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1.
I
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So
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p
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1
]
.
T
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tag
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[
2
]
,
[
3
]
.
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r
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q
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[
4
]
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B
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ap
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[
5
]
,
[
6
]
.
I
f
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to
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[
7
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,
[
8
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in
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I
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I
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P
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w
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&
Dr
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t
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Vo
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9
,
No
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4
,
Dec
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b
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2
0
1
8
:
1899
–
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1
1900
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o
u
g
h
p
er
io
d
is
u
n
ab
le
to
b
o
o
s
t
th
e
ca
p
ac
ito
r
v
o
ltag
e
at
th
e
i
m
p
ed
an
ce
n
et
w
o
r
k
m
o
r
e
th
a
n
th
e
r
eq
u
ir
ed
lev
el.
T
h
er
ef
o
r
e
,
th
is
ca
p
ac
ito
r
v
o
lta
g
e
co
n
tr
o
l
(
C
VC
)
f
o
r
Z
SI
i
s
ge
tti
n
g
a
lo
t
o
f
a
tten
tio
n
b
y
r
e
s
ea
r
ch
er
s
to
b
e
ca
r
r
ied
o
u
t r
ec
en
tl
y
.
Fo
r
e
x
a
m
p
le,
a
s
u
g
g
e
s
te
d
co
n
tr
o
ller
s
u
ch
as
tr
ad
itio
n
al
MP
PT
co
n
tr
o
ller
w
it
h
D
C
-
lin
k
co
n
tr
o
l
is
n
ee
d
e
d
in
o
r
d
er
to
p
r
o
d
u
ce
a
n
ad
d
itio
n
al
s
h
o
o
t
-
t
h
r
o
u
g
h
d
u
t
y
r
atio
a
n
d
to
i
m
p
r
o
v
e
t
h
e
r
esp
o
n
s
e
ti
m
e
o
f
MP
PT
co
n
tr
o
ller
s
as
h
a
v
e
b
ee
n
p
r
o
p
o
s
ed
in
[
9
]
,
[
1
0
]
.
P
ap
er
s
[
1
1
]
h
av
e
p
r
o
p
o
s
ed
a
u
n
i
f
ied
MP
PT
c
o
n
tr
o
l
s
tr
ateg
y
f
o
r
Z
S
I
b
ased
o
n
P
V
s
y
s
te
m
to
ac
h
ie
v
e
MP
PT
as
w
ell
a
s
Z
-
s
o
u
r
ce
ca
p
ac
ito
r
v
o
ltag
e
co
n
tr
o
l
at
th
e
m
ea
n
ti
m
e
.
A
m
o
d
if
ied
P
er
tu
r
b
an
d
O
b
s
er
v
e
(
P&
O)
tech
n
iq
u
e
h
a
s
b
ee
n
u
s
ed
f
o
r
th
e
MP
P
T
co
n
tr
o
l
a
n
d
th
e
C
VC
as
th
e
a
d
d
itio
n
al
co
n
tr
o
ll
er
.
T
h
is
m
o
d
if
ied
co
n
v
e
n
tio
n
al
alg
o
r
ith
m
s
ar
e
s
i
m
p
ler
,
les
s
co
m
p
lex
a
n
d
r
eq
u
ir
e
le
s
s
p
ar
am
eter
[
1
2
]
th
a
t
m
a
k
es
t
h
is
MP
PT
ca
n
b
e
i
m
p
le
m
en
ted
ea
s
i
l
y
i
n
to
Z
SI.
T
h
er
e
ar
e
th
r
ee
m
ai
n
f
ac
to
r
s
th
at
a
f
f
ec
t
t
h
e
e
f
f
icie
n
cies
o
f
a
P
V
p
lan
t
w
h
ic
h
a
r
e
t
h
e
in
v
er
ter
ef
f
icien
c
y
,
MP
PT
ef
f
icien
c
y
a
n
d
P
V
p
lan
t
ef
f
icie
n
c
y
.
T
h
e
ex
is
t
in
g
v
er
s
io
n
o
f
C
V
C
is
e
m
p
lo
y
ed
to
th
e
MP
PT
s
h
o
o
t
-
th
r
o
u
g
h
i
n
ter
v
al,
T
0
f
o
r
o
b
tain
in
g
t
h
e
to
tal
s
h
o
o
t
-
t
h
r
o
u
g
h
s
ta
tes,
T
sh
.
T
h
e
P
&
O
h
as
b
ee
n
u
s
ed
a
s
t
h
e
MP
PT
t
o
g
en
er
ate
th
e
m
i
n
i
m
u
m
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
,
T
0
i
n
o
r
d
er
to
ex
tr
ac
t
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
v
o
lta
g
e
f
r
o
m
t
h
e
P
V
m
o
d
u
le.
T
h
e
ex
tr
a
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
,
T
0
’
is
g
en
er
ated
b
y
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
co
n
tr
o
l
(
C
V
C
)
alg
o
r
ith
m
is
r
eq
u
ir
ed
to
in
cr
e
ase
th
e
Z
-
n
et
w
o
r
k
ca
p
ac
ito
r
v
o
ltag
e
at
t
h
e
P
V
p
an
el.
T
h
e
n
,
th
e
ex
tr
a
s
h
o
o
t
-
th
r
o
u
g
h
p
er
io
d
,
T
0
’
is
ad
d
ed
t
o
th
e
MP
PT
g
en
er
ated
s
h
o
o
t
-
th
r
o
u
g
h
i
n
ter
v
a
l,
T
0
in
o
r
d
er
to
o
b
tain
th
e
to
tal
s
h
o
o
t
-
th
r
o
u
g
h
s
tate
s
,
T
sh
as
s
h
o
w
n
in
Fi
g
u
r
e
2
(
a)
.
Ho
w
e
v
er
,
th
e
e
x
is
t
in
g
C
VC
a
lg
o
r
it
h
m
,
b
o
o
s
t
th
e
ca
p
ac
ito
r
v
o
ltag
e
to
a
g
r
ea
ter
ex
te
n
t
m
o
r
e
t
h
an
t
h
e
allo
w
ab
le
ex
tr
a
s
h
o
o
t
-
t
h
r
o
u
g
h
s
tate
w
o
u
ld
w
it
h
s
tan
d
i
n
w
h
ic
h
ca
u
s
ed
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
o
f
Z
-
s
o
u
r
ce
ca
n
n
o
t
b
e
co
n
s
tan
t
l
y
m
ai
n
tai
n
ed
.
A
s
a
r
es
u
lt,
all
t
h
e
s
y
s
te
m
ef
f
icien
c
y
e
s
p
ec
iall
y
,
f
o
r
t
h
e
i
n
v
er
ter
a
n
d
MP
PT
ef
f
icie
n
c
y
ar
e
be
en
af
f
ec
ted
.
He
n
ce
,
th
i
s
p
ap
er
in
tr
o
d
u
ce
s
an
i
m
p
r
o
v
ed
C
V
C
(i
-
C
VC
)
al
g
o
r
ith
m
b
y
ad
d
in
g
∓
∑
% o
f
ch
a
n
g
es (
Δ
T
0
’
)
in
s
h
o
o
t
-
th
r
o
u
g
h
d
u
t
y
r
atio
,
D
0
a
n
d
t
h
e
ad
d
itio
n
al
s
h
o
o
t
-
t
h
r
o
u
g
h
d
u
t
y
r
atio
,
D
0
’
in
o
r
d
er
to
in
cr
ea
s
e
th
e
ef
f
icie
n
c
y
o
f
t
h
e
w
h
o
le
P
V
s
y
s
te
m
.
T
h
e
D
0
ca
n
b
e
d
en
o
ted
as
T
0
/
T
an
d
D
0
’
is
eq
u
al
to
T
0
’
/T
as
illu
s
tr
ate
in
Fig
u
r
e
2
(
b
)
.
T
h
er
ef
o
r
e,
b
y
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in
g
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∑%
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f
ΔT
0
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to
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co
n
tr
o
ller
,
it
ca
n
r
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ce
t
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d
r
a
w
b
ac
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er
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(
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(
b
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Fig
u
r
e
2
.
Z
-
s
o
u
r
ce
I
n
v
er
ter
P
V
P
o
w
er
C
o
n
d
itio
n
i
n
g
S
y
s
te
m
C
o
n
tr
o
l B
lo
ck
Diag
r
a
m
(
a)
E
x
is
t
in
g
C
VC
Co
n
tr
o
ller
(
b
)
P
r
o
p
o
s
ed
C
VC
Co
n
tr
o
ller
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
P
r
o
p
o
s
ed
im
p
r
o
v
ed
C
V
C
alg
o
r
it
h
m
b
ased
MP
PT
in
Sectio
n
2
.
T
h
e
w
h
o
le
s
y
s
te
m
co
n
f
i
g
u
r
at
io
n
is
d
is
c
u
s
s
ed
in
Sectio
n
3
.
Sectio
n
4
co
m
p
r
is
ed
r
es
u
lt
o
f
s
i
m
u
latio
n
a
n
d
d
is
cu
s
s
io
n
,
f
o
llo
w
ed
b
y
co
n
cl
u
s
io
n
p
ar
t is
m
ad
e
in
Sectio
n
5
.
2.
P
RO
P
O
SE
D
CAP
AC
I
T
O
R
VO
L
T
A
G
E
CO
NT
RO
L
(
i
-
C
VC)
B
ASE
D
M
P
P
T
I
n
th
i
s
s
ec
t
io
n
,
t
h
e
d
ev
elo
p
m
en
t
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
w
ill
b
e
d
is
c
u
s
s
ed
.
Fo
r
a
s
o
lar
p
o
w
e
r
g
en
er
atio
n
s
y
s
te
m
,
th
e
MP
P
T
an
d
a
s
tab
le
o
u
tp
u
t
v
o
lta
g
e
a
r
e
t
w
o
m
ai
n
o
b
j
ec
tiv
es
o
f
th
e
s
y
s
te
m
i
n
o
r
d
er
to
ac
h
iev
e
h
ig
h
e
f
f
icie
n
c
y
o
u
tp
u
t
.
T
h
er
ef
o
r
e,
t
w
o
co
n
tr
o
l
v
a
r
iab
les
ar
e
in
v
o
lv
ed
i
n
Z
SI
w
h
ic
h
is
t
h
e
s
h
o
o
t
-
th
r
o
u
g
h
d
u
t
y
r
atio
an
d
t
h
e
m
o
d
u
latio
n
in
d
e
x
a
s
s
u
g
ested
f
r
o
m
[
1
3
]
th
a
t
n
ee
d
to
b
e
co
n
s
id
er
ed
.
T
h
er
ef
o
r
e,
i
-
C
VC
co
n
tr
o
l
s
ch
e
m
e
is
in
tr
o
d
u
ce
d
in
o
r
d
er
to
a
ch
iev
e
b
o
th
,
MPPT
an
d
v
o
ltag
e
co
n
tr
o
l
at
Z
-
n
et
w
o
r
k
a
s
w
e
ll
b
y
i
n
tr
o
d
u
ci
n
g
t
h
e
li
m
iter
b
o
u
n
d
ar
y
.
2
.
1
.
Co
ntr
o
l
Str
a
t
eg
y
Dev
elo
p
m
ent
T
h
e
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
(
T
0
)
is
g
e
n
er
ated
b
y
tr
ad
itio
n
al
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
b
ased
o
n
MP
PT
tech
n
iq
u
e
i
n
o
r
d
er
to
ex
tr
ac
t
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
v
o
lta
g
e
f
r
o
m
P
V
m
o
d
u
le
[
1
4
]
,
[
1
5
]
.
T
h
is
T
0
is
u
n
ab
le
to
b
o
o
s
t
th
e
ca
p
ac
ito
r
v
o
ltag
e
o
f
Z
-
n
et
w
o
r
k
f
u
r
t
h
e
r
th
an
th
e
d
esire
d
lev
el
d
u
e
t
o
th
e
u
n
co
n
tr
o
lled
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
o
f
Z
-
n
e
t
w
o
r
k
i
m
p
ed
an
ce
s
.
T
h
er
ef
o
r
e,
a
ca
p
ac
ito
r
v
o
ltag
e
co
n
tr
o
l
o
f
th
e
i
m
p
ed
an
ce
n
et
w
o
r
k
is
e
s
s
e
n
tial
i
n
o
r
d
er
to
co
n
tr
o
l
t
h
e
ca
p
ac
ito
r
v
o
lta
g
e
b
e
y
o
n
d
t
h
e
m
a
x
i
m
u
m
p
o
w
er
p
o
i
n
t
v
o
ltag
e.
I
t
n
ee
d
s
to
b
e
ca
lcu
lated
u
s
i
n
g
t
h
e
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
(
T
0
)
th
at
r
eq
u
ir
es
to
b
o
o
s
t
th
e
ca
p
ac
ito
r
v
o
ltag
e
to
th
e
MP
P
v
o
ltag
e
an
d
co
m
b
in
es
w
it
h
t
h
e
ad
d
itio
n
al
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
(
T
0
’
)
to
co
n
tr
o
l
th
e
ca
p
ac
ito
r
v
o
ltag
e
b
ey
o
n
d
th
e
MP
P
v
o
ltag
e.
Un
f
o
r
tu
n
atel
y
,
t
h
e
ad
d
itio
n
al
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
(
T
0
’
)
ha
s
s
o
m
e
d
r
a
w
b
ac
k
s
a
s
i
t
b
o
o
s
ts
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
to
a
g
r
ea
ter
ex
ten
t.
F
ig
u
r
e
3
s
h
o
w
s
t
h
e
g
en
er
atio
n
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
w
it
h
s
i
m
p
le
b
o
o
s
t
co
n
tr
o
l
m
eth
o
d
w
ith
t
wo
co
n
d
itio
n
s
o
f
b
o
u
n
d
ar
y
o
f
∆
T
0
’
w
h
ile
Fig
.
4
in
d
icate
s
th
e
co
n
tr
o
l
alg
o
r
ith
m
f
o
r
P
&
O
b
ased
MP
PT
w
it
h
e
m
b
en
d
ed
i
-
C
VC
m
ec
h
a
n
i
s
m
.
I
t
i
llu
s
tr
ates
t
h
at
,
t
w
o
r
e
f
er
en
ce
s
s
tr
aig
h
t
li
n
es
(
V
p
*
an
d
V
n
*
)
ar
e
co
n
tin
u
o
u
s
l
y
r
e
g
u
lated
to
m
ai
n
tai
n
Z
-
s
o
u
r
ce
ca
p
ac
ito
r
v
o
ltag
e
.
Fig
u
r
e
3
.
Sh
o
o
t th
r
o
u
g
h
g
e
n
er
atio
n
b
y
i
m
p
r
o
v
ed
C
VC
co
n
tr
o
l stra
teg
y
V
PV
=
V
C
=
V
C
*
T
sh
V
PV
=
V
C
V
C
*
V
PV
=
V
C
=
V
C
*
T
sh
T
0
T
0
'
Δ
T
0
'
V
P
*
V
N
*
V
c
ar
r
i
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1899
–
1
9
1
1
1902
T
h
e
n
e
w
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
(
T
sh
)
o
f
MPPT
co
n
tr
o
l
h
as
b
ee
n
s
y
n
ch
r
o
n
ized
w
it
h
i
m
p
r
o
v
ed
C
VC
alg
o
r
ith
m
a
n
d
ca
n
b
e
d
ef
in
ed
as f
o
llo
w
ed
:
'
0
0
0
%
'
T
T
T
T
sh
(
1
)
'
0
0
0
%
'
T
T
T
T
T
T
T
D
sh
sh
(
2
)
w
h
er
e
,
D
sh
ca
n
b
e
r
ef
er
r
ed
as
t
h
e
to
tal
s
h
o
o
t
-
t
h
r
o
u
g
h
d
u
t
y
r
at
io
an
d
i
s
eq
u
a
l to
T
sh
/T
.
(
T
0
)
is
u
s
ed
to
tr
ac
k
V
PV
*
b
y
ad
d
o
r
s
u
b
tr
ac
t
t
h
e
Δ
T
0
f
o
r
v
ar
io
u
s
c
li
m
ate
co
n
d
itio
n
at
th
e
P
V
i
n
p
u
t
,
w
h
ile
(
T
0
’
)
is
u
s
ed
to
co
n
tr
o
l
Z
-
s
o
u
r
ce
ca
p
ac
ito
r
v
o
ltag
e
ac
co
r
d
in
g
to
r
e
f
er
en
ce
ca
p
ac
ito
r
v
o
ltag
e,
V
C
*
.
A
t
th
e
m
ea
n
ti
m
e,
t
h
e
ad
d
itio
n
al
∓
∑%
ΔT
0
’
w
ill
tr
y
to
r
ed
u
ce
th
e
g
r
ea
ter
ex
ten
t
v
o
lta
g
e
o
cc
u
r
s
w
h
i
le
b
o
o
s
tin
g
th
e
ca
p
ac
ito
r
v
o
ltag
e
at
Z
-
n
et
w
o
r
k
b
y
(T
0
’
)
t
o
th
e
r
ef
er
en
ce
v
al
u
e.
As th
e
r
e
s
u
l
t
,
th
e
ca
p
ac
ito
r
v
o
lta
g
e
w
ill b
e
co
n
tr
o
lled
an
d
ab
le
to
m
ai
n
tai
n
th
e
D
C
lin
k
v
o
lta
g
e
as
w
e
ll.
T
h
e
r
an
g
e
o
f
th
e
n
e
w
s
h
o
o
t
-
t
h
r
o
u
g
h
ti
m
e
p
er
io
d
(
T
sh
)
,
ca
n
b
e
w
r
itte
n
as
s
u
g
g
ested
b
y
th
e
au
th
o
r
s
to
:
M
T
T
T
sh
1
%
'
0
,
(
3
)
w
h
er
e
,
M
is
t
h
e
m
o
d
u
latio
n
i
n
d
ex
.
Fro
m
eq
u
atio
n
s
(
1
)
an
d
(
3
)
th
e
f
o
llo
w
in
g
m
o
d
i
f
ied
eq
u
atio
n
is
o
b
tain
ed
:
T
T
M
T
T
T
0
'
0
'
0
1
%
.
(
4
)
T
h
er
ef
o
r
e,
th
e
m
a
x
i
m
u
m
v
al
u
e
o
f
th
e
ad
d
itio
n
a
l
s
h
o
o
t
-
t
h
r
o
u
g
h
d
u
t
y
r
atio
f
o
r
b
o
th
ca
s
e
s
ca
n
b
e
w
r
it
ten
a
s
f
o
llo
w
ed
:
T
T
M
T
T
T
0
m
a
x
'
0
'
0
1
%
w
h
e
n
V
C
*
>
V
C
,
(
5
)
T
T
M
T
T
T
0
m
a
x
'
0
'
0
1
%
w
h
en
V
C
*
<V
C
.
(
6
)
Mo
r
eo
v
er
,
th
e
m
o
d
u
la
tio
n
i
n
d
ex
(
M)
an
d
th
e
MP
P
T
s
h
o
o
t
-
t
h
r
o
u
g
h
r
atio
(
D
0
)
is
u
s
ed
to
li
m
it
t
h
e
r
an
g
e
o
f
t
h
e
ad
d
itio
n
a
l
s
h
o
o
t
-
th
r
o
u
g
h
d
u
t
y
r
atio
(
D
0
’
)
co
m
b
in
es
w
i
th
∓
∑
%
Δ
T
0
’
an
d
h
e
n
ce
ac
h
iev
e
t
h
e
Z
-
s
o
u
r
ce
ca
p
ac
ito
r
v
o
ltag
e
co
n
t
r
o
l.
T
w
o
co
n
s
tan
t
r
e
f
er
en
ce
s
ar
e
em
p
lo
y
ed
to
r
ea
lize
th
e
n
e
w
s
h
o
o
t
-
t
h
r
o
u
g
h
p
er
io
d
w
h
er
e
n
o
w
b
e
eq
u
al
to
:
'
0
'
0
*
%
1
%
1
T
D
T
T
T
V
sh
sh
P
(
7
)
*
'
0
*
%
1
P
sh
N
V
T
T
T
V
.
(
8
)
T
h
ese
t
w
o
eq
u
atio
n
s
ar
e
co
m
p
ar
ed
w
i
th
h
ig
h
-
f
r
eq
u
en
c
y
ca
r
r
ier
s
ig
n
al
i
n
o
r
d
er
to
g
en
er
ate
th
e
s
h
o
o
t
-
th
r
o
u
g
h
p
u
ls
e.
T
h
en
,
t
h
e
D
C
l
in
k
v
o
lta
g
e
o
r
th
e
ca
p
ac
ito
r
v
o
ltag
e
ca
n
b
e
i
m
p
r
o
v
ed
u
n
til
i
t
r
ea
ch
es
t
h
e
MP
P
v
o
ltag
e
o
f
th
e
P
V
m
o
d
u
le
(
V
PV
*
)
a
n
d
t
h
u
s
,
ab
le
ex
tr
ac
t a
m
a
x
i
m
u
m
p
o
w
e
r
f
r
o
m
P
V
m
o
d
u
l
e.
At
t
h
e
m
e
n
ati
m
e,
t
h
e
av
er
a
g
e
DC
li
n
k
v
o
lta
g
e
o
f
th
e
i
n
v
er
ter
ca
n
b
e
ex
p
r
ess
ed
as
:
*
'
0
'
0
%
2
1
%
1
PV
sh
sh
C
dc
V
T
D
T
D
V
v
.
(
9
)
On
t
h
e
A
C
s
id
e,
th
e
o
u
tp
u
t p
ea
k
v
o
lta
g
e
f
r
o
m
th
e
i
n
v
er
ter
ca
n
b
e
d
ef
in
e
d
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
i
-
C
a
p
a
cito
r
V
o
lta
g
e
C
o
n
tr
o
l f
o
r
P
V
Z
-
s
o
u
r
ce
S
ystem
w
ith
E
n
h
a
n
ce
d
…
(
N
o
o
r
Ma
z
liz
a
B
a
d
r
u
l S
h
a
m
)
1903
2
2
%
2
1
%
1
ˆ
*
'
0
'
0
dc
PV
sh
sh
ac
v
M
V
T
D
T
D
M
v
.
(
1
0
)
T
h
e
m
o
d
u
lat
io
n
in
d
e
x
ca
n
b
e
co
n
tr
o
lled
f
r
o
m
ze
r
o
to
V
p
*
.
I
n
th
e
m
ea
n
t
i
m
e,
t
h
e
s
h
o
o
t
-
th
r
o
u
g
h
s
tate
s
ca
n
b
e
ap
p
lied
to
all
o
f
th
e
leg
s
s
i
m
u
lta
n
eo
u
s
l
y
w
h
e
n
ev
er
t
h
e
tr
ian
g
u
lar
ca
r
r
ier
s
i
g
n
a
l is
h
i
g
h
er
t
h
a
n
t
h
e
V
p
*
o
r
lo
w
er
th
a
n
t
h
e
V
n
*
.
Fi
g
u
r
e
4
s
h
o
w
s
P
&
O
b
ased
MP
PT
alg
o
r
ith
m
w
it
h
i
m
p
r
o
v
ed
C
VC
al
g
o
r
ith
m
.
No
No
No
No
No
No
Y
e
s
Y
e
s
Y
e
s
Y
e
s
Y
e
s
Y
e
s
B
e
gi
n
R
e
a
d V
pv
,
I
pv
,
V
c
a
nd V
c
*
C
om
put
e
P
pv
Δ
P
pv
=
P
pv
(
t
)
-
P
pv
(
t
-
1
)
Δ
P
pv
>
0
V
pv
(
t
)
>
V
pv
(
t
-
1
)
V
pv
(
t
)
>
V
pv
(
t
-
1
)
T
0
=
T
-
Δ
T
0
T
0
=
T
+
Δ
T
0
T
0
=
T
+
Δ
T
0
T
0
=
T
-
Δ
T
0
V
pv
*=[
(
1
-
T
0
)
/
(
1
-
2
T
0
)
]
*
V
pv
Vc
=
V
pv
*
Vc
=
Vc
*
Vc
*
>
Vc
Eq
.
1
or
E
q
.
2
w
i
t
h
i
nc
r
e
a
s
e
of
%
Δ
T
0
'
T
sh
=
T
0
;
Δ
T
0
'
=
0
E
nd
M
P
P
T
A
l
gor
i
t
hm
I
m
pr
ov
e
d
C
V
C
A
l
gor
i
t
hm
Eq
.
1
or
E
q
.
2
w
i
t
h
de
c
r
e
a
s
e
of
%
Δ
T
0
'
Fig
u
r
e
4
.
P
&
O
B
ased
MPPT
A
l
g
o
r
ith
m
w
i
th
I
m
p
r
o
v
ed
C
V
C
A
lg
o
r
it
h
m
2
.
2
.
Co
m
p
uta
t
io
n o
f
∓
∑% ΔT
0
’
in
i
-
CVC
Alg
o
rit
h
m
I
n
th
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(
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5
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ill
i
n
cr
ea
s
e
t
h
e
ef
f
ec
ti
v
e
n
e
s
s
o
f
t
h
e
w
h
o
le
P
V
s
y
s
te
m
s
h
o
w
n
i
n
S
ec
tio
n
4
.
3.
SYST
E
M
CO
NF
I
G
URA
T
I
O
N
I
n
th
i
s
s
ec
tio
n
,
t
h
e
w
h
o
le
s
y
s
t
e
m
co
n
f
ig
u
r
atio
n
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
alg
o
r
ith
m
f
o
r
Z
SI
-
b
ased
P
V
s
y
s
te
m
w
il
l
b
e
p
r
o
v
id
ed
.
T
h
e
P
V
m
o
d
u
le
is
th
e
i
n
p
u
t
to
t
h
e
s
y
s
te
m
w
h
i
le
t
h
e
Z
-
s
o
u
r
ce
i
n
v
er
ter
is
t
h
e
p
o
w
er
co
n
v
er
ter
to
p
o
lo
g
y
th
a
t
eq
u
ip
p
e
s
w
it
h
a
n
i
m
p
r
o
v
ed
MP
PT
-
C
VC
co
n
tr
o
ller
.
T
h
is
co
n
tr
o
ller
is
u
s
ed
to
o
b
tai
n
th
e
v
o
ltag
e
r
esp
o
n
d
b
y
th
e
P
V
m
o
d
u
le
i
n
o
r
d
er
to
ac
h
iev
e
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t.
T
h
e
b
asic
P
er
tu
r
b
an
d
Ob
s
er
v
e
(
P
&
O)
alg
o
r
it
h
m
f
o
r
a
s
tan
d
alo
n
e
s
y
s
te
m
[
1
6
]
is
u
s
ed
i
n
Z
SI
w
it
h
a
co
m
b
i
n
atio
n
o
f
Z
-
s
o
u
r
ce
i
m
p
r
o
v
ed
ca
p
ac
ito
r
v
o
l
tag
e
co
n
tr
o
l.
A
t
t
h
e
e
n
d
,
th
e
C
V
C
is
ab
le
to
b
o
o
s
t
th
e
ca
p
ac
ito
r
v
o
ltag
e
at
i
m
p
ed
a
n
ce
n
et
w
o
r
k
to
b
e
t
w
ice
is
p
o
s
s
ib
l
e
o
r
m
o
r
e
th
a
n
th
e
d
esire
d
lev
el
at
DC
li
n
k
ter
m
i
n
al
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
i
-
C
a
p
a
cito
r
V
o
lta
g
e
C
o
n
tr
o
l f
o
r
P
V
Z
-
s
o
u
r
ce
S
ystem
w
ith
E
n
h
a
n
ce
d
…
(
N
o
o
r
Ma
z
liz
a
B
a
d
r
u
l S
h
a
m
)
1905
3
.
1
.
Sin
g
le
-
s
t
a
g
e
P
V
C
o
nv
er
s
io
n Sy
s
t
e
m
f
o
r
Z
-
s
o
urce
In
v
er
t
er
As
k
n
o
w
n
,
th
e
P
V
i
s
a
n
o
n
-
li
n
ea
r
cu
r
r
en
t
-
v
o
lta
g
e
a
n
d
p
o
wer
-
v
o
lta
g
e
c
h
ar
ac
ter
is
tic
is
co
n
ti
n
u
o
u
s
l
y
v
ar
ie
d
w
it
h
te
m
p
er
at
u
r
e
a
n
d
ir
r
ad
ian
ce
.
T
h
e
P
V
m
o
d
el
h
as
b
ee
n
d
ev
elo
p
ed
u
s
in
g
t
h
e
b
as
ic
cir
cu
it
eq
u
a
tio
n
o
f
th
e
s
o
lar
ce
lls
.
Her
e,
t
h
e
MS
X
-
6
0
p
o
l
y
-
cr
y
s
talli
n
e
s
ilico
n
P
V
m
o
d
u
le
p
ar
a
m
eter
s
ar
e
u
s
ed
as
i
n
p
u
t
in
to
th
e
P
V
s
y
s
te
m
eq
u
atio
n
s
w
h
ich
d
escr
ib
ed
th
e
cu
r
r
en
t
o
u
tp
u
t
o
f
th
e
P
V
s
o
lar
.
I
d
ea
lly
,
co
n
tin
u
o
u
s
v
ar
y
in
g
m
ax
i
m
u
m
p
o
w
er
p
o
in
t o
f
t
h
e
s
o
lar
P
V
m
o
d
u
le
i
s
b
ein
g
tr
ac
k
ed
u
s
i
n
g
MP
PT
co
n
tr
o
l te
ch
n
iq
u
e.
A
Z
-
s
o
u
r
ce
in
v
er
ter
p
la
y
s
a
n
i
m
p
o
r
ta
n
t
p
ar
t
in
o
r
d
er
to
in
c
r
ea
s
e
d
c
v
o
ltag
e
o
u
tp
u
t
a
n
d
as
t
h
e
DC
-
AC
co
n
v
er
s
io
n
i
n
a
s
in
g
le
s
ta
g
e
t
h
at
i
s
n
o
t
a
v
ailab
le
in
tr
ad
iti
o
n
al
P
V
p
o
w
er
co
n
d
itio
n
i
n
g
s
y
s
te
m
.
T
h
e
Z
SI
is
co
m
p
o
s
ed
o
f
s
p
lit
-
i
n
d
u
cto
r
s
L
1
&
L
2
a
n
d
ca
p
ac
ito
r
s
C
1
&
C
2
w
h
ic
h
ar
e
b
ee
n
co
n
n
ec
ted
i
n
cr
o
s
s
-
s
h
ap
e
[
1
7
]
.
T
h
e
in
d
u
cto
r
s
ar
e
u
s
ed
to
r
eg
u
late
t
h
e
cu
r
r
e
n
t
r
ip
p
les
an
d
r
ed
u
ce
s
h
ar
m
o
n
ic
s
w
h
ile
t
h
e
t
w
o
ca
p
ac
ito
r
s
ar
e
u
s
ed
to
r
eg
u
la
te
v
o
lta
g
e
r
ip
p
les
an
d
p
r
o
d
u
ce
p
u
r
e
d
c
at
th
e
in
v
er
ter
i
n
p
u
t.
T
h
e
Z
SI
h
as
t
h
r
ee
o
p
er
atio
n
m
o
d
es
s
h
o
w
n
in
F
ig
.
5
:
ac
ti
v
e
m
o
d
e,
s
h
o
o
t
-
t
h
r
o
u
g
h
m
o
d
e,
an
d
tr
ad
itio
n
al
ze
r
o
-
s
tate
m
o
d
e
[
1
8
]
.
Du
r
in
g
ac
ti
v
e
an
d
ze
r
o
-
s
tate
m
o
d
e
,
t
h
e
Z
SI
o
p
er
ates
u
n
d
er
th
e
tr
ad
itio
n
al
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
W
M)
p
atter
n
.
I
n
t
h
e
s
h
o
o
t
-
th
r
o
u
g
h
m
o
d
e,
th
e
in
v
er
ter
b
r
id
g
e
is
s
ee
n
as a
s
h
o
r
t c
ir
cu
it
f
r
o
m
t
h
e
D
C
-
lin
k
p
o
in
t o
f
v
ie
w
[
1
9
]
.
(
a)
(
b
)
Fig
u
r
e
5
.
Op
er
ati
ng
Mo
d
es o
f
Z
SI.
(
a)
Du
r
in
g
No
n
-
s
h
o
o
t
-
th
r
o
u
g
h
(
b
)
Du
r
in
g
Sh
oot
-
t
h
r
o
u
g
h
T
h
en
th
e
DC
ca
p
ac
ito
r
v
o
lta
g
e
ca
n
b
e
b
o
o
s
ted
as
,
*
2
1
1
PV
PV
sh
sh
C
dc
V
V
D
D
V
v
.
(
1
5
)
D
sh
is
th
e
n
et
s
h
o
o
t
-
t
h
r
o
u
g
h
d
u
t
y
r
atio
o
b
tain
ed
af
ter
b
o
o
s
tin
g
th
e
ca
p
ac
ito
r
v
o
lta
g
e
to
th
e
d
esire
d
lev
el.
3
.
2
.
Select
iv
e
o
f
Z
-
net
w
o
rk
P
a
r
a
m
et
er
T
h
e
m
o
s
t
c
h
alle
n
g
in
g
i
n
d
esig
n
i
n
g
t
h
e
Z
SI
cir
c
u
itr
y
i
s
th
e
esti
m
at
io
n
o
f
v
al
u
es
f
o
r
r
ea
ctiv
e
co
m
p
o
n
e
n
t
s
in
i
m
p
ed
a
n
ce
n
et
w
o
r
k
.
D
u
r
in
g
th
e
s
h
o
o
t
-
th
r
o
u
g
h
ti
m
e,
t
h
e
Z
-
s
o
u
r
ce
in
d
u
cto
r
cu
r
r
e
n
t
w
ill
d
is
ch
ar
g
e
t
h
e
ca
p
ac
ito
r
v
o
lt
ag
e
[
2
0
]
,
th
er
ef
o
r
e
,
t
h
e
r
ip
p
le
a
m
p
lit
u
d
e
o
f
t
h
e
ca
p
ac
it
o
r
v
o
ltag
e
ca
n
b
e
ex
p
r
ess
ed
as
,
C
f
I
D
V
L
C
0
0
(
1
6
)
an
d
b
y
r
ea
r
r
an
g
ed
eq
u
atio
n
1
6
,
it g
iv
e
s
C
L
V
f
I
D
C
0
0
.
(
1
7
)
T
h
e
m
a
x
i
m
u
m
c
u
r
r
en
t
th
r
o
u
g
h
th
e
i
n
d
u
cto
r
o
cc
u
r
s
w
h
e
n
th
e
m
a
x
i
m
u
m
s
h
o
o
t
-
th
r
o
u
g
h
h
a
p
p
en
s
.
T
h
is
w
il
l
ca
u
s
e
a
h
ig
h
cu
r
r
e
n
t
r
ip
p
le
to
th
e
Z
-
s
o
u
r
ce
i
n
d
u
cto
r
.
I
n
th
i
s
d
esig
n
,
6
0
%
o
f
p
ea
k
-
to
-
p
ea
k
cu
r
r
e
n
t
r
ip
p
le
th
r
o
u
g
h
th
e
Z
-
n
et
w
o
r
k
in
d
u
ct
o
r
d
u
r
in
g
m
a
x
i
m
u
m
p
o
w
er
o
p
er
a
tio
n
is
b
ee
n
ch
o
s
e
n
.
Fo
r
t
h
e
d
esi
g
n
in
g
o
f
Z
-
n
et
w
o
r
k
in
d
u
cto
r
v
a
lu
e,
a
co
n
s
ta
n
t
ca
p
ac
ito
r
v
o
lta
g
e,
V
C
a
n
d
t
h
e
r
ip
p
le
c
u
r
r
en
t
n
ee
d
to
b
e
co
n
s
id
er
ed
.
T
h
e
r
ip
p
le
am
p
lit
u
d
e
o
f
th
e
i
n
d
u
c
t
o
r
cu
r
r
en
t is g
i
v
e
n
as
,
L
f
V
D
I
C
L
0
0
.
(
1
8
)
L
1
L
2
C
1
C
2
V
pv
S
st
D
V
dc
L
2
L
1
C
1
C
2
V
pv
S
st
D
V
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1899
–
1
9
1
1
1906
Fro
m
E
q
u
atio
n
18
,
th
e
i
n
d
u
cta
n
ce
can
b
e
ca
lcu
la
ted
as
L
C
I
f
V
D
L
0
0
.
(
1
9
)
T
h
er
ef
o
r
e,
all
th
e
p
ar
a
m
eter
s
ar
e
b
ein
g
o
b
tain
ed
s
i
m
u
lt
an
eo
u
s
l
y
.
T
h
e
Z
-
n
et
w
o
r
k
i
n
d
u
ctan
ce
,
L
1
=L
2
=L
=8
7
0
µH
w
h
ile
t
h
e
f
o
r
th
e
ca
p
ac
itan
ce
,
C
1
=
C
2
=
C
=2
0
0
0
µF
an
d
ca
p
ac
itiv
e
v
alu
e
o
f
P
V
o
u
tp
u
t
v
o
ltag
e,
C
PV
=
1
0
0
0
µF.
Her
e,
t
h
e
r
en
o
n
a
n
t
cir
cu
it
r
eq
u
ir
ed
a
r
eso
n
an
t
ca
p
ac
itan
ce
,
C
r
=
1
0
0
0
µF
w
it
h
1
0
Ω
r
esis
ti
v
e
lo
ad
.
Fo
r
∓
∑
%
o
f
d
elta
s
h
o
o
t
-
t
h
r
o
u
g
h
,
Δ
T
0
’
r
eq
u
ir
ed
in
th
i
s
s
i
m
u
latio
n
tes
t
an
d
ap
p
licab
le
in
th
i
s
Z
SI
-
P
V
s
y
s
te
m
is
ab
o
u
t
12%
.
3
.
3
.
Co
ntr
o
ller
Desi
g
n P
a
ra
m
et
er
f
o
r
Vo
lt
a
g
e
Co
ntr
o
l
As
f
o
r
th
e
b
r
id
g
e
in
v
er
ter
co
n
tr
o
l,
tak
in
g
t
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
s
in
g
le
-
p
h
ase
i
n
v
er
ter
as
a
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
,
v
ac
an
d
b
ee
n
c
o
m
b
i
n
ed
w
ith
t
h
e
L
C
f
i
lter
d
esig
n
to
o
b
tain
th
e
eq
u
iv
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