Page 216 - Advances in Renewable Energies and Power Technologies

3. Necessity of Joint Adoption of Distributed Maximum Power Point 189

The second portion (for (V cost $b$I SC )/I ds max V V cost ) is represented by a
hyperbole of equation:

(5.39)
V$I ¼ V cost $b$I SC
The third portion (for V cost V V OC ) is represented by the line of equation:
V$b$I SC V oc $b$I SC
I ¼ (5.40)
V cost V oc V cost V oc
The definition of I 0 in the case of buck-based LSCPVUs is the following one:
I 0 ¼ b$I SC (5.41)
2

The value of V OC (at S ¼ 1000 W/m ,T ambient ¼ 25 C) can be evaluated as [10]:

ðT Module 25Þ
V oc ¼ V oc STC 1 þ a$ (5.42)
100
where a [%/ K] is a negative temperature coefficient (in the case of SW225 mod-

ules, it is a ¼ 0.34%/ K, T module ¼ 57.5 C, V OC_STC ¼ 36.8 V, and hence

V OC ¼ 32.7 V). It is worth noting that the parameters V OC_STC and a appearing in
Eq. (5.42) and NOCT appearing in Eq. (5.4), needed to evaluate T module , are pro-
vided by all the PV module manufacturers in their datasheets. Therefore, also in
the case of buck-based LSCPVUs, the measurement of I SC allows to evaluate the
whole approximate IeV characteristic. In the case of buck-based LSCPVUs,
because I 0 is nearly equal to I MPP and I cost ¼ I dsmax must be greater than I MPP /D
(see Eq. 5.38), it is I 0 < I cost . The set of equations that allow to obtain the approx-
imate IeV and PeV characteristics of a string composed by an arbitrary number
N of buck-based LSCPVUs are:
if I ¼ I 0k ¼ b$I SCk

P
P
½ I SCk $ V cost -V OC ފ $ V cost $I SCy
ð
i˛J y˛T
V tot ¼ V cost þ k-1Þ$V OC þ þ
ð
I SCi I SCk
n o
where k ¼ 1; 2; ...; N; J ¼ i < k: I 0i > I 0k g;T ¼ y > k: I 0y < I 0k
f
if I ¼ I costk ¼ I dsmax
" #
X V cost $b$I SCi X V cost $b$I SCi V cost $b$I SCk
V tot ¼ ; þ
I costk I costk I costk
i˛J i˛J
where k ¼ 1; 2; ...; N; J ¼ k < i < N: I costi > I costk g
f
(5.43)