Wind Turbine Operation
A wind turbine is a revolving machine that converts the kinetic energy from the wind into mechanical energy. This mechanical energy is then converted into electricity that is sent to a power grid. The turbine components responsible for these energy conversions are the rotor and the generator.
The rotor is the area of the turbine that consists of both the turbine hub and blades. As wind strikes the turbine’s blades, the hub rotates due to aerodynamic forces. This rotation is then sent through the transmission system to decrease the revolutions per minute. The transmission system consists of the main bearing, high-speed shaft, gearbox, and low-speed shaft. The ratio of the gearbox determines the rotation division and the rotation speed that the generator sees. For example, if the ratio of the gearbox is N to 1, then the generator sees the rotor speed divided by N. This rotation is finally sent to the generator for mechanical-to-electrical conversion.
Figure 1 shows the major components of a wind turbine: gearbox, generator, hub, rotor, low-speed shaft, high-speed shaft, and the main bearing. The purpose of the hub is to connect the blades’ servos that adjust the blade direction to the low-speed shaft. The rotor is the area of the turbine that consists of both the hub and blades. The components are all housed together in a structure called the nacelle.
Figure 1 . The Major Components of a Wind Turbine
Angle of Attack
The amount of surface area available for the incoming wind is key to increasing aerodynamic forces on the rotor blades. The angle at which the blade is adjusted is referred to as the angle of attack, α. This angle is measured with respect to the incoming wind direction and the chord line of the blade. There is also a critical angle of attack, αcritical, where air no longer streams smoothly over the blade’s upper surface. Figure 2 shows the critical angle of attack with respect to the blade.
Figure 2. The Critical Angle of Attack (αcritical) with Respect to the Blade
Power and Efficiency
This section explains what affects the power extracted from the wind and the efficiency of this process. Consider Figure 3 as a model of the turbine’s interaction with the wind. This diagram indicates that wind exists on either side of the turbine, and the proper balance between rotational speed and the velocity of wind are critical to regulate performance. The balance between rotational speed and wind velocity, referred to as the tip speed ratio, is calculated using Equation 1.
Where : is the blades frequency of rotation (Hz)
is the length of a blade (m)
Equation 1. Calculating the Tip Speed Ratio
The efficiency of a wind turbine is called the power coefficient, or . Theoretically, the power coefficient is calculated as the ratio of actual to ideal extracted power. You can find this calculation in Equation 2. Also, you can adjust by controlling the angle of attack, α, and the tip speed ratio, . The calculation for this case is shown in Equation 3. In Equation 3, c1-c6 and x are coefficients that wind turbine manufacturer should provide. Note that the maximum power coefficient that you can achieve with any turbine is .59, or the Betz limit.
Equation 2. The power coefficient is calculated as the ratio of actual to ideal extracted power.
Equation 3.You can adjust the by controlling the angle of attack, α, and the tip speed ratio.
Finally, you can calculate the usable power from the wind using Equation 5. From this equation, you can see that the main drivers for usable power are the blade length and wind speed.
Where: = density of air (1.2929 kg/m3)
Equation 5. Calculating Usable Power from the Wind
Figure 3. Model of the Turbine’s Interaction with the Wind
The Power Curve
It is important to understand the relationship between power and wind speed to determine the required control type, optimization, or limitation. The power curve, a plot you can use for this purpose, specifies how much power you can extract from the incoming wind. Figure 4 contains an ideal wind turbine power curve.
Figure 4. Ideal Wind Turbine Power Curve
The cut-in and cut-out speeds are the operating limits of the turbine. By staying in this range, you ensure that the available energy is above the minimum threshold and structural health is maintained. The rated power, a point provided by the manufacturer, takes both energy and cost into consideration. Also, the rated wind speed is chosen because speeds above this point are rare. Typically, you can assume that a turbine design that extracts the bulk of energy above the rated wind speed is not cost-effective.
From Figure 4, you can see that the power curve is split into three distinct regions. Because Region I consists of low wind speeds and is below the rated turbine power, the turbine is run at the maximum efficiency to extract all power. In other words, the turbine controls with optimization in mind. On the other hand, Region III consists of high wind speeds and is at the rated turbine power. The turbine then controls with limitation of the generated power in mind when operating in this region. Finally, Region II is a transition region mainly concerned with keeping rotor torque and noise low.