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Vo
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1
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ch
20
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p
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49
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e
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a
n
d
m
o
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le
o
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ra
ti
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ll
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e
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l
a
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m
s
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re
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a
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a
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m
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l
p
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t
o
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t
h
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b
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fit
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fro
m
th
is
h
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rd
wa
re
so
l
u
ti
o
n
.
S
i
n
c
e
so
ftwa
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e
imp
lem
e
n
tatio
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wa
y
i
n
teg
ra
tes
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li
m
it
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n
u
m
b
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f
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p
a
n
e
ls,
h
a
rd
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re
i
m
p
lem
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n
tatio
n
is
a
p
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m
isin
g
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l
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ti
o
n
t
h
a
t
re
d
u
c
e
s
e
x
e
c
u
ti
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n
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ime
a
n
d
th
e
re
f
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h
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e
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b
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ic
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h
a
n
n
e
ls.
F
i
n
a
ll
y
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re
su
lt
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o
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sim
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o
f
th
e
f
u
z
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h
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e
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ip
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o
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4
4
0
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c
h
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re
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se
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a
n
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m
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m
p
ro
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K
ey
w
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r
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s
:
C
h
an
n
els
Field
p
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r
a
m
m
ab
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ate
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lo
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x
im
u
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p
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p
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t tr
ac
k
i
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Ph
o
to
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ltaic
T
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rticle
u
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CC B
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li
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C
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p
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Dep
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f
r
1.
I
NT
RO
D
UCT
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Co
upl
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p
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to
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s
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s
to
th
e
elec
tr
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g
r
i
d
h
a
ve
be
co
m
e
m
o
r
e
m
o
tiv
ati
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g
s
in
ce
th
e
r
ap
i
d
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is
e
in
d
em
an
d
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o
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b
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y
.
Nee
d
s
o
n
clea
n
en
e
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g
y
will
h
av
e
t
h
e
f
ast
est
g
r
o
w
t
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in
th
e
elec
tr
icity
s
ec
to
r
.
R
ec
en
tly
,
p
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o
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en
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y
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ar
ticu
lar
ly
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ed
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s
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s
p
o
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tatio
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s
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d
in
b
u
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in
g
-
i
n
t
eg
r
ated
p
h
o
to
v
o
ltaic;
in
wh
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s
o
lar
ar
r
ay
s
ar
e
in
th
e
r
o
o
f
s
o
f
th
e
b
u
ild
in
g
s
an
d
h
o
u
s
es
[
1
]
–
[
4
]
.
Acc
u
r
ately
,
th
e
g
e
n
er
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f
p
h
o
to
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PV
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p
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t
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tem
p
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d
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ch
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T
h
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latest
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r
ea
tly
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s
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t
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cr
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s
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p
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to
m
ax
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m
,
s
u
n
tr
ac
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an
d
tech
n
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u
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o
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ac
k
in
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m
ax
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m
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in
t
a
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lar
g
ely
a
p
p
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f
o
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PV
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ay
s
[
5
]
,
[
6
]
.
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ar
lier
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n
u
m
b
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less
m
ax
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m
p
o
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p
o
in
t
tr
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k
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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f
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u
r
a
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&
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m
b
ed
d
ed
Sy
s
t
,
Vo
l.
11
,
No
.
1
,
M
ar
c
h
20
22
:
49
-
58
50
tech
n
iq
u
es
h
as
b
ee
n
d
ep
lo
y
e
d
an
d
p
u
t
in
p
r
ac
tice
[
7
]
–
[
1
0
]
.
T
h
e
r
in
cip
le
o
f
t
h
is
co
n
tr
o
l
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ec
h
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iq
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elies
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t
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tech
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cu
s
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in
[
1
1
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r
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tech
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e
s
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itab
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s
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zz
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is
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x
p
lo
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t
o
co
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tr
o
l
elec
tr
ical
s
y
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tem
s
.
I
n
s
tead
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n
tio
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es,
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tech
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d
a
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es
r
ap
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o
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tim
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[
1
2
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–
[
1
4
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.
I
t
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d
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y
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s
m
allest
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n
s
in
s
tead
y
s
tate
an
d
g
o
o
d
r
esp
o
n
s
e
u
n
d
er
r
a
p
id
ir
r
a
d
iatio
n
ch
an
g
es
[
1
5
]
,
[
1
6
]
.
Ho
we
v
er
,
th
is
tech
n
iq
u
e
is
co
m
p
lex
.
T
o
in
teg
r
ate
PV
en
e
r
g
ies
s
o
u
r
ce
s
to
DC
g
r
i
d
(
b
atter
ies
o
f
el
ec
tr
ical
v
eh
icles)
o
r
t
o
AC
u
ti
lity
g
r
id
s
,
m
an
y
p
h
o
to
v
o
ltaic
s
y
s
tem
co
n
f
ig
u
r
atio
n
s
ex
is
t
[
1
7
]
,
[
1
8
]
.
P
V
d
is
tr
ib
u
ted
s
y
s
tem
co
n
f
ig
u
r
atio
n
is
d
ee
p
ly
u
s
ed
s
in
ce
it
ac
ts
as
an
ess
en
tial
p
ar
t
o
f
th
e
elec
tr
ical
g
r
id
[
1
9
]
.
I
t
p
lay
s
a
s
u
b
s
tan
tial
r
o
le
as
a
p
o
wer
s
u
p
p
ly
r
es
s
o
u
r
ce
.
I
t
is
a
h
u
g
e
p
ar
k
in
clu
d
in
g
m
u
ltip
le
c
h
an
n
els
o
f
PV
p
an
els
wh
ich
a
r
e
p
a
r
allel
co
n
n
ec
ted
an
d
ea
ch
PV
p
an
el
is
lin
k
e
d
t
o
AC
o
r
DC
g
r
id
th
r
o
u
g
h
AC
-
DC
o
r
D
C
-
DC
co
n
v
er
ter
[
2
0
]
,
[
2
1
]
.
I
n
th
is
s
y
s
tem
,
a
lo
ca
l
co
n
tr
o
l
it
em
is
g
en
e
r
ally
in
tr
o
d
u
ce
d
to
ea
c
h
PV
s
o
u
r
ce
co
n
v
er
s
io
n
s
tag
e.
E
ac
h
PV
s
o
u
r
ce
o
p
er
ates
at
its
o
wn
m
ax
im
u
m
p
o
wer
p
o
in
t.
Mo
r
e
o
v
er
,
a
ce
n
tr
alize
d
co
n
tr
o
l
u
n
it
is
n
ec
ess
ar
y
f
o
r
t
h
e
en
tire
s
y
s
tem
m
o
n
ito
r
in
g
,
p
o
wer
s
u
p
er
v
is
io
n
an
d
p
r
o
te
ctio
n
.
T
h
is
co
n
v
en
tio
n
n
el
s
y
s
tem
s
ee
m
s
to
b
e
co
n
g
ested
an
d
n
ee
d
s
a
g
r
ea
t
n
u
m
b
er
o
f
elec
tr
o
n
ic
p
o
wer
d
e
v
ices.
T
h
e
g
r
ea
t
tech
n
o
l
o
g
ical
ch
alle
n
g
e
wh
ich
ar
is
es
with
in
teg
r
atin
g
m
u
lti
-
ch
an
n
el
p
h
o
t
o
v
o
ltai
c
s
y
s
tem
s
is
th
e
s
y
s
tem
co
n
tr
o
l.
E
a
r
ly
,
m
icr
o
co
n
tr
o
ller
s
ar
e
u
s
ed
f
o
r
s
im
p
le
s
y
s
tem
s
an
d
cla
s
s
ical
ap
p
lic
atio
n
s
esp
ec
ially
f
o
r
s
o
m
e
p
h
o
to
v
o
ltaic
s
y
s
tem
s
[
2
2
]
–
[
2
4
]
.
Nev
er
t
h
eless
,
th
is
ty
p
e
o
f
im
p
lem
en
tatio
n
co
n
f
r
o
n
ts
a
se
r
io
u
s
p
r
o
b
lem
:
it
d
o
es
n
o
t
s
u
p
p
o
r
t
a
s
izea
b
le
ap
p
licatio
n
.
I
n
d
ee
d
,
it
d
o
es
n
o
t
allo
w
ex
ce
llen
t
p
er
f
o
r
m
a
n
ce
:
th
e
f
r
eq
u
en
cy
an
d
th
e
ar
e
a
ar
e
r
elativ
ely
lim
ited
.
I
n
g
en
er
a
l,
it
is
u
n
ab
le
to
h
an
d
le
co
m
p
l
ex
ap
p
licatio
n
s
a
n
d
in
p
ar
ticu
lar
to
im
p
le
m
en
t
in
t
ellig
en
t
co
n
tr
o
l
laws.
W
ith
th
e
em
er
g
en
ce
o
f
n
ew
p
e
r
f
o
r
m
in
g
alg
o
r
ith
m
s
an
d
in
tellig
en
t
laws,
n
ew
tar
g
et
t
ec
h
n
o
lo
g
ies
ar
e
s
u
b
s
tan
tially
r
eq
u
ir
ed
.
T
h
u
s
,
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
o
r
s
(
DSPs
)
an
d
f
ield
p
r
o
g
r
am
m
a
b
le
g
ate
ar
r
ay
s
(
FP
GAs
)
s
ee
m
to
b
e
th
e
k
ey
s
o
lu
tio
n
s
[
2
5
]
,
[
2
6
]
.
Mo
s
tly
,
DSP
-
b
ased
s
y
s
tem
s
ar
e
v
e
r
y
a
p
p
r
o
p
r
i
ate
i
n
c
ase
o
f
la
r
g
e
d
at
a
s
i
ze
an
d
h
ea
v
e
m
at
h
e
m
at
ic
al
ca
lc
u
la
ti
o
n
s
o
f
c
o
n
t
r
o
l
tec
h
n
i
q
u
e.
FP
GA
-
b
ase
d
s
y
s
te
m
s
a
r
e
m
o
r
e
s
u
it
a
b
le
t
o
c
o
n
t
r
o
l
t
ec
h
n
iq
u
e
w
h
ic
h
r
e
q
u
ir
in
g
p
a
r
a
llel
p
er
f
o
r
m
i
n
g
.
I
n
d
ee
d
,
DSP a
r
e
e
x
p
l
o
it
ed
f
o
r
f
i
n
d
in
g
a
n
d
tr
ac
k
i
n
g
t
h
e
o
p
ti
m
al
p
o
in
t
o
f
P
V
p
a
n
els
as i
n
[
2
7
]
,
[
2
8
]
.
O
v
e
r
a
ll
,
t
h
is
cir
c
u
it
is
b
r
o
a
d
l
y
u
s
ed
.
H
o
we
v
e
r
,
C
c
o
m
p
i
le
r
s
ar
e
o
f
te
n
i
n
e
f
f
ici
en
t
b
e
ca
u
s
e
o
f
t
h
e
h
e
te
r
o
g
en
eo
u
s
a
r
c
h
it
ec
tu
r
e
o
f
t
h
e
DS
P
ci
r
c
u
it
w
h
i
ch
t
h
e
n
f
o
r
ce
s
d
esi
g
n
e
r
s
t
o
c
o
d
e
t
h
e
a
p
p
lic
ati
o
n
i
n
t
o
ass
e
m
b
ly
l
an
g
u
ag
e.
H
o
we
v
er
,
it
is
ted
io
u
s
w
o
r
k
a
n
d
r
e
q
u
i
r
es
a
s
i
g
n
if
ic
an
t d
ev
el
o
p
m
en
t ti
m
e
(
ti
m
e
-
to
-
m
a
r
k
et
)
.
Fu
r
t
h
er
m
o
r
e,
t
h
e
c
o
m
p
u
ti
n
g
p
o
we
r
o
f
DSPs
is
wi
d
el
y
e
x
ce
e
d
e
d
b
y
s
m
as
h
i
n
g
t
h
e
s
e
q
u
e
n
t
ial
e
x
e
cu
t
in
g
p
att
er
n
a
n
d
a
tta
in
in
g
m
o
r
e
cy
cl
es
p
e
r
cl
o
c
k
.
I
n
f
a
ct
,
d
esi
g
n
e
r
s
o
f
e
m
b
e
d
d
e
d
a
n
d
h
i
g
h
-
q
u
alit
y
p
e
r
f
o
r
m
a
n
c
e
s
y
s
t
em
s
ar
e
b
less
e
d
w
it
h
n
e
w
o
p
p
o
r
t
u
n
iti
es
a
n
d
ch
all
en
g
es
f
o
r
d
esi
g
n
i
n
g
a
p
p
l
icat
io
n
s
u
s
i
n
g
FP
G
A
-
b
ase
d
h
ar
d
wa
r
e
p
l
at
f
o
r
m
s
[
2
9
]
.
I
n
p
a
r
ti
cu
la
r
,
t
h
e
u
s
e
o
f
in
t
elli
g
en
t
an
d
c
o
m
p
le
x
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
t
r
ac
k
i
n
g
(
M
PP
T
)
c
o
n
t
r
o
l
al
g
o
r
i
th
m
s
i
n
ci
te
s
r
esea
r
ch
er
s
t
o
u
s
e
FP
GA.
So
,
th
e
p
r
o
p
o
s
e
d
s
o
lu
ti
o
n
is
t
o
u
s
e
an
FP
GA
c
h
i
p
f
o
r
o
u
r
s
y
s
tem
.
B
esi
d
es
r
o
b
u
s
tn
ess
,
F
PG
A
p
r
o
v
i
d
es
a
r
ec
o
n
f
i
g
u
r
ati
o
n
f
ea
tu
r
e
t
h
at
all
o
ws
u
p
g
r
a
d
i
n
g
c
o
n
t
r
o
l
s
y
s
t
em
e
asil
y
b
y
c
h
a
n
g
i
n
g
al
g
o
r
it
h
m
wh
ile
it
r
u
n
s
o
n
th
e
F
PGA
.
E
x
p
a
n
d
a
b
ili
ty
f
e
at
u
r
e
e
n
a
b
l
es
t
o
e
x
p
a
n
d
FP
GA
-
b
as
ed
co
n
t
r
o
l
s
y
s
te
m
t
r
e
at
m
u
lti
-
c
h
a
n
n
el
s
y
s
t
em
.
T
h
er
e
b
y
,
i
n
s
te
ad
o
f
m
u
lti
p
l
e
lo
c
al
c
o
n
t
r
o
l
u
n
its
,
t
h
e
FP
GA
d
e
v
ic
e
is
q
u
a
lif
ie
d
as
a
s
i
n
g
le
ce
n
t
r
a
l
u
n
it
t
h
a
t
p
r
o
t
o
t
y
p
es
t
h
e
s
y
s
te
m
b
e
f
o
r
e
i
ts
p
r
ac
tic
al
a
p
p
li
ca
t
io
n
[
3
0
]
,
[
3
1
]
.
FP
GAs
a
r
e
ad
v
a
n
t
ag
eo
u
s
ci
r
cu
its
f
o
r
co
n
t
r
o
lli
n
g
t
h
e
PV
s
y
s
te
m
o
w
in
g
t
o
th
e
f
ast
c
o
m
p
u
ti
n
g
,
l
o
w
c
o
n
s
u
m
p
ti
o
n
a
n
d
p
ar
all
el
a
r
c
h
it
ec
t
u
r
es
.
So
,
t
h
e
m
aj
o
r
co
n
t
r
i
b
u
ti
o
n
is
t
o
a
d
o
p
t
an
FP
GA
c
h
i
p
f
o
r
s
e
ar
ch
in
g
a
n
d
f
o
ll
o
wi
n
g
m
a
x
i
m
u
m
p
o
wer
p
o
in
t
o
f
m
u
lti
-
ch
an
n
el
p
h
o
t
o
v
o
l
tai
c
s
y
s
t
em
an
d
t
o
h
a
r
n
ess
its
p
e
r
ti
n
e
n
t
f
ea
t
u
r
es
t
o
i
n
cr
ea
s
e
m
a
x
i
m
u
m
p
o
w
er
a
n
d
s
y
s
t
e
m
ef
f
ic
ie
n
c
y
.
New
A
r
d
u
i
n
o
d
e
v
ices
w
h
i
ch
ac
t
as
m
i
cr
o
co
n
t
r
o
ll
er
ar
e
u
s
ed
f
o
r
co
m
p
a
r
is
o
n
r
es
u
lts
.
R
es
u
lts
o
f
im
p
le
m
e
n
t
ati
o
n
ar
e
g
i
v
en
t
o
p
r
o
v
e
t
h
e
e
f
f
ici
en
c
y
o
f
an
FP
G
A
-
b
ase
d
s
y
s
te
m
t
o
c
o
n
t
r
o
l
m
u
lti
p
le
PV
c
h
an
n
e
ls
.
T
h
e
r
e
m
a
in
d
e
r
o
f
t
h
is
p
a
p
er
is
s
tr
u
ct
u
r
ed
as
d
esc
r
i
b
ed
al
o
n
g
t
h
ese
li
n
es:
in
s
e
cti
o
n
2
,
a
p
h
o
t
o
v
o
ltai
c
s
y
s
te
m
a
n
d
a
n
ew
f
u
z
zy
MPP
T
c
o
n
t
r
o
lle
r
a
r
e
e
x
p
lai
n
ed
.
I
n
s
ec
ti
o
n
3
,
FP
G
A
t
ec
h
n
o
lo
g
y
is
in
v
est
ig
at
ed
a
n
d
t
h
e
co
r
r
es
p
o
n
d
i
n
g
ta
r
g
et
m
et
h
o
d
is
d
es
cr
ib
ed
.
I
n
s
ec
ti
o
n
4
,
PV
s
y
s
te
m
ca
r
r
y
i
n
g
o
u
t
is
d
et
ail
ed
t
h
e
n
s
i
m
u
la
ti
o
n
r
es
u
lts
a
r
e
g
i
v
e
n
a
n
d
d
is
c
u
s
s
ed
.
T
h
e
c
o
n
cl
u
s
i
o
n
is
d
r
aw
n
in
t
h
e
f
i
n
al
s
e
cti
o
n
.
2.
NE
W
M
P
P
T
M
E
T
H
O
D
F
O
R
P
V
SYST
E
M
2
.
1
.
P
V
s
y
s
t
em
Gen
er
ally
,
th
er
e
ar
e
two
m
ai
n
co
n
f
ig
u
r
atio
n
s
o
f
PV
s
y
s
tem
s
:
ce
n
tr
alize
d
an
d
d
is
tr
ib
u
t
ed
.
O
u
t
p
u
t
p
o
we
r
g
en
er
ati
o
n
o
f
t
h
e
t
r
ad
iti
o
n
al
c
en
tr
ali
ze
d
P
V
s
y
s
t
em
w
as
d
e
cr
ea
s
e
d
d
u
e
t
o
m
u
l
ti
p
le
r
ea
s
o
n
s
.
I
n
d
ee
d
,
th
e
wh
o
le
p
o
we
r
g
o
t
te
n
f
r
o
m
t
h
e
s
tr
i
n
g
o
f
PV
p
an
els
is
i
n
f
lu
en
ce
d
b
y
a
p
ar
t
o
f
p
an
els
i
n
th
e
PV
s
y
s
te
m
wh
ic
h
u
n
d
er
g
o
es
p
a
r
ti
al
s
h
a
d
i
n
g
.
T
h
e
co
m
p
o
n
en
ts
o
f
t
h
e
c
e
n
t
r
ali
z
ed
PV
s
y
s
t
em
a
r
r
a
n
g
e
m
e
n
t
,
p
r
ese
n
te
d
in
Fig
u
r
e
1
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
F
u
z
z
y
-
b
a
s
ed
MPP
T a
lg
o
r
ith
m
imp
leme
n
ta
tio
n
o
n
F
P
GA
ch
i
p
fo
r
mu
lti
-
ch
a
n
n
el
… (
Ha
n
e
n
A
b
b
es
)
51
ar
e
a
PV
p
a
n
e
l,
s
ta
tic
c
o
n
v
e
r
te
r
,
p
o
we
r
i
n
v
e
r
t
er
,
a
n
d
co
n
t
r
o
l
u
n
it
.
Fig
u
r
e
1
.
C
en
tr
al
PV sy
s
tem
co
n
f
ig
u
r
atio
n
T
h
e
d
is
tr
ib
u
ted
PV
s
y
s
tem
in
clu
d
es
m
u
lti
p
h
o
to
v
o
ltaic
ch
a
n
n
els,
DC
-
DC
co
n
v
er
ter
s
,
co
n
tr
o
l
u
n
it,
AC
an
d
/o
r
DC
lo
ad
.
E
ac
h
p
a
n
el
lev
el
MPPT
o
p
er
atio
n
an
d
v
o
ltag
e
m
ea
s
u
r
em
en
t
a
r
e
p
ar
allel
ca
r
r
ied
o
u
t.
E
v
er
y
DC
-
DC
co
n
v
er
ter
r
eq
u
i
r
es
elec
tr
ical
s
en
s
o
r
s
to
m
ea
s
u
r
e
v
o
ltag
e
a
n
d
cu
r
r
en
t
v
alu
es
an
d
I
n
p
u
ts
/Ou
tp
u
ts
p
o
r
ts
f
o
r
tr
ac
k
in
g
tar
g
et.
E
ac
h
o
f
th
ese
DC
-
D
C
co
n
v
er
ter
s
is
co
n
tr
o
lled
b
y
a
d
is
tr
ib
u
ted
m
ax
im
u
m
p
o
we
r
p
o
in
t
tr
ac
k
in
g
(
DM
PP
T
)
b
l
o
c
k
.
T
h
is
s
y
s
tem
ty
p
e
allo
ws
h
ar
v
est
en
er
g
y
f
r
o
m
ea
c
h
p
an
e
l.
I
t
o
v
er
c
o
m
es
th
e
co
m
m
o
n
p
r
o
b
lem
s
o
f
th
e
ce
n
t
r
alize
d
PV
s
y
s
tem
an
d
i
n
cr
ea
s
es
to
tal
en
er
g
y
ef
f
icien
c
y
[
3
2
]
.
Ab
b
es
et
a
l
.
[
3
3
]
p
r
esen
t
th
e
im
p
lem
e
n
tatio
n
o
n
FP
GA
o
f
MPPT
co
n
tr
o
l
f
o
r
a
s
im
p
le
p
h
o
to
v
o
ltaic
s
y
s
tem
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
d
is
t
r
ib
u
ted
PV
s
y
s
tem
.
As
d
r
awn
in
Fig
u
r
e
2
,
ea
c
h
p
h
o
to
v
o
ltaic
p
an
el
is
s
u
p
er
v
is
ed
b
y
MPPT
item
b
y
th
e
m
ea
n
s
o
f
a
b
o
o
s
t
co
n
v
e
r
ter
.
I
n
d
ee
d
,
a
DM
PP
T
b
lo
ck
is
d
ir
ec
tly
lin
k
ed
to
a
b
o
o
s
t
co
n
v
e
r
ter
to
g
et
th
e
o
p
tim
al
o
p
er
atin
g
p
o
in
t.
As
a
DC
-
DC
co
n
v
er
te
r
is
r
elate
d
to
o
n
ly
o
n
e
PV
p
an
el
o
f
th
e
p
h
o
to
v
o
lt
aic
p
an
els
s
et,
ea
ch
p
an
el
in
th
is
ar
ch
itectu
r
e
k
in
d
h
as to
o
p
er
ate
at
its
o
wn
m
ax
i
m
u
m
p
o
wer
p
o
i
n
t.
Fig
u
r
e
2
.
Mu
lti
-
c
h
an
n
el
PV sy
s
tem
2
.
2
.
F
uzzy
M
P
P
T
m
et
ho
d
Mo
s
t
r
esear
ch
er
s
u
s
e
tr
ad
itio
n
al
MPPT
m
eth
o
d
s
to
co
n
tr
o
l
P
V
s
y
s
tem
.
T
h
ese
m
eth
o
d
s
ar
e
u
s
ed
o
win
g
to
th
eir
s
im
p
le
an
d
ea
s
y
im
p
lem
en
tatio
n
.
No
n
eth
eless
,
s
in
ce
th
ese
m
eth
o
d
s
r
ely
o
n
a
f
ix
ed
s
tep
to
g
et
o
p
tim
al
p
o
wer
,
th
er
e
ar
e
s
o
m
e
wea
k
n
ess
:
s
lo
wly
co
n
v
er
g
in
g
to
m
a
x
im
u
m
p
o
we
r
p
o
in
t,
s
ig
n
if
ican
t
o
s
cillatio
n
s
ar
o
u
n
d
t
h
is
p
o
i
n
t
an
d
wr
o
n
g
r
esp
o
n
s
e
u
n
d
e
r
r
a
p
id
ir
r
a
d
iatio
n
c
h
an
g
es.
Fu
zz
y
co
n
ce
p
t
ex
p
r
ess
ed
b
y
th
e
f
u
zz
y
s
ets
th
eo
r
y
an
d
li
n
g
u
is
tic
r
u
les
h
as
b
ee
n
u
s
e
d
t
o
o
f
f
er
in
n
o
v
ativ
e
e
f
f
icien
t
p
e
r
f
o
r
m
a
n
ce
s
o
v
e
r
th
e
tr
ad
itio
n
al
co
n
tr
o
ller
s
[
3
4
]
.
T
h
is
co
n
ce
p
t
h
as
b
ee
n
ap
p
lied
s
in
ce
it
h
an
d
les
th
e
n
o
n
lin
ea
r
ity
an
d
it
d
o
es
n
o
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
11
,
No
.
1
,
M
ar
c
h
20
22
:
49
-
58
52
n
ee
d
a
r
ig
o
r
o
u
s
m
ath
em
atica
l
m
o
d
el.
An
im
p
r
o
v
ed
MPPT
t
ec
h
n
iq
u
e
p
r
o
p
o
s
ed
in
[
3
5
]
ai
m
s
to
o
v
er
c
o
m
e
th
e
d
r
awb
ac
k
s
o
f
class
ical
tech
n
iq
u
es a
n
d
to
tak
e
ad
v
a
n
tag
e
o
f
f
u
zz
y
lo
g
ic
c
o
n
ce
p
t.
I
ts
p
r
in
cip
le
is
b
ased
o
n
th
r
ee
s
tag
es:
i)
F
u
zz
if
icatio
n
;
ii)
I
n
f
er
en
ce
e
n
g
in
e
;
an
d
iii)
D
ef
u
z
zif
icatio
n
.
Fu
zz
if
icatio
n
’s
en
d
is
to
co
n
v
er
t
n
u
m
er
ical
in
p
u
t
v
a
r
iab
le
s
to
lin
g
u
is
tic
v
ar
ia
b
les.
T
h
e
n
,
d
u
r
in
g
in
f
er
e
n
ce
en
g
in
e
s
tag
e,
r
u
le
in
f
er
en
ce
ta
b
le
is
m
ad
e:
lo
g
ic
r
elatio
n
s
h
ip
s
ar
e
d
ef
in
ed
to
lin
k
in
p
u
ts
wi
th
o
u
tp
u
ts
.
Fin
ally
,
d
ef
u
zz
if
icatio
n
s
tag
e
aim
s
to
co
n
v
er
t
lin
g
u
is
tic
v
ar
iab
le
t
o
a
co
n
c
r
ete
v
al
u
e.
T
h
er
ef
o
r
e,
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
p
u
r
p
o
s
e
ac
ce
ler
ates
tr
ac
k
in
g
m
ax
im
u
m
p
o
wer
with
o
u
t
o
s
cillatio
n
s
.
T
h
e
id
ea
is
to
u
s
e
a
v
ar
iab
le
s
tep
i
n
p
lace
o
f
a
f
ix
e
d
s
tep
:
in
cr
em
en
tin
g
s
tep
is
b
ig
at
th
e
f
ir
s
t
,
m
ed
i
u
m
in
th
e
m
id
d
le
o
f
th
e
p
r
o
ce
s
s
a
n
d
h
as
a
s
m
all
s
ize
in
th
e
s
tead
y
s
tate.
T
h
is
v
ar
ia
b
le
s
tep
is
g
iv
en
b
y
a
f
u
zz
y
l
o
g
ic
b
lo
c
k
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
o
p
er
ates
as
f
o
llo
ws:
At
th
e
b
eg
in
n
in
g
,
I
(
k
)
an
d
V
(
k
)
a
r
e
co
m
p
u
te
d
an
d
p
r
o
v
i
d
ed
to
th
e
f
u
zz
if
icatio
n
s
tag
e.
T
h
en
,
lin
g
u
is
tic
o
u
tp
u
t
v
ar
iab
les
ar
e
ca
r
r
ied
o
u
t
in
in
f
e
r
en
ce
s
tag
e
t
o
h
av
e
d
ec
is
io
n
s
.
d
D
is
th
e
v
a
r
iab
le
s
tep
co
m
in
g
f
r
o
m
th
e
f
u
zz
y
b
lo
ck
.
Hen
ce
,
g
iv
in
g
th
e
s
ig
n
o
f
d
P/d
V,
th
e
wh
o
le
v
a
lu
e
o
f
th
e
d
u
ty
r
atio
D
is
f
in
ally
d
eter
m
in
ed
.
T
h
e
f
lo
wc
h
ar
t o
f
n
ew
f
u
zz
y
MPPT
is
g
iv
en
in
Fig
u
r
e
3.
Fig
u
r
e
3
.
Flo
wch
ar
t
o
f
n
ew
f
u
zz
y
MPPT
alg
o
r
ith
m
3.
F
P
G
A
CH
I
P
F
O
R
P
H
O
T
O
VO
L
T
A
I
C
SY
ST
E
M
Du
e
to
th
e
in
cr
ea
s
in
g
ly
p
r
o
g
r
ess
in
FP
GA
tech
n
o
lo
g
y
an
d
th
e
av
ailab
ilit
y
o
f
ad
v
a
n
ce
d
to
o
ls
,
ap
p
licatio
n
f
ield
s
o
f
FP
GAs
in
cr
ea
s
e
at
a
g
r
ea
t
r
ate
a
n
d
it
is
ex
p
ec
ted
th
at
in
th
e
u
p
co
m
in
g
y
ea
r
s
th
is
s
ed
u
ctiv
e
tech
n
o
lo
g
y
m
a
y
ev
en
r
ep
lace
ap
p
licatio
n
s
p
ec
if
ic
i
n
teg
r
ated
cir
cu
it
(
ASI
C
)
[
3
6
]
,
[
3
7
]
.
FP
GAs
ap
p
licatio
n
ar
ea
s
a
r
e
m
an
y
an
d
v
ar
io
u
s
.
B
r
o
ad
ly
s
p
ea
k
in
g
,
FP
GA
s
ar
e
p
r
esen
t
in
:
v
id
eo
p
r
o
ce
s
s
in
g
,
co
n
tr
o
l
s
y
s
tem
s
en
g
in
ee
r
in
g
,
b
io
i
n
f
o
r
m
atics,
s
o
f
twar
e
d
ef
in
ed
r
ad
io
,
ae
r
o
s
p
ac
e,
ast
r
o
n
o
m
y
,
d
ef
en
s
e
s
y
s
tem
s
,
r
ec
o
g
n
iti
o
n
s
y
s
tem
s
,
m
ed
ic
al
im
ag
in
g
,
c
o
m
p
u
t
er
h
ar
d
war
e
(
HW
)
em
u
l
ati
o
n
,
p
r
o
t
o
t
y
p
i
n
g
o
f
AS
I
C
,
r
e
co
n
f
i
g
u
r
ab
le
c
o
m
p
u
ti
n
g
a
n
d
o
t
h
e
r
s
.
3
.
1
.
F
P
G
A
t
ec
hn
o
lo
g
y
I
n
r
ec
e
n
t
y
ea
r
s
,
FP
GAs
h
av
e
b
ee
n
a
r
o
u
s
in
g
g
r
o
win
g
i
n
t
er
es
t.
T
h
is
d
ev
ice
is
p
a
r
ti
cu
la
r
l
y
g
ain
f
u
l
f
o
r
ap
p
li
ca
ti
o
n
s
b
ase
d
o
n
d
i
g
ita
l
c
o
n
tr
o
l
.
FP
GAs
g
lo
b
al
m
a
r
k
e
t
i
s
e
x
p
a
n
d
in
g
at
a
h
u
g
el
y
h
i
g
h
r
ate
a
n
d
d
a
y
b
y
d
a
y
,
FP
GAs
p
o
p
u
l
ar
it
y
is
als
o
g
r
o
w
in
g
.
FP
G
A
ch
ip
is
d
r
i
v
en
b
y
it
s
f
l
e
x
i
b
ili
ty
,
h
ar
d
w
a
r
e
-
ti
m
e
d
s
p
e
ed
a
n
d
r
elia
b
i
lit
y
,
an
d
p
ar
all
elis
m
.
Gi
v
i
n
g
i
ts
p
a
r
tic
u
la
r
a
r
c
h
i
tec
tu
r
e,
FP
GAs
ar
e
co
n
v
e
n
i
en
t
f
o
r
ap
p
l
ic
ati
o
n
s
an
d
i
m
p
le
m
e
n
ta
ti
o
n
o
f
a
lg
o
r
it
h
m
s
f
e
at
u
r
e
d
b
y
p
a
r
al
lel
p
r
o
c
ess
i
n
g
.
FP
GA
b
as
e
d
s
y
s
t
em
s
c
o
n
t
r
o
ll
er
s
p
r
o
v
i
d
e
q
u
ite
a
d
v
a
n
t
ag
es
t
h
at
b
r
i
n
g
h
i
g
h
p
e
r
f
o
r
m
a
n
c
es
i
n
r
ea
l
ti
m
e
s
y
s
te
m
s
.
Ve
r
y
i
m
p
o
r
t
an
t
a
d
v
a
n
ta
g
es
a
r
e
th
e
s
p
e
ed
a
n
d
t
h
e
lo
w
p
o
w
er
c
o
n
s
u
m
p
ti
o
n
.
I
n
f
ac
t
,
s
y
s
te
m
s
u
s
i
n
g
FP
GA
all
o
w
less
e
x
e
c
u
ti
o
n
ti
m
e
t
h
a
n
k
s
t
o
its
h
a
r
d
wa
r
e
ar
c
h
it
ec
t
u
r
e
.
B
esi
d
es
t
h
ese
b
e
n
e
f
i
ts
,
FP
GA
is
a
s
m
all
Evaluation Warning : The document was created with Spire.PDF for Python.
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&
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I
SS
N:
2089
-
4
8
6
4
F
u
z
z
y
-
b
a
s
ed
MPP
T a
lg
o
r
ith
m
imp
leme
n
ta
tio
n
o
n
F
P
GA
ch
i
p
fo
r
mu
lti
-
ch
a
n
n
el
… (
Ha
n
e
n
A
b
b
es
)
53
ch
i
p
wit
h
a
l
o
w
c
o
s
t
wit
h
r
e
g
a
r
d
s
t
o
o
t
h
e
r
p
l
at
f
o
r
m
s
.
I
n
a
d
d
i
tio
n
,
a
lg
o
r
it
h
m
s
a
r
e
d
esi
g
n
e
d
o
n
a
r
ec
o
n
f
ig
u
r
a
b
l
e
p
la
tf
o
r
m
t
h
a
t
ca
n
b
e
u
p
d
at
ed
o
r
r
e
cti
f
i
ed
e
asil
y
.
3
.
2
.
F
P
G
A
P
la
t
f
o
r
m
A
v
ar
iet
y
o
f
alt
er
n
a
ti
v
es
a
r
e
a
v
ai
la
b
l
e
t
o
f
i
r
m
s
w
h
i
ch
p
u
t
i
n
p
la
ce
FP
GA
-
b
as
ed
a
p
p
lic
ati
o
n
s
.
T
h
o
u
g
h
n
u
m
er
o
u
s
alt
er
n
ati
v
es
s
ee
m
s
i
m
il
ar
as
t
h
e
s
am
e
FP
GA
i
te
m
is
p
r
o
d
u
ce
d
,
n
am
el
y
b
y
I
n
t
el
o
r
Xi
li
n
x
f
i
r
m
.
I
t
g
o
es
wi
t
h
o
u
t
s
a
y
i
n
g
th
at
,
t
h
e
r
e
a
r
e
m
a
n
y
m
aj
o
r
d
is
s
im
ila
r
i
t
ies
b
etw
ee
n
p
l
atf
o
r
m
s
.
T
h
ese
d
is
s
i
m
il
a
r
iti
es
c
an
h
a
v
e
a
n
o
ta
b
l
e
im
p
a
ct
o
n
to
s
o
m
e
f
ac
t
o
r
s
s
u
c
h
as
t
h
e
p
h
y
s
ic
al
a
r
e
a,
t
h
e
p
o
we
r
a
n
d
c
o
o
li
n
g
t
h
ey
n
e
ed
t
o
co
n
ti
n
u
o
u
s
b
as
is
a
n
d
th
e
a
m
o
u
n
t
o
f
i
n
t
er
n
a
l
r
eso
u
r
c
es
wh
ic
h
a
r
e
p
r
im
o
r
d
ial
t
o
d
e
p
l
o
y
,
m
o
n
it
o
r
an
d
s
u
p
p
o
r
t
th
e
m
.
T
o
s
e
lec
t
t
h
e
b
es
t
t
y
p
e
o
f
p
la
tf
o
r
m
f
o
r
y
o
u
r
b
u
s
i
n
ess
,
it
is
ess
e
n
ti
al
to
h
a
v
e
i
n
t
o
c
o
n
s
id
e
r
at
io
n
t
h
e
in
t
eg
r
ati
o
n
c
o
s
ts
,
t
h
e
a
m
o
u
n
t
o
f
c
o
n
ti
n
u
o
u
s
ass
is
t
an
ce
n
ee
d
e
d
,
i
f
i
n
t
er
n
a
l
s
u
p
p
o
r
t
is
a
v
aila
b
l
e,
t
h
e
co
s
t
o
f
o
w
n
e
r
s
h
i
p
a
n
d
t
h
e
c
o
m
p
le
x
i
ty
.
T
h
e
o
p
ti
o
n
s
o
f
f
er
e
d
b
y
t
h
es
e
co
n
f
i
g
u
r
a
b
l
e
h
a
r
d
wa
r
e
p
la
tf
o
r
m
s
a
r
e
t
h
e
d
esi
g
n
o
f
cu
s
t
o
m
h
ar
d
w
ar
e
s
u
b
r
o
u
t
in
e,
in
f
u
t
u
r
e
f
r
ee
z
e
d
ates
,
f
iel
d
u
p
g
r
ad
es,
a
n
d
t
h
e
r
ed
u
cti
o
n
o
f
s
p
e
ci
f
ic
c
h
i
p
s
f
r
o
m
s
ev
er
al
t
y
p
es
o
f
ele
ct
r
o
n
i
c
p
r
o
d
u
cts
.
3
.
3
.
F
P
G
A
m
et
ho
d a
nd
des
ig
n t
o
o
ls
T
o
d
a
y
,
FP
GAs
a
r
e
m
o
r
e
a
n
d
m
o
r
e
p
r
ese
n
t
i
n
im
p
l
em
e
n
ti
n
g
co
m
p
le
x
f
u
n
ct
io
n
s
.
T
h
e
s
u
cc
es
s
o
r
f
ail
u
r
e
o
f
FP
GA
b
ase
d
s
y
s
te
m
,
m
ea
s
u
r
ed
in
ter
m
s
o
f
tim
e
-
to
-
m
a
r
k
et
an
d
th
e
f
in
al
p
e
r
f
o
r
m
an
ce
r
ea
ch
ed
,
d
e
p
en
d
s
o
n
th
e
way
th
at
th
e
ap
p
licatio
n
an
d
its
co
n
s
titu
en
t
f
u
n
ctio
n
s
ar
e
m
ap
p
ed
u
p
o
n
p
latf
o
r
m
r
e
s
o
u
r
ce
s
.
L
o
w
-
lev
el
lan
g
u
ag
es
s
u
ch
as
v
er
y
h
ig
h
-
s
p
ee
d
in
teg
r
ated
cir
cu
it
h
a
r
d
wa
r
e
d
escr
ip
tio
n
lan
g
u
a
g
e
(
VHDL
)
an
d
Ver
ilo
g
ar
e
tar
g
eted
f
o
r
c
o
n
ce
iv
in
g
th
e
al
g
o
r
ith
m
s
ca
r
r
ied
o
u
t
in
th
e
F
PGA
ch
ip
.
Sy
n
tax
n
ec
ess
itate
s
m
ap
p
ed
s
ig
n
als
to
co
n
n
ec
t
ex
ter
n
al
in
p
u
ts
/o
u
tp
u
t
s
to
in
ter
n
al
s
ig
n
als.
T
h
ese
s
i
g
n
als
ar
e
co
n
n
ec
te
d
to
f
u
n
ctio
n
s
wh
ich
f
o
r
m
th
e
alg
o
r
ith
m
s
.
On
ce
y
o
u
h
av
e
cr
ea
ted
an
FP
GA
d
esig
n
d
esc
r
ib
ed
in
h
ar
d
war
e
d
escr
ip
ti
o
n
lan
g
u
ag
e
(
HDL
)
,
it
is
s
u
b
s
tan
tial
to
in
tr
o
d
u
ce
it
in
to
a
co
m
p
ilatio
n
to
o
l
th
at
g
ets
th
e
tex
t
-
b
ased
lo
g
ic
to
v
er
if
y
it.
T
h
e
tr
ad
itio
n
al
d
esig
n
f
lo
w
is
m
a
d
e
o
f
s
u
ch
s
tep
s
f
r
o
m
t
h
e
in
itial
lo
g
ic
s
y
n
t
h
esis
to
th
e
f
in
al
p
h
y
s
ical
d
e
s
i
g
n
s
tep
to
ac
h
iev
e
FP
GA
im
p
lem
en
tatio
n
.
T
h
e
o
b
jectiv
e
is
to
s
y
n
th
esize
y
o
u
r
HDL
to
a
c
o
n
f
i
g
u
r
atio
n
f
ile
th
at
in
clu
d
es
in
f
o
r
m
atio
n
s
o
f
th
e
m
an
n
er
to
lin
k
to
g
eth
er
th
e
co
m
p
o
n
e
n
ts
.
Fo
r
d
esig
n
s
with
s
er
io
u
s
p
er
f
o
r
m
an
ce
g
o
als,
d
esig
n
er
s
f
o
u
n
d
th
at
s
o
m
e
iter
at
io
n
b
etwe
en
s
y
n
th
esis
an
d
p
h
y
s
ical
d
esig
n
ar
e
cr
u
ci
al
to
co
n
v
er
g
e
to
a
d
esire
d
im
p
lem
en
tatio
n
.
At
co
n
s
eq
u
e
n
ce
,
u
s
u
ally
,
d
esig
n
f
lo
w
co
n
s
is
ts
o
f
s
ix
m
ain
s
tep
s
:
h
ier
ar
ch
ical
d
ec
o
m
p
o
s
itio
n
,
VHDL
d
escr
ip
tio
n
,
s
y
n
th
esis
an
d
o
p
tim
izatio
n
,
p
lace
an
d
r
o
u
te,
s
im
u
l
atio
n
,
p
r
o
g
r
a
m
m
in
g
a
n
d
co
n
f
ig
u
r
atio
n
.
T
h
e
r
ef
o
r
e
,
p
o
te
n
ti
al
s
p
ec
i
f
ic
ati
o
n
s
an
d
th
ese
ch
all
en
g
es
m
a
k
e
FP
G
A
te
ch
n
o
l
o
g
y
b
r
i
g
h
t
en
e
d
an
d
u
s
e
d
to
c
o
n
t
r
o
l
s
y
s
t
em
an
d
t
o
h
a
n
d
le
m
u
lti
-
c
h
a
n
n
e
l
p
h
o
to
v
o
lt
aic
s
y
s
t
em
.
I
n
f
a
ct,
t
h
e
FP
G
A
d
e
v
ic
e
is
a
b
l
e
t
o
m
o
n
it
o
r
m
a
n
y
l
o
c
al
c
o
n
t
r
o
l
u
n
i
t
s
i
n
a
s
i
n
g
l
e
ce
n
t
r
a
l
u
n
it
a
n
d
p
r
o
to
ty
p
e
t
h
e
s
y
s
te
m
f
o
r
p
r
ac
tic
al
a
p
p
lic
ati
o
n
.
4.
SI
M
UL
A
T
I
O
N
A
N
D
E
XP
E
RIM
E
N
T
AL
R
E
S
UL
T
S
T
h
e
s
y
s
tem
is
g
iv
en
in
s
ec
tio
n
2
(
s
ee
i
n
Fig
u
r
e
2
)
is
im
p
lem
e
n
ted
o
n
FP
GA
ch
ip
.
A
d
etail
ed
s
y
s
tem
o
p
er
atio
n
d
ef
in
ed
as
tr
ac
k
in
g
o
f
m
ax
im
u
m
p
o
wer
p
o
in
t
o
f
m
u
lti
-
ch
an
n
el
p
h
o
to
v
o
ltaic
s
y
s
tem
is
g
iv
en
b
y
Fig
u
r
e
4
.
T
h
e
MPPT
task
o
n
FP
GA
ch
ip
f
o
r
m
u
ltip
le
PV
m
o
d
u
les
is
item
ized
b
y
b
lo
ck
s
.
T
h
e
ar
ch
itectu
r
e
is
o
p
tim
ized
,
aim
s
to
d
e
v
elo
p
a
s
in
g
le
u
n
if
ied
MPPT
u
n
it
o
f
c
o
n
tr
o
l
f
o
r
all
PV
m
o
d
u
les
with
r
ed
u
ce
d
tim
e
an
d
s
p
ac
e.
Fig
u
r
e
4
.
PV sy
s
tem
with
u
n
if
ied
MPPT
alg
o
r
ith
m
f
o
r
m
u
lti
p
le
ch
an
n
els
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
11
,
No
.
1
,
M
ar
c
h
20
22
:
49
-
58
54
MPPT
co
n
tr
o
l
u
n
it
r
e
ce
iv
es
i
n
p
u
ts
d
ata
o
f
v
o
lta
g
e
an
d
c
u
r
r
en
t
v
al
u
es.
I
t
p
r
o
ce
s
s
o
n
FP
GA
th
en
it
s
en
d
s
th
e
d
u
t
y
r
atio
to
co
n
tr
o
l
DC
-
DC
co
n
v
er
ter
s
witch
.
T
h
e
v
ar
iab
les
V
pvi
a
n
d
I
pvi
,
i
f
r
o
m
1
to
n
,
ar
e
s
en
t
alter
n
ately
in
o
r
d
er
to
c
o
m
p
u
te
th
e
d
u
ty
v
alu
e
f
o
r
ea
ch
p
a
n
el.
As
an
ex
am
p
le,
th
e
f
ir
s
t
PV
p
an
el
o
b
tain
s
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
u
p
d
ated
v
alu
es
V
pv1
(
k
)
an
d
I
pv1
(
k
)
.
Af
te
r
war
d
s
,
MPPT
tech
n
iq
u
e
u
s
es
an
cien
t
m
em
o
r
ized
v
alu
es
o
f
v
o
ltag
e,
c
u
r
r
e
n
t
an
d
d
u
ty
,
r
esp
ec
tiv
ely
,
V
pv1
(k
-
1
)
,
I
pv1
(k
-
1
)
,
a
n
d
d
pv1
(k
-
1
)
,
to
attain
a
n
ew
v
alu
e
o
f
d
u
ty
r
atio
,
th
en
,
it
d
o
es th
e
s
a
m
e
p
r
o
ce
s
s
f
o
r
th
e
r
em
ai
n
d
er
o
f
PV c
h
an
n
els u
n
ti
l it
r
ea
ch
es th
e
o
p
tim
al
v
al
u
e.
T
h
is
co
n
ce
p
t
en
s
u
r
es
th
at
all
m
u
l
t
i
-
ch
an
n
el
o
p
er
ate
s
y
n
ch
r
o
n
o
u
s
ly
,
a
n
d
ea
c
h
ch
a
n
n
el
o
p
e
r
ates
at
its
o
p
tim
al
o
p
er
atin
g
p
o
i
n
t.
Usi
n
g
th
e
p
r
o
p
o
s
ed
tr
ac
k
in
g
s
y
s
tem
r
ed
u
ce
s
th
e
s
ettin
g
o
f
th
e
t
r
ac
k
in
g
a
n
d
f
ac
ilit
ates
m
o
n
ito
r
in
g
a
n
d
c
o
n
tr
o
llin
g
m
u
lti
-
ch
an
n
el
PV
s
y
s
tem
.
I
n
t
h
e
f
ir
s
t
s
tep
,
PV
s
y
s
tem
b
as
ed
o
n
f
u
zz
y
MPPT
tech
n
iq
u
e
is
d
ev
el
o
p
ed
u
s
in
g
Ma
tlab
-
Simu
lin
k
e
n
v
ir
o
n
m
en
t
.
Simu
latio
n
r
esu
lts
o
f
PV
s
y
s
tem
o
p
er
atio
n
ar
e
g
iv
en
b
y
Fig
u
r
es 5
a
n
d
6
.
Fig
u
r
e
5
.
C
u
r
r
e
n
t c
u
r
v
e
o
f
PV s
y
s
tem
Fig
u
r
e
6
.
Vo
ltag
e
cu
r
v
e
o
f
PV
s
y
s
tem
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
at
e
th
at
th
e
PV
s
y
s
tem
o
p
e
r
ates
at
o
p
tim
u
m
v
alu
es
with
o
u
t
o
s
cillatio
n
s
at
s
tead
y
s
tate.
T
h
e
p
h
o
to
v
o
lt
aic
s
y
s
tem
r
ea
ch
es
o
p
tim
al
c
u
r
r
en
t
a
n
d
v
o
ltag
e
as
s
h
o
wn
b
y
Fig
u
r
es
5
an
d
6
.
T
h
en
,
PV
s
y
s
tem
b
ased
o
n
th
e
p
r
o
p
o
s
ed
MPPT
ap
p
r
o
ac
h
g
et
b
etter
a
n
d
p
er
f
o
r
m
i
n
g
r
esu
lts
in
ter
m
o
f
tr
ac
k
in
g
s
p
ee
d
an
d
s
tab
ilit
y
.
I
n
a
s
ec
o
n
d
s
tep
,
cu
r
r
en
t
an
d
v
o
ltag
e
d
ata
v
a
lu
es
ar
e
r
etr
iev
ed
f
r
o
m
p
r
ev
io
u
s
s
im
u
latio
n
s
r
esu
lts
.
T
h
ese
v
alu
es
ar
e
p
r
o
v
id
ed
to
d
esig
n
an
d
im
p
lem
e
n
t
f
u
zz
y
lo
g
ic
MPPT
co
n
tr
o
ll
er
o
n
FP
GA
cir
cu
it
u
s
in
g
Qu
ar
tu
s
p
latf
o
r
m
.
Qu
ar
t
u
s
I
I
is
d
ef
in
ed
as
a
s
y
s
tem
-
on
-
a
-
ch
ip
d
e
v
elo
p
m
e
n
t
to
o
l.
I
t
allo
ws
a
d
esig
n
o
f
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
F
u
z
z
y
-
b
a
s
ed
MPP
T a
lg
o
r
ith
m
imp
leme
n
ta
tio
n
o
n
F
P
GA
ch
i
p
fo
r
mu
lti
-
ch
a
n
n
el
… (
Ha
n
e
n
A
b
b
es
)
55
d
ig
ital
cir
cu
it
f
r
o
m
a
tr
ad
itio
n
al
s
ch
em
atic
f
o
r
m
o
r
tex
t
u
a
l
f
o
r
m
u
s
in
g
a
h
ar
d
war
e
d
es
cr
ip
tio
n
lan
g
u
ag
e:
VHDL
,
Ver
ilo
g
,
a
n
d
A
-
HDL
.
Simu
latio
n
r
esu
lts
o
f
MPPT
co
n
tr
o
ller
o
n
FP
GA
v
ia
Qu
ar
tu
s
ar
e
d
e
p
icted
in
Fig
u
r
e
7
.
Fig
u
r
e
7
.
MPP tr
ac
k
in
g
f
o
r
PV
s
y
s
tem
b
ased
o
n
FP
GA
T
h
e
illu
s
tr
atio
n
s
h
o
ws
th
at
t
h
e
v
alu
e
o
f
th
e
cy
clic
r
atio
d
em
o
n
s
tr
ates
two
p
h
ases
:
a
tr
an
s
itio
n
al
p
h
ase
an
d
a
s
tead
y
p
h
ase.
T
h
is
lat
est
is
d
escr
ib
ed
b
y
v
er
y
litt
le
o
s
cillatio
n
s
ar
o
u
n
d
th
e
o
p
t
im
al
v
alu
e.
T
h
ese
o
s
cillatio
n
s
d
ep
en
d
o
n
t
h
e
M
PP
T
alg
o
r
ith
m
.
T
h
e
th
e
o
r
etic
al
v
alu
e
is
eq
u
al
to
0
.
6
4
.
T
h
e
r
esu
ltin
g
o
p
tim
al
v
alu
e
is
b
etwe
en
0
.
6
an
d
0
.
6
8
at
th
e
(
2
5
°C
,
1
0
0
0
W
/m
2
)
.
At
co
n
s
eq
u
e
n
ce
,
we
d
e
d
u
c
e
th
at
PV
s
y
s
tem
co
n
v
er
g
es
ef
f
ec
tiv
ely
to
wa
r
d
s
its
o
p
tim
al
v
alu
e.
T
h
en
,
we
n
o
te
also
th
at
o
s
ci
llatio
n
s
g
o
to
alm
o
s
t
d
is
ap
p
ea
r
,
s
o
,
th
e
alg
o
r
ith
m
is
ac
cu
r
ate
a
n
d
r
o
b
u
s
t.
T
o
p
r
o
v
e
th
e
ef
f
icien
cy
o
f
FP
GA
b
ased
co
n
tr
o
ller
f
o
r
a
m
u
lti
-
ch
an
n
el
PV
s
y
s
tem
,
th
e
MPPT
alg
o
r
ith
m
is
im
p
lem
en
ted
o
n
v
ar
io
u
s
p
latf
o
r
m
s
th
en
ex
ec
u
tio
n
tim
e
is
co
m
p
u
te
d
.
I
n
th
e
f
i
r
s
t
s
tep
,
f
u
zz
y
lo
g
i
c
MPPT
ap
p
r
o
ac
h
is
im
p
lem
en
ted
u
s
in
g
s
o
f
twar
e
s
o
lu
tio
n
.
T
h
is
k
in
d
o
f
s
o
lu
tio
n
is
p
er
f
o
r
m
ed
u
s
in
g
Ar
d
u
in
o
d
ev
ices.
T
ab
le
1
s
u
m
m
ar
izes
th
e
im
p
lem
en
tatio
n
r
esu
lts
:
ex
ec
u
tio
n
tim
e
an
d
th
e
n
u
m
b
er
o
f
PV
ch
a
n
n
els
f
o
r
ea
ch
s
o
lu
tio
n
.
T
ab
le
1
.
I
m
p
lem
en
tatio
n
r
esu
l
ts
P
l
a
t
e
f
o
r
m
a
n
d
d
e
v
i
c
e
A
r
d
u
i
n
o
-
uno
N
i
o
s (S
t
r
a
t
i
x
I
I
I
)
A
r
d
u
i
n
o
-
d
u
e
(
A
R
M
)
F
P
G
A
(
S
t
r
a
t
i
x
I
I
I
)
P
r
o
c
e
ss
o
r
f
r
e
q
u
e
n
c
y
(
M
H
z
)
16
1
0
0
84
-
Ex
e
c
u
t
i
o
n
t
i
m
e
(
ms)
Li
mi
t
e
d
m
e
m
o
r
y
3
8
.
1
1
8
.
4
0
.
1
1
2
7
P
V
c
h
a
n
n
e
l
s
t
o
c
o
n
t
r
o
l
-
13
27
4
4
3
6
I
t
is
clea
r
th
at
FP
G
A
s
o
lu
tio
n
is
th
e
s
o
lu
tio
n
th
at
in
clu
d
es
th
e
g
r
ea
test
n
u
m
b
er
o
f
PV
ch
an
n
els
to
co
n
tr
o
l:
it
is
ab
le
t
o
co
n
tr
o
l
u
p
to
4
4
3
6
ch
a
n
n
els.
E
x
ec
u
tio
n
tim
e
is
in
d
escen
d
i
n
g
o
r
d
er
,
t
h
e
m
in
im
u
m
r
ate
is
ac
h
iev
ed
b
y
th
e
u
s
e
o
f
FP
GA
s
o
lu
tio
n
.
T
h
er
e
f
o
r
e,
PV
s
y
s
tem
b
ased
o
n
FP
GA
ch
ip
allo
ws
g
ath
er
in
g
m
u
c
h
p
o
wer
a
n
d
f
lex
ib
ly
co
n
tr
o
l
PV
ch
an
n
els.
Fo
r
p
ar
tial
s
h
a
d
in
g
,
as
we
h
av
e
m
en
tio
n
e
d
,
ce
n
tr
alize
d
PV
s
y
s
tem
ty
p
e
is
af
f
ec
ted
.
A
s
tu
d
y
ca
s
e
is
th
en
g
iv
en
b
y
T
a
b
le
2
.
T
ab
le
2
.
PV p
an
el
u
n
d
e
r
ir
r
a
d
iatio
n
s
h
ad
i
ng
P
V
p
a
n
e
l
To
t
a
l
p
o
w
e
r
(
W
)
M
e
t
r
o
l
o
g
i
c
a
l
c
o
n
d
i
t
i
o
n
s
(
°
C
,
W
/
m2
)
1
8
1
.
4
2
5
,
1
0
0
0
1
4
8
.
6
2
5
,
7
0
0
T
h
e
im
p
ac
t o
n
th
e
p
o
wer
an
d
v
o
ltag
e
r
ate
is
s
h
o
wn
in
Fig
u
r
e
8
.
Fo
r
th
e
f
ir
s
t c
ase,
PV sy
te
m
o
p
er
ates
at
2
5
°C
an
d
1
0
0
0
W
/m
2
a
n
d
at
co
n
s
eq
u
en
ce
it
r
ea
ch
es
8
1
.
4
W
as
to
tal
o
p
tim
al
p
o
wer
.
Fo
r
th
e
s
ec
o
n
d
ca
s
e
,
PV
s
y
tem
o
p
er
ates
at
2
5
°C
a
n
d
7
0
0
W
/m
2
an
d
at
co
n
s
eq
u
e
n
ce
it
r
ea
c
h
es
4
8
.
6
W
as
to
tal
o
p
tim
al
p
o
wer
.
W
e
co
n
clu
d
e
t
h
at
th
e
s
y
s
tem
is
ch
an
g
in
g
s
m
o
o
th
ly
f
r
o
m
f
ir
s
t
ca
s
e
to
s
ec
o
n
d
ca
s
e.
At
co
n
s
eq
u
en
ce
,
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
p
r
o
p
o
s
ed
p
h
o
to
v
o
ltaic
s
y
s
tem
u
n
d
er
m
etr
o
l
o
g
ical
ch
an
g
es
s
ee
m
s
ac
cu
r
ate
an
d
er
r
o
r
-
f
r
ee
r
esp
o
n
s
e.
I
t d
o
es n
o
t sh
o
w
d
iv
er
g
en
ce
an
d
d
o
es n
o
t m
o
v
e
a
way
f
r
o
m
t
h
e
n
ew
m
a
x
im
u
m
p
o
wer
p
o
in
t.
Ti
m
e
(
m
s
)
D
ut
y
rat
i
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
11
,
No
.
1
,
M
ar
c
h
20
22
:
49
-
58
56
(
a)
(
b
)
Fig
u
r
e
8
.
I
m
p
ac
t o
f
ir
r
ad
iatio
n
s
h
ad
in
g
o
n
PV sy
s
tem
f
o
r
(
a
)
Po
wer
an
d
(
b
)
Vo
ltag
e
5.
CO
NCLU
SI
O
N
I
n
th
is
s
tu
d
y
,
a
f
u
zz
y
-
b
ased
M
PP
T
co
n
tr
o
ller
is
co
n
ce
iv
e
d
a
n
d
ca
r
r
ie
d
o
u
t
o
n
a
n
FP
GA
ch
ip
s
o
as
to
co
n
tr
o
l
m
u
lti
-
ch
a
n
n
el
PV
s
y
s
tem
.
Ma
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
is
a
k
ey
tech
n
iq
u
e
th
at
en
s
u
r
es
p
h
o
to
v
o
ltaic
p
an
els
wo
r
k
at
t
h
eir
o
p
tim
al
p
o
in
t.
T
h
e
u
s
ed
ap
p
r
o
ac
h
ca
n
d
ee
p
ly
im
p
r
o
v
e
th
e
tr
ac
k
in
g
s
p
ee
d
an
d
r
eliab
ilit
y
.
Desig
n
in
g
an
i
n
tellig
en
t M
PP
T
co
n
tr
o
ller
f
o
r
d
is
tr
ib
u
ted
PV sy
s
tem
wh
ile
u
s
in
g
FP
GA
cir
cu
it,
is
ar
is
en
to
o
b
tai
n
th
e
b
est
s
p
e
ed
/co
s
t
r
atio
.
Fu
zz
y
MPPT
al
g
o
r
ith
m
r
u
n
s
o
n
FP
GA
to
f
o
ll
o
w
th
e
MPP
an
d
as
th
e
r
esu
lt
th
e
PV
s
y
s
tem
p
er
f
o
r
m
s
well
at
its
m
ax
im
u
m
p
o
wer
.
T
h
is
tech
n
iq
u
e
is
d
esig
n
ed
u
s
in
g
h
a
r
d
war
e
d
escr
ip
tio
n
lan
g
u
ag
e
u
n
d
er
Q
u
ar
tu
s
to
o
l.
T
h
e
n
,
it
is
im
p
le
m
en
ted
o
n
FP
GA
d
ev
ice.
A
h
u
g
e
n
u
m
b
er
o
f
PV
ch
an
n
els
ar
e
co
n
t
r
o
lled
v
ia
F
PGA.
Simu
latio
n
r
esu
lts
r
ev
ea
l
m
ajo
r
b
en
ef
its
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
s
u
ch
as
th
e
p
o
ten
tial
to
tr
ac
k
th
e
MPP
u
n
d
er
p
ar
tial
s
h
ad
in
g
,
r
ed
u
cin
g
tim
e
co
m
p
u
tatio
n
as
well
as
av
o
id
n
ee
d
in
g
m
u
ltip
le
MPPT
d
ev
ices.
I
n
a
d
d
itio
n
,
FP
GA
d
ev
ice
en
ab
les
ad
v
an
ce
d
s
h
ad
e
-
t
o
ler
an
t
MPP
T
to
s
wee
p
f
o
r
b
o
t
h
lo
ca
l
an
d
g
lo
b
al
m
a
x
im
a
to
m
ax
im
ize
I
-
V
cu
r
v
e.
T
h
e
p
r
o
p
o
s
ed
h
ar
d
war
e
ar
ch
itectu
r
e
af
f
o
r
d
s
h
ig
h
p
r
o
ce
s
s
in
g
with
lo
w
h
ar
d
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e
r
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r
ce
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tili
za
tio
n
.
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o
n
s
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u
en
tly
,
th
e
ch
allen
g
e
is
r
aised
s
in
ce
FP
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d
ev
ice
s
h
o
ws
a
h
ig
h
ab
ilit
y
to
in
teg
r
ate
a
g
r
ea
t n
u
m
b
er
o
f
PV c
h
a
n
n
els.
Fu
tu
r
e
wo
r
k
o
f
u
s
will
f
u
r
th
e
r
f
o
cu
s
o
n
d
ev
el
o
p
m
en
t
o
u
r
a
p
p
r
o
ac
h
an
d
d
o
i
n
g
o
th
e
r
im
p
r
o
v
em
en
ts
:
with
th
e
ar
is
e
o
f
Sm
ar
t
Gr
id
to
p
ic,
en
er
g
y
s
o
u
r
ce
s
s
u
ch
as
th
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win
d
tu
r
b
in
e
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e
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clu
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e
d
.
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h
e
co
n
tr
i
b
u
tio
n
o
f
s
m
ar
t
tech
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o
lo
g
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allo
ws:
a
m
an
ag
em
en
t
o
f
th
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itten
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elec
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n
t
in
th
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o
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s
u
m
er
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d
a
b
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tter
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g
etic
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f
f
icien
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y
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d
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cin
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lo
s
s
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im
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r
o
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in
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y
ield
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th
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o
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in
tr
o
d
u
ce
in
ter
n
et
o
f
th
in
g
s
(
I
o
T
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tech
n
o
lo
g
y
in
th
e
s
m
ar
t
g
r
id
is
an
in
ter
esti
n
g
ap
p
r
o
ac
h
to
h
asten
th
e
cy
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er
n
atio
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tr
i
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tific
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h
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a
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tern
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m
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d
A
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m
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ter
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e
d
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o
ra
to
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ENIS
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Tu
n
isia
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tt
p
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),
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n
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ra
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c
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c
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d
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a
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.
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d
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ra
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