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3
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Dec
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4
:
2603
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d
ir
e
cti
o
n
al
p
o
we
r
f
l
o
w,
e
n
s
u
r
i
n
g
t
h
a
t
t
h
e
s
y
s
te
m
c
a
n
e
f
f
e
cti
v
e
ly
u
t
ili
ze
t
h
e
e
n
er
g
y
f
r
o
m
th
e
PV
s
o
u
r
ce
t
o
c
h
a
r
g
e
th
e
b
a
tte
r
y
an
d
d
el
iv
er
p
o
we
r
to
t
h
e
l
o
a
d
as
n
ee
d
e
d
.
T
h
is
f
le
x
i
b
il
it
y
an
d
c
o
n
t
r
o
l
o
v
e
r
p
o
we
r
f
l
o
w
d
ir
ec
ti
o
n
a
r
e
c
r
u
ci
al
f
o
r
t
h
e
p
r
o
p
e
r
f
u
n
cti
o
n
i
n
g
o
f
a
s
t
an
d
-
a
lo
n
e
PV
s
y
s
te
m
wit
h
b
at
te
r
y
s
t
o
r
a
g
e
.
I
n
s
tan
d
-
alo
n
e
PV
s
y
s
tem
s
,
t
h
e
s
o
lar
en
er
g
y
g
e
n
er
atio
n
s
o
u
r
ce
s
ty
p
ically
h
av
e
lo
w
o
u
tp
u
t
v
o
ltag
e
lev
els.
T
o
in
ter
f
ac
e
th
ese
s
o
u
r
ce
s
with
th
e
in
v
er
ter
an
d
m
ee
t
th
e
v
o
ltag
e
r
eq
u
i
r
em
en
ts
o
f
th
e
s
y
s
tem
,
h
ig
h
s
tep
-
u
p
DC
-
DC
co
n
v
er
ter
s
ar
e
n
ec
ess
ar
y
.
Var
io
u
s
h
ig
h
s
tep
-
u
p
co
n
v
er
ter
s
h
a
v
e
b
ee
n
d
ev
el
o
p
ed
f
o
r
t
h
is
p
u
r
p
o
s
e,
in
co
r
p
o
r
atin
g
s
witch
ed
ca
p
ac
ito
r
s
o
r
s
witch
ed
in
d
u
cto
r
s
t
o
ac
h
iev
e
h
ig
h
v
o
ltag
e
c
o
n
v
er
s
io
n
r
atio
s
.
So
m
e
ex
am
p
les o
f
h
ig
h
s
tep
-
u
p
DC
-
DC
co
n
v
er
ter
s
in
clu
d
e:
-
Hy
b
r
id
b
o
o
s
t
co
n
v
e
r
ter
[
7
]
:
T
h
is
co
n
v
er
ter
u
tili
ze
s
a
co
m
b
i
n
atio
n
o
f
in
d
u
cto
r
s
an
d
ca
p
ac
ito
r
s
to
ac
h
iev
e
h
ig
h
v
o
ltag
e
co
n
v
er
s
io
n
.
T
h
e
v
o
ltag
e
co
n
v
er
s
io
n
r
atio
o
f
th
e
h
y
b
r
id
b
o
o
s
t c
o
n
v
er
ter
is
(
1
+
D)
/(
1
-
D)
,
wh
er
e
D
r
ep
r
esen
ts
th
e
d
u
ty
r
atio
.
-
Switch
ed
-
ca
p
ac
ito
r
-
b
ased
ac
ti
v
e
n
etwo
r
k
co
n
v
er
ter
[
8
]
:
T
h
is
co
n
v
er
ter
em
p
lo
y
s
s
witch
ed
ca
p
ac
ito
r
s
to
ac
h
iev
e
h
ig
h
v
o
ltag
e
co
n
v
e
r
s
io
n
.
T
h
e
v
o
ltag
e
co
n
v
er
s
io
n
r
atio
o
f
th
e
s
witch
ed
-
ca
p
ac
ito
r
-
b
ased
ac
tiv
e
n
etwo
r
k
co
n
v
er
ter
is
(
3
+D
)
/(
1
-
D)
,
wh
er
e
D
is
th
e
d
u
ty
r
atio
.
-
Z
-
s
o
u
r
ce
a
n
d
Qu
asi
Z
-
s
o
u
r
ce
DC
-
DC
co
n
v
er
ter
[
9
]
:
T
h
ese
c
o
n
v
er
ter
s
u
tili
ze
im
p
ed
a
n
ce
n
e
two
r
k
s
(
Z
-
s
o
u
r
ce
o
r
Qu
asi Z
-
s
o
u
r
ce
)
to
ac
h
ie
v
e
h
ig
h
v
o
ltag
e
co
n
v
er
s
io
n
.
T
h
e
v
o
ltag
e
co
n
v
e
r
s
io
n
r
atio
o
f
th
e
s
e
co
n
v
er
ter
s
is
(1
-
D)
/(
1
-
2
D)
,
wh
e
r
e
D
r
ep
r
esen
ts
th
e
d
u
ty
r
atio
.
Ho
wev
er
,
th
e
o
u
tp
u
t
v
o
ltag
es
o
f
th
ese
c
o
n
v
e
r
ter
s
ar
e
f
lo
atin
g
,
m
ea
n
in
g
th
ey
ar
e
n
o
t
r
ef
er
e
n
ce
d
to
a
f
ix
ed
p
o
ten
tial.
I
n
c
o
n
tr
ast,
in
a
p
r
o
p
o
s
ed
s
o
lu
tio
n
p
r
esen
ted
i
n
[
1
0
]
,
th
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
is
in
tr
o
d
u
ce
d
.
T
h
is
co
n
v
er
ter
o
f
f
er
s
lo
w
b
u
f
f
er
ca
p
ac
ito
r
s
tr
ess
an
d
ac
h
iev
e
s
a
v
o
ltag
e
co
n
v
er
s
io
n
r
atio
o
f
1
/(
1
-
D)
2
,
wh
er
e
D
is
th
e
d
u
t
y
r
ati
o
.
T
h
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
p
r
o
v
id
es
a
f
ix
ed
o
u
tp
u
t
v
o
ltag
e
with
a
r
e
d
u
ce
d
s
t
r
ess
o
n
th
e
b
u
f
f
er
ca
p
ac
ito
r
.
T
h
ese
d
if
f
er
en
t
co
n
v
er
te
r
to
p
o
l
o
g
ies
an
d
co
n
f
ig
u
r
atio
n
s
en
ab
l
e
h
ig
h
v
o
ltag
e
co
n
v
er
s
io
n
in
s
t
an
d
-
alo
n
e
PV
s
y
s
tem
s
,
allo
win
g
ef
f
icien
t
in
teg
r
atio
n
o
f
th
e
PV
s
o
u
r
ce
s
with
th
e
lo
ad
an
d
in
v
er
ter
s
y
s
tem
s
.
I
n
th
e
co
n
tex
t
o
f
ac
h
iev
in
g
h
ig
h
s
tep
-
u
p
v
o
l
tag
e
g
ain
in
s
tan
d
-
alo
n
e
PV
s
y
s
tem
s
,
d
if
f
er
en
t
co
n
v
er
ter
to
p
o
lo
g
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
th
e
liter
atu
r
e.
O
n
e
s
u
ch
ap
p
r
o
ac
h
is
th
e
co
u
p
led
in
d
u
cto
r
-
b
ased
co
n
v
er
ter
,
wh
ich
o
f
f
er
s
h
ig
h
v
o
ltag
e
g
ai
n
.
Ho
we
v
er
,
it
is
ass
o
ciate
d
with
ch
allen
g
es
s
u
c
h
as
leak
ag
e
en
e
r
g
y
,
in
cr
ea
s
ed
s
witch
in
g
lo
s
s
es,
an
d
elec
tr
o
m
ag
n
etic
in
ter
f
e
r
en
ce
(
E
MI
)
is
s
u
es.
T
o
m
itig
ate
th
ese
p
r
o
b
lem
s
,
an
ac
tiv
e
cla
m
p
cir
cu
it
ca
n
b
e
em
p
lo
y
ed
.
An
o
t
h
er
a
p
p
r
o
ac
h
i
s
th
e
u
s
e
o
f
two
ca
s
ca
d
e
b
o
o
s
t
co
n
v
er
ter
s
t
o
ac
h
ie
v
e
h
ig
h
v
o
lt
ag
e
g
ain
.
Ho
wev
er
,
th
is
co
n
f
ig
u
r
atio
n
in
tr
o
d
u
ce
s
a
d
d
itio
n
al
s
witch
es,
lead
in
g
to
r
ed
u
ce
d
e
f
f
icien
cy
.
On
th
e
o
t
h
er
h
an
d
,
th
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
is
a
r
elia
b
le
o
p
tio
n
th
at
o
f
f
er
s
a
wid
e
co
n
v
er
s
io
n
r
an
g
e
an
d
r
e
q
u
ir
es
o
n
ly
a
s
in
g
le
d
r
iv
er
cir
cu
it
[
1
]
.
Alth
o
u
g
h
s
tr
u
ctu
r
ally
s
im
ilar
to
ca
s
ca
d
e
d
b
o
o
s
t
co
n
v
er
te
r
s
,
th
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
te
r
p
r
o
v
id
es
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
.
T
ap
p
ed
in
d
u
cto
r
-
b
ased
b
o
o
s
t
co
n
v
er
ter
s
h
av
e
also
b
ee
n
u
tili
ze
d
f
o
r
h
ig
h
-
g
a
in
o
p
er
atio
n
.
W
h
ile
th
ese
co
n
v
er
ter
s
ca
n
ac
h
iev
e
h
ig
h
v
o
lta
g
e
g
ain
,
th
e
y
o
f
te
n
ex
p
er
ien
ce
h
ig
h
ly
p
u
ls
atin
g
in
p
u
t
cu
r
r
e
n
t,
esp
ec
ially
wh
e
n
th
e
tu
r
n
s
r
atio
is
h
ig
h
o
r
th
e
cu
r
r
en
t
is
lar
g
e.
Ho
wev
er
,
it
h
as
b
ee
n
o
b
s
er
v
e
d
th
at
tap
p
e
d
-
b
o
o
s
t
co
n
v
er
ter
s
ex
h
ib
it
lo
wer
s
witch
v
o
ltag
e
s
tr
ess
co
m
p
ar
ed
to
s
tan
d
ar
d
b
o
o
s
t
co
n
v
er
ter
s
f
o
r
th
e
s
am
e
o
u
tp
u
t
v
o
ltag
e.
T
o
a
d
d
r
ess
th
e
p
o
wer
s
u
p
p
ly
is
s
u
e
wh
en
PV
p
o
wer
is
u
n
av
ailab
le,
ad
d
itio
n
al
co
n
s
id
er
atio
n
s
n
ee
d
to
b
e
m
ad
e.
T
o
ef
f
ec
tiv
ely
co
n
tr
o
l
th
e
b
atter
y
c
u
r
r
en
t
in
a
q
u
a
d
r
atic
-
b
o
o
s
t
co
n
v
er
ter
,
w
h
ich
is
cr
u
c
ial
in
a
s
tan
d
-
alo
n
e
s
y
s
tem
,
a
b
id
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
te
r
is
in
teg
r
ated
in
t
o
th
e
s
y
s
tem
.
T
h
is
co
n
v
er
ter
en
ab
les
ef
f
icien
t
r
eg
u
lat
io
n
o
f
t
h
e
b
atter
y
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
p
r
o
ce
s
s
es.
I
n
s
u
m
m
ar
y
,
th
e
p
r
o
p
o
s
ed
to
p
o
l
o
g
ies
in
th
e
r
e
f
er
en
ce
s
co
m
b
i
n
e
q
u
a
d
r
atic
b
o
o
s
t
co
n
v
e
r
ter
s
an
d
tap
p
e
d
in
d
u
cto
r
b
o
o
s
t
co
n
v
e
r
ter
s
to
ac
h
iev
e
h
ig
h
v
o
ltag
e
g
ai
n
in
s
tan
d
-
alo
n
e
P
V
s
y
s
tem
s
.
T
h
ese
co
n
f
ig
u
r
atio
n
s
aim
to
o
v
er
c
o
m
e
ch
allen
g
es
r
elate
d
to
v
o
ltag
e
s
tr
ess
,
s
w
itch
in
g
lo
s
s
es,
an
d
in
p
u
t
cu
r
r
en
t
p
u
ls
atio
n
s
.
Ho
wev
er
,
th
e
r
ef
er
en
ce
s
d
o
n
o
t
p
r
o
v
id
e
d
etailed
a
n
aly
s
is
r
eg
ar
d
in
g
p
o
we
r
s
u
p
p
ly
in
th
e
ab
s
en
ce
o
f
PV
p
o
wer
,
an
d
a
b
id
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
ter
is
in
co
r
p
o
r
ated
to
c
o
n
tr
o
l th
e
b
atter
y
cu
r
r
en
t e
f
f
ec
tiv
ely
.
R
u
r
al
elec
tr
if
icatio
n
th
r
o
u
g
h
P
V
-
b
ased
s
tan
d
-
alo
n
e
s
y
s
tem
s
is
g
ain
in
g
p
o
p
u
lar
ity
d
u
e
to
its
ab
ilit
y
t
o
p
r
o
v
id
e
i
n
d
ep
e
n
d
en
t
an
d
r
elia
b
le
p
o
wer
g
en
e
r
atio
n
.
T
h
ese
s
y
s
tem
s
ar
e
ty
p
ically
d
esig
n
ed
with
lo
w
v
o
ltag
e
lev
els f
o
r
b
o
th
th
e
PV a
r
r
ay
a
n
d
th
e
b
atter
y
,
ty
p
ically
in
th
e
r
an
g
e
o
f
2
4
-
3
6
V.
Fig
u
r
e
1
s
h
o
ws a
ty
p
ical
s
tan
d
-
alo
n
e
PV
s
y
s
tem
.
Ho
wev
er
,
to
p
r
o
v
id
e
a
s
u
itab
le
DC
-
lin
k
v
o
ltag
e
f
o
r
an
in
v
er
ter
an
d
en
ab
le
a
2
3
0
V
AC
s
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[
1
1
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[
1
7
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ased
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ased
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ased
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[
1
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B
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s
to
ad
d
r
es
s
th
e
lim
itatio
n
s
o
f
ex
is
tin
g
n
o
n
-
is
o
lated
PV
s
tan
d
alo
n
e
s
y
s
tem
s
an
d
im
p
r
o
v
e
th
eir
ef
f
icien
cy
an
d
v
o
ltag
e
co
n
v
er
s
io
n
ca
p
ab
ilit
ies.
I
n
Fig
u
r
e
3
,
a
s
em
i
-
tap
p
ed
q
u
ad
r
atic
b
o
o
s
t
co
n
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er
ter
is
d
ep
icted
,
wh
ich
co
n
s
is
ts
o
f
an
u
n
tap
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ed
in
d
u
cto
r
L
1
a
n
d
a
ta
p
p
ed
in
d
u
cto
r
C
L
.
T
h
e
p
r
im
a
r
y
p
u
r
p
o
s
e
o
f
th
is
co
n
v
er
ter
is
to
s
tep
u
p
th
e
ty
p
ically
lo
w
v
o
ltag
e
g
e
n
er
ated
b
y
t
h
e
PV
s
y
s
tem
to
a
h
i
g
h
er
v
o
lta
g
e
le
v
e
l
s
u
itab
le
f
o
r
i
n
v
er
ter
s
o
r
o
t
h
e
r
DC
ap
p
licatio
n
s
.
T
h
e
q
u
ad
r
atic
b
o
o
s
t
c
o
n
v
e
r
ter
,
s
im
ilar
to
th
e
b
o
o
s
t
c
o
n
v
e
r
ter
,
u
tili
ze
s
a
s
in
g
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ac
tiv
e
s
witch
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,
an
d
th
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co
n
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ter
'
s
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er
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o
r
m
a
n
ce
is
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alu
ated
b
ased
o
n
th
e
s
witch
'
s
co
n
d
itio
n
.
Du
r
in
g
th
e
ON
s
tate
o
f
th
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s
witch
,
d
io
d
e
D2
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o
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iased
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I
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d
u
ct
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r
L
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a
n
d
ca
p
ac
it
o
r
C
1
a
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2603
-
2
6
1
7
2606
ch
ar
g
ed
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s
u
p
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ly
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wh
ile
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d
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ely
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o
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ased
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ap
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ito
r
s
C
1
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d
C
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ar
e
ch
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y
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h
e
s
u
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ly
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d
th
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i
n
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u
cto
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s
(
L
1
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d
C
L
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,
r
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ec
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h
e
o
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er
atio
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co
n
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itio
n
s
o
f
th
e
co
n
v
er
te
r
ar
e
illu
s
tr
ated
in
Fig
u
r
e
4
,
wh
ich
p
r
o
v
id
es
a
v
is
u
al
r
ep
r
esen
tatio
n
o
f
th
e
s
witch
s
tate
s
an
d
th
e
ch
ar
g
in
g
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d
is
ch
ar
g
in
g
o
f
t
h
e
v
ar
io
u
s
co
m
p
o
n
en
ts
(
in
d
u
cto
r
s
an
d
ca
p
ac
ito
r
s
)
d
u
r
i
n
g
th
e
O
N
an
d
OFF
s
tates
o
f
th
e
s
witch
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er
all,
th
e
s
em
i
-
tap
p
ed
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u
a
d
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o
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t
co
n
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er
ter
o
f
f
er
s
a
m
ea
n
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to
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u
p
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e
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s
lo
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v
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tp
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t,
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g
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q
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a
d
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atic
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t
tech
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e
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d
a
s
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o
r
ef
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icien
t
v
o
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e
co
n
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er
s
io
n
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Fig
u
r
e
2
.
D
u
t
y
r
a
t
i
o
v
s
v
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l
t
a
g
e
g
a
i
n
g
r
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p
h
o
f
b
o
o
s
t
a
n
d
q
u
a
d
r
a
t
i
c
b
o
o
s
t
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e
r
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e
r
a
n
d
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i
t
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d
i
f
f
e
r
e
n
t
v
a
l
u
e
s
o
f
n
Fig
u
r
e
3
.
A
ty
p
ical
PV
-
b
ased
q
u
ad
r
atic
b
o
o
s
t c
o
n
v
er
ter
with
co
u
p
led
in
d
u
ct
o
r
CL
T
h
e
r
elatio
n
s
h
ip
s
o
f
th
e
ca
p
ac
i
to
r
v
o
ltag
es a
r
e
g
iv
en
b
y
(
1
)
a
n
d
(
2
)
.
=
(
1
−
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(
1
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2
=
(
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2
(
2
)
Sin
ce
th
e
in
d
u
cto
r
L
2
is
tap
p
e
d
,
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en
th
e
o
u
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u
t
v
o
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e
b
ec
o
m
es
th
e
f
u
n
ctio
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f
th
e
t
u
r
n
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s
r
atio
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o
f
th
e
tap
p
ed
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u
cto
r
,
an
d
it
s
ig
n
if
ican
tly
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o
o
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ts
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e
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o
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h
e
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t
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Vc2
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d
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r
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=
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is
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e
s
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o
o
t
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th
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o
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u
ty
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atio
.
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h
e
c
u
r
r
en
t
r
ip
p
le
Δ
I
_
L
1
o
f
th
e
in
d
u
cto
r
L
1
ca
n
b
e
wr
itten
as
(
5
)
.
∆
1
=
1
(
5
)
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
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6
9
4
C
o
u
p
led
q
u
a
d
r
a
tic
b
o
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P
V
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p
p
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s
(
S
u
v
a
mit Ch
a
kra
b
o
r
ty
)
2607
T
o
o
b
tain
t
h
e
r
ip
p
le
co
m
p
o
n
e
n
t f
o
r
∆
I
_
L
1
,
th
e
in
d
u
ctan
ce
o
f
L
1
m
u
s
t satis
f
y
th
e
(
6
)
.
1
>
∆
(
6
)
Similar
ly
,
to
o
b
tain
th
e
r
ip
p
le
co
m
p
o
n
en
t f
o
r
∆I
_
C
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,
th
e
in
d
u
ctan
ce
o
f
C
L
m
u
s
t satis
f
y
th
e
(
7
)
.
>
(
1
−
)
∆
(
7
)
T
h
e
leak
ag
e
in
d
u
ctan
ce
L
_
k
is
n
o
t c
o
n
s
id
er
ed
as its
v
alu
e
is
n
eg
lig
ib
le.
Fig
u
r
e
4
.
Qu
a
d
r
atic
b
o
o
s
t c
o
n
v
er
ter
wh
en
s
witch
S1
is
o
n
an
d
o
f
f
a
n
d
wav
e
f
o
r
m
s
in
C
C
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2603
-
2
6
1
7
2608
3.
P
RO
P
O
SE
D
SYS
T
E
M
I
n
th
e
p
r
o
p
o
s
ed
s
tan
d
alo
n
e
PV
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
5
,
t
h
e
q
u
ad
r
atic
b
o
o
s
t
c
o
n
v
er
te
r
p
lay
s
a
cr
u
cial
r
o
le
in
b
o
o
s
tin
g
th
e
o
u
tp
u
t
v
o
lt
ag
e.
T
h
e
co
n
v
er
te
r
o
p
er
ates
s
im
ilar
ly
to
th
e
o
n
e
d
escr
ib
ed
in
r
ef
er
en
ce
[
1
]
,
wh
e
r
e
it
was
o
b
s
er
v
ed
t
h
at
th
e
o
u
tp
u
t
v
o
ltag
e
is
d
eter
m
in
ed
b
y
th
e
tu
r
n
s
r
atio
(
n
)
o
f
th
e
co
u
p
led
in
d
u
cto
r
,
allo
win
g
f
o
r
s
ig
n
if
ican
t
v
o
ltag
e
am
p
lific
atio
n
.
On
e
m
ajo
r
ad
v
a
n
tag
e
o
f
th
is
co
n
v
er
ter
is
its
ab
ilit
y
to
m
ain
tain
co
n
tin
u
o
u
s
in
p
u
t
c
u
r
r
e
n
t,
as
t
h
e
in
p
u
t
in
d
u
cto
r
is
n
o
t
tap
p
e
d
.
T
h
is
en
s
u
r
es
s
m
o
o
th
p
o
wer
tr
a
n
s
f
er
a
n
d
ef
f
icien
t
o
p
e
r
atio
n
o
f
th
e
s
y
s
tem
.
T
o
i
n
ter
f
ac
e
th
e
b
atter
y
with
t
h
e
s
y
s
tem
,
a
b
i
-
d
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
te
r
is
em
p
l
o
y
ed
.
T
h
is
co
n
v
er
ter
en
a
b
les
ef
f
ec
tiv
e
b
atter
y
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
,
p
r
o
v
id
in
g
co
n
tr
o
l
o
v
er
th
e
b
at
ter
y
'
s
en
er
g
y
f
lo
w.
C
ar
ef
u
l
co
n
tr
o
l
o
f
b
atter
y
ch
a
r
g
in
g
an
d
d
is
ch
ar
g
in
g
is
ess
en
tial
to
p
r
eser
v
e
b
atter
y
life
a
n
d
h
ea
lth
,
e
n
s
u
r
in
g
o
p
tim
al
p
er
f
o
r
m
a
n
ce
an
d
lo
n
g
ev
ity
.
Ov
e
r
all,
th
e
p
r
o
p
o
s
ed
s
y
s
tem
in
teg
r
ates
PV
m
o
d
u
le
s
,
a
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
f
o
r
v
o
ltag
e
b
o
o
s
tin
g
,
an
d
a
b
i
-
d
ir
ec
tio
n
al
DC
-
DC
co
n
v
er
ter
f
o
r
b
atter
y
in
ter
f
ac
in
g
.
T
h
is
d
esig
n
allo
ws
f
o
r
ef
f
icien
t
p
o
wer
m
a
n
ag
em
e
n
t,
ef
f
ec
tiv
e
b
atter
y
co
n
tr
o
l,
a
n
d
th
e
p
r
o
v
is
io
n
o
f
s
tab
le
v
o
lt
ag
e
lev
els
r
eq
u
ir
e
d
b
y
th
e
DC
lo
ad
s
.
Fig
u
r
e
5
.
Pro
p
o
s
ed
s
tan
d
alo
n
e
PV sy
s
tem
with
b
atter
y
3
.
1
.
P
rinciples
o
f
o
pera
t
io
n a
nd
m
o
des
a
na
ly
s
is
T
h
e
p
o
wer
f
lo
w
o
f
th
e
s
y
s
tem
in
a
s
tan
d
alo
n
e
PV
s
y
s
tem
[
1
8
]
-
[
2
0
]
ca
n
b
e
ca
teg
o
r
iz
ed
in
to
th
e
f
o
llo
win
g
s
ce
n
ar
io
s
:
-
PV
to
lo
ad
-
b
atter
y
f
u
lly
c
h
ar
g
ed
:
I
n
th
is
s
ce
n
ar
io
,
th
e
PV
ar
r
ay
g
en
er
ates
p
o
wer
a
n
d
d
ir
ec
tl
y
s
u
p
p
lies
it
to
th
e
lo
ad
with
o
u
t
i
n
v
o
lv
i
n
g
th
e
b
atter
y
.
T
h
e
b
atter
y
is
alr
ea
d
y
f
u
lly
ch
ar
g
ed
an
d
n
o
t
ac
tiv
el
y
in
v
o
lv
ed
i
n
th
e
p
o
wer
tr
an
s
f
er
.
-
PV
to
b
atter
y
-
n
o
lo
ad
co
n
d
iti
o
n
,
b
atter
y
ch
ar
g
in
g
:
wh
en
th
er
e
is
n
o
lo
a
d
o
r
t
h
e
lo
a
d
d
e
m
an
d
is
l
o
w,
th
e
s
u
r
p
lu
s
p
o
wer
g
en
e
r
ated
b
y
th
e
PV
ar
r
ay
is
u
s
ed
to
ch
a
r
g
e
t
h
e
b
atter
y
.
T
h
e
PV
p
o
wer
is
d
ir
ec
ted
to
war
d
s
th
e
b
atter
y
to
r
ep
len
is
h
its
en
e
r
g
y
s
to
r
ag
e
.
-
PV
to
b
o
th
lo
a
d
an
d
b
atter
y
-
s
u
r
p
lu
s
PV
en
er
g
y
:
wh
e
n
th
e
PV
ar
r
ay
g
en
e
r
ates
m
o
r
e
p
o
w
er
th
an
wh
at
is
r
eq
u
ir
ed
b
y
th
e
lo
ad
,
th
e
ex
ce
s
s
p
o
wer
is
u
s
ed
to
s
im
u
ltan
e
o
u
s
ly
s
u
p
p
ly
th
e
lo
ad
an
d
ch
a
r
g
e
th
e
b
atter
y
.
T
h
is
en
s
u
r
es e
f
f
icien
t u
tili
za
tio
n
o
f
th
e
s
u
r
p
l
u
s
PV e
n
er
g
y
.
-
PV
an
d
b
atter
y
t
o
lo
ad
-
d
ef
icit
in
PV
en
er
g
y
:
I
f
t
h
e
PV
ar
r
a
y
alo
n
e
ca
n
n
o
t
m
ee
t
th
e
p
o
we
r
d
em
an
d
o
f
th
e
lo
ad
,
th
e
b
atter
y
is
u
tili
ze
d
to
p
r
o
v
id
e
th
e
r
em
ain
in
g
p
o
wer
r
eq
u
ir
ed
.
T
h
e
PV
ar
r
ay
s
u
p
p
li
es
p
o
wer
to
t
h
e
lo
ad
,
an
d
if
n
ec
ess
ar
y
,
t
h
e
b
att
er
y
also
co
n
tr
i
b
u
tes to
m
ee
tin
g
th
e
lo
ad
d
em
an
d.
-
B
atter
y
to
lo
ad
-
in
s
u
f
f
icien
t
P
V
p
o
wer
:
I
n
s
itu
atio
n
s
wh
er
e
th
e
PV
ar
r
ay
is
u
n
ab
le
t
o
g
e
n
er
ate
s
u
f
f
icien
t
p
o
wer
to
m
ee
t
th
e
lo
ad
d
em
an
d
,
th
e
b
atter
y
tak
es
o
v
e
r
an
d
s
u
p
p
lies
p
o
wer
t
o
th
e
lo
a
d
.
T
h
e
b
atter
y
ac
ts
as
an
en
er
g
y
s
o
u
r
ce
to
b
r
id
g
e
th
e
g
ap
b
etwe
en
th
e
lo
ad
d
em
an
d
an
d
th
e
a
v
ailab
le
PV p
o
wer
.
-
W
o
r
s
t
ca
s
e
s
ce
n
ar
io
-
PV a
n
d
DC
b
u
s
to
B
atter
y
: T
h
is
m
o
d
e
is
ac
tiv
ated
wh
en
th
e
b
atter
y
's
s
tate
o
f
ch
ar
g
e
(
So
C
)
is
lo
w,
an
d
th
e
PV
s
o
u
r
ce
alo
n
e
ca
n
n
o
t
p
r
o
v
id
e
th
e
r
e
q
u
ir
ed
ch
ar
g
i
n
g
c
u
r
r
e
n
t
to
th
e
b
atter
y
.
I
n
th
is
ca
s
e,
th
e
s
y
s
tem
s
h
u
ts
d
o
wn
a
s
th
e
PV
p
o
we
r
an
d
th
e
DC
b
u
s
p
o
wer
ar
e
u
tili
ze
d
to
ch
ar
g
e
th
e
b
atter
y
a
n
d
r
esto
r
e
its
en
er
g
y
lev
el.
T
h
ese
p
o
wer
f
lo
w
s
ce
n
ar
io
s
r
ep
r
esen
t
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
o
f
th
e
s
y
s
tem
b
ased
o
n
th
e
av
ailab
ilit
y
o
f
PV
p
o
wer
,
lo
ad
d
em
an
d
,
a
n
d
th
e
s
tate
o
f
th
e
b
a
tter
y
.
T
h
e
s
y
s
tem
in
tellig
en
tly
m
an
ag
es
th
e
p
o
we
r
f
lo
w
to
en
s
u
r
e
ef
f
icien
t
u
tili
za
tio
n
o
f
th
e
PV
en
e
r
g
y
a
n
d
u
n
in
t
er
r
u
p
ted
p
o
wer
s
u
p
p
ly
to
th
e
l
o
ad
.
T
h
is
is
s
h
o
wn
in
Fig
u
r
e
6.
3
.
2
.
B
a
s
ic
co
ntr
o
l st
ruct
ure
a
nd
m
o
de
s
elec
t
io
n
-
MPPT
m
o
d
e:
I
n
th
is
m
o
d
e,
th
e
s
y
s
tem
u
tili
ze
s
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV
ar
r
ay
.
W
h
en
th
e
p
o
wer
g
en
er
ated
b
y
th
e
PV
s
o
u
r
ce
is
g
r
ea
ter
th
an
th
e
l
o
ad
r
e
q
u
ir
em
en
t,
th
e
ex
ce
s
s
p
o
wer
is
u
s
ed
to
s
im
u
ltan
eo
u
s
ly
s
u
p
p
ly
th
e
lo
ad
an
d
c
h
ar
g
e
th
e
b
atter
y
.
T
h
e
p
o
wer
b
ala
n
ce
eq
u
atio
n
in
MPPT
m
o
d
e
is
g
iv
en
b
y
P_
p
v
+
P_
b
at
=
P_
lo
ad
,
wh
er
e
P_
p
v
r
ep
r
esen
ts
th
e
p
o
wer
g
en
er
ated
b
y
th
e
PV so
u
r
ce
,
P_
b
at
r
ep
r
e
s
en
ts
th
e
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
C
o
u
p
led
q
u
a
d
r
a
tic
b
o
o
s
t c
o
n
v
erter
fo
r
s
ta
n
d
-
a
lo
n
e
P
V
a
p
p
li
ca
tio
n
s
(
S
u
v
a
mit Ch
a
kra
b
o
r
ty
)
2609
f
lo
win
g
in
t
o
th
e
b
atter
y
,
an
d
P_
lo
ad
r
e
p
r
esen
ts
th
e
p
o
wer
c
o
n
s
u
m
ed
b
y
th
e
l
o
ad
.
T
h
e
s
y
s
tem
r
em
ain
s
in
MPPT
m
o
d
e
u
n
til
th
e
b
atter
y
cu
r
r
e
n
t
(
I
B
)
is
b
el
o
w
a
s
p
ec
if
ied
v
al
u
e
d
eter
m
in
ed
b
y
th
e
State
o
f
C
h
ar
g
e
(
SOC
)
o
f
th
e
b
atter
y
.
T
h
is
en
s
u
r
es th
at
th
e
b
atter
y
is
n
o
t o
v
e
r
ch
ar
g
e
d
.
-
No
n
-
MPPT
m
o
d
e:
W
h
en
th
e
lo
ad
d
em
a
n
d
is
lo
wer
th
an
t
h
e
g
e
n
er
ated
p
o
wer
an
d
t
h
e
b
atter
y
c
h
ar
g
in
g
cu
r
r
en
t
ex
ce
ed
s
its
lim
it,
th
e
s
y
s
tem
s
witch
es
to
n
o
n
-
MPPT
m
o
d
e.
I
n
th
is
m
o
d
e,
th
e
p
o
wer
b
alan
ce
eq
u
atio
n
P_
p
v
+
P_
b
at
=
P_
lo
ad
s
till
h
o
ld
s
,
b
u
t
P_
b
at
b
ec
o
m
es
n
e
g
a
tiv
e,
in
d
icatin
g
th
at
th
e
b
atter
y
d
is
ch
ar
g
es
to
m
ee
t
th
e
lo
ad
d
e
m
an
d
.
T
h
e
b
atter
y
ch
ar
g
in
g
cu
r
r
en
t
is
m
ai
n
tain
ed
at
a
p
r
e
d
eter
m
in
e
d
v
alu
e
to
p
r
ev
e
n
t
o
v
er
ch
a
r
g
in
g
.
T
h
e
o
p
er
atin
g
p
o
in
t
in
n
o
n
-
MPPT
m
o
d
e
is
g
en
er
ally
o
n
th
e
d
ec
r
ea
s
in
g
s
lo
p
e
o
f
th
e
PV
cu
r
v
e,
in
d
icatin
g
a
r
e
d
u
ctio
n
in
PV p
o
wer
to
m
atch
t
h
e
lo
ad
d
em
an
d
.
-
B
atter
y
m
o
d
e:
I
n
th
e
ab
s
en
ce
o
f
PV
p
o
wer
,
th
e
s
tan
d
alo
n
e
s
y
s
tem
o
p
er
ates
in
b
atter
y
m
o
d
e.
T
h
e
s
y
s
tem
s
u
p
p
lies
p
o
wer
to
th
e
lo
ad
s
o
l
ely
f
r
o
m
th
e
b
atter
y
,
e
n
s
u
r
in
g
th
at
th
e
b
atter
y
is
n
o
t
o
v
e
r
-
d
i
s
ch
ar
g
ed
.
T
h
is
m
o
d
e
allo
ws
th
e
s
y
s
tem
to
m
ee
t
th
e
lo
ad
d
em
an
d
w
h
en
th
er
e
is
n
o
PV
p
o
wer
av
ailab
le,
with
o
u
t
r
is
k
in
g
ex
ce
s
s
iv
e
d
is
ch
ar
g
e
o
f
t
h
e
b
att
er
y
.
-
T
h
e
s
e
t
h
r
e
e
m
o
d
e
s
e
n
a
b
l
e
t
h
e
s
y
s
te
m
t
o
o
p
ti
m
i
z
e
p
o
we
r
e
x
t
r
a
c
t
i
o
n
f
r
o
m
t
h
e
P
V
a
r
r
a
y
,
p
r
e
v
e
n
t
o
v
e
r
c
h
a
r
g
i
n
g
o
r
o
v
e
r
-
d
i
s
c
h
a
r
g
i
n
g
o
f
t
h
e
b
a
t
te
r
y
,
a
n
d
e
n
s
u
r
e
c
o
n
t
i
n
u
o
u
s
p
o
w
e
r
s
u
p
p
l
y
t
o
t
h
e
l
o
a
d
u
n
d
e
r
v
a
r
y
i
n
g
c
o
n
d
i
t
i
o
n
s
.
Fig
u
r
e
6
.
Dif
f
e
r
en
t p
o
wer
f
lo
w
o
p
er
atio
n
o
f
th
e
p
r
o
p
o
s
ed
s
t
an
d
alo
n
e
PV sy
s
tem
3
.
3
.
Co
ntr
o
l o
f
s
t
a
nd
a
lo
ne
mo
des
I
n
th
e
p
r
o
p
o
s
ed
s
tan
d
alo
n
e
s
y
s
tem
,
th
e
co
n
t
r
o
l
s
y
s
tem
is
ess
e
n
tial
f
o
r
d
ete
r
m
in
in
g
th
e
o
p
er
a
tin
g
m
o
d
e
an
d
m
an
a
g
in
g
p
o
wer
f
lo
w.
T
h
e
co
n
tr
o
ller
co
n
tin
u
o
u
s
ly
m
o
n
i
to
r
s
th
e
s
y
s
tem
's
cu
r
r
en
t
s
tate
an
d
m
ak
es
d
ec
is
io
n
s
b
ased
o
n
p
o
wer
d
em
an
d
an
d
th
e
b
atter
y
'
s
s
p
ec
i
f
ied
s
ta
te
o
f
ch
ar
g
e
(
SOC
)
.
Fig
u
r
e
7
illu
s
tr
ates
th
e
MP
PT
alg
o
r
ith
m
u
s
ed
in
th
is
s
tu
d
y
,
wh
ich
is
b
ased
o
n
t
h
e
p
er
t
u
r
b
an
d
o
b
s
er
v
e
m
eth
o
d
.
I
n
MPPT
m
o
d
e,
as
d
ep
icted
in
Fig
u
r
e
8
,
th
e
c
o
n
tr
o
ller
ad
j
u
s
ts
th
e
d
u
ty
r
atio
to
en
s
u
r
e
m
ax
im
u
m
p
o
wer
ex
t
r
ac
tio
n
f
r
o
m
t
h
e
PV
ar
r
ay
.
T
h
e
MPPT
b
lo
ck
g
e
n
er
ates
a
r
e
f
er
e
n
ce
cu
r
r
en
t
(
I
p
v
-
m
p
p
)
b
ased
o
n
th
e
d
esire
d
o
p
er
atin
g
p
o
in
t
o
f
th
e
PV
ar
r
ay
.
T
h
is
r
ef
er
en
ce
c
u
r
r
en
t
is
co
m
p
ar
ed
with
th
e
ac
tu
al
PV
cu
r
r
en
t,
an
d
th
e
er
r
o
r
is
p
ass
ed
th
r
o
u
g
h
a
PI
co
n
tr
o
ller
.
T
h
e
o
u
tp
u
t
o
f
th
e
PI
co
n
t
r
o
ller
is
th
e
d
u
ty
r
atio
(
Dsh
)
f
o
r
th
e
s
witc
h
o
f
th
e
q
u
a
d
r
atic
b
o
o
s
t
co
n
v
er
ter
,
wh
ich
r
eg
u
lates
th
e
PV c
u
r
r
en
t to
tr
ac
k
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2603
-
2
6
1
7
2610
T
o
co
n
tr
o
l
th
e
DC
-
lin
k
v
o
ltag
e,
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
C
1
is
m
ea
s
u
r
ed
an
d
co
m
p
ar
ed
with
th
e
d
esire
d
v
alu
e.
T
h
e
er
r
o
r
i
s
th
en
f
ed
in
to
a
PI
co
n
tr
o
ller
,
wh
ich
g
en
er
ates
a
cu
r
r
en
t
r
e
f
er
en
ce
(
I
r
e
f
)
.
T
h
is
cu
r
r
en
t r
ef
er
e
n
ce
is
co
m
p
ar
ed
with
th
e
b
atter
y
cu
r
r
en
t (
I
b
)
,
a
n
d
th
e
r
esu
ltin
g
er
r
o
r
is
u
s
ed
t
o
g
en
e
r
ate
th
e
d
u
t
y
r
atio
(
Db
)
f
o
r
th
e
b
id
ir
ec
tio
n
al
co
n
v
e
r
ter
.
T
h
e
b
id
i
r
ec
tio
n
al
c
o
n
v
er
ter
allo
ws
p
o
wer
f
lo
w
b
e
twee
n
th
e
PV
ar
r
ay
an
d
th
e
b
atter
y
,
co
n
tr
o
llin
g
th
e
b
atter
y
ch
a
r
g
in
g
o
r
d
is
ch
ar
g
i
n
g
p
r
o
ce
s
s
.
W
h
en
th
er
e
is
n
o
PV e
n
e
r
g
y
a
v
ailab
le,
th
e
co
n
tr
o
ller
s
h
if
ts
th
e
s
y
s
tem
to
b
atter
y
o
n
ly
m
o
d
e
to
s
u
p
p
l
y
p
o
wer
to
th
e
lo
ad
s
o
lely
f
r
o
m
th
e
b
atter
y
.
T
h
e
co
n
tr
o
ller
m
u
s
t
co
n
tin
u
o
u
s
ly
m
o
n
ito
r
th
e
cu
r
r
en
t
s
tate
o
f
th
e
s
y
s
tem
,
ev
alu
atin
g
p
ar
am
eter
s
th
at
in
d
icate
p
o
wer
ex
ce
s
s
o
r
d
ef
icit.
B
ased
o
n
th
ese
p
ar
am
eter
s
,
th
e
co
n
tr
o
ller
d
eter
m
in
es
th
e
ap
p
r
o
p
r
iate
m
o
d
e
o
f
o
p
er
atio
n
f
o
r
th
e
s
y
s
tem
.
Ov
er
all,
th
e
co
n
tr
o
l
s
y
s
tem
in
th
e
p
r
o
p
o
s
ed
s
tan
d
alo
n
e
s
y
s
tem
en
s
u
r
e
s
ef
f
icien
t
p
o
wer
m
an
a
g
em
en
t,
o
p
tim
al
MPPT
o
p
er
atio
n
,
b
atter
y
ch
ar
g
in
g
/
d
is
ch
ar
g
in
g
co
n
tr
o
l,
an
d
s
ea
m
less
p
o
wer
s
u
p
p
ly
to
th
e
lo
ad
u
n
d
er
v
ar
y
i
n
g
co
n
d
iti
o
n
s
.
M
e
a
s
u
r
e
V
p
v
,
I
p
v
Y
E
S
I
p
v
_
o
l
d
=
I
p
v
_
n
e
w
P
o
l
d
=
P
n
e
w
P
n
e
w
>
P
o
l
d
NO
d
I
r
e
f
=
-
d
I
r
e
f
I
p
v
_
n
e
w
=
I
p
v
_
o
l
d
+
d
I
r
e
f
I
n
i
t
i
a
l
i
ze
P
&
O
E
v
a
l
u
a
t
e
P
n
e
w
I
p
v
_
n
e
w
=
I
p
v
_
o
l
d
+
d
I
r
e
f
W
a
i
t
T
s
Fig
u
r
e
7
.
Flo
wch
ar
t
o
f
th
e
P&
O
MPPT
alg
o
r
ith
m
T
h
e
co
n
tr
o
l
s
tr
ateg
y
f
o
r
th
e
p
r
o
p
o
s
ed
s
tan
d
alo
n
e
s
y
s
tem
in
v
o
lv
es
m
o
n
ito
r
in
g
an
d
c
o
n
tr
o
llin
g
th
e
s
y
s
tem
in
th
r
ee
d
if
f
er
e
n
t
m
o
d
es:
MPPT
m
o
d
e,
n
o
n
-
MPPT
m
o
d
e,
a
n
d
b
atter
y
o
n
ly
(
B
O)
m
o
d
e.
T
h
e
s
y
s
tem
is
d
esig
n
ed
to
s
h
if
t
b
etwe
en
th
ese
m
o
d
es
b
ased
o
n
th
e
o
p
er
at
in
g
co
n
d
itio
n
s
.
I
n
th
e
n
o
n
-
M
PP
T
m
o
d
e
s
h
o
wn
in
Fig
u
r
e
9
,
th
e
r
ef
er
en
ce
cu
r
r
e
n
t
I
r
ef
is
s
u
b
tr
ac
ted
f
r
o
m
th
e
m
ax
im
u
m
b
atter
y
cu
r
r
en
t
I
b
m
ax
to
g
en
er
ate
th
e
r
ef
er
en
ce
PV
cu
r
r
e
n
t
I
p
v
r
ef
.
T
h
is
r
ef
er
en
ce
cu
r
r
en
t
is
u
s
ed
to
r
e
g
u
late
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
V
C
1
,
en
s
u
r
in
g
its
m
ain
ten
an
ce
with
in
a
ce
r
tain
v
o
ltag
e
r
an
g
e.
I
f
th
er
e
is
a
s
u
d
d
en
ch
an
g
e
in
th
e
lo
ad
,
ca
u
s
in
g
VC
1
to
f
all
b
elo
w
a
s
p
ec
if
ied
v
o
ltag
e,
th
e
co
n
tr
o
ller
au
to
m
atica
lly
s
h
if
ts
f
r
o
m
th
e
n
o
n
-
MPPT
m
o
d
e
to
th
e
MPPT
m
o
d
e
to
o
p
tim
ize
p
o
wer
ex
t
r
a
ctio
n
f
r
o
m
th
e
PV
ar
r
a
y
.
T
h
is
tr
an
s
itio
n
allo
ws
th
e
s
y
s
tem
to
ad
ap
t
t
o
v
ar
y
in
g
lo
ad
co
n
d
itio
n
s
an
d
im
p
r
o
v
e
o
v
er
all
p
er
f
o
r
m
an
ce
.
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
C
o
u
p
led
q
u
a
d
r
a
tic
b
o
o
s
t c
o
n
v
erter
fo
r
s
ta
n
d
-
a
lo
n
e
P
V
a
p
p
li
ca
tio
n
s
(
S
u
v
a
mit Ch
a
kra
b
o
r
ty
)
2611
V
pv
I
pv
M
P
P
T
I
pv
r
e
f
+
-
I
pv
PI
D
s
h
VC
1
r
e
f
+
-
VC
1
PI
I
br
e
f
+
-
PI
Db
Ib
D
s
h
PI
VC
1
r
e
f
+
-
VC
1
PI
I
pvr
e
f
+
-
I
pv
S
O
C
I
bm
a
x
Vb
Ib
+
-
PI
Ib
Db
Fig
u
r
e
8
.
Pro
p
o
s
ed
o
p
er
atio
n
m
o
d
e
in
th
e
MPPT
m
o
d
e
Fig
u
r
e
9
.
Pro
p
o
s
ed
o
p
er
atio
n
m
o
d
e
in
th
e
n
o
n
-
MPPT
m
o
d
e
W
h
en
th
er
e
is
n
o
PV
en
er
g
y
av
ailab
le,
th
e
s
y
s
tem
en
ter
s
t
h
e
b
atter
y
-
o
n
ly
(
B
O)
m
o
d
e
as
s
h
o
wn
in
Fig
u
r
e
1
0
.
I
n
th
is
m
o
d
e,
th
e
b
atter
y
b
ec
o
m
es
th
e
s
o
le
p
o
wer
s
o
u
r
ce
an
d
is
r
esp
o
n
s
ib
le
f
o
r
s
u
p
p
ly
in
g
th
e
en
tire
lo
ad
.
T
h
e
o
p
e
r
atio
n
in
MPPT
m
o
d
e
an
d
B
O
m
o
d
e
is
s
im
il
ar
,
with
th
e
ex
ce
p
tio
n
th
at
th
e
MPPT
co
n
tr
o
ller
r
em
ain
s
id
le
in
B
O
m
o
d
e.
T
h
e
s
y
s
tem
m
ain
tain
s
s
tab
l
e
o
p
e
r
atio
n
in
th
e
B
O
m
o
d
e
to
e
n
s
u
r
e
an
u
n
in
ter
r
u
p
ted
p
o
wer
s
u
p
p
l
y
in
th
e
a
b
s
en
ce
o
f
PV e
n
er
g
y
.
T
o
f
ac
ilit
ate
th
e
co
n
tr
o
l
o
f
d
i
f
f
er
en
t
m
o
d
es,
f
o
u
r
c
o
n
tr
o
l
s
ig
n
als,
M,
NM
,
B
O,
an
d
No
n
-
B
O,
ar
e
g
en
er
ated
.
W
h
en
M=
1
an
d
N
M=
0
,
th
e
co
n
tr
o
ller
o
p
er
ates
t
h
e
PV
in
MPPT
m
o
d
e,
with
th
e
b
atter
y
m
ain
tain
in
g
th
e
DC
-
lin
k
v
o
ltag
e.
I
f
th
e
l
o
ad
r
ed
u
ce
s
o
r
s
o
lar
r
ad
iati
o
n
i
n
cr
ea
s
es,
ca
u
s
in
g
th
e
b
atter
y
cu
r
r
en
t
I
B
to
r
ea
ch
I
b
m
ax
as sp
ec
if
ied
b
y
t
h
e
s
tate
o
f
ch
a
r
g
e
(
SOC
)
,
NM
is
s
et
to
1
an
d
M
is
s
et
to
0
.
T
h
e
c
o
n
t
r
o
ller
th
en
o
p
er
ates
th
e
b
atter
y
in
a
c
o
n
s
tan
t
cu
r
r
e
n
t
m
o
d
e,
m
ain
tain
in
g
th
e
b
att
er
y
ch
ar
g
in
g
cu
r
r
en
t
at
I
b
m
ax
,
wh
ile
th
e
PV
ar
r
ay
tak
es r
esp
o
n
s
ib
ilit
y
f
o
r
m
ain
ta
in
in
g
th
e
DC
-
lin
k
v
o
ltag
e.
Fo
r
B
O=
0
an
d
n
on
-
B
O=
1
,
th
e
co
n
tr
o
ller
o
p
e
r
ates
th
e
PV
ar
r
ay
in
eith
er
MPPT
m
o
d
e
o
r
n
o
n
-
MPPT
m
o
d
e,
d
e
p
en
d
in
g
o
n
th
e
s
tatu
s
o
f
M
an
d
NM
.
W
h
en
B
O=
1
an
d
n
on
-
B
O=
0
,
in
d
icatin
g
th
e
ab
s
en
ce
o
f
PV
en
er
g
y
,
th
e
co
n
tr
o
ller
s
h
if
ts
to
th
e
b
atter
y
-
o
n
l
y
m
o
d
e,
wh
er
e
th
e
b
a
tter
y
m
ain
tain
s
th
e
DC
-
lin
k
v
o
ltag
e
an
d
s
u
p
p
lies
p
o
wer
to
t
h
e
lo
ad
.
T
h
is
co
n
tr
o
l
s
tr
ateg
y
s
h
o
wn
in
Fig
u
r
e
1
1
allo
ws
th
e
s
y
s
tem
to
ad
ap
t
to
ch
an
g
in
g
o
p
e
r
atin
g
co
n
d
itio
n
s
an
d
en
s
u
r
es e
f
f
icien
t o
p
er
atio
n
in
all
th
r
ee
m
o
d
es,
n
am
ely
MPPT
m
o
d
e,
n
o
n
-
M
PP
T
m
o
d
e,
an
d
B
O
m
o
d
e.
T
h
e
co
n
tr
o
l
s
ig
n
als
M,
NM
,
B
O,
an
d
n
on
-
B
O
en
ab
le
th
e
s
y
s
tem
to
s
witch
b
etwe
en
th
ese
m
o
d
es
an
d
d
is
ab
le
th
e
m
o
d
es
t
h
at
ar
e
n
o
t
r
eq
u
ir
ed
b
ased
o
n
th
e
p
r
ev
ail
in
g
co
n
d
itio
n
s
.
Fig
u
r
e
1
2
s
h
o
ws
th
e
alg
o
r
ith
m
t
o
id
en
tify
an
d
s
witch
b
etwe
en
d
i
f
f
er
en
t m
o
d
es.
VC
1
r
e
f
+
-
VC
1
PI
D
s
h
Fig
u
r
e
1
0
.
Pro
p
o
s
ed
o
p
er
atio
n
m
o
d
e
in
th
e
b
atter
y
-
o
n
l
y
m
o
d
e
V
pv
I
pv
M
P
P
T
I
pvm
pp
+
-
MP
PI
VC
1
r
e
f
+
-
VC
1
PI
I
r
e
f
X
X
X
X
N
on
-
MP
N
on
-
MP
MP
+
+
I
pv
+
-
PI
Db
+
+
Ib
I
br
e
f
S
O
C
I
bm
a
x
Vb
Ib
I
pvr
e
f
D
s
h
VC
1
r
e
f
+
-
VC
1
PI
BO
X
X
+
+
N
on
-
BO
X
N
on
-
BO
D
s
h
D
s
h
Db
Fig
u
r
e
1
1
.
Ov
er
all
co
n
tr
o
l stra
teg
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
5
,
No
.
4
,
Dec
em
b
er
20
2
4
:
2603
-
2
6
1
7
2612
S
t
a
r
t
S
e
n
s
e
V
c
1
,
B
a
t
t
e
r
y
V
o
l
t
a
g
e
C
h
e
c
k
I
b
r
e
f
<
I
b
i
n
F
r
o
m
S
O
C
S
e
t
M
P
=
0
N
o
n
-
M
P
=
0
I
r
e
f
>
I
b
m
a
x
F
r
o
m
S
O
C
S
e
t
M
P
=
1
N
o
n
-
M
P
=
0
S
e
t
M
P
=
0
N
o
n
-
M
P
=
1
V
c
1
>
3
6
R
e
t
u
r
n
N
o
N
o
N
o
Y
e
s
Y
e
s
Fig
u
r
e
1
2
.
Pro
p
o
s
ed
o
p
er
atio
n
m
o
d
e
id
e
n
tific
atio
n
s
tr
ateg
y
4.
SI
M
UL
A
T
I
O
N
A
ND
E
XP
E
RIM
E
N
T
AL
R
E
S
UL
T
S
4
.
1
.
Sim
ula
t
io
n r
esu
lt
o
f
pro
po
s
ed
co
nv
er
t
er
T
h
e
th
eo
r
etica
l
ass
u
m
p
tio
n
s
wer
e
v
alid
ated
t
h
r
o
u
g
h
b
o
th
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
s
e
tu
p
s
o
f
t
h
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
with
a
tap
p
ed
in
d
u
ct
o
r
.
T
esti
n
g
was
co
n
d
u
cte
d
f
o
r
b
o
th
MPPT
an
d
n
o
n
-
MPPT
m
o
d
es
u
n
d
er
r
ated
lo
ad
an
d
v
ar
ia
b
le
lo
ad
co
n
d
itio
n
s
to
en
s
u
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
s
y
s
tem
in
d
if
f
er
en
t
o
p
e
r
atin
g
s
ce
n
ar
io
s
.
T
h
e
d
esig
n
ed
s
y
s
tem
was
im
p
lem
e
n
te
d
u
s
in
g
th
e
s
im
u
latio
n
s
o
f
twar
e
PLE
C
S,
with
a
ch
o
s
en
s
witch
in
g
f
r
eq
u
en
c
y
o
f
2
0
k
Hz.
T
h
e
PV
o
p
er
atin
g
r
an
g
e
was
s
et
b
etwe
en
1
7
to
2
2
v
o
lts
,
with
an
o
p
en
cir
cu
it
v
o
ltag
e
o
f
2
2
V
an
d
an
MPP
v
o
ltag
e
o
f
th
e
s
elec
ted
PV
p
an
el
at
1
7
.
6
V.
T
h
e
b
atter
y
'
s
n
o
m
in
al
v
o
ltag
e
was
tak
en
as
2
4
V.
Fo
r
MPPT
o
p
er
atio
n
,
th
e
p
er
tu
r
b
&
o
b
s
er
v
e
(
P&
O)
m
eth
o
d
was
em
p
l
o
y
ed
to
ex
tr
ac
t
t
h
e
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
s
o
lar
p
an
el.
T
h
is
alg
o
r
ith
m
p
er
io
d
ically
p
e
r
tu
r
b
s
th
e
PV
cu
r
r
en
t
with
a
s
m
all
in
cr
em
en
tal
s
tep
an
d
co
m
p
ar
e
s
th
e
r
esu
ltin
g
p
o
wer
with
th
e
p
r
e
v
io
u
s
ly
d
eliv
er
ed
p
o
wer
,
a
llo
win
g
th
e
s
y
s
tem
to
tr
ac
k
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t.
Fig
u
r
e
1
3
s
h
o
ws
th
e
MPPT
tr
ac
k
in
g
b
y
th
e
q
u
a
d
r
atic
b
o
o
s
t
co
n
v
er
ter
th
r
o
u
g
h
th
e
Ap
lab
s
o
lar
em
u
l
ato
r
.
T
o
r
eg
u
late
th
e
b
atter
y
cu
r
r
en
t,
a
co
n
v
en
tio
n
al
p
r
o
p
o
r
tio
n
a
l
-
in
teg
r
al
(
PI)
co
n
tr
o
ller
was
u
s
ed
in
th
e
b
atte
r
y
co
n
tr
o
ller
.
T
h
is
PI
co
n
tr
o
lle
r
en
s
u
r
es
th
at
th
e
b
atter
y
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
cu
r
r
en
ts
ar
e
c
o
n
tr
o
lled
with
in
th
e
s
p
ec
if
ied
lim
its
,
th
er
eb
y
p
r
o
tectin
g
th
e
b
atter
y
a
n
d
m
ai
n
tain
in
g
its
s
tate
o
f
ch
ar
g
e
(
SOC
)
.
T
h
e
tap
p
e
d
in
d
u
cto
r
u
s
ed
in
th
e
s
y
s
tem
h
as
a
tu
r
n
s
r
atio
o
f
1
.
5
,
wh
ich
c
o
n
tr
ib
u
tes
to
ac
h
iev
in
g
th
e
d
esire
d
h
i
g
h
v
o
ltag
e
g
ain
.
B
y
co
n
d
u
ctin
g
s
im
u
latio
n
s
an
d
ex
p
e
r
im
en
tal
test
s
,
th
e
p
er
f
o
r
m
an
ce
an
d
f
u
n
ctio
n
ality
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
wer
e
e
v
alu
ated
an
d
v
ali
d
ated
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
a
te
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
q
u
a
d
r
atic
b
o
o
s
t
co
n
v
er
t
er
with
a
ta
p
p
ed
in
d
u
ct
o
r
to
p
o
lo
g
y
in
ac
h
iev
in
g
th
e
d
esire
d
p
o
wer
co
n
v
er
s
io
n
an
d
co
n
tr
o
l o
b
jectiv
es.
4
.
2
.
E
x
perim
ent
a
l r
esu
lt
o
f
pro
po
s
ed
co
nv
er
t
er
T
o
ex
p
e
r
im
en
tally
v
ali
d
ate
th
e
p
r
o
p
o
s
ed
s
y
s
tem
,
a
lab
o
r
at
o
r
y
p
r
o
to
ty
p
e
was
d
ev
el
o
p
ed
s
h
o
wn
in
Fig
u
r
e
1
4
.
T
h
e
s
witch
in
g
f
r
eq
u
en
cy
o
f
th
e
co
n
v
er
ter
was c
h
o
s
en
as 2
0
k
Hz,
c
o
n
s
id
er
in
g
th
e
tr
ad
e
-
o
f
f
b
etwe
en
p
o
wer
d
en
s
ity
a
n
d
ef
f
icien
cy
.
T
h
e
b
atter
y
b
a
n
k
was
co
n
s
tr
u
cted
b
y
c
o
n
n
ec
tin
g
two
1
2
V,
2
6
Ah
b
atter
ies
in
s
er
ies.
T
h
is
co
n
f
ig
u
r
atio
n
p
r
o
v
id
ed
th
e
n
ec
ess
ar
y
v
o
ltag
e
a
n
d
ca
p
ac
ity
f
o
r
th
e
s
y
s
tem
'
s
en
er
g
y
s
to
r
ag
e.
T
o
em
u
late
th
e
s
o
lar
ar
r
ay
,
an
Ap
l
ab
SAS1
2
0
/1
0
ODI
V
s
o
lar
ar
r
ay
s
im
u
lato
r
was
u
tili
ze
d
.
T
h
is
s
im
u
lato
r
g
en
er
ates
th
e
P
-
V
(
p
o
wer
-
v
o
ltag
e)
an
d
I
-
V
(
cu
r
r
en
t
-
v
o
ltag
e)
ch
ar
ac
ter
is
tics
o
f
th
e
PV
a
r
r
ay
b
a
s
ed
o
n
f
o
u
r
in
p
u
t
p
ar
am
eter
s
:
Vm
p
p
(
m
ax
im
u
m
p
o
wer
p
o
in
t
v
o
ltag
e)
,
Vo
c
(
o
p
en
-
cir
cu
it
v
o
ltag
e
)
,
I
m
p
p
(
m
ax
im
u
m
p
o
wer
p
o
in
t
cu
r
r
en
t)
,
an
d
I
s
c
(
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t
)
o
f
th
e
PV
m
o
d
u
le.
T
h
ese
p
ar
am
eter
s
allo
w
th
e
s
im
u
lato
r
to
m
im
ic
th
e
b
eh
av
io
r
o
f
a
r
ea
l
s
o
lar
ar
r
ay
.
T
h
e
lo
ad
s
co
n
n
ec
ted
to
th
e
co
n
v
er
ter
o
u
tp
u
t
wer
e
r
h
eo
s
tats
,
w
h
ich
ca
n
b
e
ad
ju
s
ted
to
v
ar
y
t
h
e
lo
a
d
c
o
n
d
itio
n
s
an
d
ev
alu
ate
th
e
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
u
n
d
er
d
if
f
er
en
t
s
ce
n
ar
io
s
.
T
h
e
s
em
ico
n
d
u
cto
r
d
ev
ices e
m
p
lo
y
e
d
in
th
e
la
b
o
r
ato
r
y
p
r
o
to
ty
p
e
in
clu
d
e:
i)
Qu
ad
r
atic
an
d
b
i
-
d
ir
ec
tio
n
al
s
witch
es: I
R
FP
4
6
6
8
Pb
F
(
MO
SF
E
T
)
; ii)
Dio
d
e
f
o
r
PV
p
an
el,
Dp
v
: M
B
R
1
5
3
5
C
T
; a
n
d
iii)
Qu
ad
r
atic
-
d
i
o
d
e,
D:
R
HR
G3
0
1
2
0
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