A reliable, fast and low cost maximum power point tracker for photovoltaic applications

Abstract

This work presents a new maximum power point tracker system for photovoltaic applications. The developed system is an analog version of the “P&O-oriented” algorithm. It maintains its main advantages: simplicity, reliability and easy practical implementation, and avoids its main disadvantages: inaccurateness and relatively slow response. Additionally, the developed system can be implemented in a practical way at a low cost, which means an added value. The system also shows an excellent behavior for very fast variables in incident radiation levels.

Full text

A reliable, fast and low cost maximum power point tracker
for photovoltaic applications
J.M. Enrique
*
, J.M. Andu
´jar, M.A. Boho
´rquez
Departamento de Ingenierı
´a Electro
´nica, de Sistemas Informa
´ticos y Automa
´tica, Universidad de Huelva, Spain
Received 19 February 2009; received in revised form 22 July 2009; accepted 16 October 2009
Communicated by: Associate Editor Elias Stefanakos
Abstract
This work presents a new maximum power point tracker system for photovoltaic applications. The developed system is an analog
version of the “P&O-oriented”algorithm. It maintains its main advantages: simplicity, reliability and easy practical implementation,
and avoids its main disadvantages: inaccurateness and relatively slow response. Additionally, the developed system can be implemented
in a practical way at a low cost, which means an added value. The system also shows an excellent behavior for very fast variables in
incident radiation levels.
Ó2009 Published by Elsevier Ltd.
Keywords: Analog system; Efficiency; Low cost; Maximum power point tracker; Photovoltaic array; “P&O”algorithm
1. Introduction
In the specialized literature numerous proposals of MPP
tracking systems can be found. Most of them have similar
efficiency, which can also be considered acceptable for most
applications. As a result, the interest of the authors when
implementing this work has focused on achieving a certain
added value in the proposed system, which can be found in
the accurateness, speed and low cost. This allows its appli-
cation even to household installations, where investment
costs may be the most determining factor for decision mak-
ing. The developed system presents the advantage of its
high speed which also helps to improve the photovoltaic
system efficiency.
A photovoltaic (PV) array that functions under uniform
radiation and temperature conditions presents an I–V and
P–V characteristic as the one shown in Figs. 1(a) and (b),
respectively. As can be observed, there is a single point,
called “MPP”(Maximum Power Point), where the array
provides the maximum power possible for these environ-
mental conditions (radiation and temperature), and so
functions with the maximum performance. When a load
is connected directly to a PV array (direct coupling), the
operation point is defined by the intersection of its I–V
characteristics, as shown in Fig. 1(a).
In general, this operation point does not coincide with
the MPP. Thus, in direct coupling systems, the array must
be over-dimensioned to guarantee the power demand of the
load. Obviously, this implies a more expensive system. To
solve this problem, a DC/DC (Xiao et al., 2007) converter
with an algorithm for the automatic control of its duty
cycle “d”is inserted between the photovoltaic array and
the load (see Fig. 2), resulting in what is known as MPPT
(Maximum Power Point Tracker) system.
The MPPT must control the voltage or current (through
the dof the converter) of the PV array regardless of the
0038-092X/$ - see front matter Ó2009 Published by Elsevier Ltd.
doi:10.1016/j.solener.2009.10.011
*
Corresponding author. Address: Departamento de Ingenierı
´a Electro
´-
nica, de Sistemas Informa
´ticos y Automa
´tica, Universidad de Huelva,
Huelva, Spain. Tel.: +34 959 217374/7656/7671; fax: +34 959 217348.
E-mail addresses: juanm.enrique@diesia.uhu.es (J.M. Enrique), andu
jar@diesia.uhu.es (J.M. Andu
´jar), bohorquez@diesia.uhu.es (M.A. Bo-
ho
´rquez).
www.elsevier.com/locate/solener
Available online at www.sciencedirect.com
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load, trying to place it in the MPP. The DC/DC converter
presents an input impedance (R
i
) which depends basically
on the load impedance (R
L
) and the duty cycle (d)(Enrique
et al., 2005a,b, 2007; Dura
´n et al., 2008, 2009). Therefore,
the MPPT must find the optimal dfor the operation point
of the PV array to coincide with the maximum power point
(MPP).
Although the solution to operating in the MPP may
seem immediate, it is not. This is because the location of
the MPP in the I–V curve of the PV array is not known
a priori. This point must be located, either by mathematical
calculations over a valid model, or by using some search
algorithm. This implies even more difficulty if we consider
the fact that the MPP presents non-linear dependencies
with temperature and radiation, as observed in Fig. 3.
Fig. 3(a) shows a set of I–V curves for different levels of
radiation and constant temperature. In Fig. 3(b), the same
set of curves is presented at a higher temperature. Observe
the change in the voltage and, especially, in the current of
the MPP.
Numerous MPPT algorithms have been proposed and
developed in the literature. Among them, the “Perturbation
and Observation (P&O)”algorithm is probably the most
Fig. 1. (a) I–Vcharacteristic of a PV array, MPP and system operation point. (b) P–Vcharacteristic of the PV array.
Fig. 2. Basic diagram of an MPPT system.
Fig. 3. (a) I–Vcharacteristic of a PV array at 40 °C and different radiation levels (200–400 to 600–800 and 1000 W/m
2
). (b) I–Vcharacteristic of a PV
array at 60 °C and different radiation levels (200–400 to 600–800 and 1000 W/m
2
).
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extensively used in commercial MPPT systems. However,
there is no clear agreement on which algorithm is best.
Hohm and Ropp (2002) presented a study that basically
concludes with not very different performances for most
of the different algorithms and where the traditional P&O
is quite successful.
To establish the quality of a given MPPT system (and to
be able to compare it with other systems), it is necessary to
define the “tracking efficiency (g)”, given by Eq. (1) (Hohm
and Ropp, 2002):
gMPPT ¼Rt
0PinstðtÞdt
Rt
0PmaxðtÞdt ð1Þ
where, for radiation and temperature conditions in the gi-
ven time period, P
inst
(t) is the instantaneous power supplied
by the MPPT system controlled PV array, and P
max
(t)is
the actual MPP power.
2. Algorithms for MPP tracking
A very short revision of the most usual algorithms for
MPP tracking is presented below.
2.1. Perturbation and Observation (P&O)
The Perturbation and Observation (P&O) algorithm is
probably the most frequently used in practice, mainly due
to its easy implementation (Kim et al., 1996). Its operation
is briefly explained as follows: assume that the PV array
operates at a given point, which is outside the MPP. The
PV array operational voltage is perturbed by a small DV,
and then the change in the power (DP) is measured. If
DP> 0, the operation point has approached the MPP,
and therefore, the next perturbation must take place in
the same direction as the previous one (same algebraic
sign). If, on the contrary, DP< 0, the system has moved
away from the MPP and, consequently, the next perturba-
tion must be performed in the opposite direction (opposed
algebraic sign).
As stated before, the advantages of this algorithm are its
simplicity and easy implementation. However, it has limita-
tions that reduce its tracking efficiency. When the light
intensity decreases considerably, the P–Vcurve becomes
very flat. This makes it difficult for the MPPT to locate
the MPP, since the changes that take place in the power
are small as regards perturbations occurred in the voltage.
Another disadvantage of the “P&O”algorithm is that it
cannot determine when it has exactly reached the MPP.
Thus, it remains oscillating around it, changing the sign
of the perturbation for each DPmeasured. It has also been
observed that this algorithm can show misbehavior under
fast changes in the radiation levels (Kawamura et al.,
1997).
Several improvements in the “P&O”algorithm have
been proposed (Enslin et al., 1997; Andujar et al., 2005;
Xiao et al., 2007). One of them is the addition of a waiting
time if the system identifies a series of alternate signs in the
perturbation, meaning that it is very close to the MPP. This
allows reducing the oscillation around the MPP and
improves the algorithm efficiency under constant radiation
conditions. However, this algorithm causes the MPPT to
be very slow, making its misbehavior more noticeable in
partly cloudy days.
Other modifications to the “P&O”algorithm, as the
ones detailed below, directly affect the perturbation sign
according to whether certain conditions are given.
2.1.1. “P&O”oriented algorithm
The “P&O”oriented algorithm (Andujar et al., 2005)is
able to distinguish with certain accuracy whether the sys-
tem is operating to the right or left of the MPP and act con-
sequently, so increasing tracking efficiency. However, it is
observed that whenever there is a sudden variation in the
incident radiation (caused, for example, by the passing of
a cloud) and, therefore, in the power supplied by the pho-
tovoltaic generator, the system is unable to distinguish
instantaneously the appropriate direction of the change
in d(Hohm and Ropp, 2002). This algorithm is discussed
in detailed in Section 3.
2.1.2. “P&O”modified algorithm
To correct the defect caused by sudden radiation varia-
tions in the previous algorithm, a slight variation has been
proposed (Andujar et al., 2005). As already known, varia-
tions in the light radiation have an effect mainly and
directly on the current supplied by the photovoltaic array
(Alonso, 1998). Thus, an increase in radiation will cause
a rise in the value of the MPP current (see Fig. 3). When
the algorithm detects a variation in radiation over a certain
threshold, its response is an immediate increase in d. In this
way, the DC/DC converter decreases its input impedance
R
i
, and so obliges the photovoltaic generator to move to
higher current points close to the MPP. An advantage of
this algorithm is that it does not require precise measure-
ments of radiation (this would remarkably increase the
price of its practical implementation), since it only needs
the sign of the radiation increase within an interval of mea-
sures. A simple photodiode can be useful for this purpose.
2.2. Constant voltage and current
The “Constant Voltage (CV)”algorithm (Hohm and
Ropp, 2002; Koizumi et al., 2006) is based on the fact that
in the I–Vcurves of a PV array the ratio between the max-
imum power point voltage and that of the open circuit is
roughly constant (something similar occurs with the ratio
between the current of the maximum power point and that
of the short circuit) (Noguchi et al., 2002; Mutoh et al.,
2006; Mutoh and Inoue, 2007), that is:
VMPP
VOC
ffiK<1ð2Þ
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where V
MPP
is the maximum power point voltage and V
OC
is
the open circuit voltage. The PV array is temporarily isolated
by the MPPT system to measure V
OC
. Next, the MPPT cal-
culates the correct operation point using Eq. (2) and adjusts
the voltage of the PV array until it reaches the MPP. This
operation is repeated periodically to track the MPP.
Although this method is simple, choosing the optimal K
value, which, on the other hand, is not totally constant,
may be difficult. The literature indicates good values for
Kwithin the range 0.73–0.80 (Andersen and Alvsten,
1995; van der Merwe and van der Merwe, 1998; Abou El
Ela and Roger, 1984).
This method can be implemented in a relatively easy
way using analog software. However, its efficiency is lower
than that of other methods (Hohm and Ropp, 2002). The
main reasons are:
(I) Errors in the Kvalue.
(II) The measure of V
OC
(I
SC
) requires the momentary
interruption of the power supplied by the array.
2.3. Incremental conductance
The so called “incremental conductance”method
(Hohm and Ropp, 2002) derives directly from the power
equation, which will be given in the MPP by:
dP
dV MPP
¼dðVIÞ
dV MPP
¼0)I
V¼dI
dV ð3Þ
If instantaneous conductance g
L
, and increasing conduc-
tance g
P
, are defined as:
gL¼I
V;gp¼dI
dV ð4Þ
Then, expression (3) can be re-written in the form of:
dP
dV MPP
¼0)gL¼gPð5Þ
The previous equation indicates that in the MPP the
instantaneous and incremental conductance must be equal.
If the operation point does not coincide with the MPP,
then a series of inequations directly derived from expres-
sion (5) (Hohm and Ropp, 2002; Koizumi et al., 2006)
allow us to know whether the operation voltage is higher
or lower than V
MPP
, and so to act consequently.
Once the MPP has been reached, every time a change
occurs in the radiation on the array the MPPT will tend
to increase or decrease the operation voltage to follow
the MPP.
The disadvantage of this method is that it needs a pre-
cise calculation of g
L
and g
P
, which makes the MPPT more
difficult and relatively slow.
2.4. Parasitic capacity
This algorithm is similar to the previous one, except that
in this algorithm the effect of the parasitic capacity of the
junction p–n is included. This effect can be modeled (Bramb-
illa et al., 1998) as a condenser connected between the termi-
nals of each cell. By connecting cells in parallel the parasitic
capacity observed by the MPP will increase. As a result, the
differences between the tracking efficiencies of the MPP
between “Increasing Conductance”and “Parasitic Capac-
ity”algorithms are more outstanding in high power arrays,
where there are numerous modules connected in parallel.
The practical implementation of this algorithm is com-
plex, especially for the difficulty entailed by the calculation
of increasing conductance g
P.
. A detailed study of this algo-
rithm is shown in Brambilla et al. (1998).
2.5. Model-based algorithms
If a suitable model is available for a cell or photovoltaic
array and there are precise radiation and temperature mea-
sures available (which implies a significant increase in the
price of the system, although there have recently been devel-
oped sensors of temperature and radiation at a low cost
(Martı
´nez and Andu
´jar, 2009; Martı
´nez et al., 2009), the
MPP voltage and current may be directly calculated by solv-
ing equation dP/dV = 0 (for example, using a numeric
method). Then, the MPPT would just have to adjust voltage
and current values to those calculated ones (Xiao et al., 2006).
Even so, the model-based MPPTs are not practical,
since the values for the cell parameters are not known with
accuracy and, in fact, can vary significantly between cells
from the same production series. Moreover, only the cost
of a precise light radiation sensor (pyranometer) can cause
this MPPT system to be non-viable in practice.
Having revised the most usual algorithms and methods
for MPP tracking, it seems that the P&O algorithm and,
more specifically, its “oriented”variant, is the one with
the best ratio efficiency/easiness of practical implementa-
tion. This is mainly due to its proper operation, simplicity
and low cost (note that it needs no radiation and tempera-
ture sensors). Nonetheless, as already mentioned, it has the
disadvantage of its instantaneous confusion when facing
sudden variations in the incident radiation. This disadvan-
tage could be overcome with a system fast enough to make
its reaction speed higher than the speed of the incident radi-
ation change – which is the main reason in the MPP move-
ment. To achieve this without losing the advantages of the
P&O-oriented algorithm, the authors have developed a sys-
tem which is described below.
3. P&O oriented analog system
A completely analog system able to implement the algo-
rithm for MPP tracking, known as “P&O-oriented”algo-
rithm, is presented in this section (Andujar et al., 2005).
3.1. Operation of the P&O-oriented algorithm
Consider Fig. 4, where the P–V characteristic of a pho-
tovoltaic array at a given temperature and radiation is
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shown. Assume that, due to a modification in the duty
cycle (d) of the converter, the system evolves from V
A
to
V
B
(DV> 0 and DP> 0). As observed in Fig. 4, the MPP
voltage, V
MPP
, is higher than V
B
, and therefore, the output
voltage must keep increasing. Now assume that the pertur-
bation has moved the operation point from V
B
to V
A
.In
this case, the voltage of the array must increase again to
approach V
MPP
. All possible combinations are shown in
Table 1.
The only variable to which the control system can access
is the duty cycle (d). Any increase in dimplies a decrease in
the input resistance R
i
of the DC–DC converter (and sub-
sequently, a decrease in the operation voltage of the photo-
voltaic generator) and vice versa (Enrique et al., 2005a,b,
2007; Dura
´n et al., 2008, 2009). The system starts from
an initial value (for example d= 0.5) that varies at constant
increase (Dd) according to expressions (6) and (7).
bi¼sign½ðDVÞðDPÞ ð6Þ
di¼di1þbiDdð7Þ
In each iteration “i”,DPand DVmeasures are obtained.
Next, the value of dis adjusted to approach it to the MPP.
Note that no temperature and solar radiation measures are
needed to do the tracking, which reduces the price of the
control system. The flow chart diagram of this algorithm
is shown in Fig. 5.
3.2. The developed system
The whole developed system is shown in Fig. 11.To
explain its operation, the system will be analyzed by blocks.
Fig. 6 shows the circuit that, from the voltage and current
measures at the PV array output, generates a reference sig-
nal, V
ref
, which will then be used in another block to gen-
erate a PWM signal.
From the voltage and current measures at the array out-
put (V, I), the variable power, P, is generated by using the
multiplier “Mult. 1”. Two differentiators followed by two
comparators generate the value of the functions sign(dV)
and sign(dP). These two signals are multiplied and com-
pared again to generate the analog equivalent of the bit
Fig. 4. P–Vcharacteristic of a photovoltaic array. The developed MPPT
algorithm is able to distinguish whether the system is operating to the right
or left of the MPP and act consequently.
Table 1
Possible cases and control law to enable the photovoltaic system follow the MPP.
Case System evolution Control law (V?V
MPP
)
sign(DV)sign(DP)b
i
=sign((DV)(DP)) V sign(DV)d
V
A
?V
B
+1 +1 1"+1 ;
V
B
?V
A
111"+1 ;
V
C
?V
D
+1 1+1 ;1"
V
D
?V
C
1+1+1 ;1"
Fig. 5. Flow chart of the MPPT P&O-oriented algorithm.
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“b
i
”. The iterations of expression (3) are formed by inte-
grating the subsequent b
i
. Finally, the output signal is lim-
ited in order to maintain it within the appropriate range,
generating V
ref
. This signal can be used as control signal
of a PWM generating system (Enrique et al., 2005a,b).
To perform the practical implementation of the devel-
oped system, the chip AD633J has been selected as multi-
plier block. For the comparators, the cheap (approx.
0.5 $) and extensively used op-amp TL082 has been
selected. The integrator and differentiator blocks are shown
in Fig 7. Both structures are basic in analog electronics.
The op-amp TL082 has also been used for their
implementation.
A lowpass RC filter has been inserted before each differ-
entiator block to remove part of the harmonic content of
the input signals. The output signal, V
ref
, of the system in
Fig. 6 is used as reference voltage for a PWM generator
(see Fig. 8), so that its duty cycle can be adjusted.
The output PWM signal of the circuit in Fig. 8 allows
controlling the behavior of the DC/DC converter. This
converter (boost-type, in this case) is shown in Fig. 9 con-
nected to a 25 Xload.
To reduce the price of the sensors, the voltage input is
taken from the photovoltaic array using a high impedance
voltage divider with a voltage follower. The measurement
of the current variable is performed by measuring the volt-
age fall in a very low value resistance, located at one of the
PV array terminals. This measure must be amplified before
reaching the multiplier. For this purpose, a very low offset
voltage precision op-amp OP27 has been used (see Fig. 10).
Fig. 11 shows the diagram of the whole developed
MPPT system.
4. Simulations
The developed system has been verified using PSpice
Ò
.
The photovoltaic generator has been implemented using
ABM blocks (Analog Behavioral Modeling). The parame-
ters of the generator model correspond to the “BP
Saturno”module (ns = 60 and np = 1) (CIEMAT, 2000).
Fig. 12 presents the model and I–V and P–V curves of
the module used at 21 °C and 1000 W/m
2
.Table 2 shows
the MPP power and current (P
MPP
and I
MPP,
respectively)
for different levels of radiation and constant temperature.
To verify the correct operation of the system, fast vari-
ations in the incident radiation have been applied to it
(see Fig. 13). Observe that during start-up, an initial rise
of 688.7 W/m
2
in the incident radiation (P
MPP
= 55.2 W)
is reached by the system in approximately 10 ms. Once
the maximum power point has been reached, the system
maintains it even for variations higher than 5 10
3
W/
m
2
/s, much higher than those present in nature. Addition-
ally, it can be observed that the system presents a high pre-
cision, since the actual trajectory of the MPP and the one
intended do not have practically noticeable differences.
Fig. 14 shows the current obtained with the tracker system.
Fig. 6. System generating the reference signal.
Fig. 7. Differentiator and integrator blocks used.
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With this sudden start-up, the tracking system is able to
obtain efficiencies superior to 97.2% in the first 100 ms.
Once the MPP has been reached (during the first millisec-
onds of the start-up) the system presents a tracking effi-
ciency ghigher than 99% (99.99%), even for variations in
the incident radiation as fast and extreme as those shown
in Fig. 13. This efficiency is superior to 81–85% of a classi-
cal “P&O”system (Perturb and Observed), superior to 88–
89% of an “InC”system (Incremental Conductance) and to
73–85% of a “CV”system (Constant Voltage)(Hohm and
Ropp, 2002). In Fig. 15, note how the system is able to
adjust automatically the duty cycle of the PWM signal.
Fig. 9. Boost converter used.
Fig. 8. System generating the PWM signal.
Fig. 10. Measure of variables Vand I.
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Fig. 11. Diagram of the whole developed system.
Fig. 12. Model and I–Vand P–Vcurves of the “BP Saturno”module.
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5. Conclusions
In this work, the design of a new maximum power point
(MPP) tracking system for photovoltaic systems has been
developed. The system is an analog version of the tracking
“P&O-oriented”algorithm. From the results obtained by
simulation, it can be concluded that the developed system
presents an excellent precision and speed in the MPP track-
Table 2
P
MPP
and I
MPP
for different levels of radiation and constant temperature
corresponding to the “BP Saturno”generator.
Temperature (°C) Radiation (W/m
2
)P
MPP
(W) I
MPP
(A)
21 688.7 55.2 1.86
21 1000 80.6 2.71
21 1721.8 136.2 4.76
Fig. 13. Top chart: applied variations in the incident radiation. Bottom chart: comparative between the actual trajectory of the MPP and that followedby
the developed system for variations in the incident radiation.
Fig. 14. Current supplied by the system for variations in the incident radiation.
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ing, even for very sudden variations in the levels of incident
radiation, so increasing the total energy performance of the
installation. The system is able to reach the MPP in the first
10 ms, getting high efficiency values practically from the
start-up. Once the system has reached the MPP, the effi-
ciency is superior to 99%, improving the ones obtained
by other methods (“P&O”,“InC”,“CV”). This quality,
along with its high simplicity and low price, makes the pro-
posed system highly suitable for use in any kind of photo-
voltaic installation.
Acknowledgment
The present work is a contribution of the DPI2007
62336/project, funded by The Spanish Ministry of
Education.
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