BRAUN Windturbinen GmbH

Theory of wind power

General, basics and information on wind power

General information on wind energy

Wind energy is an indirect form of solar energy. Differences in the strength of solar radiation and properties of the earth’s surface lead to different surface and air temperatures. Air pressure differences and compensatory currents (wind) are the result. The energy of these moving air masses can be used by wind turbines.
Wind turbines use part of the kinetic energy of the wind, i.e. the kinetic energy of the air mass. The kinetic energy is basically calculated by the mass and velocity of the body under consideration:

Ekin = mv2 / 2 ………. kinetic energy

The fact that part of the kinetic energy contained in the wind is used by the wind turbine reduces the speed of the air flow.

In addition to the speed, the mass of the air is also important, specifically the mass throughput that flows through a certain (rotor) area per time, the mass flow: the mass flow is the mass of air passing through a certain area per unit of time. According to the laws (mass = density * volume, i.e. mass = density * area * height (length), m = Rho * V or m = Rho * A * h), the mass flow yields:

Mass Flow = Density * Area * Velocity ( = Rho * A * v)

This is the same size in front of and behind a wind turbine, the lower speed after the turbine is compensated for by a larger area through which the wind flows.

If, in the previously mentioned formula for kinetic energy, the mass flow is now used instead of the mass, the power contained in the wind is obtained:

P = 1/2 * Rho * A * v3 ….. power contained in the wind

The prevailing wind speed is therefore of decisive importance, as its value is included in the wind power with the 3rd power.
To illustrate: a hurricane-like storm with a wind speed of 30 m/s results in a wind power (power density) of 16605 W/m2 (!), while at speeds of 5m/s there are 77 W/m2, at 1m/s 0.6 W/m2 (with an air density of 1.23 kg/m3).

However, it is not possible to use this power contained in the wind to its entirety. The ratio of the power taken from the wind to the power contained in the wind is called the power coefficient cp:

Power coefficient cp = power taken from the wind / power contained in the wind = P / PW

The best conditions result when the wind turbine reduces the wind speed to a third of its original value. In this case, it would theoretically be possible to use just under 60% (16/27 = 0.593) of wind energy. This theoretically maximum power coefficient is also referred to as Betz’s power coefficient (according to Albert Betz).

Theory of wind energy use

Wind converters use the buoyancy principle in most cases, and less often the resistance principle. Accordingly, a distinction is made between:

Buoyancy runner

These convert the lift forces generated by the rotor blades into a rotary movement. In order to achieve correspondingly high lift forces, the rotor blades must be designed as a lift profile. These result in different flow velocities and thus pressure differences on the two surfaces (suction side, pressure side) of the profile. The resulting force of this pressure difference is the buoyancy force. In addition to this desired buoyancy force, a resistance force is also created by the surface area offered to the wind in the form of the rotor blades.

Lift coefficient cA, drag coefficient cW, glide ratio

The resulting buoyancy force is proportional to the lift coefficient cA, the drag force proportional to the drag coefficient cW. According to your wishes, cA should be relatively large compared to cW. This ratio is called the glide ratio (cA/cW). Values of up to 400 can be achieved with modern rotor profiles.

Angle of attack Alpha, blade angle

The position of the rotor blades has a significant influence on the resulting forces and the power coefficient. The angle of attack alpha is the angle between the direction of inflow and the airfoil chord of the rotor blade (where the direction of inflow or the direction of the inflow velocity is the result of the vector addition of the wind speed and the rotational speed of the rotor blades). The blade adjustment angle is the angle between the rotor plane and the profile chord of the rotor blade.

For buoyancy runners, the theoretical power coefficient is just under 60% (16/27), as mentioned earlier. In practice, stocks of good investments are in the range between 0.4 and 0.5.

Examples of buoyancy rotors are the usual two- or three-bladed high-speed rotors of common wind turbines, the American wind turbine (low-speed rotor, wind rose), the Darrieus or H-Darrieus rotor or the well-known windmill.

Resistance runner

Resistance runners (intentionally and intentionally) oppose the wind and use the resulting resistance force. However, as with the Savonius rotor or a shell cross anemometer, for example, one half moves against the wind direction. This must have a lower drag coefficient cW than the other half (e.g. in open hemispheres cW = 0.34 to cW = 1.3).

The theoretical maximum power coefficient to be achieved here is 0.193, which is significantly lower than that of lift runners (0.593).

Depending on the position of the axis of rotation, a distinction is made:

Wind turbines with horizontal axis of rotation

Examples of this are the usual high-speed windmills, the American wind turbine or the old windmills. In these cases, the wind converter must be tracked according to the current wind direction (azimuth adjustment). This can be done with the help of wind vanes (control flags) for smaller turbines, or with the help of separate motor drives for larger wind turbines.

Wind turbines with vertical axis of rotation

Due to the vertical axis of rotation, no separate wind tracking is necessary. Examples are Savonius rotor, Darrieus or H-Darrieus rotor.

Locations for wind turbines

Depending on the type, intended energy yield and intended use of the wind turbine, a sufficient wind supply at the installation site is a prerequisite. The possible locations for the construction of wind turbines by private individuals are of course very much tied to the respective (local) conditions. In order to check to what extent the possible locations are suitable, the following points are helpful:

Average wind speed

This can be found in meteorological records. It represents annual mean values of wind speed. These measurements are usually carried out at a height of 10 metres. However, these values are only of limited significance, as the wind conditions that occur in each case can vary greatly with the same average values.

Relative frequency distribution

The wind speeds that occur are assigned to individual speed classes (e.g. 0-1, 1-2, 2-3,… m/s). The relative frequency of each class is given. This makes it possible to see which speeds can be calculated as a priority, so these values are more meaningful than just looking at the average wind speed.

Prevailing (main) wind direction

This is important to facilitate the orientation of the wind turbine to various obstacles such as buildings. From the main wind direction, the turbine should be flown in as unhindered as possible.

Soil roughness

This has a decisive influence on the type of flow (laminar or turbulent) and on the velocity profile (course of the wind speed as a function of the altitude above the earth’s surface). Obstacles reduce wind speeds, so the wind converter must be installed at a higher altitude. In addition, they generate turbulent flow conditions that are unsuitable for the wind turbine (care must be taken to ensure appropriate orientation or distance from obstacles).

Intended use of wind energy

Depending on the degree of dependence on the energy of the wind turbine, various flow obstacles in the surrounding area, for example, must be compensated for by appropriate mast heights. The extent to which these mast heights are permissible or subject to approval at the respective location must be clarified.

Distribution of wind supply over the course of the year

Depending on the time required for the energy, the annual distribution of the wind supply must be considered or checked. Usually, the wind supply is greater in times of less radiation, which makes it possible, for example, to combine it with the direct use of solar energy (photovoltaics, solar thermal energy).

Structure and components

Rotor

The buoyancy force generated by the rotor blades (in the case of resistance rotors, the drag force) causes the rotor to rotate. The rotor blades are mounted on the rotor hub, which is located on the rotor shaft. The rotary movement is transmitted to the gearbox via this rotor shaft.

Transmission

The gearbox is used to adapt the lower rotor speed to the higher speed required for the generator.
Smaller systems (battery chargers) are sometimes operated without a gearbox. This is possible due to the relatively high rotor speed and the use of generators with a high number of poles (e.g. 12-pole permanent magnet generators).

Generator

The generator converts the mechanical energy into electrical energy. In most cases, three-phase generators are used (asynchronous or synchronous generators).

Gondola

The nacelle (nacelle) is understood to be the enveloping construction that is mounted on the mast and contains components such as the generator and gearbox.

Control

On the one hand, the control system is the device for wind tracking, and on the other hand, the safety device in the event of excessive wind speeds (storm protection). The wind tracking is used to align the rotor exactly according to the prevailing wind direction. In the case of smaller turbines, this can be done in the form of a control flag (wind vane), in the case of larger wind turbines via a separate wind measurement system and electric motors.
The storm protection serves to protect the wind turbine. If the wind speeds are too high, the rotor is “turned out of the wind”. In the case of simple turbines, e.g. by means of a side flag, in modern and large turbines in some cases also by adjusting the rotor blades (aerodynamic brake). This changes the flow conditions and the resulting forces.

Brake

Aerodynamic brake (blade adjustment) or mechanical brake, e.g. in the form of a disc brake.

Bearing

The azimuth bearing (support bearing) enables the rotation of the wind converter for wind tracking, while the rotor bearings (main shaft bearings) accommodate the rotor shaft.

Clutch

Used to couple/decouple the generator from the gearbox.

Mast

Carries all components and lifts the rotor to a height that is adapted to the environment and wind conditions.

Plant concepts and possible applications

Wind turbines in island operation

Without a grid connection, the energy supplied by the wind turbine must be stored. In order to store the electrical energy supplied by the generator, this alternating voltage is converted into a direct voltage and an accumulator (battery) is charged with the appropriate current. This task is performed by a charge controller. It ensures that a suitable charging current flows depending on the type and size of the battery and the consideration of its current state of charge. In addition to this function of the charge, including overcharge protection, some charge controllers also take on the task of deep discharge protection. This feature increases the life of the accumulator, as most types of accumulators cannot withstand repeated over-discharge. If the charge falls below a certain value, the consumers are disconnected from the power supply. In some cases, there is also the possibility of dividing consumers according to their importance. This priority circuit only switches off “more important” consumers at a later date.

When dimensioning the wind generator, charge controller and battery, it is important to ensure that they are coordinated with each other. Furthermore, the entire design of these components must of course be chosen according to the energy demand (also broken down according to the season) and the expected wind supply. In particular, the power of the generator at the predominantly expected wind force must be taken into account (to be seen from the performance characteristics, this will be below the nominal power of the generator, especially in smaller turbines!) and in addition, the periods of calm must be bridged. This (shorter) bridging of a lack of wind supply can be achieved by sufficient storage reserves (including consideration of the efficiency of the charging process and self-discharge that takes place). The combination with a photovoltaic system (solar generator) also makes sense. Since the wind supply varies over the course of the year (it is usually lower in the summer half-year) and wind energy and radiant energy complement each other well, this combination is a good idea. Charge controllers with inputs for wind generator and solar generator are also available.

In addition to the storage of electrical energy, other variants are also conceivable, depending on the subsequent purpose of the wind energy received. Since the electrical energy supplied by the wind generator varies greatly in terms of voltage, power and frequency, it cannot be used directly for most electrical devices without prior regulation. Heating resistors are rather undemanding in this respect, a very simple control system (adjustment of the load depending on the current generator power) is sufficient. If the wind turbine, which may have been self-built, is dimensioned appropriately, this would be one of the very few exceptions in which the use of electricity for heating purposes seems to make sense. The storage of the energy would, for example, in the case of the use of cartridge heaters for a water reservoir, lie in the heat content of the storage water. Energy supply and energy demand would match well.
Another variant would be the one in which wind energy is used to pump water. If a sufficiently sized reservoir is filled with water and the water is taken from it, with a reserve for days with less wind, this water reservoir represents the reservoir. The water could possibly be pumped by a mechanically driven pump (via a rod), or by an electrically operated pump whose (wide) voltage range covers the voltages to be expected from the generator.

Grid-connected wind turbines (with switched on consumers)

These supply their consumers with energy and supply possible surpluses to the grid. To feed into the grid, appropriate equipment is required to adjust voltage, frequency and phase position (Windy Boy grid inverter). At times when the wind turbine has insufficient power, the required energy is drawn from the grid, so there is no need to store the electrical energy yourself. Energy meters balance energy fed into and withdrawn from the grid.