in Wyoming – Reuters Sept 1, 2009
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Government accelerating R&D, keeping tax credits
Grid requires upgrade to support scalable wind
Top Wind Power Producers
in TWh for Q2 2008
Country
Wind TWh
Germany
40
585
7%
USA
35
4,180
< 1%
Spain
29
304
10%
India
15
727
2%
9
45
20%
Denmark
Total TWh
% Wind
Sustained Wind-Energy Density
From: National Renewable Energy Laboratory, public domain, 2009
Yet Another Wind Map
US Wind Farms in 2006
Inside a Wind Turbine
From Wikipedia
GE Wind Energy's 3.6
megawatt wind turbine
Power Calculation

2
1
E

m
v
Wind kinetic energy:
k
air
2

Wind power:
Pwind   airr v

Electrical power:

Pgenerated  Cb N g N t Pwind
Cb  .35 (<.593 “Betz limit”)

Max value of
2 3
1
2
P
dE
dt

 14  airr 2v13 1 

Ng  .75 generator efficiency

Nt  .95 transmission efficiency
       
v2
v1
v2 2
v1
v2 3
v1
Wind v & E match Weibull Dist.
Weibull Distribution:
W ( , k )     
k
x ( k 1)

exp    
x k

Data from Lee Ranch, Colorado
wind farm
Red = Weibull distribution of wind speed over time
Blue = Wind energy (P = dE/dt)
Optimization Opportunities

Site selection


Altitude, wind strength, constancy, grid access, …
Turbine selection


Design (HAWTs vs VAWTs), vendor, size, quantity,
Turbine Height: “7th root law”
vh
vg




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 Ph 
7
3
h
g
Pg 

h 0.43
g
Pg
Greater precision for local conditions
Local topography (hills, ridges, …)



7 h
g
Turbulence caused by other turbines
Prevailing wind strengths, direction, variance
Ground stability (support massive turbines)
Grid upgrades: extensions, surge capacity, …
Non-power constraints/preferences


Environmental (birds, aesthetics, power lines, …)
Cause radar clutter (e.g. near airports, air bases)
World’s Largest Wind Turbine
(7+Megawatts, 400+ feet tall)
Oops...

What’s wrong with this picture?
• Proximity of turbines
• Orientation w.r.t.
prevaling winds
• Ignoring local
topography
•…
Near Palm Springs, CA
Economic Optimization



$1M-3M/MW capacity
$3M-20M/turbine
Questions
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Economy of scale?
NPV & longevity?
Interest rate?
Operational costs?
Price of Electricity
8% improvement in 25B invested = $2B
Price of storage vs upgrade of grid transmission vs both
Penultimate Optimization Challenge

Objective Function




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Construction: cost, time, risk, capacity, …
Grid: access & upgrade cost,
Operation: cost/year, longevity,
Risks: price/year of electricity, demand, reliability, …
Constraints



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Grid: Ave & surge capacity, max power storage, …
Physical: area, height, topography, atmospherics, …
Financial: capital raising, timing, NPV discounts, …
Regulatory: environmental, permits, safety, …
Supply chain: availability & timing of turbines, …
Energy Storage

Compressed-air storage

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Pumped hydroelectric

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Cheap & scalable
Efficiency < 50%
Advanced battery


Surprisingly viable
Efficiency ~50%
Cost prohibitive
Flywheel arrays (unviable)
Superconducting capacitors (missing technology)
Compressed-Air Storage System
Wind resource:
1.5
k = 3, vavg = 9.6 m/s,
Pwind = 550 W/m2 (Class 5)
hA = 5 hrs.
Wind farm:
PWF = 2 PT (4000 MW)
Spacing = 50 D2
vrated = 1.4 vavg
Slope ~ 1.7
1
PC = 0.85 PT
(1700 MW)
PG = 0.50 PT
(1000 MW)
Comp
Gen
0.5
0
CF = 81%
CF = 76%
CF = 72%
CF = 68%
0.5
1
hS = 10 hrs.
(at PC)
Eo/Ei = 1.30
Underground storage
Transmission:
PT = 2000 MW
1.5
Optimization To Date

Turbine blade design


Generators

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Already near optimal
Wind farm layout


Huge literature
Mostly offshore
Integer programming
Topography
Multi-site
+ Transmission
+ Storage
new
challenge
Need Wind Data


Prevalent Direction, Speed, seasonality
Measurement tower position & duration
optimization too…
US Investment in Wind Power



2008 Investment: $16.4B (private + public)
Total since 1980: $45+B
Estimate for 2009-2018: $300B-$700B
 Optimization can have a huge impact
San Goronio Pass, CA
Trusted Third Party

Wind power industry now generates studies for
public utilities



Every industry provider (Vestas, GE, Siemens, …)
shows their wind-generators are the best  no true
comparison, no site/context sensitivity.
No global optimization across designs, etc.
Modeling, optimization, assessment is complex,
requires expertise


Room for a non-profit expertise pool and models
Track evolving technologies
References
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Schmidt, Michael, “The Economic Optimization of Wind Turbine
Design” MS Thesis, Georgia Tech, Mech E. Nov, 2007.
Donovan, S. “Wind Farm Optimization” University of Auckland
Report, 2005.
Elikinton, C. N. “Offshore Wind Farm Layout Optimization”, PhD
Dissertation, UMass, 2007.
Lackner MA, Elkinton CN. An Analytical Framework for Offshore
Wind Farm Layout Optimization. Wind Engineering 2007; 31: 17-31.
Elkinton CN, Manwell JF, McGowan JG. Optimization Algorithms for
Offshore Wind Farm Micrositing, Proc. WINDPOWER 2007
Conference and Exhibition, American Wind Energy Association, Los
Angeles, CA, 2007.
Zaaijer, M.B. et al, “Optimization Through Conceptial Varation of a
Baseline Wind Farm”, Delft University of Technology Report, 2004.
First Wind Energy Optimization Summit, Hamburg, Feb 2009.
THANK YOU!
Supplementary Material
US Electrical Power in 2008
Other (4.1%) = Biomass (2%) + Wind (1%) + Solar + Geothermal + …
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