Theoretical Assessment of the Maximum Power Point Tracking

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Theoretical assessment of the maximum power point tracking

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Theoretical assessment of the maximum power point
tracking efficiency of photovoltaic facilities
with different converter topologies
J.M. Enrique
a,
*
, E. Dura´n
a
, M. Sidrach-de-Cardona
b,1
, J.M. Andu´ jar
a
a
Departamento de Ingenierı´a Electro´ nica, de Sistemas Informa´ ticos y Automa´ tica, Universidad de Huelva, Spain
b
Departamento de Fı´sica Aplicada, II, Universidad de Ma´ laga, Spain
Received 16 May 2005; received in revised form 1 March 2006; accepted 15 June 2006
Available online 24 August 2006
Communicated by: Associate Editor Hansjo¨ rg Gabler
Abstract
The operating point of a photovoltaic generator that is connected to a load is determined by the intersection point of its characteristic
curves. In general, this point is not the same as the generator’s maximum power point. This difference means losses in the system per-
formance. DC/DC converters together with maximum power point tracking systems (MPPT) are used to avoid these losses. Different
algorithms have been proposed for maximum power point tracking. Nevertheless, the choice of the configuration of the right converter
has not been studied so widely, although this choice, as demonstrated in this work, has an important influence in the optimum perfor-
mance of the photovoltaic system. In this article, we conduct a study of the three basic topologies of DC/DC converters with resistive
load connected to photovoltaic modules. This article demonstrates that there is a limitation in the system’s performance according to the
type of converter used. Two fundamental conclusions are derived from this study: (1) the buck–boost DC/DC converter topology is the
only one which allows the follow-up of the PV module maximum power point regardless of temperature, irradiance and connected load
and (2) the connection of a buck–boost DC/DC converter in a photovoltaic facility to the panel output could be a good practice to
improve performance.
Ó 2006 Elsevier Ltd. All rights reserved.
Keywords: Photovoltaic module; DC/DC converter; I–V curve; Maximum power point tracker; Losses
1. Introduction
DC/DC converters are widely used in photovoltaic gen-
erating systems as an interface between the photovoltaic
panel and the load, allowing the follow-up of the maximum
power point (MPP). Its main task is to condition the energy
generated by the array of cells following a specific control
strategy (Hua and Shen, 1998; Hussein et al., 1995;
Masoum et al., 2002). The DC/DC conversion process
implies in turn an associated effect of impedance transfor-
mation, i.e., the input impedance shows a dependence on
a number of parameters such as load resistance, duty cycle,
etc. In this sense, converters are similar to transformers
when they are used as impedance adaptors, except that in
converters the adaptation parameter is not the turns ratio
between the secondary and primary ones, but the duty
cycle d, which can be governed electronically (Singer,
1991; Jingquan et al., 2001; Tse et al., 2002, 2004), a fact
that corresponds to the maximum power point tracking
system (MPPT). This effect, which is the basis of MPPT
systems, also shows an odd property: certain input imped-
ance values can be either reached or not, depending on the
0038-092X/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.solener.2006.06.006
*
Corresponding author. Tel.: +34 959 21 7374/7655/7671/7656; fax:
+34 959 017304.
E-mail addresses: [email protected] (J.M. Enrique), msi-
[email protected] (M. Sidrach-de-Cardona).
1
Tel.: +34 952132722/23; fax: +34 952131450.
www.elsevier.com/locate/solener
Solar Energy 81 (2007) 31–38
type of converter used, which significantly affects the pho-
tovoltaic system’s performance.
MPPT is used in PV power systems to force the PV mod-
ule operating at MPP. In this way the PV module produces
the maximum power output. For this operating point, it
overcomes the disadvantages of high initial installation costs
and low energy conversion efficiency. Previously-used meth-
ods of achieving MPPT include: (1) incremental conduc-
tance (IncCond); (2) perturbation and observation (P&O);
(3) neural network and (4) curve-fitting (Hua et al., 2003).
At present there are numerous works aimed at designing
MPPT systems (Bahgat et al., 2004; Enslin et al., 1997; Gar-
cı ´a and Alonso, 2000; Hua et al., 2003; Kitano et al., 2003;
Masoum et al., 2002; Neto et al., 2000; Schilla et al., 2000;
Veerachary et al., 2002, 2003; Yu et al., 2004), where the effi-
ciency of each of them is shown and comparatives of the dif-
ferent methods of MPP tracking are established under
different operating conditions. However, the choice of the
appropriate DC/DC converter for the implementation of
both the MPPT system and its integration in the facility
array has not been explicitly studied, despite its affecting sig-
nificantly the optimumoperation of the photovoltaic system.
The aim of this work is to make a comparative of the
photovoltaic system performance using the three basic
topologies of DC/DC converters and MPPT tracker, so
that it may be possible to make a decision on the best con-
figuration to be used. This work is divided into the follow-
ing sections: Sections 2 and 3 present some characteristics
and properties of photovoltaic modules and DC/DC con-
verters, especially as regards the input impedance that they
present under certain operating conditions. The analysis
and results for each configuration are shown in Sections 4
and 5. Finally, some conclusions are drawn in Section 6.
2. Theoretical models of solar arrays
A simplified exponential expression (Gow and Manning,
1999) describes the relationship between voltage (V) and
current given by a module, Eq. (1).
I ¼ n
P
I
L
ÀI
s
e
q
V
n
S
þ
IR
S
n
P
_ __
AKT
À1
_ _
À
V
n
S
þ
IR
S
n
P
R
P
_ _
ð1Þ
P ¼ I Á V ð2Þ
P ¼ n
P
Á V Á I
L
ÀI
s
e
q
V
n
S
þ
PÁR
S
V Án
P
_ __
AKT
À1
_ _
À
V
n
S
þ
PÁR
S
V Án
P
R
P
_ _
ð3Þ
dP
dV
_ _
MPP
¼ 0 ð4Þ
The n
P
and n
S
parameters indicate the number of cells
connected in parallel and in series, respectively; R
P
and R
S
, are the intrinsic parallel and series resistances associated
to the panel; K is the Boltzman constant (1.38 · 10
À23
J/K)
and q is the charge on an electron. Factor A determines the
deviation of the characteristics of an ideal p–n junction,
and I
S
is the reverse saturation current, which presents a
dependence on the panel temperature. I
L
represents the
current (photo-current) generated by solar radiation (G).
Such a current shows a linear relation with regard to radi-
ation and temperature.
Eq. (1) (considering the dependence of its parameters on
T and G) provides the so-called I–V curves of a photovol-
taic panel, and the multiplication result of both magnitudes
provides the supplied power: Eqs. (2) and (3). This curve
changes depending on the incident irradiance and the cell
temperature. Each curve presents a maximum power point
(MPP, point of coordinate V
P
), which provides the optimal
operation point for an efficient use of the panel (Hohm and
Ropp, 2002; Hua and Shen, 1998).
The MPP is calculated solving Eq. (3) with the condition
(4). This calculation is tedious and slow, since these expres-
sions do not have an analytical solution, and therefore,
they have to be solved by numerical methods (i.e., New-
ton’s method). Other two important points of this curve
are the open-circuit voltage (V
oc
) and the short-circuit cur-
rent (I
sc
). The voltage in an open circuit represents the
maximum voltage given by the panel to a zero current
(without load), while the short circuit current represents
Nomenclature
d duty cycle
g MPP-tracking efficiency
A ideality factor of PN junction
C capacitance
I current supplied by the photovoltaic array
I
L
photo-current generated by solar radiation
I
MPP
maximum power point current
K Boltzmann constant (1.38 · 10
À23
J/K)
L inductance
n
P
number of parallel-connected cells
n
S
number of series-connected cells
P power supplied by the photovoltaic array
P
MPP
power of the maximum power point
q electro´ n charge (1.602 · 10
À19
coulombs)
R
i
input resistance
R
L
load resistance
R
MPP
maximum power point impedance
R
P
intrinsic parallel resistance
I
S
reverse saturation current
R
S
intrinsic series resistance
T temperature
T
C
conmutation period
V voltage supplied by the photovoltaic array
V
MPP
maximum power point voltage
32 J.M. Enrique et al. / Solar Energy 81 (2007) 31–38
the maximum removable current of the panel (short-circuit
load).
There are other models of photovoltaic generators
(PVG) apart from the one mentioned above. Akbaba and
Alataawi (1995) proposed a simple model which is named
the Akbaba model (Akbaba et al., 1998). Its accuracy, flex-
ibility and simplicity are demonstrated by comparing this
model with the traditional diode junction model for a
PVG whose parameters are given in Appelbaum (1986).
But the existing version of the Akbaba model is not com-
plete, since the values of its model parameters are solar radi-
ation-dependent and they need to be evaluated at each solar
radiation level. This adds additional computational burden
and hence full advantage of the model cannot be utilized.
In this work, we use the model described in Eq. (1) in
order to implement the theoretic model used in the
simulation.
3. DC/DC converters as variable resistance emulators
DC/DC converters are used in applications where an
average output voltage is required, which can be higher or
lower than the input voltage. This is achieved by governing
the times in which the converter’s main switch conducts or
does not conduct (PWMtechnique) usually to a constant fre-
quency. The ratio of the time interval in which the switch is
on (T
ON
) to the commutation period (T
C
) is called duty cycle
(d) of the converter. Both in the continuous conduction
operational mode (CCM)
2
and the discontinuous conduc-
tion mode (DCM),
3
the three basic converter topologies
can be compared to a continuous current transformer,
where the transformation ratio can be electronically con-
trolled varying the converter’s duty cycle d in the range [0, 1].
Fig. 1 shows the diagram of a solar panel connected to a
DC/DC converter, where the resistance shown at the con-
verter’s input is represented by R
i
(R
L
is the converter’s
load resistance). In relation to the photovoltaic module,
the converter is its R
i
value load resistance. Assuming con-
verters without losses, the ratio of input resistance to load
resistance is shown in Table 1, both for CCM and DCM
(Tse et al., 2002).
The converter’s operational mode is defined by the con-
stant K given in (5), where L
eqv
is the inductance equivalent
to the converter, R
L
its load resistance and T
C
the commu-
tation period (reverse to the operating frequency).
K ¼
2L
eqv
R
L
T
C
ð5Þ
If K value is lower than or equal to another one called
K
crit
, the converter will operate in DCM. Conversely, if K
exceeds the value of K
crit
, the converter will operate in
CCM. As observed in Table 1, the value of K
crit
is different
for each type of converter.
Fig. 2 shows the three basic converters which provide
the different conversion ratios given in Table 1, together
with a graphic representation of the input resistance
reflected according to the duty cycle d for CCM (Andujar
et al., 2004; Enrique et al., 2005).
4. Theoretic analysis
Fig. 3 shows the I–V curve for a given module connected
to a converter. Let us take any curve point, for example A.
The photovoltaic module will operate in A provided that
the output voltage and current match the voltage and
current of point A (V
A
, I
A
). Thus, we will call the quotient
V
A
/I
A
impedance of the operating point A (R
iA
).
Assume that B is the maximum power point, therefore
R
iB
= R
MPP
= V
MPP
/I
MP
. The system will then operate at
the maximum power point (MPP) provided that R
i
=
R
iB
= R
MPP
. In general terms, a maximum power point
tracking system tries to vary impedance at the photovoltaic
module output (R
i
) in order to take it to the R
MPP
value.
As has been mentioned above, the I–V curve of a photovo-
ltaic module varies according to the incidental temperature
and radiation, so V
MPP
, I
MPP
and R
MPP
will vary depend-
ing on how these variables do.
4.1. Analysis of the module-buck converter-load
configuration
The following expressions are deduced from Table 1 for
the buck converter:
2
CCM (Continuous Conduction Mode): DC/DC converter operational
mode, where the current intensity that circulates through the inductance of
that converter is not cancelled out at any interval of the T
C
commutation
period.
3
DCM (DCM, Discontinuous Conduction Mode): DC/DC converter
operational mode, where the current intensity that circulates through the
inductance of that converter is cancelled out during an interval of the T
C
commutation period.
Fig. 1. Panel–converter connection.
Table 1
R
i
values for converters in Fig. 4
Converter K
crit
R
i
(CCM) R
i
(DCM)
Buck 1 À d
RL
d
2 RL
4
Á 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ4K=d
2
_
_ _
2
Boost dÆ(1 À d)
2
R
L
Æ (1 À d)
2 4ÁRL
ð1þ
ffiffiffiffiffiffiffiffiffiffi
1þ4d
2
p
=KÞ
2
Buck–boost (1 À d)
2 RLÁð1ÀdÞ
2
d
2
KÁRL
d
2
With K ¼
2Leqv
RLTC
DCM happens for K 6 K
crit
J.M. Enrique et al. / Solar Energy 81 (2007) 31–38 33
lim
d!0
R
i-CCM
¼ lim
d!0
R
L
d
2
¼ 1 ð6Þ
lim
d!1
R
i-CCM
¼ lim
d!1
R
L
d
2
¼ R
L
ð7Þ
lim
d!0
R
i-DCM
¼ lim
d!0
R
L
4
Á 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4K
d
2
_
_ _
2
¼ 1 ð8Þ
R
i-DCM
¼
R
L
4
Á 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4K
d
2
_
_ _
2
PR
L
ð9Þ
lim
d!1
R
i-DCM
¼ lim
d!1
R
L
4
Á 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4K
d
2
_
_ _
2
ð10Þ
In DCM K 6 K
crit
¼ ð1 ÀdÞ, then:
lim
d!1
R
i-DCM
6 lim
d!1
R
L
4
Á 1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4ð1 ÀdÞ
d
2
¸
_
_
_
_
2
¼ R
L
ð11Þ
From (9) and (11) we have:
lim
d!1
R
i-DCM
¼ R
L
ð12Þ
Being the expressions of R
i
continuous in d, for a scan-
ning of the converter’s duty cycle d 2 [0,1], R
i
takes values
that belong to the interval [R
L
,1), being R
L
the load resis-
tance. If R
MPP
does not belong to the set of values allowed
for R
i
, the capture of MPP will not be possible, thus
Fig. 2. DC/DC converters commonly used and their input resistance. (a) Buck Converter; (b) boost converter; (c) buck–boost converter; (d) input
resistance versus d in CCM; (e) input resistance versus d in CCM and (f) input resistance versus d in CCM.
Fig. 3. Location of the operation point of a photovoltaic module.
34 J.M. Enrique et al. / Solar Energy 81 (2007) 31–38
defining a ‘‘non-capture zone’’ for R
L
> R
MPP
values.
Fig. 4 shows the effect graphically. The impedance at the
input of a buck converter is always a version scaled by a
factor greater than or equal to 1 (see Table 1) of the imped-
ance connected to its output (in our case R
L
). Therefore,
the MPP capture will only be possible for R
L
6 R
MPP
values.
4.2. Analysis of the module-boost converter-load
configuration
The following expressions are deduced from Table 1 for
the boost converter:
lim
d!0
R
i-CCM
¼ lim
d!0
R
L
Á 1 Àd ð Þ
2
¼ R
L
ð13Þ
lim
d!1
R
i-CCM
¼ lim
d!1
R
L
Á 1 Àd ð Þ
2
¼ 0 ð14Þ
lim
d!0
R
i-DCM
¼ lim
d!0
4 Á R
L
1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4d
2
K
_
_ _
2
¼ R
L
ð15Þ
lim
d!1
R
i-DCM
¼ lim
d!1
4 Á R
L
1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4d
2
K
_
_ _
2
ð16Þ
In DCM K 6 K
crit
, therefore K 6 dÆ(1 À d)
2
. Taking this
condition in Eq. (16) into account, it is deduced that:
lim
d!1
R
i-DCM
6 lim
d!1
4 Á R
L
1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4d
2
K
crit
_ _ _
2
¼ lim
d!1
4 Á R
L
1 þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ
4d
2
dÁð1ÀdÞ
2
_ _ _
2
¼ 0 ð17Þ
Given that R
i-DCM
cannot be negative, it is clear that,
when d !1, the limit matches R
i-DCM
= 0. Being the
expressions of R
i
continuous in d, both for CCM and
DCM, it is deduced that R
i
can only be at the interval
[0, R
L
]. The maximum power point tracking system will
modify the value of R
i
, trying to get R
i
= R
MPP
. However,
this will not be possible if R
MPP
does not belong to the set
of values allowed for R
i
, that is, the system will not reach
the MPP if R
L
<R
MPP
. The behaviour is clearly opposite
to that mentioned in the previous section, and therefore
there is an inversion of zones with respect to the buck con-
verter. Fig. 5 shows this effect. The impedance at the input
of a boost converter is always a lessened version in a factor
lower than or equal to 1 (see Table 1) of the impedance
connected to its output (R
L
in our case). Therefore, the
MPP capture will only be possible for R
L
PR
MPP
values.
4.3. Analysis of the module-buck/boost converter-load
configuration
The following expressions are deduced from Table 1 for
the buck–boost converter:
lim
d!0
R
i-CCM
¼ lim
d!0
R
L
Á 1 Àd ð Þ
2
d
2
¼ 1 ð18Þ
lim
d!1
R
i-CCM
¼ lim
d!1
R
L
Á 1 Àd ð Þ
2
d
2
¼ 0 ð19Þ
lim
d!0
R
i-DCM
¼ lim
d!0
K Á R
L
d
2
¼ 1 ð20Þ
lim
d!1
R
i-DCM
¼ lim
d!1
K Á R
L
d
2
ð21Þ
In DCM K 6 K
crit
, therefore K 6 (1 À d)
2
. Taking this
condition in Eq. (21) into account, it is deduced that:
lim
d!1
R
i-DCM
6 lim
d!1
K
crit
Á R
L
d
2
¼ lim
d!1
ð1 ÀdÞ
2
Á R
L
d
2
¼ 0 ð22Þ
Given that R
i-DCM
cannot be negative, it is clear that the
limit, when d !1, matches R
i-DCM
= 0. For this configura-
tion, in accordance with the results from (18)–(22), and
knowing that R
i
is a continuous function in d, a scanning
of the duty cycle, d 2 [0, 1], allows all values of R
i
, i.e., R
i
can take any value between 0 and 1. Consequently, the
imposed restrictions for the two previous converter topolo-
gies do not affect the buck–boost converter, and therefore
there is not ‘‘non capture zone’’. Fig. 6 shows this effect.
This allows the photovoltaic solar facility to achieve the
MPP regardless of the value of R
L
, thus obtaining a higher
power point tracking efficiency.
5. Examples
To support the theoretic results analysed in the previous
section, we have simulated four photovoltaic systems
Fig. 4. Chart of MPP tracking with buck DC/DC converter.
Fig. 5. Chart of MPP tracking with boost DC/DC converter.
J.M. Enrique et al. / Solar Energy 81 (2007) 31–38 35
(using MATLAB). Three systems use a DC/DC converter
(each one of a different type) with MPP tracking system,
and a fourth one uses a direct connection photovoltaic
module-load. Experimental values of cell temperature and
global irradiation corresponding to a clear day have been
used as input metereological data.
The aim is to evaluate the MPP-tracking efficiency of
each of the systems, calculated according to expression
(23):
g ¼
_
t
0
P
inst
ðtÞ Á dt
_
t
0
P
MPP
ðtÞ Á dt
ð23Þ
where P
inst
is the instantaneous power in the operating
point of the system and P
MPP
is the available power at
the photovoltaic module maximum power point under a gi-
ven cell temperature and irradiance (Hohm and Ropp,
2002). Given that according to (23) MPP-tracking effi-
ciency is the quotient between the areas under each curve,
the closer the real curve to the P
MPP
(t) trajectory, the better
efficiency.
The meteorological data used for the study have been
measured in the laboratory of photovoltaic systems of
the University of Ma´laga (Spain).The measure of the cell
temperature was carried out by means of a PT100 coupled
to the later face of the module. The incident global irradi-
ation has been measured by means of a reference solar cell
installed in the same plane that the photovoltaic module.
Both signals were taken from the weather station with
one minute intervals from the data acquisition system,
Hydra (Fluke). The measured values for the day 3rd of
October of 2002 are shown in Fig. 7. The ‘SX60’ (BP)
model was selected as photovoltaic generator for the simu-
lation. Table 2 shows its parameters.
Fig. 8 shows the calculated trajectories of V
MPP
, and
I
MPP
, for the cited day for the SX60 module. It can be
observed that the I
MPP
is directly proportional to the inci-
dent irradiance while the V
MPP
varies depending on the cell
temperature. The variation of the impedance in the maxi-
mum power point, R
MPP
, throughout the day is shown in
Fig. 9. In this case, we obtained a daily average R
MPP
value
of 9 X. To guarantee the achievement of information on
the system’s behaviour when it operates with resistive loads
different from R
MPP
, in our analysis we have differentiated
between loads higher and lower than average R
MPP
(specif-
ically, 5 X and 20 X).
Due to its simple and easy implementation, the maxi-
mum power point tracking in this work was made on the
basis of the well-known method ‘‘Perturbation and Obser-
Fig. 6. Chart of MPP tracking with buck–boost DC/DC converter. Note
that this converter allows MPP tracking in both directions.
Fig. 7. Temperature and irradiation values for a clear day in Ma´laga
(Spain).
Table 2
Photovoltaic module ‘SX60’ parameters
A = 1.2 Ideality factor of PN junction
E
g
= 1.12 eV Band gap energy
n
p
= 1 Number of parallel-connected modules
n
s
= 36 Number of series-connected cells
P
max
= 60 W Maximum power at standard conditions
a
V
max
= 16.8 V Voltage at the maximum power point
I
max
= 3.56 A Current at the maximum power point
NOTC = 47 °C Nominal Operating Cell Temperature
I
sc
= 3.87 A Short-circuit current at standard conditions
V
oc
= 21.06 V Open circuit voltage at standard conditions
k
v
= À 80 mV/°C V
oc
temperature coefficient
k
i
= 0.065%/°C I
sc
temperature coefficient
a
Standard conditions: 25 °C and 1000 W/m
2
.
Fig. 8. Maximum power point voltage V
MPP
(t) and current I
MPP
(t)
trajectories for the ‘SX60’ (BP) module for a clear day in Ma´laga (Spain).
36 J.M. Enrique et al. / Solar Energy 81 (2007) 31–38
vation P&O’’ (Hohm and Ropp, 2002; Hua and Shen,
1998; Hussein et al., 1995).
Fig. 10 shows the trajectories of the power supplied by the
load and the MPP power for the two different values of R
L
.
It is observed that when the panel is directly connected to the
resistive load, without inserting any DC/DC converter, the
system will only operate at the maximum power point when
R
MPP
and R
L
match (see Fig. 9). If a buck converter is
inserted between the panel and the load (Fig. 11), we can
observe that the system is only able to follow the maximum
power point for not very high irradiation values (depending
on R
L
), i.e., when the maximum power point impedance
R
MPP
is relatively high. At maximum solar irradiation
hours, R
MPP
reaches its minimum values, and so the system
is unable to achieve the MPP. This is even more evident that
the higher R
L
is in relation to R
MPP
. When it is used a boost
converter, (Fig. 12), the systemis able to reach the maximum
power point only at maximum irradiation hours (low
R
MPP
), with a remarkable loss of MPP-tracking efficiency
at the initial and final hours of the day.
Finally, when a buck–boost converter is used the
P
MPP
(t) and P(t) trajectories are graphically equal, with
values of 0.999 for the MPP-tracking efficiency. R
i
can take
any value with this converter. This allows the photovoltaic
solar system to reach the MPP regardless of the existing
irradiation level and R
L
, achieving a higher MPP-tracking
efficiency. Note that the MPP can be tracked for any R
L
value, regardless of its relationship with R
MPP
.
In Table 3, a comparative of the MPP-tracking effi-
ciency provided by each of the configurations for the con-
cerned day of study is given. Observe that in all cases, the
Fig. 10. Maximum power point power trajectory P
MPP(t)
and power
supplied P(t) to the 5 X and 20 X loads, without DC/DC converter
between the photovoltaic module and the load.
Fig. 11. Maximum power point power trajectory P
MPP(t)
and power
supplied P(t) to the 5 X and 20 X loads, with buck converter between the
photovoltaic module and the load.
Fig. 9. Maximum power point impedance trajectory R
MPP(t)
for the
‘SX60’ (BP) module for a clear day in Ma´laga (Spain).
Fig. 12. Maximum power point power trajectory P
MPP(t)
and power
supplied P(t) to the 5 X and 20 X loads, with boost converter between the
photovoltaic module and the load.
Table 3
MPP-tracking efficiency obtained for each DC–DC converter configura-
tion and load
Load Without
converter
(%)
Buck
converter
(%)
Boost
converter
(%)
Buck–boost
converter
(%)
R
L
= 5 X 88.5 97.2 91.2 99.9
R
L
= 20 X 40.2 40.3 99.7 99.9
J.M. Enrique et al. / Solar Energy 81 (2007) 31–38 37
configuration with buck–boost converter is the one that
presents the highest efficiency.
6. Conclusions
In this work we aimed at revealing the importance of the
correct choice of the DC/DC converter in a photovoltaic
facility in order to obtain its highest MPP-tracking effi-
ciency. In this article we demonstrate that only the buck–
boost DC/DC converter is able to manage the facility to
follow the photovoltaic panel maximum power point at
all times, regardless of cell temperature, solar global irradi-
ation and connected load.
It is important to remark that the result obtained in the
analysis is independent from the MPP tracking system, i.e.,
however efficient this system may be, the DC/DC converter
configurationimposes restrictions onit that it cannot sidestep.
‘‘Despite the fact that the study carried out in this work
is theoretical, it is important to note that from a practical
approach, the buck and boost converters are the most effi-
cient topologies for a given price. While voltage flexibility
varies, buck–boost and Cuk (Cuk is a type of structure
derived from the buck–boost topologies) converters are
always at efficiency or, alternatively, price disadvantage.
Nevertheless, there are already configurations of buck–
boost and Cuk converters where both the MOSFET and
the inductor are of a very low resistance, achieving efficien-
cies as regards input power higher than 95% and hardly 2
or 3% lower than the buck and boost topologies.’’
According to the performed analysis, we dare to suggest
that a good practice could be including a buck–boost DC/
DC converter in photovoltaic solar facilities at the PV
array output and then connecting, after the converter, the
rest of the facility elements (load). This practice guarantees
the photovoltaic panel maximum power point tracking for
any solar irradiation, cell temperature and load conditions,
which could undoubtedly redound to the facility’s higher
system efficiency.
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