In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
342~
3
5
0
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
3
42-
35
0
342
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Tra
n
s
i
ent
and
st
ea
d
y
-st
a
te
a
nalysis of
single sw
itched
capacitor converter
A
l
ex
an
d
e
r
Kush
n
e
rov
D
e
partm
e
n
t
o
f Electri
cal an
d
Com
put
er En
g
i
n
eeri
ng, Ben-G
urio
n
U
ni
versit
y
of
th
e
Neg
ev, Beers
h
eba,
Israel
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Feb
1
3
,
2
018
Re
vise
d Ju
l 1
0
,
201
8
A
c
c
e
pte
d
J
u
l
24,
201
8
Th
e
p
a
per
d
e
rives
cl
os
ed
f
o
r
m
exp
r
ess
i
o
n
s
for
tran
sien
t
and
st
e
ady
-
stat
e
op
erati
on
of
a
D
C-DC
c
on
vert
er
w
ith
s
in
g
l
e
s
w
itch
e
d
c
ap
acit
o
r.
To
t
his
end,
th
e
resul
t
o
f
each
s
w
i
tch
i
n
g
i
s
c
o
n
s
i
d
ered
a
s
a
p
o
i
n
t
i
n
t
he
i
t
erati
v
e
pro
cess
,
and
th
e
f
u
ncti
o
n
b
et
ween
t
h
e
p
oin
t
s
is
r
eco
ns
truct
e
d.
A
s
op
po
se
d
to
t
h
e
com
m
only
acce
pted
a
pp
roach,
when
each
o
f
t
h
e
t
opo
lo
g
i
es
i
s
a
p
p
r
ox
im
a
t
ed
b
y
a
f
i
r
s
t
o
r
d
e
r
c
i
r
c
u
i
t
,
t
h
e
p
r
o
p
o
s
e
d
a
n
a
l
y
s
i
s
i
s
c
a
r
r
i
e
d
o
u
t
f
o
r
s
econd
o
rder
circuit
s
.
Thi
s
a
l
l
ows
obtaining
the
waveform
o
f
outpu
t
v
oltage
ri
pp
le
a
nd
pav
e
s
t
h
e
w
a
y
to
m
ore
accu
rate
calcu
lat
i
o
n
o
f
equi
val
e
nt
r
esis
t
an
ce.
T
h
e
ob
tai
n
ed
a
nal
y
t
i
cal
e
xp
r
e
s
s
i
o
n
s
w
ere
v
e
rified
b
y
sim
u
lation
s
a
n
d
an
e
xc
el
lent
agreem
ent
b
e
t
w
een
th
e
resu
l
t
s
w
a
s
f
o
u
n
d
.
K
eyw
ord
s
:
Cha
r
ge
pump
Discret
e
-time sys
t
ems
Eq
ui
v
a
len
t
re
s
ista
nc
e
Switche
d ca
pa
cit
o
r
con
v
erte
r
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
l
exa
nde
r K
u
s
hne
r
ov,
Depa
rtem
ent o
f
E
lectr
i
c
a
l a
n
d
C
o
m
p
uter
E
n
g
i
ne
er
in
g,
B
e
n-Gurio
n
U
nive
rsit
y
o
f
t
he
N
egev,
Bee
r
sheba,
I
sr
ael.
Em
ail:
kush
n
e
r
o@ee
.b
g
u
.a
c.il
1.
I
N
TR
OD
U
C
TI
O
N
Swi
t
ch
ed
cap
aci
to
r
c
onv
e
r
t
e
rs
(
SC
C
s
)
a
r
e
fa
vo
re
d
i
n
s
ome
ap
pl
i
c
a
t
i
o
ns
due
t
o
l
o
w
EM
I
an
d
com
p
at
i
b
i
l
i
t
y
w
i
t
h
I
C
tec
hnol
o
gy.
O
ve
r
the
pa
st
f
e
w
d
e
c
a
d
e
s
,
on
g
o
i
n
g
r
e
s
e
a
rc
h
ha
s
s
h
i
f
ted
t
o
w
a
rds
sop
h
is
tica
t
e
d
S
CCs
w
i
th
l
ar
ge
num
ber
o
f
c
a
p
ac
it
ors
a
nd
ad
va
nce
d
c
ont
rol
ci
rcui
t
s
.
H
o
we
v
e
r,
o
n
l
y
a
fe
w
stud
ies
use
an
a
l
yt
ica
l
m
et
ho
ds.
The
a
n
a
l
y
s
is
p
rese
nte
d
i
n
t
h
is
pape
r
i
s
b
ase
d
o
n
t
h
e
me
thod
o
f
d
i
f
f
e
re
n
c
e
equations
[
1
]-[3]
which
allow
s
f
in
ding
t
h
e
s
o
lution
for
the
tra
ns
ien
t
a
n
d
s
t
e
a
dy-s
t
a
t
e
op
e
r
ati
o
n.
A
ltho
u
g
h
t
his
me
tho
d
i
s
un
ifi
e
d,
i
t
w
a
s
a
p
p
l
i
e
d
pre
v
i
o
usly
o
n
l
y
t
o
t
he
s
w
i
tch
e
d
i
nductor
c
onver
t
ers
[4]-[6].
H
owev
er,
som
e
ana
l
y
t
i
cal
m
et
ho
ds
f
or
a
na
l
y
sis
o
f
s
w
i
t
c
he
d
ca
pac
i
tor
c
i
r
c
ui
t
s
tha
t
b
ea
r
rese
mblanc
e
of
t
he
p
ro
pose
d
o
ne
,
w
e
r
e
pr
e
sented
i
n
[7]-
[1
0].
Le
t us c
onsi
d
er
the
S
CC
s
how
n sche
ma
t
i
c
a
l
ly
i
n
F
i
gure
1(a
)
. It
c
o
mpr
i
se
s fo
ur
s
w
i
t
c
hes
…
with
o
n
-resi
st
an
ce
s
…
.
The
corr
espo
nd
ing
pa
ir
o
f
sw
it
c
h
es
i
s
t
u
r
n
ed
o
n
/
off
by
t
w
o
n
o
n-
over
l
a
p
p
i
ng
c
l
oc
ks
and
s
how
n
i
n
F
igure
1(b)
.
Th
us,
dur
ing
t
h
e
c
a
p
a
c
ito
r
i
s
char
ge
d
by
t
h
r
ou
gh
,
a
nd
the
n
,
dur
in
g
,
is
d
i
s
c
h
arge
d
t
o
t
he
l
oa
d
t
h
ro
ug
h
,
.
Thus,
w
e
h
a
v
e
tw
o
top
o
l
og
ies,
w
hic
h
a
re
c
onsi
d
er
ed
separ
a
te
ly
i
n
S
e
c
t
io
ns
II.
A
pp
l
y
in
g
to
e
a
c
h
t
o
pol
o
g
y
t
h
e
K
i
rc
hh
off
’
s
vo
lt
a
g
e
an
d
c
u
rren
t
l
a
w
s
(KVL
a
nd
K
C
L
)
,
w
e
w
r
i
t
e
a
s
y
s
t
e
m
o
f
t
w
o
f
i
r
s
t
-
o
r
d
e
r
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
ns.
These
e
qua
t
i
o
n
s
ar
e
t
h
en
s
ol
v
e
d
usi
ng
the
Lap
l
ac
e
tra
n
sf
orm
.
T
he
s
o
l
u
t
ion
for
t
h
e
f
i
r
s
t
to
p
o
l
ogy
d
e
f
i
n
es
th
e
i
n
i
t
ia
l
c
o
n
d
it
i
o
n
s
f
or
t
he
s
e
c
o
n
d
o
ne
.
Thi
s
ena
b
le
s
u
s
t
o
com
pose
a
s
y
stem
o
f
two
first-orde
r
d
i
ffer
ence
e
q
ua
t
i
ons,
w
h
i
c
h
i
s
s
o
l
v
e
d
usi
n
g
t
h
e
Z-
t
r
a
n
s
f
o
r
m
.
T
h
u
s
,
f
o
r
a
g
i
v
e
n
p
e
r
i
o
d
,
,
w
e
know
t
he
i
n
i
t
i
a
l
v
a
l
ue
s
of
s
ta
t
e
v
aria
ble
s
a
n
d
f
unc
t
i
o
n
s
a
ccor
d
in
g
to w
h
i
ch
t
he
se
v
a
r
ia
bles c
h
a
n
g
e.
This is t
he
s
olu
t
io
n is cl
o
s
e
d
f
o
r
m.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
r
ansie
nt
a
n
d
st
e
ady-s
ta
te a
n
a
ly
sis o
f
si
n
g
le
swi
t
c
h
e
d
c
a
pa
citor
co
nve
r
te
r
(Alex
a
n
d
er K
u
shn
e
rov)
34
3
(a
)
(b
)
F
i
gure
1. (
a)
C
ons
i
d
ere
d
S
CC
(
b) a
nd tw
o n
o
n
-o
ve
rlap
p
i
n
g
c
loc
k
s
a
nd
2.
DIFFE
R
E
NTIAL
E
Q
UATIO
N
S
2.1.
Fi
r
s
t t
o
pol
o
gy
Th
e
s
w
i
t
ch
es
a
n
d
i
s
show
n
in
F
ig
ure
1(
a)
a
r
e
t
urned
o
n
dur
in
g
,
w
h
e
r
e
i
s
the n
u
m
b
er
of
peri
ods.
Th
us,
in t
he
first t
op
o
l
o
gy
as show
n
i
n
Figure 2,
.
F
i
gure
2.
F
irst t
o
p
o
l
o
gy o
f
t
he
c
onsider
ed
S
C
C
The
K
V
L
a
nd K
C
L e
qua
t
i
o
n
s
for thi
s
c
i
r
cu
it
are
(1
)
Let us
w
rite (
1) in
t
h
e
Lap
l
a
c
e
doma
i
n
u
s
in
g
(2
)
such that
(3
)
The
s
o
lution
o
f
(3)
can
be wr
i
t
t
en
a
s
:
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
34
2 –
35
0
34
4
wher
e
(
5
)
and
(6
)
The
inverse
Laplace tra
ns
f
o
rm
of
(4)
i
s
:
(
7
)
U
s
ing
a
nd
(8
)
w
e
c
an
r
e
w
r
i
t
e
(
7
)
a
s
:
(9
)
wher
e
(
10)
2.2.
S
ec
ond
top
o
log
y
The switches
and
in F
i
gur
e 1(a)
a
r
e
turne
d on d
u
r
i
ng
1
, such
t
h
a
t
i
n the
seco
nd
to
po
l
o
g
y
a
s
show
n i
n
F
igure
3
.
F
i
gure
3. S
ec
ond t
o
po
log
y
o
f the
co
ns
i
d
e
r
ed
S
CC
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
r
ansie
nt
a
n
d
st
e
ady-s
ta
te a
n
a
ly
sis o
f
si
n
g
le
swi
t
c
h
e
d
c
a
pa
citor
co
nve
r
te
r
(Alex
a
n
d
er K
u
shn
e
rov)
34
5
The
K
V
L
a
nd K
C
L e
qua
t
i
o
n
s
for thi
s
c
i
r
cu
it
are
:
(
11)
U
s
ing
(2), w
e
w
r
i
t
e
(11)
i
n t
h
e La
place
d
om
ain
:
(
12)
The
s
o
lution
o
f
(12) is:
13)
wher
e
(
14)
and
(
15)
The
inve
rse
La
place
tra
nsf
o
rm
of
(13)
i
s:
(
16)
S
i
nce
for
the
sec
ond
t
o
po
lo
gy
,
the
i
n
i
tia
l
c
o
n
d
i
t
i
o
n
s
w
il
l
be
a
nd
,
w
h
er
e
a
s
.
3.
DIFFE
R
E
NCE EQUA
T
IONS
S
ubsti
t
u
ti
ng
(1
4) a
nd (15)
in
t
o
(16),
w
e
obta
i
n t
h
e
rec
u
rre
nt
e
quat
i
o
n
s
:
(
17)
wher
e
(
18)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
34
2 –
35
0
34
6
N
o
w
,
s
ubst
i
t
u
t
i
ng
(9) in
to (
17)
, w
e
ob
ta
in
t
he
di
f
fere
n
c
e
equ
a
t
ion
s
:
(
19)
wher
e
(
20)
Be
fore
w
e
proc
eed
t
o t
h
e so
l
u
t
i
on
o
f
(
19),
l
e
t us c
o
n
si
der
t
h
e
ste
a
dy-s
t
ate
opera
tio
n,
w
her
e
(
21)
S
ubst
i
t
ut
i
ng (2
1)
i
n
t
o
(19),
we
have
(
22)
The
s
o
lution
o
f
(22) is:
(2
3
Let us
w
rite (
19) in
the
Z-do
m
a
in us
i
n
g
(
24)
such that
(
25)
The
s
o
lution
o
f
(25) is:
(
26)
wher
e
(
27)
Sin
c
e
Err
o
r! Refe
ren
ce source
n
o
t
found
.
i
s
re
p
r
esented
in t
he f
orm
of part
i
al frac
t
ion
s
, w
e
ca
n appl
y
the
in
verse
Z-tra
n
s
f
orm
to ea
c
h
t
e
rm sep
a
r
at
el
y:
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
r
ansie
nt
a
n
d
st
e
ady-s
ta
te a
n
a
ly
sis o
f
si
n
g
le
swi
t
c
h
e
d
c
a
pa
citor
co
nve
r
te
r
(Alex
a
n
d
er K
u
shn
e
rov)
34
7
(
28)
4.
SIMU
L
A
TION
R
ESULT
S
To
v
eri
f
y
t
h
e
ob
t
a
ine
d
a
na
lytica
l
e
x
p
re
ssi
o
ns
(
9)
,
(
1
7
)
a
n
d
(
2
8
)
,
t
h
e
c
i
r
c
u
i
t
s
h
o
w
n
i
n
F
i
g
u
r
e
4
w
a
s
si
m
u
late
d
i
n
P
S
I
M
9.
0.
S
ince
t
he
P
S
I
M
bid
i
rec
t
i
ona
l
sw
i
t
c
h
es
h
a
ve
z
e
r
o
on-re
si
s
t
a
n
c
e
,
tw
o
exter
n
a
l
r
esistor
s
corr
espo
n
d
in
g
to
a
nd
i
n
F
i
g
u
re
2
a
nd
F
i
g
u
r
e
3
w
e
re
a
dded.
T
he
p
ar
am
e
t
er
s
of
t
he
c
i
r
c
u
i
t
i
n
F
i
gur
e
4
are
as
f
ollows:
1
0
,
0
0
0
,
5
,
1
Ω
,
1
0
,
1
00Ω
and
1
0
0
.
F
i
gure
4.
S
im
ulat
ion
c
i
rc
uit f
o
r the
v
o
l
t
a
g
e-ha
lv
in
g S
C
C
Sin
c
e
a
nd
,
the e
xpressi
o
n
s (10)
a
nd
(18) a
re
r
e
d
u
c
ed
t
o:
(
29)
These
co
ns
tan
t
s ar
e
subs
ti
tute
d
int
o
(
20) a
nd
then
in
to (
2
8
),
w
hich se
t
s
the
ini
tia
l
con
d
iti
o
n
s for
(9)
and
(17).
The
voltages across
and
duri
ng t
h
e
first te
n
peri
ods (
0
10
) is
s
how
n
F
i
g
u
re
5, w
hic
h
c
ompa
res
the
Ma
th
CA
D
c
a
lcu
l
a
t
io
n a
n
d
PSIM sim
ul
a
t
i
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
34
2 –
35
0
34
8
01
10
5
2
10
5
3
10
5
4
10
5
5
10
5
6
10
5
7
10
5
8
10
5
9
10
5
1
10
4
0
1
2
3
4
5
6
V
1
t
()
V
o
t
()
t
(a)
(b)
F
i
gure
5.
V
olt
a
ges a
c
ross
and
for
0
10
,
M
a
thCA
D
(a) and
P
S
I
M (
b
) The
hori
z
on
ta
l
sc
ale
i
s
10
⁄
,
i.e.
e
a
c
h di
vis
i
o
n
i
s
The
vo
l
t
age
s
i
n
Fig
u
re
5
w
ere
m
e
a
s
ur
e
d
a
t
t
h
e
po
int
s
a
nd
are
given
i
n
T
a
b
l
e
1
a
l
o
ng
w
i
t
h
t
h
e
relative
er
ror,
.
Tab
l
e
1. Me
a
sured
va
lues
o
f the
v
o
l
ta
ge
s i
n
F
i
gur
e 5
[%
]
[%]
C
a
l
c
.
Si
m
u
l.
C
a
l
c.
S
im
ul.
1
2.
514
6
2.
5046
0
.
398
0.
5174
0
.
5
119
1
.
074
2
3.
498
6
3.
4937
0
.
140
0.
9542
0
.
9
449
0
.
984
3
3.
914
7
3.
9144
0
.
008
1.
3381
1
.
3
259
0
.
920
4
4.
117
2
4.
1193
0
.
051
1.
6815
1
.
6
670
0
.
870
5
4.
236
6
4.
2397
0
.
073
1.
9909
1
.
9
747
0
.
820
6
4.
321
1
4.
3254
0
.
010
2.
2706
2
.
2
531
0
.
777
7
4.
389
0
4.
3943
0
.
121
2.
5236
2
.
5
054
0
.
726
8
4.
447
4
4.
4534
0
.
135
2.
7526
2
.
7
339
0
.
684
9
4.
499
1
4.
5055
0
.
142
2.
9601
2
.
9
410
0
.
649
10
4
.
545
4
4.
5455
0
.
002
7.
1478
7
.
1
282
0
.
627
F
i
gure
6 com
p
ar
es the
M
at
h
C
A
D
calc
u
l
a
ti
o
n
a
nd P
S
IM
s
im
ula
t
i
o
n
f
or
0
1
00
. Not
e that at
60
the
S
CC
r
ea
ch
es
t
he stea
dy-s
t
a
t
e
0
2
e
-
00
5
4e-
0
0
5
6e-
0
0
5
8
e-
00
5
0
.
000
1
Ti
m
e
(
s
)
0
1
2
3
4
5
6
V1
Vo
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
r
ansie
nt
a
n
d
st
e
ady-s
ta
te a
n
a
ly
sis o
f
si
n
g
le
swi
t
c
h
e
d
c
a
pa
citor
co
nve
r
te
r
(Alex
a
n
d
er K
u
shn
e
rov)
34
9
01
10
4
2
10
4
3
10
4
4
10
4
5
10
4
6
10
4
7
10
4
8
10
4
9
10
4
0.001
0
1
2
3
4
5
6
V
1
t
()
V
o
t
()
t
(a)
(b)
F
i
gure
6. V
ol
ta
ge
s ac
ross
and
f
or
0
10
0
,
Mat
h
CA
D
(a
) a
nd P
S
IM
(
b).
Th
e ho
ri
z
ont
al
s
ca
l
e
i
s
10
0
⁄
,
i.e.
each di
v
isio
n
i
s
10
The
s
t
ea
d
y
-
s
t
a
te
v
o
l
tages ar
e show
n Fig
u
re 7. Their d
i
sc
re
t
e
va
l
u
es w
er
e
c
a
lcu
l
a
t
e
d
b
y
(
23)
a
n
d
the
n
su
bs
tit
ut
e
d
a
s t
h
e i
n
it
ial
c
ond
it
ion
s
in
t
o
(9
) a
n
d
(17
)
.
9.5
10
4
9.55
10
4
9.6
10
4
9.65
10
4
9.7
10
4
9.75
10
4
9.8
10
4
9.85
10
4
9.9
10
4
9.95
10
4
0.001
4.91
4.93
4.95
4.97
4.99
5.01
5.03
V
1
t
()
V
o
t
()
t
F
i
gure
7.
S
tea
dy-sta
t
e vo
l
t
a
g
e
s
a
c
r
oss
a
nd
f
o
r
95
10
0
0
0
.
0002
0.
0
004
0.
0006
0.
0008
0.
001
Tim
e
(
s
)
0
1
2
3
4
5
6
V1
Vo
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
34
2 –
35
0
35
0
5.
CONCL
U
S
IONS
Base
d
o
n
t
he
m
etho
d
of
d
i
f
fer
e
nce
e
q
uat
i
ons
t
he
c
l
o
se
d
form
e
xp
ress
io
ns
f
o
r
t
he
v
ol
ta
ges
ac
ross
t
h
e
c
a
p
a
c
ito
rs
i
n
th
e
v
o
lt
ag
e
-
h
a
lv
i
n
g
SC
C
we
re
d
e
r
iv
ed
.
Th
e
sol
u
ti
o
n
o
f
t
he
se
e
q
u
a
t
i
o
ns
a
l
l
ow
s
u
s
t
o
pre
d
ic
t
t
h
e
S
CC
be
ha
v
i
or
i
n
b
o
t
h
the
tra
n
sien
t
an
d
ste
a
dy-s
t
ate
o
p
era
tio
n.
That
i
s
fo
r
a
give
n
pe
ri
od,
,
w
e
know
t
he
in
itia
l
va
lue
s
o
f
t
h
e
v
o
l
t
a
g
e
s
a
n
d
f
u
n
c
t
i
o
ns
a
c
c
o
rd
in
g
to
w
h
i
c
h
t
hes
e
v
ol
t
a
ges
c
h
ange.
T
h
e
o
b
t
a
in
e
d
expre
ssi
ons
w
er
e
ver
i
fied
b
y
si
m
u
lat
i
ons.
A
s
e
vi
de
nt
f
r
o
m
Ta
bl
e
,
t
he
d
e
v
i
a
tio
n
betw
e
e
n
t
h
e
t
h
eore
t
i
c
a
l
an
d
si
m
u
lat
i
on
r
e
sul
t
s
d
o
es
n
ot
e
xce
e
d
1.1
%
.
The
use
d
m
e
t
hod
how
e
v
e
r,
i
s
ver
y
c
omp
l
ex
e
ven
in
t
he
c
as
e
o
f
t
h
e
tw
o-p
h
ase
S
C
C an
d
i
t
s e
x
te
n
s
ion
to
t
he m
ul
t
i
-
pha
se S
CC w
i
l
l
a
pp
are
n
t
l
y
r
e
quire
s
o
m
e
spec
i
a
l
assum
p
t
i
o
n
s.
REFE
RENCES
[1]
M.
F
.
Gardner
and
J.
L
.
Barnes,
“Trans
i
e
nts
i
n
L
ine
a
r
Sys
t
em
s
,
S
t
u
d
ied
b
y
t
he
L
apl
a
ce
Trans
f
o
r
m
a
ti
on
,”
v
ol.
I,
Wiley,
1
9
42.
[2]
Y.
Z
.
Tsy
pkin
,
“
S
a
m
p
lin
g
S
y
st
e
m
s
Th
eory
a
nd
its
A
ppli
cati
on,
”
v
ol.
I,
Ma
c
m
i
lla
n
, 1
96
4.
[3]
P.
M
.
Deru
sso,
R.
J
.
Roy
and
C.
M
.
Cl
o
s
e,
"
§6.
4
T
h
e
Co
ncept
o
f
State,
"
in
S
ta
te
V
ariab
l
es
f
or
E
ng
in
eers,
N
ew
Yo
rk:
Wiley,
p
p
.
4
13-4
1
5
,
1
965.
[4]
L.
R
.
Neron
e
,
"An
a
ly
ti
cal
s
o
l
u
t
io
ns
o
f
th
e
cl
ass
D
in
vert
er,"
i
n
IE
EE
In
t
e
rn
atio
nal
S
y
mp
osium o
n
Circuits
and
S
y
ste
m
s (I
S
C
AS
)
,
20
08.
[5]
A.
S
hoih
e
t
and
M
.
A
.
Sl
on
im
,
"Anal
y
sis
of
b
uck
co
nvert
er
p
roc
e
s
ses
us
in
g
d
i
ff
erence
e
q
uat
i
o
n
s
m
e
th
od
,
"
i
n
IE
EE
Con
venti
on
o
f
Electr
i
ca
l a
n
d
El
e
c
tro
n
i
c
s E
ngin
eers in
Isr
a
el (
I
EEE
I)
,
20
10
.
[6]
N.
K
rihel
y
,
M.
A
.
Sl
on
im
a
nd
S
.
Ben-Y
aako
v
,
"Trans
ien
t
a
nd
s
tea
d
y
-st
a
te
a
nal
y
s
i
s
o
f
t
hree-ph
ase
P
W
M
bu
ck
recti
fi
e
r
,
"
IET
Po
wer
Elect
ro
n
i
cs
, vo
l
.
5,
n
o.
9,
pp
. 17
6
4
-
17
7
5
,
20
12
.
[7]
A.
L
am
an
ti
a,
P
.
M
a
ranes
i
a
nd
L.
R
adri
zzani
,
"
S
m
all
-
si
gnal
m
odel
o
f
t
h
e
C
o
ckcrof
t-
W
a
lton
voltage
m
ul
t
i
p
lier,
"
IEEE Transac
t
i
ons
on
Power Elect
ronics
, vo
l
. 9
,
n
o
. 1,
p
p
.
18
-25
,
19
9
4
.
[8]
V.
V
it
chev,
"
C
al
culat
i
n
g
e
s
s
ent
i
al
c
h
a
rge-p
u
m
p
p
aram
e
t
ers,"
Po
wer Electr
o
n
i
cs
T
ech
no
log
y
,
vo
l.
7
,
pp
.
3
0-45
,
2
0
0
6
[9]
M.
E
.
Karagozler,
S.
C
.
Goldstei
n
and
D.
S
.
Rick
etts
,
"
A
nal
y
sis
a
n
d
m
odelin
g
of
capaci
tiv
e
p
ow
er
t
ransf
e
r
i
n
mic
r
o
s
y
s
te
ms,"
I
EEE Tran
sact
ions
on
C
i
rcu
its
a
n
d Systems
I: Regular
P
a
pers
,
vol.
59
,
no
.
7
,
p
p.
155
7-1
5
6
6
,
2
01
2.
[10]
R.
R
am
ezani
an
d
A.
Y
ako
v
lev
,
"
Capa
cit
o
r
discharg
ing
th
rou
g
h
asy
n
c
hro
n
o
u
s
ci
rcui
t
switching
,
"
i
n
I
E
EE In
t
.
Sym
p
o
s
iu
m o
n
Asyn
chr
o
n
ous
Circui
ts an
d S
y
st
ems
(
A
S
Y
NC)
,
2
0
13.
Evaluation Warning : The document was created with Spire.PDF for Python.