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e
r
s
a
c
c
o
r
di
n
g
t
o
w
o
r
k
[
12]
.
S
uc
h
i
nv
e
r
t
e
r
s
pr
o
vi
de
e
l
e
c
t
r
i
c
dr
i
v
e
s
w
i
t
h
:
I
n
c
r
e
a
s
e
d
c
o
n
t
r
o
l
l
a
bil
i
t
y
.
S
pe
e
d
due
to
t
h
e
a
bi
li
t
y
t
o
o
b
t
a
i
n
a
l
m
o
s
t
a
ny
r
e
qu
i
r
e
d
r
a
t
i
o
o
f
f
r
e
que
nc
y
a
n
d
a
m
p
li
t
ude
o
f
t
h
e
s
upp
ly
v
o
l
t
a
ge
.
Al
o
n
g
w
i
t
h
t
h
e
a
d
v
a
n
t
a
ge
s
,
P
W
M
i
nve
r
t
e
r
s
h
a
v
e
a
n
u
m
be
r
o
f
d
i
s
a
d
v
a
n
t
a
ge
s
i
n
d
i
c
a
t
e
d
i
n
[
12]
:
T
h
e
v
o
l
t
a
ge
a
t
t
h
e
o
u
t
pu
t
o
f
a
n
i
nv
e
r
t
e
r
wi
t
h
P
W
M
d
i
f
f
e
r
s
s
i
g
nif
i
c
a
n
t
l
y
f
r
o
m
t
h
e
s
i
n
u
s
o
i
da
l
v
o
l
t
a
ge
o
b
t
a
i
n
e
d
w
h
e
n
t
h
e
I
M
i
s
po
we
r
e
d
f
r
o
m
a
c
o
nv
e
n
t
i
o
n
a
l
a
l
t
e
r
n
a
t
i
n
g
c
ur
r
e
n
t
n
e
t
wor
k
wi
t
h
a
f
r
e
que
n
c
y
o
f
50
Hz
,
a
n
d
t
hi
s
c
i
r
c
u
m
s
t
a
n
c
e
r
e
qu
i
r
e
s
t
a
k
i
n
g
i
n
t
o
a
c
c
o
un
t
t
h
e
pr
e
s
e
n
c
e
o
f
hi
g
h
e
r
ha
r
m
o
ni
c
s
i
n
t
h
e
v
o
l
t
a
ge
c
ur
v
e
s
upp
li
e
d
f
r
o
m
t
h
e
i
nv
e
r
t
e
r
to
t
h
e
I
M
.
T
h
e
c
o
n
s
e
que
n
c
e
s
o
f
n
o
n
-
s
i
nu
s
o
i
da
l
po
we
r
s
upp
l
y
i
nc
l
ud
e
f
l
u
c
t
ua
t
i
o
n
s
i
n
t
h
e
e
l
e
c
t
r
o
m
a
g
n
e
t
i
c
f
o
r
c
e
o
f
bl
o
o
d
pr
e
s
s
ur
e
,
a
n
i
n
c
r
e
a
s
e
i
n
e
dd
y
c
ur
r
e
n
t
s
a
n
d
m
e
c
ha
ni
c
a
l
r
e
s
o
na
n
c
e
s
i
n
t
h
e
k
i
l
o
h
e
r
t
z
r
a
n
ge
,
whi
c
h
l
e
a
d
to
i
n
c
r
e
a
s
e
d
n
o
i
s
e
a
n
d
vi
br
a
t
i
o
n
.
T
or
que
f
l
u
c
t
ua
t
i
o
n
s
a
n
d
a
c
o
us
t
i
c
n
o
i
s
e
c
a
n
be
r
e
duc
e
d
by
i
nc
r
e
a
s
i
ng
t
h
e
v
a
l
ve
s
w
i
t
c
hi
ng
f
r
e
que
nc
y
.
M
o
dul
e
s
w
i
t
h
I
GB
T
t
r
a
n
s
i
s
to
r
s
h
a
v
e
t
h
e
f
o
l
l
o
w
i
ng
a
dv
a
n
t
a
ge
s
:
T
h
e
t
ur
n
-
o
n
t
i
m
e
i
s
h
u
n
dr
e
ds
o
f
n
a
n
o
s
e
c
o
n
d
s
to
a
f
e
w
m
i
c
r
o
s
e
c
o
n
ds
.
M
u
l
t
i
p
l
e
c
ur
r
e
n
t
o
v
e
r
l
o
a
ds
l
a
s
t
i
n
g
up
t
o
10
μ
s
a
r
e
a
l
l
o
we
d,
w
hi
c
h
a
l
l
o
w
s
f
o
r
t
h
e
i
r
r
e
l
i
a
bl
e
pr
o
t
e
c
t
i
o
n
a
t
t
h
e
c
o
n
t
r
o
l
i
n
put
a
c
c
o
r
di
n
g
to
[
13]
.
T
h
e
I
GB
T
i
s
c
o
n
t
r
o
l
l
e
d
by
s
pe
c
i
a
l
dr
i
ve
r
c
hi
p
s
w
i
t
h
t
h
e
i
r
o
wn
po
we
r
a
n
d
pr
ot
e
c
t
i
o
n
s
o
ur
c
e
s
a
c
c
o
r
di
n
g
to
wo
r
ks
[
14]
,
[
15
]
.
Unf
o
r
t
un
a
t
e
l
y
,
t
h
e
P
W
M
m
e
t
h
o
d
h
a
s
a
n
u
m
be
r
o
f
d
i
s
a
d
v
a
n
t
a
ge
s
:
e
f
f
i
c
i
e
nc
y
dr
o
p,
hi
g
h
c
o
s
t
o
f
po
we
r
s
w
i
t
c
h
e
s
(
t
r
a
n
s
i
s
t
or
s
)
,
h
i
g
h
e
l
e
c
t
r
o
m
a
g
n
e
t
i
c
n
o
i
s
e
[
10]
-
[1
6
].
B
ut
t
h
e
r
e
i
s
o
n
e
m
o
r
e
m
e
t
h
o
d
o
f
pu
l
s
e
c
o
n
t
r
o
l
li
ng,
n
a
m
e
ly
c
o
n
t
r
o
l
t
h
r
o
ugh
f
r
e
que
n
c
y
-
pu
l
s
e
m
o
du
l
a
t
i
o
n
(
F
P
M
)
.
T
hi
s
m
e
t
h
o
d
i
s
i
m
p
l
e
m
e
n
t
e
d
by
us
i
ng
DC
pu
l
s
e
-
f
r
e
que
n
c
y
c
o
nv
e
r
to
r
(
P
F
C
)
,
whi
c
h
pot
e
n
t
i
a
ll
y
h
a
s
a
dv
a
n
t
a
ge
s
o
v
e
r
t
h
e
P
W
M
m
e
t
h
o
d
[
3
]
:
hi
g
h
e
f
f
i
c
i
e
n
c
y
,
l
o
w
c
o
s
t
o
f
p
o
we
r
s
w
i
t
c
h
e
s
(
t
hy
r
i
s
to
r
s
)
,
l
o
w
e
l
e
c
t
r
o
m
a
g
n
e
t
i
c
n
o
i
s
e
[
1
7
]
-
[1
9
].
2.
M
E
T
HO
D
I
n
r
e
c
e
n
t
de
c
a
de
s
,
i
t
i
s
i
m
po
s
s
i
b
l
e
t
o
i
m
a
g
i
ne
t
h
e
m
o
de
r
n
b
r
a
n
c
h
o
f
e
l
e
c
t
r
i
c
a
l
e
n
g
i
ne
e
r
i
ng
a
n
d
h
o
us
e
h
o
l
d
e
l
e
c
t
r
i
c
a
l
e
n
g
i
ne
e
r
i
ng
w
i
t
h
o
ut
t
h
e
us
e
of
r
e
c
t
i
f
i
e
r
s
.
A
c
c
o
r
di
n
g
to
S
i
ga
l
a
e
t
al.
[
7
]
a
n
d
D
o
v
udo
v
[
9
]
,
to
t
h
e
t
y
pe
o
f
po
we
r
c
i
r
c
u
i
t
,
t
h
e
r
e
c
t
i
f
i
e
r
i
s
d
i
v
i
de
d
i
n
t
o
s
i
n
g
l
e
-
p
h
a
s
e
a
n
d
t
h
r
e
e
-
ph
a
s
e
,
a
c
c
o
r
di
ng
to
t
h
e
n
u
m
be
r
o
f
ph
a
s
e
s
o
f
t
h
e
s
upp
l
y
n
e
t
wo
r
k
,
s
i
n
g
l
e
-
c
y
c
l
e
a
n
d
t
w
o
-
c
y
c
l
e
.
T
h
e
v
o
l
t
a
ge
c
o
n
v
e
r
s
i
o
n
f
r
o
m
t
h
e
i
n
put
o
f
t
h
e
s
y
nc
h
r
o
n
o
us
ge
n
e
r
a
t
o
r
,
whi
c
h
c
a
n
c
h
a
n
ge
b
o
t
h
i
n
f
r
e
que
n
c
y
a
n
d
a
m
p
li
t
ude
,
i
s
c
a
r
r
i
e
d
o
ut
by
t
wo
s
e
r
i
e
s
-
c
o
nn
e
c
t
e
d
c
o
n
v
e
r
t
e
r
s
-
a
r
e
c
t
i
f
i
e
r
(
A
C
/DC
c
o
n
v
e
r
t
e
r
)
a
n
d
a
n
i
nv
e
r
t
e
r
(
DC
/A
C
c
o
n
v
e
r
t
e
r
)
.
2.
1.
M
od
e
l
in
g
t
h
e
c
ir
c
u
it
of
t
h
e
p
u
l
s
e
-
wid
t
h
c
on
ve
r
t
e
r
T
h
e
P
W
M
i
s
t
h
e
m
a
i
n
c
o
n
t
r
o
l
u
ni
t
o
f
t
h
e
pu
l
s
e
-
w
idt
h
c
o
n
ve
r
t
e
r
.
A
pul
s
e
-
w
i
dt
h
c
o
n
ve
r
t
e
r
c
o
n
ve
r
t
s
a
DC
v
o
l
t
a
ge
[
1]
i
n
t
o
a
pul
s
e
-
t
y
pe
v
o
l
t
a
ge
s
i
g
n
a
l
,
t
h
e
a
v
e
r
a
ge
va
l
ue
o
f
w
hi
c
h
(
i
.
e
.
,
i
t
s
c
o
n
s
t
a
n
t
c
om
po
n
e
n
t
s
e
pa
r
a
t
e
d
by
f
il
t
e
r
s
i
n
t
h
e
l
o
a
d)
c
a
n
be
a
d
j
u
s
t
e
d.
T
h
e
pr
i
n
c
i
p
l
e
o
f
t
h
e
P
W
C
-
b
a
s
e
d
o
u
t
pu
t
v
o
l
t
a
ge
c
o
n
t
r
o
l
i
s
b
a
s
e
d
o
n
t
h
e
pe
r
i
o
d
i
c
s
w
i
t
c
hi
ng
o
n
a
n
d
o
f
f
o
f
ga
t
e
s
w
i
t
c
h
e
s
–
t
r
a
n
s
i
s
t
o
r
s
or
t
hy
r
i
s
t
or
s
.
F
i
gur
e
1
s
h
o
ws
th
e
b
a
s
i
c
P
W
M
c
i
r
c
u
i
t
[
14]
F
i
gur
e
1(
a
)
a
n
d
t
h
e
l
o
a
d
v
o
l
t
a
ge
c
ur
v
e
F
i
gur
e
1(
b
)
.
(
a
)
(
b
)
F
i
gur
e
1.
B
a
s
i
c
P
W
M
c
i
r
c
u
i
t
(
a
)
p
ul
s
e
-
w
i
dt
h
m
o
dul
a
t
e
d
s
e
m
i
c
o
n
duc
t
o
r
c
o
n
v
e
r
t
e
r
a
n
d
(
b
)
l
o
a
d
v
o
l
t
a
ge
d
i
a
gr
a
m
s
a
t
r
-
l
o
a
d
T
h
e
c
i
r
c
u
i
t
c
o
n
s
i
s
t
s
o
f
a
VT
1
t
r
a
n
s
i
s
t
o
r
(
I
GB
T
)
,
w
hi
c
h
o
pe
r
a
t
e
s
i
n
s
w
i
t
c
h
m
o
de
,
po
we
r
s
o
ur
c
e
(
P
S
)
a
n
d
l
o
a
d
(
R
L
)
.
S
uc
h
a
c
i
r
c
u
i
t
pr
o
vi
d
e
s
o
nly
u
ni
p
o
l
a
r
m
o
du
l
a
t
i
o
n
.
W
h
e
n
t
h
e
VT
1
t
r
a
n
s
i
s
t
or
i
s
t
ur
n
e
d
o
n
(
i
n
s
w
i
t
c
h
m
o
de
)
a
p
o
s
i
t
i
v
e
v
o
l
t
a
ge
pu
l
s
e
i
s
ge
n
e
r
a
t
e
d
a
t
t
h
e
l
o
a
d.
W
he
n
t
h
e
VT
1
tr
a
n
s
i
s
t
o
r
i
s
t
ur
n
e
d
o
f
f
,
a
v
o
l
t
a
ge
pa
us
e
i
s
f
o
r
m
e
d
a
t
t
h
e
l
o
a
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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do
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[
1]
M
.
S
a
di
q
e
t
al
.
,
“
C
o
nt
in
u
o
us
-
c
o
n
tr
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l
-
s
e
t
m
o
d
e
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e
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c
t
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v
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ont
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f
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-
l
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ve
l
D
C
–
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C
c
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n
v
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r
te
r
w
it
h
unba
la
nc
e
d
l
o
a
d
s
in
bi
po
la
r
e
l
e
c
tr
i
c
ve
hi
c
le
c
ha
r
gi
ng s
ta
ti
o
ns
,”
M
at
he
m
at
ic
s
, vo
l.
1
0, no
. 19, p. 3444, S
e
p. 2022, d
o
i:
10.3390/m
a
th
10193444.
[
2]
L
.
R
.
M
e
r
c
ha
n
-
V
il
la
lb
a
,
J
.
M
.
L
oz
a
n
o
-
G
a
r
c
ia
,
J
.
G
.
A
v
in
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-
C
e
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v
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nt
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s
,
H
.
J
.
E
s
tr
a
da
-
G
a
r
c
ia
,
A
.
P
i
z
a
no
-
M
a
r
ti
ne
z
,
a
nd
C
.
A
.
C
a
r
r
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n
o
-
M
e
n
e
s
e
s
,
“
L
in
e
a
r
l
y
d
e
c
o
up
le
d
c
o
nt
r
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l
of
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d
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mi
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lt
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g
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e
s
to
r
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r
w
it
h
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ut
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n
e
r
g
y
s
t
o
r
a
g
e
,”
M
at
he
m
at
ic
s
,
vo
l.
8,
no
.
10, pp. 1
–
18, Oc
t.
2020, d
o
i:
10.3390/m
a
th
8101794.
[
3]
C
.
G
uo
,
Y
.
W
a
ng,
a
nd
J
.
L
ia
o
,
“
C
oor
di
na
te
d
c
o
nt
r
o
l
of
vo
lt
a
ge
ba
la
nc
e
r
s
f
o
r
th
e
r
e
gul
a
ti
o
n
of
unba
la
n
c
e
d
vo
l
ta
ge
in
a
mul
ti
-
n
o
d
e
bi
po
la
r
D
C
di
s
tr
ib
ut
i
o
n n
e
tw
o
r
k,”
E
le
c
tr
oni
c
s
(
Sw
it
z
e
r
la
nd)
, vol
. 11, no
. 1, p. 166, J
a
n. 2022, doi:
10.3390/
e
le
c
t
r
o
ni
c
s
1101016
6.
[
4]
M
.
J
.
H
.
M
o
gha
dda
m
e
t
al
.
,
“
I
mpr
ove
d
vo
lt
a
ge
unba
la
n
c
e
a
nd
ha
r
mo
ni
c
s
c
o
mp
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ns
a
ti
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n
c
o
nt
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o
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s
tr
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t
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g
y
f
o
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a
n
is
ol
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te
d
mi
c
r
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g
r
id
,”
E
ne
r
gi
e
s
, vo
l.
11, n
o
. 10, p. 2688, Oc
t.
2018, d
o
i:
1
0.3390/e
n11102688.
[
5]
R
.
P
a
nde
y
,
R
.
N
.
T
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th
i,
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nd
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.
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ve
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is
of
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in
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f
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ba
s
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d D
S
T
A
T
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,”
E
ne
r
gi
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s
, vo
l.
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M
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6]
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ul
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i:
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g
e
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ga
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,
2019,
pp.
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–
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981
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13
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9_4.
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.
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,
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:
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.
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. 2, pp. 345
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. 2020, d
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:
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352
0
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2
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10]
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. 10, p.
e
2609, Oc
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o
i:
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ov
.
20
20,
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.
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ppl
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, v
ol
. 48, n
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. 2, pp.
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e
b. 2020, d
o
i:
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[
13]
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.
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om
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uni
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ns
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l.
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.
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.
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105, 2022, do
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:
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[
15]
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s
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l.
15,
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o
.
3,
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-
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i:
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.
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-
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[
16]
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:
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at
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e
and E
ngi
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e
r
in
g
, v
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o
.
1, p. 012046,
N
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[
17]
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.
D
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na
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n
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18]
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ir
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hoho Univ
e
r
s
y
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tu
, v
ol
. 2020, n
o
. 2, pp. 82
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88, 2020, d
oi
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[
19]
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.
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.
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,
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l.
2,
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.
1,
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20
–
26,
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i:
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20]
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.
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.
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.
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.
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,
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t.
2016,
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1
–
6.
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i:
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C
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[
21]
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.
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.
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gnal
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g,
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C
P
C
SI
2017
,
I
E
E
E
, S
e
p. 2018, pp. 724
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o
i:
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C
P
C
S
I
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[
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.
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