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1.
I
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RO
D
UCT
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ca
d
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H
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SP
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s
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d
in
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ac
c
u
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a
n
d
ex
p
an
s
io
n
[
1
]
.
B
y
ad
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p
tin
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C
H
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ML
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to
p
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lev
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n
also
b
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p
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d
u
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d
as p
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th
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ess
en
tial [
2
]
.
So
lar
PV
an
d
win
d
ar
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eq
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itab
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a
m
in
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r
illu
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f
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eq
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-
c
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v
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n
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r
eso
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s
.
SP
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lls
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ally
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an
s
f
o
r
m
SP
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p
o
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in
to
elec
tr
ical
en
er
g
y
[
3
]
.
SP
V
p
o
wer
tr
an
s
f
o
r
m
atio
n
s
y
s
tem
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Dr
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Vo
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1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
37
-
48
38
co
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s
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t
o
f
co
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v
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ter
s
,
in
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d
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o
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ate.
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DC
co
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m
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s
o
n
alize
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to
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er
g
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lu
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n
s
with
a
u
g
m
en
te
d
p
r
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u
ctiv
ity
[
4
]
.
Mu
ltil
ev
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I
n
v
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ter
s
ca
n
b
e
s
p
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if
ied
with
in
th
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ee
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tial
ass
o
ciatio
n
s
r
elat
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e
to
th
e
s
t
atis
tics
o
f
DC
co
n
n
ec
tio
n
s
u
s
ed
in
m
o
d
er
n
in
v
er
ter
s
,
NPC
,
FC
,
an
d
C
HB
en
d
u
r
e
ev
er
y
u
ltima
te
u
n
i
v
er
s
al
to
p
o
lo
g
ies
in
th
e
in
d
u
s
tr
y
to
d
ate
[
5
]
.
T
h
o
u
g
h
C
HB
ML
I
s
u
b
s
is
t
s
,
ex
ten
d
ed
co
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v
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ien
ce
is
co
n
s
id
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wh
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is
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s
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n
s
id
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in
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th
a
t
a
s
p
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if
ic
SP
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ar
r
ay
is
an
is
o
lated
DC
s
o
u
r
ce
[
6
]
.
A
C
H
B
ML
I
co
m
p
r
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m
is
e
p
er
s
is
ts
in
s
u
p
p
o
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f
th
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u
tm
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t sch
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T
h
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m
ax
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m
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e
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d
esig
n
ed
to
tr
ac
k
th
e
MPPT’
s
s
u
cc
ess
iv
e
v
ar
iatio
n
in
th
e
illu
m
in
atio
n
o
r
tem
p
er
atu
r
e.
Ab
s
o
lu
te
MPPT
ex
ec
u
tiv
es
ar
e
wo
r
n
am
id
s
t
SP
V
p
an
el
co
n
s
tr
ain
ts
at
r
esp
ec
tiv
e
DC
lin
k
s
to
d
ec
id
e
th
e
co
m
p
licatio
n
a
b
o
u
t
a
s
ec
tio
n
al
s
h
ad
in
g
p
o
s
itio
n
o
f
p
an
els
in
SP
V
p
atter
n
[
7
]
s
u
itab
le
to
s
h
ad
in
g
ac
q
u
ir
ed
with
s
tatic
as
well
a
s
ef
f
ec
tiv
e
s
u
b
s
tan
ce
,
co
m
p
ar
ab
le
to
tr
ee
s
,
b
u
ild
in
g
s
,
b
ir
d
s
,
ag
g
r
eg
ate
d
ir
t
o
v
er
p
an
els,
as
a
s
u
b
s
titu
te
clo
u
d
.
SP
V
ar
r
an
g
e
m
en
t
ass
o
ciate
d
with
an
a
r
r
ay
am
o
n
g
a
DC
-
DC
ex
p
an
s
io
n
co
n
v
er
ter
th
r
o
u
g
h
a
lim
itatio
n
o
f
its
u
ltima
te
v
o
ltag
e
t
h
r
o
u
g
h
co
m
p
u
tin
g
a
b
y
p
ass
d
io
d
e
lat
er
ally
b
y
t
h
e
en
tire
SP
V
u
n
it
[
8
]
,
co
n
s
eq
u
en
tly
av
o
id
in
g
ci
r
cu
m
s
tan
ce
d
ev
elo
p
m
en
t
[
9
]
.
T
h
o
u
g
h
t
h
is
ac
ce
s
s
ca
u
s
es
s
ev
er
al
cr
ests
in
th
e
e
n
er
g
y
o
f
th
e
SP
V
ar
r
an
g
em
e
n
t,
r
estra
in
in
g
t
h
e
o
p
er
atio
n
o
f
t
h
e
MPPT
ap
p
r
o
ac
h
also
leav
es
r
esear
ch
er
s
f
o
c
u
s
ed
o
n
illu
m
in
atin
g
in
n
o
v
ativ
e
p
e
r
f
o
r
m
an
ce
[
1
0
]
.
T
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
(
FLC)
,
a
d
is
s
im
ilar
tr
ad
itio
n
al
ex
ec
u
tiv
e,
d
o
esn
’
t
d
esire
a
m
ath
em
atica
l
r
ep
r
esen
tatio
n
o
f
th
e
ar
r
an
g
em
e
n
t
b
ein
g
co
m
p
o
s
ed
.
Desp
ite
a
p
er
ce
p
tio
n
th
at
th
e
ar
r
an
g
em
e
n
t,
in
clu
d
in
g
th
e
r
estra
in
t
d
em
an
d
s
,
r
em
ain
s
s
ig
n
if
ican
t.
Fig
u
r
e
1
.
Mu
ltil
ev
el
in
v
er
ter
t
o
p
o
lo
g
y
Mu
lti
-
SP
V
ar
r
ay
s
,
am
o
n
g
a
n
in
ter
leav
ed
a
d
v
an
ce
d
co
n
v
er
ter
,
co
n
d
en
s
e
ev
er
y
r
ip
p
le
cu
r
r
en
t
,
en
h
an
ce
p
o
wer
q
u
ality
,
ad
a
p
t
DC
s
y
s
tem
v
o
ltag
e,
an
d
c
o
n
s
eq
u
en
tly
p
er
m
it
co
n
s
id
er
in
g
th
e
o
p
er
atio
n
o
f
a
s
elf
-
r
elian
t M
PP
T
s
u
p
er
v
is
io
n
[
1
1
]
in
s
u
p
p
o
r
t
o
f
ea
ch
SP
V
ar
r
ay
to
ac
q
u
ir
e
im
m
en
s
e
p
r
o
d
u
ctio
n
en
er
g
y
alo
n
g
with
b
etter
ef
f
icien
cy
[
1
2
]
.
Mo
d
er
n
ized
p
o
wer
s
y
s
tem
s
em
p
lo
y
C
HB
ML
I
as
th
ei
r
lo
w
T
HD
with
elec
tr
o
m
ag
n
etic
in
ter
f
e
r
en
ce
(
E
MI
)
,
with
th
eir
ca
p
ab
ilit
y
to
au
g
m
en
t p
o
wer
q
u
ality
with
r
atin
g
n
ec
ess
ity
[
1
3
]
.
C
o
r
r
elate
d
to
ty
p
ical
two
-
lev
e
l
in
v
er
ter
s
th
at
ad
o
p
t
tr
em
en
d
o
u
s
s
witch
in
g
f
r
eq
u
en
cy
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
,
a
C
HB
ML
I
ca
r
r
ies
co
n
s
id
er
ab
le
p
r
ef
er
e
n
ce
[
1
4
]
.
O
n
e
o
f
th
e
im
p
er
ativ
e
p
r
ef
er
e
n
c
es
o
f
an
ML
I
is
th
e
lim
ited
in
ten
s
ity
o
f
th
e
f
ilter
,
alo
n
g
with
its
lo
w
ex
p
en
d
itu
r
e
r
elate
d
to
a
two
-
lev
el
in
v
er
ter
.
A
C
HB
ML
I
d
im
in
is
h
es
T
HD
co
n
n
ec
ted
th
r
o
u
g
h
two
-
lev
el
in
v
e
r
ter
s
b
y
ad
o
p
tin
g
d
if
f
er
e
n
t
D
C
co
n
n
ec
tio
n
s
[
1
5
]
.
Alter
n
ativ
e
r
ec
o
g
n
itio
n
ca
r
r
ie
s
r
ed
u
ce
d
s
witch
in
g
f
r
eq
u
e
n
c
y
,
m
in
o
r
ch
ar
g
e,
o
v
er
-
s
witch
i
n
g
ac
ce
ler
atio
n
,
an
d
d
im
in
is
h
ed
v
o
ltag
e
s
witch
es
co
m
p
ar
ed
to
th
e
co
n
s
is
ten
tly
e
n
f
o
r
ce
d
two
-
le
v
el
in
v
er
ter
s
,
e
n
s
u
r
in
g
d
im
in
is
h
e
d
s
witch
in
g
ex
p
en
s
e,
tr
em
e
n
d
o
u
s
v
o
ltag
e
f
o
r
m
atio
n
,
d
ep
r
ess
ed
E
MI
lev
els,
an
d
ac
ce
p
tab
le
en
er
g
y
n
at
u
r
e
[
1
6
]
.
To
b
o
o
s
t
p
o
wer
co
n
d
itio
n
s
d
u
e
to
ef
f
ec
tiv
e
attain
m
en
t
b
ased
o
n
ex
h
au
s
tin
g
s
y
s
tem
s
,
C
HB
ML
I
d
ir
ec
tly
ex
am
in
es
tech
n
ical
r
esu
lts
[
1
7
]
,
[
1
8
]
.
D
u
e
to
t
h
eir
in
f
er
io
r
T
HD
o
u
t
p
u
t
w
av
ef
o
r
m
,
th
ey
also
co
n
tr
o
lled
ap
p
lian
ce
v
al
u
atio
n
.
C
HB
ML
I
p
r
o
d
u
ce
s
an
ac
co
m
p
lis
h
ed
an
d
im
m
e
n
s
e
v
o
ltag
e
s
tr
ateg
y
[
1
9
]
.
SP
V
u
tili
za
tio
n
,
win
d
tu
r
b
in
e
co
n
n
ec
tio
n
s
,
an
d
f
u
el
ce
lls
ca
n
b
e
co
m
b
in
e
d
with
m
u
ltil
ev
el
co
n
v
er
ter
s
[
2
0
]
,
[
2
1
]
.
Du
e
to
th
e
o
p
er
atio
n
,
th
e
PW
M
s
u
p
er
v
is
io
n
m
eth
o
d
C
HB
ML
I
ty
p
ically
im
p
ac
ts
th
eir
e
f
f
icien
cy
an
d
p
o
wer
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
o
f c
a
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
ve
r
ter w
ith
…
(
C
.
Din
a
ka
r
a
n
)
39
r
atin
g
s
[
2
2
]
,
[
2
3
]
.
Ov
e
r
th
e
p
ast
f
ew
d
ec
ad
es,
in
d
e
f
in
ite
m
o
d
u
les
h
a
v
e
ca
r
r
ied
ex
p
ec
ted
v
ar
ied
ML
I
to
p
o
lo
g
ies f
o
r
f
ewe
r
s
witch
es
[
2
4
]
.
An
in
v
esti
g
atio
n
h
as
b
ee
n
co
n
d
u
cte
d
o
n
d
y
n
am
ic
au
to
m
atio
n
ac
cu
m
u
latin
g
ef
f
icien
c
y
th
r
o
u
g
h
C
HB
ML
I
[
25
]
.
T
h
e
a
d
v
an
c
ed
ar
r
an
g
em
en
t
ca
n
o
p
e
r
ate
in
a
s
tan
d
-
alo
n
e
an
d
l
o
ad
-
in
teg
r
at
ed
m
o
d
e
[
2
6
]
,
[
2
7
]
.
T
h
e
s
ig
n
if
ican
t
r
ec
o
g
n
itio
n
o
f
th
e
ex
p
ec
ted
s
eq
u
en
ce
is
th
e
b
lo
ck
in
g
v
o
ltag
e
b
ased
o
n
th
e
en
tire
s
witch
es
en
d
u
r
e
d
is
tin
ct
alo
n
g
with
f
ewe
r
th
an
th
e
ab
s
o
lu
te
v
o
ltag
e
as a
f
ew
s
w
itch
es a
l
s
o
th
e
es
s
en
tial g
lo
b
al
s
witch
es
with
ex
p
er
t
in
ten
tio
n
s
u
r
v
iv
e
less
,
ass
is
t
a
s
th
i
s
wh
o
le
m
o
d
er
n
m
in
im
izatio
n
o
f
lo
s
s
es,
ex
p
an
d
in
g
th
e
ef
f
icien
cy
m
o
r
eo
v
e
r
s
u
p
er
io
r
n
atu
r
e
b
ased
o
n
o
u
tp
u
t
as
well
as
its
ex
ten
t
p
er
s
is
t
m
o
d
est
as
a
co
n
s
eq
u
en
ce
it
r
em
ain
s
co
m
p
etitiv
e
co
r
r
elate
th
r
o
u
g
h
th
e
tr
ad
itio
n
al
C
HB
M
L
I
.
Her
e,
th
e
s
im
u
latio
n
o
b
tain
s
ex
h
au
s
t
f
o
r
n
in
e
lev
els with
th
e
ad
v
ice
o
f
MA
T
L
AB
/
Simu
lin
k
.
2.
P
RO
P
O
SE
D
T
O
P
O
L
O
G
Y
T
h
e
d
esig
n
ed
1
-
φ,
9
-
le
v
el
in
v
er
ter
p
er
s
is
ts
o
v
er
th
e
7
-
lev
el
in
v
er
ter
.
I
t
c
o
n
s
titu
tes
a
1
-
φ
tr
ad
itio
n
al
C
HB
ML
I
,
with
th
r
ee
b
id
ir
ec
tio
n
al
s
witch
es
in
clu
d
in
g
a
ca
p
ac
ito
r
v
o
ltag
e
s
eg
m
en
t
cr
ea
te
d
o
v
e
r
C
a
,
C
b
,
C
c
,
&
C
d
with
in
ac
tiv
ities
p
r
esen
ted
in
Fig
u
r
e
2
.
T
h
e
C
HB
ML
I
t
o
p
o
lo
g
y
en
s
u
r
es
co
m
p
en
s
atio
n
o
f
m
in
o
r
p
o
wer
s
witch
es
an
d
p
o
wer
d
io
d
es,
al
o
n
g
with
a
r
e
d
u
ctio
n
o
f
th
e
ca
p
ac
ito
r
co
m
p
ar
ed
to
t
h
e
tr
ad
iti
o
n
al
in
v
er
ter
s
.
T
h
e
en
h
an
ce
d
co
n
v
er
ter
,
i.e
.
,
DC
/DC
,
co
r
r
elate
s
with
SP
V
an
d
lo
ad
.
T
h
e
en
e
r
g
y
p
r
o
d
u
ce
d
th
r
o
u
g
h
th
e
in
v
e
r
ter
is
c
o
n
v
e
y
ed
t
o
th
e
en
er
g
y
co
m
p
lex
,
s
o
th
e
ad
eq
u
ac
y
lo
ad
is
r
elativ
ely
lo
w.
T
h
e
D
C
/D
C
ad
v
an
ce
d
co
n
v
er
ter
is
ap
p
r
o
p
r
iate
f
o
r
ev
er
y
SP
V
ar
r
ay
,
tak
in
g
a
m
o
r
e
d
ep
r
ess
ed
en
er
g
y
th
an
th
e
lo
ad
v
o
ltag
e
.
I
m
m
en
s
e
DC
v
o
l
tag
es
ar
e
d
esire
d
to
f
ac
ilit
ate
th
e
en
e
r
g
y
s
tr
ea
m
f
r
o
m
t
h
e
SP
V
ar
r
ay
s
to
w
ar
d
th
e
lo
ad
.
A
f
ilter
w
as
wo
r
n
to
f
ilter
th
e
cu
r
r
en
t
d
eliv
er
e
d
to
th
e
lo
ad
ad
o
p
tin
g
in
d
u
ctan
ce
(
L
f
)
an
d
p
r
ac
tically
ac
co
m
p
lis
h
ed
T
HD
f
r
o
m
s
im
u
latio
n
r
esu
lts
as
in
d
icate
d
in
T
ab
le
1
.
C
o
n
v
en
ien
t
in
v
er
ter
s
witch
in
g
ca
n
ac
h
iev
e
n
in
e
o
u
tp
u
t
v
o
ltag
e
lev
els
(
V
dc
,
3V
dc
4
⁄
,
V
dc
2
⁄
,
V
dc
4
⁄
,
0
,
−
V
dc
,
−
3V
dc
4
⁄
,
−
V
dc
2
⁄
,
−
V
dc
4
⁄
)
ag
ain
s
t th
e
DC
s
o
u
r
ce
.
Fig
u
r
e
2
.
Pro
s
p
ec
tiv
e
1
-
φ
9
-
le
v
el
in
v
er
ter
b
ein
g
SP
V
ar
r
a
n
g
em
en
t
T
ab
le
1
.
T
h
e
o
u
t
p
u
t v
o
ltag
e
co
r
r
esp
o
n
d
s
to
t
h
e
s
witch
es'
ON
-
OFF p
o
s
itio
n
0
√
-
-
√
-
-
-
3
4
⁄
-
-
-
√
√
-
-
2
⁄
-
-
-
√
-
√
-
4
⁄
-
-
-
√
-
-
√
0
-
-
√
√
-
-
-
0
∗
√
√
-
-
-
-
-
−
4
⁄
-
√
-
-
√
-
-
−
2
⁄
-
√
-
-
-
√
-
−
3
4
⁄
-
√
-
-
-
-
√
−
-
√
√
-
-
-
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
37
-
48
40
3.
SPV
ARRA
NG
E
M
E
N
T
AN
D
DC
-
DC
CO
NVE
RT
E
R
B
Y
M
P
P
T
T
E
CH
N
I
Q
UE
T
o
b
o
o
s
t
th
e
ac
h
ie
v
em
en
t
o
f
th
e
SP
V
s
tr
u
ctu
r
e
an
d
ac
q
u
ir
e
tr
em
en
d
o
u
s
en
e
r
g
y
,
th
e
S
PV
p
an
el
r
em
ain
s
co
n
n
ec
ted
to
a
DC
-
DC
co
n
v
er
ter
th
r
o
u
g
h
MPPT
au
to
m
atio
n
th
at
p
er
f
o
r
m
s
an
e
x
ten
s
iv
e
r
o
le
d
u
r
in
g
SP
V
o
p
er
atio
n
b
y
ad
ju
s
tin
g
th
e
p
r
o
d
u
ctio
n
v
o
ltag
e
b
ased
o
n
th
e
SP
V
ar
r
a
y
.
Per
f
o
r
m
a
n
ce
b
ased
o
n
th
e
MPPT
ex
ec
u
tiv
e
is
th
e
ess
en
tial
r
ec
o
g
n
itio
n
o
f
a
DC
-
DC
co
n
v
er
te
r
en
h
an
c
em
en
t
v
a
r
iatio
n
.
Acc
o
r
d
in
g
l
y
,
a
DC
-
DC
ex
p
an
s
io
n
c
o
n
v
e
r
ter
b
y
MPPT
au
to
m
atio
n
p
r
e
v
ails
in
th
e
i
n
d
icate
d
ef
f
o
r
t
t
o
p
r
o
d
u
ce
th
e
o
p
tim
al
v
o
ltag
e
,
th
e
s
u
g
g
ested
ML
I
.
Fu
r
th
er
m
o
r
e,
it y
ield
s
th
e
u
ltima
te
en
er
g
y
a
g
ain
s
t th
e
SP
V
p
atter
n
p
ass
in
g
th
r
o
u
g
h
th
e
alter
ed
cu
m
u
lativ
e
d
eliv
e
r
y
MPPT
ap
p
r
o
ac
h
.
Dif
f
er
e
n
t
co
n
d
u
ct
an
ce
is
am
o
n
g
th
e
m
o
s
t
wid
ely
u
s
ed
MPPT
tech
n
iq
u
es,
in
clu
d
in
g
a
d
o
p
tin
g
a
f
lu
ctu
atin
g
s
tep
s
ize.
4.
M
O
DE
S O
F
P
RO
CE
SS
I
t
co
n
s
is
ts
o
f
a
s
in
g
le
-
p
h
ase
tr
ad
itio
n
al
C
HB
ML
I
,
th
r
ee
b
i
d
ir
ec
tio
n
al
s
witch
es
am
o
n
g
a
ca
p
ac
ito
r
v
o
ltag
e
d
iv
id
er
p
r
o
d
u
ce
d
with
C
a
,
C
b
,
C
c
,
an
d
C
d
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
u
p
d
ated
C
H
B
ML
I
to
p
o
lo
g
y
is
s
u
b
s
tan
tially
m
o
r
e
b
en
e
f
icial
th
an
alter
n
ativ
e
to
p
o
lo
g
ies,
i.e
.
,
lim
ited
e
n
er
g
y
s
witch
es,
b
iased
d
io
d
es,
an
d
lim
ited
ca
p
ac
ito
r
s
as
in
v
er
te
r
s
,
co
n
ce
r
n
in
g
th
e
c
o
r
r
esp
o
n
d
in
g
s
tatis
tic
o
f
lev
els.
SP
V
p
atter
n
r
em
ain
s
ass
o
ciate
d
with
ev
er
y
in
v
e
r
ter
with
a
DC
/D
C
ad
v
an
ce
d
c
o
n
v
er
ter
.
Fig
u
r
e
3
.
Nin
e
-
l
e
v
el
i
n
v
er
te
r
f
o
r
s
witch
in
g
s
eq
u
en
ce
E
n
er
g
y
c
o
m
p
o
s
ed
th
r
o
u
g
h
th
e
in
v
er
ter
is
h
eld
to
b
e
co
n
v
ey
ed
to
th
e
lo
ad
.
A
DC
/DC
ad
v
an
ce
d
co
n
v
er
ter
is
ess
en
tial,
co
n
s
id
er
in
g
th
e
SP
V
d
esig
n
tak
es
a
v
o
ltag
e
r
ed
u
ce
d
to
th
e
1
-
φ
v
o
ltag
e.
I
m
m
en
s
e
DC
b
u
s
v
o
ltag
es
ar
e
im
p
er
ativ
e
f
o
r
p
r
o
d
u
cin
g
s
p
ec
if
ic
en
er
g
y
f
lo
ws
ag
ain
s
t
th
e
S
PV
p
atter
n
to
war
d
lo
ad
s
.
T
h
e
f
ilter
is
d
esig
n
ed
to
ad
o
p
t
L
a
n
d
C
t
o
b
r
in
g
p
u
r
e
s
in
e
wav
es
an
d
,
co
n
s
eq
u
en
tly
,
is
in
clin
e
d
to
AC
lo
ad
s
.
T
h
e
co
n
s
id
er
ed
in
v
er
ter
’
s
p
r
o
ce
s
s
es c
an
p
er
s
is
t in
n
in
e
s
witch
in
g
s
tates.
Po
wer
s
witch
in
g
attr
ib
u
ted
to
th
e
in
v
er
ter
ca
n
a
ch
iev
e
n
in
e
o
u
tp
u
t
v
o
ltag
e
lev
els
(
V
dc
,
3V
dc
4
⁄
,
V
dc
2
⁄
,
V
dc
4
⁄
,
0
,
−
V
dc
,
−
3V
dc
4
⁄
,
−
V
dc
2
⁄
,
−
V
dc
4
⁄
)
ag
ain
s
t
th
e
DC
s
u
p
p
ly
v
o
lta
g
e.
T
h
e
n
o
v
el
to
p
o
lo
g
y
in
v
e
r
ter
s
p
r
o
ce
s
s
ca
n
b
e
s
p
lit in
to
n
in
e
s
witch
in
g
cir
cu
m
s
tan
ce
s
.
T
h
e
ap
p
r
o
p
r
iate
n
in
e
lev
els o
f
p
r
o
d
u
ctio
n
v
o
ltag
e
r
em
ai
n
in
d
u
ce
d
as f
o
llo
ws.
-
Ultim
ate
+V
e
o
u
tp
u
t
Vo
ltag
e
(
V
dc
)
:
S
a
is
ag
ain
s
t
m
er
g
ed
th
e
lo
ad
+V
e
in
cu
r
ab
le
o
v
er
V
dc
,
in
clu
d
in
g
S
d
r
em
ain
s
ap
p
r
o
ac
h
in
g
in
v
o
lv
ed
th
e
lo
ad
–
Ve
in
c
u
r
ab
le
o
v
er
th
e
g
r
o
u
n
d
.
I
n
te
g
r
ated
,
th
at
co
m
p
o
s
e
d
s
witch
h
as v
an
is
h
ed
.
T
h
e
v
o
lt
ag
e
en
er
g
ize
d
o
v
e
r
th
e
lo
a
d
is
in
cu
r
ab
le
V
dc
.
-
T
h
r
ee
-
f
o
u
r
th
s
+V
e
o
u
tp
u
t V
o
l
tag
e
(
3V
dc
4
⁄
)
: T
h
e
b
i
-
d
ir
ec
tio
n
al
c
o
n
t
r
o
l S
e
is
ON,
in
v
o
lv
in
g
th
e
lo
a
d
+V
e
in
cu
r
ab
le
o
v
er
V
dc
,
an
d
S
d
is
ON,
alm
o
s
t
ap
p
lied
th
e
lo
ad
–
Ve
in
cu
r
ab
le
o
v
er
th
e
g
r
o
u
n
d
.
T
h
e
in
teg
r
ated
o
th
er
co
m
p
o
s
ed
s
witch
h
as v
a
n
is
h
ed
.
T
h
e
v
o
ltag
e
e
n
er
g
ized
o
v
er
th
e
l
o
ad
d
estru
ctiv
e
is
(
3V
dc
4
⁄
)
.
-
Half
o
f
th
e
+V
e
p
r
o
d
u
ctio
n
V
o
ltag
e
(
V
dc
2
⁄
)
:
T
h
e
b
i
-
d
ir
ec
tio
n
al
s
witch
S
f
p
er
s
is
t
s
f
o
r
in
v
o
lv
in
g
th
e
lo
ad
+V
e
d
estru
ctiv
e
o
v
er
V
dc
,
in
cl
u
d
in
g
S
d
is
ON,
alm
o
s
t
in
v
o
lv
in
g
th
e
lo
ad
–
Ve
in
cu
r
a
b
le
o
v
er
th
e
g
r
o
u
n
d
.
I
n
teg
r
ated
th
at
th
e
co
m
p
o
s
ed
s
witch
r
em
ain
s
ab
s
en
t.
T
h
e
v
o
ltag
e
en
er
g
ized
o
v
er
th
e
lo
a
d
is
in
cu
r
ab
le
V
dc
2
⁄
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
o
f c
a
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
ve
r
ter w
ith
…
(
C
.
Din
a
ka
r
a
n
)
41
-
On
e
-
f
o
u
r
th
o
f
th
e
+V
e
p
r
o
d
u
c
tio
n
Vo
ltag
e
(
V
dc
4
⁄
)
: T
h
e
b
i
-
d
ir
ec
ti
o
n
al
s
witch
S
g
is
ON,
an
d
alm
o
s
t e
v
er
y
lo
ad
+V
e
in
c
u
r
ab
le
alo
n
g
with
S
d
is
ON,
p
r
ac
tically
ap
p
ly
i
n
g
th
e
lim
itatio
n
–
Ve
in
cu
r
a
b
le
to
g
r
o
u
n
d
.
I
n
teg
r
ated
d
if
f
er
e
n
t c
o
m
p
o
s
ed
s
witch
es r
em
ain
OFF th
e
en
er
g
y
ad
a
p
ted
n
ea
r
th
e
lo
ad
f
atal
is
V
dc
4
⁄
.
-
Z
er
o
o
u
t
p
u
t
Vo
ltag
e
(
0
&
0
*
)
:
T
h
e
d
esig
n
ated
s
tead
y
s
tate
ca
n
p
r
ev
ail
o
v
e
r
b
in
ar
y
s
witch
in
g
ar
r
an
g
em
e
n
ts
.
Switch
es
S
c
an
d
S
d
ar
e
ON
(
o
r
)
S
a
,
a
n
d
S
b
r
e
m
ain
s
ON,
with
th
e
o
th
e
r
co
m
p
lete
s
witch
ab
s
en
t.
T
h
e
in
cu
r
a
b
le
“1
2
”
e
n
d
u
r
es
a
s
h
o
r
t
cir
cu
it
also
.
Mo
r
eo
v
er
,
th
e
v
o
ltag
e
en
er
g
i
ze
d
to
war
d
th
e
in
d
u
ctiv
e
lo
a
d
r
em
ain
s
ze
r
o
.
-
On
e
-
f
o
u
r
th
-
Ve
o
u
tp
u
t
Vo
ltag
e
(
−
V
dc
4
⁄
)
:
T
h
e
b
i
-
d
ir
ec
tio
n
al
s
witch
S
e
is
ON,
ass
o
ciatin
g
th
e
lo
a
d
+V
e
in
cu
r
ab
le.
Als
o
,
S
b
b
e
ON
ag
ai
n
s
t
th
e
lo
ad
–
Ve
in
cu
r
ab
le
to
V
dc
.
Natu
r
al
alter
n
ativ
e
co
m
p
o
s
ed
s
witch
es
en
d
u
r
e
OFF ev
er
y
en
er
g
y
a
d
a
p
ted
n
ea
r
t
h
e
in
cu
r
ab
le
lo
ad
−
V
dc
4
⁄
.
-
Half
o
f
th
e
–
Ve
p
r
o
d
u
ctio
n
Vo
ltag
e
(
−
V
dc
2
⁄
)
:
T
h
e
s
witch
S
b
is
ON,
alm
o
s
t
in
v
o
lv
ed
th
e
lo
a
d
+V
e
in
cu
r
ab
le
o
v
er
V
dc
,
i
n
clu
d
in
g
th
e
b
i
-
d
ir
ec
tio
n
al
co
n
tr
o
l
S
f
is
ON,
in
v
o
lv
in
g
th
e
lo
a
d
–
Ve
ter
m
in
al
o
v
er
th
e
g
r
o
u
n
d
.
I
n
teg
r
ated
alter
n
a
tiv
e
co
m
p
o
s
ed
s
witch
es
h
a
v
e
v
an
is
h
ed
.
T
h
e
v
o
ltag
e
en
er
g
ized
o
v
er
t
h
e
ca
p
ac
ity
is
−
V
dc
2
⁄
.
-
T
h
r
ee
-
f
o
u
r
th
s
-
Ve
o
u
tp
u
t
Vo
ltag
e
(
−
3V
dc
4
⁄
)
:
T
h
e
b
i
-
d
ir
ec
tio
n
al
s
wi
tch
S
g
is
ON,
a
s
s
o
ciatin
g
th
e
lo
a
d
+V
e
in
cu
r
ab
le
al
o
n
g
with
S
b
is
ON,
ass
o
ciatin
g
th
e
lo
ad
–
Ve
in
cu
r
ab
le
t
o
g
r
o
u
n
d
.
I
n
teg
r
ated
d
if
f
e
r
en
t
co
m
p
o
s
ed
c
o
n
tr
o
ls
ar
e
OFF,
a
n
d
th
e
v
o
ltag
e
ad
a
p
ted
th
r
o
u
g
h
th
e
lo
ad
in
cu
r
a
b
le
is
−
3V
dc
4
⁄
.
-
Ma
x
im
u
m
-
Ve
o
u
tp
u
t
V
o
ltag
e
(
−
V
dc
)
:
S
b
is
ON,
ass
o
ciatin
g
th
e
lo
ad
–
Ve
in
c
u
r
ab
le
t
o
V
dc
alo
n
g
with
S
c
is
O
N,
ass
o
ciat
in
g
th
e
lo
ad
+V
e
f
atal
th
r
o
u
g
h
th
e
g
r
o
u
n
d
.
Per
f
ec
t
alter
n
ativ
e
co
m
p
o
s
ed
s
witch
es
ar
e
OFF,
an
d
th
e
v
o
ltag
e
is
ad
a
p
te
d
to
th
e
lo
a
d
is
−
V
dc
.
T
ab
le
1
s
h
o
ws
th
e
s
witch
in
g
ar
r
a
n
g
em
e
n
t
co
m
m
en
cin
g
t
h
e
n
i
n
e
o
u
tp
u
t
v
o
ltag
e
le
v
els
(
V
dc
,
3V
dc
4
,
V
dc
2
,
V
dc
4
,
0
,
−
V
dc
4
,
−
V
dc
2
,
−
3V
dc
4
,
−
V
dc
)
am
o
n
g
s
witch
in
g
ar
r
an
g
e
m
en
ts
co
n
s
id
er
in
g
a
s
in
g
le
-
p
h
ase
n
in
e
-
lev
el
in
v
e
r
ter
as p
r
esen
te
d
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
Switch
in
g
a
r
r
an
g
em
en
t f
o
r
s
in
g
le
p
h
ase
n
in
e
lev
el
in
v
er
ter
5.
CL
O
S
E
D
-
L
O
O
P
CO
NT
RO
L
SYS
T
E
M
T
h
e
s
u
p
e
r
v
is
io
n
a
r
r
an
g
em
en
t
co
n
s
titu
tes
an
MPPT
s
u
p
er
v
is
o
r
,
a
DC
v
o
ltag
e
p
r
o
d
u
ce
r
,
an
d
a
n
in
v
er
ter
s
u
p
er
v
is
o
r
,
as
d
em
o
n
s
tr
ated
in
Fig
u
r
e
5
.
B
ased
o
n
t
h
e
in
d
icate
d
s
eq
u
en
ce
,
th
e
in
t
en
tio
n
is
ess
en
tially
to
ac
h
iev
e
t
h
e
u
ltima
te
v
o
lu
m
e
o
f
p
o
wer
t
o
g
eth
er
ag
ain
s
t
S
PV
to
lo
ad
b
y
d
im
in
is
h
in
g
T
HD.
An
in
n
o
v
ativ
e
alg
o
r
ith
m
th
at
d
r
aws
in
s
p
ir
atio
n
f
r
o
m
n
atu
r
e
was
in
tr
o
d
u
ce
d
b
y
Mir
jalili
[
2
1
]
.
T
h
e
AL
O
im
itates
th
e
way
th
at
an
t
lio
n
s
h
u
n
t
in
th
e
wild
.
An
an
t
lio
n
lar
v
a
ex
ca
v
ates
a
co
n
e
-
s
h
ap
ed
h
o
le
in
th
e
s
an
d
b
y
m
o
v
in
g
in
a
cir
cle
an
d
ex
p
ellin
g
s
an
d
with
its
en
o
r
m
o
u
s
jaw.
T
h
e
lar
v
a
d
i
g
s
th
e
tr
ap
an
d
th
en
h
id
es
b
e
n
ea
th
th
e
co
n
e'
s
b
ase
to
wait
f
o
r
in
s
ec
ts
to
f
all
in
to
th
e
h
o
le
an
d
b
ec
o
m
e
tr
ap
p
ed
.
Si
n
ce
th
e
co
n
e'
s
ed
g
e
is
s
o
s
h
ar
p
,
in
s
ec
ts
ca
n
ea
s
ily
f
all
to
th
e
b
o
tto
m
o
f
th
e
tr
ap
.
T
h
e
an
t
lio
n
s
tar
ts
to
ca
tch
it
s
p
r
ey
as
s
o
o
n
as
it
r
ea
lizes
it
i
s
in
th
e
tr
ap
.
Af
ter
th
at,
it
g
ets
s
u
ck
ed
u
p
b
y
th
e
g
r
o
u
n
d
an
d
ea
ten
.
I
n
o
r
d
er
to
m
ak
e
r
o
o
m
f
o
r
th
e
n
ex
t
h
u
n
t,
an
t
lio
n
s
d
u
m
p
t
h
e
lef
to
v
er
p
r
ey
o
u
ts
id
e
th
e
p
it a
f
ter
ea
tin
g
it
.
H
e
r
e
,
a
h
y
b
r
i
d
t
e
c
h
n
i
q
u
e
,
a
n
A
L
O
-
t
u
n
e
d
f
u
z
z
y
r
u
l
e
b
a
s
e
s
t
r
u
c
t
u
r
e
,
i
s
a
d
o
p
t
e
d
i
n
t
h
e
M
P
P
T
a
p
p
r
o
a
c
h
f
o
r
i
t
s
m
a
n
y
n
e
t
w
o
r
k
s
.
I
t
s
y
s
t
e
m
a
t
i
c
a
l
l
y
p
r
e
s
e
n
t
s
an
A
L
O
-
f
u
z
z
y
r
u
l
e
o
b
s
e
r
v
e
r
s
t
r
u
c
t
u
r
e
a
s
e
x
p
o
s
e
d
i
n
F
i
g
u
r
e
6
.
T
h
e
S
P
V
m
a
x
i
m
u
m
v
o
l
t
a
g
e
,
a
l
o
n
g
w
i
t
h
p
r
o
d
u
c
t
i
o
n
e
n
e
r
g
y
,
c
o
r
r
e
l
a
t
e
s
w
i
t
h
a
p
a
r
t
i
c
u
l
a
r
p
r
e
c
e
d
i
n
g
F
R
B
a
l
g
o
r
i
t
h
m
.
I
f
t
h
e
e
f
f
i
c
a
c
y
i
s
g
r
o
w
i
n
g
P
l
i
m
i
t
,
t
h
e
p
e
r
f
o
r
m
i
n
g
a
p
p
r
o
a
c
h
a
c
t
i
v
i
t
y
n
e
a
r
P
spv
≥
P
l
i
m
i
t
F
R
B
c
o
o
r
d
i
n
a
t
i
o
n
i
s
e
x
t
e
n
d
e
d
i
n
a
s
i
m
i
l
a
r
g
u
i
d
a
n
c
e
.
O
t
h
e
r
w
i
s
e
,
i
n
l
a
t
e
r
r
e
v
o
l
u
t
i
o
n
s
,
P
spv
<
P
l
i
m
i
t
t
h
e
g
u
i
d
i
n
g
d
e
s
i
r
e
i
s
t
r
a
n
s
p
o
s
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
37
-
48
42
Fig
u
r
e
5
.
Nin
e
-
le
v
el
in
v
er
te
r
f
o
r
clo
s
ed
-
lo
o
p
r
estra
in
t a
lg
o
r
it
h
m
Fig
u
r
e
6
.
T
h
e
f
u
zz
y
r
u
le
v
iew
er
is
in
ten
d
ed
f
o
r
a
cl
o
s
ed
-
lo
o
p
s
y
s
tem
FR
B
ar
r
an
g
em
en
t
is
ex
h
a
u
s
ted
in
th
e
DC
-
DC
ad
v
an
ce
d
c
o
n
v
er
ter
.
I
n
ess
en
ce
,
th
e
u
ltim
ate
h
ar
v
est
en
er
g
y
o
f
MPPT
is
ac
co
m
p
lis
h
ed
ag
ain
s
t
th
e
d
u
ty
cy
cle
r
esp
o
n
s
ib
ilit
y
.
As
th
e
DC
p
o
wer
V
dc
p
r
ev
ailed
ad
ap
ted
in
9
-
lev
el
in
v
er
ter
,
th
e
p
r
o
d
u
ctio
n
u
tili
ties
o
f
SP
V
v
ar
iatio
n
s
itu
ated
s
c
h
ed
u
led
d
u
ty
cy
cle
tr
an
s
f
o
r
m
atio
n
.
SPV
-
ass
o
ciate
d
DC
/DC
ad
v
an
ce
d
co
n
v
er
ter
s
with
lo
ad
-
o
v
er
s
u
r
g
e
d
i
v
er
te
r
s
ar
e
th
e
ce
r
tain
ty
o
f
an
in
teg
r
ated
a
r
r
an
g
e
m
en
t.
T
h
e
in
p
u
t
c
o
n
n
ec
tio
n
o
f
SP
V
(
I
spv
,
V
spv
)
is
in
clin
e
d
to
MPPT
am
o
n
g
th
e
PW
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
P
erfo
r
ma
n
ce
ev
a
lu
a
tio
n
o
f c
a
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
ve
r
ter w
ith
…
(
C
.
Din
a
ka
r
a
n
)
43
ad
v
an
ce
d
co
n
v
er
ter
s
as
s
h
o
wn
in
F
ig
u
r
e
7
.
T
h
e
in
p
u
t
s
o
u
r
ce
is
V
dc
&
V
d
cr
ef
in
clin
ed
to
t
h
e
FR
B
ar
r
an
g
em
en
t.
Me
asu
r
e
th
e
p
r
o
d
u
ctiv
it
y
v
o
lt
ag
es
o
f
SP
V
alo
n
g
with
MPP
T
em
p
lo
y
in
g
a
tr
ial
-
an
d
-
er
r
o
r
m
ec
h
an
is
m
.
I
n
d
ee
d
,
th
e
o
u
tp
u
t
v
o
ltag
e
is
V
dc
&
V
dc
∗
co
n
tr
o
l
led
b
y
th
e
in
v
er
ter
o
v
er
th
e
g
atin
g
p
u
ls
es
o
f
s
witch
es
(
S
a
−
S
g
)
with
f
ee
d
to
war
d
th
e
lo
ad
th
r
o
u
g
h
t
h
e
f
ilter
.
Fig
u
r
e
7
.
Fu
zz
y
r
u
le
v
iewe
r
is
in
ten
d
ed
f
o
r
a
cl
o
s
ed
-
lo
o
p
s
y
s
tem
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
6
.
1
.
Sim
ula
t
i
o
n r
esu
lt
T
h
e
d
esig
n
ed
tech
n
iq
u
e
was
p
r
ev
io
u
s
ly
p
r
o
v
e
n
with
s
im
u
latio
n
o
u
tco
m
es
in
Fig
u
r
es
8
to
1
4
.
T
h
is
r
ep
r
esen
tativ
e
h
as
b
ee
n
f
u
r
n
is
h
ed
with
MA
T
L
AB
/
Simu
lin
k
cir
c
u
m
s
tan
ce
s
b
y
th
e
SI
MPOWE
R
s
y
s
tem
to
o
lb
o
x
.
T
h
e
MA
T
L
AB
/Si
m
u
lin
k
-
b
ased
C
HB
n
in
e
-
lev
el
in
v
er
ter
co
n
tr
o
lled
with
a
n
AL
O
-
f
u
zz
y
MPPT
s
y
s
tem
ef
f
ec
tiv
ely
in
teg
r
ates
h
y
b
r
id
o
p
tim
izatio
n
an
d
in
tell
ig
en
t
co
n
t
r
o
l
f
o
r
p
h
o
t
o
v
o
ltaic
p
o
wer
r
eg
u
latio
n
.
T
h
e
ca
s
ca
d
ed
H
-
b
r
i
d
g
e
to
p
o
l
o
g
y
g
e
n
er
ates
n
in
e
d
is
tin
ct
v
o
ltag
e
lev
els
with
r
ed
u
ce
d
s
witch
in
g
s
tr
ess
,
wh
ile
th
e
f
u
zz
y
-
b
ased
MPPT
en
h
a
n
ce
d
b
y
th
e
an
t
lio
n
o
p
tim
izer
ad
ap
ts
ef
f
icien
tly
to
en
v
ir
o
n
m
en
tal
ch
an
g
es
to
en
s
u
r
e
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
.
T
h
e
PW
M
s
u
b
s
y
s
tem
p
r
o
d
u
ce
s
m
u
lti
-
ca
r
r
ier
s
ig
n
al
s
th
at
s
y
n
th
esize
a
n
ea
r
-
s
in
u
s
o
id
al
o
u
t
p
u
t,
ac
h
iev
in
g
s
u
b
s
tan
tial
T
HD
r
ed
u
ctio
n
f
r
o
m
7
.
7
7
%
to
4
.
2
5
%
co
m
p
ar
is
o
n
T
HD
tab
le
in
d
icate
d
in
T
ab
le
2
.
T
h
is
h
y
b
r
id
c
o
n
tr
o
l
a
p
p
r
o
ac
h
d
e
m
o
n
s
tr
ates
s
u
p
er
io
r
p
o
we
r
q
u
ality
an
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
v
er
co
n
v
en
tio
n
al
co
n
tr
o
ller
s
,
an
d
its
m
o
d
u
la
r
s
tr
u
ctu
r
e
allo
ws
s
tr
aig
h
tf
o
r
war
d
s
ca
lab
ilit
y
f
o
r
h
ig
h
er
v
o
ltag
e
ap
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