**3. Small Turbines**

Small turbines are of a limited variety of designs due to cost and performance constraints. The most common design is a stall regulated, variable speed, horizontal axis, fixed pitch 3 blade, direct drive permanent magnet machine [3]. Blade pitch control would be difficult to justify economically, so the blades are given a fixed pitch, and optimized for power produc‐ tion at the rated speed. This results in poorer performance at lower speeds than could be achieved by a turbine with active pitch control. The ultimate speed of the turbine is deter‐ mined by the wind speed and the applied load. Usually a power controller is still required to prevent turbine over speed, and over charging of the batteries. This power controller may also incorporate power matching circuitry allowing optimized power extraction from the wind turbine at various wind speeds [6]. Turbine over-speed is avoided by applying a low resistance dump load to the generator, increasing the load torque to the turbine, slowing the blades, and resulting in aerodynamic stall.

**Figure 1.** Schematic of typical small wind power system including wind turbine, storage system and loads

### **3.1. Commercial Small Turbines**

<sup>3</sup> P ½ C A V turb = <sup>p</sup>r

For wind sites near sea level the atmospheric pressure is approximately 1.18 kg/m<sup>3</sup>

fairly high rates wind speed: it is the easiest way to achieve a high power output.

Small turbines are of a limited variety of designs due to cost and performance constraints. The most common design is a stall regulated, variable speed, horizontal axis, fixed pitch 3 blade, direct drive permanent magnet machine [3]. Blade pitch control would be difficult to justify economically, so the blades are given a fixed pitch, and optimized for power produc‐ tion at the rated speed. This results in poorer performance at lower speeds than could be achieved by a turbine with active pitch control. The ultimate speed of the turbine is deter‐ mined by the wind speed and the applied load. Usually a power controller is still required to prevent turbine over speed, and over charging of the batteries. This power controller may also incorporate power matching circuitry allowing optimized power extraction from the wind turbine at various wind speeds [6]. Turbine over-speed is avoided by applying a low resistance dump load to the generator, increasing the load torque to the turbine, slowing the

creases with altitude. The coefficient of performance is related to the turbine design, and has a theoretical upper limit of 0.593, referred to as the Betz limit [5]. Most sub 10kW wind tur‐ bines are rated for speeds from 8 to 12m/s. The coefficient of performance of commercial small turbines generally falls in the range of 0.25 to 0.45 based on manufacturers rated pow‐ ers, speeds and diameters. The power of a turbine is directly proportional to the swept area, thus it is proportional to the blade length squared. The factor with the largest influence on turbine power, however, is the wind speed. From the turbine cut-in speed to the rated speed a turbine's power is proportional to the cube of the wind speed. That means that a 10m/s wind will deliver eight times the power of a 5m/s wind. This is why most turbines have a

Pturb is the mechanical power of the turbine in Watts

Cp is the dimensionless coefficient of performance

ρ is the air density in kg/m<sup>3</sup>

**3. Small Turbines**

blades, and resulting in aerodynamic stall.

A is the swept area of the turbine in m2

V is the speed of the wind in m/s

Where:

268 Advances in Wind Power

(1)

and de‐

There are significant differences between how various manufacturers state turbine specifica‐ tions, however it is generally understood that the turbine will produce the rated power at the rated wind speed. Based on a survey of data published for small wind turbines we have selected the following typical commercial turbine specifications:


#### **Table 1.** Typical commercial turbine specifications

When these turbines are installed in a lower wind region the actual power produced will be significantly less than the rated power. In much of South-East Asia, for example, the average wind speed is only 3m/s. While this may be below the turbines cut in speed (the lowest speed at which it can produce power) assuming power is proportional to the cube of the wind speed we can calculate the theoretical power production at 3m/s, as enumerated in the table. It can be seen that the power production of these machines is far below the rated pow‐ er, underscoring the need for turbine optimization for low wind speed regions.

## **3.2. Analysis of speed, power and Cp**

One of the biggest factors affecting the performance of a turbine is the blade pitch angle. The pitch angle is the angle between the blade and the plane of rotation. The attack angle is the angle between the chord of the airfoil and the relative wind, as shown in figure 2.

**Figure 2.** Wind vector, blade motion, pitch angle and angle of attack.

For most airfoils lift is maximized at an attack angle between 10 and 15 degrees. Obviously the angle of attack will depend on the wind speed and the turbine speed. A convenient pa‐ rameter in the analysis of turbine performance is the Tip Speed Ratio (TSR) which is defined as the linear speed of the tip of the turbine blade divided by the prevailing wind speed. For a given wind speed, a lower pitch angle will result in a higher TSR at the maximum lift. A larger pitch angle will tend to give the maximum lift, and thus greater torque, at a lower TRS [11]. In the end higher coefficients of performance are achieved by blades with lower pitch angles and higher TRS, however at the expense of low speed torque which results in higher cut in speeds.

At very low wind speeds the turbine produces too little torque to overcome friction. Once the wind speed is sufficient to allow the turbine to rotate, the output power is approximate‐ ly proportional to the cube of the wind speed. This remains true up to the rated speed. Above this speed the power production levels off, and with stall regulated turbines actually drops as wind speeds are increased. Finally at an even higher wind speed, the furling speed, the turbine is shut down to avoid damage to the machine. A typical turbine power curve is shown in figure 4.

**Figure 3.** Coefficient of Performance variation with angle of attack versus TSR.

**Figure 4.** Turbine power versus wind speed.

**3.2. Analysis of speed, power and Cp**

270 Advances in Wind Power

**Figure 2.** Wind vector, blade motion, pitch angle and angle of attack.

higher cut in speeds.

shown in figure 4.

One of the biggest factors affecting the performance of a turbine is the blade pitch angle. The pitch angle is the angle between the blade and the plane of rotation. The attack angle is the

For most airfoils lift is maximized at an attack angle between 10 and 15 degrees. Obviously the angle of attack will depend on the wind speed and the turbine speed. A convenient pa‐ rameter in the analysis of turbine performance is the Tip Speed Ratio (TSR) which is defined as the linear speed of the tip of the turbine blade divided by the prevailing wind speed. For a given wind speed, a lower pitch angle will result in a higher TSR at the maximum lift. A larger pitch angle will tend to give the maximum lift, and thus greater torque, at a lower TRS [11]. In the end higher coefficients of performance are achieved by blades with lower pitch angles and higher TRS, however at the expense of low speed torque which results in

At very low wind speeds the turbine produces too little torque to overcome friction. Once the wind speed is sufficient to allow the turbine to rotate, the output power is approximate‐ ly proportional to the cube of the wind speed. This remains true up to the rated speed. Above this speed the power production levels off, and with stall regulated turbines actually drops as wind speeds are increased. Finally at an even higher wind speed, the furling speed, the turbine is shut down to avoid damage to the machine. A typical turbine power curve is

angle between the chord of the airfoil and the relative wind, as shown in figure 2.

Stresses in the turbine are related to the wind load, causing a bending of the blade in the direction of the wind, centrifugal forces, pulling the blades radialy outward, and various dy‐ namic stresses. The centrifugal forces are proportional to the blade weight, blade length and square of the turbine speed, and limit the maximum speed of the turbine. Assuming similar materials and blade design, in order to achieve the same level of stress a larger, heavier, blade will have to spin at a lower speed than a smaller blade. This maximum speed of tur‐ bine operation becomes one of the limiting factors in the wind turbine, requiring either an extremely robust design or an active speed control system. Stall control systems are mechan‐ ically simple to implement, and thus common on small turbine systems. As the wind speed increases above the rated speed, a large electrical load, generally a high power resistor bank, is applied to the output of the generator. This increases the torque load on the turbine, slow‐ ing it. As the TSR is reduced, the angle of attack is raised above the optimum, and lift drops off as the blade begins to stall. This subsequently reduces the turbine's torque, slowing it further. This technique has been shown effective at preventing over speed in small turbines.
