## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Wind energy

Wind energy is the kinetic energy of air in motion, also called wind.

Total wind energy flowing through an imaginary area A during the time t is:

$E = frac{1}{2}mv^2 = frac{1}{2}(Avt ho)v^2 = frac{1}{2}At ho v^3,$

where v is the wind speed; ρ is the air density; Avt is the volume of air passing through A (which is considered perpendicular to the direction of the wind); Avtρ is therefore the mass m passing per unit time. Note that ½ ρv2 is the kinetic energy of the moving air per unit volume.

Power is energy per unit time, so the wind power incident on A (e.g. equal to the rotor area of a wind turbine) is:

$P = frac{E}{t} = frac{1}{2}A ho v^3.$

Wind power in an open air stream is thus proportional to the third power of the wind speed; the available power increases eightfold when the wind speed doubles. Wind turbines for grid electricity therefore need to be especially efficient at greater wind speeds.

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