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3. Necessity of Joint Adoption of Distributed Maximum Power Point 177

severely compromise the efficiency of the system, it is necessary to adopt enough
large values of Dv b ref :

(5.13)
Dv b ref Dv b fline
The second requirement for a proper choice of Dv bref is strictly linked to the ne-
cessity to avoid that, during the scan, the voltage ratings of devices are exceeded. In
fact, it must be ensured that the steps of v bref , taking place at the sampling instants,
during the variation of v bref from V bmin to V bmax , do not cause that the output voltage
of one or more LSCPVUs exceeds V ds max . In the following analysis, let us consider
negligible the settling time of the overall system (worst-case). This means that, as a
consequence of the steps of v bref , the steady-state variations of v b and the correspond-
ing variations v outk (k ¼ 1, 2, ., N) occur near instantaneously. For simplicity,
because a unit gain of the sensor of voltage v b has been assumed and as a result of
the zero steady-state error ensured by the Bulk voltage compensation network, it
can be assumed that Dv b ¼ Dv bref . Of course, at any sampling instant, Dv b must
be shared among the N output voltages of the N LSCPVUs. The ideal situation,
from the voltage stress point of view, takes place when Dv b is uniformly shared among
the N output voltages. In such a case, the output voltage v outk (k ¼ 1, .,N) will in-
crease of a quantity equal to: Dv outk ¼ Dv bref /N (k ¼ 1, .,N). Unfortunately, this sit-
uation occurs only when the LSCPVUs work in the same operating conditions
(absence of mismatching operating conditions); but, in mismatching operating condi-
tions, Dv b is unequally shared among the N output voltages. In particular, under mis-
matching operating conditions, one or more LSCPVUs may work with their output
ports in short circuit conditions; that is, such LSCPVUs are not able to provide power
to the grid. Of course, such a situation is undesirable from the voltage stress point of
view. In fact, if m (1 < m < N) LSCPVUs are working with their output ports in short
circuit conditions, then the variation Dv b must be entirely shared only among a minor
number (N m) of LSCPVUs, that is, only among those LSCPVUs that are instead
working with their output voltages greater than zero so that the output voltages of
such (N m) LSCPVUs may become dangerously high. The occurrence of the afore-
mentioned situation, taking place under mismatching conditions, can be explained on
the basis of Eq. (5.1). The worst-case, as concerns the distribution of Dv b among the N
output voltages, takes place of course when the maximum number M of LSCPVUs is
working in short circuit conditions. M can be evaluated by considering that the
remaining (N M) LSCPVUs must operate with the highest possible output voltage,
that is v out ¼ V out lim . It is worth remembering that, in this chapter, the LSCPVUs are
listed in descending order as concerns the corresponding value of the irradiance level.
So that the first N M LSCPVUs are assumed to operate at higher irradiance values,
while the remaining M LSCPVUs are assumed to operate at very low irradiance
values. Summarizing, in the worst-case, it is v outk ¼ V out lim (k ¼ 1, .,N M), while
v bmin
v outk ¼ 0(k ¼ N Mþ1, ., N). It is M ¼ N . On the basis of the above con-
v out lim
siderations, we get:
Dv b
Dv outk ¼ ð k ¼ 1; 2; .N MÞ
N M (5.14)
Dv outk ¼ 0 ð k ¼ N M þ 1; .NÞ