﻿How to calculate the wind generator according to the formulas

# How to calculate a wind generator: formulas + practical example of calculation

Checked by a specialist: Amir Gumarov
Author: Victor Kitaev
Last update: January 2020

Alternative energy received from wind turbines is of great interest in society. There are many confirmations to this at the level of real household practice.

Owners of suburban real estate build windmills with their own hands and are content with the result, although the effect can be short-lived. The reason - during the assembly, the wind generator was not calculated properly.

Agree, I would not want to spend time and money on the project, to get an inefficient installation. Therefore, it is important to understand how to calculate the wind generator, and by what parameters to choose the main working units of the wind turbine.

The article is devoted to the solution of these questions. The theoretical part of the material is supplemented by illustrative examples and practical recommendations for assembling a wind generator.

## Calculation of a wind generator

Where to start calculating the system of reproduction of electricity from wind energy? Considering that we are talking about a wind generator, a preliminary analysis of the wind rose in a particular area seems logical.

Design parameters such as wind speed and its characteristic direction for a given territory are important design parameters. They to some extent determine the level of power of the windmill, which will be achievable.

It is difficult to imagine wind generators of such power. But similar designs exist and work effectively. However, calculations of such structures show a relatively small power compared to traditional energy sources.

What is noteworthy, this process is of a long-term nature (at least 1 month), which is quite obvious. It is impossible to calculate the most probable parameters of the wind speed and its most frequent direction with 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 a windmill

Household wind generators, 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 8-10 m high, equipped with a generator with a span of propeller blades of more than 3 m. And this is not the most powerful installation. Only about 2 kW.

To service windmills of such power, helicopters and teams of specialists, numbering up to a dozen people, are used. To calculate such a power plant, an even greater number of performers are involved

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 rotor blades, there is nothing to be surprised. According to the table, a 10-meter propeller is required for a 10 W windmill.

A screw with a diameter of 14 m will be required for a 500-watt design. Moreover, the blade span parameter depends on their number. The more blades, the smaller the scope.

But this is just a theory, due to the wind speed not exceeding 4 m / s. In practice, everything is somewhat different, and the power of domestic installations that have been in effect 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.

Table of the dependence of the power of the wind energy system on the diameter of the rotor and the number of blades. This table can be used for calculations, but taking into account its compilation for a wind speed parameter of up to 4 m / s (+)

From a theoretical point of view, the power of a wind power station is calculated by the formula:

N = p * S * V3/2,

Where:

• p - density of air masses;
• S - total blown area of ​​the propeller blades;
• V - air flow rate;
• N - air flow rate.

Since N is a parameter that dramatically affects the power of the wind generator, the real power of the installation will be close to the calculated value of N.

### Calculation of wind turbine screws

When designing a windmill, two types of screws are usually used:

• winged - rotation in the horizontal plane;
• Savonius rotor, Daria rotor - rotation in a vertical plane.

The design of the screws with rotation in any of the planes can be calculated using the formula:

Z = L * W / 60 / V

Where:

• 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 rotation of the screw;
• V - air flow rate.

Based on this formula, one can easily calculate the number of revolutions W - the rotation speed.

This is the design of the screw called "Daria Rotor". This version of the propeller is considered effective in the manufacture of wind generators of small power and size. The calculation of the screw has some features

A working ratio of revolutions 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 relation is true:

 Number of blades Degree of speed Wind speed m / s 2 5 330

Also one of the important indicators of a wind turbine prop is a step.

This parameter can be determined using the formula:

H = 2πR * tan α,

Where:

• - constant (2 * 3.14);
• R - the radius described by the blade;
• tg α - section angle.

Additional information on the choice of shape and number of blades, as well as instructions for their manufacture are given in this article.

### Selection of generators for windmills

Having the calculated value of the rotational speed of the screw (W) obtained by the above method, it is already possible to select (make) the corresponding generator.

For example, when the degree of speed Z = 5, the number of blades equal to 2 and a speed of 330 rpm. At a wind speed of 8 m / s. generator power should be approximately 300 watts.

Generator of a wind power installation "in section".A representative example of one of the possible designs of a generator of a home wind power system, assembled independently

With these parameters, the motor that is used in the construction of modern electric bicycles can be a suitable choice as a generator for a household wind farm. The traditional name of the part is a cycle motor (production of the PRC).

It looks like an electric cycle motor, on the basis of which it is proposed to make a generator for a home wind turbine. The design of the cycle motor is ideal for implementation with virtually no calculations and improvements. However, their power is small

The characteristics of the electric cycle motor are approximately as follows:

 Parameter Values Voltage 24 Power, W 250-300 Rotational speed, rpm 200-250 Torque, Nm 25

A positive feature of cycle motors is that they practically do not need to be redone. They were constructively developed as low-speed electric motors and can be successfully used for wind generators.

To make a windmill, you can use car generator or collect washing machine unit.

### Calculation and choice of charge controller

A battery charge controller is required for any type of wind power installation, including a domestic construction.

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 parameters, the main ones are:

• rated and maximum voltage of the generator;
• the maximum possible generator power;
• maximum possible battery charge current;
• battery voltage;
• ambient temperature;
• environmental humidity level.

Based on the presented parameters, charge controller assembly do it yourself or the selection of a finished device.

Battery charge controller used as part of a wind power plant. An industrial manufacturing device, choosing which you only need to carefully study the technical specifications for exact coordination with the existing system

Of course, it is desirable to select (or assemble) a device whose circuitry would provide an easy start function in the flow of weak air flows. A controller designed for use with batteries of different voltages (12, 24, 48 volts) is also welcome.

Finally, when calculating (selecting) the controller circuit, it is recommended not to forget about the presence of such a function as inverter control.

### Battery selection 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 the concrete choice will have to be made anyway. Depending on the parameters of the windmill system, the selection of the battery is carried out according to voltage, capacity, charge conditions.

The classic components for home windmills are considered 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 especially unpretentious to the conditions of charge / discharge, but it is unacceptable to include them in the system without a controller.

If there is a professionally made charge controller in the wind generator set that has a full-fledged automation system, it seems rational to use AGM or helium batteries.

Battery pack home wind generator. Not the best option, given the chaos of the wires and storage requirements. With this state of energy storage, one cannot count on their long-term effect.

Both types of energy storage devices are characterized by greater efficiency and a long service life, but they have high requirements for charging conditions.

The same applies to the so-called helium-type armored batteries. But the choice of these batteries for a household windmill is significantly limited by the price. However, the life of these expensive batteries is the longest in relation to all other types.

These batteries are also distinguished by a more significant charge / discharge cycle, but subject to the use of a high-quality charger.

### Calculation of the inverter for a home wind turbine

It should be noted right away: if the design of a home energy wind turbine contains one 12 volt battery, it makes sense to install an inverter on such a system.

On average, the household power consumption 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. For such a number of batteries, it already makes sense to install an inverter.

However, in order to provide fully energy to 10 batteries with a voltage of 24 W each and to stably maintain their charge, a wind turbine with a power of at least 2-3 kW will be required. Obviously, for household simple designs, such a power can not be pulled.

A small power inverter (600 W) that can be used for a small home power installation. You can power a TV or a small refrigerator from such equipment with a voltage of 220 volts. There isn’t enough current for the lamps in the chandelier

However, the inverter power can be calculated as follows:

1. Summarize the power of all consumers.
2. Determine the time of consumption.
3. Determine the peak load.

For a concrete example, it will look like this.

Let there be household appliances as a load: lighting lamps - 3 pcs. 40 W each, television receiver - 120 W, compact refrigerator 200 W. We summarize the power: 3 * 40 + 120 + 200 and we get 440 watts of output.

We determine the power of consumers for an average period of time of 4 hours: 440 * 4 = 1760 watts. Based on the obtained value of power according to the time of consumption, it seems logical to select 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.

The classical scheme of reproduction and distribution of energy received from a household type wind generator. However, in order to provide long-term energy with such a number of devices, a sufficiently powerful installation is needed (+)

Actually, the load from the household for a family of three people, where there is full equipment for household appliances, will be higher than calculated in the example. Usually, in terms of load connection time, the parameter exceeds 4 hours taken. Accordingly, the inverter of the wind power system will require a more powerful one.

Preliminary calculation of the windmill is useful not only for its independent assembly. It is necessary to determine the optimal parameters when choosing a finished wind generator.

## Conclusions and useful video on the topic

How the analysis of the source data and how the formulas are applied is 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 living conditions, the calculation of each node always carries with it the maximum efficiency of the device and, most importantly, the safety of operation.

Pre-made calculations determine the feasibility of the project, help to establish how costly or economical the project is.

Have experience in solving such problems? Or have questions about the topic? Please share your skills in calculating and designing a wind generator. You can leave comments and ask questions in the form below.

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1. Alexei

In short, it is very clear that if you are not an engineer, then it’s better not even to take up making a homemade windmill. In vain wasted time and money. But with ready-made elements, if you buy a separate windmill, batteries, inverter controller, practically anyone with hands grow from the right place will figure it out, and this will be the best option.Well, if there is a lot of money, you can order installation with all the equipment together.

• But why. If there is a desire and access to the Internet, then understand it really and not being an engineer. As a last resort, you will lose a little in efficiency.