Wind Turbines - Wind Energy: Renewable Energy and the Environment - page 81

The relative wind as seen by the blade is composed of two parts: the vector sum of the motion of
the blade and the motion of the wind, which is the ground wind far away from the unit.
Maximum power output for any wind speed can be obtained by letting the revolutions per minute
of the rotor for fixed-pitch operation increase as the wind speed increases, or by changing the pitch
of the blades to obtain the correct attack angle for constant rpm operation. A fixed-pitch blade or
constant-rpm rotor only reaches maximum power coefficient at a single wind speed. The power
coefficient. is the power output of the wind turbine divided by the power input (power in wind across
the rotor area). Even though rotor efficiency decreases above the point of maximum power coeffi-
cient for fixed-pitch blades, power output of the wind turbine can remain high since power available
is increasing as the cube of the wind speed.
Computer programs are available for estimating the aerodynamic performance of wind turbines,
for both HAWT and VAWT. Inputs include airfoil lift and drag versus attack angle, radius, twist
and pitch of the blade, and solidity. Wind speeds or tip speed ratios can be varied to obtain power,
forces, moments, etc., for each blade section and for the total blade.
The theoretical values of torque versus rpm were calculated for a VAWT for constant values
of wind speed (Figure 5.13). The design point was selected as a rated wind speed of 12.5 m/s,
and the other parameters of number of blades, airfoil, etc., were selected for a low-solidity rotor.
Each point on the curves is an operating point (power) along lines of constant wind speed. Wind
turbines can be operated at constant tip speed ratio (line B, maximum power coefficient), constant
rpm (line A), or constant torque (line C). As noted, the rpm is variable along line B, which is the
operation of maximum power coefficient. However, at some point there is too much power in the
wind, and the wind turbine is controlled to capture less power and, in most cases, in very high
winds to shut down. Notice that the constant torque operation soon reaches very high values of
rpm, so the wind speed range of operation is limited. For constant torque loads, high torque is nec-
essary for start-up. Therefore, it is very difficult to connect a constant torque load to a wind turbine
and obtain much efficiency. The other side of that is high-solidity rotors, like the farm windmill,
have high starting torque at low winds and tip speed ratios around 1, which means they are too
inefficient for generating electricity.

A

20.000

B

Constant
windspeed

15.000

10.000

5.000

C
25 m/s 15 20

10

5

0

0 100 200 300 400 500

Rotor Speed, rpm

figure 5.13 Theoretical curves of torque versus rpm for different wind speeds.