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

Alternative energy obtained from wind power plants is of high interest in society. There is a lot of evidence of this at the level of real everyday practice.

Country property owners build windmills with their own hands and are satisfied with the result, although the effect can be short-lived. The reason is that the wind generator was not calculated properly during assembly.

Agree, I wouldn’t want to spend time and money on implementing the project and end up with an ineffective installation. Therefore, it is important to understand how to calculate a wind generator, and by what parameters to select the main operating components of a wind turbine.

The article is devoted to solving these issues. The theoretical part of the material is supplemented with illustrative examples and practical recommendations for assembling a wind generator.

Introduction

Concern for the environment and one's own wallet prompted the bright minds of humanity to invent and implement new methods of energy production, the source of which would be inexhaustible resources: the sun, water and wind. The use of each such source has its own advantages and disadvantages, but wind energy is considered the most affordable and effective.

Of course, nature imposes certain restrictions on the use of wind generators, and the material costs of generating 1 kW of electricity from solar and wind energy are approximately comparable. But in northern latitudes, especially in coastal regions, the use of wind generators is beyond competition.

The question of the feasibility of the installation depends on the average wind speed in the region. Starting from 4 m/s, installing a wind generator is considered advisable, and at 9-12 m/s it operates with maximum efficiency. But the power of a wind generator depends not only on the speed of the wind flow (Scheme 1), but also on the diameter of the rotor and the area of ​​the blades (Scheme 2).

Calculation of coils, how many turns of wire will fit

Now that we know the dimensions of the coils, we can think about what wire to wind the coils with and how many turns will fit.
If the magnets are 10 mm wide, then the stator should be 8 m wide, since the distance between the magnets on opposite disks should be 10 mm. But I want to make a stator 10 mm thick, and the distance between the magnets will then be 12 mm. The stator is 10 mm thick, and 1 mm is the gap between the stator and the magnets. The width of the side of the coil turned out to be 14 mm, but you can make it smaller, you can reduce the inner hole of the coil a little more. I chose 14 mm optimally. If you wind with a wire with a diameter of 1 mm, then exactly 14 turns will fit along the width of the side of the coil. The thickness of the stator is 10 mm, which means the thickness of the coil is 10 mm, but since the wire of the beginning of the coil comes out from the side, it eats up 1 mm, leaving 9 mm. Thus, the dimensions for the wire turns are 14*9mm, which is 126 turns.

If the wire is, for example, 1.5 mm in diameter, then (14:1.5=9.3), (9:1.5=6), (6*9=45) 45 turns will fit. I think this is clear, there is an area, and how many turns will fit depends on the diameter of the wire.

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Model selection

The cost of a set of wind generator, inverter, mast, SHAVR - automatic transfer cabinet directly depends on power and efficiency.

As you can see, to fully or partially provide the estate with electricity, high-power generators are needed, which are quite problematic to install on your own. In any case, high capital investments and the need to install the mast using special equipment significantly reduce the popularity of wind energy systems for private use.

There are portable low-power wind generators that you can take with you on a trip. These models are compact, quickly installed on site, do not require special care, and provide enough energy for a comfortable pastime in nature.

And although the maximum power of this model is only 450 W, this is enough to illuminate the entire campsite and makes it possible to use household electrical appliances far from civilization.

For medium and small enterprises, installing several wind power generating stations could provide significant savings in energy costs. Many European companies are engaged in the production of products of this type.

These are complex engineering systems that require prevention and maintenance, but their rated power is such that it can cover the needs of the entire production. For example, in Texas, at the largest wind farm in the United States, only 420 such generators generate 735 megawatts per year.

Calculation and selection of charge controller

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

The calculation of this device comes down to selecting the electrical circuit of the device, which would correspond to the design parameters of the wind system.

Of these parameters, the main ones are:

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

Based on the presented parameters, the charge controller is assembled with your own hands or a ready-made device is selected.

Charge controller for batteries used as part of a wind power plant. An industrially manufactured device, when choosing which you only need to carefully study the technical characteristics for precise coordination with the existing system

Of course, it is advisable to select (or assemble) a device whose circuit would provide an easy start function in conditions of weak air flows. A controller designed for operation 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.

Types of wind generators

The operating principle of wind generators is in most cases similar. But there are a number of varieties. They are often distinguished by the type of materials used to make the rotor blades, their number, the position of the axis of rotation, and the pitch feature of the propeller. To have an understanding of the work of a wind generator, you need to briefly consider these types.

Two-blade wind generator

Three-bladed wind generator

Multi-blade wind generator

In addition to the number of blades, wind generators differ in the materials they are made from. The blades can be rigid (metal or fiberglass) or sail-like. The latter are less practical, but they are cheap. Based on the pitch characteristics of the screw, devices with fixed and variable pitch are distinguished. Fixed pitch wind generators are more reliable. Installations with variable pitch rotation allow you to change the speed, but their design is large and requires additional installation and maintenance costs.

Wind generator with vertical axis of rotation

• Savonius wind generator. These are several half-cylinders, hollow inside, which are fixed on a vertical axis. The advantage here is that they can rotate regardless of the strength and direction of the wind. The main disadvantage is that only 1/3 of wind energy is used;
• Helicoidal rotor. This option has twisted blades, which ensures uniform rotation. This is a durable wind generator, but complex and expensive;
• Rotor Daria. The system is a design with two or more blades in the form of flat plates. The rotor is simple to make but produces little power. To launch it, an additional mechanism will be required;
• Multi-blade systems with a vertical axis. They are the most efficient in terms of electricity generation.

Wind generators can be divided into imported and domestic. There are quite a lot of Chinese manufacturers among foreign ones. There are also products from the USA and EU. You can easily find products from Russian enterprises. The cost of wind generators depends on the power and the availability of additional functionality (for example, solar modules). Prices can vary from tens to hundreds of thousands of rubles.

Design and principle of operation

A wind generator works using the power of the wind. The design of this device must include the following elements:

• turbine blades or propeller;
• turbine;
• electric generator;
• electric generator axis;
• inverter, whose functions include converting alternating current into direct current;
• mechanism that rotates the blades;
• mechanism that rotates the turbine;
• battery;
• mast;
• rotational motion controller;
• damper;
• wind sensor;
• wind sensor shank;
• gondola and other elements.

Industrial units are equipped with a power cabinet, lightning protection, a rotating mechanism, a reliable foundation, a device for extinguishing fire, and telecommunications.

A wind generator is considered to be a device that converts wind energy into electricity. The predecessors of modern units are mills that produce flour from grain. However, the connection diagram and operating principle of the generator have remained virtually unchanged.

1. Thanks to the force of the wind, the blades begin to rotate, the torque of which is transmitted to the generator shaft.
2. Rotation of the rotor creates three-phase alternating current.
3. Through the controller, alternating current is sent to the battery. The battery is necessary in order to create stable operation of the wind generator. If there is wind, the unit charges the battery.
4. To protect against hurricanes, the wind power generation system contains elements to move the wind wheel away from the wind. This happens by folding the tail or braking the wheel using an electric brake.
5. To recharge the battery, you will need to install a controller. The functions of the latter include monitoring battery charging to prevent its breakdown. If necessary, this device can dump excess energy into ballast.
6. The batteries have a constant low voltage, but it must reach the consumer with a power of 220 Volts. For this reason, inverters are installed in wind generators. The latter are capable of converting alternating current into direct current, increasing its strength to 220 Volts. If an inverter is not installed, you will need to use only those devices that are designed for low voltage.
7. The converted current is sent to the consumer to power heating batteries, room lighting, and operation of household appliances.

How much power do you need?

Before buying a wind power plant, you should fully determine the value of the peak total power consumed by all household appliances, appliances and electrical installations in the house, everything that can be connected to the network at the same time

And here it is very important whether the wind farm will be used as an additional or backup source of energy, or whether you want to transfer your farm to a completely autonomous power supply

In the first case, you just need to know the minimum energy consumption that is necessary in the event of a blackout of external power supply, and buy an installation of the appropriate power. For complete energy autonomy, it is necessary to purchase high-power wind generators that can ensure the total consumption of all home appliances. Of course, this is not cheap, but you will no longer need to buy electricity from the outside.

To summarize the above: is a wind generator profitable?

The presented results clearly prove the return on costs of purchasing and launching a wind generator. Moreover:

• The cost of a kilowatt is constantly rising due to inflation.
• When using a windmill, the object becomes energy independent.
• “Excess” generated electricity can be accumulated and stored in case of calm weather thanks to an uninterruptible power supply system.
• Many objects remote from the centralized energy supply network are forced to exist in the absence of electricity, since their connection is unprofitable.

So, a wind generator is profitable. Its acquisition for energy-intensive consumers without power supply is economically feasible. A hotel outside the city, an agricultural farm or livestock enterprise, a cottage community - in any case, the costs of connecting an alternative source of power supply will be justified. All that remains is to select the appropriate windmill model and install it, guided by the manufacturer’s recommendations. The power of the device should correspond to the average wind speed in your region. You can clarify it using a special wind map or according to data from a local weather station.

Please note: for wind generators from Chinese manufacturers, the rated power of the device is calculated taking into account wind speed at 50-70% of ground level. Installing a wind turbine at such a height is problematic

A mast that is too high is expensive and has strict requirements for its strength. In addition, at the specified height, gusts of wind form strong vortex flows. They not only slow down the operation of the wind generator, but can also cause the blades to break. The solution is to install the device at a height of 30-35m, which will provide access to strong winds, but will prevent damage to the windmill.

Windmill care

The following procedures are carried out as regular maintenance of the structure:

• Lubrication of moving parts (at least 2 times a year)
• tightening bolts and electrical connections
• checking mechanisms for rust and loose stretch marks
• blade breakage control

The most common windmill damage is blade separation. In winter, a crust of ice appears on them. Frequent cleaning will extend the life of the structure. Parts are painted as needed. Once a year you need to completely inspect the structure for damage.

A homemade windmill is very different in power values ​​from factory-made products. This is due to inaccurate calculations. A horizontal windmill with a theoretical power of 101 W will produce only 90, and a vertical windmill with 69 W will produce about 60.

Thus, assembling a vertical windmill is a fairly simple option for providing a residential building with electricity. This is due to the ease of assembly of the structure, the low cost of the project and the high efficiency of the device. In addition, it requires minimal maintenance and produces electricity constantly. How to make a windmill yourself is shown in the video:

Conclusions and useful video on the topic

How the source data is analyzed and how the formulas are applied is presented in the video:

It is necessary to use calculated data in any case. Whether it is an industrial power plant or one manufactured for domestic use, the calculation of each unit always ensures maximum efficiency of the device and, most importantly, operational safety.

Preliminary calculations determine the feasibility of implementing the project and help determine how costly or economical the project is.

Do you have experience in solving similar problems? Or still have questions on the topic? Please share your wind turbine calculation and design skills. You can leave comments and ask questions in the form below.

How much energy is hidden in the wind?

To begin with, let's roughly estimate the power that we want to use for our own purposes. Let's calculate the energy released by an air flow with density ? and speed V, exerting pressure on area S according to the simple formula:

P = V3•?•S

If we take air density ?=1.25 kg/m3, wind speed V=5 m/s, and the cross-sectional area of ​​a turbine with a radius of 2 meters S=12.5 m2, the result will be 1953 W, i.e. slightly less than 2 kW . However, of this impressive power, even the most advanced wind power plants (WPPs) today are capable of converting only a relatively small share into electrical energy.

The greatest losses are associated with turbulence in the air flow in the turbine and bending around the windmill blades. They are taken into account by the wind energy conversion coefficient ?, which in modern installations does not exceed 0.4 - 0.5. Taking into account the efficiency of the gearbox and generator, we take them equal to 0.9 and 0.85, respectively. And the value of the output power of the same power plant, calculated using a refined formula:

P = ? • ?•R2 • V3 • ? • Efficiency ed • Efficiency gen = 0.45 • 12.5 • 125 • 1.25 • 0.9 • 0.85 = 672 W,

which is approximately a third of all wind energy used. Currently, the total efficiency of existing wind generators does not exceed 40%. This rough calculation of a wind generator shows that there is not much energy output, especially compared to modern portable diesel power plants.

alternative energy

Wind load can also bring benefits, for example, by converting wind power in wind generators. So, at a wind speed of V = 10 m/sec, with a circle diameter of 1 meter, the windmill has blades d = 1.13 m and produces about 200–250 W of useful power. An electric plow, consuming such an amount of energy, will be able to plow about half a hundred (50 m²) of land on a personal plot in one hour.

If you use a large wind generator - up to 3 meters, and an average air flow speed of 5 m/sec, you can get 1-1.5 kW of power, which will completely provide a small country house with free electricity. With the introduction of the so-called “green” tariff, the payback period for equipment will be reduced to 3–7 years and, in the future, can bring net profit.

All wind generators can be classified according to several principles:

1. Axes of rotation.
2. Number of blades.
3. The material from which the blades are made.
4. Screw pitch.

Classification by axis of rotation:

1. Horizontal.
2. Vertical.

Scheme of work

The most popular are horizontal wind generators, the rotation axis of which is parallel to the ground. This type is called a "windmill", the blades of which rotate against the wind. The design of horizontal wind generators provides for automatic rotation of the head part (in search of wind), as well as rotation of the blades to use low-power wind.

Vertical wind turbines are much less efficient. The blades of such a turbine rotate parallel to the surface of the earth in any direction and strength of the wind. Since, in any wind direction, half of the wind wheel blades always rotate against it, the windmill loses half of its power, which significantly reduces the energy efficiency of the installation. However, this type of wind turbine is easier to install and maintain, since its gearbox and generator are located on the ground. The disadvantages of a vertical generator are: expensive installation, significant operating costs, and also the fact that installing such a wind turbine requires a lot of space.

Horizontal wind generators are more suitable for producing electricity on an industrial scale; they are used in the case of creating a system of wind power plants. Vertical ones are often used for the needs of small private farms.

Classification by number of blades:

1. Two-blade.
2. Three-blade.
3. Multi-bladed (50 or more blades).

Based on the number of blades, all installations are divided into two- and three- and multi-blades (50 or more blades). To generate the required amount of electricity, it is not the fact of rotation that is required, but reaching the required number of revolutions.

Each blade (additional) increases the total resistance of the wind wheel, which makes reaching the operating speed of the generator more difficult. Thus, multi-blade installations do indeed begin to rotate at lower wind speeds, but they are used in cases where the fact of rotation itself matters, as, for example, when pumping water. Wind generators with a large number of blades are practically not used to generate electricity. In addition, it is not recommended to install a gearbox on them, because this complicates the design and also makes it less reliable.

Classification according to blade materials:

1. Wind generators with rigid blades.
2. Sailing wind generators.

It should be noted that sail blades are much simpler to manufacture and therefore less expensive than rigid metal or fiberglass. However, such savings may result in unexpected costs. If the diameter of the wind wheel is 3 m, then at a generator speed of 400-600 rpm, the tip of the blade reaches a speed of 500 km/h. Taking into account the fact that the air contains sand and dust, this fact is a serious test even for hard blades, which, under stable operation conditions, require annual replacement of the anti-corrosion film applied to the ends of the blades. If you do not update the anti-corrosion film, the hard blade will gradually begin to lose its performance characteristics.

Sail-type blades require replacement not once a year, but immediately after the first serious wind occurs. Therefore, autonomous power supply, which requires significant reliability of system components, does not consider the use of sail-type blades.

Classification by propeller pitch:

1. Fixed propeller pitch.
2. Variable propeller pitch.

Of course, variable propeller pitch increases the range of effective operating speeds of the wind generator. However, the introduction of this mechanism leads to a complication of the blade design, an increase in the weight of the wind wheel, and also reduces the overall reliability of the wind turbine. The consequence of this is the need to strengthen the structure, which leads to a significant increase in the cost of the system not only during acquisition, but also during operation.

Blade calculation

The efficiency of a wind generator is significantly influenced by the aerodynamic characteristics of the blades installed on it, therefore, before their manufacture, special calculations are made. As a result of such calculations, products are checked for compliance of the results obtained with the required parameters and other requirements imposed on them.

The wind exerts an impact on the generator blades and this force, or in other words, pressure, acts in the direction of the air flow. In turn, a lifting force acts perpendicular to the pressure force, which is what works in wind generators with a horizontal axis of rotation (shown in the diagram below).

When calculating the geometric dimensions of the blade, the width of its chord and the angle of its installation are determined, in diagram β, over the entire length of the device element.

When carrying out calculations, the finite element method is used, the essence of which is that the blade is considered as a set of individual elements that make up its composition.

The force of pressure of wind flows is directed against the movement of the blade (in the diagram it is called “true wind”) and in the diagram it is decomposed into vectors - “wind speed” and “peripheral speed”. The peripheral speed ensures the movement of the blades in the plane of rotation, while the lifting force acts in this direction.

The pressure force and lift force determine the performance of the wind generator (the formula is given in the “Main characteristics” section) and depend on the lift coefficient, as well as the drag coefficient. In addition, these coefficients are directly dependent on the geometric profile of the blade and the angle between its chord line and the direction of the air flow.

The chord line is the longest line when considering its cross-section, from the tip of the blade to its trailing edge.

The angle between the chord line and the direction of the air flow (incoming flow) is called the angle of attack (angle α).

The lift and drag coefficients are determined experimentally and recorded in special journals (atlases). The graph of lift versus angle of attack (blade shape) looks like this:

The best aerodynamic performance is achieved by similar elements with an angle α (angle of attack) equal to – 5.

The blade width (dimension “b”) is also an important parameter that requires appropriate calculation. The most important part is the outer part, due to the wind ring and the coverage area with which this part of the device works.

The calculation is performed using the formula:

Where:

R – outer radius of rotation;

r – internal radius of rotation, excluding the butt and butt part;

Z – tip speed.

i – number of blades.

From this formula it is clear that:

• The width is inversely proportional to the internal radius of its rotation, and which, in turn, suggests that the most optimal shape is the shape of a triangle;
• A wind generator with a small number of blades must have wider blades;
• Increasing speed reduces their width.

Speed ​​with the indicator “5” is the most optimal, which allows you to reduce installation losses with the maximum number of blades. The figure below shows how the number of similar elements installed on a wind generator affects its speed:

High speed allows you to increase the efficiency of wind generators, while the negative factors when operating such devices will be:

• Increased noise level;
• Vibration when using one or two blades;
• Increased edge erosion;
• Difficulty starting with low wind flows.

To reduce noise levels, the tips of the blades are made pointed, and to make starting easier, the bases are made slightly wider than size “b”.

Calculation of wind turbine propellers

When constructing a windmill, two types of propellers are usually used:

1. Rotation in a horizontal plane (vane-type).
2. Rotation in a vertical plane (Savonius rotor, Darrieus rotor).

Screw designs with rotation in any plane can be calculated using the formula:

Z=L*W/60/V

For this formula: Z – degree of speed (low speed) of the propeller; L – size of the length of the circle described by the blades; W – speed (frequency) of rotation of the propeller; V – air flow speed.

This is what the design of the screw called the “Darieu Rotor” looks like. 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

Based on this formula, you can easily calculate the number of revolutions W - rotation speed. And the working relationship between revolutions and wind speed can be found in tables that are available on the Internet. For example, for a propeller with two blades and Z=5, the following relation is valid:

Also, one of the important indicators of a windmill propeller is the pitch. This parameter can be determined using the formula:

H=2πR* tan α

Here: 2π – constant (2*3.14); R – radius described by the blade; tan α – section angle.

Selection of generators for wind turbines

Having the calculated value of the number of screw revolutions (W), obtained using the method described above, you can already select (manufacture) the appropriate generator. For example, with a 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, the generator power should be approximately 300 W.

Cross-sectional view of a wind power plant generator. Demonstrative example of one of the possible designs of a home wind power system generator, assembled independently

Given these parameters, a suitable choice as a generator for a domestic wind power plant may be the motor used in the designs of modern electric bicycles. The traditional name of the part is bicycle motor (made in China).

This is what an electric bicycle motor looks like, on the basis of which it is proposed to make a generator for a home windmill. The design of the bicycle motor is ideal for implementation with virtually no calculations or modifications. However, their power is low

The characteristics of an electric bicycle motor are approximately as follows:

A positive feature of bicycle motors is that they practically do not need to be altered. They were structurally designed as low-speed electric motors and can be successfully used for wind generators.

Calculation of wind generator power

Making a windmill yourself also requires preliminary calculations. Nobody wants to waste time and materials on manufacturing who knows what; they want to have an idea of ​​the capabilities and expected power of the installation in advance. Practice shows that expectations and reality have a weak correlation with each other; installations created on the basis of rough estimates or assumptions not supported by accurate calculations produce weak results.

Therefore, simplified calculation methods are usually used, which give results that are fairly close to the truth and do not require the use of a large amount of data.

How to produce?

To calculate a wind generator, you need to perform the following steps:

• determine the home's electricity needs. To do this, it is necessary to calculate the total power of all devices, equipment, lighting and other consumers. The resulting amount will show the amount of energy required to power the house
• the resulting value must be increased by 15-20% in order to have some power reserve just in case. There should be no doubt that this reserve is needed. On the contrary, it may turn out to be insufficient, although, more often than not, the energy will not be fully used
• Knowing the required power, you can estimate which generator can be used or manufactured to solve the given problems. The final result of using a windmill depends on the capabilities of the generator; if they do not meet the needs of the house, then you will have to either change the device or build an additional set
• wind wheel calculation. Actually, this moment is the most difficult and controversial in the entire procedure. Formulas for determining flow power are used

For example, consider the calculation of a simple option. The formula looks like this:

Where P is the flow power.

K - wind energy utilization coefficient (a value inherently close to efficiency) is assumed to be in the range of 0.2-0.5.

R is the air density. It has different values, for simplicity we will take it equal to 1.2 kg/m 3.

V is the wind speed.

S is the wind wheel coverage area (covered by the rotating blades).

We calculate: with a wind wheel radius of 1 m and a wind speed of 4 m/s

P = 0.3 × 1.2 × 64 × 1.57 = 36.2 W

The result shows that the flow power is 36 W. This is very little, but a meter-long impeller is too small. In practice, wind wheels with a blade span of 3-4 meters are used, otherwise the performance will be too low.

What to consider?

When calculating a windmill, the design features of the rotor should be taken into account. There are impellers with vertical and horizontal rotation types, with different efficiencies and performance. Horizontal structures are considered the most effective, but they require high installation points.

Equally important will be to ensure that the impeller has sufficient power to rotate the generator rotor. Devices with tight rotors, which allow obtaining a good energy output, require considerable shaft power, which can only be provided by an impeller with a large area and diameter of the blades.

An equally important point is the parameters of the source of rotation - the wind. Before making calculations, you should learn as much as possible about the strength and prevailing wind directions in a given area. Take into account the possibility of hurricanes or squalls, find out with what frequency they can occur. An unexpected increase in flow speed is dangerous due to the destruction of the windmill and the failure of the converting electronics.

Calculation of an inverter for a home windmill

It should be noted right away: if the design of a home wind turbine contains one 12-volt battery, there is no point in installing an inverter on such a system.

On average, household power consumption is at least 4 kW at peak loads. Hence the conclusion: the number of rechargeable batteries for such power should be at least 10 pieces and preferably with a voltage of 24 volts. For such a number of batteries it makes sense to install an inverter.

Low power inverter (600 W), which can be used for home small power installations. You can power a TV or a small refrigerator from such equipment with a voltage of 220 volts. There is no longer enough current for the lamps in the chandelier

However, to fully provide energy to 10 batteries with a voltage of 24 W each and stably maintain their charge, a windmill with a power of at least 2-3 kW will be required. Obviously, simple household structures cannot handle such power.

However, you can calculate the inverter power as follows:

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

In a specific example it will look like this.

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

Let's determine the power of consumers for an average period of 4 hours: 440*4=1760 W. Based on the obtained power value over time of consumption, it seems logical to select an inverter from among such devices with an output power of 2 kW or more.

Based on this value, the current-voltage characteristic of the required device is calculated: 2000*0.6=1200 V/A.

A classic scheme for the reproduction and distribution of energy obtained from a household wind generator. However, to provide long-term energy to such a number of devices, a sufficiently powerful installation is needed (+)

In reality, the household load on a family of three people, which is fully equipped with household appliances, will be higher than calculated in the example. Typically, the load connection time also exceeds the required 4 hours. Accordingly, the wind power system inverter will need a more powerful one.

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

Vertical wind generator

Let's take a closer look at the vertical wind generator. There are many design options, most of which are just projects and are not produced or commercially available. A short search on the Internet reveals the following picture: in the presence of efficient and productive prototypes, only different versions of orthogonal rotors are produced. The cost varies significantly - Chinese models are noticeably cheaper, although the stated figures are quite consistent with European or American installations.

Considering the actual output is 10% of the nominal, we will consider installations with a capacity of 20 kW. A 20 kW Falcon Euro wind generator costs RUB 1,050,000. It will be able to produce about 48 kW per day. The simplest calculation shows that over 20 years of service it will produce 350,400 kW of energy. Dividing the price of the kit by the amount of energy, we get the price of 1 kW about 3 rubles. This price is an estimate; in practice, costs will increase and output will decrease.

If you use more affordable Chinese models, then the question of quality arises. To what extent can the equipment perform its functions in severe frost conditions, what is its service life? Only practice can answer these questions, so the use of such devices is limited. The best option remains the independent production of vertical structures, which allows you to use the most productive designs and significantly reduce the costs of materials and installation.

Wind power utilization rate

It should be noted that wind generators have their own specific efficiency indicator - KIEV (Wind Energy Utilization Coefficient). It indicates what percentage of the air flow passing through the working section directly affects the windmill blades. Or, to put it more scientifically, it demonstrates the ratio of the power received at the shaft of the device to the power of the flow acting on the wind surface of the impeller. Thus, KIEV is a specific analogue of efficiency, applicable only to wind generators.

Today, the KIEV values ​​from the initial 10-15% (indicators of ancient windmills) have increased to 356-40%. This is due to improvements in the design of wind turbines and the emergence of new, more efficient materials and technical parts, components that help reduce losses due to friction or other subtle effects.

Theoretical studies have determined the maximum wind energy utilization factor to be 0.593.

Where to locate the wind power station?

Of course, it is best to leave the choice of wind farm location to specialists. But there are 3 basic rules that should be followed:

• Eliminate turbulence in the air flow near the turbine. The height of the wind turbine on the mast should be 10 m higher than all high-rise objects within 100 m around. This applies, for example, to both poles and power line wires.
• Take advantage of the natural advantages of the terrain. The fact is that gorges and canyons are natural wind tunnels and in places where they narrow, the wind speed increases significantly.
• Locate the wind farm in the most open areas, such as a field, the shore of a reservoir or the top of a hill.

Do-it-yourself windmills for home: review of designs

As you already understood, the very first part that receives wind energy is the wind wheel. Not a single windmill scheme for a home can do without it.

It can be done:

• with a vertical axis of rotation;
• or horizontal.

Vertical wind generator

I’ll show you a photograph of one of the easy-to-manufacture structures, made from an ordinary steel barrel.

Such a vertical wind generator, made by hand, and located above the ground itself, surrounded by buildings and plants, will not be able to develop normal speed to generate enough electricity to power a private house.

It will be able to perform only some single tasks for low-power equipment. Moreover, the low rotation speed of its rotor will require the mandatory use of a step-up gearbox, which means additional energy losses.

Such designs were popular at the beginning of the last century on steamships. The water wheel, with its blades located along the direction of movement of the vessel, ensured its movement.

Now it is a rarity that has lost its relevance. In aviation, such a design not only did not take root, but was not even considered.

Onipko rotor

Among low-speed wind wheel designs, the Onipko rotor is now being widely distributed via the Internet. Advertisers show it spinning even in very light winds.

However, for some reason I also have a critical attitude towards this development, although repeating it with your own hands is not so difficult. I did not find rave reviews among buyers, nor did I find scientific calculations of the economic feasibility of its use.

If any of the readers can dissuade me from this opinion, I will be grateful.

Horizontal wind generator

From the very beginning, aircraft engines began to use a propeller that drives air flow along the body of the aircraft. Its shape and design are chosen so as to use a reactive component in addition to the active pressure force.

Any horizontal wind generator, whether made industrially or with your own hands, works on this principle. I show an example of a homemade design with a photograph.

Based on the principle of using wind energy, this is a more efficient design, and in terms of its design, it is low-power for providing household energy supply issues.

A small electric motor, the rotor of which spins a windmill, can, even with optimal pressure and wind strength, produce only low power as a generator. You can connect a weak LED light bulb to it.

Think for yourself whether you need to assemble such a weather vane with lighting or not. This design will not cope with other tasks. Although it can still be used to scare away moles on the site. They really don't like noises accompanied by the rotation of metal parts.

In order to fully use the electricity obtained from the wind, the impeller of the wind generator must have dimensions corresponding to the power consumption. Count on approximately five meters in diameter.

When creating it, you will encounter a technical difficulty: you will have to accurately balance large parts. The center of mass must always be at the midpoint of the axis of rotation.

This will minimize bearing beating and rocking of the structure located at a high altitude. However, this balancing act is not so easy to achieve.

How to install a wind generator: a reliable mast diagram for mounting at height

The weight of the impeller for normal production of electrical energy is quite decent. It cannot be installed on a simple stand.

It will be necessary to create a solid concrete foundation for the metal mast and guy anchor bolts. Otherwise, the entire structure, assembled with great difficulty, may collapse at any inopportune moment.

A stand for a wind generator raised to a height can be made:

1. in the form of a prefabricated mast assembled from sections with braces;
2. or conical tubular support.

Both schemes will require reinforcement against capsizing by creating several tiers of guy ropes, which are necessary to hold the mast in heavy gusts of wind. They will have to be securely attached to stoppers and anchors.

From personal unsuccessful experience: while using analog television, the “Spider Web” antenna with a hoop diameter of 2 m worked. It was located at a height of 8 meters and was fixed on a wooden pole with two levels of guy wires. Heavy gusts of wind rocked it so much that the stand fell apart.

Modern digital television, fortunately, requires the use of much smaller antennas. Not only are they easy to make with your own hands, but they are also not that difficult to attach.

How to make a mast for a windmill

Immediately pay attention to creating a durable, trouble-free structure. Otherwise, just repeat the sad experience of YantarEnergo workers, who had an accident during a storm: a multi-ton mast collapsed, and fragments from the blades scattered throughout the area.

The construction of the mast will require calculating the amount of materials required to create a structure from a steel angle of various sections. The shape and dimensions are selected according to local conditions.

It is made of three or four vertical posts. Each of them is mounted on a stop from below. At the top of the mast a platform is created for installing a wind turbine.

Since the length of the corners is limited, the mast is assembled from several sections. The rigidity of the overall fastening is provided by side ribs attached through braces.

A mandatory element of the foundation are embedded metal elements. They will be used to fasten parts. You will have to take care of welding and connecting bolts.

Don't neglect additional braces.

How to make a pipe support

A telescopic structure made from steel pipes of the appropriate profile is easier to assemble, but it should be more carefully calculated for strength. The bending moment created by the heavy top during a storm wind should not exceed a critical value.

In this case, difficulties will arise with preventive maintenance, inspection and repair of the assembled air power plant. If you can climb to a height using a mast like a ladder, it is problematic to do this using a pipe. And working at the top is very dangerous.

Therefore, it is immediately necessary to consider the option of safely lowering the equipment to the ground and an accessible way to lift it. This allows you to do one of two schemes with:

1. Rotary axis on the main support.
2. The thrust lever on the bottom of the support post.

In the first case, a solid foundation is created for installing the main support. A welded pipe structure with a windmill and a pulley system on steel cables is attached to its axis of rotation.

There is a counterweight located at the bottom of the pipe, which facilitates the work of lifting and lowering using a hand winch.

The picture does not show the safety ropes of the guy belts. They simply hang from their mountings down to the ground as the mast is raised and lowered, and are attached to permanent concrete stakes for permanent operation.

The diagram for installing and lowering the windmill according to the second option is shown below.

The mast and a thrust lever with a counterweight located at right angles to it, reinforced with a stiffening rib, are turned in the vertical direction by a winch with a pulley system.

The axis of rotation of the created structure is located at the apex of the right angle and is fixed in guides built into the foundation. When raising or lowering the mast, the guy ropes are removed from the stationary fastenings on the ground. They can be used as safety lines.

Wind generator: device and principle of operation of the electrical circuit in simple words

Industrial wind farms are designed to be able to immediately supply electrical energy to the grid for consumers. You can't do this with your own hands.

When choosing a generator that will spin a wind wheel, the principle of reversibility of electric machines is used. Torque is applied to the electric motor and the stator windings are excited.

However, the idea of ​​spinning the rotor of a three-phase asynchronous electric motor as a generator to produce an electric current of 220/380 volts is realized from internal combustion engines, water pressure, but not wind.

The overall design of the generator with the rotor will have a lot of weight, otherwise it will not be possible to ensure high shaft speeds.

For small capacities you can:

• use a car generator that produces 12/24 volts;
• use a wheel motor from an electric bike;
• assemble a structure from neodymium magnets with coils of copper wire.

You can also use a windmill sold in China as a basis. But he needs to immediately carry out an audit: pay attention to the quality of installation of the windings, the condition of the bearings, the strength of the blades, and the overall balancing of the rotor.

You will have to be prepared for the fact that the output voltage of the generator will vary greatly depending on the wind speed. Therefore, batteries are used as an intermediate link.

They must be charged by the controller.

Household appliances on a 220-volt network must be powered by alternating current from a special converter - an inverter. The simplest diagram of a home wind power plant is as follows.

It can be significantly simplified because consumer digital electronics: computers, televisions, telephones operate on DC 12 volt power supplies.

If they are excluded from operation and digital equipment is powered directly from batteries, then electrical energy losses will be reduced by eliminating double conversion in the inverter and units.

Therefore, I recommend making separate 12-volt sockets and powering them directly from batteries.

Inside the electrical circuit, you will have to maintain the same power balance as in the mechanical design. Each connected load must comply with the energy characteristics of the upstream source.

220 volt household appliances should not overload the inverter. Otherwise, it will be disconnected from the built-in protection, and if it malfunctions, it will simply burn out. Batteries, power contacts of the controller, and the generator itself work on the same principle.

Circuit breaker protection of a domestic wind turbine must be carried out without fail.

To do this, it must be correctly selected strictly according to scientific recommendations, tested and adjusted.

An accidental overload, much less the occurrence of a short circuit current, cannot be foreseen. Therefore, this module must be installed as the main protection.

The connection diagram for batteries, inverter and controller for a wind generator is practically no different from that used in solar stations with light panels.

Therefore, a reasonable conclusion immediately suggests itself: to assemble a combined home power plant powered by wind and solar energy simultaneously. These two sources together complement each other well, and the cost of assembling single stations is significantly reduced.

There are a lot of channels on YouTube dedicated to wind generators for the home. I liked the work of the owner of Solar Panels. I believe that he is quite objective when presenting this topic. Therefore, I recommend that you take a closer look.

Batteries for a wind generator: another problem for the home owner

One of the costly challenges of a wind or solar power plant is the issue of storing electrical energy, which only batteries can solve. They will have to be purchased and updated, and the cost is quite high.

To select them, you need to know the operating characteristics: voltage and capacitance. Usually, composite batteries from 12 V batteries are used, and the number of ampere-hours in each specific case should be determined experimentally, based on the power of consumers and their operating time.

You will have to choose batteries for a wind generator from a fairly wide range. I will limit myself to not a complete review, but only to four popular types of acid batteries:

1. conventional automotive starter;
2. AGM type;
3. gel;
4. armored.

Sellers do not recommend purchasing starter batteries for wind power plants because they are designed to operate in critical vehicle operating conditions:

• when stored in cold weather, they must withstand the enormous starter currents that are created when spinning up a cold engine;
• are subject to vibrations and shaking while driving;
• recharging occurs in buffer mode from the generator when the car is moving at different engine speeds.

Wherein:

• serviced batteries, requiring periodic electrolyte levels and topping up with distilled water, are designed to withstand 100 discharge/charge cycles;
• maintenance-free - have a more complex design and the number of cycles is 200.

However, the wind generator battery when used inside the house:

• usually placed in the basement, where the temperature, maintained year-round at +5÷+10 degrees, is optimal;
• not subject to shocks and vibrations, permanently installed in a stationary state;
• do not receive extreme loads during starter start, and when turning on household appliances through the inverter, they operate in a gentle mode;
• are charged from the generator with small currents, which have a beneficial effect on the desulfation mode of the plates.

All this is the most favorable conditions for their operation. Therefore, I suggest taking note of this option for those who are not too lazy to periodically monitor the voltage on the banks and monitor the electrolyte level in them.

AGM batteries are more complex in design. They have the same plates, but glass mats are impregnated with acid, which simultaneously act as a dielectric layer. Their discharge/charge cycle is 250÷400. Overcharging is dangerous.

Goal batteries are also created with a maintenance-free design with a sealed case and an electrolyte thickened to a gel state. They really don't like overcharging, but are more resistant to deep discharge. The number of calculation cycles is 350.

Armor-mounted batteries are among the most modern developments. Their electrode plates are protected by polymers from acid attack. Range of operating cycles: 900÷1500.

All these four types of batteries differ significantly in price and operating conditions. If you take into account the recommendations of sellers, you will have to shell out a fairly decent amount of money.

However, I recommend that you first listen to the useful advice that the same owner of “Solar Batteries” gives in his video “How to choose batteries for a wind farm and a solar station.”

He has his own, opposite opinion on this matter. How you treat him is your own business. However, to know information from opposing sources and choose the most suitable option from it: the optimal solution for a thinking person.

Real power of a homemade wind generator

A feature of homemade devices is the use of improvised materials and devices. In such conditions, it is not always possible to ensure full compliance with design data. At the same time, the difference in calculated and real indicators can be either negative or positive.

The quantities that determine the capabilities of the kit are the power of the wind wheel and generator. To the extent that they correspond to each other, this and the total power of the wind generator will be obtained as a result.

For example, if a generator requires a rotation speed of 2000 rpm for rated performance, then no wind wheel can provide the required values.

Therefore, first of all, low-speed generators should be selected that are capable of generating large amounts of energy at low rotation speeds. To do this, ready-made devices are modernized (for example, neodymium magnets are installed on the rotor of car generators), and our own designs are manufactured based on the same neodymium magnets with pre-calculated power and performance.

Calculation of wind wheel parameters

Calculation of a wind wheel is important when creating a wind generator. It is the impeller that receives the wind flow and transfers its energy in the form of rotational motion to the generator rotor. For the calculation, you will first need to know the parameters of the generator - power, rated rotor speed, etc.

It should be taken into account that increasing the number of blades reduces the rotation speed, but increases the power of the rotational movement. Accordingly, a small number of blades should be used on high-speed generators, and a large number should be used on tori that require a large rotation force.

Z = L × W / 60 / V,

Where Z is the desired value (speed),

L is the length of the circle described by the blades.

W is the frequency (speed) of rotation of the impeller.

V is the wind speed.

Experts recommend choosing multi-bladed samples with a number of blades of 5 or more for self-production. They do not require balancing, have more stable aerodynamics and more actively absorb the energy of the air flow.

The amount of savings obtained from using a wind generator is calculated using our own data. It consists, on the one hand, of the costs of purchasing and assembling a windmill or its parts, and the costs of servicing the kit. On the other hand, the cost of network electricity in a given region, or the price of connection and other costs associated with this, is taken into account.

The difference in the values ​​obtained will be the amount of savings. It is also necessary to take into account the lack of connectivity in some areas, where a wind generator becomes the only available option. In such cases, talking about saving becomes irrelevant.

The amount of energy generated depends on the parameters of the impeller and the generator itself. The maximum possible quantity should be considered the nominal data of the generator, reduced by the value of the impeller KIEV. In practice, the indicators are much lower, since wind speed, which cannot be predicted in advance, is of great importance in obtaining the result.

In addition, there are various subtle effects that together have a noticeable impact on the final performance of the windmill. The fundamentally important values ​​are the diameter of the impeller and the wind speed; the amount of energy received directly depends on them.

Minimum wind speed - in this case, this is the value at which the windmill blades begin to rotate. This value shows the degree of sensitivity of the impeller, but has little effect on the final result. The generator has its own needs; for it, rotation alone does not solve all the issues.

A certain speed and stability of movement, the absence of sudden jerks, is required. The minimum rotation speed should be considered only from the standpoint of the overall efficiency of the impeller, which allows one to evaluate its ability to provide energy production at low flows.

Calculation of wind generator payback

Having invested hundreds of thousands of rubles in purchasing the device, the new owner has the right to count on its obvious benefits and the return on investment of the windmill. Let's try to calculate the price of a kilowatt of electricity using a standard 4-5 kW generator model.

At a wind speed of 4-5 m/s, the device will produce about 350 kW per month, or 4200 kW per year. The service life of the generator is about 25 years, the cost of most device models is within 280,000 rubles.

We divide the cost by the product of annual production and service life:

280,000 / 4200*25 = 2.666 rubles

Thus, the cost of a kilowatt of energy from a payback wind generator will be just over 2.5 rubles. Compared to the current price level, there is a benefit, but it is not as great as we would like when using alternative energy sources.

The above calculations give a different result if the wind speed is about 7-8 m/s. A wind generator with a power of 6-7 kW will produce about 780 kW per month or 9000 kW per year.

With the cost of such wind turbines being about 310,000, we get the following result:

310,000 / 9000*25 = 1.3722 rubles This cost is an obvious benefit, especially for energy-intensive facilities.

Pros and cons of installing a wind generator

This equipment, like solar panels, belongs to the category of alternative energy sources. But, unlike photovoltaic cells, which require sunlight, a wind generator can operate effectively 24 hours a day, 365 days a year.

To balance all these pros and cons, a combination is often made: a wind generator with a solar panel. These installations complement each other, thereby reducing the dependence of electricity generation on the sun and wind.

An example of calculating blades from a 160th pipe for this generator

speed

I got the best result from a 160mm pipe with a diameter of 2.2m and a speed of Z3.4 - 6 blades, but it’s better not to make such a diameter of a propeller from a 160mm pipe, the blades will be too thin and flimsy. At 3 m/s, the nominal propeller speed was 84 rpm and the propeller power was 25 watts, that is, approximately suitable. Of course, it is necessary to make a margin for the efficiency of the generator, but the 160th pipe is already thin and most likely flutter will be observed already at 7 m/s. But for the sake of example it will do

Now, if you change the wind speed in the table, you can see that the power of the propeller and its speed will approximately coincide with the parameters of the propeller, which is what we need, since it is important that the propeller is not overloaded or underloaded - otherwise it will go wrong in a strong wind. >. So with different winds I got the following propeller data

Below in the screenshot are the propeller data at 3m/s, the maximum propeller power (KIEV) at speed Z3.4. The revolutions and power in this case approximately coincide with the power of the generator at these revolutions

So with different winds I got the following propeller data. Below in the screenshot are the propeller data at 3m/s, the maximum propeller power (KIEV) at speed Z3.4. The revolutions and power in this case approximately coincide with the power of the generator at these revolutions

Generator speed 100 rpm - 2 Ampere 30 watts >

Next, we enter a speed of 5 m/s, this is, as can be seen in the screenshot, 141 rpm of the propeller and the power on the propeller shaft is 124 watts, which also approximately coincides with the generator. Generator speed 150 rpm - 8 Amperes 120 watts

At 7 m/s, the propeller begins to overtake the generator in power and, naturally, underloaded, gains high speed, so I increased the speed to Z4, and the result was also an approximate coincidence in power and speed with the generator. Generator speed 200 rpm -14 Ampere 270 watts

At 10 m/s the propeller has become much more powerful than the generator at rated speed since it is low-speed

and cannot spin the generator faster.
So with Z4 the propeller power is 991 watts, and the speed is only 332 rpm. Generator speed 300 rpm - 26 Amps 450 watts. But an underloaded generator allows the propeller to spin up to a speed of Z5 and higher, while the KIEV of the propeller drops
, and therefore the power, but at the same time the speed increases, so it turned out that the propeller will spin the generator a little more, but at the same time it will lose power and somewhere there will be balance. The data in this case will approximately coincide with the generator, but the propeller is clearly ahead of the generator in power, so in this wind it is time to make protection by moving the propeller out of the wind.

So we fitted a screw from a PVC pipe with a diameter of 160 mm to the generator. I’ll say right away that it was the six-bladed propeller of such speed that turned out to be the most suitable. And so you can consider a propeller of any diameter and number of blades. It’s just that a three-bladed propeller with a diameter of 2.3 m turned out to be too high-speed for this generator and it would not gain speed for its maximum KIEV, since the generator would immediately begin to slow it down.

Therefore, by increasing the number of blades, I lowered the propeller speed and maintained its power. So the propeller turned out to be suitable for the generator, but the 160th pipe introduced its limitations, in particular, the diameter is already too large and in a wind of 7 m/s a propeller with flimsy and thin blades will most likely get flutter and rumble like a helicopter taking off. Yes, and with this propeller we remove from the generator, roughly speaking, with a wind of 10 m/s, only 600-700 watts, but it can be twice as much if you increase the speed of the propeller and slightly increase its diameter.

Below is a screenshot from the “Blade Geometry” tab. These are the dimensions for cutting a blade from a pipe

Calculation of the diameter of generator disks

The optimal arrangement of magnets in a circle should be with a distance between magnets equal to half the width of the magnets.
I have magnets 50x30x10 mm. The width of the magnets is 30 mm, add half the width (30+15=45 mm), and multiply by 8 magnets, and divide by π(3.14). The internal diameter according to the magnets (30+15*8:π= 114.5 mm) is 114 mm. To find out the outer diameter you need to add the height of the magnets; my magnet height is 50 mm. This means (114+50+50=214 mm). Now I know the diameter of the disks, I will make the disks with a diameter of not 214 mm, but 220 mm, and add 6 mm in diameter. For example:

if you want, for example, to put 12 magnets on disks, and the magnets are 40x40x10 mm in size, then you get (40+20*12:π+40+40) diameter 309mm. Or if the magnets are 45*25*8 mm, then (45+22.5*12:π+45+45) the diameter of the disks will be 347 mm. In general, it doesn’t matter what size the magnets are, or their number in a circle, the diameter of the disks is based on the width of the magnets, and the distance between the magnets should be equal to half the width of the magnets.

I did it like this, I drew not on paper, but on a tablet. Then you will have to draw again on real disks. I think there shouldn’t be any problems with marking on the disks; we mark the disk into sectors, in my case into 8 sectors, and stick magnets on it.

>

How to make the right choice?

So what should you pay attention to when choosing a wind turbine? You should not assume that the most expensive and imported wind generator will be the best. First of all, you need to proceed not from the price, but from your needs

Before you make a purchase, calculate how much electricity you plan to use.

It is clear that you need to choose the model that is capable of generating the amount of energy you need. However, be careful. Each wind generator is designed for a specific wind speed. This means that it is capable of delivering the power declared by the manufacturer at the speed specified in the instructions for it.

If a wind turbine develops its maximum power at a wind speed of 10–12 m/s, and in your area the average does not exceed 4–5 m/s, then you should not expect the device to generate the declared amount of electricity. You'll end up paying extra money for something you don't get.

The power of a wind generator is directly dependent on the diameter of the wheel formed by the blades. With an error of 20%, it can be calculated using the formula: multiply the square of the diameter by the cube of the average wind speed and divide the resulting value by 7000. That is, with a wheel diameter of two meters and an average wind speed in your area of ​​3 m/s, you will get about 0.015 kW electricity. If the diameter is doubled, then the wind generator at the same wind speed will produce 4 times more electricity - 0.6 kW. Thus, with all other characteristics being the same, a windmill with larger blades is more productive.

It is equally important when choosing a wind generator to pay attention to the battery capacity. If you do not live in a coastal zone, then calm in your area is not uncommon. In this case, the system will run on battery power.

And it tends to discharge. Therefore, it is desirable that in addition to it there is a backup energy source

In this case, the system will operate on battery power. And it tends to discharge. Therefore, it is desirable that in addition to it there is a backup source of energy.

For this purpose, you can purchase an installation with solar panels, or connect the windmill to the network. In this case, it will only compensate for the lack of electricity if necessary.

What to consider when choosing a generator

When you decide to purchase such a useful device as a wind generator, you need to consider the following parameters:

• power of a wind generator using neodymium magnets. If your area does not have strong winds, you need a generator with low power
• Direction of the wind. If the winds often change direction, only a vertical wind generator with movable blades is suitable for you
• brand. The price of the device directly depends on the manufacturer. It should be remembered that imported goods are always more expensive than Russian analogues

Of course, first of all you need to calculate the power.