WIND TURBINE PERFORMANCE MEASURES

Part B Module 1 – Wind Energy

POWER COEFFICIENT • Indicates the fraction of power

available in the wind that is produced as electrical output:

𝐶𝑃 =𝑃𝑎𝑎𝑎𝑎𝑎𝑎12𝜌𝜌𝑉0

3

• Depends on wind speed and on

rotor speed

• Characterize rotor speed by tip speed ratio:

𝑇𝑇𝑇 𝑆𝑇𝑆𝑆𝑆 𝑅𝑅𝑅𝑇𝑅 =2𝜋𝑅𝜋𝑉0

where: R = blade radius N = rotor speed (rpm) ρ = air density V0 = upstream wind speed

PERFORMANCE CHARACTERISTICS

• Power coefficient vs Tip speed ratio

• Representative CP max • Tip speed ratio

operating range 0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7Po

wer

coef

ficie

nt C

P Tip speed ratio

Ideal Glauert

Betz limit

Dutch

Muitiblade

Savonius

2 bladeDarrieus

Propeller

POWER OUTPUT VS. WIND SPEED • Electrical power

output • Cut-in wind speed • Cut-out wind speed

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25 30Po

wer

Out

put (

kW)

Wind Speed (m/s)

3.6 MW Wind Turbine Power Output

Cut-in wind speed Cut-out

wind speed

GENERATOR POWER LIMITATION

• Maximum output is limited by electrical generator capacity – Here 3.6 MW – Prevents burnout of

generator

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25 30Po

wer

Out

put (

kW)

Wind Speed (m/s)

3.6 MW Wind Turbine Power Output

POWER LIMIT 2 • Turbine rotor power increases

with V3 • Generator power absorption

limited by ability to dissipate heat.

• Practical limitations on size/weight of generator

• Compromise between power capacity and size/weight 0 5 10 15 20

Pow

er/R

otor

Are

a (a

rbitr

ary

units

)

Wind speed (m/s)

Betz limit power

generator powerlimit

Power limitedwind turbine

RATED SPEED

• The lowest wind speed at which the wind turbine produces its maximum rated power output – here, 12.9 m/s

0 5 10 15 20

Pow

er/R

otor

Are

a (a

rbitr

ary

units

)

Wind speed (m/s)

generator power limitPower limited wind turbine

Rated wind speed

MECHANICAL POWER LIMITATION How to limit power output developed by rotor? • Reduce power coefficient

– Reduction required shown

• Active blade pitch control • Change blade pitch angle φ

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 10 20

Pow

er co

effic

ient

CP

Wind speed (m/s)

CAPACITY FACTOR – EQUIPMENT UTILIZATION • Depends on local wind conditions as well as equipment performance!

𝐶𝑅𝑇𝑅𝐶𝑇𝑅𝐶 𝐹𝑅𝐶𝑅𝑅𝐹 𝐶𝐹 = 𝜌𝐶𝑅𝐴𝑅𝐴 𝑅𝑎𝑎𝐴𝑅𝐴 𝑆𝐴𝑆𝐶𝑅𝐹𝑇𝐶𝑇𝑅𝐶 𝑅𝐴𝑅𝑇𝐴𝑅

𝑃𝑅𝑅𝑆𝑎𝑅𝑇𝑅𝐴 𝑅𝑎𝑎𝐴𝑅𝐴 𝑆𝐴𝑆𝐶𝑅𝐹𝑇𝐶𝑇𝑅𝐶 𝑅𝐴𝑅𝑇𝐴𝑅

𝐶𝐹 = 𝜌𝐶𝑅𝐴𝑅𝐴 𝑅𝑎𝑎𝐴𝑅𝐴 𝑆𝐴𝑆𝐶𝑅𝐹𝑇𝐶𝑇𝑅𝐶 𝑅𝐴𝑅𝑇𝐴𝑅

8760 ℎ𝑅𝐴𝐹𝑜𝐶𝑆𝑅𝐹 𝑥 𝑤𝑇𝑎𝑆 𝑅𝐴𝐹𝑡𝑇𝑎𝑆 𝐹𝑅𝑅𝑆𝑆 𝑇𝑅𝑤𝑆𝐹 𝑅𝐴𝑅𝑇𝐴𝑅

• Example: Offshore with 9.5m/s average wind speed

𝐶𝐹 =17000 𝑀𝑀ℎ

8760 ℎ𝑅𝐴𝐹𝑜𝐶𝑆𝑅𝐹 𝑥 3.6 𝑀𝑀= 0.539 𝑅𝐹 53.9%

WIND TURBINE PERFORMANCE MEASURES SUMMARY

• CP and TSR characterize wind turbine performance at an individual wind speed

• Manufacturers typically provide wind turbine performance characteristics in the form of power output vs wind speed data

• A variety of types of wind turbines are available and each has advantages and disadvantages

• Capacity factor (CF) is an important measure of in-use performance – Depends on the local wind conditions and the wind turbine

performance

PRACTICE EXERCISES

REFERENCES AND PHOTO CREDITS • "Eoliennes Gaspesie" by guillom - Own work. Licensed under Creative Commons

Attribution-Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Eoliennes_Gaspesie.jpg#mediaviewer/File:Eoliennes_Gaspesie.jpg

• H-Darrieus-Rotor by Stahlkocker, http://commons.wikimedia.org/wiki/File:H-Darrieus-Rotor.jpg#mediaviewer/File:H-Darrieus-Rotor.jpg. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons

• Taiwan 2009 JinGuaShi Historic Gold Mine Combined Darrieus Savonius Wind Turbines FRD 8638" by Fred Hsu, http://commons.wikimedia.org/wiki/File:Taiwan_2009_JinGuaShi_Historic_Gold_Mine_Combined_Darrieus_Savonius_Wind_Turbines_FRD_8638.jpg#mediaviewer/File:Taiwan_2009_JinGuaShi_Historic_Gold_Mine_Combined_Darrieus_Savonius_Wind_Turbines_FRD_8638.jpg. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons