Wind Power and Wind Turbines  

Wind Power and Wind Turbines  

Wind Power and Wind Turbines


Wind power is the energy extracted from the wind, which is essentially moving air. Wind has kinetic energy which can be harnessed and converted to other forms, either mechanical ore electrical, which can be used to do work. Wind energy is extracted using sails and wind turbines. Early wind power technology involved the use of windmills that produced mechanical energy for running wind pumps that pumped water.  Currently, wind energy is a big renewable energy resource that delivers thousands of Giga watts of electrical energy annually to national grids globally. As a renewable energy, wind power is a clean source of energy with no negative impacts on the environment. By supplanting fossil fuels, wind energy reduces the discharge of greenhouse gases into the atmosphere, thereby reducing fuel related air-pollution. This paper focuses on wind energy technology.

The use of wind turbines is the primary method for wind power extraction for electricity generation application. Turbines are mounted on tall pillars referred to as masts. An array of wind turbines is referred to as a wind farm. Wind farms can be onshore or offshore, depending on the wind resource available and others logistics factors such as land availability and legal regulations. Onshore wind farms are cheaper to install and maintain than offshore wind due to the technical challenges posed by the marine conditions.  Nevertheless, offshore wind farms are not limited by the constraints of space. Also, the farms dot not pose any risk of harm or inconvenience to humans as there are no people living in the direct environment (AENews, n.d.).

Wind energy fluctuates with the changes in wind speeds; therefore, the generated electrical energy is relative to the wind conditions. For this reason, wind energy generation is very hard to predict. Current generation projections done in the industry are based on weather forecasts from meteorological sources. Therefore, wind energy is not considered suitable for supporting the base load in a grid system and is used to compliment other conventional energy sources such as hydro or thermal power plants (Wind Power Program, n.d.).

Wind turbines in a wind farm are interconnected and power generated from the individual turbines is fed to a main bus bar before regulation and modification in order to synchronize the power characteristics with the grid parameters. The turbines generate power at a medium voltage, usually 34.5kV, and a substation in the wind farm steps it up to a high voltage before connection to high tension transmission lines for evacuation (Renewable Energy World, n.d.).

Wind turbines

Wind turbines are aerodynamically optimized to convert kinetic energy to mechanical energy and then to electricity energy. A wind turbine system, which is placed on a tall pillar, has several components that are involved in the generation of electrical energy. The turbine blades are rotated by wind, and they in turn generate torque, a form of mechanical energy, which in turn rotates a shaft coupled to an electrical generator. In most turbines, the generator is located at the top of the pillar adjacent to the turbine blades. Wind turbines can be grouped into two major categories, the common horizontal axis wind turbine (HAWT), and the vertical axis wind turbine (VAWT).

  1. Horizontal axis wind turbine (HAWT) 


    Figure 1 above shows a typical horizontal axis wind turbine (HAWT). The rotor blades of the HAWT rotate along a horizontal axis perpendicular to their direction of rotation. Also, the individual blades can rotate on their individual axis at point 2 as shown in the diagram, an action referred to as pitching. Pitching adjusts the blades position relative to the rotor axis in order to maximize wind energy extraction (Energy.Gov, n.d.). In large turbines, dedicated pitch control gearboxes equipped with pitch drive gear motor control the pitching moments of the blades. The rotor blades are attached to a hub which transfers their rotary motion to a low speed shaft labeled 5. A gear train housed in a gear box controls the rotor input torque and speed to values suitable for the generator. The rotor speed is too low for electrical power generation with the required frequency; therefore, the rotary speed is raised by a high speed shaft, number 12 in the diagram, which has smaller gears to ensure multiple rotations per a single rotor revolution (Renewable Energy World, n.d.). Brakes in wind turbines, number 4, slow or stop rotor rotation in high winds in order to avoid damage to the turbine blades. Strong winds cause shear loading on the turbines due to differences in wind speeds at different heights above the ground. Such loading can cause fatigue failure on the blades (Energy.Gov, n.d.).

    Also, it’s important that the turbine faces the wind direction. A yawing mechanism, which consists of a yawing motor and a yawing drive, is used to rotate the rotor and the whole nacelle in a vertical axis such that the rotor is always facing the direction in which the wind is coming from.  The enhanced torque from the gear box is fed to the generator, which produces electrical energy and feeds it to drop cables within the pillar (Renewable Energy World, n.d.). A wind vane and an anemometer are used to determine the wind direction and speed, whose values are then fed to controller. The controller is responsible for the yawing and pitching actions of the turbines in line with the wind conditions for maximum power generation. The nacelle houses all the turbine components from the low speed shaft to the controller while the wind turbine tower supports the weight of the whole system and raises it to a level with steady and even wind speeds (Energy.Gov, n.d.).

    The blades of HAWT produce turbulence behind them; therefore, the rotor is always in an upwind position relative to the tower. Most commercial turbines have three blades and are operated by a computerized controller. Such a system enables for low torque ripple and high efficiencies with blade tip speeds of around 200mph. Turbine towers have a maximum length of about 90 meters and are always hollow. The bore inside the mast houses a ladder used by technicians to access the nacelle. Alternatively, some turbine nacelles are equipped with a helicopter pad that enables aerial access of the turbine (Energy Saving Trust, 2014). Turbine blades vary in length from 20 meters to 150 meters.

    1. Vertical axis wind turbines (VAWT)

    Vertical axis wind turbines (VAWT) have rotor blades that rotate along a vertical axis. The VAWTs have several advantages and disadvantages over the HAWTs. For example, the VAWTs do not require a yawing system. This makes VAWTs very appealing in regions where wind direction is constantly changing. Also, the turbines are more suitable for building integrated wind generators as they have fewer provisions for steering the rotor. In addition, the nature of the turbine allows the generator and the gear train to be placed on the ground with a single low speed shaft between the rotor and gear train (Energy Saving Trust, 2014). However, the VAWTs have several drawbacks that limit their applications. For example, VAWTs have very low rotational speeds which translate to very high torque. Therefore, heavy investment is necessitated for a robust gear transmission train. Also, the rotor rotates at 360 degrees within the flowing wind. As a result, there are dynamic and cyclic stresses imposed on the rotor blades which results in early fatigue failures. Other problems exhibited by the VAWTs include pulsating torque and the unavailability of accurate wind flow models due to the difficulty of analyzing and designing efficient rotor prototypes.

    VAWTs can further be classified into three categories: Darrieus, Giromill, and Savonious wind turbines (Energy Saving Trust, 2014). The VAWTs have low efficiency and capacity than HAWTs and therefore they are not commercially used.

    1. Wind turbine operation

    Operation of wind turbines and the amount of power generated depends on the available wind speeds. The turbines are set to operate when the wind speed reaches a certain threshold and to go stop when wind speed extend past a given limit. The generated power is directly proportional to the wind speed. Therefore, a wind turbine generation curve starts at the cut in speed and steadily rises up to the cut out speed where generation stops.

    Figure 2: Wind turbine power generation curve (Wind Power Program, n.d.).

As shown in figure 2 above, most turbines have a cut in speed of around 3m/s and a cut out speed of about 25m/s. Winds with speed below the cut-in speed have very low energy and as such cannot rotate the rotor blades. When the wind speed rises above the cut in level, the controller actuates the system to operate. At wind speeds above the cut-out value, the brakes kick in bringing the rotor to a stop.  Soon after the cut-in speed is achieved, the generated power rises rapidly as shown by the figure 6 above. At wind speed as about 12 to 17m/s, the power output is equal to the rated capacity of the generator and therefore the generation curve flattens out. The speed at which the rated power output is achieved is referred to as the rated output wind speed.  After this rated power output is reached, the turbine control system adjusts itself to lower the impact of the wind on the blades and hence reduce the speed of rotation. In most turbine designs, this is done through blade pitching.  

  1. Betz law and the turbine efficiency

Albert Betz was a German physicist who defined the limit of energy conversion by a wind turbine as 59.3%.  Betz postulated that according to the laws of conservation of mass and energy, the maximum amount of kinetic energy that can be extracted from wind is no more than 59.3% or 16/27 of the total available energy. Using modern computerized turbine modeling, the Betz limit can be raised by 70 to 80% of its initial value.

From the Betz limit, a Betz law was formulated. The Betz law is used to calculate maximum amount of power that can be drawn from wind by a turbine operating in open flow conditions. The Betz law assumes the use of a standard turbine design and that the results are not influenced by superior or inferior turbine performance. In studying the Betz law, the behavior of air flowing through an “actuator disk” in regard to conservation of mass and the resulting momentum after energy has been extracted from the wind stream (Wind Power Program, n.d.).

In calculation of the Betz limit, it’s assumed that air behind the turbine must keep moving for more wind to be admitted to the turbine. If 100% of the wind energy was extracted, the air movement would stop as soon as it’s discharged from the turbine hence no more wind would run through the turbine and consequently energy extraction would stop. The other argument is that a considerable amount of the kinetic energy would be used to push a static column of air stalled behind the turbine. Therefore, wind has to keep moving in the upwind and downwind sides of the turbine. Betz showed that when energy is extracted from wind, it slows down and spreads over a wider area as it exits the turbine sweep. Hence, geometry rules limit the maximum turbine efficiency to 59.3 (Wind Power Program, n.d.).

The Betz limit is used in assessing wind farm sites. This is because the law sets an upper limit on the amount of energy that can be possibly generated from a given site with hypothetical wind conditions. When the wind data for a given location is obtained, the theoretically generation capacity cannot be higher than the Betz limit. Therefore, the capacity factor of wind power that can possibly be extracted from a site ranges from 25 to 60% of the possible theoretical generation capacity at constant wind speeds throughout the year. Hence, the actual energy that can be obtained from a site lowers to a range of 14.8% to 35% of the total wind resource (Wind Power Program, n.d.).

To determine the economic viability of a wind farm site, energy production is assessed per unit area of the total area swept by the rotor. A high energy yield per unit area lowers the cost of power production. Hence, efficient energy capture devices lower the cost of power production and raise the profitability of the project. The efficiency of the energy capture devices such as turbines can be raised by optimizing design parameters to wind conditions in a specific site. Increasing system efficiency to the upper levels of the Betz limit lowers per unit cost of power production.

  1. Derivation of the Betz law equation

Using the principle of conservation of mass and energy, the Betz law can be mathematically derived. Several assumptions are made during the derivation in order to hypothesize ideal aerodynamic conditions.


  1. The rotor is infinitely thin and is in the form of a disc that draws energy from wind passing within its cross-section area.
  2. Wind behind the disc travels at a reduced speed than wind in the upstream side.
  3. The turbine rotor does not have a hub and has an infinite number of blades with no drag at all.
  4. The wind flow in turbine is axial and the volume flow rate is controlled whereby the air volume entering and leaving the turbine is accounted for.
  5. The air is incompressible and therefore density remains constant. Also, the air does not transmit heat.
  6. The hypothetical disc has uniform thrust over its surface

Principle of conservation of mass

Figure 9: Betz theoretical flow tube. The turbine disc is at the middle of the tube represented by the shaded part (Wind Power Program, n.d.).

According to figure 9 above, the mass flow rate can be given as:

preservation of mass

Where V1 and V2 are the upstream and downstream wind velocities respectively, M is the mass flow rate and V is the velocity of the rotor disc, ρ the density of air, S the area of sweep of the turbine rotor and A1 and A2 are the cross-section area of the fluid directly before and after running through the turbine.

According to the principle of mass conservation, the density multiplied by the cross-section area and the  speed of flow at the three points in the tube should all be the same.

The force due to the action of wind on the turbine can be given as mass multiplied by acceleration from Newton’s laws of motion.





Where m is the mass flow rate

From the equation above, the thrust generated at the turbine is equal to the acceleration multiplied the air density, speed of wind at the turbine, and the area swept by the rotor blades.

  1. Calculation of power generated by a turbine

The force generated by the wind at the turbine does work when it runs the generator and produces power.

The work done by a wing gust can be given as:

Power is the rate of doing work, hence:

The force equation can be merged with the power equation as:

Alternatively, power developed can be computed from the kinetic energy of the wind:

The mass flow rate can me merged with the above equation to simplify it to:

From the above equations, power has been expressed in two ways, as a derivative of the wind force and the kinetic energy. Both of these expressions are mathematically valid and as such, they can be equated to each other as:

From the expression above, a certain relationship can be derived between the velocities on both sides of the equation as:


Therefore the speed of wind through the air tunnel at the rotor can be given as:


This means that velocity of wind going through the rotor is a mean of wind speed before and after it hits the rotor blades.

  1. Mathematical derivation of the Betz law

The above rotor wind speed expression and the kinetic energy equation can be used to mathematically prove the validity of the Betz law. These two equations can be merged to give:

The right side of the equation above can be expanded to give:

When the kinetic field E is differentiated with respect to speeds

for wind speed V1 and rotor area S, it is found out that E maximum value is obtained when the ration

The ratio can be substituted to the power equation to give:

Where Cp is the power coefficient of a turbine that can alternatively be given as:



The power coefficient describes the efficiency of turbine and has a maximum value of 16/27 or 0.593 which is expressed as 59.3%.

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