I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS)
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
,
p
p
.
1
9
5
0
~
1
9
6
1
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
7
.
i
3
.
p
p
1
9
5
0
-
1
9
6
1
1950
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Desig
n of a
no
v
el
sing
le
-
so
urce
15
-
l
ev
el inverter
wi
th
self
-
ba
la
ncing
capa
citors a
nd senso
rless
PWM
co
ntrol
T
a
o
ufiq El An
s
a
ri
,
Ay
o
ub
E
l
G
a
da
ri,
Yo
us
s
ef
O
un
ej
j
a
r
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
M
o
u
l
a
y
I
smai
l
U
n
i
v
e
r
si
t
y
,
H
i
g
h
S
c
h
o
o
l
o
f
Te
c
h
n
o
l
o
g
y
,
M
e
k
n
e
s
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ap
r
9
,
2
0
2
6
R
ev
is
ed
Au
g
4
,
2
0
2
6
Acc
ep
ted
Au
g
2
4
,
2
0
2
6
M
u
lt
il
e
v
e
l
in
v
e
rters
(M
LIs)
a
re
wid
e
ly
u
se
d
i
n
e
n
e
rg
y
-
c
o
n
v
e
rsio
n
sy
ste
m
s
b
e
c
a
u
se
th
e
y
g
e
n
e
ra
te
h
ig
h
-
q
u
a
li
ty
AC
v
o
lt
a
g
e
s
with
re
d
u
c
e
d
h
a
rm
o
n
ic
d
isto
rti
o
n
.
H
o
we
v
e
r,
e
x
isti
n
g
M
LIs
o
ften
re
q
u
ire
n
u
m
e
ro
u
s
p
o
w
e
r
d
e
v
ice
s,
m
u
lt
ip
le
DC
so
u
rc
e
s,
v
o
lt
a
g
e
se
n
so
rs,
o
r
d
e
d
ica
ted
c
a
p
a
c
it
o
r
-
b
a
lan
c
in
g
c
o
n
tro
ll
e
rs,
wh
ic
h
i
n
c
re
a
se
s
b
o
th
h
a
rd
wa
re
c
o
st
a
n
d
c
o
n
tr
o
l
c
o
m
p
l
e
x
it
y
.
T
h
is
p
a
p
e
r
p
r
o
p
o
se
s
a
sin
g
le
-
p
h
a
se
1
5
-
lev
e
l
in
v
e
rter
d
e
riv
e
d
fro
m
t
h
e
P
a
c
k
e
d
U
-
Ce
ll
stru
c
tu
re
.
It
e
m
p
l
o
y
s a
sin
g
le DC so
u
rc
e
,
th
re
e
c
a
p
a
c
it
o
rs,
a
n
d
a
re
d
u
c
e
d
n
u
m
b
e
r
o
f
p
o
we
r
sw
it
c
h
e
s.
Ba
se
d
o
n
th
e
n
u
m
b
e
r
o
f
p
o
we
r
sw
it
c
h
e
s,
g
a
te
d
riv
e
rs,
d
io
d
e
s,
c
a
p
a
c
it
o
rs,
DC
so
u
rc
e
s,
o
u
tp
u
t
lev
e
ls,
a
n
d
t
o
tal
sta
n
d
in
g
v
o
lt
a
g
e
p
e
r
u
n
it
(T
S
Vp
u
),
th
e
p
ro
p
o
se
d
t
o
p
o
lo
g
y
a
c
h
iev
e
s
a
lo
we
r
c
o
st
fu
n
c
ti
o
n
t
h
a
n
th
e
c
o
m
p
a
re
d
to
p
o
lo
g
ies
re
p
o
rte
d
i
n
t
h
e
li
tera
tu
re
.
Th
e
p
ro
p
o
se
d
to
p
o
lo
g
y
a
c
h
iev
e
s
a
re
lativ
e
ly
l
o
w
to
tal
sta
n
d
in
g
v
o
l
tag
e
p
e
r
u
n
it
(
TS
Vp
u
)
o
f
4
.
4
3
.
S
e
n
so
rles
s
o
p
e
n
-
l
o
o
p
S
P
WM
o
ffe
rs
i
n
h
e
re
n
t
c
a
p
a
c
it
o
r
-
v
o
lt
a
g
e
se
lf
-
b
a
lan
c
in
g
,
e
li
m
in
a
ti
n
g
th
e
n
e
e
d
f
o
r
v
o
lt
a
g
e
se
n
so
rs
o
r
a
d
d
it
i
o
n
a
l
b
a
lan
c
in
g
lo
o
p
s.
M
ATLAB/S
imu
li
n
k
v
a
li
d
a
ti
o
n
a
t
2
k
Hz
a
n
d
a
m
o
d
u
lati
o
n
in
d
e
x
o
f
1
c
o
v
e
rs
ste
a
d
y
-
sta
te
o
p
e
ra
ti
o
n
,
lo
a
d
tran
sie
n
ts,
n
o
n
li
n
e
a
r
lo
a
d
i
n
g
,
a
n
d
DC
-
so
u
rc
e
v
o
lt
a
g
e
flu
c
tu
a
ti
o
n
s.
F
o
r
a
5
0
Ω
–
2
0
m
H
lo
a
d
,
th
e
c
u
rre
n
t
TH
D
is
2
.
2
0
%
with
o
u
t
a
n
o
u
tp
u
t
fi
lt
e
r,
c
o
n
firmin
g
su
it
a
b
il
it
y
f
o
r
e
n
e
rg
y
-
c
o
n
v
e
rsio
n
sy
ste
m
s.
K
ey
w
o
r
d
s
:
Mu
ltil
ev
el
in
v
er
ter
s
Pack
ed
U
-
c
ell
P
u
ls
e
wid
th
m
o
d
u
latio
n
T
o
tal
s
tan
d
in
g
v
o
ltag
e
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
ao
u
f
iq
E
l A
n
s
ar
i
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
M
o
u
lay
Ism
a
il
Un
iv
e
rsit
y
,
Hig
h
S
c
h
o
o
l
o
f
Tec
h
n
o
l
o
g
y
M
e
k
n
e
s,
M
o
ro
c
c
o
E
m
ail:
tao
u
f
iq
.
elan
s
ar
i@
ed
u
.
u
m
i.a
c.
m
a
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
wid
esp
r
ea
d
d
ep
lo
y
m
en
t
o
f
r
en
ewa
b
le
en
er
g
y
tech
n
o
lo
g
ies
[
1
]
an
d
t
h
e
in
teg
r
atio
n
o
f
h
ig
h
-
en
er
g
y
-
d
en
s
ity
b
atter
ies
in
to
m
o
d
er
n
s
y
s
tem
s
h
av
e
g
r
ea
tly
in
cr
ea
s
e
d
in
ter
est
in
m
u
ltil
ev
el
in
v
e
r
ter
s
(
ML
I
s
)
in
p
o
wer
elec
tr
o
n
ics
[
2
]
.
C
u
r
r
e
n
t
a
p
p
licatio
n
s
(
elec
tr
ic
v
e
h
icles,
m
icr
o
g
r
id
s
,
r
en
ewa
b
le
en
er
g
ies,
an
d
c
h
ar
g
i
n
g
in
f
r
astru
ctu
r
e)
n
ec
ess
itate
h
ig
h
ef
f
icien
c
y
,
co
m
p
ac
t
p
o
wer
d
en
s
ity
,
an
d
lo
w
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
wh
ich
ML
I
s
ef
f
ec
tiv
ely
ad
d
r
ess
th
r
o
u
g
h
im
p
r
o
v
e
d
wav
e
q
u
ality
an
d
r
ed
u
ce
d
s
witch
in
g
co
n
s
tr
ain
ts
[
3
]
.
Ho
wev
er
,
c
o
n
v
e
n
tio
n
al
t
o
p
o
l
o
g
ies
[
4
]
,
in
cl
u
d
in
g
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
HB
)
,
n
eu
tr
al
-
p
o
i
n
t
-
clam
p
ed
(
NPC
)
,
an
d
f
ly
in
g
-
ca
p
ac
ito
r
(
FC
)
in
v
er
ter
s
,
h
av
e
s
tr
u
ctu
r
al
lim
itatio
n
s
:
th
ey
r
eq
u
i
r
e
a
lar
g
e
n
u
m
b
er
o
f
co
m
p
o
n
en
ts
,
C
HB
o
f
ten
r
e
q
u
i
r
es
s
ev
er
al
is
o
lated
DC
s
o
u
r
ce
s
,
an
d
FC
r
eq
u
ir
es
d
ed
icate
d
c
ap
ac
ito
r
b
ala
n
cin
g
m
ec
h
an
is
m
s
.
I
n
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
lev
els
g
en
e
r
ally
in
cr
ea
s
es
th
e
n
u
m
b
er
o
f
s
witch
es,
co
s
t,
f
o
o
tp
r
in
t,
an
d
co
n
tr
o
l c
o
m
p
lex
ity
.
T
h
is
h
as led
to
t
h
e
em
er
g
en
ce
o
f
n
ew
co
n
f
ig
u
r
atio
n
s
aim
ed
at
r
ed
u
cin
g
co
m
p
o
n
en
ts
wh
il
e
m
ain
tain
in
g
wav
e
q
u
ality
[
5
]
.
Ho
wev
er
,
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
s
witch
es
ca
n
in
cr
ea
s
e
th
e
to
tal
s
tan
d
in
g
v
o
ltag
e
(
T
SV)
s
u
p
p
o
r
ted
b
y
ce
r
tain
s
e
m
ico
n
d
u
ct
o
r
s
,
with
a
p
o
s
s
ib
le
im
p
ac
t o
n
lo
s
s
es a
n
d
r
eliab
ilit
y
if
th
e
ar
c
h
itec
tu
r
e
is
n
o
t
o
p
tim
ized
[
6
]
.
An
o
t
h
er
ch
allen
g
e
ass
o
ciate
d
with
co
n
v
en
tio
n
al
m
u
ltil
ev
el
in
v
er
ter
s
lies
in
th
e
d
esig
n
o
f
th
eir
co
n
tr
o
l
s
tr
ateg
ies.
I
n
th
is
co
n
tex
t,
s
ev
er
al
ad
v
an
ce
d
ap
p
r
o
ac
h
es
h
av
e
b
ee
n
d
ev
elo
p
e
d
,
in
clu
d
in
g
r
o
b
u
s
t
ad
ap
tiv
e
co
n
tr
o
l,
in
teg
r
al
s
li
d
in
g
-
m
o
d
e
c
o
n
tr
o
l,
f
u
zz
y
-
o
b
s
er
v
er
-
b
ased
s
lid
in
g
-
m
o
d
e
c
o
n
tr
o
l,
a
n
d
h
y
b
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
o
f a
n
o
ve
l sin
g
le
-
s
o
u
r
c
e
1
5
-
leve
l in
ve
r
ter w
ith
s
elf
-
b
a
la
n
cin
g
c
a
p
a
cito
r
s
…
(
Ta
o
u
fi
q
E
l A
n
s
a
r
i
)
1951
r
ea
ch
in
g
-
law
tech
n
i
q
u
es
[
7
]
-
[
9
]
.
Ho
wev
er
,
th
ese
m
eth
o
d
s
m
ay
in
cr
ea
s
e
co
m
p
u
tatio
n
al
b
u
r
d
e
n
,
p
ar
am
eter
-
tu
n
in
g
r
e
q
u
ir
em
e
n
ts
,
an
d
im
p
lem
en
tatio
n
co
m
p
lex
ity
.
Hig
h
-
q
u
alit
y
m
u
lti
le
v
el
v
o
l
ta
g
e
g
en
e
r
ati
o
n
g
e
n
e
r
a
ll
y
r
e
q
u
ir
e
s
n
u
m
er
o
u
s
s
e
m
ic
o
n
d
u
ct
o
r
d
e
v
ic
es
a
n
d
is
o
l
ate
d
DC
s
o
u
r
c
es
[
1
0
]
.
Ho
wev
er
,
m
u
l
ti
p
le
i
n
p
u
t
s
o
u
r
c
es
in
c
r
ea
s
e
co
n
v
e
r
t
er
c
o
s
t
,
s
iz
e,
an
d
im
p
l
e
m
e
n
ta
ti
o
n
co
m
p
le
x
it
y
.
Si
n
g
le
-
s
o
u
r
c
e
a
r
c
h
it
ec
t
u
r
es
a
r
e
th
er
ef
o
r
e
p
r
e
f
e
r
r
e
d
i
n
a
p
p
lic
ati
o
n
s
s
u
ch
as
el
ec
t
r
ic
v
e
h
i
cl
es
an
d
r
e
n
ew
a
b
le
-
e
n
er
g
y
s
y
s
te
m
s
[
1
1
]
.
Ac
co
r
d
i
n
g
l
y
,
s
wit
ch
ed
-
ca
p
a
cit
o
r
ML
I
s
g
en
er
ate
m
u
l
ti
p
le
v
o
lta
g
e
l
ev
els
f
r
o
m
o
n
e
DC
s
o
u
r
c
e
b
y
ch
a
r
g
in
g
a
n
d
d
is
c
h
a
r
g
i
n
g
ca
p
a
cit
o
r
s
t
h
r
o
u
g
h
a
p
p
r
o
p
r
i
at
e
s
wit
ch
in
g
s
t
at
es
u
n
d
er
o
p
e
n
-
l
o
o
p
o
r
clo
s
e
d
-
lo
o
p
c
o
n
tr
o
l
[
1
2
]
.
T
h
e
p
ac
k
e
d
U
-
C
ell
(
PUC
)
t
o
p
o
l
o
g
y
[
1
3
]
e
f
f
ec
t
iv
el
y
a
d
d
r
ess
es
t
h
e
m
aj
o
r
c
o
n
s
tr
ai
n
ts
o
f
m
u
lti
-
c
ell
c
o
n
v
er
te
r
s
,
s
u
ch
as
s
in
g
l
e
-
s
o
u
r
ce
p
o
we
r
s
u
p
p
l
y
,
r
e
d
u
c
ti
o
n
i
n
t
h
e
n
u
m
b
e
r
o
f
c
o
m
p
o
n
e
n
ts
,
T
S
V
lim
i
tat
io
n
,
a
n
d
m
i
n
i
m
i
za
t
io
n
o
f
h
a
r
m
o
n
i
c
d
is
to
r
t
io
n
.
I
n
h
e
r
it
in
g
t
h
e
a
d
v
a
n
t
a
g
es
o
f
ca
s
c
a
d
e
d
H
-
B
r
id
g
e
(
C
HB
)
a
n
d
f
l
y
i
n
g
ca
p
ac
i
to
r
(
FC
)
s
t
r
u
ct
u
r
e
s
,
t
h
is
h
y
b
r
i
d
ar
c
h
it
ec
t
u
r
e
s
ta
n
d
s
o
u
t
f
o
r
i
ts
a
d
v
a
n
t
ag
e
o
u
s
T
S
V
m
a
n
ag
em
e
n
t
[
1
4
]
.
Sev
er
al
in
v
er
ter
co
n
f
ig
u
r
atio
n
s
d
er
iv
ed
f
r
o
m
th
e
PUC
co
n
ce
p
t
h
av
e
b
ee
n
in
v
esti
g
ated
,
alt
h
o
u
g
h
s
ev
er
al
p
r
ac
tical
co
n
s
tr
ain
ts
r
em
ain
.
T
h
e
to
p
o
lo
g
ies
in
tr
o
d
u
ce
d
i
n
[
1
5
]
,
[
1
6
]
u
tili
ze
r
ed
u
n
d
a
n
t
s
witch
in
g
co
m
b
in
atio
n
s
to
m
ain
tain
th
e
ca
p
ac
ito
r
v
o
ltag
es
at
th
eir
r
eq
u
ir
e
d
lev
els
with
o
u
t
t
h
e
n
ee
d
f
o
r
ad
d
itio
n
al
b
alan
cin
g
co
n
tr
o
ller
s
.
Nev
er
t
h
eless
,
th
e
u
s
e
o
f
two
s
ep
ar
ate
DC
s
o
u
r
ce
s
in
cr
ea
s
es
th
e
s
u
p
p
ly
r
eq
u
ir
em
e
n
ts
an
d
r
ed
u
ce
s
th
eir
s
u
itab
ilit
y
f
o
r
ap
p
licatio
n
s
b
ased
o
n
a
s
in
g
le
D
C
b
u
s
.
T
h
e
ca
p
ac
ito
r
v
o
ltag
es
ar
e
r
eg
u
lated
th
r
o
u
g
h
a
clo
s
ed
-
lo
o
p
s
ch
em
e
th
at
d
ep
en
d
s
o
n
v
o
ltag
e
a
n
d
c
u
r
r
e
n
t
m
ea
s
u
r
em
e
n
ts
[
1
7
]
.
T
h
is
s
o
lu
tio
n
im
p
r
o
v
es
co
n
tr
o
llab
ilit
y
b
u
t
r
eq
u
ir
es
s
en
s
in
g
d
ev
ices,
s
ig
n
al
-
p
r
o
ce
s
s
in
g
cir
cu
its
,
an
d
a
d
d
itio
n
al
c
o
n
tr
o
l
h
ar
d
war
e,
th
er
eb
y
in
cr
ea
s
in
g
th
e
im
p
lem
en
tatio
n
co
s
t
an
d
s
y
s
tem
co
m
p
lex
it
y
.
T
h
e
c
o
n
v
e
r
ter
s
r
ep
o
r
ted
i
n
[1
8
],
[
1
9
]
e
m
p
lo
y
tr
an
s
f
o
r
m
er
s
to
o
b
tain
th
e
r
e
q
u
ir
ed
v
o
ltag
e
co
n
v
er
s
io
n
an
d
o
u
t
p
u
t
le
v
els.
Alth
o
u
g
h
tr
a
n
s
f
o
r
m
er
s
p
r
o
v
i
d
e
g
alv
an
ic
is
o
latio
n
an
d
v
o
lta
g
e
ad
ap
tatio
n
,
th
e
y
also
a
d
d
v
o
lu
m
e
,
weig
h
t,
m
ag
n
etic
lo
s
s
es,
an
d
d
esig
n
co
n
s
tr
ain
ts
ass
o
ciate
d
with
tu
r
n
s
r
atio
s
,
l
ea
k
ag
e
in
d
u
ctan
ce
,
an
d
in
s
u
latio
n
r
e
q
u
ir
em
e
n
ts
.
T
h
ese
d
r
awb
ac
k
s
h
ig
h
lig
h
t
th
e
in
te
r
est
in
a
tr
an
s
f
o
r
m
er
less
PUC
-
d
er
iv
ed
to
p
o
lo
g
y
s
u
p
p
lied
b
y
a
s
in
g
le
DC
s
o
u
r
ce
an
d
ca
p
ab
le
o
f
ac
h
iev
in
g
in
h
e
r
en
t c
ap
ac
ito
r
-
v
o
ltag
e
b
alan
cin
g
with
o
u
t se
n
s
o
r
s
o
r
d
e
d
icate
d
clo
s
e
d
-
lo
o
p
r
eg
u
latio
n
.
I
n
th
is
wo
r
k
,
a
n
ew
1
5
-
le
v
el
in
v
er
ter
b
ased
o
n
th
e
PUC
co
n
f
i
g
u
r
atio
n
is
p
r
o
p
o
s
ed
t
o
ac
h
iev
e
a
r
ed
u
ce
d
co
m
p
o
n
en
t
c
o
u
n
t,
s
in
g
le
-
s
o
u
r
ce
o
p
er
atio
n
,
a
n
d
g
o
o
d
wa
v
ef
o
r
m
q
u
ality
.
I
ts
p
er
f
o
r
m
an
ce
i
s
ev
alu
ated
u
s
in
g
a
co
s
t f
u
n
ctio
n
(
C
F),
an
d
t
h
e
o
b
tain
ed
r
esu
lts
ar
e
v
alid
ated
in
MA
T
L
AB
/S
im
u
lin
k
.
T
h
e
n
o
v
elty
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
is
d
em
o
n
s
tr
ated
th
r
o
u
g
h
a
co
m
p
ar
is
o
n
with
ex
is
tin
g
s
o
lu
tio
n
s
.
T
h
e
m
ai
n
co
n
tr
ib
u
tio
n
s
in
clu
d
e
a
r
ed
u
ce
d
C
F,
lo
w
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
r
ed
u
c
ed
to
tal
s
tan
d
in
g
v
o
ltag
e
(
T
SV)
,
an
d
a
r
eliab
le
s
en
s
o
r
less
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
ap
er
is
o
r
g
a
n
ized
as
f
o
llo
ws
:
i)
Sectio
n
2
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
,
o
p
e
r
atin
g
m
o
d
es,
ca
p
ac
ito
r
s
izin
g
,
a
n
d
s
witch
-
v
o
ltag
e
s
tr
ess
;
ii)
Sectio
n
3
p
r
o
v
i
d
es
a
co
m
p
ar
ativ
e
a
n
a
ly
s
is
; iii)
Sect
io
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
;
an
d
iv
)
Sectio
n
5
c
o
n
cl
u
d
es th
e
p
ap
e
r
.
2.
M
E
T
H
O
D
2
.
1
.
P
r
o
po
s
ed
co
nv
er
t
er
co
n
f
ig
ura
t
io
n a
nd
o
pera
t
ing
s
wit
ching
m
o
des
T
h
e
b
asic
SP
UC
5
s
tr
u
ctu
r
e
m
en
tio
n
ed
in
[
2
0
]
is
b
ased
o
n
f
iv
e
p
o
wer
s
witch
es.
I
t
is
p
o
wer
ed
b
y
a
s
in
g
le
DC
s
o
u
r
ce
c
o
u
p
le
d
to
two
ca
p
ac
ito
r
s
,
e
n
ab
lin
g
th
e
p
r
o
d
u
ctio
n
o
f
a
f
i
v
e
-
s
tep
o
u
t
p
u
t
v
o
ltag
e.
As
a
n
ex
ten
s
io
n
o
f
th
is
d
esig
n
,
a
n
ew
co
n
f
ig
u
r
atio
n
is
in
tr
o
d
u
ce
d
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
co
m
b
in
es
th
e
ex
is
tin
g
SP
UC
5
in
v
er
t
er
with
a
PUC
ce
ll
to
in
cr
ea
s
e
th
e
n
u
m
b
er
o
f
lev
els
g
en
er
ated
to
f
if
teen
.
T
h
e
r
esu
ltin
g
ass
em
b
ly
i
n
co
r
p
o
r
ates
n
in
e
s
witch
p
o
s
itio
n
s
,
in
clu
d
in
g
o
n
e
b
id
ir
ec
tio
n
al
s
witch
,
r
esu
ltin
g
in
a
to
tal
o
f
ten
I
GB
T
s
,
a
s
in
g
le
D
C
s
o
u
r
ce
,
an
d
th
r
ee
ca
p
ac
ito
r
s
.
I
n
ad
d
itio
n
,
t
h
e
s
witch
in
g
p
a
ir
s
(
T
1
-
T
2
)
,
(
T
6
-
T
7
)
,
an
d
(
T
8
-
T
9
)
a
r
e
u
s
ed
in
a
co
m
p
lem
en
tar
y
m
a
n
n
er
.
T
h
is
ar
r
a
n
g
em
en
t
en
a
b
les
a
f
if
teen
-
lev
el
v
o
ltag
e
o
u
tp
u
t
to
b
e
ac
h
iev
ed
b
y
th
e
d
e
v
elo
p
e
d
in
v
er
ter
with
a
r
e
d
u
ce
d
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
m
u
ltil
ev
e
l in
v
er
ter
s
.
T
h
e
p
r
o
p
o
s
ed
in
v
er
ter
co
n
f
ig
u
r
atio
n
u
tili
ze
s
a
DC
s
o
u
r
ce
an
d
c
o
n
n
ec
ts
it
to
t
h
r
ee
c
ap
a
cito
r
s
.
T
h
is
co
n
f
ig
u
r
atio
n
is
ab
le
to
g
en
er
a
te
f
if
teen
v
o
ltag
e
lev
els wh
ile
at
th
e
s
am
e
tim
e
en
s
u
r
in
g
th
e
in
tr
in
s
ic
b
alan
ce
o
f
th
e
v
o
ltag
es
in
th
e
ca
p
ac
ito
r
s
.
T
h
e
DC
s
o
u
r
ce
an
d
th
e
ca
p
ac
ito
r
s
ar
e
co
n
n
ec
ted
u
s
in
g
co
n
tr
o
llab
le
s
witch
es.
T
h
ese
s
witch
es d
eter
m
in
e
th
e
cu
r
r
en
t
p
ath
s
ac
co
r
d
i
n
g
to
t
h
e
o
u
tp
u
t.
Fo
r
test
in
g
p
u
r
p
o
s
es,
th
e
in
p
u
t
s
o
u
r
ce
is
s
et
to
E
=
6
V
dc
.
I
n
o
p
en
-
lo
o
p
o
p
er
ati
o
n
,
th
e
ca
p
ac
ito
r
v
o
ltag
es
n
atu
r
ally
c
o
n
v
e
r
g
e
to
s
tab
le
v
alu
es
o
f
V
C1
=V
C2
=
E
/2
=
3
V
dc
an
d
V
C3
=
E
/6
=
V
dc
.
T
h
is
i
s
a
co
n
f
ir
m
atio
n
o
f
th
e
to
p
o
lo
g
y
’
s
a
b
ilit
y
to
s
elf
-
b
alan
ce
in
v
o
ltag
e.
I
t
is
a
v
er
i
f
icatio
n
o
f
th
e
p
r
o
p
e
r
d
is
tr
ib
u
tio
n
o
f
t
h
e
v
o
ltag
e,
wh
ich
allo
ws u
s
to
ac
h
ie
v
e
th
e
f
if
teen
lev
els o
f
v
o
ltag
e.
T
h
e
co
r
r
esp
o
n
d
en
ce
o
f
ea
ch
v
o
ltag
e
lev
el
with
its
r
esp
ec
tiv
e
s
witch
co
n
f
ig
u
r
atio
n
is
s
h
o
wn
in
T
ab
le
1
.
Fig
u
r
e
2
s
h
o
ws
th
e
cu
r
r
en
t
f
lo
w
f
o
r
th
e
p
o
s
itiv
e
h
alf
-
cy
cle.
I
t
is
im
p
o
r
tan
t
to
p
o
in
t
o
u
t
t
h
at
th
e
p
r
o
d
u
ctio
n
o
f
ea
ch
o
f
th
e
lev
el
s
is
ac
h
iev
ed
b
y
ac
tiv
atin
g
f
o
u
r
s
witch
es,
th
er
eb
y
r
ed
u
cin
g
t
h
e
n
u
m
b
e
r
o
f
d
ev
ices
in
co
n
d
u
ctio
n
a
n
d
r
esu
ltin
g
in
a
h
ig
h
ef
f
icien
cy
o
f
th
e
s
y
s
te
m
.
T
h
e
o
p
er
atin
g
m
o
d
es
ca
n
b
e
e
x
p
lain
ed
as
f
o
llo
ws:
Fo
r
th
e
f
ir
s
t
o
u
tp
u
t
lev
el
(
State
1
)
,
s
witc
h
es
T
2
,
T
3
,
T
7
,
an
d
T
8
ar
e
ac
tiv
ate
d
,
as
s
h
o
wn
in
Fig
u
r
e
2
(
a
)
.
T
h
is
co
n
f
ig
u
r
atio
n
allo
ws
ca
p
ac
ito
r
C
3
to
d
is
ch
ar
g
e,
en
s
u
r
i
n
g
th
at
a
v
o
ltag
e
o
f
7
V
dc
is
p
r
o
d
u
ce
d
at
t
h
e
o
u
tp
u
t.
I
n
s
tate
2
,
co
n
d
u
ctio
n
is
p
r
o
v
id
ed
b
y
T
2
,
T
3
,
T
6
,
a
n
d
T
8
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1950
-
1
9
6
1
1952
g
en
er
atin
g
a
n
o
u
t
p
u
t
v
o
ltag
e
o
f
6
V
dc
as
s
h
o
wn
in
Fig
u
r
e
2
(
b
)
.
Fo
r
s
tate
3
,
s
witch
es
T
2
,
T
3
,
T
6
,
an
d
T
9
a
r
e
ac
tiv
ated
as
s
h
o
wn
in
Fig
u
r
e
2
(
c)
,
ca
u
s
in
g
ca
p
ac
ito
r
C
3
to
c
h
ar
g
e
a
n
d
p
r
o
d
u
cin
g
a
v
o
ltag
e
o
f
5
V
dc
.
I
n
v
ar
ian
t
4
,
th
e
s
im
u
ltan
e
o
u
s
co
n
d
u
ctio
n
o
f
T
2
,
T
5
,
T
7
,
an
d
T
8
ca
u
s
es
ca
p
ac
it
or
C
2
to
c
h
ar
g
e
an
d
C
3
to
d
is
ch
ar
g
e
,
also
en
s
u
r
in
g
an
o
u
tp
u
t
o
f
4
V
dc
as
s
h
o
wn
in
Fig
u
r
e
2
(
d
)
.
I
n
s
tate
5
,
s
witch
es
T
2
,
T
5
,
T
6
,
an
d
T
8
ar
e
ac
tiv
ated
,
with
C
1
in
th
e
d
is
ch
ar
g
in
g
p
h
ase,
r
esu
ltin
g
in
an
o
u
tp
u
t
lev
el
o
f
3
V
dc
as
s
h
o
wn
in
Fig
u
r
e
2
(
e)
.
I
n
s
tate
6
,
cu
r
r
en
t
f
lo
ws
th
r
o
u
g
h
T
2
,
T
5
,
T
6
,
a
n
d
T
9
.
C
ap
ac
ito
r
s
C
2
an
d
C
3
ar
e
ch
ar
g
e
d
,
en
s
u
r
i
n
g
th
e
p
r
o
d
u
ctio
n
o
f
a
v
o
ltag
e
eq
u
iv
alen
t
t
o
2
V
dc
as
s
h
o
wn
in
Fig
u
r
e
2
(
f
)
.
I
n
s
tate
7
,
th
e
co
n
d
u
ctio
n
o
f
T
2
,
T
4
,
T
7
,
an
d
T
8
allo
ws
C
3
to
d
is
ch
ar
g
e,
wh
ich
m
ain
tain
s
th
e
o
u
tp
u
t
at
V
dc
as
s
h
o
wn
in
Fig
u
r
e
2
(
g
)
.
I
n
s
tate
8
,
to
o
b
tain
t
h
e
ze
r
o
le
v
el,
s
witch
es
T
2
,
T
4
,
T
7
,
an
d
T
9
ar
e
ac
tiv
ated
as
s
h
o
wn
in
Fig
u
r
e
2
(
h
)
.
T
h
e
o
th
e
r
s
tates
o
f
th
e
n
eg
ativ
e
alter
n
atio
n
ar
e
s
h
o
wn
in
T
ab
le
1
.
I
t sh
o
u
ld
b
e
n
o
te
d
th
a
t th
er
e
ar
e
two
r
e
d
u
n
d
an
t states
ass
o
ciate
d
with
a
ze
r
o
-
o
u
tp
u
t
v
o
ltag
e.
Fig
u
r
e
1
.
Pro
p
o
s
ed
in
v
er
ter
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
Fig
u
r
e
2
.
Op
e
r
atio
n
al
m
o
d
es
a
n
d
ass
o
ciate
d
s
witch
in
g
s
tates
:
(
a)
V
L
=
7
V
dc
,
(
b
)
V
L
=
6
V
dc
,
(
c)
V
L
=
5
V
dc
,
(
d
)
V
L
=
4
V
dc,
(
e)
V
L
=
3
V
dc
,
(
f
)
V
L
=
2
V
dc
,
(
g
)
V
L
=
V
dc
,
an
d
(
h
)
V
L
=
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
o
f a
n
o
ve
l sin
g
le
-
s
o
u
r
c
e
1
5
-
leve
l in
ve
r
ter w
ith
s
elf
-
b
a
la
n
cin
g
c
a
p
a
cito
r
s
…
(
Ta
o
u
fi
q
E
l A
n
s
a
r
i
)
1953
T
ab
le
1
.
Op
e
r
atin
g
an
d
s
witch
in
g
s
tates
S
t
a
t
e
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
T
9
C
1
C
2
C
3
I
n
t
e
r
c
o
n
n
e
x
i
o
n
V
o
l
t
a
g
e
1
0
1
1
0
0
0
1
1
0
-
-
D
i
s
E+
V
c3
7
V
dc
2
0
1
1
0
0
1
0
1
0
-
-
-
E
6
V
dc
3
0
1
1
0
0
1
0
0
1
-
-
Ch
E
-
V
C3
5
V
dc
4
0
1
0
0
1
0
1
1
0
-
Ch
D
i
s
E
-
V
c2
+V
c3
4
V
dc
5
0
1
0
0
1
1
0
1
0
D
i
s
-
-
V
c1
3
V
dc
6
0
1
0
0
1
1
0
0
1
-
Ch
Ch
E
-
V
C2
-
V
C3
2
V
dc
7
0
1
0
1
0
0
1
1
0
-
-
D
i
s
V
C3
V
dc
8
0
1
0
1
0
0
1
0
1
-
-
-
0
0
8’
1
0
1
0
0
1
0
1
0
-
-
-
0
0
9
1
0
1
0
0
1
0
0
1
-
-
D
i
s
-
V
C3
-
V
dc
10
1
0
0
0
1
0
1
1
0
Ch
-
Ch
-
E+
V
c1
+V
c3
-
2
V
dc
11
1
0
0
0
1
0
1
0
1
-
D
i
s
-
-
V
C2
-
3
V
dc
12
1
0
0
0
1
1
0
0
1
Ch
-
D
i
s
-
E+
V
c1
-
V
C3
-
4
V
dc
13
1
0
0
1
0
0
1
1
0
-
-
Ch
-
E+
V
C3
-
5
V
dc
14
1
0
0
1
0
0
1
0
1
-
-
-
-
E
-
6
V
dc
15
1
0
0
1
0
1
0
0
1
-
-
D
i
s
-
E
-
V
c3
-
7
V
dc
D
i
s:
D
i
sc
h
a
r
g
i
n
g
.
C
h
:
C
h
a
r
g
i
n
g
.
2
.
2
.
Ca
pa
ci
t
o
r
des
ig
n
On
e
o
f
th
e
m
ajo
r
p
r
o
b
lem
s
in
m
u
ltil
ev
el
in
v
er
ter
s
is
th
e
p
r
o
b
lem
o
f
b
ala
n
cin
g
t
h
e
v
o
ltag
es
o
f
f
lo
atin
g
ca
p
ac
ito
r
s
,
wh
ich
is
s
o
lv
e
d
u
s
i
n
g
s
o
m
e
c
o
n
tr
o
l
alg
o
r
ith
m
s
.
I
n
th
e
s
u
g
g
ested
1
5
-
lev
el
in
v
e
r
te
r
,
th
is
p
r
o
b
lem
h
as
b
ee
n
au
to
m
atica
lly
ad
d
r
ess
ed
with
th
e
h
elp
o
f
a
s
elf
-
b
alan
ce
f
ea
tu
r
e
t
h
at
o
b
v
iates
th
e
n
ee
d
f
o
r
s
o
p
h
is
ticated
co
n
tr
o
l
alg
o
r
ith
m
s
.
Desp
ite
th
at,
in
an
y
k
in
d
o
f
in
v
e
r
ter
,
o
n
e
o
f
th
e
ca
u
s
es
o
f
p
o
wer
lo
s
s
is
th
e
v
o
ltag
e
r
ip
p
les
o
f
th
e
ca
p
ac
ito
r
s
as
th
ey
ch
ar
g
e
an
d
d
is
ch
ar
g
e
in
s
eq
u
en
ce
.
T
h
e
v
o
ltag
e
r
i
p
p
les
s
h
o
u
l
d
n
o
t
e
x
ce
ed
a
li
m
it
o
f
5
%
to
1
0
% f
o
r
th
e
o
u
tp
u
t v
o
ltag
e
to
r
em
ain
o
f
h
ig
h
q
u
ality
.
As s
h
o
wn
in
Fig
u
r
e
3
,
wh
ich
d
ep
ic
ts
th
e
v
ar
iatio
n
s
o
f
ca
p
ac
ito
r
v
o
ltag
e
a
n
d
th
eir
m
a
x
im
u
m
d
is
ch
ar
g
e
p
er
io
d
,
t
h
e
v
ar
iatio
n
is
d
e
p
en
d
e
n
t o
n
th
e
v
a
lu
e
o
f
ca
p
ac
itan
ce
,
th
e
d
is
ch
ar
g
e
cu
r
r
en
t,
a
n
d
th
e
t
im
e
in
ter
v
al.
T
h
u
s
,
th
er
e
s
h
o
u
l
d
b
e
a
s
tu
d
y
o
f
th
e
o
p
er
atio
n
c
y
cle
an
d
co
n
s
tr
ain
ts
o
n
cu
r
r
e
n
t
to
ac
cu
r
ately
s
ize
th
e
ca
p
ac
ito
r
s
.
Usi
n
g
th
is
ap
p
r
o
ac
h
,
it
is
f
ea
s
ib
le
to
r
eg
u
lat
e
th
e
p
ea
k
-
to
-
p
ea
k
r
ip
p
le
o
f
th
e
v
o
ltag
e
o
f
ca
p
ac
it
o
r
C
i,
wh
ich
ca
n
b
e
ex
p
r
ess
ed
as
(
1
)
:
=
=
1
∫
(
)
(
1
)
wh
er
e
(
t)
d
e
n
o
tes
th
e
l
o
ad
cu
r
r
e
n
t
f
or
a
se
r
i
es
R
–
L
l
oad
oper
at
i
ng
un
der
si
nuso
i
dal
st
eady
-
st
at
e
condi
t
i
ons
,
an
d
is
ex
p
r
ess
ed
a
s
(
2
)
.
(
)
=
s
in
(
−
)
(
2
)
The pe
ak cur
r
e
nt
i
s gi
ven by
(
3)
.
=
√
2
+
(
)
2
(
3
)
W
h
er
e
ω
is
th
e
an
g
u
lar
f
r
eq
u
en
cy
an
d
φ
is
th
e
p
h
ase
lag
o
f
th
e
cu
r
r
en
t
r
elativ
e
to
th
e
v
o
ltag
e,
an
d
V
m
is
th
e
p
ea
k
v
alu
e
o
f
th
e
v
o
ltag
e.
T
h
e
r
ip
p
le
v
o
ltag
es o
f
th
e
ca
p
ac
ito
r
s
at
th
e
MD
PC
i tim
e
in
te
r
v
als ar
e
d
eter
m
in
e
d
u
s
in
g
(
4
)
-
(
6
)
.
1
=
1
1
=
1
1
∫
s
in
(
−
)
4
3
(
4
)
2
=
2
2
=
1
2
∫
s
in
(
−
)
18
17
(
5
)
3
=
3
3
=
1
3
∫
s
in
(
−
)
2
1
(
6
)
T
h
e
ca
p
ac
ito
r
v
alu
es
wer
e
d
et
er
m
in
ed
b
y
s
o
lv
in
g
(
4
)
,
(
5
)
,
a
n
d
(
6
)
with
th
e
d
esig
n
cr
iter
i
o
n
th
at
th
e
v
o
ltag
e
r
ip
p
le
m
u
s
t n
o
t e
x
ce
ed
1
0
% o
f
th
e
d
esire
d
v
alu
e,
co
n
s
id
er
in
g
a
lo
ad
c
o
m
p
o
s
ed
o
f
a
5
0
Ω
r
e
s
is
to
r
co
n
n
ec
ted
in
s
er
ies
with
a
2
0
m
H
in
d
u
cto
r
,
with
a
f
u
n
d
am
en
tal
f
r
eq
u
en
c
y
o
f
6
0
Hz,
a
n
d
a
n
in
p
u
t
DC
v
o
ltag
e
o
f
E
=1
8
0
V
.
B
ased
o
n
th
is
an
aly
s
is
,
th
e
ca
p
ac
itan
ce
s
wer
e
s
et
to
C
1
=
C
2
=
1
2
0
0
µF
an
d
C
3
=
2
0
0
0
µF.
T
h
ese
ch
o
s
en
v
al
u
es
g
u
ar
an
tee
a
d
eq
u
ate
v
o
ltag
e
s
tab
ilit
y
ac
r
o
s
s
b
o
th
ca
p
ac
ito
r
s
an
d
m
ain
tain
th
ei
r
f
l
u
ctu
atio
n
s
with
in
to
ler
ab
le
b
o
u
n
d
s
u
n
d
e
r
all
o
p
e
r
atin
g
co
n
d
itio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1950
-
1
9
6
1
1954
Fig
u
r
e
3
.
W
av
ef
o
r
m
o
f
th
e
lo
a
d
v
o
ltag
e
with
ca
p
ac
ito
r
c
h
ar
g
in
g
-
d
is
ch
ar
g
i
n
g
2
.
3
.
Vo
l
t
a
g
e
s
t
re
s
s
Fo
r
th
e
p
r
o
p
o
s
ed
f
if
teen
-
lev
el
in
v
er
ter
to
p
o
l
o
g
ical
co
n
f
i
g
u
r
atio
n
,
a
s
et
o
f
n
in
e
p
o
wer
s
witch
es
h
as
b
ee
n
in
cl
u
d
ed
,
o
f
wh
ich
a
b
id
i
r
ec
tio
n
al
s
witch
h
as
b
ee
n
i
n
co
r
p
o
r
ated
in
to
th
e
a
r
ch
itectu
r
e.
T
h
e
v
o
ltag
e
s
tr
ess
o
f
ea
ch
d
ev
ice
h
as
b
ee
n
o
b
tain
ed
b
y
co
n
s
id
er
in
g
th
e
o
p
er
at
in
g
m
o
d
es
o
f
th
e
p
r
o
p
o
s
ed
n
o
v
el
co
n
f
ig
u
r
atio
n
.
T
h
e
b
lo
ck
i
n
g
v
o
ltag
e
o
f
ea
ch
d
ev
ice
is
as
(
7
)
-
(
9
)
.
V
T1
=V
T2
=V
T3
=V
T4
=E
(
7
)
V
T6
=V
T7
=V
T8
=V
T9
=V
C3
(
8
)
V
T5
=V
C1
(
9
)
T
h
e
ag
g
r
eg
ate
b
l
o
ck
in
g
v
o
ltag
e
s
u
s
tain
ed
b
y
all
s
em
ico
n
d
u
ct
o
r
d
ev
ices,
d
esig
n
ated
as
th
e
t
o
tal
b
lo
ck
in
g
v
o
ltag
e
(
T
B
V)
,
is
m
ath
em
atica
lly
f
o
r
m
u
lated
as:
T
B
V=
4
E
+V
C1
+4
V
C3
(
1
0
)
R
eg
ar
d
in
g
th
e
v
o
ltag
e
r
atio
s
a
d
o
p
ted
t
h
r
o
u
g
h
o
u
t
th
is
s
tu
d
y
,
E
=
6
V
dc
,
V
C1
=
3
V
dc
,
an
d
V
C3
=
V
dc
,
th
e
to
tal
b
lo
ck
in
g
v
o
ltag
e
is
d
eter
m
in
e
d
as
(
1
1
)
.
T
B
V=
3
1
V
dc
(
1
1
)
2
.
4
.
G
a
in o
f
t
he
des
ig
ned inv
er
t
er
T
h
e
v
o
ltag
e
a
m
p
lific
atio
n
f
ac
to
r
o
f
t
h
e
in
tr
o
d
u
ce
d
to
p
o
l
o
g
y
i
s
m
ath
em
atica
lly
d
ef
in
ed
as
(
1
2
)
.
=
7
6
=
1
.
17
(
1
2
)
2
.
5
.
Co
ntr
o
l st
ra
t
eg
y
T
h
e
p
r
o
p
o
s
ed
1
5
-
lev
el
in
v
er
t
er
is
co
n
tr
o
lled
u
s
in
g
a
s
in
u
s
o
id
al
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
SP
W
M)
s
ch
em
e,
s
elec
ted
f
o
r
its
s
im
p
le
im
p
lem
en
tatio
n
an
d
ac
c
u
r
a
te
g
en
er
atio
n
o
f
th
e
r
eq
u
ir
ed
s
witch
in
g
in
s
tan
ts
.
Fig
u
r
e
4
p
r
esen
ts
th
e
co
m
p
lete
m
o
d
u
latio
n
a
r
r
an
g
e
m
en
t.
Fig
u
r
e
4
(
a
)
illu
s
tr
ates th
e
co
m
p
a
r
is
o
n
o
f
a
s
in
u
s
o
id
al
r
ef
er
en
ce
s
ig
n
al
with
f
o
u
r
teen
ca
r
r
ier
s
ig
n
als
h
av
in
g
id
en
tical
am
p
litu
d
es
an
d
f
r
eq
u
en
cies,
wh
er
ea
s
Fig
u
r
e
4
(
b
)
s
h
o
ws
th
e
elec
tr
ical
cir
cu
it
u
s
ed
to
g
e
n
er
ate
th
e
co
r
r
esp
o
n
d
i
n
g
g
ate
p
u
ls
es.
T
h
e
im
p
lem
en
ted
cir
cu
it
o
p
er
ates
with
o
u
t
v
o
ltag
e
o
r
c
u
r
r
e
n
t
s
en
s
o
r
s
an
d
d
o
es
n
o
t
r
e
q
u
ir
e
a
d
e
d
icate
d
ca
p
ac
ito
r
-
v
o
ltag
e
co
n
t
r
o
l
lo
o
p
.
Acc
o
r
d
in
g
to
th
e
g
en
er
ated
s
witch
in
g
s
ig
n
als,
th
e
ca
p
ac
ito
r
s
ar
e
p
er
io
d
ically
co
n
n
ec
ted
to
th
e
DC
s
o
u
r
ce
an
d
th
e
lo
ad
th
r
o
u
g
h
s
u
itab
le
c
h
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
p
at
h
s
.
T
h
is
p
e
r
io
d
ic
en
e
r
g
y
ex
ch
a
n
g
e
m
ai
n
tain
s
th
e
ca
p
ac
ito
r
v
o
ltag
es
clo
s
e
to
t
h
eir
d
esire
d
v
alu
es
wh
ile
s
elec
tin
g
th
e
ap
p
r
o
p
r
iate
s
witch
in
g
s
tates
r
eq
u
ir
ed
to
s
y
n
th
esize
th
e
f
if
teen
o
u
t
p
u
t
-
v
o
ltag
e
lev
els.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
o
f a
n
o
ve
l sin
g
le
-
s
o
u
r
c
e
1
5
-
leve
l in
ve
r
ter w
ith
s
elf
-
b
a
la
n
cin
g
c
a
p
a
cito
r
s
…
(
Ta
o
u
fi
q
E
l A
n
s
a
r
i
)
1955
(
a)
(
b
)
Fig
u
r
e
4
.
SP
W
M:
(
a)
r
ef
er
e
n
c
e
an
d
ca
r
r
ier
s
ig
n
als an
d
(
b
)
s
e
n
s
o
r
less
g
ate
-
p
u
ls
e
g
en
er
atio
n
cir
cu
it
3.
CO
M
P
ARA
T
I
V
E
S
T
UDY
A
d
etailed
b
en
c
h
m
ar
k
i
n
g
e
v
alu
atio
n
p
r
o
ce
s
s
is
p
er
f
o
r
m
ed
t
o
o
b
jectiv
ely
q
u
an
tify
th
e
p
e
r
f
o
r
m
an
ce
-
to
-
co
s
t
r
atio
o
f
v
ar
io
u
s
ML
I
s
.
T
h
e
b
en
c
h
m
ar
k
i
n
g
cr
iter
ia
a
r
e
b
a
s
ed
o
n
a
s
et
o
f
s
p
ec
if
ic
s
tr
u
ctu
r
al
an
d
tech
n
o
lo
g
ical
p
ar
am
eter
s
,
wh
ich
ar
e
wid
ely
u
s
ed
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
v
a
r
io
u
s
p
o
wer
co
n
v
er
s
io
n
s
y
s
tem
s
,
th
e
n
u
m
b
er
o
f
in
d
ep
en
d
en
t
DC
s
o
u
r
ce
s
(
N
dc
)
,
th
e
to
tal
n
u
m
b
er
o
f
p
o
we
r
s
I
GB
T
s
d
ev
ices
(
N
Sw
)
,
th
e
n
u
m
b
er
o
f
d
io
d
es
(
N
d
)
,
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
v
o
l
tag
e
le
v
els
(
N
L
)
,
th
e
n
u
m
b
er
o
f
g
ate
d
r
iv
er
cir
c
u
its
(
N
Gd
)
,
an
d
th
e
n
u
m
b
er
o
f
ca
p
ac
ito
r
s
(
N
C
)
.
Mo
r
eo
v
e
r
,
an
ad
d
itio
n
al
p
a
r
am
e
ter
,
to
tal
Stan
d
in
g
Vo
ltag
e
p
er
u
n
it
(
T
SVp
u
)
,
h
as
also
b
ee
n
in
tr
o
d
u
ce
d
to
q
u
a
n
tify
th
e
v
o
ltag
e
s
tr
ess
o
f
p
o
wer
d
ev
ices.
All
o
f
th
e
af
o
r
em
en
ti
o
n
ed
p
ar
a
m
eter
s
ar
e
in
teg
r
ated
in
t
o
a
s
in
g
le
C
o
s
t
Fu
n
ctio
n
(
C
F),
w
h
ich
e
n
ab
les
a
f
air
co
m
p
ar
is
o
n
o
f
th
e
v
ar
i
o
u
s
ML
I
t
o
p
o
lo
g
ies
p
r
esen
ted
in
th
e
e
x
is
tin
g
liter
atu
r
e.
T
h
e
weig
h
tin
g
c
o
e
f
f
icien
t
α
ad
j
u
s
ts
th
e
r
elativ
e
im
p
o
r
ta
n
ce
o
f
s
em
ico
n
d
u
cto
r
v
o
lt
ag
e
s
tr
ess
with
r
esp
ec
t to
h
ar
d
war
e
co
m
p
lex
ity
.
A
l
o
wer
v
al
u
e
o
f
α
em
p
h
asizes co
m
p
o
n
en
t
co
u
n
t,
w
h
er
ea
s
a
h
ig
h
er
v
alu
e
ass
ig
n
s
g
r
ea
ter
im
p
o
r
tan
ce
to
T
SVp
u
.
T
h
e
m
ath
e
m
atica
l
ex
p
r
ess
io
n
g
o
v
er
n
in
g
th
e
co
s
t f
u
n
ctio
n
is
f
o
r
m
u
lated
as
[
2
]
:
=
(
+
+
+
+
)
(
1
3
)
T
h
e
T
SV
pu
o
f
th
e
in
t
r
o
d
u
ce
d
i
n
v
er
ter
is
p
r
esen
ted
b
y
(
1
4
)
[2
1
]
.
=
=
31
7
=
4
.
43
(
1
4
)
T
ab
le
2
p
r
esen
ts
a
co
m
p
ar
ati
v
e
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
an
d
o
th
e
r
m
u
ltil
ev
e
l
in
v
er
ter
to
p
o
lo
g
ies
r
ep
o
r
ted
i
n
th
e
liter
atu
r
e,
b
ased
o
n
th
e
c
o
s
t
f
u
n
cti
o
n
d
ef
i
n
ed
p
r
ev
io
u
s
ly
.
T
h
e
w
eig
h
tin
g
co
e
f
f
icien
t
α
co
n
tr
o
ls
th
e
r
elativ
e
im
p
o
r
tan
ce
ass
ig
n
ed
to
th
e
t
o
tal
s
tan
d
in
g
v
o
ltag
e
a
n
d
h
a
r
d
war
e
co
m
p
o
n
en
t
co
u
n
t.
A
h
ig
h
er
v
alu
e
o
f
α
=
1
.
5
g
iv
es
g
r
ea
ter
im
p
o
r
tan
ce
to
s
em
ico
n
d
u
cto
r
v
o
ltag
e
s
tr
ess
,
wh
er
ea
s
α
=
0
.
5
em
p
h
asizes
co
m
p
o
n
en
t r
ed
u
ctio
n
.
T
h
er
ef
o
r
e,
a
s
en
s
itiv
ity
an
aly
s
is
is
p
er
f
o
r
m
ed
u
s
in
g
b
o
th
weig
h
tin
g
c
o
n
d
itio
n
s
.
+
-
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-
S
wit
c
h
ing
t
able
T
2
T1
T
4
T
3
T
5
T
9
T
r
ia
ngul
ar
s
ignal
1
Sinus
oid
al
r
e
f
er
enc
e
Sinus
oid
al
r
e
f
er
enc
e
T
6
T
8
T
7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1950
-
1
9
6
1
1956
As
s
h
o
wn
in
T
ab
le
2
,
t
h
e
c
o
s
t
f
u
n
ctio
n
o
f
th
e
p
r
o
p
o
s
ed
t
o
p
o
lo
g
y
in
c
r
ea
s
es
f
r
o
m
1
.
6
1
at
α
=
0
.
5
to
1
.
9
1
at
α
=
1
.
5
.
T
h
is
m
o
d
er
ate
v
ar
iatio
n
s
h
o
ws
th
e
in
f
l
u
en
ce
o
f
th
e
t
o
tal
s
tan
d
in
g
v
o
ltag
e
o
n
th
e
c
o
s
t
f
u
n
ctio
n
.
Nev
er
th
eless
,
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
m
ain
tain
s
a
f
av
o
r
a
b
le
co
s
t
-
f
u
n
ctio
n
v
alu
e
u
n
d
er
b
o
th
weig
h
tin
g
co
n
d
itio
n
s
,
co
n
f
ir
m
in
g
a
r
o
b
u
s
t c
o
m
p
r
o
m
is
e
b
etwe
en
h
ar
d
war
e
co
m
p
lex
ity
an
d
s
em
ico
n
d
u
c
to
r
v
o
ltag
e
s
tr
ess
.
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
with
o
th
er
to
p
o
lo
g
ies
To
p
o
l
o
g
y
Y
e
a
r
N
L
N
dc
N
c
N
Sw
N
Gd
N
d
TSV
p
u
C
F
(
α=0
.
5
)
C
F
(
α=1
.
5
)
[2
2
]
2
0
2
3
7
2
4
8
8
2
5
.
6
6
7
.
0
9
8
.
7
1
[2
3
]
2
0
2
4
7
1
2
7
7
2
5
2
.
9
3
3
.
6
4
[
2
]
2
0
2
5
7
1
2
8
8
2
5
.
6
7
3
.
2
6
4
.
0
7
[2
4
]
2
0
2
2
13
1
3
15
15
0
5
2
.
7
3
3
.
1
2
[2
5
]
2
0
2
2
13
1
3
14
13
4
5
.
5
0
2
.
8
3
3
.
2
5
[2
1
]
2
0
2
5
13
1
3
11
10
3
6
.
3
3
2
.
3
2
2
.
8
1
[
1
6
]
2
0
2
6
15
2
1
10
9
0
4
.
4
3
2
.
9
6
3
.
5
5
[2
6
]
2
0
2
2
15
2
1
10
10
1
4
.
8
6
3
.
2
6
3
.
9
1
[2
7
]
2
0
2
5
15
3
0
10
10
0
3
.
4
2
4
.
3
4
5
.
0
3
[
28
]
2
0
2
3
19
2
2
9
9
6
7
.
2
3
.
1
2
3
.
8
7
[
29
]
2
0
2
5
19
2
2
10
10
4
6
.
5
5
3
.
0
8
3
.
7
7
P
r
o
p
o
se
d
---
15
1
3
10
9
0
4
.
4
3
1
.
6
1
1
.
9
1
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
An
ex
h
a
u
s
tiv
e
ass
ess
m
en
t
co
n
ce
r
n
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
in
tr
o
d
u
ce
d
in
v
er
ter
,
wh
ich
is
o
p
er
atin
g
in
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
m
o
d
e,
h
as
b
ee
n
p
er
f
o
r
m
e
d
b
y
co
n
d
u
ctin
g
s
im
u
latio
n
s
in
MA
T
L
AB
/S
im
u
lin
k
s
o
f
twar
e.
T
h
e
ass
ess
m
en
t
h
as
b
ee
n
p
er
f
o
r
m
ed
in
two
p
h
ases
.
First,
th
e
in
v
er
ter
h
as
b
ee
n
s
im
u
lated
in
its
n
o
m
in
al
o
p
er
atin
g
co
n
d
itio
n
s
,
an
d
t
h
en
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
y
s
tem
an
d
th
e
ef
f
icac
y
o
f
th
e
co
n
tr
o
l sch
em
e
h
av
e
b
ee
n
v
ali
d
ated
b
y
in
tr
o
d
u
cin
g
c
h
an
g
es i
n
th
e
o
p
er
atin
g
p
ar
am
eter
s
o
f
th
e
in
v
er
ter
.
4
.
1
.
Sim
ula
t
i
o
n und
er
co
ns
t
a
nt
pa
ra
m
e
t
er
s
T
ab
le
3
p
r
o
v
id
es
a
co
m
p
r
e
h
e
n
s
iv
e
o
v
er
v
iew
o
f
th
e
s
im
u
lat
io
n
s
etu
p
p
ar
a
m
eter
s
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
tem
p
o
r
al
v
a
r
iatio
n
o
f
t
h
e
lo
ad
v
o
ltag
e
V
L
alo
n
g
with
th
e
ca
p
ac
ito
r
v
o
ltag
es
V
C1
,
V
C2
,
an
d
V
C3
.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
p
r
o
p
o
s
ed
in
v
er
ter
is
ca
p
ab
le
o
f
g
e
n
er
ati
n
g
a
f
if
tee
n
-
lev
el
o
u
t
p
u
t
v
o
ltag
e.
I
n
a
d
d
itio
n
,
t
h
e
ca
p
ac
ito
r
v
o
ltag
es
ar
e
ac
cu
r
at
ely
r
eg
u
lated
a
r
o
u
n
d
th
eir
r
ef
e
r
en
ce
v
alu
es,
n
am
ely
V
C1
=
V
C2
=
E
/2
=
9
0
V
a
n
d
V
C3
=
E
/6
=
3
0
V.
Ma
in
tain
i
n
g
th
ese
v
o
ltag
e
lev
els
is
ess
en
tial
to
en
s
u
r
e
p
r
o
p
er
o
p
er
at
io
n
an
d
to
ac
h
iev
e
a
h
ig
h
-
q
u
ality
o
u
t
p
u
t
v
o
ltag
e
.
T
h
is
in
h
er
en
t
v
o
lta
g
e
b
alan
cin
g
p
r
eser
v
es
u
n
if
o
r
m
v
o
ltag
e
s
tep
s
an
d
s
u
p
p
o
r
ts
th
e
n
ea
r
ly
s
in
u
s
o
id
al
lo
a
d
cu
r
r
en
t
s
h
o
wn
in
Fig
u
r
e
6
.
Fig
u
r
e
7
p
r
esen
ts
th
e
h
ar
m
o
n
ic
s
p
ec
tr
a
,
wh
er
e
Fig
u
r
e
7
(
a)
s
h
o
ws
an
o
u
tp
u
t
-
v
o
ltag
e
T
H
D
o
f
9
.
4
1
%
,
wh
ile
Fig
u
r
e
7
(
b
)
in
d
icate
s
a
lo
ad
-
cu
r
r
en
t
T
HD
o
f
2
.
2
0
%.
T
h
ese
r
ed
u
ce
d
T
HD
v
alu
es
r
esu
lt
f
r
o
m
th
e
s
tab
le
ca
p
ac
ito
r
v
o
lta
g
es
an
d
ac
cu
r
ate
g
en
e
r
atio
n
o
f
th
e
f
if
teen
o
u
t
p
u
t
lev
els,
wh
ile
th
e
in
d
u
ctiv
e
n
at
u
r
e
o
f
t
h
e
R
–
L
lo
ad
f
u
r
t
h
er
att
en
u
ates h
ig
h
-
f
r
eq
u
en
cy
c
u
r
r
e
n
t h
ar
m
o
n
ics
lev
els.
Fig
u
r
e
5
.
W
av
ef
o
r
m
s
o
f
t
h
e
lo
ad
v
o
ltag
e
(
V
L
)
an
d
th
e
ca
p
ac
i
to
r
v
o
ltag
es (
V
C1
, V
C2
,
an
d
V
C3
)
Fig
u
r
e
6
.
W
av
ef
o
r
m
o
f
lo
ad
c
u
r
r
en
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
o
f a
n
o
ve
l sin
g
le
-
s
o
u
r
c
e
1
5
-
leve
l in
ve
r
ter w
ith
s
elf
-
b
a
la
n
cin
g
c
a
p
a
cito
r
s
…
(
Ta
o
u
fi
q
E
l A
n
s
a
r
i
)
1957
T
ab
le
3
.
Simu
latio
n
s
itti
n
g
s
P
a
r
a
me
t
e
r
s
E
R
L
C1
C2
C3
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
M
o
d
u
l
a
t
i
o
n
i
n
d
e
x
S
a
mp
l
i
n
g
f
r
e
q
u
e
n
c
y
V
a
l
u
e
s
1
8
0
V
5
0
Ω
2
0
mH
1
2
0
0
µ
F
1
2
0
0
µ
F
2
0
0
0
µ
F
2
0
0
0
H
z
1
20
k
Hz
(
a)
(
b
)
Fig
u
r
e
7
.
FFT
-
b
ased
f
r
eq
u
e
n
c
y
an
aly
s
is
o
f
(
a)
th
e
lo
ad
ter
m
i
n
al
v
o
ltag
e
a
n
d
(
b
)
th
e
l
o
ad
cu
r
r
en
t w
av
ef
o
r
m
4
.
2
.
Respo
ns
e
t
o
DC
s
up
ply
v
o
lt
a
g
e
f
luct
ua
t
io
n
T
o
ass
es
s
th
e
d
y
n
am
ic
r
o
b
u
s
tn
ess
o
f
th
e
d
esig
n
ed
to
p
o
lo
g
y
,
t
h
e
DC
in
p
u
t
v
o
ltag
e
E
was
s
te
p
p
ed
f
r
o
m
1
8
0
V
to
9
0
V
at
t
=
3
s
.
T
h
e
ca
p
ac
ito
r
a
n
d
lo
ad
v
o
ltag
es
ar
e
s
h
o
wn
in
Fig
u
r
e
8
.
Fig
u
r
e
9
p
r
o
v
id
es
a
clo
s
e
-
up
v
iew
o
f
th
e
lo
ad
a
n
d
ca
p
ac
ito
r
v
o
ltag
es
b
ef
o
r
e
a
n
d
d
u
r
in
g
th
e
d
is
tu
r
b
an
ce
.
I
n
itially
,
V
C1
an
d
V
C2
r
em
ain
clo
s
e
to
E
/2
,
wh
ile
V
C3
r
em
ain
s
n
ea
r
E
/6
,
co
n
f
ir
m
in
g
s
tab
le
s
en
s
o
r
less
v
o
ltag
e
b
ala
n
cin
g
.
T
h
e
s
u
d
d
en
v
o
ltag
e
d
r
o
p
cr
ea
tes
a
tem
p
o
r
ar
y
en
er
g
y
im
b
alan
ce
in
th
e
ca
p
ac
ito
r
s
an
d
c
au
s
es
s
h
o
r
t
v
o
ltag
e
d
e
v
iatio
n
s
.
Ho
wev
er
,
th
e
PW
M
s
witch
in
g
s
tates
r
esto
r
e
th
e
p
er
io
d
ic
ch
a
r
g
in
g
an
d
d
is
ch
ar
g
in
g
p
r
o
ce
s
s
,
allo
win
g
th
e
ca
p
ac
ito
r
v
o
ltag
es
to
r
ec
o
v
er
th
eir
r
ef
er
e
n
ce
v
alu
e
s
af
ter
ap
p
r
o
x
im
ately
0
.
3
5
s
,
as
s
h
o
wn
in
Fig
u
r
e
1
0
.
T
h
i
s
tr
an
s
ien
t
d
u
r
atio
n
r
ep
r
esen
ts
th
e
tim
e
r
eq
u
i
r
ed
t
o
r
esto
r
e
th
e
ca
p
ac
ito
r
en
er
g
y
b
alan
ce
.
Mo
r
e
o
v
er
,
t
h
e
p
r
eser
v
ed
1
5
-
lev
el
o
u
t
p
u
t
wav
ef
o
r
m
c
o
n
f
ir
m
s
co
r
r
ec
t v
o
ltag
e
-
lev
el
g
en
er
atio
n
d
u
r
in
g
a
n
d
af
ter
t
h
e
d
is
tu
r
b
a
n
ce
.
Fig
u
r
e
1
1
s
h
o
ws
th
e
lo
ad
-
cu
r
r
en
t
r
esp
o
n
s
e,
wh
ile
Fig
u
r
es
1
2
an
d
1
3
p
r
o
v
id
e
en
la
r
g
ed
v
ie
ws
b
ef
o
r
e,
d
u
r
in
g
,
an
d
af
ter
th
e
in
p
u
t
-
v
o
ltag
e
d
is
tu
r
b
an
ce
.
I
m
m
e
d
iately
af
ter
th
e
v
o
ltag
e
d
r
o
p
,
th
e
cu
r
r
en
t
ex
h
ib
its
a
tr
an
s
ien
t
d
ev
iatio
n
ca
u
s
ed
b
y
th
e
s
u
d
d
en
v
a
r
iatio
n
in
th
e
p
o
wer
tr
an
s
f
er
r
e
d
to
th
e
lo
ad
.
T
h
e
cu
r
r
e
n
t
t
h
en
r
ec
o
v
er
s
its
q
u
asi
-
s
in
u
s
o
id
al
wav
ef
o
r
m
af
ter
a
p
p
r
o
x
im
ately
0
.
3
5
s
,
in
d
icatin
g
th
at
s
tab
le
o
p
er
atio
n
is
r
esto
r
e
d
.
T
h
is
tr
an
s
ien
t
d
u
r
atio
n
co
r
r
esp
o
n
d
s
to
th
e
tim
e
r
eq
u
ir
e
d
f
o
r
t
h
e
co
n
v
er
ter
an
d
th
e
lo
a
d
to
r
e
ac
h
a
n
ew
o
p
er
atin
g
eq
u
ilib
r
iu
m
.
T
h
e
in
d
u
ctiv
e
lo
ad
lim
its
cu
r
r
en
t
v
ar
iatio
n
s
,
wh
ile
s
en
s
o
r
less
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
m
ain
tain
s
th
e
s
witch
in
g
s
eq
u
en
ce
,
th
u
s
en
s
u
r
in
g
ca
p
ac
ito
r
v
o
ltag
e
r
eg
u
latio
n
an
d
a
s
atis
f
ac
to
r
y
d
y
n
am
ic
r
esp
o
n
s
e
in
ca
s
e
o
f
i
n
p
u
t
v
o
lta
g
e
d
is
tu
r
b
an
ce
s
.
Fig
u
r
e
8
.
W
av
ef
o
r
m
s
o
f
t
h
e
lo
ad
v
o
ltag
e
(
V
L
)
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
es (
V
C1
, V
C2
,
an
d
V
C3
)
d
u
r
in
g
th
e
ch
an
g
e
o
f
th
e
DC
s
o
u
r
ce
F
i
g
u
r
e
9
.
Z
o
o
m
o
n
t
h
e
w
a
v
e
f
o
r
m
s
o
f
t
h
e
l
o
a
d
v
o
l
t
a
g
e
(V
L
)
a
n
d
t
h
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
s
(
V
C1
, V
C2
,
a
n
d
V
C3
)
b
e
f
o
r
e
a
n
d
d
u
r
i
n
g
t
h
e
c
h
a
n
g
e
o
f
t
h
e
D
C
s
o
u
r
c
e
Fig
u
r
e
1
0
.
Z
o
o
m
ed
-
in
wa
v
ef
o
r
m
s
o
f
th
e
lo
a
d
v
o
ltag
e
(
V
L
)
a
n
d
th
e
ca
p
ac
ito
r
v
o
ltag
es (
V
C1
, V
C2,
an
d
V
C3
)
af
ter
t
h
e
ch
an
g
e
o
f
th
e
DC
s
o
u
r
ce
Fig
u
r
e
1
1
.
W
av
ef
o
r
m
o
f
th
e
lo
ad
cu
r
r
e
n
t d
u
r
in
g
th
e
ch
an
g
e
o
f
th
e
DC
s
o
u
r
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1950
-
1
9
6
1
1958
Fig
u
r
e
1
2
.
Z
o
o
m
-
in
o
n
th
e
wa
v
ef
o
r
m
o
f
th
e
lo
ad
cu
r
r
en
t d
u
r
in
g
t
h
e
ch
an
g
e
o
f
th
e
DC
s
o
u
r
ce
Fig
u
r
e
1
3
.
Z
o
o
m
in
o
n
th
e
wa
v
ef
o
r
m
o
f
th
e
lo
ad
cu
r
r
en
t a
f
ter
t
h
e
ch
an
g
e
o
f
th
e
DC
s
o
u
r
ce
4
.
3
.
O
pera
t
io
n und
er
f
luct
ua
t
ing
lo
a
d c
o
nd
it
io
ns
I
t
is
v
er
y
im
p
o
r
tan
t
to
ass
ess
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
in
v
er
te
r
in
v
ar
iab
le
lo
ad
co
n
d
itio
n
f
o
r
en
s
u
r
in
g
its
p
er
f
o
r
m
a
n
ce
u
n
d
er
p
r
ac
tica
l
wo
r
k
in
g
s
itu
atio
n
s
.
I
n
th
is
r
e
g
ar
d
,
t
h
e
p
e
r
tu
r
b
atio
n
in
th
e
f
o
r
m
o
f
a
v
a
r
iat
io
n
o
f
b
o
th
r
esis
tan
ce
an
d
in
d
u
ctan
ce
v
alu
es a
t
th
e
s
am
e
tim
e
o
cc
u
r
r
ed
at
t =
3
s
,
wh
e
n
th
e
r
esis
tan
ce
v
alu
e
in
c
r
ea
s
ed
f
r
o
m
5
0
Ω
to
9
0
Ω
,
an
d
th
e
in
d
u
ctan
ce
v
al
u
e
in
cr
ea
s
ed
f
r
o
m
2
0
m
H
to
3
0
0
m
H.
Un
lik
e
in
n
o
r
m
al
ca
s
es,
th
is
v
ar
iatio
n
d
o
es
n
o
t
cr
ea
te
a
n
o
ti
ce
ab
le
tr
an
s
ien
t
s
tate.
T
h
e
ca
p
ac
ito
r
v
o
ltag
es
ad
ap
t
alm
o
s
t
in
s
tan
tly
to
th
eir
n
ew
wo
r
k
in
g
co
n
d
itio
n
s
d
u
e
to
th
e
s
y
s
tem
’
s
v
er
y
h
ig
h
ad
ap
tab
ilit
y
.
T
h
is
b
eh
av
io
r
is
ex
p
lain
ed
b
y
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
en
s
o
r
less
PW
M
co
n
tr
o
l
s
tr
ateg
y
,
wh
i
ch
en
s
u
r
es
o
p
tim
al
s
elec
tio
n
o
f
s
witch
in
g
s
tates a
n
d
im
m
ed
iate
lo
a
d
b
alan
ci
n
g
.
I
n
s
tead
y
s
tate,
th
e
ca
p
ac
ito
r
v
o
ltag
es
co
n
v
er
g
e
to
war
d
t
h
eir
r
ef
er
en
ce
v
alu
es,
with
V
C1
an
d
V
C2
s
tab
ilizin
g
ar
o
u
n
d
E
/2
=
9
0
V
an
d
V
C3
clo
s
e
to
E
/6
=
3
0
V.
T
h
is
r
ap
id
s
tab
ilizatio
n
co
n
f
ir
m
s
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
elf
-
b
alan
cin
g
m
ec
h
a
n
is
m
,
ev
en
in
th
e
p
r
esen
ce
o
f
s
ig
n
if
ican
t
v
ar
iatio
n
s
i
n
lo
ad
p
ar
a
m
eter
s
.
Ma
in
tain
in
g
th
ese
v
o
ltag
e
lev
els
en
s
u
r
es
th
at
a
1
5
-
lev
el
m
u
ltil
ev
el
o
u
t
p
u
t
v
o
ltag
e
is
p
r
eser
v
ed
,
b
o
th
b
ef
o
r
e
an
d
af
ter
th
e
d
is
tu
r
b
an
ce
,
as sh
o
wn
i
n
Fig
u
r
e
1
4
.
Fig
u
r
e
1
5
s
h
o
ws
th
e
wav
ef
o
r
m
o
f
lo
ad
cu
r
r
e
n
t.
Alth
o
u
g
h
th
er
e
ar
e
d
if
f
e
r
en
t
lo
a
d
p
ar
a
m
eter
s
,
th
e
wav
ef
o
r
m
o
f
lo
ad
c
u
r
r
e
n
t
r
em
ain
s
s
in
u
s
o
id
al
in
n
atu
r
e.
T
h
e
r
ea
s
o
n
b
eh
in
d
t
h
is
p
h
en
o
m
en
o
n
lies
in
th
e
f
ac
t
th
at
th
e
lo
ad
ac
ts
as a
n
in
d
u
cto
r
,
w
h
ich
i
m
p
r
o
v
es f
ilter
in
g
ac
tio
n
an
d
s
u
p
p
r
ess
es f
ast f
lu
ctu
atio
n
s
.
Ultim
ately
,
it
is
ev
id
en
t
f
r
o
m
th
ese
r
esu
lts
th
at
th
e
s
u
g
g
ested
in
v
er
ter
to
p
o
lo
g
y
o
f
f
e
r
s
s
u
p
er
io
r
r
o
b
u
s
tn
ess
ag
ain
s
t
an
y
ch
a
n
g
es
in
th
e
lo
ad
.
T
h
e
i
n
s
tan
tan
eo
u
s
s
tab
ilizatio
n
o
f
ca
p
ac
ito
r
v
o
ltag
es
a
n
d
t
h
e
m
ain
ten
an
ce
o
f
a
1
5
-
lev
el
o
u
tp
u
t
v
o
ltag
e
with
ex
ce
llen
t
cu
r
r
en
t
q
u
ality
ar
e
in
d
icativ
e
o
f
t
h
e
r
eliab
ilit
y
o
f
th
e
s
u
g
g
ested
to
p
o
lo
g
y
.
Fig
u
r
e
1
4
.
W
av
ef
o
r
m
s
o
f
th
e
l
o
ad
v
o
lta
g
e
(
V
L
)
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
es (
V
C1
, V
c2
an
d
V
C3
)
d
u
r
in
g
th
e
ch
a
n
g
e
o
f
th
e
lo
a
d
Fig
u
r
e
1
5
.
W
av
ef
o
r
m
o
f
th
e
lo
ad
cu
r
r
e
n
t d
u
r
in
g
th
e
ch
an
g
e
o
f
th
e
lo
ad
4
.
4
.
O
pera
t
io
n und
er
no
nli
n
ea
r
lo
a
d c
o
nd
it
io
ns
E
v
alu
atin
g
th
e
p
er
f
o
r
m
a
n
ce
o
f
an
in
v
er
ter
u
n
d
er
n
o
n
lin
e
ar
lo
ad
co
n
d
itio
n
s
is
ess
en
tia
l,
as
th
ese
co
n
d
itio
n
s
ar
e
r
ep
r
esen
tativ
e
o
f
r
ea
l
-
wo
r
ld
p
o
wer
elec
tr
o
n
i
cs
ap
p
licatio
n
s
.
Fo
r
th
e
an
aly
s
is
o
f
th
e
r
o
b
u
s
tn
ess
o
f
th
e
s
u
g
g
ested
1
5
-
lev
el
in
v
er
ter
,
a
s
im
u
latio
n
a
n
aly
s
is
is
p
er
f
o
r
m
ed
with
co
n
s
id
er
atio
n
o
f
a
tr
a
n
s
itio
n
to
a
n
o
n
lin
ea
r
lo
ad
.
I
n
itially
,
a
p
u
r
el
y
r
esis
tiv
e
lo
ad
is
co
n
n
ec
ted
.
At
tim
e
t
=
3
s
,
it
is
r
ep
lace
d
b
y
a
n
o
n
lin
ea
r
lo
a
d
with
a
d
io
d
e
r
ec
tifie
r
.
As
s
h
o
wn
in
Fig
u
r
e
1
6
,
th
e
c
ap
ac
ito
r
v
o
ltag
es
r
em
ain
p
r
o
p
er
ly
b
alan
ce
d
an
d
s
tab
ilize
ar
o
u
n
d
th
eir
r
ef
er
en
ce
v
alu
es
d
esp
ite
th
e
ap
p
lied
d
is
tu
r
b
an
ce
.
T
h
is
r
es
u
lt
d
em
o
n
s
tr
ates
th
e
ef
f
icien
cy
o
f
th
e
co
n
t
r
o
ller
s
ch
em
e
in
ac
h
iev
in
g
b
alan
ce
d
v
o
ltag
es
u
n
d
er
n
o
n
lin
ea
r
cu
r
r
en
t
co
n
d
itio
n
s
.
Ad
d
itio
n
ally
,
th
e
o
u
tp
u
t
v
o
ltag
e
m
ain
tain
s
its
m
u
ltil
ev
el
s
tep
p
e
d
wav
ef
o
r
m
,
ty
p
ical
o
f
a
1
5
-
le
v
el
in
v
er
ter
,
th
e
r
eb
y
p
r
o
v
i
n
g
t
h
e
r
eliab
ilit
y
o
f
th
e
s
u
g
g
ested
to
p
o
lo
g
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Desig
n
o
f a
n
o
ve
l sin
g
le
-
s
o
u
r
c
e
1
5
-
leve
l in
ve
r
ter w
ith
s
elf
-
b
a
la
n
cin
g
c
a
p
a
cito
r
s
…
(
Ta
o
u
fi
q
E
l A
n
s
a
r
i
)
1959
Fig
u
r
e
1
7
s
h
o
w
s
th
at
th
e
n
o
n
lin
ea
r
lo
ad
in
tr
o
d
u
ce
s
ad
d
it
i
o
n
al
h
ar
m
o
n
ic
co
m
p
o
n
en
t
s
t
h
r
o
u
g
h
t
h
e
r
ec
tif
ier
,
in
cr
e
a
s
in
g
th
e
lo
ad
-
cu
r
r
en
t
T
HD
f
r
o
m
9
.
2
5
%
to
1
0
.
4
5
%
.
D
esp
i
te
th
i
s
d
is
tu
r
b
an
ce
,
th
e
cu
r
r
en
t
r
em
a
in
s
q
u
a
s
i
-
s
i
n
u
s
o
id
al,
an
d
th
e
T
H
D
i
n
cr
e
a
s
e
i
s
l
im
it
ed
to
1
.
2
0
p
er
ce
n
tag
e
p
o
in
t
s
.
T
h
is
r
esu
lt
in
d
ic
at
e
s
th
at
th
e
p
r
o
p
o
s
ed
in
v
er
ter
m
a
in
t
ai
n
s
s
t
ab
l
e
v
o
lt
ag
e
-
lev
el
g
en
er
at
io
n
an
d
s
at
i
s
f
a
cto
r
y
h
ar
m
o
n
i
c
p
er
f
o
r
m
an
c
e
u
n
d
e
r
n
o
n
lin
ea
r
lo
a
d
in
g
,
co
n
f
ir
m
in
g
th
e
ef
f
ec
t
iv
en
es
s
o
f
th
e
s
en
s
o
r
le
s
s
m
o
d
u
la
tio
n
an
d
c
ap
a
ci
to
r
-
v
o
l
tag
e
-
b
a
lan
cin
g
m
ec
h
an
i
s
m
.
Fig
u
r
e
1
6
.
W
av
ef
o
r
m
s
o
f
th
e
l
o
ad
v
o
lta
g
e
(
V
L
)
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
es (
V
C1
, V
c2
an
d
V
C3
)
d
u
r
in
g
n
o
n
lin
ea
r
l
o
ad
o
p
er
atio
n
Fig
u
r
e
1
7
.
W
av
ef
o
r
m
o
f
th
e
lo
ad
cu
r
r
e
n
t d
u
r
in
g
th
e
n
o
n
lin
ea
r
l
o
ad
o
p
er
atio
n
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
p
r
esen
ted
a
n
ew
1
5
-
lev
el
in
v
er
ter
to
p
o
lo
g
y
d
er
iv
ed
f
r
o
m
th
e
Pack
ed
U
-
C
ell
s
tr
u
ctu
r
e
an
d
s
u
p
p
lied
b
y
a
s
in
g
le
DC
s
o
u
r
ce
.
T
h
e
p
r
o
p
o
s
ed
co
n
f
ig
u
r
atio
n
em
p
lo
y
s
th
r
ee
ca
p
ac
ito
r
s
an
d
a
r
e
d
u
ce
d
n
u
m
b
er
o
f
p
o
wer
co
m
p
o
n
e
n
ts
,
r
esu
ltin
g
in
a
lo
wer
co
s
t
f
u
n
ctio
n
co
m
p
ar
ed
with
s
ev
er
al
m
u
ltil
ev
el
in
v
er
ter
to
p
o
lo
g
ies
r
ep
o
r
ted
in
t
h
e
liter
atu
r
e.
A
s
en
s
o
r
less
PW
M
s
tr
ateg
y
en
s
u
r
es
th
e
n
at
u
r
al
s
elf
-
b
alan
cin
g
o
f
th
e
ca
p
ac
ito
r
v
o
ltag
es
with
o
u
t
r
e
q
u
ir
in
g
v
o
ltag
e
s
en
s
o
r
s
o
r
a
d
d
itio
n
al
b
alan
cin
g
co
n
tr
o
l
lo
o
p
s
.
T
h
e
p
r
o
p
o
s
ed
in
v
er
ter
ac
h
ie
v
es a
lo
w
T
HD,
co
n
f
ir
m
in
g
its
ef
f
ec
tiv
en
ess
u
n
d
er
th
e
i
n
v
esti
g
ated
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
s
u
g
g
ested
co
n
v
e
r
ter
was
test
ed
o
n
d
if
f
er
en
t
s
ce
n
ar
io
s
,
in
clu
d
in
g
v
a
r
iab
le
lo
ad
s
,
d
if
f
er
en
t
DC
v
o
ltag
es,
an
d
n
o
n
-
lin
ea
r
lo
ad
s
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
r
e
is
an
e
x
ce
llen
t
b
alan
ce
b
etwe
en
t
h
e
c
ap
ac
ito
r
s
'
v
o
ltag
es,
with
s
tab
ilit
y
o
b
s
er
v
ed
d
u
r
in
g
b
o
th
s
tatic
an
d
d
y
n
am
ic
s
tate
s
.
Du
e
to
its
ea
s
e
o
f
co
n
tr
o
l
a
n
d
s
u
p
er
io
r
p
o
wer
q
u
ality
,
it
is
a
s
u
itab
le
ch
o
ice
f
o
r
r
en
ewa
b
le
e
n
er
g
y
,
elec
tr
ic
tr
ac
tio
n
,
an
d
s
m
ar
t
g
r
i
d
s
.
Nev
er
th
eless
,
s
o
m
e
lim
itatio
n
s
ex
is
t.
On
th
e
o
n
e
h
an
d
,
t
h
e
ab
s
en
ce
o
f
a
co
m
m
o
n
g
r
o
u
n
d
m
ay
co
m
p
licate
its
in
teg
r
atio
n
in
to
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
On
th
e
o
th
er
h
a
n
d
,
th
e
v
o
ltag
e
g
ai
n
is
r
elativ
ely
lo
w,
an
d
th
is
lim
its
its
p
o
s
s
ib
le
ap
p
licatio
n
s
in
s
tr
u
ctu
r
es
wh
er
e
a
v
o
ltag
e
b
o
o
s
ter
is
n
ee
d
ed
,
g
iv
en
th
at
G
=
1
.
1
7
.
T
h
ese
lim
itatio
n
s
s
u
g
g
est
s
ev
er
al
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
Fu
tu
r
e
ef
f
o
r
ts
will
f
o
cu
s
o
n
d
ev
elo
p
i
n
g
s
tr
u
ctu
r
es
with
a
co
m
m
o
n
r
ef
er
en
ce
p
o
in
t,
im
p
r
o
v
in
g
v
o
l
tag
e
g
ain
wh
ile
m
ain
tain
in
g
a
co
m
p
ac
t stru
ctu
r
e
an
d
lo
w
co
m
p
o
n
e
n
t c
o
u
n
t,
a
n
d
p
er
f
o
r
m
in
g
d
etailed
co
n
d
u
cti
o
n
a
n
d
s
witch
in
g
lo
s
s
an
aly
s
es.
Mo
d
el
p
r
e
d
ictiv
e
c
o
n
tr
o
l
an
d
ex
p
e
r
im
en
tal
v
alid
atio
n
u
n
d
er
p
r
ac
tical
o
p
e
r
atin
g
co
n
d
itio
n
s
will a
ls
o
b
e
in
v
esti
g
ated
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
T
ao
u
f
iq
E
l A
n
s
ar
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Ay
o
u
b
E
l G
a
d
ar
i
✓
✓
✓
✓
✓
✓
Yo
u
s
s
ef
Ou
n
ejjar
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.