Renewable Energy 35 (2010) 845–851
Contents lists available at ScienceDirect
Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Research and development of maximum power transfer tracking system
for solar cell unit by matching impedance
Tun-Ping Teng a, *, Hwa-Ming Nieh a, Jiann-Jyh Chen b, Yu-Cheng Lu c
a
Department of Industrial Education, National Taiwan Normal University, 162, He-ping East Road, Section 1, Taipei 10610, Taiwan, ROC
Department of Electrical Engineering, Nei-Hu Vocational High School, Taipei, 11493, Taiwan, ROC
c
Department of Electrical Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, ROC
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 2 January 2009
Accepted 5 September 2009
Available online 13 October 2009
Employing the theorem that matching impedance produces maximum power transfer, the current study
develops a low-cost and highly efficient ‘‘maximum power point tracker for a solar cell unit,’’ for the
purpose of allowing a solar cell to achieve optimal power transfer under different solar intensities and
temperatures. Circuit control takes a single-chip microprocessor as the core and the booster circuit
design undergoes the solar cell charging operation even though the solar cell output voltage is lower
than the rated storage battery voltage. Experiments conducted in this study prove that the tracker this
study develops effectively enhances the utilization efficiency of a solar cell. When a solar cell is at an
output voltage above 30% of the rated voltage, it can charge a storage battery. When it reaches above 80%
of the rated voltage, its power conversion efficiency can reach above 85%. The charge and discharge
management mechanism of the device also avoids excessive charge and discharge of the storage battery,
and extends storage battery longevity.
Ó 2009 Elsevier Ltd. All rights reserved.
Keywords:
Solar cell
Maximum power transfer
Matching impedance
Booster circuits
1. Introduction
By adjusting the solar cell unit axial direction, the solar tracking
system helps the solar cell unit possess the best receiving effect
[1–8]. After the received energy is transformed as electric energy, it
is delivered to the storage battery for charging or loading. If electric
energy is required to perform parallel connection with an electricity system or supply general home appliances, an inverter is
needed to transform the direct current (DC) to an alternative
current (AC). To date, there are many highly efficient designs [9].
Nevertheless, the power transfer value of solar cell changes with
solar intensity. The solar tracker acquires maximum solar power
only when it is under the same light intensity, but it is unknown
whether transformed electricity can be most efficiently utilized. As
to the control of charge and discharge load, although the conventional relay-operated structure is simple, it cannot perform accurate load adjustment [10]. To achieve load control, many researches
have adopted a microcontroller-based method to control solar
transfer to achieve continuous control [11–14]. Circuit detection is
typically employed to detect ever-changing electric signals, and
further match with different arithmetic methods to control the
* Corresponding author. Tel.: þ886 2 77343358; fax: þ886 2 23929449.
E-mail address: tube.t5763@msa.hinet.net (T.-P. Teng).
0960-1481/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2009.09.001
charge and discharge mode, to acquire highest utilization efficiency
of a solar cell.
The current study is based on the concept of maximum power
transfer. Equal system impedance and load impedance achieve
maximum power transfer, acquiring the highest utilization efficiency of a solar cell. The controller proposed by this study uses
a microprocessor (microcontroller unit, or MCU) as the control core.
Detecting power transfer change of solar cell units, achieves power
impedance. Matching impedance is performed by pulse width
modulation (PWM), achieving maximum power transfer without
needing to use a complicated control circuit and arithmetic
procedures. This method does not need to focus on the characteristic curve of the solar cell unit to undergo design. Instead, directly
referring to the actual situation acquires maximum power transfer
under this situation. Changing different solar cell unit by this
method only requires performing simple software modification
according to different specifications. Concerning using booster
circuits to solve the problem of excessive low output voltage of
a solar cell, even though it is under very low voltage output
condition, charging can still be carried out for a storage battery,
extending chargeable time and raising charging efficiency. Finally,
through the charge and discharge management mechanism of
a storage battery, charging voltage is controlled to be within the
rated 120%, and discharge voltage to be within the rated 80%. Such
a design effectively extends storage battery longevity. Apart from
846
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
Fig. 1. Schematic demonstration of maximum power transfer for solar cell unit.
enhancing charging performance, the design also achieves environmental protection and decreases waste.
2. Related theories
The solar cell is a type of power, and its power transfer changes
with solar intensity. Any changes of solar cell power transfer, also
change its voltage and internal impedance. Circuit analysis is
sometimes interested in determining the maximum power delivered to a load. By employing Thevenin’s theorem, this work
determines the maximum power a circuit can supply and the
manner for adjusting the load in order to affect maximum power
transfer.
Suppose that the given circuit is shown in Fig. 1. The power
delivered to the load is expressed as:
PL ¼ IL2 RL ¼
VTH
RTH þ RL
2
RL
(1)
We want to determine the RL value that maximizes this quantity.
Hence, we differentiate the expression with respect to RL and
equate the derivative to zero.
2 2V 2 R ðR
ðRTH þ RL Þ2 VTH
dPL
TH L TH þ RL Þ
¼
¼ 0
dRL
ðRTH þ RL Þ4
(2)
which yields
RL ¼ RTH
(3)
In other words, maximum power transfer takes place when the
load resistance RL ¼ RTH. Although this is a very important result,
this study derives it using a simple network indicated in Fig. 1.
When RL is adjusted to equal RTH, the maximum power transfer for
solar cell units can be acquired.
According to the above concept of maximum power transfer, the
simplest way to achieve maximum power transfer is to use a group
of variable resistors to achieve matching impedance (RL ¼ RTH). This
method achieves maximum power transfer of a solar cell under
different solar intensities. Actual application of this theory would
be restricted. The power transfer of a solar cell, no matter whether
it is connected to a storage battery or a service load, still has load
impedance. For example, for a storage battery load, the internal
impedance (RB) of the storage battery would change as affected by
the charging situation. The maximum adjustment range of variable
resistance would be limited in the range of RB w RVR þ RB. If internal
impedance of the solar cell is outside of this range, the theoretical
value of maximum power transfer will not exist. But the adjustable
best situation under this condition can still be achieved. Manual
adjustment of variable resistance cannot achieve automation with
the constantly changing output impedance of the solar cell and
storage battery. When solar cell output voltage is lower than
storage battery voltage, the charge also cannot be achieved. To solve
these problems, pulse width modulation (PWM) can be used to
control the pulse width and change the impedance value by the
side of the load. PWM only requires adjusting the pulse width
moderately, and then the equivalent impedance by the side of the
load can change to match with the internal impedance of the solar
cell unit. This process achieves maximum power transfer of the
above limitation condition. Using booster circuits, even though
solar cell output voltage is lower than storage battery voltage,
charging can still be undergone.
3. Description of system and control circuits
Fig. 2 shows the circuit block diagram of the experiment in
which the microprocessor (MCU) is the core, and circuits attain the
voltage and current of the solar cell unit. The experiment calculates
solar cell unit power and controls booster circuits using MCU,
charging batteries even though the sunlight is very weak. This
study conducts moderate battery voltage surveillance, and controls
battery charge and discharge. Fig. 3 shows the complete control
circuits, indicating their main operation as follows:
3.1. Signal sampling circuits for voltage and current
In Fig. 3(a), block A shows the signal sampling circuits used in
this study. The voltage sampling adopts voltage division between R1
and R2, taking the applicable range of the matched AD converter.
The current sampling employs the voltage drop caused after the
current goes through R10. The voltage drop is converted to current
value by Ohm’s law, and further amplified by the reversing
amplifier built-in MCU. For calculating electric power, the CPU
calculates the measured voltage and current values after they have
performed AD conversion, eventually acquiring the solar cell power
transfer. PWM transfer adjustment uses power comparison. The
current detected power rate is compared with that of the previous
sampling time. By comparing the results, the PWM transfer is
adjusted before storage battery charging, achieving matching
impedance, and keeping power transfer at maximum value.
3.2. Driving and booster circuits
Fig. 2. Block diagram of control circuits.
In Fig. 3(a), block B shows the driving and booster circuits used
in this study. The driving circuit conducts current amplification
using a pair of bipolar junction transistors (BJTs). When n-channel
metal-oxide-semiconductor (NMOS), which serves as a switch,
increases its duties, the output voltage of storage battery drops, and
rises contrarily. Using the driving current increases output ability
and improves transient effect of the electric capacitor. Connecting
the NMOS gate with resistance (R15) reduces interruption by
confused signals and maintains a stable output. Booster circuits are
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
847
Fig. 3. Schematic diagram of the full control circuits. (a) Main circuits, (b) microprocessor circuits, (c) power supply.
used to solve the problem of failed charging for the excessively low
solar cell output. Suppose that the solar cell output voltage is 8 V
and the specific storage battery voltage is 12 V. In this case, solar
cell units cannot undergo storage battery charging. If charging is
needed, the charging voltage has to be higher than that of storage
voltage. Therefore, the current study suggests using booster circuits
to achieve this goal, thus enabling the charging operation despite
weaker solar intensity. Under charging mode, NMOS is at the cutoff period, and diode D1 is forward bias, making the storage battery
and electric capacitor C4 to start charging. During this time, voltage
applied to the two ends of the storage battery is the sum of the solar
cell’s output voltage and inductor L1’s voltage, achieving voltage
rise. Through the charge and discharge time of the electric capacitor, the voltage size at the two ends of the inductor can be changed
immediately, changing total output voltage value. In Fig. 3(a), block
C shows the discharge control circuits. The circuits prescribe that
120% of rated storage battery voltage is at a fully charged status, and
the charging device does not need further charging. The level lower
than 80% of rated voltage is at ceased output status, and the battery
does not supply power anymore.
848
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
theorem. This research uses PWM to adjust the pulse cycle to adjust
system impedance and acquire maximum power transfer under this
actual condition. The built-in operational amplifier (OPA) forms
a signal amplifying circuit with an external feedback component and
further amplifies the measured signal to match signal sampling
circuits.
3.4. Power supply
Fig. 3(c) shows the power supply circuits used for circuit control.
The power supply circuits stabilize the voltage by a three-terminal
voltage stabilizing component (HT-7550). Such power supply at
stable voltage has positive output voltage. To improve transient
response, both input and output ends are in parallel connection
with the electric capacitor to reach a status with more stabilized
power supply. The output end is attached with an LED for understanding the working condition of power circuits.
3.5. Software flowchart
Fig. 4. Flowchart of control program.
3.3. Microprocessor
Fig. 3(b) presents the single-chip controller circuits used in this
study. The single chip used (EM78P419N) belongs to the high-speed
small-sized central processing unit (CPU), which contains input,
output, control arithmetic logic unit and memory unit. The working
frequency can reach 20 MHz and uses 5 V DC power with interrupting
function. The circuit adopts a 16 MHz oscillator and each command
needs two oscillation cycles. Every command takes around 0.125
microsecond’s time to execute. Functions of this single chip include
analog-to-digital converter (ADC), pulse width modulation (PWM) and
reversing amplifier, effectively shrinking circuit space. ADC is
employed to convert current and voltage data by converting analog
signals to digital signals, readable by a microcomputer to make analysis
and calculation. Using the calculated power, this work judges whether
the next step needs charge, discharge or a stand-by procedure and
performs matching impedance based on the maximum power transfer
Fig. 4 presents the flowchart of the MCU control software. The
circuit operation directly uses the solar cell as a daytime or nighttime sensor. When there is sufficient light, charging (Voc > 3 V) is
carried out; and at night (Voc < 1 V), it is purely in output mode,
and SW2 manually determines whether power supply is needed.
When carrying out charging in the daytime, this study must
determine whether the battery is fully charged. If it is fully charged
and stays at stand-by, battery charging is not performed. Charging
time is carried out by comparing power transfers. When current
power (Pn) is greater than the previous transferred power (Pn1), it
enters voltage comparison. Current output voltage (Vn) that is also
higher than the previous voltage (Vn1) implies that current voltage
output should steadily increase, raising output voltage continuously. When current power is smaller than previous power transfer,
it enters another comparison mode. These comparisons are used to
perform matching impedance. At nighttime, the mode allows the
storage battery to perform discharge. During this time, the
discharge circuit is turned on, allowing the storage battery to
transfer electricity. Currently, the storage battery output voltage is
under surveillance. If it is lower than 80% of rated voltage, power
supply will cease. If it detects that daytime is coming, it will enter
daytime mode to carry out charging.
4. Experimental design and procedures
The solar cell unit used in this study is under AM1.5, and its rated
output voltage and output current are 10 V and 3 A respectively,
with storage battery specifications being 12 V/7 Ah. To confirm
maximum power performance of the controller, the current
Fig. 5. Experiment of maximum power transfer.
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
Fig. 6. Diagram of maximum power transfer performance experiment simulated by DC
power supply.
849
Fig. 8. Diagram of maximum power transfer performance experiment by solar cell
units with variable resistance.
investigation employs an actual experiment to compare the difference between the maximum power value simulated by variable
resistance and the maximum power value tracked by the controller.
As Fig. 5 indicates, to consider both the stability and authenticity
of the experiment, this study uses power supply and the solar cell
unit respectively to prove maximum power transfer performance of
the tracking solar cell unit of this controller. First, power supply is
used to simulate transfer of the solar cell unit. Through the limitation
of maximum output current, the experiment simulates maximum
transfer of a solar cell unit under different light intensities. The
experimental procedures are: use the SWb to switch the current to
connection with variable resistance. Set the DC power supply at
different short-circuit currents (ISC) and open-circuit voltages (VOC).
Adjust the variable resistance RL until it reaches maximum power
transfer (PO,Res). Record the maximum power value of every current
output condition. After that, use the SWb to switch the current to
connection with the controller. Observe the power transfer (PO,Con)
of this time, and use the variable resistance difference during
adjustment. When using the controller to conduct the experiment
under each of the different conditions, the storage battery should be
connected by the controller with 20 W halogen light for discharging
until the controller stops discharging automatically. Doing this
keeps each experiment at the same standard value.
To understand maximum power tracking performance of the
solar cell unit, this study replaces power supply by solar cell units to
carry out the same experiment. Using a simulated light source
(mercury-arc lamp) of different intensities, the experiment adjusts
solar cell light absorption and compares maximum power tracking
between the controller and variable resistance under different
conditions, confirming controller performance when tracking
maximum power transfer.
Fig. 7. Diagram of maximum power ratio simulated by DC power supply.
Fig. 9. Comparison of maximum power transfer performance by solar cell.
5. Uncertainty analysis
This experiment determines experimental result uncertainty by
measurement errors of the parameters, such as voltage, current and
lighting power. The maximum power transfer performance
850
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
Fig. 10. Comparison of output voltage of solar cell at maximum power transfer point.
experiment, simulated by DC power supply, measured power from
readings of the digital voltage meter (V) and digital current
meter (A).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2
DV
DA
þ
¼
P
V
A
dP
(4)
The precision of the digital voltage meter was 10 mV. The
precision of the digital current meter was 10 mA. Experiment
uncertainty was therefore less than 1.5%.
The maximum power transfer performance experiment by solar
cell units measured power from readings of the digital voltage
meter (V) and digital current meter (A); solar power was determined by solar power meter (SP) readings.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 DV
DA
DSP 2
þ
þ
¼
P
V
A
SP
dP
(8)
The precision of the digital voltage meter was 10 mV. The
precision of the digital current meter was 10 mA. The precision of
the solar power meter was 5%. Experiment uncertainty was
therefore less than 7%.
6. Result and discussion
Fig. 6 shows using DC power supply to simulate maximum power
transfer of variable resistance and the controller under different
open-circuit voltages and short-circuit currents. To avoid the
unstable phenomenon when the preset value of minimum charging
voltage is around 3 V, the minimum experimental voltage is preset
at 4 V. The figure shows that when voltage is above 8 V, the
controller tracks above 72% of the theoretical value simulated by
variable resistance. However, when it is at low voltage, controller
performance reduces drastically; when open-circuit voltage is 4 V
and short-circuit voltage is 3 A, controller performance reduces to
around 6%; and rated voltage around 10 V, achieves the best efficiency. Fig. 7 shows the maximum power ratio tracked by the
controller and variable resistance under different open-circuit
voltages and short-circuit currents. Although the maximum power
transfer efficiency at low voltage is very low, charging operation can
still be carried out. When voltage of the charging circuit traditionally
switched by relay is lower than storage battery voltage, charging
cannot be carried out. However, the controller proposed by this
study does not have this drawback. Low power transfer occurring at
the voltage far lower than the rated voltage is mainly caused by
booster circuits, to keep the voltage connected to the end of the
storage battery higher than the storage battery voltage, for charging
operation. Booster component C4 and L1 charge–discharge delay are
the main reasons for reducing power transfer performance.
Fig. 8 presents the diagram of experimental results after using the
solar cell unit to conduct a maximum power transfer experiment under
different light intensities and resistance variations. The figure shows
that different light intensities acquire the maximum power transition
point by adjusting variable resistance. The solar cell unit is then
switched to the controller to carry out the same experiment. This
research compares maximum power tracked by the controller and
variable resistance under different light intensities, as Fig. 9 shows.
Except under lower light intensity (30 W/m2), with maximum power
efficiency tracked below 80%, all others are higher than 80%. The rather
poor effect at low light intensity rate is caused by lower output voltage of
the solar cell. Fig. 10 shows that controller voltage during maximum
power tracking is lower than the voltage when maximum power is
adjusted by variable resistance. When controller voltage is lower than
storage battery voltage, charging can still be carried out. Power transfer
is lower than the simulated value of variable resistance not only because
of the delay phenomenon caused by booster circuits, but also because of
extreme limitation adjustment for equivalent controller impedance.
Impedance of the entire control system is composed of variable
controller impedance (RVR) and internal storage battery impedance (RB).
The control system can therefore be adjusted to the impedance range,
RB w RVR þ RB. In the case of RTH > RVR þ RB or RTH < RB, the controller
cannot track the theoretical value of maximum power. Although such
a limitation makes tracking unavailable for the theoretical value of
maximum power transfer, the maximum value under limited conditions can be reached. Hence, the control circuit proposed by this study
effectively enhances utilizing solar generation efficiency.
7. Conclusion
The tracker designed by this study has excellent tracking performance of the maximum power transfer point and uses the solar cell to
serve as a light sensor to judge the operation mode, without needing
to install a light sensor. When the rated solar cell voltage is 10 V, this
work makes a comparison with the theoretical value, with its output
efficiency reaching above 90%. Charging can also be performed under
low power transfer, effectively enhancing utilization efficiency of the
solar cell. If enhancing output power or replacing solar cells of
different specifications is necessary, we are only required to amplify
power component specifications and replace sampling circuit resistance value. The manufacturing cost of this tracker is also lower than
US$10, so it has extremely high promotion value.
Acknowledgement
The authors would like to thank the National Science Council of
the Republic of China, Taiwan for their financial support for this
research under Contract No. NSC-97-2514-S-588-001-GJ and NSC98-2514-S-003-009-NE.
References
[1] Baltas P, Tortoreli M, Russel P. Evaluation of power output for fixed and step
tracking photovoltaic arrays. Solar Energy 1986;37(2):147–63.
[2] Sala G, Anton I, Arborio JC, Luque A, Camblor E, Mera E. The 480 kWP
EUCLIDESTM – thermie power plant: installation, setup and first results. In:
Proceeding of the 16th European photovoltaic solar energy conference and
exhibition. Glasgow, Scotland: WIP - Stephens & Associates; May 2000.
T.-P. Teng et al. / Renewable Energy 35 (2010) 845–851
[3] Poulek V, Libra MA. Very simple solar tracker for space and terrestrial applications. Solar Energy Materials and Solar Cells 2000;60:99–103.
[4] Abdallah S, Salem N. Two axes sun tracking system with PLC control. Energy
Conversion and Management 2004;45(11–12):1931–9.
[5] Clifford MJ, Eastwood D. Design of a novel passive solar tracker. Solar Energy
2004;77(3):269–80.
[6] Roth P, Georgiev A, Boudinov H. Cheap two axis sun following device. Energy
Conversion and Management 2005;46(7–8):1179–92.
[7] Rubio FR, Ortega MG, Gordillo F, López-Martı́nez M. Application of new control
strategy for sun tracking. Energy Conversion and Management 2007;48:2174–84.
[8] Huang BJ, Sun FS. System analysis of 1-axis three-position tracking solar
PV. Journal of the Chinese Society of Mechanical Engineers 2007;28(3):
307–13.
851
[9] Lee SH, Song SG, Park SJ, Moon CJ, Lee MH. Grid-connected photovoltaic
system using current-source inverter. Solar Energy 2008;82:411–9.
[10] Preiser K, Kuhmann J, Biennann E, Herberg T. Quality of charge controllers in solar
home systems: results of a detailed test. In: ISES conference. Harare: FhG-ISE; 1995.
[11] Remote Area Power Supply (RAPS) design manual. IRDC/DMEA Publication;
1992.
[12] Masheleni H, Carelse XF. Microcontroller-based charge controller for standalone photovoltaic system. Solar Energy 1997;61(4):225–30.
[13] Krauter S, Ochs F. Integrated solar home system. Renewable Energy 2004;29:
153–64.
[14] Chu CC, Chen CL. A variable step maximum power point tracking for photovoltaic power system. Journal of the Chinese Society of Mechanical Engineers
2008;29(3):225–31.