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k
v
o
ltag
e
at
its
r
ef
er
en
ce
v
alu
e
b
y
r
eg
u
latin
g
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
wer
[
1
1
]
.
Usi
n
g
a
s
y
n
ch
r
o
n
o
u
s
d
–
q
r
e
f
er
en
ce
f
r
am
e
with
Par
k
tr
an
s
f
o
r
m
atio
n
,
th
e
VOC
m
e
th
o
d
s
y
n
ch
r
o
n
izes
th
e
in
v
e
r
ter
o
u
tp
u
t
with
th
e
g
r
id
[
1
2
]
.
Alig
n
in
g
th
e
g
r
id
v
o
ltag
e
v
ec
t
o
r
alo
n
g
t
h
e
d
-
ax
is
allo
ws
in
d
ep
en
d
en
t
co
n
tr
o
l
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
c
u
r
r
e
n
ts
,
en
s
u
r
in
g
u
n
ity
p
o
wer
f
ac
to
r
an
d
s
tab
le
o
p
er
at
io
n
[
1
3
]
,
[
1
4
]
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
p
ap
er
is
as
f
o
llo
ws:
i)
T
h
e
m
o
tiv
atio
n
an
d
b
ac
k
d
r
o
p
ar
e
p
r
esen
te
d
in
Sectio
n
1
;
ii)
Sectio
n
2
e
x
p
lain
s
th
e
d
esig
n
o
f
th
e
p
ar
tial
p
o
wer
p
r
o
ce
s
s
in
g
u
tili
zin
g
a
h
alf
-
b
r
id
g
e
L
L
C
r
eso
n
a
n
t
co
n
v
er
ter
an
d
th
e
MPPT
alg
o
r
ith
m
;
iii)
Sectio
n
3
d
etails
th
e
co
n
tr
o
l
s
tr
ateg
y
f
o
r
th
e
v
o
lt
ag
e
-
o
r
ien
te
d
co
n
t
r
o
l
in
v
er
ter
co
n
n
ec
ted
to
th
e
g
r
id
;
iv
)
Sectio
n
4
p
r
esen
ts
s
im
u
latio
n
r
esu
lts
u
n
d
er
v
ar
y
in
g
ir
r
ad
ian
ce
co
n
d
itio
n
s
,
v
er
if
y
in
g
s
o
f
t
-
s
witch
in
g
,
MPPT
ef
f
ec
tiv
e
n
ess
,
an
d
g
r
id
s
y
n
c
h
r
o
n
izatio
n
;
an
d
v
)
Sectio
n
5
co
n
clu
d
es
with
k
ey
f
in
d
in
g
s
an
d
p
er
f
o
r
m
a
n
ce
h
ig
h
lig
h
ts
.
(
a
)
(
b
)
Fig
u
r
e
1
.
PV
in
v
e
r
ter
co
n
f
ig
u
r
atio
n
s
:
(
a)
s
in
g
le
-
s
tag
e
an
d
(
b
)
two
-
s
tag
e
2.
P
ARTI
A
L
P
O
W
E
R
CO
NV
E
RT
E
R
AN
D
M
P
P
T
A
L
G
O
RIT
H
M
I
n
a
f
u
ll
p
o
w
er
c
o
n
v
er
t
e
r
(
FP
C
)
s
y
s
te
m
,
b
o
t
h
th
e
DC
-
DC
an
d
DC
-
AC
co
n
v
e
r
t
er
s
ta
g
es
h
a
n
d
le
t
h
e
wh
o
le
p
o
we
r
P
V
s
y
s
te
m
th
at
d
eli
v
e
r
s
el
ec
t
r
i
cit
y
to
t
h
e
g
r
i
d
[
1
5
]
.
H
o
w
e
v
e
r
,
t
h
e
a
d
d
iti
o
n
al
s
t
a
g
e
i
n
tr
o
d
u
c
es
ex
t
r
a
c
o
n
d
u
cti
o
n
,
s
wit
ch
in
g
,
a
n
d
m
a
g
n
eti
c
l
o
s
s
es
,
w
h
i
c
h
r
e
d
u
c
e
t
h
e
e
f
f
ici
en
c
y
o
f
t
h
e
co
n
v
er
t
er
al
o
n
g
wi
th
t
h
e
p
o
we
r
h
a
n
d
li
n
g
ca
p
a
cit
y
o
f
ea
ch
c
o
n
v
er
te
r
.
Pa
r
ti
al
-
p
o
we
r
p
r
o
c
ess
i
n
g
(
PP
P)
o
p
er
ates
o
n
t
h
e
p
r
in
ci
p
le
t
h
a
t
o
n
l
y
a
f
r
a
cti
o
n
o
f
t
h
e
t
o
t
al
p
o
we
r
is
m
a
n
a
g
ed
b
y
a
DC
-
DC
c
o
n
v
e
r
t
er
,
w
h
e
r
e
as
t
h
e
m
aj
o
r
it
y
o
f
e
n
e
r
g
y
t
r
a
n
s
f
e
r
s
d
i
r
e
ctl
y
f
r
o
m
t
h
e
s
o
u
r
ce
t
o
t
h
e
o
u
tp
u
t
w
it
h
o
u
t
u
n
d
er
g
o
i
n
g
p
r
o
c
ess
i
n
g
[
1
6
]
.
I
n
a
s
e
r
ies
-
c
o
n
n
ec
t
ed
p
a
r
ti
al
-
p
o
w
e
r
co
n
v
e
r
te
r
(
S
-
PP
C
)
,
t
h
e
i
n
p
u
t s
o
u
r
ce
a
n
d
t
h
e
DC
-
DC
c
o
n
v
er
t
er
'
s
o
u
t
p
u
t
ar
e
co
n
n
e
cte
d
i
n
s
er
ies
[
1
7
]
,
[
1
8
]
.
Fo
r
th
e
S
-
PP
C
co
n
v
er
ter
,
an
i
s
o
lated
DC
-
DC
co
n
v
er
ter
s
er
v
es
as
a
f
u
n
d
am
en
tal
cir
c
u
it
c
o
m
p
o
n
en
t
an
d
is
c
u
s
to
m
ized
f
o
r
its
s
p
ec
if
ic
o
p
er
atio
n
al
r
e
q
u
ir
em
e
n
t
s
.
R
eso
n
an
t
co
n
v
er
ter
s
b
ased
o
n
h
ig
h
-
f
r
e
q
u
en
c
y
tr
an
s
f
o
r
m
er
s
d
eliv
er
en
h
a
n
ce
d
ef
f
icien
cy
ac
r
o
s
s
a
b
r
o
ad
s
p
ec
tr
u
m
o
f
l
o
ad
s
an
d
o
f
f
er
g
alv
a
n
ic
is
o
latio
n
,
wh
ich
m
ak
es it h
ig
h
ly
s
u
itab
le
f
o
r
th
e
PP
C
to
p
o
lo
g
ies [
1
9
]
.
T
h
e
o
u
tp
u
t v
o
ltag
e
o
f
th
e
r
eso
n
an
t c
o
n
v
er
ter
is
r
eg
u
lated
b
y
ad
ju
s
tin
g
its
s
witch
in
g
f
r
eq
u
en
cy
.
S
o
f
t
-
s
w
it
c
h
e
d
r
es
o
n
an
t
c
o
n
v
e
r
t
e
r
s
t
y
p
i
c
a
ll
y
o
f
f
e
r
im
p
r
o
v
e
d
e
f
f
i
c
i
e
n
c
y
c
o
m
p
a
r
e
d
t
o
h
a
r
d
-
s
w
i
t
c
h
e
d
DC
/
DC
t
o
p
o
l
o
g
i
es
,
a
n
d
t
h
e
a
v
a
i
la
b
i
l
i
t
y
o
f
g
a
l
v
a
n
i
c
is
o
l
at
i
o
n
e
n
a
b
l
e
s
t
h
e
h
a
l
f
-
b
r
i
d
g
e
s
e
r
i
es
L
L
C
t
o
b
e
p
a
r
t
i
c
u
l
a
r
l
y
w
e
l
l
-
s
u
i
t
e
d
f
o
r
S
-
PP
C
t
o
p
o
l
o
g
i
e
s
.
Z
V
S
a
n
d
Z
C
S
t
e
c
h
n
i
q
u
es
r
e
d
u
c
e
t
h
e
s
w
it
c
h
i
n
g
l
o
s
s
e
s
o
f
L
L
C
r
e
s
o
n
a
n
t
c
o
n
v
e
r
t
e
r
s
,
t
h
e
r
e
b
y
e
n
h
a
n
c
i
n
g
DC
/
DC
c
o
n
v
e
r
t
e
r
s
t
a
g
e
e
f
f
i
c
i
e
n
c
y
[
2
0
]
.
2
.
1
.
P
ro
po
s
ed
DC/DC
co
nv
er
t
er
T
h
e
p
r
o
p
o
s
ed
s
tr
u
ctu
r
e
o
f
t
wo
-
s
tag
e
PV
s
y
s
tem
s
m
ain
ly
co
n
s
is
ts
o
f
a
h
al
f
-
b
r
i
d
g
e
s
er
ies
L
L
C
r
eso
n
an
t
co
n
v
er
ter
alo
n
g
with
PP
C
to
p
o
lo
g
y
in
th
e
DC
/DC
s
tag
e.
T
h
e
in
p
u
t
is
co
n
n
ec
te
d
in
s
er
ies
with
th
e
s
ec
o
n
d
ar
y
s
id
e
o
f
th
e
HB
s
er
ies
L
L
C
r
eso
n
an
t
co
n
v
er
ter
f
o
r
th
e
d
ev
elo
p
m
en
t
o
f
PP
C
.
T
h
e
L
L
C
r
eso
n
a
n
t
co
n
v
er
ter
h
as
a
r
eso
n
an
t
ta
n
k
co
n
s
is
tin
g
o
f
C
r
an
d
L
r
,
t
h
e
p
r
im
ar
y
r
eso
n
an
t
ca
p
ac
ito
r
an
d
p
r
im
ar
y
r
eso
n
a
n
t
in
d
u
cto
r
,
r
esp
ec
tiv
ely
,
an
d
L
m
,
th
e
m
ag
n
etizin
g
in
d
u
cto
r
.
I
n
an
L
L
C
r
eso
n
an
t
c
o
n
v
er
ter
,
th
e
r
eso
n
a
n
t
f
r
eq
u
e
n
cy
f
r
o
f
th
e
r
eso
n
an
t ta
n
k
is
d
eter
m
in
e
d
b
y
(
1
)
.
=
1
2
√
(
1
)
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
.
2
,
J
u
n
e
20
2
6
:
1
1
3
0
-
1141
1132
Vo
ltag
e
g
ain
(
G
LLC
)
o
f
th
e
L
L
C
r
eso
n
an
t
tan
k
d
e
p
en
d
s
o
n
th
e
q
u
ality
f
ac
t
o
r
(
Q
e
)
,
r
atio
o
f
en
tire
p
r
im
ar
y
i
n
d
u
ctan
ce
to
r
eso
n
a
n
t
in
d
u
ctan
ce
(
m
)
,
a
n
d
r
atio
o
f
s
witch
in
g
f
r
e
q
u
en
c
y
to
n
o
r
m
alize
d
r
eso
n
an
t
f
r
eq
u
e
n
cy
(
f
n
)
.
=
2
(
−
1
)
√
(
2
−
1
)
2
+
2
.
(
2
−
1
)
2
.
(
−
1
)
2
.
2
(
2
)
=
√
⁄
(
3
)
=
+
(
4
)
=
(
5
)
Kir
ch
h
o
f
f
'
s
laws
ar
e
ap
p
lied
to
th
e
S
-
PP
C
co
n
f
ig
u
r
atio
n
,
as
s
h
o
wn
in
Fig
u
r
e
2
,
to
d
et
er
m
in
e
th
e
v
o
ltag
e
g
ain
o
f
th
e
p
r
o
p
o
s
ed
co
n
v
er
ter
.
T
h
e
p
o
r
tio
n
o
f
a
ctiv
e
p
o
wer
h
a
n
d
led
b
y
th
e
DC
-
DC
co
n
v
er
ter
co
m
p
ar
ed
with
th
e
s
o
u
r
ce
in
p
u
t p
o
wer
to
th
e
DC
-
DC
s
tag
e
is
k
n
o
wn
as th
e
p
a
r
tial p
o
wer
r
atio
(
K
pr
)
as (
6
)
.
=
(
6
)
W
h
er
e
V
pv
:
PV
ar
r
ay
o
u
tp
u
t
v
o
ltag
e
,
I
conv
:
c
o
n
v
e
r
ter
o
u
t
p
u
t
cu
r
r
en
t
,
I
in
:
PV
ar
r
a
y
o
u
tp
u
t
cu
r
r
en
t
,
a
n
d
n
=
tr
an
s
f
o
r
m
er
r
atio
.
T
h
e
HB
-
L
L
C
s
er
ies r
eso
n
an
t c
o
n
v
er
ter
v
o
ltag
e
g
ain
G
conv
ca
n
b
e
ex
p
r
ess
ed
as
(
7
)
.
=
2
(
7
)
T
h
e
p
r
o
p
o
s
ed
c
o
n
v
er
te
r
v
o
ltag
e
g
ain
ca
n
b
e
wr
itten
as
(
8
)
.
−
=
2
(
8
)
T
h
e
v
o
ltag
e
g
ain
o
f
th
e
to
tal
D
C
-
DC
co
n
v
er
ter
s
tag
e,
th
e
g
l
o
b
al
g
ain
,
G
v
ca
n
b
e
ex
p
r
ess
ed
as
(
9
)
.
=
1
+
2
(
9
)
T
h
e
b
e
h
av
io
u
r
o
f
th
e
v
o
ltag
e
g
ain
f
u
n
ctio
n
f
o
r
ch
a
n
g
in
g
v
al
u
es
o
f
Q
e
is
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
L
L
C
r
eso
n
an
t
c
o
n
v
er
te
r
o
p
er
ates
with
in
a
s
p
ec
if
ic
f
r
eq
u
en
cy
r
an
g
e
th
at
is
p
r
im
ar
il
y
d
eter
m
in
ed
b
y
th
e
r
eso
n
a
n
t
f
r
eq
u
e
n
cy
(
f
0
)
a
n
d
th
e
p
ea
k
g
ain
f
r
eq
u
e
n
cy
(
f
p
)
.
T
h
e
c
o
n
v
er
ter
ty
p
ically
o
p
er
ates
a
r
o
u
n
d
its
r
eso
n
an
t
f
r
eq
u
e
n
cy
to
m
in
im
ize
s
witch
in
g
lo
s
s
es
an
d
ac
h
ie
v
e
ze
r
o
v
o
l
tag
e
s
witch
in
g
(
Z
VS)
o
v
er
a
wid
e
r
an
g
e
o
f
lo
a
d
s
an
d
in
p
u
t
c
o
n
d
itio
n
s
.
T
h
e
p
ea
k
g
ain
o
cc
u
r
s
b
etwe
en
f
p
an
d
f
0
,
a
n
d
th
is
f
r
e
q
u
en
c
y
r
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n
g
e
ca
n
v
ar
y
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ased
o
n
lo
ad
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n
d
itio
n
s
(
Q
e
)
an
d
t
h
e
r
atio
b
etwe
en
th
e
m
a
g
n
eti
zin
g
in
d
u
cta
n
ce
(
L
m
)
a
n
d
th
e
p
r
im
ar
y
leak
a
g
e
in
d
u
ctan
ce
L
r
.
Sin
ce
Kp
r
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
th
e
v
o
lt
ag
e
g
ain
,
o
p
e
r
atio
n
clo
s
e
to
=1
h
elp
s
to
k
ee
p
Kp
r
v
alu
es
lo
w
to
im
p
r
o
v
e
o
v
er
all
ef
f
icien
cy
an
d
r
ed
u
ce
t
h
e
p
o
wer
-
h
an
d
lin
g
r
e
q
u
ir
em
e
n
t
o
f
th
e
PP
C
s
tag
e.
L
o
wer
Kp
r
v
alu
es
allo
w
t
h
e
d
c
–
d
c
s
tag
e
to
b
e
d
esig
n
e
d
with
r
ed
u
ce
d
co
n
v
er
ter
s
ize,
wh
ile
also
en
s
u
r
in
g
m
in
im
al
r
eso
n
an
t
-
tan
k
cu
r
r
en
t
,
d
ev
ice
s
tr
ess
,
an
d
th
er
m
al
lo
ad
in
g
.
Fig
u
r
e
2
.
Pro
p
o
s
ed
p
ar
tial p
o
wer
co
n
v
er
te
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
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&
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I
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2088
-
8
6
9
4
Desig
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n
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ma
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a
tio
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f a
s
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p
a
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l
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p
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er LLC
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(
S
eb
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vis
K
u
r
ich
ip
a
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a
mb
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1133
Fig
u
r
e
3
.
B
eh
av
i
o
r
o
f
th
e
v
o
ltag
e
g
ain
f
u
n
ctio
n
2
.
2
.
M
P
P
T
a
lg
o
rit
h
m
Dep
en
d
in
g
o
n
th
e
s
witch
in
g
f
r
eq
u
en
c
y
,
th
e
L
L
C
r
eso
n
a
n
t
ta
n
k
r
u
n
s
in
eith
er
b
o
o
s
t
o
r
b
u
c
k
m
o
d
e.
I
f
th
e
co
n
v
er
ter
s
witch
in
g
f
r
eq
u
en
cy
is
h
ig
h
er
th
an
th
e
r
eso
n
an
t
f
r
e
q
u
en
c
y
,
th
e
co
n
v
er
ter
f
u
n
ctio
n
s
in
b
u
ck
m
o
d
e
[
2
1
]
.
C
o
n
v
er
s
ely
,
wh
en
th
e
s
witch
in
g
f
r
eq
u
e
n
cy
is
lo
wer
th
an
th
e
r
eso
n
an
t
f
r
e
q
u
en
cy
,
th
e
co
n
v
er
ter
f
u
n
ctio
n
s
in
b
o
o
s
t
m
o
d
e.
MPPT
tr
ac
k
in
g
is
ac
co
m
p
lis
h
ed
b
y
ad
ju
s
tin
g
th
e
s
witch
in
g
f
r
eq
u
en
cy
to
ac
h
iev
e
th
e
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
DC
-
DC
s
tag
e.
B
y
ad
ju
s
tin
g
th
e
s
witch
in
g
f
r
eq
u
en
cy
,
t
h
e
MPPT
co
n
tr
o
ller
r
aises
o
r
lo
wer
s
th
e
co
n
v
er
ter
g
ain
in
r
esp
o
n
s
e
to
v
ar
iatio
n
s
in
s
o
lar
ir
r
ad
iatio
n
i
n
o
r
d
er
to
ac
h
iev
e
th
e
n
ew
m
ax
im
u
m
p
o
wer
p
o
in
t.
I
n
te
g
r
atio
n
o
f
f
r
eq
u
en
c
y
-
m
o
d
u
lated
MPPT
c
o
n
tr
o
l
with
in
th
e
PP
C
–
L
L
C
co
n
v
er
ter
en
a
b
les
s
im
u
ltan
eo
u
s
s
o
f
t
-
s
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g
a
n
d
p
ar
tial p
o
wer
p
r
o
ce
s
s
in
g
,
c
r
ea
tin
g
a
u
n
iq
u
e
s
y
s
tem
co
n
f
ig
u
r
atio
n
.
T
h
e
f
lo
wch
ar
t
o
f
th
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
m
eth
o
d
,
illu
s
tr
ated
in
Fig
u
r
e
4
,
b
eg
in
s
b
y
m
ea
s
u
r
in
g
th
e
PV
v
o
ltag
e,
V
pv
(
n
)
,
an
d
th
e
PV
cu
r
r
en
t,
I
p
v
(
n
)
,
in
th
e
n
th
cy
cle
to
d
eter
m
in
e
th
e
PV
p
o
wer
,
P
pv
(
n
)
.
Su
b
s
eq
u
en
tly
,
P
pv
(
n
)
an
d
V
pv
(
n
)
a
r
e
c
o
m
p
ar
e
d
wit
h
th
e
PV
p
o
wer
,
P
pv
(n
-
1
)
,
a
n
d
th
e
PV
v
o
ltag
e,
V
pv
(n
-
1
)
,
f
r
o
m
th
e
p
r
ev
io
u
s
c
y
cle.
T
h
er
ef
o
r
e,
th
e
f
r
e
q
u
en
c
y
p
er
tu
r
b
atio
n
Δ
f
s
is
ad
ju
s
ted
t
o
eith
er
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e.
Ap
p
ly
i
n
g
a
s
m
all
p
e
r
tu
r
b
atio
n
im
p
r
o
v
es
tr
ac
k
in
g
a
cc
u
r
ac
y
b
u
t
r
ed
u
ce
s
tr
ac
k
in
g
s
p
ee
d
.
On
th
e
o
th
e
r
h
an
d
,
u
s
in
g
a
lar
g
e
p
er
t
u
r
b
ati
o
n
en
h
a
n
ce
s
tr
ac
k
in
g
s
p
ee
d
b
u
t
d
ec
r
ea
s
es
tr
ac
k
in
g
ac
cu
r
ac
y
.
T
h
er
ef
o
r
e,
o
p
tim
al
p
er
tu
r
b
atio
n
is
ap
p
lied
b
ased
o
n
th
e
to
tal
PV p
o
wer
.
Fig
u
r
e
4
.
Pro
p
o
s
ed
MPPT
alg
o
r
ith
m
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
.
2
,
J
u
n
e
20
2
6
:
1
1
3
0
-
1141
1134
3.
T
H
RE
E
-
P
H
ASE
I
NV
E
RT
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R
CO
NT
RO
L
ST
R
AT
E
G
Y
T
h
e
s
ec
o
n
d
s
tag
e
o
f
th
e
p
r
o
p
o
s
ed
two
-
s
tag
e
PV
s
y
s
tem
u
s
es
a
s
elf
-
co
m
m
u
tated
in
v
er
ter
VSI
in
th
e
p
r
o
p
o
s
ed
d
esig
n
f
o
r
p
o
wer
co
n
v
er
s
io
n
an
d
o
p
tim
izin
g
co
n
tr
o
l.
I
t
is
m
an
ag
ed
u
s
in
g
th
e
V
OC
m
eth
o
d
,
wh
ich
m
o
d
els
th
e
VSI
as
a
co
n
tr
o
lled
AC
v
o
ltag
e
s
o
u
r
ce
.
T
h
is
co
n
tr
o
l
s
y
s
tem
u
tili
ze
s
a
d
o
u
b
le
-
lo
o
p
co
n
tr
o
l
m
o
d
e,
f
ea
tu
r
in
g
an
i
n
n
er
cu
r
r
e
n
t
lo
o
p
f
o
r
r
e
g
u
latin
g
b
o
th
ac
tiv
e
c
u
r
r
en
t
(
I
d
)
an
d
r
ea
ctiv
e
cu
r
r
e
n
t
(
I
q
)
an
d
a
n
o
u
ter
v
o
ltag
e
lo
o
p
.
T
h
e
co
n
tr
o
l
s
tr
at
eg
y
,
im
p
le
m
en
ted
i
n
th
e
d
q
s
y
n
ch
r
o
n
o
u
s
r
e
f
er
en
ce
f
r
am
e,
s
im
p
lifie
s
co
n
tr
o
l
b
y
co
n
v
er
tin
g
g
r
id
m
ea
s
u
r
e
m
en
t
s
in
to
d
ir
ec
t
c
u
r
r
en
t
(
DC
)
v
a
lu
es.
T
o
s
y
n
c
h
r
o
n
ize
in
jecte
d
cu
r
r
e
n
ts
with
g
r
id
v
o
ltag
es
an
d
e
n
ab
le
t
h
e
ab
c
-
d
q
tr
an
s
f
o
r
m
atio
n
,
a
p
h
ase
-
lo
c
k
ed
lo
o
p
(
PLL
)
e
x
tr
ac
ts
th
e
cr
u
cial
p
h
ase
a
n
g
le
o
f
th
e
g
r
id
v
o
ltag
e.
T
h
is
d
o
u
b
le
-
lo
o
p
co
n
tr
o
l
s
y
s
tem
with
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
co
n
tr
o
ller
s
r
eg
u
lates
b
o
th
g
r
id
cu
r
r
en
t
an
d
DC
-
lin
k
v
o
ltag
e
(
Vd
c)
[
2
2
]
.
T
h
e
o
u
ter
v
o
ltag
e
lo
o
p
s
tab
ilizes
Vd
c,
an
d
its
o
u
tp
u
t
b
ec
o
m
es
th
e
r
ef
er
en
ce
v
alu
e
f
o
r
ac
tiv
e
c
u
r
r
en
t
(
I
d
)
.
T
o
f
u
r
t
h
er
s
im
p
lify
c
o
n
tr
o
l
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
c
u
r
r
en
ts
(
I
d
an
d
I
q
)
,
a
f
ee
d
-
f
o
r
wa
r
d
d
ec
o
u
p
lin
g
s
t
r
ateg
y
is
im
p
lem
en
ted
.
No
tab
ly
,
s
ettin
g
th
e
r
ea
ctiv
e
cu
r
r
en
t
r
ef
er
en
ce
(
I
q
)
to
ze
r
o
en
s
u
r
es th
e
g
r
id
in
v
er
ter
o
p
er
ates a
t u
n
ity
p
o
wer
f
ac
to
r
(
PF
)
.
3
.
1
.
M
o
dellin
g
o
f
t
he
t
hree
-
ph
a
s
e
VS
I
C
o
n
s
id
er
in
g
ac
ce
s
s
to
th
e
p
o
wer
g
r
id
th
r
o
u
g
h
an
R
L
f
ilter
(
R
+
jω
L
)
as
s
h
o
wn
i
n
Fig
u
r
e
5
,
th
e
f
o
llo
win
g
eq
u
atio
n
s
d
escr
ib
e
t
h
e
g
r
id
i
n
v
er
ter
v
o
ltag
es a
s
(
1
0
)
.
=
+
+
=
+
+
=
+
+
(
1
0
)
W
h
er
e
“V
ga
,
V
gb
,
V
gc
”,
“i
a
,
i
b
,
i
c
,
”
an
d
“V
ia
,
V
ib
,
V
ic
”
ar
e
g
r
id
v
o
ltag
e,
in
v
er
ter
cu
r
r
en
t,
a
n
d
in
v
er
te
r
v
o
ltag
e
,
r
esp
ec
tiv
ely
.
B
y
ap
p
ly
in
g
th
e
d
-
q
tr
an
s
f
o
r
m
atio
n
,
th
e
m
at
h
em
atica
l
m
o
d
el
o
f
th
e
g
r
i
d
in
v
er
ter
in
th
e
d
-
q
s
y
n
ch
r
o
n
o
u
s
r
ef
e
r
en
ce
f
r
am
e
ca
n
b
e
o
b
tain
ed
as (
11
)
.
=
+
−
+
=
+
+
+
(
1
1
)
Fo
r
p
o
wer
ca
lcu
latio
n
s
,
th
e
g
r
id
-
s
id
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
eq
u
atio
n
s
ex
p
r
ess
ed
in
s
p
ac
e
v
ec
to
r
f
o
r
m
ar
e
g
iv
en
b
y
(
1
2
)
.
=
3
2
(
+
)
=
3
2
(
−
)
(
1
2
)
T
h
e
d
ir
ec
t
co
m
p
o
n
e
n
ts
o
f
th
e
g
r
id
v
o
ltag
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ad
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r
e
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ts
o
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th
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g
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id
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r
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en
t.
As th
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y
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tem
h
as to
o
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er
ate
at
u
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ity
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o
wer
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ac
to
r
in
n
o
r
m
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n
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s
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wer
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o
s
s
es
ca
n
b
e
n
e
g
lecte
d
.
T
h
e
n
,
V
q
is
ze
r
o
f
o
r
a
b
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d
s
y
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tem
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h
u
s
,
th
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atio
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ec
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m
e
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1
3
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.
=
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2
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−
3
2
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1
3
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3
.
2
.
G
rid inv
er
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ntr
o
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eg
y
Ma
in
tain
in
g
a
co
n
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tan
t
DC
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lin
k
v
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e
en
s
u
r
es
o
p
tim
al
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o
wer
tr
an
s
f
er
f
r
o
m
th
e
DC
s
id
e
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AC
s
id
e,
co
n
f
ir
m
in
g
ef
f
icien
t
o
p
er
atio
n
[
2
3
]
.
T
h
is
ap
p
r
o
ac
h
i
s
wid
ely
u
s
ed
in
PV
s
y
s
tem
s
with
a
co
n
tin
u
o
u
s
p
o
wer
s
u
p
p
ly
f
r
o
m
PV
ar
r
a
y
s
,
g
u
ar
an
teein
g
m
ax
im
u
m
p
o
wer
d
eliv
er
y
to
t
h
e
lo
ad
.
I
n
g
r
i
d
-
tied
ap
p
licatio
n
s
,
th
e
DC
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lin
k
v
o
ltag
e
m
u
s
t
b
e
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ig
h
er
th
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th
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ea
k
g
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v
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ltag
e
to
f
ac
ilit
ate
p
r
o
p
er
p
o
wer
in
jectio
n
[
2
4
]
.
Acc
o
r
d
in
g
to
th
e
in
s
tan
tan
eo
u
s
p
o
wer
t
h
eo
r
y
,
a
lo
s
s
less
p
o
wer
co
n
v
er
te
r
m
u
s
t
b
alan
c
e
in
p
u
t
an
d
o
u
tp
u
t
p
o
wer
,
en
s
u
r
in
g
ef
f
icien
t e
n
er
g
y
co
n
v
er
s
io
n
.
I
n
p
u
t D
C
p
o
wer
=
Ou
tp
u
t A
C
p
o
wer
=
3
2
(
+
)
(
1
4
)
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
Desig
n
a
n
d
p
erfo
r
ma
n
ce
ev
a
l
u
a
tio
n
o
f a
s
o
ft
-
s
w
itch
ed
p
a
r
tia
l
-
p
o
w
er LLC
…
(
S
eb
in
Da
vis
K
u
r
ich
ip
a
r
a
mb
il
)
1135
B
y
alig
n
in
g
th
e
d
q
r
ef
er
e
n
ce
f
r
am
e’
s
r
o
tatio
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al
s
p
ee
d
with
th
e
g
r
id
f
r
eq
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e
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cy
,
t
h
e
tr
a
n
s
f
o
r
m
ed
v
ar
iab
les
r
em
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tead
y
in
a
s
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le
s
tate,
s
tr
ea
m
lin
in
g
c
o
n
tr
o
ller
im
p
lem
en
tatio
n
.
T
h
is
s
y
n
ch
r
o
n
izatio
n
is
ac
co
m
p
lis
h
ed
th
r
o
u
g
h
a
PLL
,
wh
ich
tak
es
an
alter
n
atin
g
g
r
id
v
o
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as
in
p
u
t
a
n
d
p
r
o
d
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ce
s
th
e
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h
ase
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g
le
n
ec
ess
ar
y
f
o
r
a
b
c
-
to
-
d
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co
n
v
er
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.
Ass
u
m
in
g
th
at
th
e
P
L
L
ac
cu
r
ately
tr
ac
k
s
th
e
o
u
t
p
u
t
v
o
ltag
e
v
ec
to
r
,
alig
n
in
g
th
e
d
-
a
x
is
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
d
q
r
ef
er
en
ce
f
r
a
m
e
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ch
th
at
Vq
=0
,
th
e
tr
a
n
s
f
er
f
u
n
ctio
n
s
ca
n
b
e
d
er
iv
ed
[
2
5
]
.
T
h
ese
tr
an
s
f
er
f
u
n
ctio
n
s
r
ep
r
esen
t
th
e
r
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n
s
h
ip
b
etwe
en
th
e
DC
-
lin
k
v
o
ltag
e
o
u
t
p
u
t,
r
ea
ctiv
e
p
o
wer
,
an
d
th
e
d
-
ax
is
cu
r
r
en
t.
T
h
ey
ca
n
b
e
ex
p
r
ess
ed
as (
1
5
)
:
(
)
(
)
=
3
2
(
)
(
1
5
)
T
h
er
e
ex
is
ts
an
in
ter
ac
tio
n
b
etwe
en
th
e
d
-
ax
is
an
d
q
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ax
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co
m
p
o
n
e
n
ts
,
wh
ich
ca
n
im
p
ac
t
th
e
co
n
tr
o
ller
’
s
d
y
n
am
ic
r
esp
o
n
s
e.
T
o
en
h
an
ce
p
er
f
o
r
m
an
ce
,
it
is
cr
u
cial
to
elim
in
ate
th
is
cr
o
s
s
-
co
u
p
lin
g
ef
f
ec
t.
A
f
ee
d
f
o
r
war
d
c
o
m
p
en
s
atio
n
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b
ased
d
ec
o
u
p
lin
g
s
tr
ateg
y
ca
n
b
e
im
p
lem
en
ted
to
ac
h
iev
e
i
n
d
ep
en
d
en
t
co
n
tr
o
l
o
f
b
o
t
h
ax
es
.
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h
e
cr
o
s
s
-
co
u
p
lin
g
ca
n
b
e
d
ec
o
u
p
led
b
y
(
4
)
.
Hen
ce
,
th
e
d
-
a
x
is
cu
r
r
e
n
ts
id
a
n
d
q
-
a
x
is
cu
r
r
en
ts
iq
ca
n
b
e
co
n
tr
o
lled
in
d
e
p
en
d
en
tly
b
y
r
ef
er
e
n
ce
cu
r
r
en
t
id
*
an
d
iq
*
,
r
esp
ec
tiv
ely
.
As
a
r
e
s
u
lt,
PI
co
n
tr
o
ller
s
ar
e
em
p
lo
y
ed
to
en
s
u
r
e
a
r
a
p
id
d
y
n
am
ic
r
esp
o
n
s
e
wh
ile
m
ai
n
tain
in
g
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
.
As
a
r
esu
lt,
PI
co
n
tr
o
ller
s
ar
e
im
p
lem
e
n
ted
to
p
r
o
v
i
d
e
a
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
an
d
elim
in
ate
s
tead
y
-
s
tate
er
r
o
r
s
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
g
r
id
-
c
o
n
n
ec
ted
VSI
ca
n
b
e
e
x
p
r
ess
ed
as (
1
6
)
.
(
)
=
1
(
+
1
)
(
+
(
1
6
)
Fo
r
p
r
ec
is
e
an
d
r
a
p
id
t
r
ac
k
in
g
o
f
th
e
c
u
r
r
e
n
t
s
ig
n
al,
t
h
e
c
u
r
r
en
t
l
o
o
p
m
u
s
t
ex
h
ib
it
s
tr
o
n
g
p
e
r
f
o
r
m
an
ce
.
Fo
r
R
=
0
.
1
Ω,
L
=
3
m
H,
T
s
=
0
.
1
6
7
ms
,
an
d
d
esig
n
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ased
o
n
th
e
s
y
s
tem
ty
p
e
1
f
o
r
a
d
am
p
in
g
r
atio
o
f
0
.
7
0
7
to
en
s
u
r
e
o
p
tim
al
s
tab
ilit
y
an
d
r
e
s
p
o
n
s
e,
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
PI
co
n
t
r
o
ller
is
g
iv
en
b
y
(
1
7
)
.
(
)
=
9
−
8
.
95
−
1
(
1
7
)
Fig
u
r
e
5
.
PV in
v
e
r
ter
co
n
tr
o
l a
lg
o
r
ith
m
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
h
e
p
r
o
p
o
s
ed
PV
g
r
id
-
c
o
n
n
ec
ted
s
y
s
tem
was
s
im
u
lated
in
MA
T
L
AB
/Si
m
u
lin
k
to
v
er
if
y
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
c
o
n
v
e
r
ter
ar
ch
itectu
r
e,
with
s
p
ec
ial
f
o
cu
s
o
n
th
e
DC
-
DC
s
tag
e.
T
h
e
DC
-
DC
co
n
v
er
ter
em
p
lo
y
s
a
h
alf
-
b
r
id
g
e
s
er
ies
L
L
C
r
eso
n
an
t
to
p
o
lo
g
y
in
teg
r
ated
with
PP
C
,
d
esig
n
ed
to
o
p
er
ate
u
n
d
er
s
o
f
t
-
s
witch
in
g
co
n
d
itio
n
s
.
T
h
e
s
ch
em
atic
d
iag
r
am
o
f
th
e
m
o
d
el
u
s
ed
f
o
r
th
e
s
im
u
latio
n
s
tu
d
y
is
s
h
o
wn
in
Fig
u
r
e
6
.
T
h
is
s
tag
e
p
lay
s
a
cr
u
cial
r
o
le
in
b
o
th
ef
f
icien
t
en
e
r
g
y
c
o
n
v
er
s
io
n
a
n
d
s
u
cc
ess
f
u
l
MPPT
im
p
lem
en
tatio
n
,
m
ak
in
g
it
ce
n
tr
al
to
th
e
o
v
er
al
l
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
T
h
e
P&
O
m
eth
o
d
is
im
p
lem
e
n
ted
i
n
r
ea
l
-
tim
e
to
a
d
ju
s
t
th
e
o
p
er
atin
g
f
r
eq
u
en
cy
s
u
c
h
th
at
th
e
PV
p
an
el
co
n
s
is
ten
tly
o
p
er
ates
at
o
r
n
e
ar
its
m
ax
im
u
m
p
o
wer
p
o
in
t,
d
esp
ite
v
ar
iatio
n
s
in
ir
r
a
d
ian
c
e.
A
two
-
s
tag
e
PV
in
v
er
ter
with
a
th
r
ee
-
p
h
ase
VSI
g
r
i
d
-
co
n
n
e
cted
in
v
er
ter
in
t
h
e
DC
-
AC
s
t
ag
e
,
an
d
a
h
alf
-
b
r
id
g
e
s
er
ies
L
L
C
r
eso
n
an
t
co
n
v
er
ter
with
PP
C
to
p
o
l
o
g
y
in
th
e
f
ir
s
t
s
tag
e
is
m
o
d
e
lled
in
th
is
s
ec
tio
n
.
A
s
im
u
latio
n
s
tu
d
y
is
co
n
d
u
ct
ed
in
th
e
m
o
d
el
b
ased
o
n
t
h
e
th
eo
r
etica
l
b
asis
o
f
an
aly
s
is
d
o
n
e
in
th
e
p
r
ev
io
u
s
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
.
2
,
J
u
n
e
20
2
6
:
1
1
3
0
-
1141
1136
ch
ap
ter
s
.
I
n
o
r
d
er
to
ac
co
m
p
l
is
h
th
e
p
r
o
p
o
s
ed
two
-
s
tag
e
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
with
a
p
o
wer
ca
p
ac
ity
o
f
1
0
0
k
W
,
th
e
PV
s
y
s
tem
ar
r
ay
co
n
s
is
ts
o
f
1
8
p
ar
allel
s
tr
in
g
s
an
d
1
8
PV
m
o
d
u
les
co
n
n
e
cted
in
s
er
ies.
T
h
e
m
ain
p
ar
a
m
eter
s
o
f
t
h
e
s
elec
ted
PV
p
an
el
a
r
e
s
h
o
wn
in
T
ab
le
1
.
W
aa
r
ee
E
n
er
g
ies
W
SM
-
3
1
5
m
o
d
el
PV
m
o
d
u
le
was
s
elec
ted
f
r
o
m
M
AT
L
AB
/Si
m
u
lin
k
to
r
ea
lize
th
e
1
0
0
k
W
PV
ar
r
ay
s
y
s
tem
f
o
r
th
e
s
im
u
latio
n
en
v
ir
o
n
m
en
t.
Fig
u
r
e
6
.
Sch
em
atic
-
d
iag
r
am
o
f
g
r
id
co
n
n
ec
ted
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
T
ab
le
1
.
PV m
o
d
u
le
m
ain
p
ar
a
m
eter
s
P
a
r
a
me
t
e
r
s
o
f
t
h
e
P
V
m
o
d
u
l
e
V
a
l
u
e
N
o
mi
n
a
l
m
a
x
i
m
u
m
p
o
w
e
r
(
P
ma
x
)
3
1
5
W
O
p
t
i
mu
m
o
p
e
r
a
t
i
n
g
v
o
l
t
a
g
e
(
V
m
p
)
3
5
V
O
p
t
i
mu
m
o
p
e
r
a
t
i
n
g
c
u
r
r
e
n
t
(
I
mp
)
9
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
e
)
4
3
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
l
sc)
9
.
7
7
A
N
o
o
f
c
e
l
l
7
2
N
o
s
A
1
0
0
k
W
h
alf
-
b
r
id
g
e
L
L
C
r
eso
n
an
t
co
n
v
er
ter
is
im
p
lem
en
ted
as
p
ar
t
o
f
a
s
er
ies
p
ar
tial
p
o
wer
co
n
v
er
ter
(
SP
PC
)
to
p
o
lo
g
y
,
w
ith
a
tr
an
s
f
o
r
m
e
r
o
f
a
1
:1
tu
r
n
s
r
atio
an
d
o
p
er
atin
g
o
v
e
r
a
s
witch
in
g
f
r
eq
u
en
cy
r
an
g
e
o
f
7
2
k
Hz
to
1
2
0
k
Hz.
T
h
e
r
eso
n
an
t f
r
eq
u
e
n
cy
is
s
et
at
1
2
0
k
Hz
to
en
a
b
le
s
o
f
t
s
witch
in
g
,
en
s
u
r
in
g
Z
VS
f
o
r
th
e
p
r
im
a
r
y
s
witch
es
an
d
Z
C
S
f
o
r
th
e
s
ec
o
n
d
ar
y
r
ec
t
if
ier
.
T
h
e
r
eso
n
an
t
tan
k
co
n
s
is
ts
o
f
a
r
eso
n
an
t
ca
p
ac
ito
r
o
f
3
8
0
n
F,
a
r
eso
n
an
t
in
d
u
cto
r
o
f
ap
p
r
o
x
im
ately
4
.
6
3
µH
,
an
d
a
m
ag
n
etiz
in
g
in
d
u
ctan
ce
o
f
2
3
.
1
5
µH
,
m
ain
tain
i
n
g
an
/
r
atio
o
f
5
.
T
h
e
c
o
n
v
e
r
ter
o
p
er
ates
with
a
v
ar
iab
le
s
witch
in
g
f
r
eq
u
e
n
cy
to
im
p
lem
en
t
MPPT,
wh
ile
th
e
o
u
tp
u
t
DC
b
u
s
v
o
ltag
e
is
r
eg
u
l
ated
at
6
0
0
V
th
r
o
u
g
h
th
e
v
o
lt
ag
e
co
n
tr
o
l
lo
o
p
o
f
th
e
g
r
id
-
tied
in
v
er
ter
.
T
h
e
g
r
i
d
-
tied
in
v
er
ter
d
esig
n
p
a
r
am
e
ter
s
lis
ted
in
T
ab
le
2
ar
e
ap
p
lied
to
th
e
DC
/AC
s
tag
e
o
f
t
h
e
s
im
u
latio
n
.
T
h
e
MA
T
L
AB
b
lo
ck
s
u
s
ed
in
s
im
u
latio
n
s
tu
d
ies
o
f
th
e
ab
o
v
e
t
o
p
o
lo
g
y
a
n
d
co
n
tr
o
l
ar
e
s
h
o
wn
in
Fig
u
r
e
7
.
T
h
e
s
im
u
latio
n
was
co
n
d
u
cted
u
n
d
er
d
if
f
e
r
en
t
ir
r
a
d
ian
ce
c
o
n
d
itio
n
s
:
4
0
0
,
6
0
0
,
8
0
0
,
a
n
d
1
0
0
0
W
/m
².
I
n
all
ca
s
es,
th
e
L
L
C
co
n
v
e
r
ter
was
ab
le
to
d
y
n
am
ically
ad
ju
s
t
its
f
r
eq
u
en
c
y
to
en
s
u
r
e
o
p
tim
al
p
o
wer
ex
tr
ac
tio
n
.
T
h
e
MPPT
also
s
h
o
ws
f
ast
co
n
v
er
g
en
ce
,
s
ettlin
g
to
th
e
n
ew
o
p
er
atin
g
p
o
in
t
with
in
ap
p
r
o
x
im
ately
8
–
1
2
m
s
d
u
r
in
g
i
r
r
ad
ian
ce
c
h
an
g
es.
T
h
e
co
n
v
er
ter
m
ai
n
tain
s
a
s
tab
le
o
u
tp
u
t
at
6
0
0
V
D
C
,
wh
ich
is
f
ed
in
to
th
e
DC
-
lin
k
ca
p
ac
ito
r
an
d
s
u
b
s
eq
u
en
tly
in
to
th
e
th
r
ee
-
p
h
ase
in
v
er
ter
.
T
h
e
ap
p
lied
ir
r
ad
ian
ce
,
alo
n
g
with
th
e
o
u
tp
u
t
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
f
ed
to
th
e
g
r
id
,
is
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
ef
f
ec
tiv
e
o
p
er
atio
n
o
f
th
e
v
o
ltag
e
co
n
tr
o
ller
,
wh
ich
h
elp
s
to
m
ain
tain
th
e
DC
b
u
s
v
o
ltag
e
a
t
6
0
0
V
an
d
th
u
s
en
s
u
r
es
th
e
m
ax
im
u
m
p
o
wer
av
ailab
le
in
th
e
PV
ar
r
ay
,
is
a
ls
o
v
is
ib
le
in
Fig
u
r
e
7
.
A
k
e
y
ad
v
an
tag
e
o
f
th
e
L
L
C
to
p
o
lo
g
y
in
th
is
s
y
s
tem
is
its
ab
ilit
y
to
o
p
er
ate
u
n
d
er
s
o
f
t
s
witch
in
g
ac
r
o
s
s
a
wid
e
in
p
u
t
p
o
wer
r
an
g
e
.
T
h
e
r
eso
n
a
n
t
in
d
u
cto
r
c
u
r
r
e
n
t
(
I
r
)
an
d
m
ag
n
etizin
g
c
u
r
r
en
t
(
I
m
)
wav
ef
o
r
m
s
wer
e
s
h
o
wn
in
Fig
u
r
e
9
at
ea
ch
ir
r
ad
ian
ce
lev
el.
T
h
e
r
esu
lts
co
n
f
ir
m
th
at
Z
VS
f
o
r
th
e
p
r
im
ar
y
s
witch
es
an
d
Z
C
S
f
o
r
th
e
s
ec
o
n
d
ar
y
-
s
id
e
r
ec
tifie
r
s
wer
e
c
o
n
s
is
ten
tly
ac
h
iev
ed
.
So
f
t
s
witch
in
g
w
as
m
ain
tain
ed
e
v
en
u
n
d
er
l
o
w
ir
r
ad
ia
n
ce
(
4
0
0
W
/m
²)
,
d
em
o
n
s
tr
atin
g
th
e
r
o
b
u
s
tn
ess
o
f
th
e
d
esig
n
.
T
h
e
s
y
s
tem
was
test
ed
f
o
r
tem
p
er
atu
r
e
v
ar
iatio
n
s
(
2
5
–
6
0
°
C
)
an
d
±
2
0
%
lo
ad
ch
an
g
es,
m
ain
tain
in
g
Z
VS/ZCS
o
p
er
atio
n
a
n
d
DC
-
lin
k
v
o
ltag
e
s
tab
ilit
y
with
in
±
2
% o
f
t
h
e
r
ef
er
en
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
Desig
n
a
n
d
p
erfo
r
ma
n
ce
ev
a
l
u
a
tio
n
o
f a
s
o
ft
-
s
w
itch
ed
p
a
r
tia
l
-
p
o
w
er LLC
…
(
S
eb
in
Da
vis
K
u
r
ich
ip
a
r
a
mb
il
)
1137
T
ab
le
2
.
Par
am
eter
s
o
f
th
e
g
r
i
d
-
co
n
n
ec
ted
th
r
ee
-
p
h
ase
in
v
er
ter
P
a
r
a
me
t
e
r
V
a
l
u
e
G
r
i
d
l
i
n
e
v
o
l
t
a
g
e
4
0
0
V
G
r
i
d
f
r
e
q
u
e
n
c
y
5
0
H
z
DC
-
l
i
n
k
-
v
o
l
t
a
g
e
6
0
0
V
D
C
b
u
s
c
a
p
a
c
i
t
a
n
c
e
0
.
2
2
F
F
i
l
t
e
r
i
n
d
u
c
t
o
r
0
.
1
mH
F
i
l
t
e
r
r
e
s
i
st
a
n
c
e
0
.
2
m
Ω
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
2
k
H
z
P
I
p
a
r
a
met
e
r
o
f
t
h
e
c
u
r
r
e
n
t
l
o
o
p
K
p
=
0
.
3
,
K
i
=
2
0
P
I
p
a
r
a
met
e
r
o
f
t
h
e
v
o
l
t
a
g
e
l
o
o
p
K
p
=
2
,
K
i
=
4
0
0
Fig
u
r
e
7
.
PV g
r
i
d
-
co
n
n
ec
ted
s
y
s
tem
with
p
ar
tial
-
p
o
wer
L
L
C
co
n
v
er
te
r
s
im
u
lated
u
s
in
g
M
AT
L
AB
Simu
lin
k
Fig
u
r
e
8
.
Simu
latio
n
r
esp
o
n
s
e
o
f
p
o
wer
an
d
DC
b
u
s
v
o
ltag
e
f
o
r
v
a
r
y
in
g
ir
r
ad
ian
ce
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
.
2
,
J
u
n
e
20
2
6
:
1
1
3
0
-
1141
1138
At
1
0
0
0
W
/m
²,
th
e
co
n
v
er
te
r
ac
h
iev
ed
a
p
ea
k
ef
f
icien
c
y
o
f
9
8
.
3
2
%.
No
tab
ly
,
e
v
en
at
r
ed
u
ce
d
ir
r
ad
ian
ce
lev
els
o
f
8
0
0
,
6
0
0
,
an
d
4
0
0
W
/m
²,
th
e
ef
f
icien
cie
s
r
em
ain
ed
h
ig
h
:
9
8
.
2
9
%,
9
8
.
3
4
%,
an
d
9
7
.
8
6
%,
r
esp
ec
tiv
ely
.
T
h
e
DC
–
DC
s
ta
g
e
u
s
in
g
t
h
e
h
alf
-
b
r
id
g
e
L
L
C
r
eso
n
an
t
c
o
n
v
e
r
ter
with
PP
C
ac
h
iev
ed
a
h
ig
h
er
ef
f
icien
cy
o
f
9
8
.
1
–
9
9
.
3
%,
wh
ile
th
e
DC
–
AC
s
tag
e
em
p
lo
y
i
n
g
th
e
th
r
ee
-
p
h
ase
VSI
m
ain
t
ain
ed
an
ef
f
icien
c
y
r
an
g
e
o
f
9
8
.
0
–
9
8
.
9
%.
I
n
th
e
ca
s
e
o
f
1
0
0
0
W
/m
²
an
d
2
5
°C
,
th
e
PV
ar
r
ay
s
u
p
p
lies
ab
o
u
t
1
0
1
k
W
DC
,
f
r
o
m
wh
ich
th
e
in
v
e
r
ter
d
eliv
er
s
9
9
.
3
k
W
AC
to
th
e
g
r
i
d
.
On
l
y
2
4
.
6
k
W
is
p
r
o
ce
s
s
ed
b
y
th
e
PP
C
–
L
L
C
s
tag
e
(
2
5
.
9
%
o
f
to
tal
p
o
wer
)
,
y
et
th
e
co
n
v
er
ter
m
ain
tain
s
s
o
f
t
s
witch
in
g
a
n
d
ac
h
iev
es
u
p
to
9
9
.
3
%
ef
f
icien
cy
,
d
u
e
to
lo
wer
s
witch
in
g
lo
s
s
es.
T
h
e
PP
C
ar
ch
itectu
r
e
co
n
tr
ib
u
tes s
ig
n
if
ican
tly
to
th
is
r
esu
lt
b
y
en
s
u
r
in
g
th
at
o
n
l
y
a
p
o
r
tio
n
o
f
th
e
t
o
tal
p
o
wer
f
lo
ws
th
r
o
u
g
h
th
e
h
ig
h
-
f
r
e
q
u
en
c
y
s
witch
in
g
s
tag
e,
t
h
er
eb
y
r
e
d
u
cin
g
co
n
d
u
ctio
n
lo
s
s
es
an
d
im
p
r
o
v
in
g
s
y
s
tem
-
lev
el
ef
f
icien
c
y
.
T
h
e
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
e
r
ter
(
VSI
)
f
o
r
m
s
t
h
e
s
ec
o
n
d
s
tag
e
o
f
th
e
s
y
s
tem
an
d
is
u
s
ed
f
o
r
g
r
id
in
teg
r
atio
n
.
I
t
o
p
er
ates
u
n
d
er
a
VOC
s
ch
em
e
th
at
en
s
u
r
es
s
y
n
ch
r
o
n
izatio
n
with
th
e
g
r
id
an
d
m
ain
tain
s
a
u
n
ity
p
o
wer
f
ac
to
r
.
Fig
u
r
e
9
.
Key
o
p
er
ati
o
n
wav
ef
o
r
m
o
f
th
e
L
L
C
at
d
if
f
e
r
en
t ir
r
ad
ian
ce
lev
els
Simu
lated
wav
ef
o
r
m
s
at
t
h
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
s
h
o
w
well
-
s
h
ap
ed
s
in
u
s
o
id
al
v
o
ltag
es
an
d
c
u
r
r
en
ts
,
with
m
in
im
al
d
is
to
r
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
10
.
T
h
e
g
r
id
r
ec
eiv
es
ac
tiv
e
p
o
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f
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tly
,
with
r
ea
ctiv
e
p
o
w
er
n
ea
r
ze
r
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u
n
d
er
all
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r
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ce
lev
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Po
wer
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e
f
o
r
m
s
f
u
r
th
er
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at
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r
esp
o
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h
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atch
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er
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ce
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e
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n
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ter
d
em
o
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ates
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ain
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ig
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r
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ter
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u
r
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p
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[
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6
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c
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ar
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ed
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d
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o
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et
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d
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r
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ef
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d
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er
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h
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p
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o
p
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s
ed
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f
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ich
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ased
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ased
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ically
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[
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icatin
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h
at
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itectu
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ased
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h
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itectu
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th
r
o
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g
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n
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ter
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d
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o
f
in
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ter
s
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en
ab
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ig
h
ef
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icien
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n
d
s
o
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t
-
s
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g
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o
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a
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ce
at
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ig
h
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ab
le
3
.
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ter
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m
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Ef
f
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c
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c
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(
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D
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o
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p
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V
O
C
+
A
N
N
M
P
P
T
[
2
4
]
5
–
1
2
ms
97
–
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8
%
2
–
3%
H
i
g
h
M
e
d
i
u
m
–
H
i
g
h
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r
e
d
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c
t
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v
e
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t
r
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l
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P
C
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n
c
-
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o
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d
[
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5
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V
e
r
y
h
i
g
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z
z
y
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P
P
T
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6
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10
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ms
95
–
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7
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1
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V
e
r
y
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i
g
h
H
i
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se
d
m
e
t
h
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d
P
P
C
–
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C
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O
C
8
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8
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M
e
d
i
u
m
Lo
w
–
M
e
d
i
u
m
5.
CO
NCLU
SI
O
N
A
h
ig
h
-
ef
f
icien
cy
two
-
s
tag
e
PV
g
r
id
-
c
o
n
n
ec
te
d
s
y
s
tem
is
p
r
esen
ted
,
in
teg
r
ati
n
g
a
Half
-
B
r
i
d
g
e
Ser
ies
L
L
C
r
eso
n
an
t
co
n
v
er
ter
with
PP
C
to
en
ab
le
s
o
f
t
s
witch
i
n
g
an
d
f
r
eq
u
en
cy
-
b
ased
MP
PT,
wh
ile
a
VOC
-
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
en
s
u
r
es
s
tab
le
g
r
id
i
n
teg
r
atio
n
.
T
h
e
co
n
v
er
ter
c
o
n
s
is
ten
tly
ac
h
iev
es
Z
VS/ZCS
ac
r
o
s
s
a
wid
e
ir
r
ad
ian
ce
r
an
g
e
,
r
ed
u
cin
g
s
witch
in
g
lo
s
s
es a
n
d
im
p
r
o
v
i
n
g
o
v
er
all
ef
f
icien
cy
,
a
n
d
th
e
co
m
b
in
ed
MPPT
–
VOC
f
r
am
ewo
r
k
m
ain
tain
s
r
ap
id
p
o
wer
tr
ac
k
in
g
,
DC
-
lin
k
s
tab
ilit
y
,
an
d
u
n
ity
p
o
wer
f
ac
to
r
d
u
r
in
g
g
r
id
o
p
e
r
atio
n
.
T
h
e
n
o
v
elty
o
f
th
is
wo
r
k
lies
in
u
n
if
y
in
g
p
ar
tial
p
o
wer
p
r
o
ce
s
s
in
g
,
r
eso
n
an
t
s
o
f
t
s
witch
in
g
,
an
d
a
f
u
lly
m
o
d
ele
d
g
r
i
d
-
in
teg
r
atio
n
s
tr
ateg
y
wit
h
in
a
s
in
g
le
s
y
s
tem
-
lev
el
a
r
ch
itectu
r
e.
Ho
wev
er
,
th
e
s
tu
d
y
is
lim
ited
to
s
im
u
la
tio
n
,
an
d
h
ar
d
war
e
v
alid
atio
n
,
as
well
as
d
etailed
th
er
m
al
a
n
d
s
tr
ess
an
aly
s
is
,
r
em
ain
f
o
r
f
u
t
u
r
e
in
v
esti
g
atio
n
.
Fu
tu
r
e
r
esear
ch
will
f
o
cu
s
o
n
ex
p
er
im
e
n
tal
im
p
lem
en
tatio
n
,
ad
ap
tiv
e
MPPT
s
tr
ateg
ies,
an
d
ex
p
an
d
ed
g
r
id
-
s
u
p
p
o
r
t
f
u
n
ctio
n
s
s
u
ch
as
L
VR
T
ca
p
ab
ilit
y
.
Ov
er
all,
th
e
PP
C
–
L
L
C
ar
ch
itectu
r
e
d
em
o
n
s
tr
ates
s
tr
o
n
g
p
o
te
n
tial
as
a
s
ca
lab
le
an
d
h
ig
h
-
ef
f
icien
cy
s
o
lu
tio
n
f
o
r
n
ex
t
-
g
en
er
atio
n
PV
g
r
id
in
ter
f
ac
es.
Evaluation Warning : The document was created with Spire.PDF for Python.