(Technology and Economics)
The wind is a source of free energy which has been used since ancient times in windmills for pumping water or grinding flour. The technology of high power, geared transmissions was developed centuries ago by windmill designers and the fantail wheel for keeping the main sales pointing into the wind was one of the world's first examples of an automatic control system.
Though modern technology has made dramatic improvements to the efficiency of windmills, they are still dependent on the vagaries of the weather. Not just on the wind direction but on the intermittent and unpredictable force of the wind. Too little wind and they can't deliver sufficient sustained power to overcome frictional losses in the system. Too much and they are susceptible to damage. Between these extremes, cost efficient installations have been developed to extract energy from the wind.
- Theoretical Power
The power P available in the wind impinging on a wind driven generator is given by:
P = ½CAρv3
where C is an efficiency factor known as the Power Coefficient which depends on the machine design, A is the area of the wind front intercepted by the rotor blades (the swept area), ρ is the density of the air (averaging 1.225 Kg/m3 at sea level) and v is the wind velocity.
Note that the power is proportional to area swept by the blades, the density of the air and to the cube of the wind speed. Thus doubling the blade length will produce four times the power and doubling the wind speed will produce eight times the power.
Note also that the effective swept area of the blades is an annular ring, not a circle, because of the dead space around the hub of the blades.
A similar equation applies to the theoretical power generated by a "run of river" and "tidal flow" hydro turbines.
- Practical Power and Conversion Efficiency
German aerodynamicist Albert Betz showed that a maximum of only 59.3% of the theoretical power can be extracted from the wind, no matter how good the wind turbine is, otherwise the wind would stop when it hit the blades. He demonstrated mathematically that the optimum occurs when the rotor reduces the wind speed by one third. After inefficiencies in the design and frictional losses are taken into account the practical power available from the wind will rarely exceed 40% of the theoretical power.
Converting this wind power into electrical power incurs further losses of 10% or more in the drive train and the generator and another 10% in the inverter and cabling such that ultimately, the wind turbine will capture only about 30% to 35% of the wind energy available.
Note that the power output from commercially available wind turbines is usually specified at a steady, gust free, wind speed of 12.5 m/s. (Force 6 on the Beaufort scale corresponding to a strong breeze)
In the many locations, particularly urban installations, the prevailing wind will rarely reach this speed.
- Yaw Control
Windmills can only extract the maximum power from the available wind when the plane of rotation of the blades is perpendicular to the direction of the wind. To ensure this the rotor mount must be free to rotate on its vertical axis and the installation must include some form of yaw control to turn the rotor into the wind.
For small, lightweight installations this is normally accomplished by adding a tail fin behind the rotor in line with its axis. Any lateral component of the wind will tend to push the side of the tail fin causing the rotor mount to turn until the fin is in line with the wind. When the rotor is facing into the wind there will be no lateral force on the fin and the rotor will remain in position. Friction and inertia will tend to hold it in position so that it does not follow small disturbances.
Large turbine installations have automatic control systems with wind sensors to monitor the direction of the wind and a powered mechanism to drive the rotor into its optimum position.
- Capacity Factor
Electrical generating equipment is usually specified at its rated capacity. This is normally the maximum power or energy output which can be generated in optimal conditions. Since a wind turbine rarely works at its optimal capacity the actual energy output over a year will be much less than its rated capacity. The capacity factor is simply the wind turbine generator's actual energy output for a given period divided by the theoretical energy output if the machine had operated at its rated power output for the same period. Typical capacity factors for wind turbines range from 0.25 to 0.30. Thus a wind turbine rated at 1 MegaWatt will deliver on average only about 250 kiloWatts of power. (For comparison, the capacity factor of thermal power generation is between 0.70 and 0.90)
- Wind speed
Though the force and power of the wind are difficult to quantify, various scales and descriptions have been used to characterise its intensity. The Beaufort scale is one measure in common use. The lowest point or zero on the Beaufort scale corresponds to the calmest conditions when the wind speed is zero and smoke rises vertically. The highest point is defined as force 12 when the wind speed is greater than 34 metres per second (m/s) or 75 m.p.h. as occurs in tropical cyclones when the countryside is devastated by hurricane conditions.
Wind turbines generally operate between force 3 and force 7 on the Beaufort scale with the rated capacity commonly being defined at force 6 with a wind speed of 12m/s.
Below force 3 the wind turbine will not generate significant power.
At force 3, wind speeds range from 3.6 to 5.8 m/s or 8 to 13 m.p.h. Wind conditions are described as "light" and leaves are in movement and flags begin to extend.
At force 7, wind speeds range from 14 to 17 m/s or 32 to 39 m.p.h. Wind conditions are described as "strong" and whole trees are in motion.
With winds above force 7 the wind turbine should be shut down to prevent damage.
- Wind Consistency
Wind power has the advantage that it is normally available 24 hours per day, unlike solar power which is only available during daylight hours. Unfortunately the availability of wind energy is less predictable than solar energy. At least we know that the sun rises and sets every day. Nevertheless, based on data collected over many years, some predictions about the frequency of the wind at various speeds, if not the timing, are possible.
- Wind Speed Distribution
Care should be taken in calculating the amount of energy available from the wind as it is quite common to overestimate its potential. You can not simply take the average of the wind speeds throughout the year and use it to calculate the energy available from the wind because its speed is constantly changing and its power is proportional to the cube of the wind speed. (Energy = Power X Time). You have to weigh the probability of each wind speed with the corresponding amount of energy it carries.
Experience shows that for a given height above ground, the frequency at which the wind blows with any particular speed follows a Rayleigh Distribution. An example is shown below.
- The modal wind speed, that is the the speed at which the wind most frequently blows, is less than the average wind speed which is the speed often quoted as representing the typical wind conditions. For reference, the average wind speed across the UK quoted by the Department of Trade and Industry (DTI), is approximately 5.6 metres per second [m/s] at 10 metres above ground level (agl)."
- Published average wind speeds are only reliable for open rural environments. Wind speeds just above roof level in urban environments will be considerably less than the quoted averages because of turbulence and shielding caused by buildings and trees. A wind turbine sited below the ridge of a building or at a similar height in the garden of an urban dwelling as often shown in the product sales literature is unlikely to provide the energy levels claimed in the specifications.
- The distribution does not represent the energy content of the wind since this is proportional to the cube of the wind speed.
- A distribution such as the one above is only valid for the prevailing wind conditions at a particular height above the ground. Average wind speeds usually tend to increase with height then level off which is why wind turbines are usually installed as high above ground as possible.
An empirical formula developed by D.L. Elliott of Pacific Northwest Labs gives the wind speed V at a height H above ground level as
V = Vref ( H / Href )α
Where Vref is the reference wind speed at a reference height Href and the exponent α is a correction factor dependent on obstacles on the ground, the density of the air and wind stability factors. In wind resource assessments α is commonly assumed to be a constant 1/7th . The histogram below shows this relationship.
Wind Energy Distribution
The histogram below shows the resulting distribution of the wind energy content superimposed on the the Rayleigh wind speed distribution (above) which caused it. Unfortunately not all of this wind energy can be captured by conventional wind turbines.
- The peak wind energy occurs at wind speeds considerably above both the modal and average wind speeds since the wind energy content is proportional to the cube of its speed.
- Very little energy is available at low speeds and most of this will be needed to overcome frictional losses in the wind turbine. Energy generation typically does not cut in until wind is blowing at speeds of at least 3 m/s to 5 m/s.
- High wind speeds cause high rotation speeds and high stresses in the wind turbine which can can result in serious damage to the installation. To avoid these dangerous conditions, wind turbines are usually designed to cut out at wind speeds of around 14 m/s either by braking or feathering the rotor blades allowing the wind to spill over the blades.
- Because of the upper speed limit at which the wind turbine can safely be used, it may capture only half or less of the available wind energy.
For a given wind speed the wind energy also depends on the elevation of the wind turbine above sea level. This is because the density of the air decreases with altitude and the wind energy is proportional to the air density. This effect is shown in the following histogram.
- For a given wind speed the wind energy density decreases with increases in altitude. However at the same time the actual wind speeds tend to increase with height above ground level. Since the wind energy is proportional to the cube of the wind speed, the net effect is that wind energy tends to increase with the height above ground level.
- As the density of air decreases with altitude, the wind energy density also decreases. By contrast the available solar energy increases with altitude due to lower atmospheric absorption.
- Location Considerations
Generally marine locations and exposed hilltops provide the most favourable wind conditions with wind speeds consistently greater than 5 m/s.
Turbulent conditions will reduce the amount of energy which can be extracted from the wind reducing in turn the overall efficiency of the system. This is more likely to be the case over land than over the sea. Raising the height of the turbine above the ground effectively lifts it above the worst of the turbulence and improves efficiency.
Domestic wind turbines located between buildings in urban environments rarely operate at peak efficiency suffering from turbulence as well as being shielded from the wind by buildings and trees.
Large scale wind turbine generators of up to 5 MWe or more with rotor diameters of up to 120 metres are now functioning in many regions of the world.
A typical system employs a fixed speed rotor with three variable pitch blades which are controlled automatically to maintain a fixed rotation speed for any wind speed. The rotor drives a synchronous generator through a gear box and the whole assembly is housed in a nacelle on top of a substantial tower with massive foundations requiring hundreds of cubic metres of reinforced concrete.
Source US DOE (EERE)
Large rotor blades are necessary to intercept the maximum air stream but these give rise to very high tip speeds. The tip speeds however must be limited, mainly because of unacceptable noise levels, resulting in very low rotation speeds which may be as low as 10 to 20 rpm for large wind turbines. The operating speed of the generator is however is much higher, typically 1200 rpm, determined by the number of its magnetic pole pairs and the frequency of the grid electrical supply. Consequently a gearbox must be used to increase the shaft speed to drive the generator at its synchronous speed.
Grid connected systems are dimensioned for average wind speeds 5.5 m/s on land and 6.5 m/s offshore where wind turbulence is less and wind speeds are higher. While offshore plants benefit from higher sustainable wind speeds, their construction and maintenance costs are higher.
Grouping 10 to 100 wind turbines together in so called "wind farms" can lead to savings of 10% to 20% in construction, distribution and maintenance costs.
According to NREL the"footprint" of land needed to provide space for turbine towers, roads, and support structures is typically between 0.1 and 0.2 hectares (0.25 and 0.50 acres) per turbine. With the typical capacity of the current generation of wind turbines being around 2 MW, it would take a wind farm with 2000 wind turbines covering up to 200 hectares (1000 acres) just to replace the power generated by the UK's Drax coal fired power station.
Domestic Wind Turbine Installations
In a typical domestic system the wind turbine is coupled directly to a three phase asynchronous permanent magnet AC generator mounted on the same shaft. To save on capital costs, domestic installations do not have variable pitch rotor blades so the rotor speed varies with the wind speed. The generator output voltage and frequency are proportional to the rotor speed and the current is proportional to the torque on the shaft. The output is rectified and fed through a buck-boost regulator to an inverter which generates the required fixed amplitude and frequency AC voltage.
Note: There is possible confusion in the classification of the generator. It is actually a synchronous generator because the frequency of its output is directly synchronised with the rotor speed. In this application however it is called an asynchronous generator because the output frequency of the generator is not synchronised with the mains/utility frequency.
- Urban Installations
Wind turbine blade sizes in urban applications are usually limited for practical reasons to less than about 1 metre (2 metres diameter) as well as by local planning ordinances and for similar reasons the height of the turbine above ground is limited to just above rooftop level but below treetop level.
A typical domestic installation with a 1.75m swept diameter, (swept area of 2.4m2), costs around £1500 ($2250). At the rated wind speed of 12.5m/s (28 mph) the wind power intercepted will be 2870 Watts, but after taking into account all the unavoidable system losses, the actual electrical output power will be around 1000 Watts. However this is at the upper end of the performance possibilities. Wind turbulence and shielding due to buildings and trees inhibits sustained strong, gust free wind flow and in any case, for most of the time, the wind speed will more likely be towards the lower end of the performance specification at 4 m/s (9 mph), that is a light breeze. At this speed the power output of the system will be about 32 Watts - Not enough to power a single light bulb. For much of the time the power generated could be less than the quiescent power drain of the inverter.
Running with a constant power output of 32 Watts for a full year would generate only 280 kWh (280 Units) of electrical energy worth £28 at todays price of £0.10 ($0.15) per kWh. To put it into perspective, a typical UK household consumes about 5,000 kWh of electrical energy per year.
Because the system is connected directly to the grid there is no need for battery back-up and in any case the cost of the batteries would make an already weak economic case for the system even weaker. See also Grid Connected Systems
Thus small domestic rooftop wind turbine installations do not make a serious contribution to the household energy supply.
Self sufficiency and selling surplus energy back to the utility are out of the question and the payback period on the capital investment is out of sight.
- Carbon Footprints
As with solar power, if the investment fails the conventional economic tests, the notion of carbon footprints is often used to jusify the expense, based on the potential for reducing the amount of greenhouse gases emitted by alternative methods of power generation.
- Rural Installations
The economics of rural and remote locations make wind power more attractive than for urban locations. Because of the remoteness, connection to the electricity grid may be impossible or prohibitively expensive. Furthermore, larger, more efficient wind power installations are possible and the prevailing winds will also be higher. See also Stand Alone Systems
- Hybrid Installations
Hybrid systems combining wind and solar power provide energy diversity reducing the risk of power outages. Wind speeds are often high in the winter when the available solar energy is low and low in the summer when the available solar energy is high.
Hybrid systems are discussed in more detail in the section on Remote Area Power Systems
Wind power provides a valuable complement to large scale base load power stations. Where there is an economic back-up, such as hydro power or large scale storage batteries, which can be called upon at very short notice, a significant proportion of electricity can be provided from wind.
See also Generators
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