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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 796
DUAL AXIS SOLAR TRACKER USING MICROCONTROLLER
Ajinkya Chabuk*1, Akshay Shinde*2, Mahadev Narale*3,Pritam Gonjari*4 Prof. Mr. P. S.Magdum*5
1234Students, Electrical, Sanjay Ghodawat Institutes, Atigre, India
5Professor, Dept. of Electrical Engineering, Sanjay Ghodawat Institutes, Maharashtra, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Solar energy is more rapidly gaining popular as
an importantmeansof increasingrenewableenergyresources.
Our project will include the design and construction of a
microcontroller-based solar panel tracking system. Solar
tracking receives more energy from sun because the solar
array is able to remain inclined to the sun. Solar tracking
system is the most appropriate technology to enhance the
efficiency of solar cell by tracking the sun. This paper aims at
the development of a simple process to track the sun and
attain maximum efficiency using Microcontroller
Key Words: Solar Energy, Tracking, Solar Panel, 8051
Microcontroller, RTC.
1.INTRODUCTION
The total populace is expanding step by step and the
interest for vitality is expanding as needs be. Oil and coal as
the primary wellspring of vitality now days, is required to
wind up from the world amid the current century which
investigates a significant issue in giving the humankind a
moderate and solid wellspring of vitality. The need of our
own is renewable vitality assets with modest running
expenses. Sunlight based vitality is considered as one of the
principle vitality assets in warm nations.
As a rule, India has a generally long sunny days over ten
months and halfway shady sky for a large portion of the
times of the rest two months. This makes our nation,
particularly the deserts sides in the west, which incorporate
Rajasthan, Gujarat, Madhya Pradesh and so on extremely
rich is sun based vitality. Many ventures have been done
utilizing photovoltaic cells in gathering sun based radiation
and changing over it into electrical vitality however the vast
majority of these activities did not considerthedistinctionof
the sun edge of frequency by introducing the boards in a
settled introduction which impacts exceptionally the
sunlight based vitality gathered by the board.
We realize that, the edge of slant ranges between -90degree
after sun rise and +90 degree before sun set going with zero
degree at twelve. This makes the collected solar radiations
be 0% at the sun rise and sun set and 100% at noon. This
variation of solar radiations collectionleadsthephotovoltaic
panel to lose more than
40% of the collected energy.
In July 2009, India unveiled a US$19 billion plan to produce
20 GW (20000MW) of solar power by 2020. Under the plan,
the use of solar-powered equipment and applicationswould
be made compulsory in all government buildings, as well as
hospitals and hostels. On November 18, 2009, it was
reported that India was ready to launch it National Solar
Mission under the National Action Plan on Climatic Change,
with plans to generate 1000 MW of power by2013
The day by day normal sun based vitality occurrence over
India fluctuates from 4 to 7 kwh/m^2 with around 1500-
2000 daylight hours for each year (contingent on areas),
which is significantly more than current aggregate vitality
utilization.
2.METHODOLOGY
In the block diagram shown in fig.1 shows the complete
structure of the tracking system the solar panel is kept on
the frame which is rotated by using stepper motor. The
stepper motor is connected to the microcontroller. By using
the real time clock microcontroller gives the angle to the
stepper motor gets rotating as per given angle of inclination.
There are mainly two poles ofstructureoneisstationaryand
other is moving. Now by using movingpolewecanadjustthe
axis of rotating panel. The stepper motor is placed at fixed
pole.
RTC
Real Time
Clock
Microcontroller Unit
8051 based CPU
L293D/
ULN2003 Motor
Driver Unit
Stepper Motor Solar Panels
Fig. 1 System Block Diagram
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 797
Solar Panels
Charge
Controller Unit
DC Battery Unit
Power LED
Bulbsas a
Load
Fig.2 Lighting System
Block diagram of the RTC based solar tracking system.
The positional direction of the sun with respect to time has
been measured and implemented as an algorithm in the
controller. Then, the controllerinthechipdeliversanoutput,
the corresponding PWM signals, to drive the stepping
motors. Thus, the directions of the single dimensional solar
platform can be tuned to achieve optimal energy,
respectively.
Fig. 3 System Block Diagram
Programmed the controller will constantly peruses the Real
Time Clock (RTC) and contrasts and the unthinkable
qualities put away, on the off chance that it matches with
those qualities the relating positional qualities will be send
to the PWM generator which will make theengineto work to
pivot sun oriented board to words sun sparkle,Bytuning the
two dimensional sun oriented stage, the ideal effectiveness
of creating force will be accomplished.
START
DISPLAY CURRENT DATE AND TIME
CHECK THE CURRENT TIME
IF CURRENT TIME==6:30:30AM
ROTATE THE PANEL
6" ROTATION USING STEPPER
MOTOR
IF CURRENT TIME==6:31:00AM
ROTATE THE PANEL
6" ROTATION USING STEPPER
MOTOR
IF CURRENT TIME==6:35:30AM
ROTATE THE PANEL
TO ZEROTH POSITION USING
STEPPER MOTOR
YES
NO
YES
YES
NO
NO
Fig .4 Flowchart
The stepper engines requires a +9V supply and four control
beats at its terminals. One stage point of the engine is
equivalent to 1.8°. On the off chance that the distinction
amongst S1 and S2 is more noteworthy thanthe blunder, the
stepper engine ought to turn forward; if the contrast
amongst S2 and S1 is more noteworthy than the mistake, it
ought to pivot invert bearing keeping in mindthe endgoal to
keep the level board hitting to body, theboardisconstrained
as vertically with a level of 50° (Figure 5).Inthismanner, the
azimuthally drives can turn on a sum of level of 260° amid
day times.
Fig. 5. Limits for movement of the solar panel
When all is said in done applications, the board ought to be
turned towards East heading keepingin mindtheendgoal to
make it prepared for operation on the following day.
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 798
COMPONENTS
1. REAL TIME CLOCK (RTC)
DS1307
64 x 8, Serial, I2C Real-Time Clock
The DS1307 serial constant clock (RTC) is a low-control, full
parallel coded decimal (BCD) clock/timetable in addition to
56 bytes of NV SRAM. Address and information are
exchanged serially through an I2C, bidirectional transport.
The clock/timetable givesseconds,minutes,hours,day,date,
month, and year data. The finish of the month date is
naturally balanced for quite a long time with less than 31
days, including revisions for jump year. The check works in
either the 24-hour or 12-hour arrange with AM/PM pointer.
The DS1307 has an inherent power-sense circuit that
distinguishescontrol disappointmentsandnaturallychanges
to the reinforcement supply. Timekeeping operation
proceeds while the part works from the reinforcement
supply.
2.LCD DISPLAY
16×2 Liquid Crystal Display which will show the 32
characters at once in two lines (16 characters in one
column). Each character in the show of size 5×7 pixel grid.
There are 16 sticks in the LCD module.
3.STEPPER MOTOR
A stepper engine or step engine or venturing engine is a
brushless DC electric engine that partitions a full turn into
various equivalent strides. The engine's positioncanthen be
charged to move and hold at one of these means with no
input sensor (an open-circle controller), the length of the
engine is precisely measured to the application in regard to
torque and speed.
4.SOLAR PANEL
Solar panels get energy from the sun for people to use.
Heat from solar panels is often used for space heating and
for hot water.
Solar panels collect renewable energy. At the ending of 20th
century some panels used the heat of the sun to make steam
for a steam engine to turn a generator. Nowadays producing
electricity from the sun's light is cheaper.
5.8051 MICROCONTROLLER
The 8051 design gives many capacities (focal preparingunit
(CPU), arbitrary get to memory (RAM), read-just memory
(ROM), input/yield (I/O), intrude on rationale, clock, and so
on.) in one bundle. The gadget additionally hasfour8-bitI/O
ports, three 16-bit clock/occasion counters, a multi-source,
four-need level, settledinterferewithstructure,animproved
UART and on-chip oscillator and timing circuits The gadget
bolsters 6-clock/12-clock mode determination by
programming a Flashpieceutilizingparallel programmingor
In-System Programming. What's more, a SFR bit (X2) in the
clock control enlist (CKCON) likewise chooses between 6-
clock/12-clock mode. Furthermore, when in 6-clock mode,
peripherals may utilize either 6 timekeepers for each
machine cycle or 12 tickers for each machine cycle. This
decision is accessible exclusively for every fringe and is
chosen by bits in the CKCON enlist.
SIMULATION MODEL–
Fig. 5 SIMULATION MODEL
3.RESULTS
After fulfillment of equipment of venture there is have to
perform test on it to think about his effectiveness To check
whether the framework tracks the sun's position precisely,
we had keep the sun oriented following framework in open
space where daylight accessible for the duration of the day
effortlessly and taking the readings of force created hourly.
This test is completed independently on two following
frameworks level plate & dual hub every day separately. In
the wake of watching the readings we have presumethatthe
proposed framework is more effective than other.
Maximum Power Pm (Wp) 100W
Maximum Power Voltage
Vmp (V)
14.0V
Open circuit Voltage Voc
(V)
21.0V
Maximum Power Current
Imp (A)
5.90A
Short CircuitCurrentIsc(A) 6.35A
Maximum System Voltage 1000V
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 799
Time
Flat
Plate
Single
Axis
Dual
Axis
Temp.
range
°C
6:00 0.02 0.015 0.07 24
7:00 0.061 0.037 15.8 25
8:00 0.65 0.45 19.8 26
9:00 12.5 16.1 25 29
10:00 16.4 17.8 26.6 31
11:00 15.9 16 27.6 33
12:00 16.8 22.2 28.4 34
13:00 13.1 14.5 24 34
14:00 13.9 14.3 22.2 34
15:00 6.5 15.5 21.4 34
16:00 6.5 6 19.6 34
17:00 0.5 0.7 5.8 33
18:00 0.5 3.2 3.58 30
103.331 126.802 239.85
Chart-1:Flat Plate
Chart-2:Single Axis
Chart-3:Dual Axis
Chart-4: Combined Chart
4. CONCLUSION
The designed solar trackersystemcouldtrack themovement
of the sun with the help of microcontroller and stepper
motor. This system can work properly irrespective of
weather conditions and location. Dual-axis tracking system
works well even in all weather conditions when compared
with single-axis tracker,hence the efficiency of dual-axis
tracker system is higher when compared with single-axis
tracker system.The proposed paper of the dual axis solar
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 800
tracker is capable of tracking the sun throughout the year.
The dual axis tracker provides higher output power when
compared to single axis tracker and fixed panel.
5. REFERENCES
[1] Kenneth Ayala, “The 8051 Microcontroller Architecture,
Programming and Applications,” Penram International, 2nd
Edition.
[2] S. R. Bull, “Renewable energy today and tomorrow,”IEEE
Proc., vol.89, no. 8, pp. 1216-1226
[3] V K Mehta, Rohit Mehta, “Principles of Electronics”, S.
Chand & Company Ltd.
[4] J.B.Gupta, “Principles of electrical machines ”
[5] Mohamed Azab, “ A New MaximumPowerPointTracking
For PhotovoltaicSystems”,International Journal OfElectrical
And Electronics Engineering, 2009.
[6] M. T. A. Khan et al., “Design and construction of an
automatic solar tracking system,” in Proc. 6th International
Conference on Electrical and Computer Engineering, 2010,
pp. 326-329

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Dual-axis solar tracker using microcontroller

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 796 DUAL AXIS SOLAR TRACKER USING MICROCONTROLLER Ajinkya Chabuk*1, Akshay Shinde*2, Mahadev Narale*3,Pritam Gonjari*4 Prof. Mr. P. S.Magdum*5 1234Students, Electrical, Sanjay Ghodawat Institutes, Atigre, India 5Professor, Dept. of Electrical Engineering, Sanjay Ghodawat Institutes, Maharashtra, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Solar energy is more rapidly gaining popular as an importantmeansof increasingrenewableenergyresources. Our project will include the design and construction of a microcontroller-based solar panel tracking system. Solar tracking receives more energy from sun because the solar array is able to remain inclined to the sun. Solar tracking system is the most appropriate technology to enhance the efficiency of solar cell by tracking the sun. This paper aims at the development of a simple process to track the sun and attain maximum efficiency using Microcontroller Key Words: Solar Energy, Tracking, Solar Panel, 8051 Microcontroller, RTC. 1.INTRODUCTION The total populace is expanding step by step and the interest for vitality is expanding as needs be. Oil and coal as the primary wellspring of vitality now days, is required to wind up from the world amid the current century which investigates a significant issue in giving the humankind a moderate and solid wellspring of vitality. The need of our own is renewable vitality assets with modest running expenses. Sunlight based vitality is considered as one of the principle vitality assets in warm nations. As a rule, India has a generally long sunny days over ten months and halfway shady sky for a large portion of the times of the rest two months. This makes our nation, particularly the deserts sides in the west, which incorporate Rajasthan, Gujarat, Madhya Pradesh and so on extremely rich is sun based vitality. Many ventures have been done utilizing photovoltaic cells in gathering sun based radiation and changing over it into electrical vitality however the vast majority of these activities did not considerthedistinctionof the sun edge of frequency by introducing the boards in a settled introduction which impacts exceptionally the sunlight based vitality gathered by the board. We realize that, the edge of slant ranges between -90degree after sun rise and +90 degree before sun set going with zero degree at twelve. This makes the collected solar radiations be 0% at the sun rise and sun set and 100% at noon. This variation of solar radiations collectionleadsthephotovoltaic panel to lose more than 40% of the collected energy. In July 2009, India unveiled a US$19 billion plan to produce 20 GW (20000MW) of solar power by 2020. Under the plan, the use of solar-powered equipment and applicationswould be made compulsory in all government buildings, as well as hospitals and hostels. On November 18, 2009, it was reported that India was ready to launch it National Solar Mission under the National Action Plan on Climatic Change, with plans to generate 1000 MW of power by2013 The day by day normal sun based vitality occurrence over India fluctuates from 4 to 7 kwh/m^2 with around 1500- 2000 daylight hours for each year (contingent on areas), which is significantly more than current aggregate vitality utilization. 2.METHODOLOGY In the block diagram shown in fig.1 shows the complete structure of the tracking system the solar panel is kept on the frame which is rotated by using stepper motor. The stepper motor is connected to the microcontroller. By using the real time clock microcontroller gives the angle to the stepper motor gets rotating as per given angle of inclination. There are mainly two poles ofstructureoneisstationaryand other is moving. Now by using movingpolewecanadjustthe axis of rotating panel. The stepper motor is placed at fixed pole. RTC Real Time Clock Microcontroller Unit 8051 based CPU L293D/ ULN2003 Motor Driver Unit Stepper Motor Solar Panels Fig. 1 System Block Diagram
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 797 Solar Panels Charge Controller Unit DC Battery Unit Power LED Bulbsas a Load Fig.2 Lighting System Block diagram of the RTC based solar tracking system. The positional direction of the sun with respect to time has been measured and implemented as an algorithm in the controller. Then, the controllerinthechipdeliversanoutput, the corresponding PWM signals, to drive the stepping motors. Thus, the directions of the single dimensional solar platform can be tuned to achieve optimal energy, respectively. Fig. 3 System Block Diagram Programmed the controller will constantly peruses the Real Time Clock (RTC) and contrasts and the unthinkable qualities put away, on the off chance that it matches with those qualities the relating positional qualities will be send to the PWM generator which will make theengineto work to pivot sun oriented board to words sun sparkle,Bytuning the two dimensional sun oriented stage, the ideal effectiveness of creating force will be accomplished. START DISPLAY CURRENT DATE AND TIME CHECK THE CURRENT TIME IF CURRENT TIME==6:30:30AM ROTATE THE PANEL 6" ROTATION USING STEPPER MOTOR IF CURRENT TIME==6:31:00AM ROTATE THE PANEL 6" ROTATION USING STEPPER MOTOR IF CURRENT TIME==6:35:30AM ROTATE THE PANEL TO ZEROTH POSITION USING STEPPER MOTOR YES NO YES YES NO NO Fig .4 Flowchart The stepper engines requires a +9V supply and four control beats at its terminals. One stage point of the engine is equivalent to 1.8°. On the off chance that the distinction amongst S1 and S2 is more noteworthy thanthe blunder, the stepper engine ought to turn forward; if the contrast amongst S2 and S1 is more noteworthy than the mistake, it ought to pivot invert bearing keeping in mindthe endgoal to keep the level board hitting to body, theboardisconstrained as vertically with a level of 50° (Figure 5).Inthismanner, the azimuthally drives can turn on a sum of level of 260° amid day times. Fig. 5. Limits for movement of the solar panel When all is said in done applications, the board ought to be turned towards East heading keepingin mindtheendgoal to make it prepared for operation on the following day.
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 798 COMPONENTS 1. REAL TIME CLOCK (RTC) DS1307 64 x 8, Serial, I2C Real-Time Clock The DS1307 serial constant clock (RTC) is a low-control, full parallel coded decimal (BCD) clock/timetable in addition to 56 bytes of NV SRAM. Address and information are exchanged serially through an I2C, bidirectional transport. The clock/timetable givesseconds,minutes,hours,day,date, month, and year data. The finish of the month date is naturally balanced for quite a long time with less than 31 days, including revisions for jump year. The check works in either the 24-hour or 12-hour arrange with AM/PM pointer. The DS1307 has an inherent power-sense circuit that distinguishescontrol disappointmentsandnaturallychanges to the reinforcement supply. Timekeeping operation proceeds while the part works from the reinforcement supply. 2.LCD DISPLAY 16×2 Liquid Crystal Display which will show the 32 characters at once in two lines (16 characters in one column). Each character in the show of size 5×7 pixel grid. There are 16 sticks in the LCD module. 3.STEPPER MOTOR A stepper engine or step engine or venturing engine is a brushless DC electric engine that partitions a full turn into various equivalent strides. The engine's positioncanthen be charged to move and hold at one of these means with no input sensor (an open-circle controller), the length of the engine is precisely measured to the application in regard to torque and speed. 4.SOLAR PANEL Solar panels get energy from the sun for people to use. Heat from solar panels is often used for space heating and for hot water. Solar panels collect renewable energy. At the ending of 20th century some panels used the heat of the sun to make steam for a steam engine to turn a generator. Nowadays producing electricity from the sun's light is cheaper. 5.8051 MICROCONTROLLER The 8051 design gives many capacities (focal preparingunit (CPU), arbitrary get to memory (RAM), read-just memory (ROM), input/yield (I/O), intrude on rationale, clock, and so on.) in one bundle. The gadget additionally hasfour8-bitI/O ports, three 16-bit clock/occasion counters, a multi-source, four-need level, settledinterferewithstructure,animproved UART and on-chip oscillator and timing circuits The gadget bolsters 6-clock/12-clock mode determination by programming a Flashpieceutilizingparallel programmingor In-System Programming. What's more, a SFR bit (X2) in the clock control enlist (CKCON) likewise chooses between 6- clock/12-clock mode. Furthermore, when in 6-clock mode, peripherals may utilize either 6 timekeepers for each machine cycle or 12 tickers for each machine cycle. This decision is accessible exclusively for every fringe and is chosen by bits in the CKCON enlist. SIMULATION MODEL– Fig. 5 SIMULATION MODEL 3.RESULTS After fulfillment of equipment of venture there is have to perform test on it to think about his effectiveness To check whether the framework tracks the sun's position precisely, we had keep the sun oriented following framework in open space where daylight accessible for the duration of the day effortlessly and taking the readings of force created hourly. This test is completed independently on two following frameworks level plate & dual hub every day separately. In the wake of watching the readings we have presumethatthe proposed framework is more effective than other. Maximum Power Pm (Wp) 100W Maximum Power Voltage Vmp (V) 14.0V Open circuit Voltage Voc (V) 21.0V Maximum Power Current Imp (A) 5.90A Short CircuitCurrentIsc(A) 6.35A Maximum System Voltage 1000V
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 799 Time Flat Plate Single Axis Dual Axis Temp. range °C 6:00 0.02 0.015 0.07 24 7:00 0.061 0.037 15.8 25 8:00 0.65 0.45 19.8 26 9:00 12.5 16.1 25 29 10:00 16.4 17.8 26.6 31 11:00 15.9 16 27.6 33 12:00 16.8 22.2 28.4 34 13:00 13.1 14.5 24 34 14:00 13.9 14.3 22.2 34 15:00 6.5 15.5 21.4 34 16:00 6.5 6 19.6 34 17:00 0.5 0.7 5.8 33 18:00 0.5 3.2 3.58 30 103.331 126.802 239.85 Chart-1:Flat Plate Chart-2:Single Axis Chart-3:Dual Axis Chart-4: Combined Chart 4. CONCLUSION The designed solar trackersystemcouldtrack themovement of the sun with the help of microcontroller and stepper motor. This system can work properly irrespective of weather conditions and location. Dual-axis tracking system works well even in all weather conditions when compared with single-axis tracker,hence the efficiency of dual-axis tracker system is higher when compared with single-axis tracker system.The proposed paper of the dual axis solar
  • 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 800 tracker is capable of tracking the sun throughout the year. The dual axis tracker provides higher output power when compared to single axis tracker and fixed panel. 5. REFERENCES [1] Kenneth Ayala, “The 8051 Microcontroller Architecture, Programming and Applications,” Penram International, 2nd Edition. [2] S. R. Bull, “Renewable energy today and tomorrow,”IEEE Proc., vol.89, no. 8, pp. 1216-1226 [3] V K Mehta, Rohit Mehta, “Principles of Electronics”, S. Chand & Company Ltd. [4] J.B.Gupta, “Principles of electrical machines ” [5] Mohamed Azab, “ A New MaximumPowerPointTracking For PhotovoltaicSystems”,International Journal OfElectrical And Electronics Engineering, 2009. [6] M. T. A. Khan et al., “Design and construction of an automatic solar tracking system,” in Proc. 6th International Conference on Electrical and Computer Engineering, 2010, pp. 326-329