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174 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

By assuming T ambient ¼ 25 C and NOCT ¼ 46 C, we get T module ¼ 57.5 C. The
derivative term appearing in Eq. (5.3) has been evaluated at a voltage equal to V oc
(open circuit voltage). In fact, at V oc , the magnitude of the slope of the PeV module
characteristic is the highest possible. So that, in correspondence of a given variation
Dv pan1 ¼ Dv pan ref of the voltage, the corresponding variation DP pan1 provided by
(5.3) assumes its maximum value (DP pan1_max ). The total variation DP tot of the po-
wer extracted by the string of N LSCPVUs is given as
N
X
DP tot ¼ DP pank ¼ ðN 2Þ$DP pan1 max (5.5)
k¼1
Because in practical applications, N > 2 (in fact typically 10 < N < 20) then DP tot
is < 0. Therefore, it is possible to state that the total variation DP tot evaluated by using
Eqs. (5.2)e(5.5) assumes the lowest possible value. Summarizing, if the value
assumed by DP pan1 is maximum (DP pan1_max ), then the value assumed by DP tot in
Eq. (5.5) is minimum and, as it will be clear in the following, this in turn leads to
the highest possible value of Dv out1 (see Eq. 5.1). In case of LSCPVUs, we get:

DP pan1 ¼ DP pan1 max z v out1 $Di out1 þ Dv out1 $i out1
(5.6)
z V out lim $Di out þ Dv out1 $i out
It is worth noting that, as a result of the series connection of the LSCPVUs, a
unique output current flows, so that in Eq. (5.6), the symbol i out has been used in
place of i out1 and the symbol Di out in place of Di out1 . From Eq. (5.6) we get:

Dv out1 z DP pan1 max V out lim $Di out (5.7)
i out
Theinequalitythatmustbefulfilledto avoid exceedingthe voltageratingV ds max is

v out1 þ Dv out1 z V out lim þ Dv out1 V ds max (5.8)
It is worth noting that Eq. (5.8) states an obvious principle: the lower Dv out1
(best-case), the higher the value that can be assigned to V out lim and, therefore, as
discussed at the beginning of this section, the higher the energetic efficiency, which
can be obtained by the PV system. From Eqs. (5.7) and (5.8), we get

DP pan1 max
v ds max
i out
V out lim (5.9)
Di out
1
i out
The worst-case (lowest) value of the threshold that must not be exceeded by V out
lim can be found by minimizing the right-hand side term in Eq. (5.9). This objective
can be obtained by exploiting the following equalities:

P pan1
i out min ¼
v ds max
(5.10)
DP tot
Di out min ¼
N$v oc