# Wind energy and calculation formulas used in wind energy Wind energy is the kinetic energy of the air, which refers to the energy carried by the wind. The magnitude of wind energy depends on the wind speed and the density of the air. The energy of the wind is converted from solar radiant energy. The energy radiated by the sun per hour to the earth is 174 423 000 000 000 kW. In other words, the earth receives 1.74 x 1017 watts of energy per hour. Wind energy accounts for 1% to -2% of the total energy provided by the sun. Part of the solar radiation energy is converted into biomass energy by plants on the earth, and the total amount of wind energy converted is 50 to 100 times that of biomass energy. The famous wind energy formula is:
E=(1/2)(ρ×t×S×ν3) (1)
In the formula, ρ is the air density (kg/m2); ν is the wind speed (m/s); t is the time (s); S is the cross-sectional area (m2).
It is a commonly used formula in the utilization of wind energy. It can be seen from the wind energy formula that wind energy is mainly related to three factors: wind speed, area through which the wind flows, and air density. The relationship is as follows:
(1) The magnitude of wind energy (E) is proportional to the cube (ν3) of wind speed, that is to say, the biggest factor affecting wind energy is wind speed.
(2) The size of wind energy (E) is proportional to the area (S) that the wind flows through. For a wind turbine, the wind energy is proportional to the area swept by the wind wheel of the wind turbine when it rotates. Since the diameter of the wind wheel is usually used as the main parameter of the wind turbine, the wind energy is proportional to the square of the diameter of the wind wheel.
(3) The magnitude of wind energy (E) is proportional to the air density (p). Air density refers to the mass (kg) of air contained per unit volume (m3). Therefore, when calculating wind energy, the air density ρ value must be known. The air density ρ value is related to the humidity, temperature and altitude of the air, which can be found from the relevant information.
Air movement has kinetic energy. If the area swept by the blades of a wind turbine rotor when it rotates once is Α, when air with a wind speed of ν flows through the rotor in a unit time, the wind energy power (generally called For wind energy) as:
p=(1/2)ρν2·Aν=(1/2)ρΑν3 (2)
In the formula, p is the air density (kg/m3); Α is the area swept by the wind turbine blades in one revolution (m2); ν is the wind speed
(m/s); P is the wind energy that the air flows through the cross-sectional area of ​​the wind turbine rotor per second, that is, the wind power (W).
If the diameter of the wind turbine wheel is D, then:
A=(π/4)D2 (3)
but
P=(1/2)ρν3×(π/4)D2=(π/8)ρD2ν3 (4)
If the effective wind speed time is t, the wind energy in time t is:
E=P·t=(π/8)ρD2ν3 t (5)
It can be seen from formula (5) that wind energy is proportional to the air density ρ, the square of the diameter of the wind wheel D2, the cube ν3 of the wind speed, and the wind duration t. Generally speaking, the density of air within a certain height range can be regarded as a constant. Therefore, when the wind wheel of the wind generator is larger, the effective wind speed time is longer, especially the higher the wind speed, the greater the wind energy that the wind generator can obtain.
To characterize the wind energy resources of a location, it depends on the average annual wind energy density of the area. Wind energy density is the wind energy per unit area. For wind turbines, wind energy density refers to the wind energy swept by the wind wheel per unit area, namely:
W=ρ/A=0.5ρ×ν3 (W/m2) (6)
In the formula, W is the wind energy density (W/m2); ρ is the air density (kg/m3); ν is the wind speed (m/s).
The annual average wind energy density is:
W﹣=(1/T)∫T0(1/2)ρν3dt (7)
In the formula, W-is the average wind energy density (W/m2); T is the total time (h).
In practical applications, the following formula is often used to calculate the annual (month) wind energy density of a certain place, namely:
W year (month)=(W1t1 +W2t2 +…+Wntn)/(t1 +t2 +…+tn) (8)
In the formula, ▔W year (month) is the year (month) wind energy density (W/m2); Wi(1≤i≤n) is the wind energy density (W/m2) at each level of wind speed; Ti(1≤i≤ n) is the time (h) when the wind speed of each grade appears in each year (month).
Regardless of the utilization factor of wind turbines, the wind energy power obtained per unit area is called wind energy density (W/m2), which is used to characterize the amount of wind energy in a certain place:
W=0.5ρν3 (9)
The wind energy power that drives the operation of the wind turbine is:
P1=0.5ρν3A (10)
In the formula, ρ is the air mass density (kg/m3); ν is the wind speed (m/s); A is the area swept by the impeller of the wind turbine (m2).
Because it is impossible for a wind turbine to convert all the wind energy of the blade rotation into mechanical energy output by the shaft, the actual power of the wind wheel is:
P=0.5ρν3ΑCP (11)
In the formula, Cp is the wind energy utilization coefficient, that is, the kinetic energy of the wind received by the wind wheel and the kinetic energy value of the entire wind swept by the wind wheel A.
Taking the horizontal axis wind turbine as an example, the theoretical maximum wind energy utilization coefficient is about 0.593, but considering the wind speed change and blade aerodynamic loss and other factors, the wind energy utilization coefficient can reach 0.4 is quite high.
Wind turbines should be designed according to the local wind conditions to determine a wind speed. This wind speed is called “design wind speed” or “rated wind speed”, which corresponds to “rated power”. Due to the randomness of wind, wind turbines cannot always operate at the rated wind speed. Therefore, the wind turbine has a working wind speed range, that is, from the cut-in wind speed to the cut-out wind speed, which is called the working wind speed, that is, the effective wind speed, and the calculated wind energy density is called the effective wind energy density.