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Although the power equation above gives us the power in the wind, the actual
power that we can extract from the wind is significantly less than this figure
suggests. The actual power will depend on several factors, such as the type of
machine and rotor used, the sophistication of blade design, friction losses, and
the losses in the pump or other equipment connected to the wind machine. There
are also physical limits to the amount of power that can be extracted
realistically from the wind. It can been shown theoretically that any windmill
can only possibly extract a maximum of 59.3% of the power from the wind (this is
known as the Betz limit). In reality, this figure is usually around 45%
(maximum) for a large electricity producing turbine and around 30% to 40% for a
windpump, (see the section on coefficient of performance below). So, modifying
the formula for 'Power in the wind' we can say that the power which is produced
by the wind machine can be given by:
PM = 1/2.Cp.ñ.A.V^3
where,
PM is power (in watts) available from the machine
Cp is the coefficient
of performance of the wind machine
It is also worth bearing in mind that a
wind machine will only operate at its maximum efficiency for
a fraction of the time it is running, due to variations in
wind speed. A rough estimate of the output from a wind
machine can be obtained using the following equation;
PA = 0.2 A V^3
where,
PA is the average power output in watts over the year
V is the mean
annual windspeed in m/s
Principles of wind energy conversion
There are two primary physical principles by which energy can be extracted
from the wind; these are through the creation of either lift or drag force (or
through a combination of the two). The difference between drag and lift is
illustrated by the difference between using a spinnaker sail, which fills like a
parachute and pulls a sailing boat with the wind, and a Bermuda rig, the
familiar triangular sail which deflects with wind and allows a sailing boat to
travel across the wind or slightly into the wind.
Drag forces provide the
most obvious means of propulsion, these being the forces
felt by a person (or object) exposed to the wind. Lift
forces are the most efficient means of propulsion but being
more subtle than drag forces are not so well understood. The
basic features that characterise lift and drag are:
- drag is in the direction of air flow
- lift is perpendicular to the direction of air flow
- generation of lift always causes a certain amount of drag to be developed
-
with a good aerofoil, the lift produced can be more than thirty times greater
than the drag
- lift devices are generally more efficient than drag devices
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There are two main families of windmachines: vertical axis machines and
horizontal axis machines. These can in turn use either lift
or drag forces to harness the wind. The horizontal axis lift
device is the type most commonly used. In fact other than a
few experimental machines virtually all windmills come under
this category. There are several technical parameters that
are used to characterise windmill rotors. The tipspeed ratio
is defined as the ratio of the speed of the extremities of a
windmill rotor to the speed of the free wind. Drag devices
always have tip-speed ratios less than one and hence turn
slowly, whereas lift devices can have high tip-speed ratios
(up to 13:1) and hence turn quickly relative to the wind.
The proportion of the power in the wind that the rotor can extract is termed
the coefficient of performance (or power coefficient or efficiency; symbol Cp)
and its variation as a function of tipspeed ratio is commonly used to
characterise different types of rotor. As mentioned earlier there is an upper
limit of Cp = 59.3%, although in practice real wind rotors have maximum Cp
values in the range of 25%-45%.
Solidity is usually defined as the percentage of the area of the
rotor, which contains material rather than air. Low-solidity machines run at
higher speed and tend to be used for electricity generation. High-solidity
machines carry a lot of material and have coarse blade angles. They generate
much higher starting torque (torque is the twisting or rotary force produced by
the rotor) than low-solidity machines but are inherently less efficient than
low-solidity machines. The windpump is generally of this type. High solidity
machines will have a low tip-speed ratio and vice versa.
There are various
important wind speeds to consider:
- Start-up wind speed - the wind speed that will turn an unloaded
rotor
- Cut-in wind speed - the wind speed at
which the rotor can be loaded
- Rated wind speed -
the windspeed at which the machine is designed to run
(this is at optimum tip-speed ratio
- Furling wind
speed - the windspeed at which the machine will be
turned out of the wind to prevent damage
- Maximum
design wind speed - the windspeed above which damage
could occur to the machine
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