Download Low-Complexity MPPT Technique Exploiting the PV Module MPP

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009
1531
Low-Complexity MPPT Technique Exploiting the
PV Module MPP Locus Characterization
Vladimir V. R. Scarpa, Student Member, IEEE, Simone Buso, Member, IEEE, and Giorgio Spiazzi, Member, IEEE
Abstract—This paper proposes a method for tracking the maximum power point (MPP) of a photovoltaic (PV) module that
exploits the relation existing between the values of module voltage
and current at the MPP (MPP locus). Experimental evidence
shows that this relation tends to be linear in conditions of high
solar irradiation. The analysis of the PV module electrical model
allows one to justify this result and to derive a linear approximation of the MPP locus. Based on that, an MPP tracking strategy is
devised which presents high effectiveness, low complexity, and the
inherent possibility to compensate for temperature variations by
periodically sensing the module open circuit voltage. The proposed
method is particularly suitable for low-cost PV systems and has
been successfully tested in a solar-powered 55-W battery charger
circuit.
Index Terms—Maximum power point (MPP) tracking, standalone photovoltaic (PV) systems.
I. I NTRODUCTION
I
N ORDER to ensure the optimal use of the available solar
energy, the tracking of the maximum power point (MPPT)
is an essential part of any photovoltaic (PV) system [1]. This
function is implemented by suitably controlling the power
processing circuit which is almost always used as an interface
between the PV generator and the load or the energy accumulator. In the last few years, several novel MPPT methods
have been proposed, as well as improvements for the already
established ones [2]–[6].
Many of those methods aim at tracking the maximum power
operating point of a PV generator by satisfying, in a closed
loop regulation, the condition dPPV /dVPV = 0, where PPV
and VPV represent the PV module output power and voltage,
respectively. As an example, the very popular Perturb and
Observe (P&O) [7]–[10] and the Incremental Conductance
(IncCond) [11]–[13] make use of this relation. Due to the
complexity of the required mathematical operations, a digital
signal processor or a relatively powerful microcontroller are
typically needed to implement them, which increases the cost
of the power processing circuit.
Manuscript received April 21, 2008; revised October 17, 2008. First published November 25, 2008; current version published April 29, 2009. This work
was supported by the Program Alban, the European Union Program of High
Level Scholarships for Latin America, under Scholarship E05D049801BR.
V. V. R. Scarpa and G. Spiazzi are with the Department of Information Engineering, University of Padova, 35131 Padova, Italy (e-mail:
[email protected]; [email protected]).
S. Buso is with the Department of Technology and Management of Industrial Systems, University of Padova, 36100 Vicenza, Italy (e-mail: simone.
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2008.2009618
A less complicated way of tracking the maximum power
point (MPP) is through a convenient estimation technique,
based on an offline module characterization. In these methods, the optimal value of the PV voltage (VMPP ) or current
(IMPP ) is estimated as a function of the module short circuit
current (ISC ) [14], [15], open circuit voltage (VOC ) [16]–[18],
or temperature (T ) [19]. Although estimation methods are
generally much cheaper and simpler than those previously
mentioned based on hill climbing algorithms, they often rely on
approximated relations which, in certain operating conditions,
can drive the system excessively far from the true MPP, thus
significantly reducing the effectiveness of the power processing
circuit. Therefore, their use has been limited mainly to low-cost
low-power PV applications.
Intermediate solutions can also be devised, as the one discussed in [20], where a linear relation between the values
of module voltage and current at the MPP is used to reduce
the convergence time in the P&O and IncCond methods. This
paper shows how and why the relation exploited in [20] can
actually be used as an alternative estimation technique, allowing the implementation of a novel low-complexity MPPT
method.
The analytical derivation of the estimation equation from
the electrical model of a PV module allows one to identify
its parameters, expressing them in terms of module quantities.
Furthermore, the proposed solution suggests a simple and effective way to compensate the estimation equation for temperature
variations, which only requires the periodic sensing of the
VOC . As it will be further demonstrated, the proposed method
presents better results when compared to other offline methods
of comparably low complexity.
This paper is organized as follows. In the first part, Section II,
the mathematical analysis of a PV module electrical model is
presented, which clarifies the underlying physical background
and derives the analytical expression of the MPP locus. In
the following part, comprising Sections III–V, the method
is presented, the effect of temperature on its performance is
discussed, and its effectiveness is compared with that of the
very popular Fractional VOC method. Finally, in Sections VI
and VII, the experimental application of the proposed strategy
to a 55-Wp PV-powered battery charger is discussed.
II. MPP L OCUS C HARACTERIZATION
In a PV module, the MPP locus can be defined as the couple
(VMPP , IMPP ), expressed as a function of module irradiation
at a given operating temperature. The basic result presented in
this paper is how to find a linear equation that approximates the
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TABLE I
PV MODULE DATA AND SIMULATION PARAMETERS
Fig. 1. Equivalent electrical model of a PV module with N series-connected
cells.
MPP locus and consequently allows one to implement a lowcomplexity MPPT method.
We start the analytical derivation of the module MPP locus
from the usual equivalent electrical model shown in Fig. 1.
The model represents a generic PV module, composed by N
series-connected cells, each of them presenting an equivalent
series resistance RS and shunt resistance RSH . As usual, the
current source Ig represents the photogenerated current, while
series-connected diodes Di are lumped representations of the
internal electron-hole recombination processes. We can write
the following expression for the module current IPV :
V +N ·R I
PV
S PV
VPV + N · RS IPV
IPV = Ig − Isat · e N ·(nVT )
−1 −
N · RSH
(1)
where
Isat = C · T e
3
−Eg
VT
Fig. 2. Difference between VOC and VMPP for several irradiation conditions
in a 55-Wp PV module (dots) and in the corresponding model (solid line),
according to (6).
(6), which expresses the difference between VOC and VMPP and
determines the relation between the variables (VMPP , IMPP )
VMPP
∼
VOC − VMPP = N · RS IMPP + nVT · ln
+1
N · nVT
= N · (RS IMPP + VDO ) .
(2)
is the cell inverse saturation current, and n is the so-called ideality factor. In (2), C is a suitable constant (in Ampere/◦ K−3 ),
VT = kT /q is the temperature equivalent voltage, being k the
Boltzmann’s constant, q the electron charge, T the temperature
in kelvin, and Eg represents the energy gap of silicon in
electronvolts.
Since in almost all practical cases the cell shunt resistance
RSH is relatively high, the current through it can be neglected
and, consequently, the module output power can be well approximated by
V +N ·R I
PV
S PV
− 1 . (3)
PPV ∼
= VPV · Ig − Isat · e N ·(nVT )
Calculating the partial derivative of (3) with respect to VPV
and imposing it to be zero, it is possible to derive the following
relation, valid at the MPP:
VMPP +N ·RS IMPP
Ig
VMPP
N ·nVT
+1=e
· 1+
.
(4)
Isat
N · nVT
Equation (1) can now be rearranged to approximate the value
of VOC as
Ig
+1
(5)
VOC ∼
= N · nVT · ln
Isat
where the term related to RSH has been neglected once again.
Combining (4) and (5) and rearranging the terms, we obtain
(6)
In (6), the term named Differential Offset Voltage (VDO ) has
been implicitly defined. We will now introduce the hypothesis,
which we will verify in the immediate following, that VDO
variations with irradiation can be neglected, and hence, the
difference between VOC and VMPP , expressed by (6), increases
linearly with IMPP .
Experimental verification of (6) has been done on a 36-cell
module by Helios Technology (Model H580) whose data, given
by the manufacturer [21], are presented in Table I. The same
table also shows the parameter values needed to emulate the
module’s characteristics with the model of Fig. 1. The obtained
results are shown in Fig. 2. As can be seen, the measured values
follow the linear trend corresponding to (6).
However, the relation between VMPP and IMPP with respect
to irradiation is not linear, because VOC is a logarithmic function of Ig , as clearly shown by (5). Nonetheless, it is possible
to linearize this relation for an interval where the value of VOC
is sufficiently insensitive to irradiation. Indeed, from (5), it is
possible to derive the sensitivity of VOC to Ig (SVOC ,Ig ) as
SVOC ,Ig =
dVOC Ig
1
.
·
≈ Ig
VOC dIg
ln Isat + 1
(7)
If we predefine a threshold value for SVOC ,Ig (e.g., 5%),
from (7), we can calculate a minimum irradiation condition,
corresponding to a photogenerated current Ig∗ , above which
the sensitivity is lower than the selected threshold, at a given
∗
,
temperature T ∗ . Associated to Ig∗ and T ∗ are the values VOC
∗
∗
∗
IMPP , VMPP —shown in Fig. 3 —, and VT . Now, the desired
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SCARPA et al.: MPPT TECHNIQUE EXPLOITING THE PV MODULE MPP LOCUS CHARACTERIZATION
Fig. 3. (Black lines) I–V curves for several irradiation conditions, (blue line)
the MPP locus curve, and (red line) the VLR, calculated for Ig∗ = 2.5 A.
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Fig. 4. Simulated effectiveness of the VLR as a function of irradiation, for
three different values of RS .
TABLE II
VLR PARAMETERS AT T ∗ = 25 ◦ C
linear relation, approximating the MPP, will be defined as the
tangent to the MPP locus curve for Ig = Ig∗ . The tangent line is
named Voltage Linear Reference (VLR), and is shown in Fig. 3.
As can be seen, the choice of the irradiation range guarantees a
maximum relative VOC variation of about 4.9%. The VLR can
also be analytically derived from (6) as
dVOC − N · RS IMPP + VOFFSET (8)
VLR ≡
dIMPP Ig =Ig∗
∗
VOC
∗
(VDO
VT∗ )
∗
VDO
where VOFFSET =
−n·
+
and
is calculated for Ig = Ig∗ . Considering that IMPP is roughly proportional to Ig (see [14] and [15]), dVOC /dIMPP can be
calculated as
dVOC
dVOC dIg
n · VT∗
=
·
≈
. (9)
∗
dIMPP Ig =Ig∗
dIg dIMPP Ig =Ig∗
IMPP
The parameters used to analytically derive the VLR for the
simulated PV module are presented in Table II.
According to (8) and (9), for the particular case where
∗
> RS , the VLR has negative slope. However, this
nVT∗ /IMPP
is not a necessary condition for the proposed method to operate
properly, since (6) is valid independently from the value of RS .
Nevertheless, as will be seen in Section VI, the slope sign has a
role in the way the method is implemented.
In order to evaluate the accuracy of the proposed approximation, the electrical power of each point of the VLR was
calculated and compared with the power of the MPP locus at
the same irradiation condition. The ratio between these two
values, which we can define as the effectiveness (ε) of the VLR
approximation, is shown in Fig. 4. As can be seen, in order to
assess the sensitivity of the achievable effectiveness to different
values of RS , two other VLRs were calculated through (8).
In the three cases, the effectiveness is very near to unity for
Fig. 5. (VDO + n · VT ) obtained through simulation, with the parameters of
Table I, for three different temperature conditions.
any Ig > Ig∗ . Beneath this value, the effectiveness decreases,
reaching a value of ε = 0.9 for Ig = 0.3 A.
III. P ROPOSED M ETHOD
Based on the previous analysis, it is possible to implement
a simple MPPT method by forcing the PV module to operate
over the VLR. The MPPT can be based on any dc–dc switching
converter, driven by a suitable input voltage (or input current)
control circuitry that, using the VLR equation over the values of
module voltage and current, automatically drives the module to
the point where the VLR intercepts the current I–V curve. At
that point, the equilibrium condition VPV ∼
= VMPP (or IPV ∼
=
IMPP ) holds.
Of course, the effectiveness of the method is conditioned
by the accuracy of (8), which can be very high for high
irradiation—and thus high power—conditions, as shown in
Fig. 4. Furthermore, in order to guarantee the same performance
for any temperature condition, the proposed method must also
include some kind of compensation for temperature variations.
This will be discussed in the next section.
IV. E FFECT OF T EMPERATURE V ARIATIONS
It is known that, assuming constant irradiation, the value of
VOC in a PV module varies by about −2.5 mV/◦ C per cell
∗
is a function of temperature.
[19], and thus the value of VOC
In addition, according to (6), it is expected that the MPP locus
is shifted by the same amount, since it is normally acceptable
to consider RS independent from temperature and, from Fig. 5,
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009
Fig. 6. MPPs for T = 0 ◦ C, T = 25 ◦ C, T = 50 ◦ C, and (black lines) their
respective VLRs calculated through (7).
one can observe that VDO variation with temperature can also
be neglected.
∗
variation with temperaFurthermore, if we neglect the IMPP
ture, and considering that, as shown in Fig. 5, the sum (VDO +
n · VT ) varies only about 6% for a 50 ◦ C temperature variation,
one can conclude that not only the characterization for the
VLR calculation can be done at any temperature condition, but
also that it is possible to compensate for temperature variations
∗
(T ). This is demonstrated
simply by sampling the value of VOC
by Fig. 6, where the VLR, calculated for T = T ∗ = 25 ◦ C,
approximates the MPP locus with similar accuracy for any
∗
is updated.
temperature condition, as long as VOC
Hence, to take advantage of this property, a practical implementation of the method would require the periodic sensing
of VOC at the irradiation condition that corresponds to Ig =
Ig∗ . However, this solution would not be convenient, since it
requires the additional sensing of Ig or the use of an irradiation sensor. Therefore, this paper proposes a simpler and
cost-effective implementation: the value of VOC is sensed and
simply inserted in (8), without any concern about temperature
or irradiation conditions at the moment of sensing. As it will be
further discussed in the next section, it will not only determine
the required compensation, but also inherently increase the
effectiveness of the estimation, particularly for lower irradiation conditions, i.e., those below Ig∗ . Given the relatively slow
thermal time constants, this only requires the periodic sampling
of VOC at a very low frequency, which helps to minimize
the negative impact on the effectiveness of the temperature
compensation process.
V. S TUDY OF THE M ETHOD E FFECTIVENESS
This section presents the study of the effectiveness of the
proposed method. First, the impact of the proposed solution for
temperature compensation on the effectiveness of the method
will be considered. Later, the VLR method will be compared
to the very popular Fractional VOC (F racVOC ) method, to
evaluate the effectiveness improvement obtained with respect
to a method with similar implementation complexity.
A. Influence of Irradiation at VOC Sampling
As explained above, during operation, VOC is periodically
sensed, and VOFFSET is adjusted accordingly. The slope of
Fig. 7. Effectiveness of the VLR method for several values of irradiation
condition at Voc sensing (marked with points).
Fig. 8. (Blue lines) Effectiveness of the VLR method and (red lines) the
Fractional Voc method for three different temperature conditions.
the VLR, instead, remains the same one, calculated offline.
Therefore, in the presence of variable irradiation conditions, the
system moves across several effectiveness curves, each related
to the particular, more recently sampled, VOC value.
Using the parameters of Table I and temperature T = 25 ◦ C,
Fig. 7 shows several effectiveness curves of the proposed
method for the entire Ig range. The curves differ in the value
of Ig at which VOC has been sensed, given by the marked point
on each curve. As an example, assuming that VOC is sensed
for Ig = 1.5 A (point A in Fig. 7), if the value of Ig decreases
to Ig = 0.2 A (point B), the operation point will go far from
the MPP, as predicted in Section II. However, if a new sample
of VOC is taken, this will result in more suitable parameters
for the estimation equation, increasing the effectiveness. Please
note that the same fact is observed in the inverse situation, i.e.,
if irradiation increases between two VOC samples.
B. Comparison With the Fractional VOC Method
The proposed solution will now be compared with the
F racVOC method ([12] and [13]) that estimates the VMPP
value as
VFrac = kFrac · VOC .
(10)
The idea is to compare the effectiveness of each method as
a function of irradiation and temperature. Parameter kFrac was
defined as kFrac = 0.75, and the VLR has the same parameters
presented in Table I. For each value of Ig , the VOC was sampled
and the effectiveness of each method, for the three values of
temperature, was calculated and reported in Fig. 8.
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SCARPA et al.: MPPT TECHNIQUE EXPLOITING THE PV MODULE MPP LOCUS CHARACTERIZATION
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TABLE III
COMPARISON OF THE MEAN EFFECTIVENESS FOR
VLR AND F racVOC METHODS
The average value of the effectiveness (εm ) for each method
and for the range of Ig defined above can be calculated as
m
εm ≡
εi
i=1
m
(11)
where m is the total number of Ig samples. Applying (11)
to the results, the mean effectiveness of each method for the
three simulated temperature conditions can be derived, and
is presented in Table III. As can be seen, in any condition,
the proposed solution offers better results than the F racVOC
method.
VI. M ETHOD I MPLEMENTATION
For a given PV module, it might be not so immediate to
measure all the parameter values required by (8). A more
convenient way to implement the proposed solution consists in
the graphic determination of the VLR over offline measured
I–V curves. Then, the VLR can be arranged to generate a
reference value for the module voltage, through an equation of
the form
S
− Veq
Vref = Req · IPV + VOC
(12)
S
represents the periodically sampled VOC while
where VOC
Req and Veq are the parameters extracted from the analysis of
the I–V curves. Their physical interpretation is given by the
comparison of (12) and (8).
Since the parameters Req and Veq are related to physical
characteristics of the considered PV module, it is expected that
they will be only affected by fabrication process tolerances,
resulting in a reasonable repeatability, at least within the same
production lot.
If needed, (12) can also be straightforwardly transformed to
give a reference value for the module current Iref
S
S
Iref = VPV −VOC
+Veq /Req = VPV −VOC
+Veq · Geq .
(13)
With the help of Fig. 9, we would now like to illustrate the
method’s convergence to the MPP. In doing that, we assume
that we are dealing with a current controlled dc–dc converter,
whose controller has, at least, an integral characteristic and is
designed to guarantee a suitable stability margin, in particular
when (13) is used to determine the current set point.
In addition, we suppose the pulse width modulation (PWM)
modulator is organized so that, when the PV module is such
that Req < 0, IPV increases for a negative current error. The
opposite must occur if Req > 0, so that we are always closing
a negative feedback loop.
Fig. 9. Convergence process of the proposed MPPT strategy. (a) Explanation
of the process. (b) Example of convergence to the MPP (simulation: VMPP =
16 V, IMPP = 2.3 A).
As shown in Fig. 9(a), starting from the condition VPV =
S
, both the calculated Iref and the error are negative. As
VOC
the value of IPV increases, thanks to the integral controller’s
action and to a proper organization of the modulator, the error
decreases in absolute value, until the steady-state equilibrium
point is reached, at the intersection between the VLR and the
module I–V curve. It is worth recalling that, if the VLR estimation error is low, the equilibrium point will be very close to
the MPP, as we have shown in Section V. Once the equilibrium
point is reached, a further increase of the current is prevented
by the error sign reversal. Therefore, the equilibrium point is
inherently stable. An interesting consequence of this fact is that,
with the proposed method, phenomena like oscillations around
the MPP or control losses due to sudden illumination variations (that can take place with other methods, e.g., P&O and
IncCond) are not possible. As can be recognized, the situation
shown in Fig. 9(a) is general and applies to all the operating
conditions. Therefore, the convergence to the equilibrium point
is guaranteed by the hardware organization, i.e., the system will
always move toward the equilibrium point, independently from
its initial conditions.
Of course, we need to make sure that the small signal stability
around the equilibrium point is guaranteed as well. Indeed, the
current reference generation is based on the measured module
voltage and, therefore, represents a further feedback loop, with
a purely proportional compensator in it, whose gain is equal to
Geq (13). In order to guarantee the small signal stability of this
controller, i.e., its capability to steadily maintain the module on
the equilibrium point of Fig. 9(a), rather than oscillating around
it, the crossover frequency and phase margin of the external
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TABLE IV
CONVERTER COMPONENT VALUES
Fig. 10. Battery charger schematic with the proposed control strategy.
loop have to be properly chosen. As the loop gain cannot be
modified (it is imposed by the VLR), a simple and robust way
to do that is by limiting the loop bandwidth, to give to the
loop gain a first-order compensated behavior. This result can be
obtained reducing the current controller speed of response, i.e.,
adjusting the current controller gain until a properly damped response is achieved. Please note that this does not imply any real
performance penalization, as the required speed of response
for an effective MPPT does not need to be very high. As we
will show in the following (Fig. 10), in our implementation,
the reference current is digitally generated, even if the current
controller is still implemented by an analog circuit. In this
case, to avoid any stability problem, it is only required to keep
the digital controller update, or iteration, frequency fMPPT
high enough to introduce a negligible delay in the reference
generation loop. We observed that setting the reference update
frequency, at least, two or three times higher than the current controller bandwidth guarantees a satisfactory response.
Indeed, in these conditions, the digital implementation of the
current reference generator behaves very much like the sampled
data version of an analog one and does not pose any additional
stability problem. Of course, the iteration frequency must also
be compatible with the reference computation time, which is
limited by the A/D and D/A conversion speed and by the time
required for the numerical calculation of Iref (13). However,
unless a very low-performance digital control hardware is
adopted, there is normally no problem to achieve an acceptable
speed of response. An example of the typical response that can
be obtained with a proper design is shown in Fig. 9(b), where
the module voltage, current and power are shown, together with
the current reference, digitally generated according to the VLR
equation (13). The reference update frequency is, in this case,
equal to 200 Hz, as in our experimental prototype.
In order to validate the proposed method, an experimental
setup was built, based on the buck–boost topology, that operates
as a battery charger, as shown in Fig. 10. The implementation
is conventional, except for an additional logic switch, inserted
in the output of the PWM block.
It determines if the MOSFET will be driven by the duty
cycle D, if Req > 0, or by its complement (1-D), if Req < 0,
for the reasons explained above. This guarantees the required negative feedback for the convergence process shown
in Fig. 9. The parameters of the circuit are presented in
Table IV.
It is worth noting that the proposed method is not in any way
topology dependent and can be adapted to all types of converters with input current or input voltage control. The choice of
the buck–boost topology is only motivated by practical reasons,
as it allows both series and parallel connection of batteries. In
particular applications, the choice of an optimized topology is,
of course, recommended. As shown in Fig. 10, even though
Iref is calculated by a microcontroller, it passes through a D/A
converter and feeds an analog closed loop current controller,
to avoid the need for fast A/D conversion and digital PWM
modulation.
Given the simple operations involved in the Iref
calculation—sum and multiplication between a sensed variable
and a predefined constant—and the low repetition frequency—
typically below 1 kHz—a simple 8-bit microcontroller has
been used, whose high quantity price is below 1USD.
This is, in fact, one of the advantages of the proposed solution
when compared to more sophisticated methods, such as P&O
and IncCond. These algorithms need the calculation of the
module power, i.e., the multiplication of two sensed variables,
and, therefore, cannot take advantage of any of the optimized
multiplication routines that can be generally used, in low-cost
microcontrollers, when one of the multiplication parameters is
a constant.
A flow chart of the algorithm executed by the microcontroller
is shown in Fig. 11. The frequency of the MPPT calculation,
according the aforementioned considerations, has been defined
as fMPPT = 200 Hz, while the value of VOC is sampled every
5 minutes.
VII. E XPERIMENTAL R ESULTS
The aforementioned, practical way to obtain the equation of
the VLR is shown in Fig. 12, where, after defining the value of
Ig∗ = 2.5 A, the MPPs at this condition and at two other ones
in the vicinity of Ig∗ are connected by a straight line. This line
represents the VLR.
As can be seen, the process can be repeated for any temperature condition, since, as we have shown, the slope of the VLR
is practically insensitive to this parameter. Once the control
parameters are extracted, the proposed method can be applied
straightforwardly.
Fig. 13(a) shows the dynamic behavior of the system for an
irradiation decrease. As it can be observed, while the irradiation
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Fig. 11. Flowchart of the Iref computation algorithm.
Fig. 13. (a) Dynamic behavior of the system for an irradiation decrease. (From
top to bottom) Module voltage (2 V/div), module power (20 W/div), module
current (0.5 A/div), current reference (1.2 A/div). Horizontal scale: 50 ms/div.
(b) Same transition over the I–V plane.
Fig. 12. VLR determination for two different temperature conditions.
varies, the module operation smoothly moves over the VLR.
The Iref oscillation visible in the steady state condition is due to
the limit cycle caused by the finite resolution of the calculation.
In Fig. 13(b), the same process is represented in the I–V plane.
Since the irradiation step occurs between two samples of VOC ,
the effectiveness obviously decreases in the new irradiation
condition, from ε = 0.99 to ε = 0.91. The effectiveness of
the circuit for an entire sunny day measurement is shown in
Fig. 14.
It was calculated as the ratio between maximum available
power and extracted power (thus not including the converter
efficiency, by the way about 85% on average). As can be
seen, it is very close to 100% in the higher irradiation conditions, remaining above 90% even for the lower irradiation
conditions.
VIII. C ONCLUSION
This paper has presented an MPPT method that is based on
the offline characterization of the MPP locus of a PV module.
Fig. 14. (Lower black line) Maximum available power, (gray line) average
extracted power, and (upper black line) the effectiveness of the MPPT.
This paper has shown why and under what hypotheses the MPP
locus can be well approximated by a line. Once the parameters of the estimation equation are extrapolated from offline
measurements, the method allows one to track the MPP of the
module requiring only the measurement of the input voltage
and current. As any other estimation method, its effectiveness
can be impaired by variations in the operating conditions.
However, due to the effect of the module series resistance, the
method will present better results in the high irradiation, high
power conditions, with respect to the conventional solutions.
Furthermore, this paper shows how, by simply measuring the
module open circuit voltage, it is possible to compensate for
temperature variations. The method has been implemented in
a low-cost 8-bit microcontroller and tested in a battery charger
application with satisfactory results.
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1538
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 5, MAY 2009
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Vladimir V. R. Scarpa (S’05) was born in
Uberlândia, Brazil, in 1980. He received the B.Sc.
and M.Sc. degrees in electrical engineering from
the Federal University of Uberlândia, Uberlândia, in
2003 and 2005, respectively. He is currently working
toward the Ph.D. degree in information engineering
at the University of Padova, Padova, Italy.
His research interests include power electronics
applied to renewable energy sources and digital control of switching power supplies.
Simone Buso (M’97) received the M.Sc. degree
in electronic engineering and the Ph.D. degree in
industrial electronics from the University of Padova,
Padova, Italy, in 1992 and 1997, respectively.
He is currently an Associate Professor of electronics with the Department of Technology and Management of Industrial Systems, University of Padova.
His main research interests are in the industrial and
power electronics fields and are specifically related
to dc/dc and ac/dc converters, digital control and robust control of power converters, solid-state lighting,
and renewable energy sources.
Giorgio Spiazzi (S’92–M’95) received the M.Sc.
degree (cum laude) in electronic engineering and
the Ph.D. degree in industrial electronics from the
University of Padova, Padova, Italy, in 1988 and
1993, respectively.
He is currently an Associate Professor with the
Department of Information Engineering, University of Padova. His main research interests are in
the fields of power-factor correctors, soft-switching
techniques, lamp ballasts, renewable energy applications, and electromagnetic compatibility in power
electronics.
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