Aerodynamic Factors Affecting Wind Turbine Power Generation

Aerodynamic Factors Affecting Wind Turbine Power Generation

Jayanna Kanchikere*

* Lecturer in Electrical Section, Higher College of Technology, PB 74, PC 133, Muscat, Sultanate of OMAN.

Abstract

The potential of wind energy in this power starved county is the brightest one among all others, owing to its free availability even at various remote places. In this paper, a matlab model is developed to study the aerodynamic factors that affect the wind turbine power generation and this simulink model is valid for wide range of wind turbines. It is tested for vestas Type V27, V39 and V52 wind turbines. The study observes that the operational parameters has a direct effect on the generated power which will lead the designer to focus on priority factor that should be considered for optimizing the new generation wind turbines.

Keywords: wind Energy; wind turbine; Aerodynamic factors; Gearbox.

1. Introduction

   For all renewable energy sources in India, Wind Electric Generation (WEG) is the largest in terms of installed capacity. India holds a wind energy potential of more than 45000MW, out of which 14000MW is technically feasible now but India secures fourth position globally with a capacity of 8698MW(2007- 08). Poor performance of WEGs installed will have serious negative impact on new developments.

   Wind turbines are classified on the basis of their axis in which the turbine rotates into horizontal and vertical axis wind turbines. Horizontal axis wind turbines are considered more commonly because of their ability to collect maximum amount of wind energy for the particular time of day and season. Wind turbines coupled with generators convert wind energy to electrical energy. All vestas RRB turbines are equipped with microprocessor-controlled optimal pitch regulation ensuring continuous and optimal adjustment of the angles of the blades in relation to the prevailing wind, thus generating maximum power. The energy conversion for modern wind turbines will be of fixed speed & variable speed. In Fixed speed machines, the generator is directly connected to the main supply grid. The frequency of the grid determines the rotational speed of the turbine rotor, which in turn is converted into the generator rotational speed through gear box. The generator speed depends on the number of pole pairs and the frequency of the grid. In variable speed machines the generator is connected to the grid by an electronic inverting system or the generator excitation windings are fed by an external frequency from an inverter. The rotor will operate with variable speed adjusted to the actual wind speed situation.

2. Proposed mathematical model

   The wind turbine component rotor consists of blades for converting wind energy to an intermediate low speed rotational energy. The generator component consists of electric generator, control electronics & gear box for converting the low speed rotational energy to electrical energy.

   1. Wind stream Power

      The kinetic energy in air of an object of mass m moving with speed is equal to:

      E = ½ m 2 (1)

      The power in the moving air (assuming constant wind velocity) is equal to:

      Pwind = dE / dt = ½ m v2 (2)

      Where m is the mass flow rate per second. When the air passes across an area A (e.g. the area swept by the rotor blades), the power in the air can be calculated as( Mukund, R. 1999)

      Pwind = ½ Av3 (3)

      Where is the air density. Air density varies with air pressure and temperature in accordance with the gas law:

      = P/ RT (4)

      Where, Density of air in kg/m3 T Temperature

      R gas constant

      The pressure and temperature varies with the wind turbine location. Some publishers give formula for air density as a function of the turbine elevation above sea level H:

      = 0 1.194 x 10 -4 H (5)

      Where 0 = 1.225 kg/m3 is the air density at sea level at temperature T = 288 K.

   2. Mechanical Power Extracted from the Wind

   The air energy cannot be transferred into mechanical energy with 100% conversion efficiency by any energy converter. The power extracted from the air stream by any energy converter will be less than the wind power Pwind also because the power achieved by the energy converter Pww can be computed as the difference between the power in the moving air before and after the converter.

   The extracted mechanical power from the air stream by the energy converter is equal to: Pww = Cp Pwind = Cp ½ Av3 = 16/27. Pwind (6)

   Where the coefficient Cp < 1; Actual maximum power coefficients can be between 0.15 to 0.593 for different rotor designs & is defining as the ratio of the mechanical power extracted by the converter to the power in the air stream is called the power coefficient (Betzs factor.). The coefficient is equal to Cp = Pww

   / Pwind.

   The power coefficient of real converters Cp achieves lower values than that computed above because of various aerodynamic losses that depend on the rotor construction. The rotor power coefficient is usually given as a function of two parameters: the tip-speed ratio and the blade pitch angle . The blade pitch angle is defined as the angle between the plane of rotation and the blade cross-section chord and the tip- speed ratio is defined as

   = u / v = R / v (7)

   Where u = tangential velocity of blade tip

   = angular velocity of rotor R = rotor radius

   Summing up the above, it can be seen that the mechanical power Pww extracted from the wind converter and the torque ww for the given rotor and for the given wind velocity v, rotor angular velocity and the blade pitch angle can be computed as

   Pww = Cp (, ) Pwind = Cp (, ) ½ Av3 (8)

   ww = Pww / = C (, ) ½ Av2 R (9)

   The rotor power and torque coefficients in these models can be utilized in the form of look-up tables or in the form of a function. Often, for a given blade, the characteristics of the drag Cd and the lift C1 ratios as functions of the blade pitch angle are available. In such a case, the rotor power coefficient Cp can be defined as a function of these quantities. Such a function which is defined as

   Cp (, ) = 16/27[1 – C1/ N] 2 [e (- C2/1.29) (Cd / C1) ] (10)

   Where,

   N – Number of blades,

   Cd / C1 – average drag-to-lift ratio of blade airfoil, C1, C2 – coefficients

3. Proposed Simulation model

   Power from a given rotor would be controlled by quantities viz. air density , turbine swept area A, air velocity v and power coefficient Cp. The Matlab/Simulink model is developed to observe how these quantities affect the generated power from wind turbine. Koçak (2008) focused entirely on wind speed persistence during weather forecast, site selection for wind turbines and synthetic generation of the wind speed data. This model is valid for wide ranges of wind turbines. It is tested for V27, V39 and V52 turbines and compared the results. The specifications of wind turbines are given in Table 1. A Matlab/simulink model is shown in Fig.1and power output curves are shown in figure 2-6.

   Table 1. The specifications of V27, V39 & V52 wind turbines (Vestas wind systems2000)

   Details	Vestas Type V27	Vestas type V39	Vestas Type V52
   Rated Power output	225 KW	500 KW	850 KW
   Cut-in wind speed	3.5 m/s	4 m/s	4 m/s
   Rated wind speed	1 m/s	15 m/s	16 m/s
   Cut-out wind speed	25 m/s	25 m/s	25 m/s
   Rotor Diameter	27m	39m	52m
   Swept area	573 m2	1735 m2	2124 m2
   Number of Blades	3	3	3
   Power Regulation	Pitch	Pitch	Pitch/Optispeed

   t

   Clock

   wind speed (m/s)

   1 1

   s s

   6 v ^3

   Wind speed (m/s)

   Integrator

   Integrator1

   Gain

   wind speed ^3

   13.5

   turbine radius m

   Product1

   pi Gain2

   Product

   0.5

   Gain1

   power power

   power

   powerpower

   powe

   r

   output

   1.225

   power vs wind speed

   air density (kg/m3)

   Cp (power coeff)

   Ramp1

   Cp behavior

   Power, Cp

   Fig.1. Matlab/simulink model

   vestas V27 with airdensity 1.225 kg/m3

   4500

   4000

   3500

   3000

   power

   2500

   2000

   1500

   1000

   500

   0

   -5000 0.5 1 1.5 2 2.5

   time

   Fig2. Power Output curve for vestas V27 with air density 1.225 kg/m3

   power output curve for V39 with air density 1.225 kg/m3

   14000

   12000

   10000

   8000

   power

   6000

   4000

   2000

   0

   -2000

   0 0.5 1 1.5 2 2.5

   time

   Fig3. Power Output curve for vestas V39 with air density 1.225 kg/m3

   Power output of V52 with air density 1.225 kg/m3

   16000

   14000

   12000

   10000

   Power

   8000

   6000

   4000

   2000

   0

   -2000

   0 0.5 1 1.5 2 2.5

   time

   Fig4. Power Output curve for vestas V52 with air density 1.225 kg/m3

   output of V27 with air density 1.172 kg/m3

   4500

   4000

   3500

   3000

   power

   2500

   2000

   1500

   1000

   500

   0

   -500

   0 0.5 1 1.5 2 2.5

   time

   Fig5. Power Output curve for vestas V27 with air density 1.172 kg/m3

   output of V27 with air density 1.342kg/m3

   5000

   4000

   3000

   power

   2000

   1000

   0

   -1000

   0 0.5 1 1.5 2 2.5

   time

   Fig 6. Power Output curve for vestas V27 with air density 1.342 kg/m3

4. Results and Discussion

   Wind turbines are optimized by considering swept area and wind speed in terms of local area conditions to extract maximum power. The output power of a wind turbine is directly proportional to cube of wind speed and swept area of its blades. The larger the diameter of its blades, the more power can be extracted from the wind. In this paper, power output of three Vestas wind turbines V27, V39 and V52 with different diameters 27m, 39m and 52m respectively with same air density 1.225 kg/m3 are compared in Fig. 2,3 &4. The power output of Vestas V52 type is greater than V39 and V27 types.

   Khalfallah, M. and Koliub, M. 2007 shown that Wind speed has a significant effect on wind turbine performance. The power available in the wind is directly proportional to the cube of wind speed and swept area of blades. As swept area of blades increases, the available power also increases. The output of a wind turbine is also directly proportional to air density. As air density increases, the available power also increases. It can be observed from Fig.2, 5&6 for Vestas type V27 with different air densities.

5. Conclusion

Many factors have to be considered while manufacturing wind turbines i.e., turbine swept area, air density, wind speed and power coefficient as a function of pitch angle and blade tip speed. Air density has a significant effect on wind turbine performance. As air density increases, the available power also increases. The power output of wind turbine is directly related to swept area of blades. As swept area of blades increases, the output power also increases. |The good exploitation of wind energy may enhance the renewable power generation capabilities and participate in generating at good costs.

References

1. Vestas wind systems.2000, V52-850KW wind turbine.

2. L.Fingersh, M.Hand & A.Laxson, Wind turbine design cost and scaling model, Technical Report, NREL/TP500-40566, Dec.2006.

3. T.Ackermann, Wind Power in Power Systems, New York, John Wiley and Sons, 2005

4. www.vestas-V39.com

5. www.windpioneer.co.uk

6. www.wind-energy-the-facts.org

7. Omar Badran, Emad Abdulhadi, Evaluation of factors affecting wind power generation in Jordan,

   The seventh Asia-Pacific Conference on wind Engineering, 2009, Taipei, Taiwan

8. Jan Vargauwe, Andre Martinez, Alberto Ribas, Optimization of a wind turbine using permanent magnet synchronous generator, International conference on renewable Energies and Power Quality, Bilbao, March 2012.

9. Kocak, K. 2008. Practical ways of evaluating wind speed persistence. Energy, 33(1): PP65-70.

10. Herbert, G.M. Iniyan, S., Sreevalsan, E, and Rajapandian, S.A. 2007. Review of wind energy technologies. Renewable and Sustainable Energy Reviews, 11(6): 1117-1145.

11. Wind Resource Assessment Handbook, (1997), Wind Resource Assessment Handbook. 1997. Report no. SR-440-22223. Subcontract no. TAT-5-15283-01. Golden, CO. National Renewable Energy Laboratory, USA.

12. Wind Resource Assessment Handbook, (2010), Wind Resource Assessment Handbook.Final Report 10-30, 2010, New york State Energy Research and Development Authority, USA.

[13]. Khalfallah, M., and Koliub, M. 2007. Suggestions for improving wind turbines power curves. Desalination, 209(1-3): 221-222.

[14]Mukund, R. 1999. Wind and solar power systems. USA: CRC press.