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3. Necessity of Joint Adoption of Distributed Maximum Power Point 183

be easily extracted from PV modules datasheets. Moreover, as it will be clear in the
sequel, it is useful to define the following current:

V cost $I cost
I 0 ¼
V ds max
(5.22)
V cost $b$I SC
ð
¼ < I cost since V cost < V ds max Þ
V ds max
From Eq. (5.22), it is evident that, if I SC is known not only I cost but also I 0 is
known. The meaning of I 0 and I cost are clarified in Fig. 5.7A. As described in detail
in [59e62], the set of equations that allow to obtain the IeV and PeV approximate
characteristics of a string composed by an arbitrary number N of boost based
LSCPVUs are:

V cost $I costk V cost $b$I SCk
if I ¼ I 0k ¼ ¼
V ds max V ds max
P (5.23)
V cost $I costi
i˛J
V tot ¼ k$V ds max þ
I 0k
where k ¼ 1, 2, ., N and J ¼ {i > k: I cost i > I 0k }. In Eq. (5.23) the set J may also be
empty.

if I ¼ I costk ¼ b$I SCk
P P
2 3
V cost $I costi V cost $I costi
i˛J i˛J
V tot ¼ m$V ds max þ ; m$V ds max þ þ V cost 5
4
I costk I costk
(5.24)
where, k ¼ 1, 2, .,N; m ¼ max {i < k: I 0i > I costk }; J ¼ {m < i < k:
I costi > I costk }. In Eq. (5.24) the set J may also be empty. Eqs. (5.23) and (5.24) repre-
sent the core of the FEMPValgorithm suited for boost-based LSCPVUs. By looking
at Eqs. (5.23) and (5.24), it is clear that the key quantities are represented by currents
I costk ¼ b I SCk (k ¼ 1, 2, ., N). Once I SCk (k ¼ 1, 2, ., N) are known, then the
(3N þ 1) points of the approximated IeV (and hence the approximated PeV) char-
acteristic of the string of LSCPVUs can be obtained. Finally, the IeV and PeV
approximate characteristic can be obtained by connecting, by means of proper seg-
ments, the (3N þ 1) points obtained by using Eqs. (5.23) and (5.24). As an example,
let us consider a string composed by N ¼ 11 boost-based LSCPVUs. The set of irra-

diance values characterizing the N PV modules, operating at T ambient ¼ 25 C, are the
2
following [1000, 1000, 600, 600, 400, 400, 200, 200, 100, 100, 100] W/m . The cor-
responding values of b I SCk and I 0k (k ¼ 1, 2, ., 11) are, respectively equal to [7.67,
7.67, 4.58, 4.58, 3.05, 3.05, 1.52, 1.52, 0.76, 0.76, 0.76] A and [3.37, 3.37, 2.01,
2.01, 1.34, 1.34, 0.67, 0.67, 0.33, 0.33, 0.33] A. The 3 N ¼ 33 points belonging to