# 4 Power from Wind

Theoretical Wind Power

• Energy = Power * time
• Power = Energy/time
• wind energy = ½ ρAtv^3
• wind power = ½ ρAv^3

Betz Factor

• The ratio of practical power to the power in the wind is called the Betz Factor
• Betz Factor = 16/27 = 0.593

Practical Wind Power

• wind power = ½cpρAv^3
• where cp = 0.593 for wind turbines using the lift (not drag) Betz Factor

Clipper Wind: Actual Power Curve

Clipper Wind: Actual Power Curve

• Any power generated by the turbine will be significantly less than ½cpρAv3.
• This is a result of losses in converting mechanical to electrical power, friction, etc.

Clipper Wind: Actual Power Curve

• power = ½cpρAv3
• For example at v = 10m/s, theoretical
power = ½(0.593)*
(1.2 kg/m3)*(7854m2)*
(10m/s)3 = 2.79 MW
• At 10 m/s, Actual Power ≅ 1800 kW = 1.8 MW
• Efficiency = 64%

Clipper Wind: Actual Power Curve

• At 5 m/s, Power ≅ 225 kW
• At 10 m/s, Power ≅ 1800 kW
• This is an 8x increase as expected by
wind power ∝ v3

Clipper Wind: Actual Power Curve

• After 10 m/s,
wind power ∝ v3 will not accurately predict the power.
• This is due to the generator and other mechanical components of the turbine being unable to increase power output proportional to the wind velocity

Clipper Wind: Actual Power Curve

• The cut-out wind velocity of this turbine is 25m/s
• The constant output of power between 13m/s and 25 m/s is achieved through pitch control

Clipper Wind – Pitch Control

• Pitch control allows the blade of each turbine to be oriented in a manner to maximize wind power prior to 2.5MW on the Liberty 2.5 MW Wind Turbine.
• Once the output reaches 2.5 MW, pitch control will be used to limit the power from the wind in order to maintain a constant 2.5MW output from the generator.

Theoretical Power from the Wind (power point)

Practical Power from the Wind (power point)

Power from the Wind (work sheet) 