Wind turbines – Wind power

Posted on by

Content – Energy sources

Wind power is generated from kinetic energy derived from energy from the sun.

Wind occurs due to uneven heating of the atmosphere and earth by the sun, the irregularities of the earth’s surface, and rotation of the earth.

A wind turbine makes it possible to utilise the kinetic energy from the wind to drive a generator that convert the kinetic energy into electrical power.

Wind turbines are manufactured as vertical or horizontal types.

Main components of a typical horizontal wind turbine for electrical power generation:

• Rotor, made up of blades ( normally 2 -3 blades) that are fixed to a hub. The blades are shaped similar to airplane wings such that lift is created when the wind is blowing and the wing turns. This transforms the wind energy into kinetic energy.
• Normally there will be a pitch drive to enable turning the blades to reduce or increase the lift.
• Nacelle is where the rotor is attached and encloses all the components on top of the tower.
• Brake, in addition to the blade pitch drive enables braking og parking the rotor.
• Low speed shaft directly connected to the rotor (20 – 400 rpm, pending on size and design).
• Gear box, increase the speed to around 1500 rpm (1200 – 1800 rpm) to align with required generator rpm and electrical grid frequency.
• High-speed shaft, attached to the generator.
• Yaw drive, rotates the rotor such that it is facing the wind.
• Generator converts the kinetic energy into electrical power.
• Cooling system, cools the generator
• Controllers and meters, controls the turbine operation relative to wind speeds and direction.
• Tower, brings the rotor to the desired height above the ground.

Typical capacity for wind turbines

Wind Power Density

Wind power density is a measure based on calculations of the mean annual power available per square meter of swept area of a turbine.

There has been established tabulation of wind power density for many geographical areas in the USA.

The calculation of wind power density takes into account the effect of wind velocity and air density. The wind power density is devided into power density classes. Wind power density classes range from Class 1 (200 watts per square meter or less at 50 m altitude) to Class 7 (800 to 2000 watts per square m). Commercial wind farms normally would be sited in Class 3 or higher areas,

Wind turbines are classified by design wind speed, from class I (10 m/s)to class IV (6 m/s), with an additional class A or B referring to the turbulence.

The maximum theoretical power that may be generated by a wind turbine related to the available wind power would be around 60%, this is based on the assumption that the air speed reduction over the rotor is around 2/3.

Two significant factors for wind power generation are the wind speed (available and the turbine area (squared) and rotor area (third power). The diameter of the rotor (or the length of the rotor blades) determines the turbine area.

Typically a 600 kW turbine would have a diameter of 44 meters. Since the area is squared in relation the rotor diameter increase, doubling the rotor diameter would provide a 4 times larger turbine area.

Since the power is a function of the wind speed and the turbine area the doubling of the rotor diameter would also theoretically produce 4 times the power.

A large power generator requires stronger wind to generate power than a smaller generator therefore turbine diameters and generator capcity needs to be optimised related to the wind power density at the actual location.

Formula for wind power

Wind power density:

$Power = \dfrac{1}{2}\rho v^2 (W/m^2)$

Power = 0,5 * 1,225 * v3 ,

Example:
Wind speed = 8 m/s
Air density= = 1,225 kg/m3

Power = 0,5 * 1,225 * 83 = 313,6 W/m2

From the above calculation we can derive the following values for wind powewr density at various wind speeds:

 m/s W/m2 m/s W/m2 1 0,6 13 1345,7 2 4,9 14 1680,7 3 16,5 15 2067,2 4 39,2 16 2508,8 5 76,5 17 3009,2 6 132,3 18 3572,1 7 210,1 19 4201,1 8 313,6 20 4900 9 446,5 21 5672,4 10 612,5 22 6521,9 11 815,2 23 7452,3 12 1058,4

Using the average wind speed to calculate average wind power in most cases will provide too low values due to the distribution and significant effect of peak wind loads.

The avaiable effect of the wind, which passes perpendicularly through a circular surface, is:

PA = ½ ρv3πr2
PA = Wind power (W).
ρ = Density of dry air = 1.225 kg/m3 (at 15° C and athmosferic pressure at sea level)
v = Wind speed (m/s)
π = 3.14159

Example:
Wind speed = 8 m/s
Air density= = 1,225 kg/m3
PA = ½ ρv3πr2

PA = 0,5 * 1,225 * 83 * 3,14159 * 402 = 1576 kW

To see for yourself how the wind speed and rotor blade lenght affect the output from a wind turbine please have look at over wind power calculator: Wind power calculator

The actual power is limited by the efficiency (Cp) of the wind turbine. The maximum efficiency of any horizontal axis wind turbine (and any other horizontal axis turbines) is limited by “Betz law”, which determines that the efficiency can not exceed 59,3% (Betz coefficient) in addition there will be design limitations and compromises that will reduce the actual efficiency further.

The concept of Betz law (Betz limitation) is that, for the wind (or other fluid) to move through the turbine the wind needs to have a certain velocity when leaving the turbine such that all the kinetic energy of the wind cannot be captured.

Therefore the actual delivered power from the turbine will be:

P = PA * Cp

The actual amount electrical power generated and delivered will be further reduced by the efficiency or losses within the transmission (gearbox) and generation systems.

The concept of Betz law is that, for the wind (or other fluid) to move through the turbine the wind needs to have a certain velocity when leaving the turbine such that all the kinetic energy of the wind cannot be captured.