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182 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

corresponding exact and approximated IeV and PeV characteristics of the associ-
ated boost-based LSCPVU. The approximated IeV characteristic of the LSCPVU
(dashed line in Fig. 5.7A) is obtained by substituting the part of the IeV
characteristic for V V MPP , part which cannot be expressed in easy explicit form
I ¼ f(V) [9,55], with a simpler constant characteristic:
I ¼ I cost ¼ b$I SC (5.20)
where the factor b represents the ratio between I MPP_STC and I SC_STC . In the case of
SW225 modules, it is b ¼ 0:93. This approximation can be justified by considering
that the exact IeV characteristic is more or less flat, for V V MPP , and it is con-
tained in the quite narrow band I MPP I I SC (usually I MPP /I SC z 0.9). The hyper-
bolic equation of the portion of the approximate PeV characteristic for
V MPP V V ds max is of course V$I ¼ V MPP $I cost . It is worth noting that of course
other, more accurate, forms of approximation of the IeV curve for V V MPP might
be adopted; for example, a piecewise linear approximation. But, as it will be shown
in the following, it is not necessary at all. In fact, the use of the simple approximation
I ¼ I cost for V V MPP and V$I ¼ V MPP $I cost for V MPP V V ds max allows to
easily carry out in closed form, with enough accuracy, the calculations needed by
the HMPPTF technique to maximize the energetic efficiency of the PV system.
Indeed, some additional considerations are needed concerning the values to adopt
for V MPP . For a given PV module, V MPP is generally weakly dependent on the irra-
diance and on the module temperature [9,10]. Usually the variations of V MPP are
relatively small. Therefore, because of the approximate nature of the analysis to
be carried out, in the following V MPP will be considered constant and not time-
varying. In particular, V MPP will be considered equal to the value V cost assumed
2

by the MPP voltage at S max ¼ 1000 W/m and T ambient ¼ 25 C. In such conditions,
by using Eq. (5.4) it is possible to evaluate the module temperature T module . With

specific reference to SW225 modules, it is T module ¼ 57.5 C. Hence, the desired
value of V cost can be finally obtained [10]:

ðT Module 25Þ
V cost ¼ V MPP STC 1 þ a$ (5.21)
100

where a [%/ K] is a negative temperature coefficient (in the case of SW225 mod-

ules, it is a ¼ 0.34%/ K and hence V cost ¼ 26.24 V). It is worth noting that the pa-
rameters V MPP_STC and a appearing in Eq. (5.21) are provided by all the PV module
manufacturers in their datasheets. In conclusion, V cost can be easily evaluated by us-
ing the data extracted from PV module datasheets.
Therefore, I cost is the only time-varying parameter because it depends on I SC
(I cost ¼ b I SC z P MPP /V cost ), which exhibits a strong dependence on irradiance
values. The short circuit current I SC of the PV module is a quantity that can be quite
easily measured. Therefore, by using the approximate relation I cost ¼ b$I SC , even
I cost can be quite easily evaluated. It is worth noting that also the value of b can