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### 59 devendra

1. 1. CALIBRATION OF SOLAR POWER METER BY LINEAR REGRESSION METHOD Authored By Tanisha Gaur, Devendra Singh, Anil Kumar and Prasant Baredar Presented By Tanisha Gaur & Devendra Singh Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA 1
2. 2. Introduction • Solar power meters are used to measure solar radiation intensity coming on to the earth surface. • Calibration is a stastical technique of enhancing the accuracy by reducing the error in the instrument’s reading. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
3. 3. Calibration Technique Used • Linear regression defines relationships between variables, usually under an assumption of normally distributed errors. • Linear regression uses the fact that there is a statistically significant correlation between two variables to allow you to make predictions about one variable based on your knowledge of the other. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
4. 4. Experimentation Setup • The solar radiation data was collected (global and diffused radiation) by Solar power meters for one day on 11/05/2013, from 11:00 AM to 05:00 PM through both TM 206 and TM 207, simultaneously at both horizontal and inclined surfaces in MANIT Bhopal. • The angle of inclination was set on 23o as latitude (23.2500o N) of the Bhopal. The angle of inclination of solar energy systems is set up according to the latitude of the place. Then data collected was analyzed and a relationship was established between them. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
5. 5. Instruments Used • Solar power meter model TM 206 made by TENMARS is considered as a reference instrument and calibration is done for model TM 207. • In this analysis solar power meter TM 207 needs to be calibrated through linear regression method as TM 207 gives the values of solar radiation intensity on a earth surface more than 1000W/m2, which is not practically possible in partial cloudy weather conditions. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
6. 6. Tenmars TM 206 Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
7. 7. Tenmars TM 207 Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
8. 8. Linear Regression Equation • Relationship between global radiations of both the solar power meters on horizontal surface are expressed by means of a linear equation of the form Y = mX + c. • Normally, it agrees to reserve “Y” for the variable, which is to be predicted in terms of other. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
9. 9. The Coefficient Of Correlation Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
10. 10. Calculations of Coefficient of Correlation n Tm 207 (Y) TM 206 (X) XY X2 Y2 1 864 835488 746496 935089 2 967 1038 895 929010 801025 1077444 3 1036 925 958300 855625 1073296 4 1053 938 987714 879844 1108809 5 1015 914 925680 831744 1030225 6 914 788 720232 620944 835396 7 832 590720 504100 692224 8 927 710 802 743454 643204 859329 9 742 601 445942 361201 550564 10 587 464 272368 215296 344569 11 246 55350 60516 50625 12 225 246 140 34440 19600 60516 SUM ∑Y= 9582 ∑X= 8285 ∑XY= 7498698 ∑X2 = 6539595 ∑Y2 = 8618086
11. 11. • Now, the value of coefficient of correlation is calculated mathematically, by putting values of “X” and “Y”, in the mentioned equation. • Value of r2 is not perfectly equal to “1”,that means there is some error between the two values of solar power meter TM 206 and TM 207, and thus the need of calibration of TM 207, arises. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
12. 12. Error in TM 207 250 1200 r² = 0.979 1000 r² = 0.6931 200 Value of 207 Value of 207 800 150 600 Series1 Series1 Linear (Series1) 100 400 Linear (Series1) 50 200 0 0 200 400 600 800 1000 Value of 206 Global radiations of both the solar power meters 0 0 50 100 150 200 Value of 206 Diffused radiations of both the solar power meters Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
13. 13. Calibration Procedure Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
14. 14. Calculations for Regression Constants XY X2 864 835488 746496 1038 895 929010 801025 3 1036 925 958300 855625 4 1053 938 987714 879844 5 1015 914 925680 831744 6 914 788 720232 620944 7 832 710 590720 504100 8 927 802 743454 643204 9 742 601 445942 361201 10 587 464 272368 215296 11 225 246 55350 60516 12 246 140 34440 19600 ∑XY= 7498698 ∑X2 = 6539595 n Tm 207 (Y) 1 967 2 SUM ∑Y= 9582 TM 206 (X) ∑X= 8285
15. 15. Regression constants Surface Global Global Diffused Diffused radiation radiation radiation radiation “M” “C” “M” “C” Horizontal 1.0776 5.737 1.2203 54.473 Inclined 1.0842 28.51 1.0092 17.161 Average value m= 1.0809 c= 17.1235 m= 1.11475 c= 35.817 Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
16. 16. Cont…. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
17. 17. Cont…. • To prove the mathematical relationship of closeness between two values, between the original and modified values of TM 207, the coefficient of correlation is again calculate. • Now the value of “r2” is obtained “1”, that is perfect closeness between them. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
18. 18. Minimized Error in TM 207 300 1200 1000 y = 1.0809x + 35.815 r² = 1 y = 1.1148x + 17.123 r² = 1 250 800 Value of 207 Value of 207 200 150 600 y Linear (y) 400 y Linear (y) 100 50 200 0 0 0 200 400 600 800 1000 Modified calibrated value of 207 Global radiations of both the solar power meters 0 50 100 150 200 250 Modified calibrated value of 207 Diffused radiations of both the solar power meters Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
19. 19. Conclusion • Calibration of Solar power meter modal TM 207 can done using linear regression method. • Calibration factor are calculated for both global and diffused radiation. The obtained values are: global (m = 35.817 and c = 1.0809) and diffused (m = 17.1235 and c = 1.11475). • This study is useful for the manufacturing company TENMARS, and similar method can be adopted for calibration of other doubtful instruments. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
20. 20. References [1] Fourth edition, Modern Elementary Statistics, by John E. Freund professor of mathematics, Arisona state University. [2] http://www.tenmars.com. [3] http://www.biddle.com/documents/bcg_comp chapter3.pdf. [4] http://people.duke.edu/~rnau/regintro.htm. [5] Karmel, P.H. and Polasek, M. 1986; Applied Statistics for Economists, Fourth Edition, Chapter 8,Khosla Publishing House, Delhi. Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA
21. 21. THANK YOU Department of Energy Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA