How to calculate a wind generator: formulas + practical example of calculation
Alternative energy received from wind power plants causes high interest in society. Evidence of this at the level of real household practice abounds.
Owners of suburban real estate build windmills with their own hands and are satisfied with the result, although the result is also short-lived. The reason is that the construction of the installation did not calculate the wind generator properly.
Calculation of wind generator installation
How to start counting the system of reproduction of electricity from wind energy? Given that we are talking about a wind generator, a preliminary analysis of the wind rose in a specific area seems logical.
Such design parameters as wind speed and its characteristic direction for a given territory are important design parameters.They to some extent determine the power level of the windmill, which will be really achievable.
What is remarkable, this process is long-term (at least 1 month), which is quite obvious. It is impossible to calculate the most probable parameters of wind speed and its most frequent direction by one or two measurements. Dozens of measurements will be required. Nevertheless, this operation is really necessary if there is a desire to build an effective productive system.
How to calculate the power of the windmill
Domestic wind turbines, especially those made with their own hands, have not yet had to surprise people with high power. It is understandable. One has only to imagine a massive mast with a height of 8-10 meters, equipped with a generator with a span of the propeller blades of more than 3 meters. And this is not the most powerful installation. Only about 2 kW.
In general, if you rely on a standard table showing the ratio of the power of the wind generator and the required span of the propeller blades, there is something to be surprised about. According to the table, a two-meter propeller is required for a 10 W windmill. A 500-watt design will require a screw with a diameter of 14 meters. In this case, the parameter of the magnitude of the blades depends on their number. The larger the blades, the smaller the swing.
But this is only a theory due to the wind speed not exceeding 4 m / s. In practice, everything is somewhat different, and the power of domestic installations, which are actually operating for a long time, has never exceeded 500 watts. Therefore, the choice of power here is usually limited to the range of 250-500 W with an average wind speed of 6-8 m / s.
From a theoretical position, the power of a wind power station is calculated by the formula:
N = p * S * V3/2
Herep- density of air masses;S- total blown area of the propeller blades;V- air velocity;N- air flow rate. Since N is a parameter that drastically affects the power of a wind generator, in fact, the actual capacity of the installation will be close to the calculated value N.
Calculation of screws wind turbines
When designing a windmill, two types of screws are usually used:
- Rotation in the horizontal plane (wing).
- Rotation in the vertical plane (Savonius rotor, Darier rotor).
The design of screws with rotation in any of the planes can be calculated using the formula:
Z = L * W / 60 / V
For this formula:Z- the degree of speed (low speed) of the screw;L- the size of the length described by the blades of the circle;W- speed (frequency) of the screw;V- air flow rate.
Based on this formula, you can easily calculate the number of revolutions W - the speed of rotation.A working ratio of speed and wind speed can be found in the tables that are available on the network. For example, for a screw with two blades and Z = 5, the following relationship holds true:
Number of blades | Degree of rapidity | Wind speed m / s |
2 | 5 | 330 |
Also one of the important indicators of a wind turbine screw is a step. This parameter can be determined by using the formula:
H = 2πR * tg α
Here:2π- constant (2 * 3.14);R- the radius described by the blade;tg α- section angle.
Selection of generators for wind turbines
Having the calculated value of the screw speed (W), obtained by the above method, you can already select (produce) the corresponding generator. For example, when the degree of rapidity is Z = 5, the number of blades is 2, and the rotational speed is 330 rpm. at a wind speed of 8 m / s., the power of the generator should be approximately 300 watts.
With such parameters, the motor used in the construction of modern electric bicycles can be a suitable choice as a generator for a household wind power plant.The traditional name of the part is the cycle motor (made in China).
The characteristics of an electric cycle motor are as follows:
Parameter | Meanings |
Voltage, V | 24 |
Power, W | 250-300 |
Rotational speed, rpm | 200-250 |
Torque Nm | 25 |
A positive feature of velomotors is that they practically do not need to be redone. They were constructively developed as electric motors with low revolutions and can be successfully used for wind generators.
Calculation and selection of charge controller
A battery charge controller is required for a wind power plant of any type, including a household structure.
The calculation of this device is reduced to the selection of the electrical circuit of the device, which would correspond to the calculated parameters of the wind system. Of these basic parameters are:
- generator rated and maximum voltage;
- maximum possible generator power;
- maximum possible battery charge current;
- voltage on the battery;
- ambient temperature;
- environmental humidity level.
Based on the presented parameters, the assembly is carried out by hand or the selection of a ready-made battery charge control device - a controller.
Of course, it is desirable to select (or assemble) a device whose circuit would provide the function of an easy start in conditions of the flow of weak air flows. A controller designed for operation with batteries of different voltages (12, 24, 48 volts) is also welcome. Finally, when calculating (matching) the controller circuit, it is recommended not to forget about the presence of such a function as inverter control.
Selection of the battery for the system
In practice, different types of batteries are used and almost all are quite suitable for use as part of a wind energy system. But you have to make a specific choice anyway.Depending on the parameters of the wind turbine system, the selection of the battery is carried out according to voltage, capacity, charge conditions.
The traditional components for home windmills are the classic lead-acid batteries. They showed good results in a practical sense. In addition, the cost of this type of battery is more acceptable compared to other types. Lead-acid batteries are particularly unpretentious to charge / discharge conditions, but it is unacceptable to include them in a system without a controller.
In the presence of a wind generator unit, install a professionally made charge controller with a full-fledged automation system, it seems reasonable to use AGM or helium type batteries. Both types of energy storage devices are characterized by greater efficiency and long service life, but they place high demands on charge conditions.
The same applies to the so-called helium-type armored batteries.But the choice of these batteries for domestic windmill is significantly limited by the price. However, the life of these expensive batteries is the longest with respect to all other types. These batteries are also allocated a more significant charge / discharge cycle, but subject to the application of high-quality charger.
Calculation of the inverter for home windmill
We should immediately make a reservation: if the design of a home energy wind installation contains one 12 volt battery, it makes no sense to install an inverter on such a system.
The average power consumption of the household is at least 4 kW at peak loads. Hence the conclusion: the number of batteries for such power should be at least 10 pieces and preferably under a voltage of 24 volts. On such a number of batteries, it already makes sense to install an inverter.
However, in order to fully supply 10 batteries with a voltage of 24 volts each and to maintain their charge stably, a windmill with a capacity of at least 2-3 kW will be required. Obviously, for household unpretentious designs such power is not to pull. However, the inverter power can be calculated as follows:
- Summarize the power of all consumers.
- Determine the time of consumption.
- Determine peak load.
Onspecific exampleit will look like this.
Let as a load there are household electrical appliances: lighting lamps - 3 pcs. 40 W each, TV receiver 120 W, compact 200 W refrigerator. We sum up the power: 3 * 40 + 120 + 200 and get 440 W at the output.
Determine the power of consumers for an average time period of 4 hours: 440 * 4 = 1760 watts. Based on the obtained power value over the time of consumption, it seems logical to choose an inverter from among such devices with an output power of 2 kW. Based on this value, the current-voltage characteristic of the required device is calculated: 2000 * 0.6 = 1200 V / A.
In reality, the load from a household to a family of three people, where there is a full-fledged equipment with household appliances, will be higher than that calculated in the example. Usually and in connection with the load time, the parameter exceeds the 4 hours taken. Accordingly, a wind power inverter will need a more powerful one.
Conclusions and useful video on the topic
How the source data is analyzed and how the formulas are applied are presented in the video:
It is necessary to use the calculated data in any case. Whether it is an industrial power plant or manufactured for domestic conditions, the calculation of each node always carries with it the maximum efficiency of the device and, most importantly, the safety of operation. Often, pre-made calculations determine the feasibility of a project, help determine how costly or economical a project is.