This document describes the calibration of a solar power meter (TM 207) using linear regression analysis. Solar radiation data was collected from two meters (TM 206 and TM 207) and a linear relationship between the data was established. The TM 206 readings were used as the reference to calibrate the TM 207 meter. The regression constants calculated for global and diffused radiation were used to minimize the error in the TM 207 readings. The analysis showed that linear regression is an effective method for calibrating the TM 207 solar power meter.

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. 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. 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. 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. 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. Tenmars TM 206
Department of Energy
Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

7. Tenmars TM 207
Department of Energy
Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

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. The Coefficient Of Correlation
Department of Energy
Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

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. • 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. 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. Calibration Procedure
Department of Energy
Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

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. 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. Cont….
Department of Energy
Maulana Azad National Institute of Technology, Bhopal (M.P.) INDIA

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. 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. 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. 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. THANK YOU
Department of Energy
Maulana Azad National Institute of Technology, Bhopal
(M.P.) INDIA