Page 212 - Advances in Renewable Energies and Power Technologies

3. Necessity of Joint Adoption of Distributed Maximum Power Point 185

is evident that, while the PV module operating point remains in the MPP, the lower
the output voltage the higher the output current. By indicating with I MAX, the
maximum allowed value of I, we get:
P MPP
V 1 ¼ (5.25)
I MAX
Therefore, V 1 is the left value of the voltage range where the output characteristic
of the buckeboost based LSCPVU is hyperbolic (V$I ¼ P MPP ) and it can be calcu-
lated by using Eq. (5.25) once I MAX is known. As shown in the following, I MAX de-
pends on I ds max and I MPP . Without the adoption of a proper overcurrent protection
circuitry, values of V lower than V 1 would give rise to output currents I greater
than I MAX . So that, for V V 1 , it is assumed that the output current is limited
to I MAX by means of a proper overcurrent protection circuitry and that the PV mod-
ule operating point moves away from the MPP because the output power becomes of
course lower than P MPP . By indicating with D, the duty-cycle of the buckeboost con-
verter, when the PV module operates in the MPP, it is [50]:
V MPP $I MPP I MPP
I ¼ ¼
V D
1 D (5.26)

I MPP
I s peak ¼
D
where I s peak is the peak current value of the switches of the buckeboost. From
Eq. (5.26) it is evident that, while the PV module operating point remains in the
MPP, the lower D (and hence the lower V) the higher both the output current
and the peak current of the switches. By indicating with D 1 the value of D in
correspondence of which the peak current of the switches is equal to I ds max and
therefore the output current also assumes its maximum value I MAX , from
Eq. (5.26) we get:
I MPP
I MAX ¼
D 1
1 D 1 (5.27)
I MPP
I ds max ¼
D 1
From Eq. (5.27) it is easy to get the value of I MAX :I MAX ¼ I ds max I MPP .As
concerns the value of V 2 , by remembering that in a buckeboost the voltage across
the switches in the OFF state is equal to the sum of the input voltage and of the
output voltage V [53], we get:
V ds max ¼ V 2 þ V MPP (5.28)
That is, not only for V < V 1 but also for V > V 2 the operating point of the PV
module cannot be the MPP because of the action of overcurrent or overvoltage pro-
tection circuitries, respectively. It is therefore assumed that, for V > V 2 , the PV