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3. Necessity of Joint Adoption of Distributed Maximum Power Point 197

HMPPTS technique is adopted in a grid-connected PV system adopting boost-based
2
LSCPVUs. In particular, by taking into account that, for S max ¼ 1000 W/m and

T ambient ¼ 25 C, the values of P pan1 , DP pan1 and V OC are, respectively, equal to
192 W, 8.89 W, and 36.8 V, we have that the value of V out lim must belong to the range
[36.8e53.8] V. Because it is convenient to adopt a value of V out lim which is as high as
possible, V out lim has been chosen equal to 53 V. As discussed previously, when adopt-
ing the HMPPTF technique, it is possible to estimate in advance the number N MPP of
LSCPVUs operating in their MPPs and the number N SC of LSCPVUs operating with
an output voltage equal to 0. This is very useful; in fact, the quantity DP tot appearing in
Eq. (5.11) can be evaluated with greater accuracy with respect to the worst-case value
used when adopting the HMPPTS strategy:
DV 2 pan
DP tot ¼ ðN N SC N MPP Þ$DP pan1 $N MPP $ (5.44)
R MPP
where R MPP is the PV module differential resistance evaluated at the MPP [1].Itis
worth noting that, thanks to the data obtained by means of the FEMPValgorithm, the
quantities P pan1 and DP pan1 appearing in Eq. (5.11) can also be more or less accu-
rately estimated:
P pan1 ¼ V cost $I SC1 (5.45)

DP pan1 ¼ DV pan1 $I SC1 (5.46)
where I SC1 is the largest measured short circuit current. Instead, only worst-case
values can be assumed in place of P pan1 and DP pan1 when adopting the HMPPTS
strategy. In the CASE I, the values of I SC1 ,N SC , and N MPP are, respectively, equal
to 8.17 A, 4, and 7. By using Eqs. (5.11), (5.12), (5.44) and (5.46) we have that
the value of V out lim must belong to the range [36.8e59.3] V. The value V out lim
has been chosen equal as 59 V. The PeV exact characteristics of the 11 series-
connected LSCPVUs are reported in Fig. 5.17A with reference to V out lim ¼ 53 V
(which is the value adopted in HMPPTS technique) and V out lim ¼ 59 V (which is

(A) (B)
1500
P-V characteristic
1000 of eleven series 1000
connected SCPVUs
[W] [W]
500 500 Approximate P-V characteristic
of eleven series connected SCPVUs
Exact P-V characteristic
inverter allowed
input voltage range of eleven series connected SCPVUs
0 0
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
[V] [V]
FIGURE 5.17
(A) Exact PeV characteristics of 11 series-connected Lossless Self-Controlled
Photovoltaic Units (LSCPVUs) obtained by considering two different values of V out lim ,
(B) exact and approximate PeV characteristics of 11 series-connected LSCPVUs (V out
lim ¼ 59 V HMPPTF technique).