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188 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

point moves away from the MPP because the output power becomes lower than
P MPP . By indicating with D the duty-cycle of the buck converter, when the PV mod-
ule operates in the MPP, it is [53]:

V MPP $I MPP I MPP
I ¼ ¼
V D
(5.36)
I MPP
I s peak ¼
D
where I s peak , is the peak current value of the switches of the buck. From Eq. (5.36) it
is evident that, while the PV module operating point remains in the MPP, the lower D
(and hence the lower V) the higher both the output current and the peak current of
the switches. By indicating with D 1 the value of D in correspondence of which the
peak current of the switches is equal to I ds max and therefore the output current also
assumes its maximum allowed value I MAX and by considering Eq. (5.36) we get:
(5.37)
I MAX ¼ I ds max
In Fig. 5.10, the IeV(Fig. 5.10A) and PeV(Fig. 5.10B) characteristics of a
2

SolarWorld SW225 PV module (T ambient ¼ 25 C, S ¼ 1000 W/m ) are reported
together with the corresponding exact and approximated IeV(Fig. 5.10A) and
PeV(Fig. 5.10B) characteristics of the associated buck-based LSCPVU.
Fig. 5.10 has been obtained by assuming I ds max ¼ 16 A; because V MPP ¼ 25.52 V
and I MPP ¼ 7.56 A, we get V 1 ¼ 12.06 V and I MAX ¼ 16 A. The approximate char-
acteristic of LSCPVU based on the buck microconverter, which is needed for the
implementation of the HMPPTF technique, is composed of the three following
different portions. The first portion (for 0 V (V cost $b$I SC )/I dsmax ) is represented
by the constant line of equation:
I ¼ I cost ¼ I ds max (5.38)

(A) (B)
P-V characteristic of
I-V characteristic
20 of a PV module 200 a PV module
I cost exact I-V characteristic exact P-V characteristic
of a buck based SCPVU of a buck based SCPVU
MPP
MPP 150 approximate P-V
[A] 10 approximate I-V [W] characteristic of
characteristic of
a buck based SCPVU
a buck based SCPVU 100
I V V
0 (V cost .β. I SC )/I ds_max cost oc 50 (V cost .β . I SC )/I ds_max V cost V oc
0 0
0 10 20 30 40 0 10 20 30 40
[V] [V]
FIGURE 5.10
(A) IeV characteristic of a photovoltaic (PV) module and exact and approximate IeV
characteristics of a buck-based lossless self-controlled PV unit (LSCPVU), (B) PeV
characteristic of a PV module and exact and approximate PeV characteristics of a buck-
based LSCPVU.