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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
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