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3. Necessity of Joint Adoption of Distributed Maximum Power Point 173

assigned to V out lim can be evaluated on the basis of the following considerations. We
will consider a string composed by N LSCPVUs and we will assume that all the var-
iations of v pan refk (k ¼ 1, 2, ., N), as a worst-case, take place at the same instant t 0
(even if in practical applications they are not synchronous at all). Further, we will
consider negligible the settling time of the LSCPVU equipped with a linear input
voltage feedback control circuitry. This means that the steady-state variations of
all the variables of interest (the powers extracted from the LSCPVUs, their input
or output voltages etc.), occurring as a consequence of the variations of v pan refk ,
þ
take place immediately at t 0 . Because of the unit gain of the sensor of the PV
voltage and the zero steady-state error, ensured by the action of the PV voltage
compensation network, we get: Dv pank ¼ Dv pan ref , where Dv pank is the variation
of the PV voltage of the k-th LSCPVU (k ¼ 1, 2, ., N). Because the LSCPVUs
have been ordered in descending order, with reference to the corresponding values
of the irradiance level, the first LSCPVU is characterized by the highest value of the
irradiance level, and therefore (see Eq. 5.1), its output voltage is relatively high and
-
may be in the proximity of V out lim . Therefore, let’s assume that at t 0 , that is, imme-
diately before the occurrence of the variations of v pan refk (k ¼ 1, 2, ., N), the value
v out1 of the output voltage of the first LSCPVU is nearly equal to the guard level V out
lim (v out1 z V out lim ).
Further, let us suppose that the variation of v pan ref1 driven at t 0 by the DMPPT
controller of the first LSCPVU causes a positive variation DP pan1 of the power
P pan1 . This is certainly possible because it is coherent with the working principle
of the MP&O DMPPT technique because it has been assumed that v out1 z V out lim

at t 0 . In addition, let us suppose that all the other power variations DP pank
þ
(k ¼ 2, ., N), occurring at t 0 , are negative so that, as suggested by Eq. (5.1),a
positive variation Dv out1 of v out1 takes place. We are interested in evaluating the
worst-case value of Dv out1 , that is, the highest possible value of Dv out1 ,because we
are searching for conditions granting that the output voltage of the first LSCPVU
does not exceeds V ds max . The worst-case value of Dv out1 can be evaluated by
assuming that:

DP pank ¼ DP pan1 max ðk ¼ 2; .; NÞ (5.2)
where

vP pan1 n; S; Tð Þ
module
DP pan1 max ¼ j $Dv pan1
vv S max; V OC; T m
(5.3)

vP pan1 n; S; Tð Þ
module
¼ j $Dv pan ref
vv S max; V OC; T m
In Eq. (5.3) DP pan1_max is assessed by considering the PeV module characteristic
associated to the maximum possible value S max of the irradiance level
2
(S max ¼ 1000 W/m ) and to a module temperature T module given by [10]:
T module ¼ T ambient þðNOCT 20 CÞ$ S max (5.4)

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