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s
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a
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p
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ti
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we
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rtain
to
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ty
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wly
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e
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n
e
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e
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e
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ti
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d
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ss
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g
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k
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m
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tes
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tral
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P
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ti
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su
lt
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g
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a
l
o
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k
a
g
e
c
u
rre
n
t.
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re
o
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r,
th
e
i
n
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re
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se
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o
u
tp
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t
v
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g
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k
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t
a
c
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c
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ted
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ATLAB/S
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imp
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re
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re
li
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le
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l
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ti
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g
rid
-
c
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c
ted
s
o
lar P
V ap
p
li
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ti
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s.
K
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w
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s
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t
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ltil
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Sin
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CC B
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C
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Dep
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Un
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UT
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J
o
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u
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J
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Dar
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ail:
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tm
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m
y
1.
I
NT
RO
D
UCT
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O
N
I
n
p
h
o
to
v
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ltaic
(
PV)
ap
p
licatio
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s
,
tr
an
s
f
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er
s
ar
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co
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m
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ly
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s
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wev
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ter
wh
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d
p
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en
s
ity
.
T
o
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d
r
ess
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is
s
u
es
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d
p
r
ev
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t
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af
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ce
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lik
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d
f
au
lt
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d
leak
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o
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t a
d
d
itio
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p
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au
tio
n
s
[
1
]
–
[
4
]
.
Var
io
u
s
to
p
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g
ical
to
p
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ies,
in
clu
d
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ase
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AC
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DC
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is
s
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ested
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r
r
en
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p
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o
b
lem
s
[
5
]
,
[
6
]
.
T
h
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m
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s
t
o
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te
n
u
s
ed
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d
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tiv
e
to
p
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f
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k
in
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(
HE
R
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C
)
to
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ilt
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AC
d
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p
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iq
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in
th
is
s
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d
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Oth
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DC
to
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tain
H5
an
d
v
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s
f
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s
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H
6
.
B
u
t
s
till
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leak
ag
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r
r
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t
is
s
u
e.
Fu
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th
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m
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r
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co
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lo
s
s
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an
d
th
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in
v
er
ter
'
s
in
ca
p
ac
ity
to
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m
ain
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is
ad
v
an
tag
es
o
f
s
u
c
h
in
v
e
r
ter
to
p
o
lo
g
ies
ar
e
in
cr
ea
s
ed
[
7
]
–
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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I
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Vo
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Ma
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:
673
-
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Vo
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s
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tr
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p
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-
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NPC
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in
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els
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ality
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ce
d
an
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in
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ter
s
tr
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ctu
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e
s
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p
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ased
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ty
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ac
tiv
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n
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tr
al
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p
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t
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ANPC
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.
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tly
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a
f
iv
e
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v
er
ter
b
u
ilt o
n
a
n
im
p
ed
a
n
ce
s
o
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r
ce
was d
escr
ib
ed
in
[
1
5
]
–
[
1
9
]
.
T
h
is
in
v
er
ter
'
s
p
o
o
r
v
o
ltag
e
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ain
,
lar
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e
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ig
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wh
ic
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e
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ter
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s
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s
ely
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th
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m
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s
t
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th
er
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e,
a
two
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s
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e
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lar
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y
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tem
s
[
2
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]
,
[
2
1
]
.
As
an
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ativ
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a
u
n
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e
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y
in
g
th
e
d
em
an
d
s
o
f
g
r
id
-
c
o
n
n
ec
ted
r
en
ewa
b
l
e
en
er
g
y
s
o
u
r
ce
s
,
p
ar
ticu
lar
ly
P
V
s
o
u
r
ce
s
,
is
to
u
s
e
(
C
G)
T
I
th
at
m
ay
elim
in
ate
th
e
is
s
u
e
o
f
h
ig
h
-
f
r
eq
u
en
cy
(
C
MV
)
,
wh
ich
ca
u
s
es
leak
ag
e
cu
r
r
e
n
t.
B
ased
o
n
t
h
e
co
m
m
o
n
-
g
r
o
u
n
d
m
eth
o
d
,
SC
ML
I
s
f
o
r
r
ed
u
cin
g
leak
ag
e
cu
r
r
en
t
h
av
e
lately
ac
q
u
ir
ed
a
cc
ep
tan
ce
in
th
e
liter
atu
r
e.
T
h
ey
ar
e
d
escr
ib
e
d
as
a
u
n
iq
u
e
5
-
L
co
m
m
o
n
-
g
r
o
u
n
d
CG
-
ty
p
e
in
v
er
ter
u
s
in
g
d
u
al
SC
s
,
s
ix
s
witch
es,
an
d
a
d
io
d
e
d
esig
n
ed
f
o
r
PV
s
y
s
tem
s
.
Ad
d
itio
n
al
s
en
s
o
r
s
ar
e
re
q
u
ir
ed
to
b
alan
ce
th
e
SC
v
o
ltag
es
[
2
2
]
–
[
2
6
]
.
C
o
m
p
ac
t
ML
I
s
with
b
o
o
s
tin
g
ca
p
ab
ilit
ies
an
d
m
in
im
al
T
HD
v
o
ltag
e
g
en
er
atio
n
ar
e
r
eq
u
ir
e
d
f
o
r
PV
s
y
s
tem
s
.
ML
I
s
b
ased
o
n
s
witch
ed
ca
p
ac
ito
r
s
(
SC
)
h
a
v
e
r
ec
en
tly
b
ec
o
m
e
p
o
p
u
lar
as
DC
/AC
v
o
ltag
e
co
n
v
er
ter
s
with
b
o
o
s
tin
g
ca
p
ab
i
liti
es
[
2
7
]
.
T
h
e
SC
u
n
it
'
s
o
u
tp
u
t
v
o
ltag
e
r
an
g
e
is
ch
an
g
ea
b
le.
I
t
is
d
ep
en
d
en
t
o
n
t
h
e
ar
r
an
g
e
m
en
t
an
d
s
p
an
s
a
wid
e
r
a
n
g
e.
A
tr
ad
itio
n
al
ac
tiv
e
n
e
u
tr
al
p
o
in
t
clam
p
(
ANPC
)
ar
ch
itectu
r
e
u
tili
zin
g
ca
p
ac
ito
r
s
was
cr
ea
ted
[
2
8
]
.
F
iv
e
o
u
tp
u
t
v
o
ltag
e
lev
els
b
ey
o
n
d
th
e
lo
ad
m
a
y
b
e
p
r
o
d
u
ce
d
with
a
s
in
g
le
DC
v
o
ltag
e
s
o
u
r
ce
,
ei
g
h
t
I
GB
T
s
,
an
d
th
r
ee
ca
p
ac
ito
r
s
.
Ho
wev
e
r
,
th
er
e
is
n
o
way
to
b
o
o
s
t p
r
o
d
u
ctio
n
lev
els in
th
e
lo
ad
ter
m
in
al.
Nev
er
th
eless
,
th
is
ar
r
an
g
em
en
t
d
o
es
n
o
t
h
av
e
a
way
to
r
ais
e
th
e
o
u
tp
u
t
v
o
ltag
e.
T
wo
n
e
w
k
in
d
s
o
f
ANPC
to
p
o
lo
g
ies
wer
e
p
r
esen
ted
i
n
[
2
9
]
.
T
h
ese
to
p
o
lo
g
ies
ar
e
u
n
ab
le
t
o
en
h
an
ce
v
o
lta
g
e,
an
d
th
is
p
ap
e
r
d
escr
ib
es
a
n
ew
5
-
lev
el
b
o
o
s
t
in
v
er
ter
with
co
n
tin
u
o
u
s
g
a
in
co
n
tr
o
ller
ca
p
ab
ilit
ies.
T
h
e
in
v
er
ter
n
ee
d
s
an
in
d
u
cto
r
t
o
s
u
p
p
l
y
co
n
tin
u
o
u
s
in
p
u
t
cu
r
r
en
t
i
n
b
o
t
h
DC
an
d
AC
m
o
d
es,
ess
en
tial
f
o
r
p
h
o
t
o
v
o
ltaic
an
d
o
th
er
r
en
ewa
b
le
en
er
g
y
ap
p
licatio
n
s
.
B
ec
au
s
e
th
e
n
eg
ativ
e
en
d
o
f
t
h
e
DC
s
o
u
r
ce
is
lin
k
ed
to
th
e
n
eu
tr
al
ter
m
in
al
o
f
th
e
g
r
id
,
t
h
e
d
esig
n
h
as m
in
im
al
L
C
an
d
f
ew
co
m
p
o
n
e
n
ts
.
T
h
e
p
ap
e
r
'
s
s
tr
u
ctu
r
e
f
o
llo
ws:
s
ec
tio
n
2
ex
p
lain
s
th
e
c
o
n
s
tr
u
ctio
n
o
f
th
e
s
u
g
g
ested
5
-
lev
el
m
u
ltil
ev
el
b
o
o
s
t
in
v
e
r
ter
.
Sectio
n
3
ex
p
lain
s
th
e
s
witch
m
ec
h
a
n
is
m
an
d
p
u
ls
e
-
g
en
e
r
atin
g
m
eth
o
d
.
Sectio
n
4
s
h
o
ws
MA
T
L
AB
Simu
lin
k
f
in
d
in
g
s
f
o
r
th
e
in
v
er
ter
,
wh
ic
h
en
d
s
in
s
ec
tio
n
5
.
2.
P
RO
P
O
SE
D
T
O
P
O
L
O
G
Y
Fig
u
r
e
1
s
h
o
ws
th
e
in
v
er
te
r
'
s
ci
r
cu
it
ar
ch
itectu
r
e,
wh
ich
i
n
clu
d
es
a
b
o
o
s
t
in
d
u
cto
r
to
s
u
s
tain
co
n
tin
u
o
u
s
in
p
u
t
c
u
r
r
e
n
t
an
d
g
iv
e
ad
ju
s
tab
le
g
ain
v
o
ltag
e,
s
ev
en
s
witch
es,
an
d
two
ca
p
ac
ito
r
s
.
T
h
e
i
n
v
er
ter
u
s
es
a
s
in
g
le
DC
s
o
u
r
ce
d
esig
n
ed
s
p
ec
if
ical
ly
f
o
r
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
.
Ad
d
itio
n
ally
,
t
h
is
p
r
o
v
id
e
s
a
lar
g
e
b
o
o
s
t g
ain
,
with
th
e
p
ea
k
o
u
tp
u
t
v
o
ltag
e
s
et
at
2
M/(
1
-
D)
f
o
r
a
5
-
lev
el
o
u
tp
u
t.
Fig
u
r
e
1
.
T
h
e
b
asic b
lo
c
k
o
f
th
e
p
r
o
p
o
s
ed
5
-
lev
el
in
v
e
r
ter
to
p
o
lo
g
y
2
.
1
.
O
pera
t
ing
mo
des
I
n
th
is
s
ec
tio
n
,
Fig
u
r
e
2
(
a
)
illu
s
tr
ates
th
e
p
r
im
ar
y
o
p
er
atio
n
al
m
o
d
es
o
f
th
e
p
r
o
p
o
s
ed
5
-
lev
el
co
n
v
er
ter
.
T
h
ese
estab
lis
h
d
is
tin
ct
o
p
er
ati
n
g
s
ettin
g
s
f
o
r
ea
ch
v
o
ltag
e
s
tag
e,
g
u
ar
a
n
teein
g
a
co
n
s
is
ten
t
o
u
tp
u
t
v
o
ltag
e
e
v
en
d
u
r
in
g
f
a
u
lts
.
Mo
r
eo
v
er
,
th
e
s
y
s
tem
in
co
r
p
o
r
ates
m
u
ltip
le
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
m
o
d
es
to
s
u
it
v
ar
y
i
n
g
lev
els
o
f
in
v
er
ter
p
o
wer
.
T
h
is
d
esig
n
m
ain
tain
s
th
e
eq
u
ilib
r
iu
m
o
f
th
e
ca
p
ac
ito
r
s
'
v
o
ltag
e
an
d
s
im
p
lifie
s
th
e
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
S
in
g
le
-
s
ta
g
e
tr
a
n
s
fo
r
mer le
s
s
mu
ltil
ev
el
b
o
o
s
t in
ve
r
ter w
ith
z
ero
…
(
Da
lya
Ha
mza
h
A
l
-
Ma
mo
o
r
i
)
675
co
n
tr
o
l
o
f
th
e
b
o
o
s
t
d
u
ty
cy
c
le,
r
esu
ltin
g
i
n
a
d
d
itio
n
al
b
e
n
ef
its
,
f
o
r
in
s
tan
ce
,
ca
p
ac
ito
r
v
o
ltag
e
b
alan
ci
n
g
.
Fu
r
th
er
m
o
r
e
,
th
e
in
p
u
t
i
n
d
u
cta
n
ce
with
in
th
is
in
v
e
r
ter
u
n
d
e
r
g
o
es
ch
ar
g
in
g
d
u
r
in
g
th
e
co
n
d
u
ctio
n
p
h
ase
o
f
t
h
e
I
GB
T
S1
,
wh
ile
it
ex
p
er
ien
ce
s
d
is
ch
ar
g
e
wh
en
th
e
p
o
wer
s
w
itch
S1
tr
an
s
itio
n
s
to
th
e
o
f
f
s
t
ate.
C
o
n
s
eq
u
en
tly
,
th
e
k
ey
wa
v
ef
o
r
m
s
p
er
tin
en
t
t
o
th
e
p
r
o
p
o
s
ed
in
v
e
r
ter
ar
e
illu
s
tr
ated
in
Fig
u
r
e
2
(
b
)
.
As
illu
s
tr
ated
in
Fig
u
r
e
2
(
a
)
,
th
e
s
tate
(
+1
)
co
n
s
is
ts
o
f
two
o
p
er
atio
n
al
co
n
d
itio
n
s
:
th
e
s
tate
o
f
in
d
u
cto
r
c
h
ar
g
in
g
an
d
th
e
s
tate
o
f
in
d
u
cto
r
d
is
ch
ar
g
in
g
;
d
u
r
in
g
t
h
e
ch
ar
g
in
g
p
h
ase,
th
e
in
d
u
cto
r
is
en
er
g
i
ze
d
b
y
th
e
d
ir
ec
t
cu
r
r
e
n
t
(
DC
)
s
o
u
r
ce
wh
en
s
witch
S1
is
ac
tiv
ated
,
in
t
h
is
s
tate
th
e
s
witch
es
S1
,
S3
,
S4
,
S6
ar
e
ac
tiv
ated
to
r
ea
ch
th
e
+
1
lev
el.
Du
r
in
g
th
e
d
is
ch
ar
g
in
g
p
h
ase,
s
witch
S
2
is
ac
tiv
ated
,
wh
ile
s
witch
es
S3
,
S4
,
an
d
S6
r
em
ain
c
o
n
d
u
ctin
g
to
r
ea
ch
th
e
-
1
lev
el,
a
n
d
th
e
s
am
e
o
p
er
atio
n
p
r
in
cip
le
is
u
s
ed
f
o
r
t
h
e
r
est s
tate
s
.
(
a)
S
1
-
G
at
e
P
u
l
s
e
t
ON
O
F
F
IL
t
IC
1
,C
2
t
M
od
e
1
M
od
e
2
(
b
)
Fig
u
r
e
2
.
Op
e
r
atio
n
al
m
o
d
es o
f
th
e
(
a)
c
h
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
s
tag
es o
f
th
e
in
p
u
t b
o
o
s
t in
d
u
cto
r
an
d
(
b
)
k
ey
wav
ef
o
r
m
s
ass
o
ciate
d
with
th
e
in
v
er
te
r
d
u
r
in
g
b
o
th
ch
ar
g
e
an
d
d
is
ch
ar
g
e
f
u
n
ct
io
n
s
2
.
2
.
Vo
l
t
a
g
e
g
a
in a
na
ly
s
is
T
h
e
g
ai
n
o
f
th
e
s
u
g
g
ested
in
v
er
ter
ca
n
b
e
d
eter
m
i
n
ed
as
f
o
l
lo
ws,
co
n
s
id
er
in
g
th
e
DC
s
o
u
r
ce
v
o
ltag
e
an
d
th
e
AC
o
u
tp
u
t v
o
ltag
e
.
=
2
1
−
(
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
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
673
-
682
676
Sin
ce
ev
er
y
ca
p
ac
ito
r
in
th
e
p
r
o
p
o
s
ed
in
v
er
ter
h
as
th
e
s
am
e
am
o
u
n
t
o
f
ch
ar
g
e,
th
e
v
o
ltag
e
o
f
e
v
er
y
ca
p
ac
ito
r
m
ay
b
e
d
eter
m
in
ed
as f
o
llo
ws:
1
=
2
=
1
−
(
2
)
As
a
r
esu
lt,
th
e
h
ig
h
est
m
ax
im
u
m
v
o
ltag
e
is
eq
u
al
to
th
e
t
o
tal
v
o
ltag
es
ac
r
o
s
s
th
e
p
r
ev
i
o
u
s
ly
s
tated
ca
p
ac
ito
r
s
.
T
h
u
s
,
th
e
f
o
llo
win
g
m
eth
o
d
s
ca
n
b
e
u
s
ed
to
o
b
ta
in
it:
,
=
2
1
−
(
3
)
T
ab
le
1
s
h
o
ws
eq
u
atio
n
s
d
em
o
n
s
tr
atin
g
th
e
r
elatio
n
s
h
i
p
b
etwe
en
th
e
o
u
tp
u
t
v
o
lta
g
e
an
d
th
e
m
o
d
u
latio
n
in
d
ex
.
Var
iatio
n
s
i
n
th
e
d
u
ty
cy
cle
(
D)
m
a
y
af
f
ec
t th
e
p
ea
k
v
alu
e
o
f
th
e
wav
e
f
o
r
m
.
T
ab
le
2
s
h
o
ws
th
e
d
is
p
ar
ities
in
m
ax
im
u
m
o
u
tp
u
t
v
o
ltag
e
.
W
h
en
th
e
m
o
d
u
latio
n
in
d
ex
s
u
r
p
ass
es
0
.
5
,
t
h
e
lev
el
s
h
if
t
PW
M
(LS
-
PW
M)
ap
p
r
o
ac
h
cr
ea
tes
a
5
-
lev
el
wav
ef
o
r
m
f
o
r
th
e
i
n
v
er
ter
o
u
t
p
u
t
f
r
o
m
a
s
in
u
s
o
id
al
r
ef
er
en
ce
v
o
ltag
e
s
ig
n
al.
W
h
en
th
e
m
o
d
u
latio
n
i
n
d
ex
f
alls
b
elo
w
0
.
5
,
t
h
e
co
n
v
er
ter
o
u
tp
u
t switch
es to
a
th
r
e
e
-
lev
el
wav
ef
o
r
m.
T
ab
le
1
.
T
h
e
ass
o
ciatio
n
b
etw
ee
n
a
m
o
d
u
latio
n
in
d
ex
a
n
d
th
e
o
u
tp
u
t w
a
v
ef
o
r
m
O
u
t
p
u
t
v
o
l
t
a
g
e
R
a
n
g
o
f
mo
d
u
l
a
t
i
o
n
i
n
d
e
x
R
a
n
g
e
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
w
a
v
e
f
o
r
m
=
2
1
−
0
t
o
1
2
0
1
DC
O
V
V
t
o
D
=
−
T
ab
le
2
.
illu
s
tr
ates v
ar
io
u
s
m
o
d
u
latio
n
in
d
ex
r
a
n
g
es
M
o
d
u
l
a
t
i
o
n
i
n
d
e
x
O
u
t
p
u
t
l
e
v
e
l
s
G
a
i
n
v
o
l
t
a
g
e
M
>
0
.
5
5
,
=
2
1
−
M
<
0
.
5
3
,
=
1
1
−
2
.
3
.
Desig
n f
a
c
t
o
rs
T
h
is
s
ec
tio
n
co
v
e
r
s
th
e
s
u
g
g
e
s
ted
in
v
er
ter
m
o
d
el
co
n
ce
r
n
s
f
o
r
s
witch
es,
in
p
u
t
b
o
o
s
t
in
d
u
cto
r
s
,
an
d
ca
p
ac
ito
r
s
.
As
d
em
o
n
s
tr
ated
b
y
th
e
p
r
ec
ed
in
g
f
o
r
m
u
latio
n
s
,
eq
u
atio
n
s
in
d
icatin
g
th
e
v
o
ltag
e
s
tr
ess
o
f
th
e
s
witch
es a
r
e
co
n
s
tr
u
cted
.
4
,
6
=
1
1
−
,
1
,
2
,
3
,
5
,
7
=
2
1
−
(
4
)
Ad
d
itio
n
ally
,
th
e
i
n
p
u
t
b
o
o
s
t i
n
d
u
cto
r
m
ay
b
e
d
ev
el
o
p
ed
b
y
th
e
s
u
b
s
eq
u
en
t e
q
u
atio
n
:
≥
(
5
)
Fu
r
th
er
m
o
r
e
,
th
e
f
o
llo
win
g
d
e
f
in
itio
n
m
ay
b
e
ap
p
lied
to
th
e
v
alu
es o
f
th
e
i
n
v
er
ter
ca
p
ac
ito
r
s
:
1
,
2
,
.
.
.
≥
(
1
−
)
(
6
)
3.
M
E
T
H
O
DO
L
O
G
Y
Du
e
to
th
e
in
p
u
t
an
d
o
u
tp
u
t
ter
m
in
als
s
h
ar
in
g
c
o
m
m
o
n
g
r
o
u
n
d
,
th
e
s
u
g
g
ested
i
n
v
er
ter
h
as
z
er
o
C
MV
.
Fig
u
r
e
3
(
a)
s
h
o
ws
th
at
th
e
s
in
u
s
o
id
al
wav
ef
o
r
m
v
alu
e
f
r
o
m
p
o
in
t
B
to
n
eu
t
r
al
p
o
in
t
N
is
z
er
o
(
VB
N)
.
T
h
e
PV
ar
r
ay
'
s
p
ar
asit
ic
ca
p
ac
ito
r
(
C
PV
)
is
s
h
o
r
t
-
cir
cu
it
d
u
e
to
th
e
in
v
er
ter
'
s
co
m
m
o
n
g
r
o
u
n
d
ca
p
ab
ili
ties
.
C
o
n
s
eq
u
en
tly
,
th
e
leak
ag
e
cu
r
r
en
t th
r
o
u
g
h
C
PV
is
also
ze
r
o
.
As a
r
esu
lt,
th
e
i
n
v
er
ter
’
s
C
MV
v
alu
e
ca
n
b
e
c
alcu
lated
as
(
7
)
.
.
=
2
+
(
)
(
−
1
2
(
1
)
)
=
0
(
7
)
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
S
in
g
le
-
s
ta
g
e
tr
a
n
s
fo
r
mer le
s
s
mu
ltil
ev
el
b
o
o
s
t in
ve
r
ter w
ith
z
ero
…
(
Da
lya
Ha
mza
h
A
l
-
Ma
mo
o
r
i
)
677
3
.
1
.
M
o
du
la
t
io
n a
nd
s
wit
chi
ng
rules
T
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
p
r
o
d
u
ce
s
a
s
in
u
s
o
id
al
wav
ef
o
r
m
at
t
h
e
o
u
t
p
u
t
b
y
c
o
n
tr
o
llin
g
th
e
I
GB
T
s
with
lev
el
s
h
if
t
m
o
d
u
latio
n
.
Fig
u
r
e
3
(
b
)
s
h
o
ws
th
e
ca
r
r
ier
s
ig
n
al
wav
ef
o
r
m
s
co
n
ce
r
n
in
g
th
e
r
e
f
er
en
ce
s
in
u
s
o
id
al
wav
ef
o
r
m
.
Fo
u
r
tr
ian
g
u
lar
ca
r
r
ier
wav
ef
o
r
m
s
ar
e
in
clu
d
e
d
in
a
5
-
lev
el
in
v
er
ter
.
E
v
er
y
v
o
ltag
e
s
tate
o
f
th
e
in
v
er
ter
c
o
r
r
esp
o
n
d
s
to
o
n
e
o
r
m
o
r
e
s
witch
in
g
s
itu
atio
n
s
.
T
ab
le
3
s
h
o
ws
th
e
s
witch
in
g
ta
b
le
with
f
iv
e
lev
els
f
r
o
m
-
2
V
to
+
2
V3
.
(
a)
(
b
)
Fig
u
r
e
3
.
T
h
e
in
v
e
r
ter
s
tr
u
ctu
r
e
co
m
m
o
n
g
r
o
u
n
d
an
d
th
e
lev
el
s
h
if
t
PW
M
,
(
a)
th
e
p
lan
n
ed
in
v
er
ter
ass
o
ciatio
n
to
th
e
AC
g
r
id
'
s
g
en
er
al
s
ch
em
atic
an
d
(
b
)
tr
ian
g
le
ca
r
r
ier
s
ig
n
als co
m
p
ar
e
d
to
th
e
s
u
g
g
es
ted
in
v
er
ter
'
s
r
ef
er
en
ce
s
in
u
s
o
id
al
wa
v
ef
o
r
m
T
ab
le
3
.
Switch
in
g
s
tates f
o
r
5
-
lev
el
ML
I
Le
v
e
l
/
S
w
i
t
c
h
e
s
P
o
w
e
r
sw
i
t
c
h
e
s
I
n
d
u
c
t
o
r
S
1
S
2
S
3
S
4
S
5
S
6
S
7
0
1
0
1
0
1
0
1
C
h
a
r
g
e
0
1
1
0
1
0
1
D
i
sch
a
r
g
e
+1
1
0
1
0
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0
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h
a
r
g
e
0
1
1
1
0
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0
D
i
sch
a
r
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h
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r
g
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h
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r
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C
h
a
r
g
e
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
As
p
r
ev
io
u
s
ly
ex
p
lain
e
d
,
th
e
p
r
o
p
o
s
ed
in
v
er
ter
o
p
er
ates
i
n
co
n
tin
u
o
u
s
b
o
o
s
t
m
o
d
e
with
a
co
n
s
tan
t
in
p
u
t
cu
r
r
en
t
an
d
0
%
leak
a
g
e
c
u
r
r
en
t.
Fu
r
th
er
m
o
r
e,
th
e
lo
s
s
v
alu
e
f
in
d
i
n
g
s
u
s
in
g
th
e
PLE
C
S
s
o
f
twar
e
illu
s
tr
ate
th
e
p
r
o
p
o
r
tio
n
o
f
lo
s
s
es
f
o
r
ea
c
h
in
v
er
ter
co
m
p
o
n
en
t.
T
h
e
c
r
itical
p
ar
am
eter
v
al
u
es
u
s
ed
th
r
o
u
g
h
th
e
s
im
u
latio
n
ar
e
d
etailed
in
T
a
b
le
4
.
T
a
b
le
5
co
n
tr
asts
th
e
p
r
o
p
o
s
ed
i
n
v
er
t
er
to
a
v
a
r
iety
o
f
t
o
p
o
lo
g
ies.
Fig
u
r
e
4
(
a)
illu
s
tr
ates
th
e
f
iv
e
-
lev
el
o
u
tp
u
t
v
o
ltag
e
ch
ar
ac
te
r
ized
b
y
a
p
ea
k
v
al
u
e
o
f
2
4
0
V,
u
tili
zin
g
th
e
p
ar
am
eter
s
p
ec
if
icatio
n
s
p
r
o
v
id
ed
in
T
ab
le
4
.
Fig
u
r
e
4
(
b
)
illu
s
tr
ates
th
e
v
ar
iatio
n
s
in
o
u
tp
u
t
v
o
ltag
e
as
th
e
d
u
ty
c
y
cle
is
a
d
ju
s
ted
in
in
cr
e
m
en
ts
o
f
1
0
%,
r
an
g
in
g
f
r
o
m
D
=
8
0
%
to
D
=
2
0
%.
A
n
o
tab
le
attr
ib
u
te
o
f
th
e
p
r
o
p
o
s
ed
in
v
e
r
ter
is
its
ab
ilit
y
to
r
eg
u
late
t
h
e
p
ea
k
o
u
tp
u
t
v
o
ltag
e
ac
r
o
s
s
a
b
r
o
ad
o
p
e
r
atio
n
al
s
p
ec
tr
u
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
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
673
-
682
678
Fig
u
r
e
4
(
c)
illu
s
tr
ates
th
e
m
o
d
u
latio
n
in
d
e
x
v
alu
e
alter
e
d
f
r
o
m
0
to
its
m
ax
im
u
m
(
M
=
1
)
.
T
h
e
c
o
n
v
er
te
r
p
r
o
d
u
ce
s
a
th
r
ee
-
lev
el
v
o
ltag
e
wh
en
M
<
0
.
5
an
d
a
f
iv
e
-
lev
e
l w
av
ef
o
r
m
wh
en
M
>
0
.
5
,
as d
etailed
in
T
ab
le
2
.
Fig
u
r
es 5
(
a)
an
d
5
(
b
)
p
r
esen
t t
h
e
v
o
ltag
e
m
ea
s
u
r
em
en
ts
o
f
th
e
to
p
o
lo
g
y
ca
p
ac
ito
r
s
(
C
1
an
d
C
2
)
.
T
ab
le
4
.
Simu
latio
n
p
ar
am
eter
esti
m
ates o
f
th
e
p
r
o
p
o
s
ed
in
v
er
ter
V
a
l
u
e
P
a
r
a
me
t
e
r
V
a
l
u
e
P
a
r
a
me
t
e
r
3
mH
I
n
p
u
t
i
n
d
u
c
t
o
r
(
L
b
)
2
4
V
S
o
u
r
c
e
(
V
dc
)
1
0
0
Ω
+
1
0
mH
I
n
d
u
c
t
i
v
e
l
o
a
d
1
2
0
0
µ
F
C
a
p
a
c
i
t
o
r
(
C
1
a
n
d
C
2
)
Le
v
e
l
sh
i
f
t
P
W
M
PWM
1
0
k
H
z
F
(S
W
)
8
0
%
D
1
M
T
ab
le
5
.
C
o
m
p
a
r
is
o
n
o
f
5
-
lev
e
l b
o
o
s
t
in
v
er
ter
s
with
o
th
er
in
v
er
ter
to
p
o
lo
g
ies
S
t
r
u
c
t
u
r
e
S
D
C
L
N
L
e
v
e
l
G
a
i
n
CC
CG
[
2
7
]
3
6
2
2
3
(
1
−
)
[
2
8
]
7
0
2
1
5
2
[
2
9
]
6
3
2
1
3
(
1
−
)
P
r
o
p
o
se
d
5
-
l
e
v
e
l
7
0
2
1
5
2
(
1
−
)
*
S
:
S
w
i
t
c
h
i
n
g
n
u
mb
e
r
,
D
:
D
i
o
d
e
s
n
u
mb
e
r
,
C
:
C
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I
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g
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n
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its
s
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ch
as
(
a)
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b
)
(
c)
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
S
in
g
le
-
s
ta
g
e
tr
a
n
s
fo
r
mer le
s
s
mu
ltil
ev
el
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t in
ve
r
ter w
ith
z
ero
…
(
Da
lya
Ha
mza
h
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l
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mo
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681
en
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alid
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t
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e
in
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ter
'
s
ef
f
icien
cy
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
P
.
K
a
z
m
i
e
r
k
o
w
s
k
i
,
“
G
r
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d
C
o
n
v
e
r
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r
s
a
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d
P
o
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e
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E
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t
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i
c
s
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r
e
v
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w
o
f
"
G
r
i
d
C
o
n
v
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e
r
s
f
o
r
P
h
o
t
o
v
o
l
t
a
i
c
a
n
d
W
i
n
d
P
o
w
e
r
S
y
st
e
ms:
T
e
o
d
o
r
e
sc
u
,
R
.
,
e
t
a
l
.
;
2
0
1
1
)
[
B
o
o
k
N
e
w
s]
,
”
I
EEE
I
n
d
u
st
ri
a
l
E
l
e
c
t
r
o
n
i
c
s
Ma
g
a
zi
n
e
,
v
o
l
.
5
,
n
o
.
2
,
p
p
.
5
4
–
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4
,
Ju
n
.
2
0
1
1
,
d
o
i
:
1
0
.
1
1
0
9
/
M
I
E.
2
0
1
1
.
9
4
1
1
1
6
.
[
2
]
E.
G
u
b
í
a
,
P
.
S
a
n
c
h
i
s,
A
.
U
r
sú
a
,
J.
L
ó
p
e
z
,
a
n
d
L.
M
a
r
r
o
y
o
,
“
G
r
o
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d
c
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r
e
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t
s
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si
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g
l
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-
p
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se
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r
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o
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merl
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p
h
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t
o
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l
t
a
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s
y
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e
ms,
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Pro
g
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i
n
P
h
o
t
o
v
o
l
t
a
i
c
s:
Re
s
e
a
r
c
h
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n
d
Ap
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t
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s
,
v
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.
1
5
,
n
o
.
7
,
p
p
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6
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9
–
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0
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,
d
o
i
:
1
0
.
1
0
0
2
/
p
i
p
.
7
6
1
.
[
3
]
Y
.
Y
a
n
g
a
n
d
F
.
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B
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H
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S O
F
AUTH
O
RS
Da
ly
a
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y
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ra
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n
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g
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r
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ly
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m
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d
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ste
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e
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s.
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c
a
n
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c
o
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tac
ted
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m
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sh
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u
tm.m
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d
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if
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k
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lay
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rin
g
h
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D,
h
is
re
se
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rc
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p
rima
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se
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d
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g
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l
c
ircu
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d
e
sig
n
s f
o
r
M
LI,
a
n
d
h
e
re
c
e
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d
re
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g
n
it
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o
n
fo
r
h
is wo
rk
fr
o
m
th
e
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o
f
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h
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r
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c
a
ti
o
n
,
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lay
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h
is
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a
rly
c
a
re
e
r,
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S
a
a
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g
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t
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ro
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ts,
o
n
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th
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rn
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e
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t
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n
d
t
h
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th
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th
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tral
g
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v
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rn
m
e
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t
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n
d
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g
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g
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n
c
y
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se
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rc
h
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o
c
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se
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d
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l
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ircu
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e
sig
n
s
fo
r
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LI
in
p
o
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r
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tro
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ic sy
ste
m
s
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n
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e
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m
e
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t
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sy
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m
s
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e
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ra
ll
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e
rfo
rm
a
n
c
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o
f
p
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we
r
sy
ste
m
s
a
n
d
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n
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ra
ted
re
n
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wa
b
le
e
n
e
rg
y
sy
ste
m
s.
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c
o
n
tri
b
u
ted
t
o
t
h
e
field
o
f
p
o
we
r
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tro
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n
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e
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th
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li
c
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s,
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n
d
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ro
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se
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s.
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h
a
s
r
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c
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se
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ra
l
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rd
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n
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o
m
n
a
ti
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l
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tern
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ti
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l
b
o
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ies
.
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a
fa
c
u
lt
y
m
e
m
b
e
r
o
f
Alig
a
rh
M
u
slim
Un
iv
e
rsity
,
Dr.
S
a
a
d
c
o
n
t
in
u
e
s
to
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o
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u
c
t
c
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tt
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g
-
e
d
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e
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se
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rc
h
in
th
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f
ield
o
f
p
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we
r
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tro
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s
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n
d
re
n
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le
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n
e
rg
y
sy
ste
m
s.
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a
lso
m
e
n
to
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n
u
m
e
r
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s
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ra
d
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a
te
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d
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c
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g
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s
in
p
ro
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ss
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l
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o
c
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su
c
h
a
s
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E.
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is
d
e
d
ica
ted
to
c
o
n
ti
n
u
i
n
g
h
is
re
se
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rc
h
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n
d
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tri
b
u
t
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g
to
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e
a
c
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d
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m
ic
c
o
m
m
u
n
it
y
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t
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ig
a
r
h
M
u
slim
Un
i
v
e
rsity
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
sa
a
d
.
e
e
@a
m
u
.
a
c
.
in
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