Maximum Power Tracking for Photovoltaic Power
Systems
Joe-Air Jiang1, Tsong-Liang Huang2, Ying-Tung Hsiao2* and Chia-Hong Chen2
1Department of Bio-Industrial Mechatronics Engineering, National Taiwan University
Taipei, Taiwan 106, R.O.C.
2Department of Electric Engineering, Tamkang University
Tamsui, Taiwan 251, R.O.C.
Abstract
The electric power supplied by a photovoltaic power generation system depends on the solar
radiation and temperature. Designing efficient PV systems heavily emphasizes to track the maximum
power operating point. This work develops a novel three-point weight comparison method that avoids
the oscillation problem of the perturbation and observation algorithm which is often employed to track
the maximum power point. Furthermore, a low cost control unit is developed, based on a single chip to
adjust the output voltage of the solar cell array. Finally, experimental results confirm the superior
performance of the proposed method.
Key Words: Photovoltaic, Perturbation and Observation Algorithm, Maximum Power Point Tracking
1. Introduction
Photovoltaic (PV) generation is becoming increas-
ingly important as a renewable source since it offers
many advantages such as incurring no fuel costs, not be-
ing polluting, requiring little maintenance, and emitting
no noise, among others. PV modules still have relatively
low conversion efficiency; therefore, controlling maxi-
mum power point tracking (MPPT) for the solar array is
essential in a PV system.
The amount of power generated by a PV depends on
the operating voltage of the array. A PV’s maximum
power point (MPP) varies with solar insulation and tem-
perature. Its V-I and V-P characteristic curves specify a
unique operating point at which maximum possible pow-
er is delivered. At the MPP, the PV operates at its highest
efficiency. Therefore, many methods have been devel-
oped to determine MPPT. For example: Ibrahimm and
Houssing employed the look-up table on a microcom-
puter, to track MPP [1]. Midya et al. applied a dynamic
MPP tracker to PV appliances [2]. Enslin and Snymam
suggested the concept of “perturb and observe” (P&O)
[3], alternatives to which have been recently presented
[4,5]. Koutroulis et al. [6] and Hussein et al. [7] offered
the incremental conductance (IncCond) technique, since
when, enhanced IncCond techniques have been proposed
[8,9]. Several investigations have recently applied fuzzy
logic to resolve this problem [10,11].
In MPPT, most control schema use the P&O tech-
nique because it is easy to implement. But the oscillation
problem is unavoidable. This research developed an ex-
tended P&O technique - a three-point weight comparison
method based on an 8-bit single-chip control unit - by
utilizing a boost converter to adjust the output voltage of
the PV for tracking the MPP. Models and simulations of
this PV system and MPPT algorithms are offered with
experimental results.
The rest of this paper is organized as follows. Section
II introduces the basic principle of the PV system. Sec-
tions III and IV describe the traditional P&O and the pro-
posed algorithm three-point weight comparison method,
respectively. Section V shows the configuration of the
proposed PV system. Section VI discusses experimental
results as illustrations. Conclusions are finally drawn in
Tamkang Journal of Science and Engineering, Vol. 8, No 2, pp. 147�153 (2005) 147
*Corresponding author. E-mail: hsiao@mail.tku.edu.tw
the last section.
2. Mathematical Model
The building block of PV arrays is the solar cell,
which is basically a p-n semiconductor junction, shown
in Figure 1. The V-I characteristic of a solar array is given
by Eq. (1) [4].
(1)
where V and I represent the output voltage and current
of the PV, respectively; Rs and Rsh are the series and
shunt resistance of the cell; q is the electronic charge;
ISC is the light-generated current; Io is the reverse satura-
tion current; n is a dimensionless factor; k is the Boltzman
constant, and Tk is the temperature in
oK.
Equation (1) was used in computer simulations to
obtain the output characteristics of a solar cell, as shown
in Figure 2. This curve clearly shows that the output
characteristics of a solar cell are non-linear and are cru-
cially influenced by solar radiation, temperature and load
condition. Each curve has a MPP, at which the solar array
operates most efficiently.
3. Maximum Power Point Tracking
Several techniques for tracking MPP have been pro-
posed, as described in Section I. Two algorithms are com-
monly used to track the MPPT - the P&O method and
IncCond method. The P&O method has been broadly used
because it is easy to implement. Figure 3 presents the con-
trol flow chart of the P&O algorithm. The MPP tracker
operates by periodically incrementing or decrementing
the solar array voltage. If a given perturbation leads to an
increase (decrease) the output power of the PV, then the
subsequent perturbation is generated in the same (oppo-
site) direction. In Figure 3, set Duty out denotes the pertur-
148 Joe-Air Jiang et al.
( )
exp 1S SSC O
k sh
q V R I V R I
I I I
nkT R
� �
� �
� �
� �
� � � �
� �
� �
�
� �
Figure 1. Equivalent circuit of PV array.
Figure 2. V-I characteristic of a solar cell. Figure 3. Flow chart of the P&O algorithm.
bation of the solar array voltage, andDuty+ andDuty� rep-
resent the subsequent perturbation in the same or opposite
direction, respectively.
4. Three-point Weight Comparision Method
The P&O algorithm compares only two points, which
are the current operation point and the subsequent pertur-
bation point, to observe their changes in power and thus
decide whether increase or decrease the solar array volt-
age. The P&O algorithm oscillates around the MPP, re-
sulting in a loss of PV power, especially in cases of rap-
idly changing solar radiation [6]. Therefore, the three-
point weight comparison method is proposed to avoid
having to move rapidly the operation point, when the so-
lar radiation is varying quickly or when a disturbance or
data reading error occur. Restated, the MPPT can be
traced accurately when the solar radiation is stable and
power loss is low.
The algorithm of the three-point weight comparison
is run periodically by perturbing the solar array terminal
voltage and comparing the PV output power on three
points of the V-P curve. The three points are the current
operation point (A), a point, B, perturbed from point A,
and a point, C, with doubly perturbed in the opposite di-
rection from point B. Figure 4 depicts the nine possible
cases. In these cases, for the point A and B, if the Wattage
of point B is greater than or equal to that of point A, the
status is assigned a positive weighting. Otherwise, the
status is assigned a negative weighting. And, for the
point A and C, when the Wattage of point C is smaller
than that of point A, the status is assigned a positive
weighting. Otherwise, the status is assigned a negative
weighting. Of the three measured points, if two are posi-
tively weighted, the duty cycle of the converter should be
increased. On the contrary, when two are negatively
weighted, the duty cycle of the converter should be de-
creased. In the other cases with one positive and one neg-
ative weighting, the MPP is reached or the solar radiation
has changed rapidly and the duty cycle is not to be
changed. Figure 5 presents a flow chart of the three-point
weight comparison algorithm.
5. Configuration of the PV System
Figure 6 shows the system configuration of the pro-
posed PV system. This system consists of a solar array
(75 W) with an open voltage of 21 V and a short circuit
current of 4.6 A, an A/D and D/A converter, a 20 �/100
W resistor as the load, and a control unit on a single-chip.
Figure 7 depicts the circuits of the boost converter con-
nected from the output of the solar cell. The power flow
is controlled by varying the on/off duty cycle of the
Maximum Power Tracking for Photovoltaic Power Systems 149
Figure 4. Possible states of the three perturbation points.
Figure 5. Algorithm for the three-point weight comparison.
switching. The average output voltages are determined
by the Eq. (2) [10].
(2)
Where Vout and Vin are the output and input voltage of
the converter and D is the duty cycle of the switch S.
The input power of the converter is equal to the output
power of the converter if the converter is ideal, yielding
the following equations.
(3)
(4)
From Eq. (4), when the load (Rout), is fixed, the input
resistance Rin can be controlled by varying the duty cy-
cle. Therefore, the operating point of the solar cell can be
controlled by the duty cycle.
A simulated solar source was established to compare
results under the same environmental conditions for vari-
ous test cases. Figure 8 shows the configuration of the
simulated solar source with a maximum energy of 32.68
mA/cm2.
6. Simulation Results
A prototype MPPT system has been developed using
the described method and tested in the laboratory. The
PV array gives a 75 W maximum power, a 21 V open-
circuit voltage and a close-circuit current of 4.6 A at a so-
lar energy of 1 kW/m2 and a temperature of 25 �C. The
PV array was simulated with two solar energy cases,
32.68 mA/cm2 (case A) and 12.49 mA/cm2 (case B) to
test the proposed system under specific atmospheric con-
ditions. Figures 9 and 10 plot the V-I and V-P curves un-
der the two cases at 65 �C.
Figures 11 and 12 show the output voltage (CH1)
and the current (CH2) waveforms. The solar energy is
changed form A to B in Figure 11. In Figure 12, the solar
energy is changed form B to A. In the case A, the MPP is
13.65 V, 3.76 A and 51.324 W. And for the case B, the
MPP is 16.14 V, 1.32 A and 21.305 W. From Figure 11
150 Joe-Air Jiang et al.
Figure 6. Configuration of the PV system.
Figure 7. Circuits of the boost converter.
Figure 8. Configuration of the simulated solar source.
1
(1 )
out
in
V
V D
�
�
(1 )out inI I D� � �
2 2(1 ) (1 )in outin out
in out
V V
R D R D
I I
� � � � �
Figure 9. V-I curve under the cases A and B at 65 �C.
and 12, it is noted that the operating points of a PV array
are different under the two cases.
Figure 13 displays the waveforms of the voltage
(CH1), current (CH2) and power (CHM) with uniformly
changing energy from zero to B and finally to A, and then
decreasing to B and finally to zero at the same rate. Fig-
ure 13 reveals that the rate of change of voltage and cur-
rent differ. In the beginning, the voltage of the PV in-
creases rapidly with the solar energy but the current
changes slowly. As the solar energy increases further, the
voltage changes slowly, and the current increases fast.
When the temperature increases, the voltage decreases.
Maximum Power Tracking for Photovoltaic Power Systems 151
Figure 10.V-P curve under the cases A and B at 65 �C.
Figure 11.Output voltage and current of the PV array. (The
solar energy is changed from A to B.)
Figure 12.Output voltage and current of the PV array. (The
solar energy is changed from B to A.)
Figure 13.Wave form of the voltage, current and power as the
solar energy changes uniformly from zero to B and
finally to A, and then decreases to B and finally to
zero, at the same rate.
Figure 14.Trace of V-I curve under as the solar energy in-
creases slowly from B to A.
These trends satisfy the characteristic of solar cells.
Figure 14 depicts the V-I trace as the solar energy in-
crease slowly from B to A. Figure 15 displays the V-I
curve as the solar energy increases slowly from zero to
A. Figure 16 presents the V-I trace under as the solar en-
ergy increases rapidly from zero to A. Figures 14 to 16,
show that, regardless of how the luminous flux changes,
the output power point is well tracked, and stays on the
MPP.
7. Conclusion
This paper proposed a single and robust algorithm
for MPPT. Moreover, the three-point weight point com-
parison method was developed to avoid the oscillation
problem in the traditional P&O algorithm. This work
also developed a low-cost hardware system. The system
includes a boot converter and a micro controller on a sin-
gle-chip unit, which controls the converter directly ac-
cording to the PV array output power measurements. The
experimental tests verified the tracking efficiency.
Acknowledgment
The authors would like to thank the National Science
Council of the Republic of China for financially support-
ing this research under Contract No. NSC 90-2213-E-
032-018.
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Manuscript Received: Dec. 10, 2004
Accepted: Mar. 14, 2005
Maximum Power Tracking for Photovoltaic Power Systems 153