Geometric Scaling and Long-Run Reductions in Cost:

The case of wind turbines Srikanth Narasimalu

Ph.D. StudentJeffrey Funk

Associate ProfessorDivision of Engineering & Technology Management

National University of Singapore

Wind Turbines on Land and at Sea

Large Wind Farms in the Ocean and on Land

Preliminary Observation:Larger Wind Turbines are Being Installed

So Conventional Wisdom is Probably Not Very Relevant

• Cost of producing a product drops a certain percentage each time cumulative production doubles in so-called learning or experience curve (Arrow, 1962; Ayres, 1992; Huber, 1991; Argote and Epple, 1990; March, 1991)• as automated manufacturing equipment is introduced and organized into

flow lines (Utterback, 1994)• Although learning curves do not explicitly exclude activities

done outside a factory, the fact that these learning curves link cost reductions with cumulative production • focuses policy and other analyses on the production of the final product• imply that learning done outside of a factory is either unimportant or is

being driven by the production of the final product• If major impact of installing more wind turbines was on lowering

manufacturing cost, firms would install small wind turbines so there would be high volumes of small blades, towers, etc.

Of Course, the Wind Doesn’t Blow Everywhere (and all the Time)

Wind Speed Measurements at 8,000 Stations

Source: http://www.worldchanging.com/archives/002770.html

Frequency of Wind Speed in a Ranch in Texas

2009:159 GW

2010194 GW

Installed Global Capacity of Wind Power (MW)

Country     Total capacityend 2009(MW)    

Total capacityJune 2010

(MW)    

United States 35,159 36,300

China 26,010 33,800

Germany 25,777 26,400

Spain 19,149 19,500

India 10,925 12,100

Italy 4,850 5,300

France 4,521 5,000

United Kingdom 4,092 4,600

Portugal 3,535 3,800

Denmark 3,497 3,700

Rest of world 21,698 24,500

Total 159,213 175,000

Installed Wind Capacity by Country

TWh: Tera Watt Hours

But Wind Contributes a Small Percentage of Overall Electricity Generation (1)

Wind Contributes Small Percentage of Electricity Generation (2)

Blue is actual, red is forecastedWorld Wind Energy Association World Wind Energy Report 2009

How Much Will this Contribution Increase in the Future?

The Future of Wind Power

• Will wind power continue to diffuse?• Advantages

• It has lower carbon and other environmental emissions

• Disadvantages• Wind doesn’t blow all the time (actual output about 1/3 of rated

output)• Wind is often far from large population centers, so transmission

costs are high• Wind turbines are considered ugly by many people• Wind power is still more expensive than fossil fuels

• But will wind power become cheaper than fossil fuels• Will countries continue to subsidize wind power or implement a

carbon tax?• Are wind turbines becoming cheaper on an cost per Watt basis?

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs needed?• Where are the entrepreneurial opportunities?

Wind Farm Level Costs

•Wind energy: 75% of costs paid upfront

•Conventional power: less capital intensive – uncertain fuel and carbon costs

Data source: EWEA for a 2MW Turbine.

Main Components in Terms of Costs

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs Needed?• Where are the entrepreneurial opportunities?

Figure 1. Horizontal Axis Wind Turbine

Focus on Horizontal Axis Wind Turbine

Ref: Srikanth in JEC(2009).

Figure 1. Horizontal Axis Wind Turbine

Three Key Dimensions in Geometric Scaling: 1) rotor diameter; 2) swept area of blades; and 3) hub or tower height

Theoretical Output From Wind Turbine

Turbine power output by Rotor 2 33.229RP D V

P = electric power (energy per second or watts)D = rotor diameter (meters)V = wind speed (meters/second)

• Output from rotor depends on square of rotor diameter; thus cost of electricity from wind turbine might fall as diameter increases, as long as cost of wind turbine rises at a rate less than diameter squared

• Cost of electricity from wind turbine might fall as diameter increases, if larger diameter rotors enable a wind turbine to handle higher wind speeds.

(Equation 1)

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs Needed?• Where are the entrepreneurial opportunities?

Empirical Data Finds Stronger Relationship

Equation (2)

Data source from Henderson et al.(2003) & manufacturer catalogue.

Reason for Discrepancy

•Above equation does not contain wind velocity:• which as noted above has large impact on output

• It does not contain wind velocity since the turbines used for the collection of data on power and rotor diameter for Figure 3 • operate under different wind speeds• these wind conditions depend on the respective region

•The impact of rotor diameter and other factors on wind speed was investigated in four ways

First, relationship between diameter and maximum rated wind speed

Rated wind speed (m/sec) = 9.403D0.081

Data source: Hau (2008).

Best fit curve:Maximumrated windspeed =

Second, data on efficiency of wind turbines was also collected

• Efficiency is the ratio of annual turbine power output compared to the energy available in the wind

• Less of wind can be harnessed at tips of blades than near center of the rotor

Average wind speed (m/sec)

Maximum Power density achievable

(W/m^2)

Small turbine (<25 meters)

efficiency Large turbine (>25 meters) efficiency

4 75 19% 35%

5 146 20% 37%

6 253 18% 35%

7 401 17% 31%

8 599 15% 26%

9 853 14% 21%

Third, Larger Rotor Diameter Better Utilizes Most Common Wind Speeds

Data source: Vestas website

Fourth, Higher Towers, Higher Speeds

• Wind velocity is often lower near ground due to uneven terrain or buildings

• The factor alpha depends on the condition of the terrain and in particular on the impact of the terrain on wind friction and is usually about 0.32

• Combining equations (4) and (1) leads to equation (5). Since the exponent for the ratio of the two heights is 3α, an α of 0.32 would cause a doubling of the tower height to result in a 94% increase in power output.

refref H

H

V

V

3

refref H

HPP

Equation (4)

Equation (5)

Comparison of Wind resource at different altitude (Indiana, USA)

Data source: EWEA

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs Needed?• Where are the entrepreneurial opportunities?

Cost of Wind Turbines

• More than 2/3 the cost of electricity from wind turbine farms comes from capital cost of wind turbine and almost half the capital costs are in tower and blades (Krohn et al, 2009)

• Beginning with tower, WindPACT analysis (Malcom and Hansen, 2006) found regression coefficient of 0.999

c = cost of steel ($/Kg); H = tower height; D = rotor diameter

• Comparing equations (5) and (6), output from turbine increases faster than costs as height is increased.

• For example, if alpha is 0.32 as was shown above and assuming a constant rotor diameter,

• increasing height from 10 meters to 20 meters would cause output to rise by 94% and costs to rise by 9 percent

Tower cost (in $) = 0.85 (cD2H) – 1414 Equation (6)

Cost of the Rotor:

Does not increase linearly

Data source: Hau (2008) and EWEA (2010) .

Rotor Cost Per “Swept Area” of Turbine Blades (1)

Figure 4. Manufacturing cost of rotor on per unit swept area for different rotor diameter.

Equation (8)Equation (9)

Compare them to Equation (2) in which

Data source: Hau (2008) and EWEA (2010) .

Rotor Cost Per “Swept Area” of Turbine Blades (2)

• Benefits from increasing scale• diameters < 50 meters; Yes• diameters > 50 meters; Maybe Not

• “Maybe” because equation (2) does not take into account • the impact of increased tower height or rotor diameter on maximum

rated wind speeds or increased efficiencies.

• Including the increased efficiencies, maximum rated wind speeds, and greater tower heights, which are partly represented by equations (3) and (5) • would provide a further improvements in our understanding of scaling• would probably show some benefits to increases in scale

Cost of Blades (3)

• The reason for the change in slopes for < and > than 50 meters is that lighter, thus higher cost materials are needed:• for diameters > 50 meters (carbon fiber-based blades). • than for diameters < 50 meters (aluminum, glass fiber reinforced

composites, and wood/epoxy).

• Early blades can be manufactured with methods borrowed from pleasure boats such as “hand lay up” of fiber-glass reinforced with polyester resin.

• Carbon-based blades require better manufacturing methods such as vacuum bagging process and resin infusion method that have been borrowed from the aerospace industry (Ashwill, 2004)

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs needed?• Where are the entrepreneurial opportunities?

Remember the Conventional Wisdom

• Cost of producing a product drops a certain percentage each time cumulative production doubles in so-called learning or experience curve (Arrow, 1962; Ayres, 1992; Huber, 1991; Argote and Epple, 1990; March, 1991)• as automated manufacturing equipment is introduced and organized into

flow lines (Utterback, 1994)• Although learning curves do not explicitly exclude activities

done outside a factory, the fact that these learning curves link cost reductions with cumulative production • focuses policy and other analyses on the production of the final product• imply that learning done outside of a factory is either unimportant or is

being driven by the production of the final product• If major impact of installing more wind turbines was on lowering

manufacturing cost, firms would install small wind turbines so there would be high volumes of small blades, towers, etc.

New Materials are Needed

•Stronger and lighter materials are needed for further increases in scaling• Lighter materials are needed in order to reduce

inertia of large rotors• Stronger materials are needed to withstand high

wind speeds

•Without new materials, there will be few (or no) benefits from further scaling

•Perhaps too large of wind turbines have already been installed

Material Technology Choice for Blades

Note: Squared meters is for swept area of rotorSource (Srikanth, 2009)

Other Data on Blade Cost Also Reinforces Need for Better Materials

Table 1. Comparison chart of blades with increasing sizes (30m to 70m ) (Data

source. TPI composites(2003)).

Parameter Blade length 30 m

Blade length 50 m

Blade length 70 m

Materials (Kg) 4108 18856 50238

Materials cost ($) $12241 $ 55523 $149079

Blade manuf. labor 450 hours 1201 hours 2802 hours

Plant cost ($/year) $1319968 $1840160 $2439360

Production tooling cost $239669 $660883 $1335166

Ref: Srikanth in JEC(2009).

Policy Implications• Promote adoption of new materials and manufacturing processes

for the turbine blades to continue the cost reductions in electricity from wind turbines.

• Support for this R&D (in form of direct funding or R&D tax credits) will probably have a larger impact on reducing costs of electricity from wind turbines than from merely subsidizing their implementation

• Subsidizing their implementation is partly based on notion that costs primarily fall • as cumulative production rises (Arrow, 1962; Ayres, 1992; Huber, 1991;

Argote and Epple, 1990; March, 1991), and • as automated manufacturing equipment is introduced and organized into

flow lines (Utterback, 1994)

One Caveat

• Maybe we have reached the limits to scaling

• Maybe it would be better if firms produced large volumes of “optimally” sized wind turbine

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs needed?• Where are the entrepreneurial opportunities?

The “Aerogenerator:” Implementation of 275 meter diameter turbine by 2014

Tethered Wind Turbine

Tethered Wind Turbine

What about increasing size of fins?

Implications for Policy

•Maybe policies should promote the development of these kinds of radical designs• What are there costs? • Will they benefit from increases in scale?• Are new materials needed and what are the

impact of these materials on costs of electricity?

•Remember that current policies just encourage the implementation of wind turbines

Outline• Overview of Wind Turbine Costs• Theoretical Output from Wind Turbines (function of diameter squared, wind speed cubed)

• Empirical Data• Power output vs. rotor diameter• Impact of rotor diameter and other factors on rated wind

speed• Cost of wind turbines

• Implications of Analysis• New materials are needed• Are new designs needed?• Where are the entrepreneurial opportunities?