Important Mathematical Formula

1. Simple Calculation of Wind Power

The power (i.e. energy per second) in the wind flowing into a wind turbine with a certain swept area is given by inserting the mass per second calculation into the standard kinetic energy equation (above) resulting in the following vital equation:

Power = 0.5 x Swept Area x Air Density x Velocity3

 

The units of measurement are:

Power - Watts (i.e. joules/second)

Swept area - square metres

Air density - kilograms per cubic metre

Velocity - metres per second

 

     2.   Actual Energy Exerted From the Wind by the Wind Turbine

 

No turbine can capture more than 16/27 (59.3%) of the kinetic energy of the wind according
to German physicist, Albert Betz. This limit is known as the Betz Limit and has nothing to
do with inefficiencies in the generator, but how turbines actually work.Wind turbines extract energy and so slow down the wind passing through them. For a wind turbine to extract 100% of the energy it would need to stop 100% of the wind. If it did this it would then stop working. Instead it extracts enough energy to still allow the wind to continue to pass through it.

To calculate the power more accurately the Betz Limit must be taken into consideration.

Power = 0.5 x Swept Area x Air Density x Velocity3 x Cp

 

Where Cp is the power coefficient of the wind turbine.

 

 

 

 

 

Large Scale Wind Farm Examples

a. London Array
an offshore wind farm under construction in the outer Thames Estuary in the United Kingdom. With 1,000 megawatt (MW) nameplate capacity, it is expected to become the world's largest offshore wind farm.

b. The Alta Wind Energy Centre
  A wind farm located in Tehachapi Pass of the Tehachapi Mountains, in Kern County, California. As of 2013, it is the largest wind farm in the world, with a combined installed capacity of 1,320 MW (1,770,000 hp).

Factors for Determining Ideal Position

Key factors determining a wind turbine location

a.       Wind consistency (could be the most important factor)

A location with strong, steady wind.

Small scale wind turbine is usually installed 2 times higher than the roof.

b.      Ease of construction

The base of the tower needs to stay still.

c.       Appropriate environment

Decrease the damage of wind turbine from the environmental factors. for example corrosion.

d.      Distance to people

wind farm should near to the power grid. However, there should be a enough distance to reduce the noise.

Materials

A small scale wind power generator has several components consists of a rotor which has a hub with blades attached; a nacelle mainly contains a gearbox, a generator and other machinery; a tower and ground-mounted system. Each part is composed of different materials in a certain percentage. In general, a wide range of materials are applied on the wind turbines, and also there are various percentage of materials used on each component in current market. In this report, there is only a rough description on percentage of materials used in some main components

Components	Materials properties	Materials used
Rotor Blades	Strength and low weight  composites	GFRP (i.e. E-glass fibers, S-glass fibers ) or CFRP
Nacelle :   Gearbox	-	Steel
Generator	Permanent magnetic	Permanent magnetic materials, copper and steel
Frame and                       machinery	Light and corrosion preventive	Steel,  aluminium, copper and a little FRP
Tower	Reinforced and corrosion preventive	Steel or prestressed concrete

There are several basic requirements that the materials of wind turbine should satisfy.

a.    Low density

b.    High fatigue strength

c.    Another property that wind turbine should have is corrosion resistance, especially for off-shore wind turbine.

d.    Lower-cost and low maintenance costs for wind turbine.

Wind speed and Power Output Statistics

• The mean wind speed in rural areas is 5.26 metres/second. However the wind is very unsteady and usually is not around the mean value. This unsteadiness of the wind speed is called the standard deviation.  The standard deviation is around 62%.
• Taking two examples of locations we compared wind speed distributions in urban areas:

Example 1:

A small wind turbine is mounted next to a building with a near by row of trees (as seen in the picture below). The mean wind speed is only 2.14 metres/second and the site is very turbulent. There is a standard wind speed deviation of 87% which is far off from the standard deviation of 62%. This is not a convenient site for the turbine to achieve it maximum power output capacity.


Example 2:

In this example the small scale wind turbine is situated on the roof of a seven story building. The mean wind speed is 4.46 metres/second which is still low for the turbine to really cut costs. However in this case the standard deviation is 59% much closer to the standard 62% mark.

Week 2

The following video shows how simple it is to build a small wind turbine at home.

Week 2 : Details on Optimum Position

There are three primary types of wind turbine:

a. VAWT Savonious

b. HAWT towered

c. VAWT Darrieus

For HAWTs, since cyclical turbulence may lead to fatigue failures, most of them are of upwinds.

However, for VAWTs, key advantage is that the turbine does not need to be pointed into the wind to be effective.

Installation for Small-Scale Wind Power Generation
Turbines are often mounted on a tower to raise then above any nearby obstacles.

One rule of thumb:

Turbines should be at least 30 ft (9.1m) higher than anything within 500ft (150m).

Better locations for wind turbines are far away from large upwind obstacles. A small wind turbine can be installed on a roof. Installation issues include the strength of the roof, vibration and the turbulence caused by roof ledge.

The torque ripple is relevant to the stability of turbines.

http://www.greenspec.co.uk/small-wind-turbines.php

Some position may be suitable for installing small wind turbine:

1. roof
2. coast
3. mountains
4. ships
5. plain