**Wind energy utilization factor and wind turbine efficiency**

The theory shows that when all the kinetic energy of the air close to the wind wheel is absorbed by the rotating wind wheel blades, the air behind the wind wheel will stop flowing, but this is obviously impossible. Therefore, even if the wind energy that passes vertically through the rotating surface of the impeller (the collective name of the blade and the wheel) cannot be absorbed and used by the impeller, the wind energy capture efficiency of the wind turbine can never reach 1. In other words, no matter how the wind wheel design is optimized, the wind energy cannot always be converted into wind wheel mechanical energy. Generally, people call the wind energy utilization coefficient the percentage of the wind wheel of a wind turbine that can absorb energy from natural wind energy and the wind energy of the undisturbed air flow in the area swept by the wind wheel, which is represented by the letter C_{p}, that is

In the formula: P is the actual shaft power (W) obtained by the wind turbine; p is the air density (kg/m²); S is the swept area of the wind turbine (m²); v is the upstream wind speed (m/s). Generally, the larger the C_{p} value, the larger the percentage of energy that the wind turbine can obtain from nature, and the higher the efficiency of the wind turbine, that is, the higher the utilization rate of wind energy by the wind turbine. After long-term experimental and theoretical research, scientists have concluded the Bates theory of wind energy conversion. The theory shows that the maximum theoretical value of the wind energy utilization coefficient of a wind turbine is 0.593, and the actual value is much smaller than this value, about 0.45.

For practical wind turbines, the wind energy utilization factor mainly depends on the aerodynamic design and structural design of the wind turbine blades (such as the angle of attack, pitch angle, blade airfoil) and the level of manufacturing technology, as well as the speed of the wind turbine. In order to obtain the overall efficiency of the wind power generation device, in addition to the conversion efficiency of the wind turbine itself, other losses of the wind turbine, such as the loss of the transmission mechanism and the loss of the generator, must also be considered.

Taking a typical wind power generation device as an example, if the wind turbine efficiency is 70%, the transmission efficiency and generator efficiency are both 80%. Since the wind energy utilization factor of the ideal wind turbine is 0.593, the wind energy utilization factor of the device is

C_{p}=10.593×0.7×0. 8=0. 332

**Tip speed ratio**

In wind turbine design theory, people call the ratio of the blade tip rotation rate of the blade to the upstream undisturbed wind speed as the tip speed ratio, which is often expressed by letters, namely

In the formula: n represents the rotation speed of the wind wheel (r/min); R represents the radius of the blade tip (m); v represents the upstream wind speed (m/s); ω represents the angular velocity of the wind wheel rotation (rad/s).

Generally, the tip speed ratio reflects the speed of the wind turbine at a certain wind speed. As shown in Figure 1, the corresponding relationship between the wind energy utilization coefficient C_{p} and the tip speed ratio a of the wind turbine is given. From this figure, it can be found that when the tip speed ratio takes a certain value, the C_{p} value is the largest. People call the tip speed ratio corresponding to the maximum C_{p} value as the best tip speed ratio. Therefore, in order to maintain the maximum value of C_{p}, when the wind speed changes, the wind turbine speed also needs to change accordingly to make it run at the best tip speed. Practical experience shows that for any given wind turbine, the best tip speed ratio depends on the number of blades and the width of each blade.

**Volume ratio**

Generally, people refer to the percentage of the “entity” used to represent the swept area as the volume ratio, also known as the solidity. Multi-blade wind turbines have a high volume ratio, so they are called high volume ratio wind turbines; wind turbines with a small number of narrow blades are called low volume ratio wind turbines.

In wind design, in order to effectively absorb energy, the blades must interact as much as possible with the wind passing through the swept area of the rotor. High volume ratio, multi-blade wind turbines interact with almost all winds at a very low tip speed ratio; in order to interact with all passing wind, wind turbine blades with low volume ratios must “fill up” the swept area at a very high speed. If the tip speed ratio is too low, some wind will directly blow across the swept area of the rotor without acting on the blades; if the blade tip speed ratio is too high, the wind turbine will produce excessive resistance to the wind, and some airflow will bypass the wind turbine.

Practice has proved that the best blade tip speed ratio of a two-blade wind turbine rotor with the same blade width as a three-blade rotor is higher than that of a three-blade rotor; for a single blade with the same blade width as a two-blade rotor, the best tip speed ratio will be twice that of a two-blade rotor. For modern wind turbines with low volume ratios, the best tip speed ratio is 6-20. Because multiple blades will interfere with each other, wind turbines with high volume ratios are generally less efficient than wind turbines with low volume ratios. Among the low volume ratio wind turbines, the three-blade rotor has the highest efficiency, followed by the two-blade rotor, and finally the single-blade rotor. Wind turbines with multiple blades generally produce less aerodynamic noise than wind turbines with fewer blades. A wind turbine absorbs mechanical energy from the wind, which is equal to the product of the angular velocity of the wind turbine and the moment produced by the wind. For a certain wind energy, if the angular velocity decreases, the torque increases; conversely, if the angular velocity increases, the torque decreases. In other words, the output power of high-speed wind turbines is large, and the torque coefficient is small; the output power of low-speed wind turbines is small, and the torque coefficient is large. Generally, we can summarize the relationship between wind turbine volume ratio, blade tip speed ratio, torque and efficiency as follows:

(1) Low-speed wind turbines have large volume ratios, low blade tip speed ratios, large torque and low efficiency.

(2) The high-speed wind turbine has small volume ratio, high blade tip speed ratio, low torque and high efficiency.