1. Wind Turbine Project Earlham College BY AMARA YEB

2. How does a wind turbine work?  It first converts kinetic energy in the wind into rotational kinetic energy in the turbine  then it converts the rotational kinetic energy into electrical energy that can be distributed for household usage.  The conversion energy process mainly depends on the wind speed and the swept area of the turbine.

3. Electricity Consumption at Earlham YearsElectricity Consumption (kWh) 2008-2009 13,571,150 2009-2010 13,754,406 2010-2011 12,657,243 2011-2012 13,674,575 2012-2013 11,703,801 Average 13,072,235 Minimum load at 3am 900

4. 1. Constant Wind Speed ManufacturerSymbolsGeneral Electric Model GE 1.7-103 Air Density (kg/m^3) 1.195 Nameplate Capacity 1.7mW Rotor Diameter(m)d 103 Rotor Radius (m)r 51.5 Hub Height (m) 96 Mean Speed (m/s) u = C 6.52 Efficiency Factore 0.367 Power Generated by the Turbine (kW) per dayPw1, 380 Usable Power/electric power (kW) per dayPe506 Usable Power (kWh) per yearPe (year) 4, 436, 241 As of Earlham Usage Percentageratio 0.34

5. Weakness of this model:  we assume that wind speed is constant with 6.52m/s throughout the year.  It is an unrealistic assumption for a place like Richmond, Indiana.  Thus, in order to improve our prediction of wind turbine power production, we introduce another model that studies three different stages of wind speeds that can result in an average power produced each year.

6. 2. Three Stages of Wind Speeds

7. Average Wind Turbine Power Graph

8. Weibull Distribution

9. Average Power Formula

10. Variables

11. UcUrUf Per (kW) Value of "a" value of "b"XoX1X2 Pe(average) per day (kW) Pe(average) per year (kWh) 31120 2,432 (125.01) 9.740.163.3713.51 617.37 5,408,130.30 31220 3,157 (131.34) 10.230.164.1313.51 663.17 5,809,334.51 31320 4,014 (137.69) 10.730.164.9713.51 702.90 6,157,439.37 31420 5,014 (144.01) 11.220.165.9013.51 738.86 6,472,404.16 31520 6,167 (150.25) 11.710.166.9313.51 772.51 6,767,174.33 31620 7,483 (156.40) 12.190.168.0513.51 804.75 7,049,619.17

12. UcUrUfPer (kW) Value of "a" value of "b"Xo X1X2 Pe(average) per day (kW) Pe(average) per year (kWh) 3.51120 2,432 (182.88) 9.960.24 3.3713.51 586.27 5,135,757.42 3.51220 3,157 (191.32) 10.420.24 4.1313.51 628.12 5,502,303.32 3.51320 4,014 (199.92) 10.890.24 4.9713.51 664.18 5,818,175.32 3.51420 5,014 (208.59) 11.360.24 5.9013.51 696.71 6,103,164.88 3.51520 6,167 (217.23) 11.830.24 6.9313.51 727.17 6,369,993.60 3.51620 7,483 (225.78) 12.300.24 8.0513.51 756.42 6,626,255.53

13. UcUrUf Per (kW) Value of "a" value of "b"XoX1X2 Pe(average) per day (kW) Pe(average) per year (kWh) 41120 2,432 (256.40) 10.240.323.3713.51 550.99 4,826,643.73 41220 3,157 (266.78) 10.660.324.1313.51 588.41 5,154,437.16 41320 4,014 (277.66) 11.090.324.9713.51 620.36 5,434,387.76 41420 5,014 (288.83) 11.540.325.9013.51 649.09 5,686,059.69 41520 6,167 (300.08) 11.990.326.9313.51 676.01 5,921,890.68 41620 7,483 (311.31) 12.430.328.0513.51 701.96 6,149,141.56

14. UcUrUf Per (kW) Value of "a" value of "b"XoX1X2 Pe(average) per day (kW) Pe(average) per year (kWh) 4.51120 2,432 (348.66) 10.590.423.3713.51 512.34 4,488,079.14 4.51220 3,157 (360.32) 10.950.424.1313.51 545.00 4,774,200.15 4.51320 4,014 (373.17) 11.340.424.9713.51 572.57 5,015,680.64 4.51420 5,014 (386.73) 11.750.425.9013.51 597.24 5,231,786.43 4.51520 6,167 (400.65) 12.170.426.9313.51 620.39 5,434,604.97 4.51620 7,483 (414.71) 12.600.428.0513.51 642.81 5,631,004.72

15. Results and Conclusion

16. References  http://www.mathworks.com/products/symbolic/code- examples.html?file=/products/demos/symbolictlbx/Wind_turbine/Wind_turbine_power.htmlhttp://www.mathworks.com/products/symbolic/code- examples.html?file=/products/demos/symbolictlbx/Wind_turbine/Wind_turbine_power.html  Other Data are from Earlham College Sustainability Office.