Page 205 - Advances in Renewable Energies and Power Technologies

178 CHAPTER 5 DMPPT PV System: Modeling and Control Techniques

Our objective is to ensure that
Dv b
v outk þ Dv outk z v out lim þ Dv outk ¼ v out lim þ
N M
Dv bref
¼ v out lim þ v ds max ð k ¼ 1; 2; .N MÞ
N M
From which we get

v b min
Dv b ref ðv ds max v out lim Þ$ (5.15)
v out lim
As for the choice of T b , a preliminary consideration is necessary. In correspon-
dence of an arbitrary value v b ¼ v a of the inverter voltage, the working conditions of
the N LSCPVUs will depend on the distribution of irradiance values. In particular,
some LSCPVUs (those ones characterized by the highest irradiance values) will
operate with an output voltage nearly equal to V out lim . Other LSCPVUs will operate
with an output voltage comprised between 0 and V out lim and, finally, the remaining
LSCPVUs (those characterized by the lowest irradiance values) will operate with
output short-circuit conditions. The number of LSCPVUs operating with an output
voltage nearly equal to V out lim will be indicated with N lim , the number of LSCPVUs
operating with an output voltage comprised between 0 and V out lim will be indicated
with N r , while the number of LSCPVUs operating with an output voltage equal to
0 will be indicated with N SC . Summarizing, by remembering the adopted ordering
rule, we get:

v outk ¼ v out lim 1 k N lim
0 < v outk < v out lim N lim þ 1 k N lim þ N r (5.16)
v outk ¼ 0 N lim þ N r þ 1 k N
Of course, it is N lim þ N r þ N sc ¼ N; moreover, N lim ,N r ,and/or N sc can be equal
to zero. Let us suppose that, during the scan, v b must change from v a to v a þ Dv bref .In
the new steady-state condition, at v b ¼ v a þ Dv bref , two or three numbers among
N lim ,N r ,and N sc may change. In fact, it may happen that, in the new steady-state con-
dition, one or more LSCPVUs (among those ones with index 1 k N lim þ N r )will
reduce their output power; that is, N lim and/or N r may change. Let us indicate with N d
the number of LSCPVUs that, in the new steady-state condition, will reduce their
output power (N d N lim þ N r ). Such a power reduction may also allow in turn one
or more LSCPVUs to increase their output power and therefore to increase their
output voltage. That is, in the new steady-state condition, N SC and/or N r may change.
Let us indicate with N i the number of LSCPVUs that, in the new steady-state condi-
tion, will increase their output power. Of course, the process described so far cannot
take place instantaneously. In fact, it needs, in the worst case, the time T 1 necessary to
the N d LSCPVUs to move their input operating voltage in the direction from V MPP to
zero, to decrease their output power, plus the time T 2 necessary to the N i LSCPVUs