59 devendra

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CALIBRATION OF SOLAR POWER METER

BY LINEAR REGRESSION METHOD

Presented By

Tanisha Gaur &

Devendra Singh

Authored By

Tanisha Gaur, Devendra Singh, Anil Kumar and Prasant Baredar

Department of EnergyMaulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

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.


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.


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.


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

Tenmars TM 206


Tenmars TM 207


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.


The Coefficient Of Correlation

• Coefficient of correlation “r2” which measures the degree of association between the two values of related variables given in the data set.

Where, “X” will be values of TM 206

“Y” will be values of TM 207.


Calculations of Coefficient of Correlationn Tm 207

(Y)TM 206

(X)XY X2 Y2

1 967 864 835488 746496 9350892 1038 895 929010 801025 10774443 1036 925 958300 855625 10732964 1053 938 987714 879844 11088095 1015 914 925680 831744 10302256 914 788 720232 620944 8353967 832 710 590720 504100 6922248 927 802 743454 643204 8593299 742 601 445942 361201 550564

10 587 464 272368 215296 34456911 225 246 55350 60516 5062512 246 140 34440 19600 60516

SUM ∑Y= 9582 ∑X= 8285 ∑XY= 7498698

∑X2 =6539595

∑Y2 =8618086

• 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.


Error in TM 207

Global radiations of both the solar power meters

100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

1200

f(x) = 1.08416135515408 x + 17.161375442304R² = 0.978988662174831

Series1

Linear (Series1)

Value of 206

Val

ue

of 2

07

Diffused radiations of both the solar power meters

70 80 90 100 110 120 130 140 150 160 1700

20

40

60

80

100

120

140

160

180

200

f(x) = 1.00923724519624 x + 28.5095035792701R² = 0.693139014758766

Series1Linear (Series1)

Value of 206

Val

ue

of 2

07


Calibration Procedure• Now for this experimental setup, linear

equation Y=mX+c, can be solved for calculating “m” and “c” using formulaes:


Calculations for Regression Constantsn Tm 207 (Y) TM 206 (X) XY X2

1 967 864 835488 746496

2 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

SUM ∑Y= 9582 ∑X= 8285 ∑XY= 7498698∑X2 =

6539595

Regression constantsSurface Global

radiation“M”

Global radiation

“C”

Diffused radiation

“M”

Diffused radiation

“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


Cont….

• Using above equations , Average values of “m” and “c” are calculated.

• Now, the modified calibrated values of TM 207 are calculated by putting values of average “m” & “c” in the following equation.

• Where, “X” represents modified calibrated values of TM 207.


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.


Minimized Error in TM 207

Global radiations of both the solar power meters

100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

1200

f(x) = 1.0809 x + 35.8155000000007R² = 1

Series1yLinear (y)

Modified calibrated value of 207

Val

ue

of 2

07

Diffused radiations of both the solar power meters

40 60 80 100 120 140 160 180 200 2200

50

100

150

200

250

300

f(x) = 1.11475 x + 17.1235000000001R² = 1

yLinear (y)

Modified calibrated value of 207

Val

ue

of 2

07


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

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.


http://www.tenmars.com/

http://www.biddle.com/documents/bcg_comp_chapter3.pdf



http://people.duke.edu/~rnau/regintro.htm

THANK YOU

Department of EnergyMaulana Azad National Institute of Technology, Bhopal

(M.P.) INDIA