Wind Turbine Design Methods

Robert Scott

rscott@gatech.edu

November 1, 2007

Advantages of Wind Power

• Clean• Flexible• Large Potential for Growth• Economically Viable (most of the time – peak

opportunity)

Design

• Siting• Configurations• Sizing• Rotor• Tower• Generator

Siting

• Wind speed• Climate Conditions• Inland or at sea• Terrain• Surrounding

Community

Configurations

• Vertical Axis– Darrieus– H-Type– Savonius

• Disadvantages– Size limits– Reliability

Configurations

• Horizontal Axis– 3-bladed most

common, structures and dynamic considerations

– 1 and 2-bladed designs exist, but don’t even bother.

– Upwind or Downwind

Sizing

• Designs exist for capacities of <1 kW up to 5 MW.

• What are you designing for?– Utilities– Individual Use– Special Use

Rotor• Diameter

– Larger = higher capacity and higher costs, helps for lower windspeed

• Blades– Airfoils– Shape (Twist)

• Control– Stall/Pitch regulated– Rotational Speed

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 20 40 60 80 100 120

Rotor Diameter (m)

Rat

ed C

apac

ity

(MW

)

Rotor

• Control– Stall/Pitch regulated– Rotational Speed– Cut-in, rated, cut-out

velocities

Tower

• Type– Tubular– Lattice

• Height– Tall = smoother air– Short = better for

construction

Wind Variability

• The terrain of the site affects the wind speed.

• Higher roughness lengths slow the wind down more at low elevations.

0

0

ln

ln)(

zz

zz

zU

zU

anem

hub

anem

hub

Generator

• Enclosed?• Gearbox?• Direct-drive?

Design Process

• Performance– Efficiency– Reliability

• Economics– Infrastructure (~ $1.7 Million per MW)– Construction – Operational Costs (~ 2% of acquisition

costs/yr)– Subsidies

The Power Curve

Published power curve for a 1.5 megawatt wind turbine.Nordex S70. Vc-o≈ 2VR

Wind Variability

• Model the wind as a probability density function– The Weibull

distribution

kxk

exk

kxf

1

,;

22

U

eU

Uf

k

x

ekxF

1,;

For wind,

2

1

U

eUF

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 5 10 15 20 25

wind speed (m/s)

pro

b d

ist

fun

ct,

ƒ

Ū = 5 m/s

Ū = 7 m/s

Ū = 9 m/s

Ū = 11 m/s

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

wind speed (m/s)

cum

ul.

dis

t, F

Ū = 5 m/s

Ū = 7 m/s

Ū = 9 m/s

Ū = 11 m/s

What does all this tell us?Capacity Factor:

max

0

E

E

tP

Pdt

CFrated

t

A capacity factor of 35% for a wind turbine is considered good.

Ū = 5 m/s CF = 0.05

Ū = 7 m/s CF = 0.18

Ū = 9 m/s CF = 0.42

Ū = 11 m/s CF = 0.73

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Capacity Factor

pro

b d

ist

fun

ct, ƒ

Ū = 5 m/s

Ū = 7 m/s

Ū = 9 m/s

Ū = 11 m/s

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Capacity Factor

1 -

F

Ū = 5 m/s

Ū = 7 m/s

Ū = 9 m/s

Ū = 11 m/s

Sensitivity Studies – HOMER

Sensitivity to wind speedŪ = 5 m/s:225,000K kWh/yr @ $0.15/kWh

Ū = 14 m/s:1,000,000K kWh/yr @ $0.055/kWh

Sensitivity to hub heightzH = 40 m500,000K kWh/yr @ $0.087/kWh

Ū = 5 m/s:675,000K kWh/yr @ $0.07/kWh

The Power Coefficient

The power output normalized to the energy density of the wind and the rotor area.

AU

PC p 3

21

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20 25

wind speed (m/s)

po

wer

co

eff

Cp

Measures the amount of power actually converted out of the power available in the wind

Optimized Costs of Energy• High wind speed areas, U > 10 m/s

consistently• Maximized hub heights, zH = 100 m• Large development – Economies of

scale reduce per unit price of turbines.

Optimized Cost of Energy: • $0.038/kWh (3% interest)• $0.040/kWh (4% interest)• $0.042/kWh (5% interest)• $0.044/kWh (6% interest)

Comparison with other fuels:

Coal $0.02 – 0.03/kWh

Natural Gas $0.05 – 0.08/kWh

Nuclear $0.02 – 0.03/kWh

Note: Other fuels, especially coal and nuclear, benefit from not having to include their high external costs in the price of energy. Wind energy also receives a $0.015/kWh tax credit.

Useful Websites

• List of wind farms: http://www.fplenergy.com/portfolio/contents/portfolio_by_source.shtml

• Wind turbine Manufacturers– http://www.skystreamenergy.com/skystream/– http://www.enercon.de/en/_home.htm– http://www.nordex-online.com/en/– http://www.gamesa.es/index.php/en– http://www.suzlon.com/

• Current Events– http://www.cnn.com/2007/TECH/science/10/09/pip.wind.energy/– www.wind-watch.org