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186 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques
(A) (B)
approximate I-V characteristic P-V characteristic
MPP of a PV module
of a buck-boost based SCPVU 200 exact P-V
10 I characteristic
MAX I cost of a buck-boost
150 based SCPVU
[A] [W] MPP
approximate P-V
5 I 100 characteristic of
. .
.
. . 0 . (V cost β I )/(I -β I ) V -V a buck-boost
(V cost β I )/(I -β I ) V ds_max -V V 50 SC ds_max SC ds_max cost based SCPVU
SC ds_max SC cost ds max V
ds_max
0 0
0 20 40 60 80 0 20 40 60 80
[V] [V]
FIGURE 5.9
(A) IeV characteristic of a photovoltaic (PV) module and exact and approximate IeV
characteristics of a buckeboost based lossless self-controlled PV unit (LSCPVU), (B) PeV
characteristic of a PV module, and exact and approximate PeV characteristics of a
buckeboost based LSCPVU.
voltage is equal to V ds max Vand hence the output power of the LSCPVU is equal
to P(V ds max V). In Fig. 5.9, the IeV(Fig. 5.9A) and PeV(Fig. 5.9B) character-
2
istics of a SolarWorld SW225 PV module (T ambient ¼ 25 C, S ¼ 1000 W/m ) are re-
ported together with the corresponding exact and approximated IeV and PeV
characteristics of the associated buckeboost based LSCPVU. Fig. 5.9 has been ob-
tained by assuming V ds max ¼ 80 V and I ds max ¼ 16 A; because it is
V MPP ¼ 25.52 V and I MPP ¼ 7.56 A, we get V 1 ¼ 22.86 V, V 2 ¼ 54.48 V,
I MAX ¼ 8.44 A. As concerns buckeboost based LSCPVUs the approximate charac-
teristic, which is needed for the implementation of the HMPPTF technique, is
composed by three different portions. The first portion (for
0 V (V cost $b$I SC )/(I ds max b$I SC )) is represented by the constant line of
equation:
(5.29)
I ¼ I cost ¼ I ds max bI SC
The second portion (for (V cost $b$I SC )/(I ds max b$I SC ) V (V ds max V cost ))
is represented by a hyperbole of equation:
(5.30)
V$I ¼ V cost $b$I SC
The third portion (for (V ds max V cost ) V V ds max ) is represented by the
curve of equation:
(5.31)
V$I ¼ V cost $b$I SC V cost $I SC þðV ds max VÞ$I SC
The definition of I 0 in the case of buckeboost based LSCPVU is the following
one:
V cost $b$I SC
I 0 ¼ (5.32)
V ds max V cost
The meaning of I 0 and I cost is indicated in Fig. 5.9A. By analyzing Eqs. (5.29)e
(5.32), it is evident that, also in the case of buckeboost based LSCPVUs, it is enough