I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
,
p
p
.
863
~
871
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
7
.
i3
.
p
p
8
6
3
-
871
863
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JP
E
DS
A Review
on Desig
n
a
nd Contro
l M
ethods
o
f
M
o
dula
r Multilev
el
Co
nv
erte
r
Ra
m
y
a
G
,
Ra
m
a
pra
b
ha
R
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
E
n
g
in
e
e
rin
g
,
S
S
N Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Ka
lav
a
k
k
a
m
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
1
2
,
2
0
1
5
R
ev
i
s
ed
Mar
2
8
,
2
0
1
6
A
cc
ep
ted
A
p
r
29
,
2
0
1
6
M
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
(M
M
C)
a
re
a
n
e
m
e
r
g
in
g
v
o
lt
a
g
e
so
u
rc
e
c
o
n
v
e
rter
to
p
o
lo
g
y
su
it
a
b
le
f
o
r
m
a
n
y
a
p
p
li
c
a
ti
o
n
s.
Du
e
to
a
b
u
n
d
a
n
t
u
ti
li
z
a
ti
o
n
o
f
HV
DC
p
o
w
e
r
tran
s
m
issio
n
,
t
h
e
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
h
a
s
b
e
c
o
m
e
p
o
p
u
lar
c
o
n
v
e
rter
ty
p
e
to
b
e
u
se
d
in
h
ig
h
v
o
lt
a
g
e
a
p
p
li
c
a
ti
o
n
s.
Oth
e
r
a
p
p
li
c
a
ti
o
n
s
i
n
c
lu
d
e
in
terf
a
c
in
g
re
n
e
w
a
b
le
e
n
e
r
g
y
p
o
w
e
r
so
u
rc
e
s
to
th
e
g
rid
a
n
d
m
o
to
r
d
riv
e
s.
M
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
a
re
b
e
n
e
f
ici
a
l
f
o
r
h
ig
h
v
o
lt
a
g
e
a
n
d
h
ig
h
p
o
w
e
r
m
o
to
r
d
riv
e
s
b
e
c
a
u
se
of
th
e
p
ro
p
e
rti
e
s
o
f
th
is
c
o
n
v
e
rter
to
p
o
lo
g
y
,
su
c
h
a
s,
lo
w
d
isto
rti
o
n
,
h
ig
h
e
ff
icie
n
c
y
,
e
tc
.
F
o
r
th
e
p
a
st
f
e
w
y
e
a
rs
sig
n
i
f
ica
n
t
re
se
a
rc
h
h
a
s
b
e
e
n
c
a
rried
o
u
t
to
a
d
d
re
ss
th
e
tec
h
n
ica
l
c
h
a
ll
e
n
g
e
s
a
s
so
c
iate
d
w
it
h
o
p
e
ra
ti
o
n
a
n
d
v
o
lt
a
g
e
b
a
lan
c
in
g
o
f
M
M
C.
In
th
is
p
a
p
e
r,
a
d
e
tailed
tec
h
n
ica
l
re
v
iew
o
n
th
e
c
o
n
tr
o
l
stra
teg
ies
is
p
r
e
se
n
ted
f
o
r
re
a
d
y
re
f
e
re
n
c
e
.
K
ey
w
o
r
d
:
C
ap
ac
ito
r
v
o
ltag
e
b
alan
c
in
g
Mo
d
u
lar
m
u
l
tile
v
el
co
n
v
er
ter
Mo
d
u
latio
n
tec
h
n
iq
u
es
C
ir
cu
lat
in
g
cu
r
r
e
n
t c
o
n
tr
o
l
Hig
h
v
o
lta
g
e
d
ir
ec
t c
u
r
r
en
t
(
HVDC)
Co
p
y
rig
h
t
©
201
6
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
G.
R
a
m
y
a,
Dep
ar
t
m
en
t o
f
E
letr
ical
an
d
E
l
ec
tr
o
n
ics E
n
g
i
n
ee
r
in
g
,
SS
N
C
o
lle
g
e
o
f
E
n
g
i
n
ee
r
i
n
g
,
R
aj
iv
Gan
d
h
i Sala
i,
Kala
v
a
k
k
a
m
,
C
h
en
n
ai
6
0
3
1
1
0
,
I
n
d
ia
.
E
m
ail:
r
a
m
y
a
m
r
o
s
e
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
m
o
d
u
lar
m
u
ltil
e
v
el
co
n
v
e
r
ter
h
as
b
ec
o
m
e
t
h
e
m
o
s
t
attr
ac
tiv
e
m
u
ltil
e
v
el
co
n
v
er
ter
to
p
o
lo
g
y
f
o
r
me
d
iu
m
/
h
i
g
h
-
p
o
w
er
ap
p
licatio
n
s
.
T
h
ese
co
n
v
er
ter
s
ca
n
b
e
u
s
ed
f
o
r
m
ed
i
u
m
a
n
d
h
ig
h
v
o
ltag
e
ap
p
licatio
n
s
w
it
h
lo
w
v
o
lta
g
e
I
GB
T
s
w
it
ch
es
[
1
].
T
h
er
e
ar
e
s
ev
er
al
t
y
p
es
o
f
m
u
lti
lev
el
co
n
v
er
ter
to
p
o
lo
g
ies
.
E
v
e
n
th
o
u
g
h
th
e
f
u
n
d
a
m
e
n
tal
co
n
ce
p
ts
ar
e
s
i
m
ilar
,
th
er
e
ar
e
d
if
f
er
en
ce
s
in
t
h
e
co
n
tr
o
l
r
eq
u
ir
em
en
ts
ac
r
o
s
s
th
e
s
e
v
ar
io
u
s
to
p
o
lo
g
ie
s
.
MM
C
h
a
s
s
ev
er
al
ad
v
an
ta
g
e
s
co
m
p
ar
ed
w
it
h
o
th
er
m
u
ltil
e
v
el
to
p
o
lo
g
ies
s
u
ch
a
s
it
s
m
o
d
u
lar
s
tr
u
ct
u
r
e
an
d
s
ca
lab
il
it
y
,
h
i
g
h
ef
f
ici
e
n
c
y
,
lo
w
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
2
]
.
I
n
r
ec
en
t
y
ea
r
s
,
ad
d
r
ess
in
g
th
e
is
s
u
es b
ased
o
n
o
p
er
atio
n
a
n
d
co
n
tr
o
l o
f
MM
C
h
as b
ec
o
m
e
s
ig
n
if
ican
t
.
T
h
er
e
h
a
s
b
ee
n
s
u
b
s
tan
t
ial
p
r
o
g
r
ess
i
n
th
e
d
ev
e
lo
p
m
en
t
o
f
p
u
l
s
e
-
w
i
d
th
m
o
d
u
latio
n
tec
h
n
iq
u
es,
v
o
ltag
e
b
alan
ci
n
g
al
g
o
r
ith
m
s
an
d
co
n
v
e
n
tio
n
a
l
co
n
tr
o
l a
p
p
r
o
ac
h
es a
p
p
licab
le
to
m
o
d
u
lar
m
u
ltil
e
v
el
co
n
v
er
t
er
s
.
T
h
e
m
ai
n
o
b
j
ec
tiv
e
o
f
t
h
i
s
p
a
p
er
is
to
p
r
o
v
id
e
b
etter
u
n
d
er
s
tan
d
in
g
o
f
MM
C
co
n
s
id
er
in
g
th
e
i
s
s
u
es.
T
h
is
p
ap
er
d
ea
ls
w
it
h
co
m
p
lete
tech
n
ica
l
r
ev
ie
w
o
n
t
h
e
o
p
er
atio
n
al
is
s
u
es,
co
n
tr
o
l
an
d
m
o
d
u
latio
n
tech
n
iq
u
es.
T
h
e
p
ap
er
is
o
r
g
an
i
s
ed
as
f
o
llo
w
s
:
S
ec
tio
n
I
I
b
r
ief
s
ab
o
u
t
th
e
o
p
er
atio
n
o
f
MM
C
.
Sectio
n
I
I
I
d
escr
ib
es
v
ar
io
u
s
m
o
d
u
latio
n
tech
n
iq
u
es
a
n
d
v
ar
io
u
s
o
p
er
atio
n
al
is
s
u
e
s
s
u
ch
as
ca
p
ac
ito
r
v
o
ltag
e
b
alan
c
in
g
an
d
cir
cu
lati
n
g
cu
r
r
e
n
t
co
n
tr
o
l
an
d
also
th
e
r
ed
u
ctio
n
o
f
r
ip
p
le
in
ca
p
ac
it
o
r
v
o
ltag
e
b
y
v
ar
i
o
u
s
tech
n
iq
u
e
s
ar
e
also
ex
p
lain
ed
.
T
h
e
co
n
clu
d
i
n
g
r
e
m
ar
k
s
ar
e
p
r
esen
ted
in
Sect
io
n
I
V.
2.
M
O
DULAR M
UL
T
I
L
E
V
E
L
CO
NVE
RT
E
R
-
ANO
V
E
R
VIE
W
T
h
e
s
ch
e
m
a
tic
o
f
t
h
r
ee
p
h
ase
m
o
d
u
lar
m
u
lt
ilev
e
l
co
n
v
er
ter
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
MM
C
co
n
s
i
s
ts
o
f
a
s
eq
u
en
ce
o
f
s
u
b
-
m
o
d
u
le
co
n
n
ec
ted
in
s
er
ies
f
o
r
ea
ch
p
h
ase
o
f
th
e
co
n
v
er
ter
.
E
ac
h
s
u
b
-
m
o
d
u
le
co
n
s
i
s
ts
o
f
t
wo
s
w
itc
h
es
co
n
n
ec
ted
in
h
al
f
-
b
r
id
g
e
to
p
o
lo
g
y
w
it
h
ca
p
ac
ito
r
ac
r
o
s
s
t
h
e
d
ev
ice
w
h
ich
is
u
s
ed
as
t
h
e
e
n
e
r
g
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
863
–
8
7
1
864
s
to
r
ag
e
an
d
s
u
p
p
l
y
d
ev
ice
.
T
h
e
o
u
tp
u
t
ter
m
in
al
s
ar
e
co
n
n
e
cted
to
th
e
co
n
v
er
ter
ac
r
o
s
s
t
h
e
lo
w
er
s
w
itc
h
i
n
g
d
ev
ice.
T
h
is
s
h
o
w
s
th
at
t
h
e
ca
p
ac
ito
r
ac
r
o
s
s
t
w
o
d
e
v
ices
is
eit
h
er
d
ir
ec
tl
y
co
n
n
ec
ted
to
th
e
co
n
v
er
ter
o
r
s
h
o
r
ted
o
u
t
d
e
p
en
d
in
g
o
n
t
h
e
g
ati
n
g
s
ig
n
al
s
[
3
]
.
T
h
e
s
eq
u
en
ce
o
f
s
ub
-
m
o
d
u
le
s
alo
n
g
with
a
n
ar
m
in
d
u
cto
r
m
ak
e
s
an
ar
m
o
f
t
h
e
co
n
v
er
t
er
.
T
h
e
s
in
g
le
p
h
a
s
e
o
f
t
h
e
c
o
n
v
er
ter
co
n
s
i
s
ts
o
f
t
w
o
ar
m
s
s
u
c
h
as
u
p
p
er
ar
m
an
d
lo
w
er
ar
m
.
E
ac
h
p
h
a
s
e
i
s
co
n
n
ec
ted
to
t
h
e
s
u
p
p
l
y
b
y
th
e
e
n
d
o
f
th
e
s
u
b
-
m
o
d
u
le
.
T
h
e
ar
m
i
n
d
u
cto
r
p
r
esen
t in
ea
c
h
ar
m
is
u
s
ed
to
li
m
it
th
e
cir
c
u
lati
n
g
cu
r
r
en
t a
n
d
to
f
ilter
th
e
h
ar
m
o
n
ics.
T
h
e
n
u
m
b
er
o
f
le
v
els
in
MM
C
d
ep
en
d
s
o
n
t
h
e
n
u
m
b
e
r
o
f
s
u
b
-
m
o
d
u
le
s
p
r
esen
t
in
e
ac
h
ar
m
.
T
h
e
n
u
m
b
er
o
f
le
v
el
s
is
d
eter
m
i
n
ed
b
y
N=
2
S+1
,
w
h
er
e
S i
s
th
e
n
u
m
b
er
o
f
s
u
b
-
m
o
d
u
le
p
r
ese
n
t in
ea
ch
ar
m
[
4]
.
T
h
e
co
n
d
u
ctio
n
p
ath
o
f
th
e
s
u
b
-
m
o
d
u
le
d
ep
en
d
s
o
n
s
w
i
t
ch
i
n
g
o
f
t
h
e
s
w
itc
h
i
n
g
d
ev
i
ce
s
.
E
ac
h
s
u
b
-
m
o
d
u
le
w
ill
b
e
in
o
n
e
o
f
t
h
e
t
w
o
s
tates
(
i.e
.
o
n
e
s
w
itc
h
in
ON
s
tate
a
n
d
o
th
er
at
OF
F
s
ta
te)
[
5
]
.
T
h
e
co
n
d
u
ctio
n
p
ath
is
e
x
p
l
ain
ed
w
h
en
t
h
e
c
u
r
r
en
t
p
o
lar
it
y
i
s
p
o
s
it
iv
e
an
d
n
e
g
ati
v
e
w
h
ic
h
i
s
s
h
o
w
n
i
n
Fig
u
r
e
2.
Fig
u
r
e
1
.
Sch
e
m
atic
o
f
t
h
r
ee
p
h
ase
MM
C
Fig
u
r
e
2
.
MM
C
C
o
n
d
u
ctio
n
p
ath
(
a)
P
o
s
itiv
e
cu
r
r
en
t (
b
)
Neg
ati
v
e
cu
r
r
en
t
3.
RE
VI
E
W
O
N
D
E
S
I
G
N,
M
O
DULA
T
I
O
N
AN
D
CO
NT
R
O
L
T
E
CH
NI
Q
U
E
S O
F
M
M
C
I
n
th
i
s
s
ec
tio
n
,
th
e
m
at
h
e
m
a
tical
m
o
d
elli
n
g
o
f
MM
C
,
m
o
d
u
latio
n
tec
h
n
iq
u
es,
v
o
ltag
e
b
alan
cin
g
co
n
tr
o
l,
cir
cu
latin
g
cu
r
r
e
m
t
c
o
n
tr
o
l
an
d
Su
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le
r
ed
u
ctio
n
co
n
tr
o
l
m
eth
o
d
s
ar
e
ex
p
lain
ed
b
r
ief
l
y
.
3
.
1
.
M
a
t
he
m
a
t
ica
l
M
o
dellin
g
o
f
M
M
C
T
h
r
ee
p
h
ase
MM
C
b
ased
h
alf
-
b
r
id
g
e
s
u
b
-
m
o
d
u
le
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
T
h
e
ad
d
itio
n
o
f
ar
m
r
esis
ta
n
ce
m
o
d
el
s
t
h
e
p
o
w
er
l
o
s
s
w
it
h
i
n
ea
c
h
ar
m
o
f
MM
C
.
T
h
e
d
etailed
d
escr
ip
tio
n
o
n
m
o
d
ell
in
g
o
f
MM
C
is
g
i
v
e
n
in
[
6
]
.
T
h
e
u
p
p
er
an
d
th
e
lo
w
er
ar
m
cu
r
r
en
t o
f
ea
ch
p
h
ase
is
g
i
v
en
b
y
,
2
x
i
x
,
c
i
r
c
i
3
dc
i
x
,
u
i
(
1
)
2
x
i
x
,
c
i
r
c
i
3
dc
i
x
,
l
i
(
2
)
w
h
er
e
x
=
a,
b
,
c
(
p
h
ase)
,
i
u,
x
an
d
i
l,
x
ar
e
th
e
u
p
p
er
an
d
lo
w
er
ar
m
c
u
r
r
en
t,
i
circ,
x
is
t
h
e
cir
cu
lati
n
g
c
u
r
r
en
t
i
n
ea
ch
p
h
ase.
T
h
e
cir
cu
lati
n
g
cu
r
r
en
t is g
i
v
e
n
b
y
,
3
dc
i
2
x
,
l
i
x
,
u
i
x
,
c
i
r
c
i
(
3
)
T
h
e
d
y
n
a
m
ic
b
e
h
av
io
u
r
o
f
M
MC is
d
escr
ib
ed
by
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
R
ev
iew
o
n
Desig
n
a
n
d
C
o
n
tr
o
l Meth
o
d
s
o
f Mo
d
u
l
a
r
Mu
ltil
ev
el
C
o
n
ve
r
ter
(
R
a
mya
G.
)
865
cm
V
x
V
x
,
u
i
0
R
dt
x
,
u
di
0
L
x
,
u
V
2
dc
V
(
4
)
cm
V
x
V
x
,
l
i
0
R
dt
x
,
l
di
0
L
x
,
l
V
2
dc
V
(
5
)
w
h
er
e
V
u,
x
an
d
V
l,
x
ar
e
t
h
e
u
p
p
er
an
d
lo
w
er
ar
m
v
o
ltag
e,
V
x
is
t
h
e
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t
a
n
d
V
cm
i
s
t
h
e
co
m
m
o
n
m
o
d
e
v
o
lta
g
e.
T
h
e
M
MC
p
h
a
s
e
v
o
ltag
e
is
e
x
p
r
es
s
ed
as
i
n
(
6
)
an
d
MM
C
cir
c
u
l
atin
g
c
u
r
r
en
t
i
s
g
iv
e
n
by
(
7
)
.
dt
x
di
2
0
L
x
i
2
0
R
2
x
l,
V
x
u,
V
cm
V
x
V
(
6
)
3
dc
i
0
R
2
x
l,
V
x
u,
V
2
dc
V
x
c
i
r
c
,
i
0
R
dt
x
c
i
r
c
,
di
0
L
(
7
)
T
h
e
u
p
p
er
an
d
th
e
lo
w
er
ar
m
v
o
ltag
e
s
o
f
MM
C
ar
e
g
i
v
en
b
y
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
s
.
x
c
u
,
V
x
u,
n
x
u,
V
(
8
)
x
c
l
,
V
x
l,
n
x
l,
V
(
9
)
w
h
er
e
V
cu,
x
an
d
V
cl,
x
ar
e
th
e
i
n
d
iv
id
u
al
s
u
b
m
o
d
u
le
ca
p
ac
it
o
r
v
o
ltag
e
o
f
u
p
p
er
an
d
th
e
l
o
w
er
ar
m
.
E
ac
h
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
o
f
t
h
e
MM
C
is
m
o
d
eled
b
y
t
h
e
p
o
w
er
p
r
o
ce
s
s
ed
b
y
ea
c
h
ar
m
.
T
h
e
p
o
w
er
p
r
o
ce
s
s
ed
b
y
ea
c
h
ar
m
i
s
g
i
v
e
n
b
y
x
,
u
i
x
,
cu
V
x
,
u
n
x
,
u
i
x
,
u
V
x
,
u
P
(
1
0
)
x
,
l
i
x
,
cl
V
x
,
l
n
x
,
l
i
x
,
l
V
x
,
l
P
(
1
1
)
E
ac
h
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le
ca
n
b
e
d
ef
in
ed
as
x
,
u
n
2
x
i
x
,
c
i
r
c
i
3
dc
i
SM
NC
1
x
,
u
n
SM
NC
x
,
u
i
dt
x
,
cu
dV
(
1
2
)
x
,
l
n
2
x
i
x
,
c
i
r
c
i
3
dc
i
SM
NC
1
x
,
l
n
SM
NC
x
,
l
i
dt
x
,
cl
dV
(
1
3
)
T
h
e
g
en
er
alis
ed
d
y
n
a
m
ic
m
o
d
el
o
f
MM
C
is
g
i
v
en
b
y
ab
o
v
e
eq
u
atio
n
s
a
n
d
is
u
s
ed
in
t
h
e
co
n
tr
o
l
p
u
r
p
o
s
e.
T
h
e
d
y
n
a
m
ic
m
o
d
el
lin
g
o
f
MM
C
is
p
r
o
p
o
s
ed
[
7
]
b
y
co
n
s
id
er
in
g
th
e
s
u
m
m
at
io
n
o
f
s
u
b
-
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
i
n
ea
ch
ar
m
i
n
s
tead
u
s
i
n
g
o
f
i
n
d
i
v
id
u
al
s
u
b
-
m
o
d
u
le
ca
p
ac
ito
r
v
o
l
t
ag
e
i
n
g
e
n
er
alize
d
d
y
n
a
m
ic
m
o
d
el.
T
h
e
d
ir
ec
t
an
d
in
d
ir
ec
t
m
o
d
u
latio
n
s
tr
ate
g
ies
to
d
eter
m
i
n
e
t
h
e
MM
C
d
y
n
a
m
ic
m
o
d
el
i
s
pr
o
p
o
s
ed
[
8
]
b
y
u
s
in
g
th
e
n
u,
x
an
d
n
l,
x
ex
p
r
es
s
io
n
.
I
t
r
esu
l
ts
in
t
h
e
co
n
ti
n
u
o
u
s
d
y
n
a
m
i
c
m
o
d
el
s
in
ce
lo
w
f
r
eq
u
en
c
y
co
m
p
o
n
e
n
t
s
ar
e
co
n
s
id
er
ed
.
Ma
n
y
m
et
h
o
d
s
o
f
co
n
tin
u
o
u
s
m
o
d
elli
n
g
o
f
M
MC
an
d
f
r
eq
u
e
n
c
y
d
o
m
ai
n
m
o
d
elli
n
g
ar
e
p
r
o
p
o
s
ed
[
9
]
.
T
h
e
m
ai
n
ad
v
a
n
ta
g
e
o
f
t
h
is
m
o
d
ell
in
g
co
m
p
ar
ed
to
g
en
er
al
m
o
d
elli
n
g
o
f
MM
C
is
th
at
f
aster
co
m
p
u
tati
o
n
o
f
s
y
s
te
m
s
ta
tes
f
o
r
in
cr
ea
s
e
in
n
u
m
b
er
o
f
lev
els.
He
n
ce
i
t
is
u
n
d
er
s
to
o
d
th
at
th
e
d
y
n
a
m
ic
m
o
d
el
ca
n
b
e
o
p
t selec
tio
n
w
h
ile
s
i
m
u
lat
in
g
M
MC
w
it
h
g
r
id
in
ter
f
ac
i
n
g
ap
p
licatio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
863
–
8
7
1
866
3
.
2
.
M
o
du
la
t
io
n T
ec
hn
iq
ues
Ma
n
y
p
u
ls
e
w
id
t
h
m
o
d
u
lat
io
n
tech
n
iq
u
es
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
in
MM
C
t
h
at
ar
e
d
is
cu
s
s
ed
b
elo
w
.
C
ar
r
ier
d
is
p
o
s
itio
n
p
u
l
s
e
w
id
t
h
m
o
d
u
latio
n
tec
h
n
iq
u
e
w
a
s
p
r
o
p
o
s
ed
[
10
]
w
h
ic
h
r
eq
u
ir
e
N
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
t
h
at
ar
e
d
is
p
lace
d
p
r
o
p
o
r
tio
n
all
y
w
it
h
r
esp
ec
t
to
ze
r
o
ax
is
.
T
h
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
is
o
b
tain
ed
b
y
co
m
p
ar
i
n
g
t
h
e
p
h
a
s
e
v
o
lta
g
e
r
ef
er
en
ce
w
it
h
t
h
e
ca
r
r
ier
s
ig
n
a
l.
B
ased
o
n
t
h
e
s
h
i
f
t
i
n
t
h
e
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
al
th
i
s
P
W
M
tech
n
iq
u
e
i
s
f
u
r
t
h
er
clas
s
i
f
ied
i
n
to
p
h
a
s
e
d
is
p
o
s
itio
n
(
P
D)
,
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
P
OD)
an
d
alter
n
ate
p
h
ase
o
p
p
o
s
itio
n
d
is
p
o
s
itio
n
(
A
P
OD)
.
T
h
e
ca
r
r
ier
s
ig
n
als
o
f
ab
o
v
e
te
ch
n
iq
u
es
ar
e
s
h
o
w
n
in
Fig
u
r
e
3
.
T
h
e
m
ai
n
d
r
a
w
b
a
ck
o
f
t
h
ese
P
W
M
tech
n
iq
u
e
s
i
s
t
h
at
u
n
eq
u
al
v
o
lta
g
e
d
i
s
tr
ib
u
tio
n
a
m
o
n
g
th
e
s
u
b
m
o
d
u
le
w
h
ich
r
es
u
lt
s
in
t
h
e
i
n
cr
ea
s
e
in
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
T
o
r
ep
o
r
t
th
is
is
s
u
e
t
h
e
d
if
f
er
e
n
t
m
o
d
u
latio
n
tech
n
iq
u
e
s
s
u
ch
a
s
s
i
m
p
le
ca
r
r
ier
r
o
tatio
n
,
m
o
d
if
ied
ca
r
r
ier
r
o
tatio
n
PW
M
tec
h
n
iq
u
es
ar
e
u
s
ed
to
eq
u
alize
th
e
v
o
lta
g
e
d
is
tr
ib
u
t
io
n
a
m
o
n
g
t
h
e
s
u
b
m
o
d
u
le.
Ho
w
e
v
er
th
e
T
HD
is
r
elativ
e
l
y
h
i
g
h
.
Hen
ce
t
h
e
m
o
d
i
f
ied
P
D
-
P
W
M
tech
n
iq
u
e
w
i
th
ca
p
ac
ito
r
v
o
ltag
e
b
ala
n
c
in
g
is
p
r
o
p
o
s
ed
[
1
1
]
.
I
n
th
is
t
ec
h
n
iq
u
e
p
ar
ticu
lar
g
ati
n
g
s
eq
u
e
n
ce
i
s
n
o
t
ass
ig
n
ed
to
a
s
p
ec
i
f
ied
s
u
b
m
o
d
u
le.
T
h
e
co
m
p
ar
is
o
n
o
f
r
ef
er
e
n
ce
s
i
g
n
al
w
i
th
th
e
ca
r
r
ier
s
ig
n
al
p
r
o
d
u
ce
N+
1
le
v
el
i
n
th
e
o
u
tp
u
t
s
id
e
w
h
ic
h
d
eter
m
i
n
es
t
h
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
le
to
b
e
ad
d
ed
in
u
p
p
er
an
d
lo
w
er
a
r
m
.
T
h
e
P
D
-
P
W
M
w
it
h
s
elec
ti
v
e
lo
o
p
b
ias
m
ap
p
in
g
m
et
h
o
d
is
p
r
o
p
o
s
ed
f
o
r
v
o
ltag
e
b
alan
cin
g
i
n
th
e
m
o
d
u
le.
T
h
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
an
d
d
ir
ec
tio
n
o
f
i
n
d
u
cto
r
cu
r
r
e
n
t
ar
e
th
e
f
ee
d
b
ac
k
s
ig
n
al
s
u
s
ed
in
t
h
is
m
et
h
o
d
.
T
h
e
o
th
er
tec
h
n
iq
u
es
ar
e
t
h
at
t
h
e
p
h
ase
s
h
i
f
t
ca
r
r
ier
m
o
d
u
latio
n
tech
n
iq
u
e
[
1
2
]
in
w
h
ic
h
ea
c
h
ca
r
r
ier
is
p
h
a
s
e
s
h
i
f
ted
b
y
3
6
0
/(
N
-
1
)
.
T
h
e
n
u
m
b
er
o
f
ca
r
r
ier
s
i
g
n
als
u
s
e
d
in
t
h
i
s
tec
h
n
iq
u
e
d
ep
en
d
s
o
n
th
e
n
u
m
b
er
o
f
lev
el
in
MM
C
.
I
n
th
i
s
tech
n
iq
u
e
ea
ch
s
u
b
m
o
d
u
le
o
f
MM
C
is
co
n
tr
o
lled
in
d
ep
en
d
en
tl
y
a
n
d
v
o
ltag
e
b
alan
ci
n
g
co
n
tr
o
l
i
s
d
o
n
e
b
y
av
er
ag
i
n
g
co
n
tr
o
l
a
n
d
b
alan
c
in
g
co
n
tr
o
l.
T
h
es
e
co
n
tr
o
l
tech
n
iq
u
e
co
n
tr
o
l
t
h
e
av
er
ag
e
s
u
b
m
o
d
u
le
v
o
lta
g
e
i
n
ea
ch
p
h
a
s
e
an
d
al
s
o
in
d
iv
id
u
all
y
b
alan
ci
n
g
th
e
ca
p
ac
ito
r
v
o
ltag
e
o
f
ea
ch
s
u
b
m
o
d
u
le
.
T
h
e
s
w
itc
h
i
n
g
s
ig
n
al
s
ar
e
g
iv
e
n
to
ea
ch
s
u
b
m
o
d
u
l
e
b
y
co
m
p
ar
i
n
g
t
h
e
r
ef
er
en
ce
v
o
ltag
e
w
it
h
f
r
o
m
ea
ch
p
h
a
s
e
w
it
h
th
e
tr
ian
g
u
lar
ca
r
r
ier
s
i
g
n
al.
T
h
e
m
ai
n
d
r
a
w
b
ac
k
o
f
th
is
m
o
d
u
latio
n
tec
h
n
iq
u
e
is
th
a
t
co
m
p
le
x
it
y
w
i
th
in
cr
ea
s
e
in
t
h
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
le
a
n
d
in
s
tab
il
it
y
u
n
d
er
ce
r
tain
co
n
d
itio
n
.
T
h
is
is
s
u
e
is
o
v
er
co
m
e
b
y
i
n
tr
o
d
u
cin
g
th
e
ar
m
b
alan
ce
co
n
tr
o
l
in
th
e
r
ef
er
en
ce
s
ig
n
al
b
ased
o
n
th
e
d
i
f
f
er
e
n
ce
in
t
h
e
ca
p
a
cito
r
v
o
ltag
es
o
f
u
p
p
er
an
d
t
h
e
lo
w
er
ar
m
.
T
h
e
d
if
f
er
e
n
t
P
W
M
tech
n
iq
u
es
ar
e
s
h
o
w
n
b
elo
w
i
n
Fi
g
u
r
e
3.
C
o
m
p
ar
i
s
o
n
o
f
ab
o
v
e
m
e
n
tio
n
ed
m
o
d
u
latio
n
tech
n
iq
u
e
s
is
s
u
m
m
ar
ized
in
T
ab
le
1
.
Fig
u
r
e
3
.
Mu
ltil
e
v
el
ca
r
r
ier
s
: (
a)
P
D,
(
b
)
P
O
D,
(
c)
A
P
OD,
(
d
)
p
h
ase
-
s
h
i
f
ted
ca
r
r
ier
s
I
n
ad
d
itio
n
to
t
h
e
ab
o
v
e
m
o
d
u
latio
n
tec
h
n
iq
u
es
th
e
SHE
-
P
W
M
tech
n
iq
u
e
i
s
p
r
o
p
o
s
ed
[
13
]
in
w
h
ic
h
th
e
s
w
itc
h
i
n
g
p
atter
n
is
d
eter
m
i
n
ed
to
eli
m
i
n
ate
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ic
s
i
n
th
e
o
u
tp
u
t
v
o
lta
g
e.
T
h
e
m
o
d
u
latio
n
tec
h
n
iq
u
e
b
a
s
ed
o
n
f
u
n
d
a
m
en
tal
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
h
a
s
b
ee
n
i
n
v
e
s
ti
g
ated
.
T
h
e
n
ea
r
es
t
lev
el
co
n
tr
o
l
m
o
d
u
latio
n
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
[
1
4
]
in
w
h
i
ch
v
o
ltag
e
l
e
v
el
n
ea
r
est
to
th
e
d
esire
d
v
o
ltag
e
is
co
n
s
id
er
ed
.
T
h
is
tec
h
n
iq
u
e
i
s
v
er
y
ea
s
y
to
i
m
p
le
m
e
n
t
a
n
d
ca
n
b
e
o
p
er
ated
at
t
h
e
f
u
n
d
a
m
en
tal
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
.
T
h
e
tech
n
iq
u
e
p
r
o
p
o
s
ed
is
b
ased
o
n
a
f
ix
ed
p
u
ls
e
p
atter
n
f
ed
in
to
th
e
s
u
b
m
o
d
u
le
to
m
ain
tain
t
h
e
s
tab
ili
t
y
o
f
th
e
s
to
r
ed
en
er
g
y
,
w
it
h
o
u
t
m
ea
s
u
r
i
n
g
th
e
ca
p
ac
it
o
r
v
o
ltag
es
o
r
an
y
o
t
h
er
f
ee
d
b
ac
k
co
n
tr
o
l,
an
d
to
r
e
m
o
v
e
ce
r
tai
n
o
u
tp
u
t
v
o
lta
g
e
h
ar
m
o
n
ics
at
a
n
y
ar
b
itra
r
y
m
o
d
u
latio
n
i
n
d
ex
a
n
d
o
u
tp
u
t
-
v
o
ltag
e
p
h
ase
a
n
g
le.
T
h
e
o
p
tim
ized
m
o
d
u
latio
n
t
ec
h
n
iq
u
e
is
p
r
o
p
o
s
ed
[
1
5
]
t
h
at
o
p
ti
m
ize
th
e
p
u
ls
e
p
atte
r
n
to
m
i
n
i
m
ize
t
h
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
at
t
h
e
o
u
tp
u
t.
T
h
is
tec
h
n
iq
u
e
i
s
o
p
p
o
s
ed
to
th
e
P
W
M
tech
n
iq
u
e
w
h
er
e
th
e
ca
r
r
ier
f
r
eq
u
en
c
y
h
as
ef
f
ec
t
s
o
n
th
e
o
u
tp
u
t
v
o
lta
g
e
f
r
eq
u
en
c
y
.
B
ased
o
n
th
e
ab
o
v
e
liter
at
u
r
e
o
n
m
o
d
u
latio
n
tec
h
n
iq
u
es i
n
MM
C
it is
k
n
o
wn
th
at
t
h
e
p
h
a
s
e
s
h
i
f
ted
P
W
M
is
ea
s
y
to
i
m
p
le
m
en
t
w
i
th
r
ed
u
ce
d
T
HD.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
R
ev
iew
o
n
Desig
n
a
n
d
C
o
n
tr
o
l Meth
o
d
s
o
f Mo
d
u
l
a
r
Mu
ltil
ev
el
C
o
n
ve
r
ter
(
R
a
mya
G.
)
867
T
ab
le
1.
Key
co
n
tr
ib
u
t
io
n
s
o
n
d
if
f
er
e
n
t
m
o
d
u
latio
n
tec
h
n
iq
u
es
M
o
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
P
r
o
p
o
se
d
C
o
n
t
r
i
b
u
t
i
o
n
o
f
t
h
e
a
u
t
h
o
r
s
C
a
r
r
i
e
r
d
i
sp
o
s
i
t
i
o
n
t
e
c
h
n
i
q
u
e
T
h
e
d
e
si
r
e
d
o
u
t
p
u
t
v
o
l
t
a
g
e
i
s
o
b
t
a
i
n
e
d
w
i
t
h
l
o
w
h
a
r
mo
i
n
c
s
w
i
t
h
t
h
i
s
t
e
c
h
n
i
q
u
e
.
T
h
e
c
a
r
r
i
e
r
si
g
n
a
l
t
h
a
t
a
r
e
d
i
s
p
l
a
c
e
d
p
r
o
p
o
r
t
i
o
n
a
l
l
y
w
i
t
h
r
e
sp
e
c
t
t
o
z
e
r
o
a
x
i
s.
T
h
e
y
a
r
e
c
l
a
ssi
f
i
e
d
i
n
t
o
P
D
P
W
M
,
P
O
D
P
W
M
,
a
n
d
A
P
O
D
P
W
M
.
S
i
mp
l
e
c
a
r
r
i
e
r
r
o
t
a
t
i
o
n
a
n
d
mo
d
i
f
i
e
d
c
a
r
r
i
e
r
r
o
t
a
t
i
o
n
P
W
M
t
e
c
h
n
i
q
u
e
s
T
h
i
s
mo
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
e
q
u
a
l
i
z
e
d
t
h
e
v
o
l
t
a
g
e
d
i
st
r
i
b
u
t
i
o
n
a
mo
n
g
t
h
e
s
u
b
mo
d
u
l
e
.
M
o
d
i
f
i
e
d
P
D
-
P
W
M
t
e
c
h
n
i
q
u
e
T
h
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
c
a
r
r
i
e
d
o
u
t
w
i
t
h
e
q
u
a
l
v
o
l
t
a
g
e
d
i
s
t
r
i
b
u
t
i
o
n
a
mo
n
g
t
h
e
su
b
-
mo
d
u
l
e
w
i
t
h
l
o
w
TH
D
.
I
n
t
h
i
s
t
e
c
h
n
i
q
u
e
r
e
f
e
r
e
n
c
e
si
g
n
a
l
i
s
c
o
m
p
a
r
e
d
w
i
t
h
t
h
e
c
a
r
r
i
e
r
si
g
n
a
l
p
r
o
d
u
c
e
N
+
1
l
e
v
e
l
i
n
t
h
e
o
u
t
p
u
t
si
d
e
.
T
h
e
g
a
t
i
n
g
si
g
n
a
l
s
a
r
e
a
ssi
g
n
e
d
t
o
s
p
e
c
i
f
i
e
d
su
b
mo
d
u
l
e
f
o
r
t
h
e
d
e
si
r
e
d
o
u
t
p
u
t
.
PD
-
P
W
M
w
i
t
h
se
l
e
c
t
i
v
e
l
o
o
p
b
i
a
s m
a
p
p
i
n
g
T
h
e
su
b
mo
d
u
l
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
d
o
n
e
w
i
t
h
t
h
i
s
me
t
h
o
d
.
T
h
e
mai
n
a
d
v
a
n
t
a
g
e
o
f
t
h
i
s
me
t
h
o
d
i
s
t
h
a
t
a
b
se
n
c
e
a
d
d
i
t
i
o
n
a
l
r
e
f
e
r
e
n
c
e
si
g
n
a
l
t
o
c
o
n
t
r
o
l
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
a
n
d
a
l
so
e
a
sy
i
mp
l
e
me
n
t
a
t
i
o
n
.
P
h
a
se
s
h
i
f
t
c
a
r
r
i
e
r
mo
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
T
h
e
d
e
si
r
e
d
o
u
t
p
u
t
v
o
l
t
a
g
e
i
s
o
b
t
a
i
n
e
d
c
o
mp
a
r
e
d
t
o
o
t
h
e
r
mo
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
s w
i
t
h
v
e
r
y
l
o
w
T
H
D
.
3
.
3
.
Vo
lt
a
g
e
B
a
la
ncing
Co
ntr
o
l
I
t
is
n
ec
es
s
ar
y
to
b
ala
n
ce
t
h
e
s
u
n
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
at
V
dc
/N.
T
h
e
v
o
ltag
e
b
alan
ci
n
g
tech
n
iq
u
e
b
ased
o
n
P
SC
-
P
W
M
w
a
s
p
r
o
p
o
s
ed
[
12
]
t
o
b
alan
ce
th
e
s
u
b
m
o
d
u
le
b
y
p
r
o
v
id
i
n
g
ap
p
r
o
p
r
iate
P
W
M
s
ig
n
al
s
to
ea
ch
s
u
b
m
o
d
u
le.
T
h
is
v
o
ltag
e
b
ala
n
ci
n
g
tec
h
n
iq
u
e
d
o
es n
o
t n
ee
d
to
m
ea
s
u
r
e
th
e
ar
m
c
u
r
r
en
t
w
h
ic
h
r
ed
u
ce
s
th
e
co
m
p
le
x
it
y
i
n
th
e
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
clo
s
ed
lo
o
p
v
o
ltag
e
b
alan
cin
g
m
et
h
o
d
is
p
r
o
p
o
s
ed
[
3
]
in
w
h
ic
h
t
h
e
clo
s
ed
lo
o
p
co
n
tr
o
l
m
et
h
o
d
is
i
m
p
le
m
e
n
ted
f
o
r
ea
ch
s
u
b
m
o
d
u
le
f
o
r
t
h
e
v
o
lt
ag
e
b
alan
c
in
g
.
T
h
e
p
r
ed
i
ctiv
e
s
tr
ate
g
y
w
a
s
p
r
o
p
o
s
ed
f
o
r
t
h
e
co
n
tr
o
l
o
f
MM
C
i
n
w
h
ic
h
t
h
e
s
u
b
m
o
d
u
le
v
o
lta
g
e
i
s
b
ala
n
ce
d
b
ased
o
n
t
h
e
p
r
ed
ef
i
n
ed
co
s
t
f
u
n
c
tio
n
.
T
h
e
v
o
ltag
e
b
alan
ci
n
g
b
ase
d
o
n
t
h
e
s
o
r
ti
n
g
m
et
h
o
d
is
p
r
o
p
o
s
ed
[
1
2
]
in
w
h
ic
h
th
e
v
o
ltag
e
b
alan
ci
n
g
i
s
ca
r
r
ie
d
o
u
t
b
y
m
ea
s
u
r
i
n
g
t
h
e
v
o
ltag
e
o
f
ea
c
h
s
u
b
m
o
d
u
le
a
n
d
s
o
r
t
in
g
.
I
n
th
i
s
m
et
h
o
d
if
th
e
u
p
p
er
/lo
w
er
ar
m
cu
r
r
e
n
t
is
p
o
s
iti
v
e
th
e
s
u
b
m
o
d
u
le
w
it
h
lo
w
e
s
t
v
o
lta
g
e
ar
e
id
en
ti
f
ied
an
d
in
s
er
ted
a
m
o
n
g
s
u
b
m
o
d
u
le
p
r
esen
t
in
ea
ch
ar
m
.
T
h
e
in
s
er
ted
s
u
b
m
o
d
u
le
is
ch
ar
g
ed
an
d
th
e
co
r
r
e
s
p
o
n
d
in
g
v
o
ltag
e
i
s
in
cr
ea
s
ed
.
Si
m
ilar
l
y
if
th
e
u
p
p
er
/lo
w
er
ar
m
c
u
r
r
en
t
i
s
n
e
g
ati
v
e
th
e
s
u
b
m
o
d
u
le
w
it
h
h
ig
h
e
s
t
v
o
lta
g
e
ar
e
id
e
n
ti
f
ied
an
d
i
n
s
er
ted
a
m
o
n
g
s
u
b
m
o
d
u
le
p
r
ese
n
t i
n
ea
ch
ar
m
.
T
h
e
in
s
er
ted
s
u
b
m
o
d
u
le
is
d
is
ch
ar
g
ed
a
n
d
t
h
e
co
r
r
esp
o
n
d
in
g
v
o
lta
g
e
is
d
ec
r
ea
s
ed
.
T
h
e
m
a
in
d
r
a
w
b
ac
k
o
f
th
is
m
eth
o
d
is
th
at
i
n
cr
ea
s
ed
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
,
p
o
w
er
lo
s
s
an
d
p
r
o
v
id
es
s
w
it
ch
in
g
tr
an
s
itio
n
a
m
o
n
g
th
e
s
u
b
m
o
d
u
le.
T
h
e
o
th
er
v
o
lta
g
e
b
alan
cin
g
m
et
h
o
d
s
ar
e
p
r
o
p
o
s
ed
to
r
ed
u
ce
th
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
.
An
o
p
en
lo
o
p
m
et
h
o
d
f
o
r
t
h
e
v
o
lt
a
g
e
b
alan
cin
g
is
ca
r
r
ied
o
u
t
[
1
6
]
b
ased
o
n
th
e
s
elec
tiv
e
h
ar
m
o
n
ic
eli
m
i
n
atio
n
P
W
M
tech
n
iq
u
e.
A
h
y
b
r
id
b
alan
ci
n
g
m
et
h
o
d
[
1
7
]
b
ased
o
n
th
e
p
r
ed
ictiv
e
er
r
o
r
s
o
r
tin
g
m
eth
o
d
an
d
t
h
e
co
n
v
e
n
tio
n
al
v
o
ltag
e
s
o
r
tin
g
alg
o
r
it
h
m
i
s
i
m
p
le
m
e
n
ted
f
o
r
t
h
e
v
o
ltag
e
b
alan
ci
n
g
o
f
MM
C
.
I
t
is
b
ased
o
n
t
h
e
s
o
r
tin
g
o
f
er
r
o
r
b
et
w
ee
n
t
h
e
p
r
ed
icted
ca
p
ac
ito
r
v
o
ltag
e
an
d
n
o
m
i
n
al
v
o
ltag
e
v
al
u
e
an
d
th
e
s
u
b
m
o
d
u
le
w
it
h
m
i
n
i
m
u
m
er
r
o
r
is
in
s
er
ted
.
T
ab
le
2
.
Key
co
n
tr
ib
u
t
io
n
s
o
n
d
if
f
er
e
n
t v
o
lta
g
e
b
alan
ci
n
g
m
e
th
o
d
V
o
l
a
t
g
e
B
a
l
a
n
c
i
n
g
M
e
t
h
o
d
C
o
n
t
r
i
b
u
t
i
o
n
o
f
t
h
e
a
u
t
h
o
r
s
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
t
e
c
h
n
i
q
u
e
b
a
se
d
o
n
P
S
C
-
P
W
M
I
n
t
h
i
s
me
t
h
o
d
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
c
a
r
r
i
e
d
o
u
t
w
i
t
h
o
u
t
me
a
su
r
i
n
g
t
h
e
a
r
m
c
u
r
r
e
n
t
t
h
a
t
r
e
d
u
c
e
s t
h
e
c
o
mp
l
e
x
i
t
y
.
C
l
o
se
d
l
o
o
p
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
me
t
h
o
d
T
h
e
su
b
mo
d
u
l
e
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
c
a
r
r
i
e
d
o
u
t
w
i
t
h
c
l
o
se
d
l
o
o
p
c
o
n
t
r
o
l
.
P
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
me
t
h
o
d
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
o
f
t
h
e
M
M
C
i
s
c
a
r
r
i
e
d
o
u
t
b
a
se
d
o
n
c
a
l
c
u
l
a
t
i
n
g
t
h
e
a
mo
u
n
t
o
f
c
h
a
r
g
e
st
o
r
e
d
i
n
su
b
mo
d
u
l
e
c
a
p
a
c
i
t
o
r
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
b
a
se
d
o
n
t
h
e
so
r
t
i
n
g
me
t
h
o
d
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
c
a
r
r
i
e
d
o
u
t
b
y
me
a
su
r
i
n
g
t
h
e
v
o
l
t
a
g
e
o
f
e
a
c
h
s
u
b
mo
d
u
l
e
a
n
d
so
r
t
i
n
g
i
t
.
O
p
e
n
l
o
o
p
me
t
h
o
d
f
o
r
t
h
e
v
o
l
t
a
g
e
b
a
l
a
n
c
i
ng
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
d
o
n
e
b
a
se
d
o
n
t
h
e
se
l
e
c
t
i
v
e
h
a
r
mo
n
i
c
e
l
i
mi
n
a
t
i
o
n
P
W
M
t
e
c
h
n
i
q
u
e
.
H
y
b
r
i
d
b
a
l
a
n
c
i
n
g
me
t
h
o
d
T
h
e
v
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
i
m
p
l
e
me
n
t
e
d
b
y
u
si
n
g
p
r
e
d
i
c
t
i
v
e
e
r
r
o
r
so
r
t
i
n
g
me
t
h
o
d
a
n
d
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
v
o
l
t
a
g
e
so
r
t
i
n
g
a
l
g
o
r
i
t
h
m.
F
u
n
d
a
me
n
t
a
l
-
f
r
e
q
u
e
n
c
y
b
a
l
a
n
c
i
n
g
st
r
a
t
e
g
y
,
V
o
l
t
a
g
e
b
a
l
a
n
c
i
n
g
i
s
c
a
r
r
i
e
d
o
u
t
b
a
se
d
o
n
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
so
r
t
i
n
g
me
t
h
o
d
,
e
x
e
c
u
t
e
d
a
t
t
h
e
p
r
e
-
sp
e
c
i
f
i
e
d
p
h
a
se
a
n
g
l
e
s.
O
p
t
i
mi
z
e
d
c
a
p
a
c
i
t
o
r
b
a
l
a
n
c
i
n
g
a
l
g
o
r
i
t
h
m
I
n
t
h
i
s
me
t
h
o
d
a
mai
n
t
a
i
n
i
n
g
f
a
c
t
o
r
i
s
i
n
t
r
o
d
u
c
e
d
a
n
d
mu
l
t
i
p
l
i
e
d
b
y
t
h
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
s
o
f
t
h
e
su
b
mo
d
u
l
e
w
i
t
h
h
i
g
h
e
r
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
t
o
m
a
i
n
t
a
i
n
t
h
e
v
o
l
t
a
g
e
b
a
l
a
n
c
e
o
f
t
h
e
su
b
mo
d
u
l
e
.
C
l
o
se
d
-
l
o
o
p
mo
d
i
f
i
e
d
so
r
t
i
n
g
me
t
h
o
d
I
n
t
h
i
s
t
e
c
h
n
i
q
u
e
p
h
a
se
-
sh
i
f
t
e
d
c
a
r
r
i
e
r
P
W
M
st
r
a
t
e
g
y
i
s
i
mp
l
e
me
n
t
e
d
,
i
n
w
h
i
c
h
t
h
e
i
n
se
r
t
i
o
n
/
b
y
p
a
ss
i
n
g
o
f
t
h
e
su
b
mo
d
u
l
e
i
s
c
a
r
r
i
e
d
o
u
t
b
a
se
d
o
n
me
a
s
u
r
i
n
g
t
h
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
863
–
8
7
1
868
A
f
u
n
d
a
m
e
n
tal
-
f
r
eq
u
e
n
c
y
b
al
an
cin
g
s
tr
ate
g
y
,
w
h
ic
h
is
b
as
ed
o
n
th
e
co
n
v
e
n
tio
n
al
s
o
r
tin
g
m
et
h
o
d
,
ex
ec
u
ted
at
t
h
e
p
r
e
-
s
p
ec
i
f
ied
p
h
ase
an
g
le
s
.
A
p
r
ed
icti
v
e
alg
o
r
ith
m
i
s
p
r
o
p
o
s
ed
f
o
r
v
o
ltag
e
b
alan
c
in
g
b
y
ca
lcu
lati
n
g
th
e
a
m
o
u
n
t o
f
c
h
ar
g
e
s
to
r
ed
in
th
e
SM
ca
p
ac
it
o
r
s
.
T
h
e
o
p
ti
m
ized
ca
p
ac
ito
r
b
alan
cin
g
alg
o
r
it
h
m
i
s
i
m
p
le
m
en
ted
in
w
h
ich
t
h
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
i
s
ad
j
u
s
ted
b
ef
o
r
e
s
o
r
tin
g
.
T
h
e
s
u
b
m
o
d
u
le
w
i
th
h
ig
h
er
v
o
lta
g
e
th
at
e
x
ce
ed
s
t
h
e
ce
r
tain
li
m
it
is
co
n
s
id
er
ed
.
A
m
a
in
ta
in
i
n
g
f
a
cto
r
is
in
tr
o
d
u
ce
d
an
d
m
u
ltip
l
ied
b
y
t
h
e
ca
p
ac
ito
r
v
o
ltag
es
o
f
th
e
s
u
b
m
o
d
u
l
e
w
it
h
h
i
g
h
er
ca
p
ac
ito
r
v
o
ltag
e
to
m
ai
n
tai
n
t
h
e
v
o
ltag
e
b
alan
ce
o
f
th
e
s
u
b
m
o
d
u
le.
A
p
r
ed
ictiv
e
co
n
tr
o
l
m
et
h
o
d
[
1
8
]
is
im
p
le
m
e
n
ted
f
o
r
v
o
ltag
e
b
alan
cin
g
o
f
t
h
e
MM
C
b
ased
o
n
ca
lcu
lati
n
g
th
e
am
o
u
n
t
o
f
ch
ar
g
e
s
to
r
ed
in
s
u
b
m
o
d
u
le
ca
p
ac
it
o
r
.
A
clo
s
ed
-
lo
o
p
m
o
d
if
ied
s
o
r
tin
g
m
et
h
o
d
is
p
r
o
p
o
s
ed
w
ith
co
m
b
i
n
atio
n
o
f
p
h
ase
-
s
h
i
f
ted
ca
r
r
ier
P
W
M
s
tr
ateg
y
,
in
w
h
ich
th
e
in
s
er
tio
n
/
b
y
p
as
s
i
n
g
o
f
t
h
e
s
u
b
m
o
d
u
le
i
s
ca
r
r
ied
o
u
t
b
ased
o
n
m
ea
s
u
r
in
g
t
h
e
ca
p
ac
ito
r
v
o
ltag
e.
I
n
th
i
s
m
et
h
o
d
,
o
n
l
y
a
li
m
ited
n
u
m
b
er
o
f
s
u
b
m
o
d
u
l
es
ar
e
s
o
r
ted
w
it
h
i
n
ea
ch
co
n
tr
o
l
c
y
c
le.
I
f
t
h
e
s
u
b
m
o
d
u
le
n
ee
d
s
to
b
e
ON/OF
F
to
o
b
tain
th
e
r
eq
u
ir
ed
v
o
lta
g
e
lev
el
t
h
e
s
o
r
ti
n
g
i
s
ca
r
r
ied
o
u
t
w
it
h
i
n
t
h
e
s
u
b
m
o
d
u
le
w
it
h
O
FF
/ON
s
ta
te
i
n
ea
ch
ar
m
.
Ma
n
y
v
o
lta
g
e
b
ala
n
ci
n
g
m
et
h
o
d
s
ar
e
p
r
o
p
o
s
ed
b
y
v
ar
io
u
s
r
esear
ch
e
r
s
an
d
it is
co
m
p
ar
ed
an
d
lis
te
d
in
T
ab
le
2
.
3
.
4
.
Circ
ula
t
ing
Curre
nt
Co
ntr
o
l
T
h
e
v
o
ltag
e
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
t
h
r
ee
p
h
a
s
eM
M
C
lead
s
t
o
cir
cu
lati
n
g
cu
r
r
e
n
t
f
lo
w
t
h
r
o
u
g
h
ea
c
h
leg
.
T
h
e
cir
cu
lati
n
g
cu
r
r
en
t
co
n
tain
s
n
e
g
ati
v
e
s
eq
u
en
c
e
co
m
p
o
n
e
n
t
s
w
it
h
t
h
e
f
r
e
q
u
en
c
y
t
w
ice
t
h
e
f
u
n
d
a
m
en
ta
l
f
r
eq
u
e
n
c
y
[
19
]
.
T
h
e
p
r
esen
ce
o
f
cir
cu
lat
in
g
c
u
r
r
en
t
m
a
y
lead
to
in
cr
ea
s
e
i
n
t
h
e
p
ea
k
a
n
d
r
m
s
v
alu
e
o
f
p
h
a
s
e
c
u
r
r
en
t
i
n
ea
c
h
le
g
an
d
al
s
o
in
cr
ea
s
e
in
th
e
p
o
w
er
lo
s
s
a
n
d
r
ip
p
le
co
n
ten
t
in
t
h
e
s
u
b
m
o
d
u
l
e
ca
p
ac
ito
r
v
o
ltag
es
.
He
n
ce
t
h
e
cir
cu
lati
n
g
cu
r
r
en
t
co
n
tr
o
ller
tech
n
iq
u
e
i
s
p
r
o
p
o
s
ed
to
li
m
it
th
e
s
e
is
s
u
es.
T
o
co
n
tr
o
l
th
e
cir
cu
la
tin
g
c
u
r
r
en
t
v
ar
io
u
s
tec
h
n
iq
u
es
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
in
th
e
tech
n
ical
liter
at
u
r
e.
T
h
e
cir
cu
lati
n
g
cu
r
r
en
t
m
o
d
el
i
s
p
r
o
p
o
s
ed
b
ased
o
n
co
n
tr
o
llin
g
th
en
cir
cu
la
tin
g
c
u
r
r
en
t
a
s
t
h
e
cu
r
r
e
n
t
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
[
2
0
]
.
I
t
is
u
s
ed
to
co
n
tr
o
l
th
e
v
o
lta
g
e
to
r
ed
u
ce
th
e
p
r
ese
n
ce
o
f
ac
co
m
p
o
n
e
n
t
s
i
n
t
h
e
cir
cu
lati
n
g
cu
r
r
e
n
t.
T
h
e
f
ir
s
t
o
r
d
er
m
o
d
el
i
s
p
r
o
p
o
s
ed
to
m
o
d
el
th
e
cir
c
u
lati
n
g
c
u
r
r
en
t
al
o
n
g
w
it
h
d
c
a
n
d
ac
co
m
p
o
n
e
n
t
s
w
h
ic
h
is
u
s
ed
to
m
o
d
el
th
e
co
n
tr
o
l
s
y
s
te
m
ea
s
i
l
y
.
T
h
e
d
esi
g
n
o
f
ar
m
i
n
d
u
cto
r
an
d
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
w
h
ich
l
i
m
its
th
e
cir
cu
lati
n
g
cu
r
r
en
t
b
y
e
s
ti
m
ati
n
g
th
e
p
er
ce
n
ta
g
e
o
f
ac
co
m
p
o
n
en
ts
p
r
ese
n
t
i
n
t
h
e
ar
m
c
u
r
r
e
n
t
a
n
d
cir
cu
la
tin
g
c
u
r
r
en
t.
T
h
e
i
n
d
ir
ec
t
m
o
d
u
lati
o
n
tech
n
iq
u
e
[
21
]
is
p
r
o
p
o
s
ed
w
h
ic
h
li
m
it
s
t
h
e
cir
cu
lati
n
g
c
u
r
r
en
t
in
th
e
M
MC.
T
h
e
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
is
p
r
o
p
o
s
ed
to
lim
it
t
h
e
ci
r
cu
lati
n
g
c
u
r
r
en
t
b
y
in
tr
o
d
u
ci
n
g
t
h
e
ac
ti
v
e
r
esis
ta
n
ce
in
ea
ch
ar
m
.
T
ab
le
3
.
Key
co
n
tr
ib
u
t
io
n
s
o
n
d
if
f
er
e
n
t c
ir
cu
la
tin
g
c
u
r
r
en
t e
l
i
m
i
n
atio
n
m
et
h
o
d
C
i
r
c
u
l
a
t
i
n
g
C
u
r
r
e
n
t
C
o
n
t
r
o
l
C
o
n
t
r
i
b
u
t
i
o
n
o
f
t
h
e
a
u
t
h
o
r
s
C
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
c
o
n
t
r
o
l
mo
d
e
l
I
n
t
h
i
s
me
t
h
o
d
t
h
e
su
b
mo
d
u
l
e
v
o
l
t
a
g
e
i
s
c
o
n
t
r
o
l
l
e
d
t
o
r
e
d
u
c
e
t
h
e
p
r
e
se
n
c
e
o
f
a
c
c
o
mp
o
n
e
n
t
s
i
n
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
.
F
i
r
st
o
r
d
e
r
mo
d
e
l
I
n
t
h
i
s
mo
d
e
l
t
h
e
d
e
si
g
n
o
f
a
r
m
i
n
d
u
c
t
o
r
a
n
d
su
b
mo
d
u
l
e
c
a
p
a
c
i
t
o
r
a
r
e
d
e
si
g
n
e
d
w
h
i
c
h
l
i
mi
t
s
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
b
y
e
st
i
mat
i
n
g
t
h
e
p
e
r
c
e
n
t
a
g
e
o
f
a
c
c
o
mp
o
n
e
n
t
s
p
r
e
se
n
t
i
n
t
h
e
a
r
m c
u
r
r
e
n
t
a
n
d
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
.
I
n
d
i
r
e
c
t
mo
d
u
l
a
t
i
o
n
t
e
c
h
n
i
q
u
e
I
n
t
h
i
s
t
e
c
h
n
i
q
u
e
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
i
s
e
l
i
mi
n
a
t
e
d
i
n
d
i
r
e
c
t
l
y
b
y
c
o
n
t
r
o
l
l
i
n
g
t
h
e
t
o
t
a
l
e
n
e
r
g
y
i
n
e
a
c
h
p
h
a
se
o
f
t
h
e
sy
st
e
m.
P
r
o
p
o
r
t
i
o
n
a
l
c
o
n
t
r
o
l
l
e
r
t
e
c
h
n
i
q
u
e
T
h
i
s
me
t
h
o
d
l
i
m
i
t
s
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
b
y
i
n
t
r
o
d
u
c
i
n
g
t
h
e
a
c
t
i
v
e
r
e
si
st
a
n
c
e
i
n
e
a
c
h
a
r
m.
D
o
u
b
l
e
l
i
n
e
f
r
e
q
u
e
n
c
y
a
b
c
-
d
q
t
r
a
n
sf
o
r
ma
t
i
o
n
T
h
i
s
me
t
h
o
d
i
s
u
se
d
t
o
e
l
i
mi
n
a
t
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
,
t
h
e
c
o
n
t
r
o
l
o
f
t
h
e
d
q
c
o
mp
o
n
e
n
t
s
u
si
n
g
P
I
c
o
n
t
r
o
l
l
e
r
.
P
R
c
o
n
t
r
o
l
l
e
r
t
e
c
h
n
i
q
u
e
I
n
t
h
i
s
t
e
c
h
n
i
q
u
e
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
i
s
e
l
i
mi
n
a
t
e
d
b
y
l
i
mi
t
i
n
g
t
h
e
a
c
c
o
mp
o
n
e
n
t
s
p
r
e
se
n
t
i
n
i
t
.
M
o
d
i
f
i
e
d
sw
i
t
c
h
i
n
g
f
u
n
c
t
i
o
n
me
t
h
o
d
T
h
i
s
t
e
c
h
n
i
q
u
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
i
s
e
l
i
mi
n
a
t
e
d
b
a
se
d
o
n
t
h
e
p
r
e
d
i
c
t
e
d
v
o
l
t
a
g
e
r
i
p
p
l
e
e
st
i
mat
i
o
n
.
T
h
e
m
ai
n
d
r
a
w
b
ac
k
o
f
t
h
i
s
te
ch
n
iq
u
e
is
t
h
at
t
h
e
s
tead
y
s
ta
te
er
r
o
r
is
o
b
tain
ed
d
u
e
to
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
.
B
ased
o
n
th
e
d
o
u
b
le
lin
e
f
r
eq
u
en
c
y
ab
c
-
d
q
tr
an
s
f
o
r
m
atio
n
to
eli
m
i
n
ate
cir
cu
lati
n
g
c
u
r
r
en
t,
th
e
co
n
tr
o
l
o
f
t
h
e
d
q
co
m
p
o
n
en
t
s
u
s
i
n
g
P
I
co
n
tr
o
ller
is
ca
r
r
i
ed
o
u
t.
T
h
e
m
a
in
is
s
u
e
o
f
th
is
tec
h
n
iq
u
e
i
s
t
h
a
t
r
o
b
u
s
tn
es
s
u
n
d
er
ac
s
id
e
i
m
b
a
lan
ce
.
T
h
e
P
R
co
n
tr
o
ller
[
22
]
is
p
r
o
p
o
s
ed
to
elim
i
n
ate
t
h
e
ac
co
m
p
o
n
e
n
t
s
in
th
e
cir
cu
lati
n
g
c
u
r
r
en
t.
T
h
e
co
n
tr
o
l
m
eth
o
d
w
as
p
r
o
p
o
s
ed
to
co
n
tr
o
l
d
c
co
m
p
o
n
e
n
ts
o
f
cir
cu
lati
n
g
c
u
r
r
en
t
to
i
m
p
r
o
v
e
t
h
e
s
tab
il
it
y
o
f
t
h
e
s
y
s
te
m
u
n
d
er
u
n
b
ala
n
ce
c
o
n
d
itio
n
.
T
h
e
r
ef
er
en
ce
f
o
r
d
c
co
m
p
o
n
e
n
t
s
is
d
eter
m
in
ed
f
r
o
m
t
h
e
av
er
a
g
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e.
T
h
e
m
o
d
if
ied
s
w
itc
h
in
g
f
u
n
ctio
n
m
et
h
o
d
w
a
s
p
r
o
p
o
s
ed
to
elim
in
a
te
th
e
cir
c
u
lati
n
g
c
u
r
r
en
t
in
MM
C
.
T
h
is
tech
n
iq
u
e
is
b
ased
o
n
th
e
p
r
ed
ict
ed
v
o
ltag
e
r
ip
p
le
w
h
ic
h
is
d
i
f
f
icu
l
t
to
ca
lcu
late
u
n
d
er
all
o
p
er
atio
n
co
n
d
itio
n
.
T
h
e
m
o
d
el
b
ase
d
p
r
ed
ictiv
e
co
n
tr
o
l
m
et
h
o
d
w
a
s
i
m
p
le
m
en
ted
to
l
i
m
it
t
h
e
cir
cu
lati
n
g
cu
r
r
en
t.
T
h
e
m
ai
n
d
r
a
w
b
ac
k
o
f
th
is
m
et
h
o
d
is
th
at
e
s
ti
m
atio
n
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
R
ev
iew
o
n
Desig
n
a
n
d
C
o
n
tr
o
l Meth
o
d
s
o
f Mo
d
u
l
a
r
Mu
ltil
ev
el
C
o
n
ve
r
ter
(
R
a
mya
G.
)
869
cir
cu
lati
n
g
c
u
r
r
en
t
co
m
p
o
n
e
n
t
s
is
d
if
f
ic
u
lt
w
it
h
lar
g
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
le
s
.
T
ab
le
3
ex
p
lain
s
t
h
e
d
if
f
er
en
t
m
et
h
o
d
s
o
n
cir
cu
lati
n
g
cu
r
r
en
t
eli
m
i
n
atio
n
i
n
MM
C
.
3
.
5
.
Sub
M
o
du
le
Ca
pa
cit
o
r
Vo
lt
a
g
e
Ripp
le
Reduct
io
n Co
ntr
o
l
M
et
ho
ds
T
h
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le
is
m
ai
n
l
y
d
u
e
to
f
u
n
d
a
m
e
n
tal
an
d
s
ec
o
n
d
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
s
.
T
h
e
s
izi
n
g
o
f
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
is
also
m
a
in
f
ac
to
r
in
m
ai
n
tai
n
i
n
g
t
h
e
v
o
ltag
e
r
ip
p
le
w
i
th
i
n
th
e
ce
r
tai
n
li
m
it
.
Ma
n
y
tech
n
i
q
u
es
h
a
v
e
b
ee
n
ca
r
r
ied
o
u
t
f
o
r
th
e
r
ed
u
ctio
n
o
f
v
o
ltag
e
r
ip
p
l
e
in
t
h
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
.
So
m
e
o
f
t
h
e
tec
h
n
i
q
u
es
ar
e
d
is
c
u
s
s
ed
b
elo
w
.
T
h
e
r
ip
p
le
co
n
ten
t
o
f
t
h
e
n
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
ca
n
b
e
r
ed
u
ce
d
b
y
ad
d
in
g
t
h
e
h
ar
m
o
n
ic
co
n
te
n
t
i
n
th
e
cir
cu
la
tin
g
cu
r
r
en
t
[
2
3
]
.
B
y
ca
lcu
lati
n
g
th
e
p
o
w
er
p
r
o
d
u
ce
d
b
y
ea
c
h
ar
m
a
s
u
itab
le
s
ec
o
n
d
h
ar
m
o
n
ic
cir
cu
lati
n
g
cu
r
r
en
t
is
d
eter
m
i
n
ed
to
r
ed
u
ce
th
e
r
ip
p
les
in
th
e
ca
p
ac
ito
r
v
o
ltag
e.
B
y
i
n
j
ec
tin
g
s
ec
o
n
d
an
d
f
o
u
r
th
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
s
in
cir
c
u
lati
n
g
c
u
r
r
en
t
it
o
p
ti
m
i
s
es
t
h
e
en
er
g
y
v
ar
iatio
n
i
n
ea
ch
ar
m
w
h
ic
h
also
r
ed
u
ce
s
t
h
e
r
ip
p
le
in
ca
p
ac
ito
r
v
o
ltag
e
.
T
h
e
r
ip
p
le
o
f
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
is
r
ed
u
ce
d
b
y
o
p
ti
m
i
zin
g
th
e
r
m
s
v
al
u
e
o
f
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
r
ip
p
le
u
s
i
n
g
s
ec
o
n
d
h
ar
m
o
n
ic
i
n
t
h
e
cir
cu
lati
n
g
c
u
r
r
en
t
.
T
h
e
clo
s
e
d
lo
o
p
co
n
tr
o
l
m
et
h
o
d
is
p
r
o
p
o
s
ed
to
eli
m
i
n
ate
s
ec
o
n
d
h
ar
m
o
n
ic
co
m
p
o
n
en
t
o
f
th
e
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le
[
24
]
.
T
h
e
ab
o
v
e
tech
n
iq
u
es
in
r
e
d
u
ctio
n
o
f
r
ip
p
le
in
s
u
b
m
o
d
u
l
e
ca
p
ac
ito
r
v
o
ltag
e
m
a
y
lead
to
in
cr
ea
s
e
i
n
th
e
p
e
ak
an
d
r
m
s
v
al
u
e
o
f
th
e
ar
m
cu
r
r
en
t
an
d
i
n
cr
ea
s
e
in
p
o
w
er
lo
s
s
.
A
tec
h
n
iq
u
e
i
s
p
r
o
p
o
s
ed
to
r
ed
u
ce
th
e
r
ip
p
le
in
ca
p
ac
ito
r
v
o
lta
g
e
b
y
m
a
in
ta
in
i
n
g
th
e
r
m
s
v
a
lu
e
o
f
ar
m
cu
r
r
en
t
w
it
h
i
n
ce
r
tai
n
li
m
it
t
h
er
eb
y
li
m
iti
n
g
th
e
p
o
wer
lo
s
s
.
T
h
e
s
in
e
w
a
v
e
tec
h
n
iq
u
e
w
as
p
r
o
p
o
s
ed
f
o
r
th
e
r
ed
u
ctio
n
o
f
r
ip
p
le
in
th
e
ca
p
ac
ito
r
v
o
ltag
e.
I
n
t
h
is
tec
h
n
iq
u
e
a
co
m
m
o
n
m
o
d
e
v
o
lta
g
e
an
d
cir
c
u
lati
n
g
cu
r
r
e
n
t
i
s
i
n
j
ec
ted
in
ea
c
h
p
h
ase.
I
t is g
i
v
en
b
y
t
s
i
n
cm
M
cm
m
(
1
4
)
3
dc
i
2
x
i
x
m
t
s
i
n
cm
M
2
x
m
1
x
i
x
,
c
i
r
c
i
(
1
5
)
w
h
er
e,
M
cm
an
d
ɷ
ar
e
th
e
m
a
g
n
it
u
d
e
an
d
an
g
u
lar
f
r
eq
u
e
n
c
y
o
f
co
m
m
o
n
m
o
d
e
v
o
lta
g
e.
T
h
e
r
ef
er
en
ce
w
a
v
e
f
o
r
m
s
o
f
t
h
e
s
in
e
P
W
M
tech
n
iq
u
e
is
u
s
e
d
to
co
n
tr
o
l
t
h
e
u
p
p
er
an
d
lo
wer
ar
m
s
o
f
ea
ch
p
h
a
s
e
w
h
ic
h
g
en
er
ate
s
t
h
e
co
m
m
o
n
-
m
o
d
e
v
o
ltag
e.
A
p
p
r
o
p
r
iate
p
h
ase
s
h
i
f
t
is
g
i
v
e
n
to
ea
ch
s
u
b
m
o
d
u
le
s
o
th
at
th
e
lo
w
f
r
eq
u
en
c
y
co
m
p
o
n
en
ts
ar
e
n
o
t
p
r
esen
t
in
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
ltag
e.
I
n
th
is
tec
h
n
iq
u
e
th
e
m
ag
n
it
u
d
e
o
f
cir
cu
lat
in
g
cu
r
r
en
t
in
cr
ea
s
e
s
w
h
ich
i
n
cr
ea
s
es
th
e
p
o
w
er
lo
s
s
in
t
h
is
s
y
s
te
m
.
T
o
o
v
er
co
m
e
t
h
is
is
s
u
e
t
h
e
s
q
u
ar
e
w
a
v
e
tech
n
iq
u
e
[
2
5
]
w
a
s
p
r
o
p
o
s
ed
to
r
ed
u
c
e
th
e
p
ea
k
a
n
d
r
m
s
v
al
u
e
o
f
ci
r
cu
lati
n
g
cu
r
r
en
t b
y
s
q
u
ar
e
w
a
v
e
co
m
m
o
n
m
o
d
e
v
o
ltag
e
an
d
cir
c
u
lati
g
n
g
cu
r
r
e
n
t
i
n
j
ec
tio
n
tec
h
n
iq
u
e.
A
h
y
b
r
id
tech
n
iq
u
e
i
s
t
h
e
co
m
b
i
n
atio
n
o
f
s
q
u
ar
e
-
w
a
v
e
co
m
m
o
n
-
m
o
d
e
v
o
lta
g
e
an
d
a
s
in
u
s
o
id
al
cir
c
u
lati
n
g
c
u
r
r
en
t
.
T
h
e
ad
v
an
tag
e
o
f
th
is
tec
h
n
iq
u
e
o
v
er
t
h
e
s
i
n
e
-
wav
e
tech
n
iq
u
e
i
s
t
h
e
r
ed
u
ctio
n
in
p
ea
k
an
d
r
m
s
v
alu
e
o
f
cir
cu
latin
g
cu
r
r
en
ts
a
n
d
th
e
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
v
o
lta
g
e
r
ip
p
le.
3
.
6
.
Appl
ica
t
io
ns
o
f
M
M
C
T
h
e
MM
C
w
as
i
n
tr
o
d
u
ce
d
m
ain
l
y
f
o
r
HVDC
ap
p
licatio
n
s
.
T
h
e
MM
C
is
u
s
ed
in
m
ed
i
u
m
v
o
lta
g
e
v
ar
iab
le
s
p
ee
d
d
r
iv
es
d
u
e
to
its
ad
v
an
tag
e
s
o
v
er
o
th
er
m
u
ltil
ev
el
co
n
v
er
ter
.
I
n
r
ec
en
t
y
ea
r
s
th
e
MM
C
h
as
b
ee
n
u
s
ed
in
g
r
id
co
n
n
ec
ted
ap
p
licatio
n
d
u
e
to
it
s
ad
v
a
n
ta
g
e
o
f
m
ed
i
u
m
an
d
h
i
g
h
v
o
lta
g
e
ap
p
licatio
n
.
T
h
e
MM
C
w
it
h
in
te
g
r
ated
en
er
g
y
s
to
r
ag
e
to
in
ter
f
ac
e
lo
w
/
m
ed
i
u
m
v
o
ltag
e
b
atter
ies
to
g
r
id
is
p
r
o
p
o
s
ed
[
26
]
.
T
h
e
s
tu
d
y
o
f
o
p
ti
m
al
d
es
ig
n
o
f
M
MC
f
o
r
tr
an
s
f
o
r
m
er
le
s
s
g
r
id
co
n
n
ec
ted
s
ta
n
d
alo
n
e
h
ig
h
p
o
w
er
en
er
g
y
s
to
r
ag
e
s
y
s
t
em
.
A
p
o
w
er
elec
tr
o
n
ic
tr
an
s
f
o
r
m
er
b
ased
o
n
a
n
MM
C
f
o
llo
w
ed
b
y
a
n
i
s
o
lated
d
u
al
-
a
ctiv
e
-
b
r
id
g
e
d
c
–
d
c
co
n
v
er
ter
a
n
d
a
n
i
n
v
er
ter
is
p
r
o
p
o
s
ed
[
2
7
]
.
T
h
e
p
o
s
s
ib
ilit
y
o
f
u
s
i
n
g
MM
C
a
s
a
n
in
ter
f
ac
e
b
et
w
ee
n
th
e
g
r
id
an
d
p
h
o
to
v
o
lt
aic
p
an
els
w
as
d
is
cu
s
s
ed
.
A
f
a
m
i
l
y
o
f
m
ed
iu
m
/h
i
g
h
v
o
lta
g
e
d
c
–
d
c
co
n
v
er
ter
s
b
ased
o
n
th
e
MM
C
to
p
o
lo
g
y
h
a
s
b
ee
n
r
ec
en
tl
y
in
tr
o
d
u
ce
d
an
d
in
v
es
tig
a
t
ed
[
2
8
]
.
A
m
e
th
o
d
o
lo
g
y
to
o
p
ti
m
ize
t
h
e
d
esig
n
o
f
th
e
d
c
–
d
c
co
n
v
er
ter
b
ased
o
n
MM
C
w
it
h
r
eg
ar
d
t
o
s
ilico
n
ar
ea
w
as p
r
o
p
o
s
ed
.
4.
CO
NCLU
SI
O
N
T
h
e
s
ig
n
i
f
ica
n
t
f
ea
t
u
r
es
o
f
M
MC
s
u
c
h
a
s
it
s
m
o
d
u
lar
it
y
a
n
d
s
ca
lab
ilit
y
m
a
y
lead
to
a
n
y
n
u
m
b
er
o
f
v
o
ltag
e
lev
el
s
w
i
th
r
ed
u
ce
d
h
ar
m
o
n
ic
a
n
d
h
i
g
h
er
ef
f
icie
n
c
y
.
I
n
r
ec
e
n
t
y
ea
r
s
t
h
e
MM
C
h
a
s
b
ec
o
m
e
m
o
r
e
s
u
p
er
io
r
th
a
n
o
th
er
p
o
w
er
co
n
v
er
ter
s
f
o
r
v
ar
io
u
s
m
ed
i
u
m
to
h
ig
h
v
o
lta
g
e/p
o
w
er
s
y
s
te
m
s
a
n
d
in
d
u
s
tr
ial
ap
p
licatio
n
s
i
n
cl
u
d
in
g
HVD
C
tr
an
s
m
is
s
io
n
s
y
s
te
m
s
,
F
AC
T
S,
m
ed
iu
m
-
v
o
l
tag
e
v
ar
iab
le
-
s
p
ee
d
d
r
iv
es,
an
d
m
ed
i
u
m
/h
i
g
h
v
o
lta
g
e
d
c
–
d
c
co
n
v
er
ter
s
.
T
h
er
e
ar
e
m
a
n
y
tech
n
iq
u
es
d
i
s
cu
s
s
ed
b
ased
o
n
v
o
lta
g
e
b
alan
c
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
863
–
8
7
1
870
o
f
s
u
b
m
o
d
u
le
ca
p
ac
ito
r
an
d
also
eli
m
i
n
ati
n
g
th
e
c
ir
cu
lati
n
g
cu
r
r
en
t
i
n
ea
ch
ar
m
.
T
h
e
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le
r
ed
u
ctio
n
tec
h
n
iq
u
e
s
ar
e
al
s
o
d
is
cu
s
s
ed
w
it
h
o
u
t
s
ac
r
i
f
ici
n
g
t
h
e
co
n
v
er
ter
e
f
f
icie
n
c
y
a
n
d
co
s
t
e
f
f
ec
ti
v
e.
Ma
n
y
m
o
d
u
latio
n
tech
n
iq
u
e
s
h
av
e
b
ee
n
d
is
cu
s
s
ed
in
m
a
n
y
l
iter
atu
r
es
th
at
en
ab
le
h
i
g
h
e
f
f
icien
c
y
an
d
r
ed
u
ce
d
s
tr
ess
o
n
th
e
d
e
v
ice.
C
o
n
s
id
er
in
g
t
h
e
b
en
ef
it
s
o
f
M
MC
i
n
r
ec
en
t
a
p
p
licatio
n
in
p
r
ese
n
t
s
ce
n
ar
io
it
is
k
n
o
w
n
t
h
at
t
h
e
d
ev
elo
p
m
en
t
o
f
n
o
v
el
m
o
d
u
la
tio
n
a
n
d
co
n
tr
o
l
s
tr
ateg
ies
w
ill
b
e
a
m
aj
o
r
d
r
iv
in
g
f
ac
to
r
f
o
r
t
h
e
u
s
e
o
f
M
MC
i
n
f
u
tu
r
e
ap
p
licatio
n
s
.
T
h
is
p
ap
er
g
iv
es
a
co
m
p
r
eh
e
n
s
i
v
e
r
e
v
ie
w
o
n
t
h
e
co
n
tr
o
l
s
tr
ateg
ie
s
o
f
MM
C
w
h
ile
ch
o
o
s
in
g
t
h
e
to
p
o
lo
g
y
f
o
r
a
p
ar
ticu
lar
ap
p
licatio
n
.
RE
F
E
R
E
NC
E
S
[1
]
J.
Do
rn
,
D.
Hu
a
n
g
a
n
d
D.
Re
tzm
a
n
,
"
A
n
e
w
M
u
lt
il
e
v
e
l
V
o
l
tag
e
-
S
o
u
rc
e
d
Co
n
v
e
rter
T
o
p
o
l
o
g
y
f
o
r
HV
DC
A
p
p
li
c
a
ti
o
n
s"
,
CIGRE
,
p
p
.
1
-
8
,
2
0
0
8
.
[2
]
S
re
e
d
h
a
rM
a
d
ich
e
tt
y
,
Da
sg
u
p
taA
b
h
ij
i
t,
S
iv
a
ji
Jin
k
a
,
―
A
S
u
rv
e
y
a
n
d
Ex
p
e
rim
e
n
tal
V
e
rif
ica
ti
o
n
o
f
M
o
d
u
lar
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
‖
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
V
o
l.
4
,
No
.
3
,
p
p
.
363
-
3
7
5
,
2
0
1
4
.
[3
]
Ch
u
e
n
L
in
g
T
o
h
,
L
a
rs
Ei
n
a
r
No
ru
m
,
―
V
HD
L
I
m
p
le
m
e
n
tatio
n
o
f
Ca
p
a
c
it
o
r
Vo
lt
a
g
e
Ba
lan
c
in
g
Co
n
tro
l
w
it
h
L
e
v
e
l
-
S
h
if
ted
P
W
M
f
o
r
M
o
d
u
lar
M
u
lt
i
lev
e
l
Co
n
v
e
rter
‖
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
V
o
l
.
7
,
No
.
1
,
M
a
rc
h
2
0
1
6
.
[4
]
M
.
G
u
a
n
a
n
d
Z.
Xu
,
―
M
o
d
e
li
n
g
a
n
d
c
o
n
tro
l
o
f
a
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
-
b
a
se
d
HV
DC
s
y
ste
m
u
n
d
e
r
u
n
b
a
la
n
c
e
d
g
rid
c
o
n
d
it
io
n
s‖
,
IEE
E
T
ra
n
s.
P
o
we
r E
lec
tro
n
.,
v
o
l.
2
7
,
n
o
.
1
2
,
p
p
.
4
8
5
8
–
4
8
6
7
,
De
c
.
2
0
1
2
.
[5
]
G
.
T
.
S
o
n
,
H.J.
L
e
e
,
T
.
S
.
Na
m
,
Y.H.
Ch
u
n
g
,
a
n
d
U.H.
L
e
e
,
―
De
sig
n
a
n
d
c
o
n
tro
l
o
f
a
m
o
d
u
lar
m
u
lt
il
e
v
e
l
HV
DC
c
o
n
v
e
rter
w
it
h
re
d
u
n
d
a
n
t
p
o
w
e
r
m
o
d
u
les
f
o
r
n
o
n
-
in
terr
u
p
t
ib
le
e
n
e
rg
y
tr
a
n
sf
e
r
‖
,
IEE
E
T
ra
n
s.
P
o
we
r
De
l.
,
v
o
l.
2
7
,
n
o
.
3
,
p
p
.
1
6
1
1
–
1
6
1
9
,
Ju
l
.
2
0
1
2
.
[6
]
N.
T
h
it
ich
a
iw
o
ra
k
o
rn
,
M
.
Ha
g
iw
a
r
a
,
a
n
d
H.
A
k
a
g
i,
―
Ex
p
e
ri
m
e
n
tal
v
e
rif
ica
ti
o
n
o
f
a
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
a
sc
a
d
e
in
v
e
rter
b
a
se
d
o
n
d
o
u
b
le
-
sta
r
b
ri
d
g
e
-
c
e
ll
s
(M
M
CI
–
DSBC)‖
,
IEE
E
T
ra
n
s.
I
n
d
.
Ap
p
l
.
,
v
o
l
.
P
P
,
n
o
.
9
9
,
p
p
.
1
–
1
,
Ja
n
.
2
0
1
3
.
[7
]
D.
S
iem
a
s
z
k
o
,
A
.
A
n
to
n
o
p
o
u
lo
s,
K.
Ilv
e
s,
M
.
V
a
silad
io
t
is,
L
.
A
n
g
q
u
ist,
a
n
d
H
.
P
.
Ne
e
,
“
Eva
l
u
a
ti
o
n
o
f
c
o
n
tro
l
a
n
d
mo
d
u
l
a
ti
o
n
me
th
o
d
s fo
r
mo
d
u
l
a
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
rs
”
,
in
P
ro
c
.
I
n
t.
P
o
w
e
r
El
e
c
tro
n
.
C
o
n
f
.
,
p
p
.
7
4
6
–
7
5
3
,
2
0
1
0
.
[8
]
L
.
Ha
rn
e
f
o
rs
,
A
.
A
n
to
n
o
p
o
u
lo
s
,
S
.
No
rrg
a
,
L
.
A
n
g
q
u
ist,
a
n
d
H
.
Ne
e
,
―
D
y
n
a
m
i
c
a
n
a
l
y
sis
o
f
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
‖
,
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l.
6
0
,
n
o
.
7
,
p
p
.
2
5
2
6
–
2
5
3
7
,
J
u
l.
2
0
1
3
[9
]
S
re
e
d
h
a
r
M
a
d
ich
e
tt
y
a
n
d
A
b
h
ij
i
t
Da
sg
u
p
ta,
―
M
o
d
u
lar
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
P
a
rt
-
I
:
A
Re
v
ie
w
o
n
T
o
p
o
l
o
g
ies
,
M
o
d
u
latio
n
,
M
o
d
e
li
n
g
a
n
d
C
o
n
tro
l
S
c
h
e
m
e
s
‖
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
),
V
o
l
.
4
,
No
.
1
,
M
a
rc
h
2
0
1
4
p
p
.
3
6
-
50.
[1
0
]
J.
M
e
i,
B.
X
iao
,
K.
S
h
e
n
,
L
.
T
o
lb
e
rt,
a
n
d
J.
Y
.
Zh
e
n
g
,
―
M
o
d
u
lar
m
u
lt
il
e
v
e
l
in
v
e
rt
e
r
w
it
h
n
e
w
m
o
d
u
lati
o
n
m
e
th
o
d
a
n
d
it
s
a
p
p
li
c
a
ti
o
n
t
o
p
h
o
to
v
o
l
taic
g
rid
-
c
o
n
n
e
c
ted
g
e
n
e
ra
to
r
‖
,
IE
EE
T
ra
n
s.
P
o
we
r
El
e
c
tro
n
.
,
v
o
l.
2
8
,
n
o
.
1
1
,
p
p
.
5
0
6
3
–
5
0
7
3
,
No
v
.
2
0
1
3
[1
1
]
D.W
.
Ka
n
g
,
W
.
K.
L
e
e
,
a
n
d
D.
S
.
Hy
u
n
,
―
Ca
rrier
-
Ro
tatio
n
stra
t
e
g
y
f
o
r
v
o
lt
a
g
e
b
a
lan
c
in
g
in
f
ly
i
n
g
c
a
p
a
c
it
o
r
m
u
lt
il
e
v
e
l
in
v
e
rter
‖
,
IEE
P
r
o
c
.
—
El
e
c
tri
c
P
o
w
e
r
A
p
p
l.
,
v
o
l.
1
5
1
,
n
o
.
2
,
p
p
.
2
3
9
–
2
4
8
,
2
0
0
4
.
[1
2
]
M
.
Ha
g
iwa
ra
a
n
d
H.
A
k
a
g
i,
―
Co
n
tro
l
a
n
d
e
x
p
e
rim
e
n
t
o
f
p
u
lse
w
id
th
m
o
d
u
late
d
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
‖
,
IEE
E
T
ra
n
s.
P
o
we
r E
lec
tro
n
.
,
v
o
l
.
2
4
,
n
o
.
7
,
p
p
.
1
7
3
7
–
1
7
4
6
,
Ju
l
.
2
0
0
9
.
[1
3
]
M
.
Ha
g
iw
a
ra
,
R.
M
a
e
d
a
,
a
n
d
H.
Ak
a
g
i,
―
Co
n
tro
l
a
n
d
a
n
a
ly
sis
o
f
th
e
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
a
sc
a
d
e
c
o
n
v
e
rter
b
a
se
d
o
n
d
o
u
b
le
-
sta
r
c
h
o
p
p
e
r
-
c
e
ll
s (M
M
C
C
–
DSCC)‖
,
IEE
E
T
ra
n
s.P
o
we
r E
lec
tro
n
.
,
v
o
l
.
2
6
,
n
o
.
6
,
p
p
.
1
6
4
9
–
1
6
5
8
,
J
u
n
.
2
0
1
1
[1
4
]
K.
Ilv
e
s
,
A
.
A
n
to
n
o
p
o
u
lo
s,
S
.
No
rrg
a
,
a
n
d
H.
P
.
Ne
e
,
―
A
n
e
w
m
o
d
u
latio
n
m
e
th
o
d
f
o
r
th
e
m
o
d
u
lar
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter allo
w
in
g
f
u
n
d
a
m
e
n
tal
s
w
it
c
h
in
g
f
re
q
u
e
n
c
y
‖
,
IEE
E
T
ra
n
s.
P
o
w
e
r
El
e
c
tro
n
.
,
v
o
l.
2
7
,
n
o
.
8
,
p
p
.
3
4
8
2
–
3
4
9
4
,
A
u
g
.
2
0
1
2
.
[1
5
]
J.
Hu
b
e
r
a
n
d
A
.
Ko
rn
,
“
O
p
ti
mize
d
p
u
l
se
p
a
tt
e
rn
mo
d
u
la
ti
o
n
fo
r
m
o
d
u
la
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
r
h
ig
h
-
sp
e
e
d
d
riv
e
,
”
in
P
r
o
c
.
I
n
t.
P
o
w
e
r
El
e
c
tro
n
.
M
o
ti
o
n
Co
n
tr
o
l
C
o
n
f
.
,
2
0
1
2
,
p
p
.
L
S
1
a
-
1
.
4
-
1
–
L
S
1
a
-
1
.
4
-
7.
[1
6
]
J.
Qin
a
n
d
M
.
S
a
e
e
d
if
a
rd
,
―
Re
d
u
c
e
d
sw
it
c
h
in
g
-
f
re
q
u
e
n
c
y
v
o
lt
a
g
e
b
a
lan
c
in
g
stra
teg
ies
f
o
r
m
o
d
u
lar
m
u
lt
il
e
v
e
l
HV
DC c
o
n
v
e
rters
‖
,
IEE
E
T
ra
n
s
.
Po
we
r De
l
.
,
v
o
l.
2
8
,
n
o
.
4
,
p
p
.
2
4
0
3
–
2
4
1
0
,
Oc
t.
2
0
1
3
.
[1
7
]
M
.
G
u
a
n
,
Z.
X
u
,
a
n
d
H.
Ch
e
n
,
“
Co
n
tro
l
a
n
d
mo
d
u
la
ti
o
n
stra
te
g
ies
fo
r
mo
d
u
la
r
mu
lt
i
lev
e
l
c
o
n
v
e
rte
r
b
a
se
d
HVDC
S
y
ste
m
”
,
in
P
ro
c
.
C
o
n
f
.
IEE
E
In
d
.
El
e
c
tro
n
.
S
o
c
.,
2
0
1
1
,
p
p
.
8
4
9
–
8
5
4
.
[1
8
]
K.
Ilv
e
s,
L
.
Ha
rn
e
f
o
rs,
S
.
No
rrg
a
,
a
n
d
H.
P
.
Ne
e
,
―
Pre
d
ictive
so
rti
n
g
a
lg
o
rith
m
fo
r
mo
d
u
la
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
rs
min
imizin
g
t
h
e
sp
re
a
d
i
n
t
h
e
su
b
mo
d
u
le
c
a
p
a
c
it
o
r
v
o
lt
a
g
e
s”
,
in
P
r
o
c
.
IE
EE
E
n
e
rg
y
Co
n
v
e
rs.
Co
n
g
r.
Ex
p
o
.
A
sia
Do
w
n
u
n
d
e
r,
2
0
1
3
,
p
p
.
3
2
5
–
3
3
1
.
[1
9
]
Q.
T
u
,
Z.
X
u
,
H.
H
u
a
n
g
,
a
n
d
J.
Zh
a
n
g
,
“
Pa
r
a
me
ter
d
e
sig
n
p
rin
c
ip
le
o
f
th
e
a
rm
i
n
d
u
c
to
r
in
m
o
d
u
l
a
r
mu
l
ti
lev
e
l
c
o
n
v
e
rte
r b
a
se
d
HVDC
”
,
in
P
ro
c
.
In
t.
C
o
n
f
.
P
o
w
e
r
S
y
ste
m
T
e
c
h
n
o
l
.
,
2
0
1
0
,
p
p
.
1
–
6.
[2
0
]
J.
W
.
M
o
o
n
,
C
.
S
.
Kim
,
J.
W
.
P
a
r
k
,
D.W
.
Ka
n
g
,
a
n
d
J.
M
.
K
im
,
―
Circu
latin
g
c
u
rre
n
t
c
o
n
tro
l
i
n
M
M
C
u
n
d
e
r
t
h
e
u
n
b
a
la
n
c
e
d
v
o
lt
a
g
e
‖
,
IEE
ET
ra
n
s.
Po
we
r De
l.
,
v
o
l
.
2
8
,
n
o
.
3
,
p
p
.
1
9
5
2
–
1
9
5
9
,
Ju
l
.
2
0
1
3
.
[2
1
]
Q.
T
u
,
Z.
X
u
,
a
n
d
L
.
Xu
,
―
Re
d
u
c
e
d
sw
it
c
h
in
g
-
f
re
q
u
e
n
c
y
m
o
d
u
latio
n
a
n
d
c
ircu
lati
n
g
c
u
rre
n
t
su
p
p
re
ss
io
n
f
o
r
m
o
d
u
lar m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
‖
,
I
EE
E
T
ra
n
s.
P
o
we
r De
l
.
,
v
o
l.
2
6
,
n
o
.
3
,
p
p
.
2
0
0
9
–
2
0
1
7
,
Ju
l
.
2
0
1
1
[2
2
]
X
.
S
h
e
,
A
.
Hu
a
n
g
,
X
.
Ni,
a
n
d
R.
Bu
rg
o
s,
“
AC
c
irc
u
la
ti
n
g
c
u
rr
e
n
ts
su
p
p
re
ss
io
n
i
n
mo
d
u
la
r mu
lt
il
e
v
e
l
c
o
n
v
e
rte
r
‖
,
in
P
r
o
c
.
Co
n
f
.
IEE
E
I
n
d
.
El
e
c
tro
n
.
S
o
c
.
,
2
0
1
2
,
p
p
.
1
9
1
–
1
9
6
.
[2
3
]
X
.
Ya
n
g
,
J.
L
i,
X.
W
a
n
g
,
W
.
F
a
n
,
a
n
d
T
.
Zh
e
n
g
,
“
H
a
rm
o
n
ic
a
n
a
lys
is
o
f
t
h
e
DC
c
a
p
a
c
it
o
r
v
o
l
ta
g
e
in
mo
d
u
la
r
mu
l
ti
lev
e
l
c
o
n
v
e
rte
r b
a
se
d
S
T
AT
COM
”
,
in
P
r
o
c
.
IEE
E
Co
n
f
.
In
d
.
El
e
c
tro
n
.
A
p
p
l
.
,
2
0
1
1
,
p
p
.
2
5
7
5
–
2
5
7
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
A
R
ev
iew
o
n
Desig
n
a
n
d
C
o
n
tr
o
l Meth
o
d
s
o
f Mo
d
u
l
a
r
Mu
ltil
ev
el
C
o
n
ve
r
ter
(
R
a
mya
G.
)
871
[2
4
]
S
.
P
.
En
g
e
l
a
n
d
R.
W
.
D.
D
o
n
c
k
e
r,
“
Co
n
tr
o
l
o
f
th
e
m
o
d
u
la
r
mu
lt
i
-
lev
e
l
c
o
n
v
e
rte
r
fo
r
mi
n
imize
d
c
e
ll
c
a
p
a
c
i
ta
n
c
e
,
‖
in
P
r
o
c
.
E
u
r.
C
o
n
f
.
P
o
w
e
r
El
e
c
tro
n
.
A
p
p
l
.
,
A
u
g
.
/S
e
p
.
2
0
1
1
,
p
p
.
1
–
1
0
.
[2
5
]
R.
P
ica
s,
J.
P
o
u
,
S
.
Ce
b
a
ll
o
s,
V.G
.
Ag
e
li
d
is,
a
n
d
M
.
S
a
e
e
d
if
a
rd
,
“
M
in
imiza
ti
o
n
o
f
t
h
e
c
a
p
a
c
it
o
r vo
l
ta
g
e
fl
u
c
t
u
a
t
io
n
s
o
f
a
mo
d
u
la
r
m
u
lt
il
e
v
e
l
c
o
n
v
e
rte
r
b
y
c
irc
u
la
t
in
g
c
u
rr
e
n
t
c
o
n
tro
l”
,
i
n
P
ro
c
.
Co
n
f
.
IEE
E
I
n
d
.
El
e
c
tro
n
.
S
o
c
.
,
p
p
.
4
9
8
5
–
4
9
9
1
,
2
0
1
2
.
[2
6
]
M
.
S
p
ich
a
rtz,
V.
S
tau
d
t,
a
n
d
A
.
S
teim
e
l,
―
An
a
lys
is
o
f
th
e
mo
d
u
le
-
v
o
lt
a
g
e
fl
u
c
tu
a
ti
o
n
s
o
f
th
e
mo
d
u
la
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
r
a
t
v
a
ria
b
le
sp
e
e
d
d
ri
v
e
a
p
p
l
ica
ti
o
n
s”
,
i
n
P
ro
c
.
I
n
t.
Co
n
f
.
Op
ti
m
iza
ti
o
n
El
e
c
tr.
El
e
c
tro
n
.
Eq
u
i
p
m
e
n
t
,
p
p
.
751
–
7
5
8
,
2
0
1
2
.
[2
7
]
A
.
Hill
e
rs
a
n
d
J.
Biela
,
“
Op
ti
ma
l
d
e
sig
n
o
f
th
e
mo
d
u
l
a
r
mu
lt
il
e
v
e
l
c
o
n
v
e
rte
r
fo
r
a
n
e
n
e
rg
y
sto
ra
g
e
sy
ste
m
b
a
se
d
o
n
sp
li
t
b
a
tt
e
rie
s”
,
i
n
P
ro
c
.
E
u
r.
C
o
n
f
.
P
o
w
e
r
El
e
c
tro
n
.
A
p
p
l.
,
p
p
.
1
–
1
1
,
2
0
1
3
.
[2
8
]
D.
M
o
n
tes
i
n
o
s
-
M
irac
le,
M
.
M
a
s
so
t
-
Ca
m
p
o
s,
J.
Be
rg
a
s
-
Ja
n
e
,
S
.
G
a
l
c
e
ra
n
-
A
re
ll
a
n
o
,
a
n
d
A
.
Ru
f
e
r,
―
De
sig
n
a
n
d
c
o
n
tro
l
o
f
a
m
o
d
u
lar
m
u
lt
il
e
v
e
l
DC/DC
c
o
n
v
e
rter
f
o
r
re
g
e
n
e
ra
ti
v
e
a
p
p
li
c
a
ti
o
n
s‖
,
IEE
E
T
ra
n
s.
P
o
we
r
El
e
c
tro
n
.
,
v
o
l.
28,
n
o
.
8
,
p
p
.
3
9
7
0
–
3
9
7
9
,
A
u
g
.
2
0
1
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.