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3
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I
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N
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8
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5
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3440
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n
(
7
)
̇
w
h
ic
h
co
r
r
esp
o
n
d
s
to
th
e
f
o
llo
w
i
n
g
s
ca
lar
d
if
f
er
en
tial e
q
u
ati
o
n
s
:
{
̇
̇
T
h
en
,
th
e
co
n
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o
l la
w
s
to
s
ati
s
f
y
a
s
tab
ilizatio
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d
ef
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b
y
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{
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(
9
)
4
.
2
.
Vo
lt
a
g
e
o
ute
r
l
o
o
p c
o
ntr
o
l
T
h
e
aim
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s
to
d
esig
n
t
u
n
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g
la
w
s
f
o
r
th
e
x
1
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a
n
d
x
3
*
.
W
e
co
n
s
id
er
:
an
d
Usi
n
g
t
h
e
E
q
u
atio
n
(
2
)
w
e
ca
n
estab
lis
h
t
h
e
f
o
llo
w
in
g
r
elatio
n
s
̇
̇
an
d
̇
[
̇
(
)
]
W
e
m
u
s
t u
s
e
a
lo
w
p
as
s
f
il
ter
f
o
r
th
e
f
ir
s
t d
er
iv
ati
v
e
̇
(
r
esp
ec
tiv
el
y
̇
)
o
f
th
e
r
ef
er
e
n
ce
(
r
esp
ec
tiv
el
y
)
ex
is
ts
,
w
e
o
b
tain
f
i
n
all
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Mo
d
ellin
g
a
n
d
P
a
s
s
ivity
-
b
a
s
ed
C
o
n
tr
o
l o
f a
N
o
n
I
s
o
la
ted
D
C
-
DC
C
o
n
ve
r
ter in
a
F
u
el
…
(
Mo
u
ta
b
ir
A
h
med
)
3441
(
)
an
d
(
)
w
it
h
:
(
√
√
*
{
∫
an
d
{
∫
5.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
n
th
is
s
ec
tio
n
,
t
h
e
p
er
f
o
r
m
an
ce
s
o
f
t
h
e
co
n
tr
o
ller
w
i
ll
b
e
illu
s
tr
ated
b
y
s
i
m
u
lat
io
n
s
i
n
t
h
e
Ma
tlab
/Si
m
u
l
in
k
en
v
ir
o
n
m
e
n
t.
T
h
e
co
n
tr
o
lled
DC
/DC
co
n
v
er
ter
h
as
th
e
f
o
llo
win
g
c
h
ar
ac
ter
is
tic
s
:
;
b
=b
’
=
3
;
;
.
T
h
e
co
n
v
er
ter
h
as
b
ee
n
s
i
m
u
l
ated
to
ch
ec
k
th
e
p
r
ev
io
u
s
s
ta
b
ilit
y
co
n
d
itio
n
s
.
T
h
e
Fi
g
u
r
e
4
s
h
o
w
s
th
e
f
u
e
l c
ell
v
o
lta
g
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
co
n
v
er
ter
an
d
h
is
r
ef
er
en
ce
th
a
t
h
av
i
n
g
t
w
o
v
al
u
es:
7
0
V
an
d
1
4
0
V
ar
e
s
h
o
w
n
in
F
ig
u
r
e
5
.
W
e
o
b
s
er
v
e
th
at
th
e
tr
ac
k
i
n
g
i
s
s
ati
s
f
ied
an
d
th
e
s
tab
il
it
y
i
s
g
u
ar
an
teed
.
T
o
an
aly
ze
th
e
r
o
b
u
s
tn
e
s
s
ca
p
ab
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
a
n
e
w
e
x
p
er
i
m
e
n
t
w
ill
b
e
p
er
f
o
r
m
ed
.
I
t
co
n
s
i
s
ts
i
n
ch
a
n
g
in
g
t
h
e
f
u
el
ce
ll
v
o
ltag
e
ac
co
r
d
in
g
to
Fi
g
u
r
e
6
.
E
x
ce
p
t
f
o
r
th
is
c
h
an
g
e,
t
h
e
r
est
o
f
th
e
co
n
v
er
ter
ch
ar
ac
ter
is
tic
s
ar
e
th
e
s
a
m
e
as
p
r
ev
io
u
s
l
y
.
T
h
e
F
ig
u
r
e
7
s
h
o
w
s
t
h
at
th
e
ef
f
ec
t
o
f
f
u
el
ce
ll
v
o
lt
ag
e
c
h
an
g
e
i
s
w
ell
co
m
p
e
n
s
ated
b
y
t
h
e
co
n
tr
o
ller
.
Fig
u
r
e
4
.
Fu
el
ce
ll
v
o
ltag
e
v
er
s
u
s
ti
m
e
Fig
u
r
e
5
.
Ou
tp
u
t
v
o
ltag
e
w
i
th
tr
ak
in
g
Fig
u
r
e
6
.
Fu
el
ce
ll
v
o
ltag
e
v
er
s
u
s
ti
m
e
Fig
u
r
e
7
.
Ou
tp
u
t
v
o
ltag
e
w
i
th
d
is
tu
r
b
an
ce
6.
CO
NCLU
SI
O
N
T
h
e
an
al
y
s
is
an
d
s
tu
d
y
o
f
th
e
in
s
er
tio
n
o
f
f
u
el
ce
l
l
i
n
p
o
w
er
s
y
s
te
m
is
i
m
p
o
r
tan
t
i
n
o
r
d
er
to
in
cr
ea
s
e
th
e
co
m
p
etiti
v
e
n
es
s
o
f
t
h
is
s
o
u
r
ce
.
A
n
o
n
li
n
ea
r
co
n
tr
o
ller
is
p
r
o
p
o
s
ed
f
o
r
DC
/D
C
ca
s
ca
d
ed
b
o
o
s
t
co
n
v
er
ter
to
ac
h
ie
v
e
v
o
lta
g
e
o
u
tp
u
t
r
eg
u
la
t
io
n
.
I
t is
d
ev
elo
p
ed
in
t
w
o
s
tep
s
.
First,
a
n
i
n
n
er
-
lo
o
p
i
s
d
esig
n
ed
,
b
ased
o
n
t
h
e
p
as
s
i
v
it
y
tec
h
n
iq
u
e.
T
h
e
in
n
er
-
lo
o
p
r
eg
u
lato
r
g
e
n
er
ates
th
e
d
u
ties
c
y
cle
an
d
.
T
h
e
s
ec
o
n
d
s
tep
co
n
s
is
t
s
i
n
d
ev
elo
p
in
g
a
n
o
u
ter
-
lo
o
p
th
at
g
e
n
er
ates
th
e
r
ef
er
e
n
ce
c
u
r
r
en
ts
s
o
t
h
at
t
h
e
s
q
u
ar
ed
o
u
tp
u
t
v
o
ltag
e
s
an
d
f
o
llo
w
s
a
g
iv
e
n
r
e
f
er
en
ce
s
i
g
n
als
.
T
h
e
s
y
n
t
h
esi
s
o
f
t
h
is
lo
o
p
in
v
o
lv
e
s
a
lin
ea
r
izi
n
g
v
ar
iab
le
ch
a
n
g
e,
a
s
ig
n
a
l
f
ilter
i
n
g
to
co
p
e
w
i
th
m
o
d
el
ti
m
e
-
v
ar
y
in
g
a
n
d
co
n
tr
o
llab
ilit
y
is
s
u
es a
n
d
a
lo
o
p
m
o
d
e
s
ep
ar
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
4
3
6
–
3
4
4
3
3442
A
f
o
r
m
al
a
n
al
y
s
i
s
a
n
d
a
s
i
m
u
latio
n
s
tu
d
y
p
r
o
v
e
t
h
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
ac
t
u
all
y
m
ee
t
it
s
o
b
j
ec
tiv
es:
tr
ac
k
i
n
g
,
s
tab
ilit
y
an
d
r
o
b
u
s
tn
es
s
g
u
ar
an
tied
.
T
h
e
r
esu
lts
o
b
tain
ed
ar
e
s
i
m
ilar
to
th
o
s
e
o
f
th
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
[
1
2
]
-
[
1
4
]
.
RE
F
E
R
E
NC
E
S
[1
]
F
.
Ou
tf
e
rd
in
e
,
e
t
a
l
.
,
“
F
e
a
sib
il
it
y
o
f
S
u
b
stit
u
ti
o
n
o
f
th
e
Co
n
v
e
n
ti
o
n
a
l
S
tree
t
L
ig
h
ti
n
g
In
sta
l
latio
n
b
y
th
e
P
h
o
t
o
v
o
lt
a
ic
Ca
se
S
tu
d
y
o
n
a
M
u
n
ici
p
a
li
ty
in
A
g
a
d
ir
in
M
o
ro
c
c
o
”
,
IJ
ECE
,
v
o
l.
7
,
n
o
.
5
,
p
p
.
2
2
8
7
-
2
2
9
9
,
Oc
t
o
b
e
r
2
0
1
7
.
[2
]
A
.
Ezz
a
id
i,
e
t
a
l
.,
“
Ev
a
lu
a
ti
o
n
o
f
th
e
En
e
rg
y
P
e
rf
o
r
m
a
n
c
e
o
f
th
e
Am
o
u
g
d
o
u
l
W
in
d
F
a
rm
,
M
o
ro
c
c
o
”
,
IJ
ECE
,
v
o
l.
7
,
n
o
.
2
,
p
p
.
6
9
2
-
7
0
5
,
A
p
ril
2
0
1
7
.
[3
]
J.M
.
Co
rre
a
,
e
t
a
l
.
,
“
A
n
El
e
c
tro
c
h
e
m
ic
a
l
Ba
s
e
d
F
u
e
l
Ce
ll
M
o
d
e
l
S
u
it
a
b
le
f
o
r
El
e
c
tri
c
a
l
E
n
g
in
e
e
ri
n
g
A
u
to
m
a
ti
o
n
A
p
p
ro
a
c
h
”
,
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
1
,
p
p
.
1
1
0
3
-
1
1
1
2
,
Oc
t
2
0
1
1
.
[4
]
D.F
im
o
ffe
n
a
n
d
M
.
Ba
su
a
ld
o
,
“
A
d
v
a
n
c
e
d
Co
n
t
ro
l
f
o
r
F
u
e
l
Ce
ll
s
C
o
n
n
e
c
ted
to
a
DC
-
DC
C
o
n
v
e
rter
a
n
d
a
n
El
e
c
tri
c
M
o
to
r”
,
Co
mp
u
ter
s a
n
d
C
h
e
mic
a
l
En
g
in
e
e
rin
g
,
2
0
1
0
.
[5
]
S
ira
-
Ra
m
i
r
e
z
H.,
e
t
a
l
.,
“
P
a
ss
iv
it
y
-
b
a
se
d
C
o
n
tro
ll
e
rs
f
o
r
th
e
S
t
a
b
il
iza
ti
o
n
o
f
DC
to
DC
P
o
w
e
r
Co
n
v
e
rters
”
,
Au
to
m
a
ti
c
a
,
v
o
l.
3
3
,
n
o
.
4
,
p
p
.
4
9
9
-
5
1
3
,
1
9
9
7
.
[6
]
W
u
Lei
-
tao
,
e
t
a
l
.,
“
In
v
e
stig
a
ti
o
n
o
f
P
a
ss
iv
it
y
-
b
a
se
d
Co
n
tro
l
o
f
DC/DC
Co
n
v
e
rter
”,
T
ra
n
sa
c
ti
o
n
s
o
f
Ch
in
a
El
e
c
tro
-
tec
h
n
ica
l
S
o
c
iety
,
v
o
l
.
1
9
,
n
o
.
4
,
p
p
.
6
6
-
6
9
,
2
0
0
4
(in
Ch
i
n
e
se
).
[7
]
X
u
e
H
u
a
a
n
d
Jia
n
g
Jia
n
-
g
u
o
,
“
S
tu
d
y
o
n
A
d
a
p
ti
v
e
P
a
ss
iv
it
y
-
b
a
s
e
d
Co
n
t
ro
l
S
trate
g
ies
o
f
S
h
u
n
t
A
c
ti
v
e
F
il
ter
s
”
.
Pro
c
e
e
d
in
g
s
o
f
t
h
e
CS
EE
2
7
(
2
5
)
,
p
p
.
1
1
4
-
1
1
8
,
2
0
0
7
(i
n
C
h
in
e
se
).
[8
]
T
z
a
n
n
-
S
h
in
L
e
e
,
“
L
a
g
r
a
n
g
ian
M
o
d
e
li
n
g
a
n
d
P
a
ss
iv
it
y
-
b
a
s
e
d
C
o
n
tr
o
l
o
f
th
re
e
-
p
h
a
se
A
C/DC
V
o
lt
a
g
e
so
u
rc
e
C
o
n
v
e
rters
”,
In
d
u
stria
l
El
e
c
tro
n
i
c
s
,
v
o
l.
5
1
,
n
o
.
4
,
p
p
.
8
9
2
-
9
0
2
,
2
0
0
4
.
[9
]
W
a
n
g
Jiu
-
h
e
,
“
P
a
ss
iv
it
y
-
b
a
se
d
Co
n
tr
o
l
T
h
e
o
ry
a
n
d
it
s
A
p
p
li
c
a
ti
o
n
”
,
Be
ij
i
n
g
:
P
u
b
li
s
h
in
g
Ho
u
se
o
f
El
e
c
tro
n
ic
s
In
d
u
stry
,
2
0
1
0
(in
Ch
i
n
e
se
).
[1
0
]
Qia
o
S
h
u
-
to
n
g
,
e
t
a
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Evaluation Warning : The document was created with Spire.PDF for Python.