CONVERSION OF WIND ENERGY TO ELECTRICAL ENERGY

  There is the further complication  of boundary layer frictional effects between the moving air and earth’s rough surface. Mountains, trees, buildings and similar obstructions impair stream line air flow. Turbulence results, and wind velocity in a horizontal direction markedly increases with altitude near the surface.
        Then there is the obvious fact of land and water with their unequal solar absorptive and thermal time constants. During day light the land heats up rapidly compared to nearby sea or water bodies, and there tends to be a surface wind flow from the water to the land.  At night the wind reverses, because the land surface cools faster than the water.

        Local winds are caused by two mechanisms. The first is differential heating of land and water. Solar insolation during the day is readily converted to sensible energy of the land surface but is partly absorbed in layers below the water surface and partly consumed in evaporating some of that water. The land mass becomes hotter than the water, which causes the air above the land to heat up and become warmer than the air above water. The warmer lighter air above the land rises, and the cooler heavier air above the water moves into replace it.  This is the mechanism of shore breeze.  At night, the direction of the breezes is reversed because the land mass cools to the sky more rapidly than the water, assuming a clear sky. The second mechanism of local winds is caused by hills and mountain  sides.

         The air above the slopes heats up during the day and cools down at night, more rapidly than the air above the low lands.  This causes heated air the day to rise along the slopes and relatively cool heavy air to flow down at night.
        It has been estimated that 2 percent of all solar radiation falling on the face of the earth is converted to kinetic energy in the atmosphere and that 30  per cent of this kinetic energy occurs in the lowest 1000m of elevation.  It is thus said that the total kinetic energy of the wind in this lowest kilometer, if harnessed, can satisfy several times the energy demand of a country.  It is also claimed that the wind power is pollution free and that its source of energy is free.  Such are the seemingly compelling arguments for wind power, not unlike those for solar power.  Although solar energy is cyclic and predictable, and even dependable in some parts of the globe, wind energy, however, is erratic, unsteady, and often not reliable, except in very few areas.  It does, however, have a place in the total energy picture, particularly for those areas with more, or less steady winds, especially those that are far removed from central power grids, and for small, remote domestic and farm needs.
        Conversion of the kinetic energy (i.e., energy of motion) of the wind into mechanical energy  that can be utilize to perform useful work, or to generate electricity.  Most machines for converting wind energy into mechanical energy consist basically of a number of sails, vanes or blades radiating from a hub or central axis. 

The axis may be horizontal, as in the more familiar windmills, or vertical, as it is in some cases.  When the wind blows against the vanes or sails they rotate about the axis and the rotational motion can be made to perform useful work.       
 Wind energy conversion devices are commonly known as Wind turbines because they convert the energy of the wind stream into energy of rotation:  The component which rotates is called the rotor.  The terms turbine and rotor are, however, often regarded as being synonymous.
        Because wind turbines produce rotational motion, wind energy is readily converted into electrical energy by connecting the turbine to an electric generator.
 The combination of wind turbine and generation is some times referred to as an aero generator.  A step-up transmission is usually required to match the relatively slow speed of the wind rotor to the higher speed of an electric generator.
        Although windmills have been used for more than a dozen centuries for grinding grain and pumping water, interest in large scale electric power generation has developed over the past 50yrs.  A largest wind generator built in recent times was the 800 kWe unit operated in France from 1958-1960.  The flexible 3 blades propeller was about 35m in diameter and produced the rated power in a 60 km/hour wind with a rotation speed of 47 rpm.  The maximum power developed was 12  MWe. 
        Wind energy is one of American’s greatest natural resources.  The U.S. government could plan for installation of wind turbine generators with a total capacity of 1 GW by 1985. 

 

and will not be available in many such areas due to the high cost of generation and distribution to small dispersed users. Secondly there is possibility of reducing the costs of the windmills by suitable design. Lastly, on small scales, the total first cost for serving a felt need and low maintenance costs are more important  than the unit cost of  energy. The last point  is illustrated easil: dry cells  provide energy  at the astronomical cost of about Rs. 300 per kWh and yet they are in common use in both rural and urban areas.  This raises the question of that the felt needs are that a windmill might satisfy while large scale energy production at some favourable sites in India is a possibility that needs to be explored, there appears to be a definite need for small sources of mechanical energy in rural areas.  For example, even casual polls among villagers quickly reveal that their first concern is invariable water for drinking, washing and irrigation; and lifting water is a task which a windmill can perform.  For such a task, a windmill should produce about 100 W, considering that a pair of bullocks, often used for lifting water in villages, typically provides about 250 W power.  Many projects on windmill systems for water pumping and for production of small amount of electrical power have been taken up by various organisers, such as National aeronautical laboratory Bangalore, central salt and Marine Chemicals Research Institute Bhavnagar, Central Arid Zone Research Institute (CAZRI) Jodhpur etc.

        Wind energy offers another source for pumping as well as electric power generation.  India has potential of over 20,000 MW for power generation and ranks as one of the promising countries for tapping this source.  The cost of power generation from wind farms has now become lower than diesel power and comparable to thermal power in several areas of our country especially near the coasts.  Wind power projects of aggregate capacity of 8 MW including 7 wind farms projects of capacity 6.85 MW have been established in different parts of the country of which 3 MW capacity has been completed in 1989 by DNES.  Wind farms are operating successfully and have already fed over 150 lakh units of electricity to the respective state grids. Over 25 MW of additional power capacity from wind is under implementation.  Under demonstration programme 271 wind pumps have been installed upto February 1989.  Sixty small wind battery chargers of capacities 300 watts to 4 kW are under installation.  Likewise to stand-alone wind electric generators of 10 to 25 kW are under installation.

        Despite the wind’s intermittent nature, wind patterns at any particular site remain remarkably constant year by year.  Average wind speeds are greater in hilly and coastal areas than they are well inland.  The winds also tend to blow more consistently and with greater strength over the surface of the water where there is a less surface drag.
        Wind speeds increase with height.  They have traditionally been measured at a standard height of ten metres where they are found to be 20 – 25% greater than close to the surface.  At a height of 60m they may be 30 – 60% higher because of the reduction in the drag effect of the earth’s surface.


 THE POWER IN THE WIND
        Wind possesses energy by virtue of its motion.  Any device capable of slowing down the mass of moving air, like a sail or propeller, can extract part of the energy and convert is into useful work.  Three factors determine the output from a wind energy converter:
        (i)  The wind speed;
        (ii)  The cross-section of wind swept by rotor; and
        (iii)  The overall conversion efficiency of the rotor, transmission system and generator or pump.

        No device, however, well designed, can extract all of the wind’s energy because the wind would have to be brought to a halt and this would prevent the passage of more air through the rotor.  The most that is possible is for the rotor to decelerate the whole horizontal column of intercepted air to about one-third of its free velocity. A 100% efficient aero generator would therefore only be able to convert up to a maximum of around 60% of the available energy in wind into mechanical energy.  Well-designed blades will typically extract 70% of the theretical maximum, but losses incurred in the gearbox, transmission system and generator or pump could decrease overall wind turbine efficiency to 35% or loss.

        The power in the wind can be computed by using the concept of kinetics.  The wind mill works on the principle of converting kinetic energy of the wind to mechanical energy.  We know that power is equal to energy per unit time.  The energy available is the kinetic energy of the wind.  The kinetic energy of any particle is equal to one half its mass times the square of its velocity, or ½ mV².  The amount of air passing in unit time, through an area A, with velocity V, is A.V, and its mass m is equal to its volume multiplied by its density p of air, or

                        m = pAV

      (m is the mass of air transversing the area A swept by the rotating blades of a wind mill type generator).

      Substituting this value of the mass in the expression for the kinetic energy, we obtain, kinetic energy = ½ pAV.V² watts

                        = ½ pAV³  watts

                                                        ….(6.2.2)

 

        Equation (6.2.2) tells us that the maximum wind available the actual amount will be somewhat less because all the available energy is not extractable – is proportional to the cube of the wind speed.  It is thus evident that small increase in wind speed can have a marked effect on power in the wind.

        Equation (6.2.2) also tell us that the power available is proportional to air density (1.225 kg/m³ at sea level).   It may vary 10-15 percent during the year because of pressure and temperature change.  It changes negligibly with water content.  Equation also tells us that the wind power is proportional to the intercept area.  Thus an aeroturbine with a large swept area has higher power than a smaller area machine; but there are added implications.  Since the area is normally circular of diameter D in horizontal axis aeroturbines, then A = й   D², (sq.m),

                     4

       which when put in equation (6.2.2) gives

       Available wind power Pa = ½ p = й   D² V³  watts

                                                              4

                                 = 1/8 pй   D² V³                   

        The equation tells us that the maximum power available from the wind varies according to the square of the diameter of the intercept area (or square of the rotor diameter), normally taken to be swept area of the aeroturbine.  Thus doubting the diameter of the rotor will result in a four-fold increase in the available wind power.  Equation (6.2.3) gives us in sight into why the designer of an aeroturbine for wind electric use would place such great emphasis on the diameter.  The combined effects of wind speed and rotor diameter variations are shown in Fig. 6.2.1.   Wind machines intended for generating substantial amounts of power should have large rotors and be located in areas of high wind speeds.  Where low or moderate powers are adequate, these requirements can be relaxed.


             Dependence of wind-rotor power in wind speed and rotor diameter.

        The physical condition in a wind turbine are such that only a fraction of the available wind power can be converted into useful power.  As the free wind stream encounters and passes through a rotor, the wind transfer some of its energy go the rotor and its speed decreases to a minimum in the rotor wake.  Subsequently, the wind stream regains energy from the surrounding air and at a sufficient distance from the rotor the free wind speed is restored (Fig. 6.2.2 upper curve).  While the

wind speed is decreasing, as just described, the air pressure in the wind stream changes in a different manner (Fig 6.2.2, lower curve).  It first increases as the wind approaches the rotor and then drops sharply by an amount Δp as it passes through and energy is transferred to the rotor.  Finally the pressure increases to the ambient atmospheric pressure.
        The power extracted by the rotor is equal to the product of the wind speed as it passes through the rotor (ie. Vr in Fig. 6.2.2) and the pressure drop.  Δp.  In order to maximize the rotor power it would therefore be desirable to have both wind speed and pressure drop as large as possible.  However, as V is increased for a given value of the free wind speed (and air density), Δp increases at first, passes through a maximum, and then decreases.  Hence for the specified free-wind speed, there is a maximum value of the rotor power.
        The fraction of the free-flow wind power that can be extracted by a rotor is called the power-coefficient; thus
                                                     Power of wind rotor____              
                                            Power of available in the wind

 

      where power available is calculated from the air density, rotor diameter, and free wind speed as shown above.  The maximum theoretical power coefficient is equal to 16/27 or 0.593.  This value cannot be exceeded by a rotor in a free-flow wind stream.  (It can be exceeded under specific conditions, as will be seen later).

        As an ideal rotor, with propeller-type blades of proper aerodynamic design, would have a power coefficient approaching 0.59.  But such a rotor would not be strong enough to with stand the stresses to which it is subjected when rotating at a high rate in a high-speed wind stream.  For the best practical rotors, the power coefficient is about) 0.4 to 0.45, so that the rotors cannot use more that 40 to 45 percent of the available wind power.  In the conversion into electric power, some of the rotor energy is lost and overall electric power, coefficient of an aero generator (i.e.. Electric power generated/available wind power) in practice is about 0.35 (35 percent).

        Returning to equation (6.2.2), but now recognizing that V, in actuality, is not constant but is represented by a statistically ‘noisy’ wind speed time curve, V (t), then the instantaneous power, in the wind would be

                Pa(t) = ½ pA(V(t)³ watts

                                                …(6.2.4)

        Since we are normally more interested in average power, we must time average both sides of equation (6.2.4), signified by the bar below

                  
                  
                   Pa(t) = ½ pA[V(t)]3 watts                                           …(6.2.4)

        Equation (6.2.5) tells us that for a non-steady state wind, it is necessary to cube the measured wind speeds and then take the average to find the average wind power available.  It is immediately obvious that this non-steady state case is more complex than the simple steady state case, and it is why for the former case such great emphasis is placed on anemometry data at a proposed wind energy conversion system (WECS) site.
       
Transposing equation (6.2.5) results in

                Pa(t) = ½ p[V(t)]³ watts/m²                                           …(6.2.6)
                 A
which says that the average available wind power per unit area is directly related to the average of the wind speed cubed.  This is one useful method of characterizing the potential specific power available in the wind over geographic area.
        There are clear advantages in selecting sites with annual mean wind speeds and building larger rather than smaller wind generators since:
        (a) the power available in the wind increases as cube of the wind speed: doubling the wind speed increases the power available by eight-fold; and

        (b) doubling  the diameter of the turbine’s rotor quadruples the swept area and hence the power output from the device (this law only applies to horizontal axis machines, for vertical axis machines the change in power output with diameter will be determined by the geometry of the rotor).
        The way rotor diameter and wind speed affect power output can be seen in Fig. 6.2.1.
        In practice a wind turbine’s output will vary.  There will be periods when there is insufficient wind for the machine to generate any power at all, and times when the wind speeds are so high that the machine has to be shut down to prevent damage.
        Maximum power.  As stated above, that the total power can not be converted to mechanical power.  Consider a horizontal-axis, propeller-type windmill, henceforth to be called a wind turbine, which is the most common type used today assume that the wheel of such in turbine has thickness a b, as shown in Fig. 6.2.3. Let pi and Vi are the wind pressure and velocity at the upstream of the turbine,  and P e and Ve  are pressure and velocity at downstream of the turbine.  Ve is less than Vi because kinetic energy is extracted by the turbine.

        Considering the incoming air between i and a as  thermodynamic system, and assuming that the air density remains constant (since changes in pressure and temperature are very small compared to ambient ), that the potential energy is zero, and no heat or work are added or removed between i and a, the general energy equation reduces to the kinetic and flow energy – terms only:
 

Thus               Piv + Vi²  = Pau + Va²
                          2gc           2gc                                                                   (6.2.7a)
(The general energy equation for steady state flow for unit mass (for a control volume) is:
Z1 + V1² + u + P1u1 + Δq = Z₂ + V2²  + u₂ + p₂u₂ + ΔWsf
         2g                                     2g  
Where    Z1  = potential energy
       V²  = kinetic energy
               2g
        u   =  internal energy
       pu  =  flow energy
        Δq = not heat added
        ΔW sf = net steady flow mechanical workdone of the system]
or
              p1 + p  V1²  = Pa +  p Va²
                                        2gc                 2gc                              (6.2.7b)
where u and p are the specific volume and its reciprocal, the density, respectively, both considered to be constant.
      

Similarly for the exist region be,
        Pr + p Ve²  = pb + p Vb²
                    2gc                2gc
        The wind velocity across the turbine decreases from a to b since kinetic energy is converted to mechanical work there.  The incoming velocity Vi does not decrease abruptly but gradually as it approaches the turbine to Va and as it leaves it to Ve.  The Vi > Va and Vb > Ve, and therefore, from equations (6.2.7) and (6.2.8), Pa > Pi; that is the wind pressure rises as it approaches, then as it leaves the wheel.  Combining these equations,
Pa – Pb = [Pi + p Vi²  – Va² ]  - [Pe + p Ve²  – Vb²  ]
                                     2gc                               2gc
    It can be assumed that wind pressure at e can be assumed to ambient, i.e.,
                        Pe = Pi
        As the blade width a.b is very thin as compared to total distance considered, it can be assumed that velocity within the turbine does not change much.
        Va – Vt = Vb
Combining equation (6.2.9) to (6.2.11) yields,

REFERENCES

 

 A Wind Energy Pioneer: Charles F. Brush. Danish Wind Industry Association. Retrieved 2008-12-28.

 Quirky old-style contraptions make water from wind on the mesas of West Texas Archived February 3, 2008, at the Wayback Machine.

 Alan Wyatt: Electric Power: Challenges and Choices. Book Press Ltd., Toronto 1986, ISBN 0-920650-00-7

 Anon. "Costa Head Experimental Wind Turbine". Orkney Sustainable Energy Website. Orkney Sustainable Energy Ltd. Retrieved 19 December 2010.

 "NREL: Dynamic Maps, GIS Data, and Analysis Tools – Wind Maps". Nrel.gov. 2013-09-03. Retrieved 2013-11-06.

  IEC Wind Turbine Classes June 7, 2006

 Small-Scale "Dragonfly" Wind Turbine Works at Low Wind Speeds

 "The Physics of Wind Turbines Kira Grogg Carleton College, 2005, p.8" (PDF). Retrieved 2013-11-06.

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