I
nte
rna
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io
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l J
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f
P
o
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E
lect
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nics
a
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Driv
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S
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(
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J
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Vo
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12
,
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.
3
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tem
b
er
2
0
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1
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~
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SS
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1620
J
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:
h
ttp
:
//ij
p
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s
.
ia
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co
m
M
o
deling
and co
ntrol o
f
a
hybrid
D
C/DC/A
C conv
ert
er t
o
trans
fer p
o
wer u
nder di
ff
er
ent
po
wer mana
g
ement
stra
tegies
Am
in Aliza
deh Asl
1
,
Ra
m
in
Aliza
deh Asl
2
1
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ter E
n
g
i
n
e
e
rin
g
,
Tab
riz U
n
iv
e
rsity
,
Ira
n
2
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
Urm
ia Un
iv
e
rsity
,
Ira
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
21
,
2
0
21
R
ev
is
ed
J
u
n
2
2
,
2
0
21
Acc
ep
ted
J
u
l 1
4
,
2
0
21
A
h
y
b
ri
d
DC/DC/AC
c
o
n
v
e
rter
c
o
n
n
e
c
ted
to
th
e
g
ri
d
with
o
u
t
a
t
h
re
e
-
p
h
a
se
tran
sfo
rm
e
r
is
c
o
n
tr
o
ll
e
d
.
T
h
e
d
e
c
e
n
tralize
d
c
o
n
tr
o
l
m
e
th
o
d
is
a
p
p
li
e
d
t
o
t
h
e
h
y
b
rid
DC
-
DC
c
o
n
v
e
rter
su
c
h
th
a
t
th
e
m
a
x
imu
m
p
o
we
r
o
f
P
V
fl
o
ws
to
t
h
e
g
rid
si
d
e
.
Th
is
c
o
n
tr
o
ll
e
r
m
u
st
c
h
a
rg
e
a
n
d
d
isc
h
a
r
g
e
th
e
b
a
tt
e
ry
a
t
th
e
p
ro
p
e
r
ti
m
e
.
It
m
u
st
a
lso
re
g
u
late
D
C
-
li
n
k
v
o
lt
a
g
e
.
An
a
d
d
i
ti
o
n
a
l
a
d
v
a
n
t
a
g
e
o
f
th
e
p
ro
p
o
se
d
c
o
n
tr
o
l
is
t
h
a
t
t
h
e
t
h
re
e
-
p
h
a
se
in
v
e
rter
d
o
e
s
n
o
t
n
e
e
d
a
se
p
a
ra
te
c
o
n
tro
ll
e
r
su
c
h
a
s
P
W
M
a
n
d
S
P
WM
.
A
sim
p
le
tec
h
n
iq
u
e
is
u
se
d
fo
r
c
re
a
ti
n
g
th
e
d
e
sire
d
p
h
a
se
sh
if
t
i
n
t
h
e
th
re
e
-
p
h
a
se
in
v
e
rter,
w
h
ich
m
a
k
e
s
th
e
a
c
ti
v
e
a
n
d
re
a
c
ti
v
e
p
o
we
r
o
f
th
e
in
v
e
rter
c
o
n
tr
o
ll
a
b
le.
A
n
e
w
c
o
n
fig
u
ra
ti
o
n
is
a
lso
p
ro
p
o
se
d
to
tran
sm
it
a
n
d
m
a
n
a
g
e
th
e
g
e
n
e
ra
ti
o
n
p
o
we
r
o
f
P
V.
In
th
is
sc
h
e
m
e
,
th
e
b
a
tt
e
ry
a
n
d
f
u
e
l
c
e
ll
a
re
e
m
p
lo
y
e
d
a
s
a
n
a
u
x
il
iar
y
so
u
rc
e
t
o
m
a
n
a
g
e
th
e
g
e
n
e
ra
ti
o
n
p
o
we
r
o
f
P
V.
F
in
a
ll
y
,
a
re
a
l
-
ti
m
e
si
m
u
latio
n
is
p
e
rfo
rm
e
d
to
v
e
rif
y
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
th
e
p
ro
p
o
se
d
c
o
n
tro
ll
e
r
a
n
d
sy
ste
m
b
y
c
o
n
sid
e
ri
n
g
th
e
re
a
l
c
h
a
ra
c
teristics
o
f
P
V an
d
F
C.
K
ey
w
o
r
d
s
:
DC
/D
C
/A
C
co
n
v
er
ter
Dec
en
tr
alize
d
m
u
ltiv
ar
iab
le
co
n
tr
o
l m
eth
o
d
FAC
T
S
PV/F
C
/
b
atter
y
h
y
b
r
id
p
o
wer
s
y
s
tem
s
Th
r
ee
-
in
p
u
t D
C
-
DC
co
n
v
er
ter
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
:
Am
in
Alizad
eh
Asl
Dep
ar
tem
en
t o
f
E
lectr
ical
an
d
C
o
m
p
u
ter
E
n
g
in
ee
r
in
g
T
ab
r
iz
Un
iv
er
s
ity
E
ast Az
er
b
aijan
Pro
v
in
ce
,
T
a
b
r
iz,
2
9
B
ah
m
a
n
B
o
u
lev
ar
d
,
I
r
a
n
E
m
ail: a
m
in
aliza
d
eh
5
9
4
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
u
s
e
o
f
PV
as
a
co
n
v
en
tio
n
al
r
eso
u
r
ce
will
b
e
p
o
s
s
ib
le
i
n
th
e
f
u
tu
r
e
.
PV
ca
n
b
e
co
m
b
in
ed
with
o
th
er
clea
n
en
er
g
y
s
o
u
r
ce
s
,
e.
g
.
,
f
u
el
ce
ll
s
an
d
b
atter
ies
[
1
]
.
P
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
,
wh
ich
h
av
e
r
ec
en
tly
m
ad
e
s
ig
n
if
ican
t
p
r
o
g
r
ess
,
ar
e
ch
ar
ac
ter
ized
b
y
t
h
eir
h
ig
h
ef
f
icien
cy
,
h
i
g
h
r
eliab
ilit
y
,
an
d
m
er
g
in
g
d
if
f
er
en
t
r
en
ewa
b
le
en
e
r
g
ies
[
2
]
.
T
h
e
m
ajo
r
ity
o
f
th
e
s
tu
d
ies
ar
e
o
n
m
u
lti
-
in
p
u
t
DC
-
DC
co
n
v
er
ter
s
in
th
e
f
ield
o
f
p
o
wer
elec
tr
o
n
ics.
Ah
r
ab
i
et
a
l
[
3
]
,
Fu
r
k
an
Ak
ar
et
a
l
[
4
]
,
B
an
ae
i
et
a
l
[
5
]
,
Dan
y
ali
et
a
l
.
[
6
]
,
Gh
av
i
d
el
et
a
l
.
[
7
]
,
Par
h
am
M
o
h
s
en
i
et
a
l
[
8
]
,
Nen
g
Z
h
an
g
et
a
l
[
9
]
h
a
v
e
in
t
r
o
d
u
ce
d
a
n
ew,
h
ig
h
ly
-
ef
f
icien
t
m
u
lti
-
in
p
u
t
DC
-
DC
co
n
v
er
ter
s
u
itab
le
f
o
r
r
en
e
wab
le
en
er
g
i
es.
T
h
e
ap
p
licatio
n
o
f
p
o
wer
elec
tr
o
n
ic
co
n
v
er
t
er
s
is
ex
p
an
d
in
g
in
m
o
d
er
n
p
o
wer
s
y
s
tem
s
[
1
0
]
-
[
1
6
]
d
u
e
to
th
e
in
teg
r
atio
n
o
f
r
en
ewa
b
le
en
er
g
y
.
W
h
ile
co
n
tr
o
llin
g
tr
an
s
m
is
s
io
n
p
o
wer
h
a
d
pr
o
b
lem
s
i
n
co
n
v
e
n
tio
n
al
p
o
we
r
s
y
s
tem
s
,
t
r
an
s
m
is
s
io
n
p
o
wer
is
co
n
tr
o
llab
le
in
m
o
d
er
n
s
y
s
tem
s
.
Pro
b
lem
s
ass
o
ciate
d
with
r
ea
l
-
tim
e
co
n
tr
o
l
o
f
tr
a
n
s
m
is
s
io
n
p
o
wer
ar
e
m
ajo
r
f
ac
t
o
r
s
lead
in
g
to
b
lack
o
u
t
in
tr
ad
itio
n
al
p
o
wer
s
y
s
tem
s
,
esp
ec
ially
wh
en
th
e
g
r
id
f
ac
e
s
ca
s
ca
d
e
o
u
tag
es
[
1
7
]
-
[
2
4
]
.
No
w
ad
ay
s
,
th
e
lack
o
f
a
s
u
itab
le
co
n
tr
o
ller
m
ak
es
t
h
e
s
y
s
tem
ap
p
r
o
ac
h
es
to
co
llap
s
e.
Ho
wev
er
,
t
h
e
co
n
tr
o
l
o
f
tr
an
s
m
is
s
io
n
p
o
wer
b
etwe
en
two
b
u
s
b
a
r
s
is
alm
o
s
t
im
p
o
s
s
ib
le
in
co
n
v
en
ti
o
n
al
p
o
wer
s
y
s
tem
s
.
B
y
em
p
lo
y
i
n
g
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
,
th
e
tr
an
s
m
is
s
io
n
p
o
wer
ca
n
b
e
co
n
tr
o
lled
,
a
n
d
im
m
ed
iate
ac
tio
n
b
ec
o
m
es
p
o
s
s
ib
le
f
o
r
th
e
o
p
er
ato
r
.
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:
2
0
8
8
-
8
694
Mo
d
elin
g
a
n
d
co
n
tr
o
l o
f a
h
yb
r
id
DC
/D
C
/AC c
o
n
ve
r
te
r
to
tr
a
n
s
fer p
o
w
er u
n
d
er
… (
A
min
A
liz
a
d
eh
A
s
l
)
1621
T
h
is
p
ap
er
f
o
c
u
s
es
o
n
t
h
e
co
n
t
r
o
l
is
s
u
es
o
f
tr
a
n
s
m
is
s
io
n
p
o
w
er
.
T
h
e
f
lex
ib
ilit
y
an
d
h
ig
h
r
el
iab
ilit
y
in
tr
an
s
f
er
r
in
g
p
o
wer
ar
e
th
e
f
e
atu
r
es
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
An
ad
v
a
n
ce
d
DC
-
DC
co
n
v
er
ter
,
th
r
ee
-
p
h
ase
in
v
er
ter
,
a
n
d
th
e
m
u
ltiv
ar
iab
le
d
ec
en
tr
alize
d
c
o
n
tr
o
l te
ch
n
iq
u
e
ar
e
u
tili
ze
d
f
o
r
th
is
p
u
r
p
o
s
e
.
T
h
er
e
is
litt
le
r
esear
ch
o
n
co
n
tr
o
llin
g
DC
-
DC
co
n
v
er
ter
s
co
n
n
ec
ted
to
a
th
r
ee
-
p
h
ase
in
v
er
ter
to
tr
an
s
f
er
th
e
m
ax
im
u
m
p
o
wer
o
f
r
en
ewa
b
le
s
o
u
r
ce
s
.
A
s
u
itab
le
m
u
ltiv
ar
ia
b
le
co
n
tr
o
l
tech
n
i
q
u
e
s
h
o
u
ld
b
e
ad
o
p
te
d
b
ec
a
u
s
e
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
ar
e
m
u
ltiv
ar
iab
le
s
y
s
tem
s
.
T
h
e
c
o
n
tr
o
l
m
et
h
o
d
m
u
s
t
ex
tr
ac
t
t
h
e
m
ax
im
u
m
p
o
wer
o
f
PV
an
d
s
im
u
ltan
eo
u
s
ly
co
n
tr
o
l
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
we
r
.
Kh
ak
i
-
Sed
ig
h
,
an
d
M
o
av
en
i
[
2
5
]
ha
s
d
elin
ea
te
d
d
if
f
er
en
t
m
u
ltiv
ar
iab
le
co
n
tr
o
l
tech
n
iq
u
es,
an
d
th
is
p
ap
e
r
h
a
s
em
p
lo
y
ed
a
d
ec
e
n
tr
alize
d
c
o
n
tr
o
l
tec
h
n
iq
u
e
to
co
n
tr
o
l th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
Fig
u
r
e
1
s
h
o
ws th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
T
h
e
o
p
er
atio
n
o
f
m
o
d
e
r
n
p
o
wer
s
y
s
tem
s
h
as
f
ac
ed
n
ew
ch
al
len
g
es
u
p
o
n
t
h
e
ex
p
a
n
d
ed
in
te
g
r
atio
n
o
f
PVs
.
On
th
e
o
n
e
h
an
d
,
th
e
m
ax
im
u
m
p
o
wer
o
f
PV
m
u
s
t
b
e
ex
tr
ac
ted
at
an
y
m
o
m
e
n
t
to
b
e
ec
o
n
o
m
icall
y
ju
s
tifie
d
.
On
th
e
o
th
er
h
an
d
,
u
n
ce
r
tain
ty
in
PV
g
en
er
atio
n
w
ill
ca
u
s
e
p
r
o
b
lem
s
,
in
clu
d
in
g
b
alan
cin
g
i
n
p
o
wer
g
en
er
atio
n
an
d
co
n
s
u
m
p
t
io
n
.
T
h
er
ef
o
r
e
,
h
er
ein
,
a
h
y
b
r
id
s
tr
u
ctu
r
e
co
n
s
is
tin
g
o
f
a
b
atter
y
an
d
f
u
el
ce
ll
is
u
tili
ze
d
to
co
n
tr
o
l
th
e
tr
an
s
f
er
r
in
g
p
o
wer
p
r
o
p
o
r
tio
n
al
t
o
th
e
d
em
a
n
d
ed
p
o
we
r
wh
ile
th
e
m
ax
im
u
m
p
o
wer
o
f
PV
is
ex
tr
ac
ted
.
A
co
m
p
r
o
m
i
s
e
ca
n
b
e
m
ad
e
b
etwe
en
u
n
ce
r
tain
ty
in
th
e
g
en
er
atio
n
p
o
wer
o
f
PV
an
d
th
e
p
o
wer
r
eq
u
i
r
ed
by
th
e
g
r
id
v
ia
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
s
tr
u
ct
u
r
e
;
if
th
e
o
u
tp
u
t
p
o
wer
o
f
PV
is
m
o
r
e
th
an
th
e
d
em
an
d
e
d
p
o
wer
,
th
e
p
r
o
p
o
s
e
d
co
n
tr
o
ller
m
u
s
t
ch
ar
g
e
th
e
b
atter
y
,
an
d
if
p
o
wer
d
em
a
n
d
e
d
by
th
e
n
etwo
r
k
is
m
o
r
e
th
a
n
th
e
o
u
tp
u
t
p
o
wer
o
f
PV,
th
e
c
o
n
tr
o
l
s
y
s
tem
m
u
s
t
ad
d
a
f
u
el
ce
ll
an
d
b
atter
y
to
th
e
s
tr
u
ctu
r
e
t
o
tr
an
s
f
er
th
e
s
et
p
o
wer
to
th
e
n
etwo
r
k
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
an
d
co
n
t
r
o
ller
p
u
r
s
u
e
s
ev
er
al
o
b
jectiv
es si
m
u
ltan
eo
u
s
ly
:
a.
E
x
tr
ac
tin
g
th
e
m
ax
im
u
m
o
u
tp
u
t p
o
wer
o
f
PV a
t a
n
y
m
o
m
en
t
b.
Ma
n
ag
in
g
tr
an
s
m
is
s
io
n
p
o
we
r
with
th
e
h
elp
o
f
th
e
b
atter
y
an
d
FC
(
with
o
u
t
d
is
tu
r
b
in
g
th
e
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
o
f
PV)
c.
R
eg
u
latin
g
DC
-
lin
k
v
o
ltag
e
T
h
e
im
p
o
r
ta
n
t
p
o
in
t
i
n
th
is
s
tr
u
ctu
r
e
is
th
at
th
e
tr
an
s
m
is
s
io
n
p
o
we
r
d
o
es
n
o
t
af
f
ec
t
th
e
ex
tr
ac
tio
n
o
f
th
e
m
ax
im
u
m
p
o
wer
o
f
PV.
First,
th
e
d
y
n
am
ic
m
o
d
el
o
f
a
h
y
b
r
id
DC
-
DC
co
n
v
er
ter
is
ac
h
iev
ed
.
T
h
en
,
a
s
u
itab
le
co
n
tr
o
ller
is
d
esig
n
ed
.
Su
b
s
eq
u
en
tly
,
th
e
p
h
ase
-
s
h
if
t
tech
n
i
q
u
e
is
ap
p
l
ied
to
a
th
r
ee
-
p
h
ase
in
v
er
ter
to
tr
a
n
s
f
er
t
h
e
s
et
p
o
wer
.
Fin
ally
,
ex
ten
s
iv
e
s
im
u
latio
n
is
p
r
ep
ar
ed
t
o
v
alid
ate
th
e
p
r
o
p
e
r
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
Fu
r
th
er
m
o
r
e
,
f
ast
f
o
u
r
ier
tr
an
s
f
o
r
m
(
FF
T
)
a
n
aly
s
is
is
co
n
d
u
cted
in
ea
ch
m
o
d
e
to
p
r
esen
t
d
etailed
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
.
Fig
u
r
e
1
.
Gen
e
r
al
s
ch
em
e
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
2.
SM
A
L
L
-
S
I
G
NA
L
M
O
D
E
L
I
NG
O
F
H
YB
RID DC
/D
C/A
C
CO
NVER
T
E
R
Fig
u
r
e
2
d
is
p
lay
s
th
e
h
y
b
r
id
D
C
-
DC
co
n
v
er
ter
th
at
is
th
e
in
v
er
ter
in
p
u
t.
Sin
ce
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
o
f
th
e
DC
-
DC
co
n
v
er
t
er
ar
e
DC
,
th
e
in
v
er
ter
an
d
g
r
id
o
r
th
e
AC
s
id
e
ar
e
m
o
d
ele
d
o
n
ly
with
s
im
p
le
r
esis
tan
ce
R
L
=V
O
/I
O
.
Ho
wev
er
,
th
e
d
esig
n
ed
co
n
tr
o
ller
is
ap
p
lied
to
th
e
tr
u
e
s
y
s
t
em
to
v
er
if
y
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
c
o
n
tr
o
ller
.
Acc
o
r
d
i
n
g
t
o
Fig
u
r
e
2
,
it
is
clea
r
th
at
a
d
is
co
n
tin
u
o
u
s
cu
r
r
en
t
is
im
p
o
s
ed
o
n
PV,
wh
ich
d
is
tu
r
b
s
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
.
A
co
n
v
en
tio
n
al
b
u
ck
-
b
o
o
s
t
is
allo
ca
ted
at
th
e
en
tr
an
ce
o
f
V
2
; c
o
n
s
eq
u
en
tly
,
I
PV
=I
L2
×d
2
.
T
h
u
s
,
th
is
p
r
o
b
lem
ca
n
b
e
s
o
lv
ed
b
y
co
n
tr
o
llin
g
I
L2
; in
th
is
ca
s
e,
th
e
m
ax
im
u
m
p
o
wer
o
f
PV is f
o
llo
wed
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
h
as th
r
ee
m
o
d
es.
I
n
th
e
f
ir
s
t
m
o
d
e
,
PV
an
d
FC
ca
n
p
r
o
d
u
ce
th
e
d
esire
d
co
n
s
u
m
p
tio
n
p
o
wer
,
s
o
th
e
b
atter
y
m
u
s
t
b
e
b
y
p
ass
ed
.
I
n
th
is
m
o
d
e,
i
t
is
a
s
s
u
m
ed
th
at
th
e
r
eq
u
ested
p
o
wer
b
y
g
r
id
is
m
o
r
e
t
h
an
th
e
m
ax
im
u
m
p
o
wer
o
f
PV.
I
n
th
e
s
ec
o
n
d
m
o
d
e,
th
e
t
o
tal
g
en
er
atio
n
p
o
we
r
o
f
PV
an
d
FC
ca
n
n
o
t
s
u
p
p
ly
t
h
e
o
u
t
p
u
t,
s
o
th
e
b
atter
y
is
DC
Sid
e
T
hree
-
in
pu
t
H
y
brid
DC
-
DC
Co
nv
er
t
er
In
p
u
t
1
In
p
u
t
2
S
t
o
r
a
g
e
T
hree
-
ph
a
s
e
inv
er
t
er
AC
Sid
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
162
0
–
163
1
1622
d
is
ch
ar
g
ed
.
I
n
t
h
e
th
ir
d
m
o
d
e,
it
is
ass
u
m
ed
th
at
th
e
w
h
o
le
g
en
er
ati
o
n
p
o
wer
o
f
PV
an
d
FC
is
lar
g
er
th
an
t
h
e
r
eq
u
ir
ed
co
n
s
u
m
p
tio
n
p
o
wer
in
th
e
o
u
tp
u
t
s
tag
e,
s
o
t
h
e
s
u
r
p
lu
s
en
e
r
g
y
is
s
av
ed
in
th
e
b
atter
y
.
A
s
ep
ar
at
e
co
n
tr
o
ller
m
u
s
t
b
e
d
esig
n
ed
i
n
ea
ch
m
o
d
e
b
ec
au
s
e
th
e
s
tate
-
s
p
ac
e
m
o
d
el
o
f
t
h
e
s
y
s
tem
is
d
if
f
er
e
n
t.
All
th
r
ee
m
o
d
es
co
v
er
th
e
r
ea
lity
in
th
e
g
r
id
.
T
h
er
e
f
o
r
e,
in
f
ir
s
t
s
tep
,
th
e
co
n
tr
o
ller
m
u
s
t
id
en
tify
th
e
m
o
d
e
o
f
o
p
er
ati
o
n
an
d
th
en
in
th
e
s
ec
o
n
d
s
tep
,
ac
t su
ch
th
at
th
e
in
ten
d
ed
co
n
tr
o
l o
b
jectiv
es
be
ac
h
iev
e
d
.
D
2
S
2
S
1
D
1
S
3
D
3
S
4
D
4
B
a
t
t
e
r
y
V
2
V
1
L
1
r
1
L
2
r
2
Co
vo
Vc
i
co
i
D
1
i
L
1
i
s
1
ic
i
D
2
i
L
2
i
s
3
i
D
3
i
s
4
i
D
4
i
B
a
t
t
e
r
y
i
s
2
V
S
2
V
S
1
V
S
3
V
S
4
RL
Io
Fig
u
r
e
2
.
T
h
e
Hy
b
r
id
D
C
-
DC
C
o
n
v
er
ter
2
.
1
.
F
irst
o
pera
t
io
n m
o
de
(
Su
pp
ly
ing
t
he
lo
a
d wit
ho
ut
t
he
co
ntr
ibu
t
io
n o
f
t
he
ba
t
t
er
y
)
T
o
b
y
p
ass
th
e
b
atter
y
in
th
is
m
o
d
e,
S3
an
d
S4
m
u
s
t
b
e
t
u
r
n
ed
o
f
f
an
d
tu
r
n
ed
o
n
,
r
es
p
ec
tiv
ely
.
C
o
n
s
eq
u
en
tly
,
d
4
(
d
u
t
y
cy
cle
o
f
S4
)
=1
an
d
d
3
(
d
u
t
y
cy
cle
o
f
S3
)
=0
;
th
u
s
,
d
4
an
d
d
3
as
co
n
tr
o
l
s
ig
n
als
ar
e
m
is
s
ed
.
On
ly
d
1
(
d
u
ty
cy
cle
o
f
S1
)
an
d
d
2
(
d
u
t
y
cy
cle
o
f
S2
)
ar
e
u
tili
ze
d
to
ex
tr
ac
t th
e
m
ax
i
m
u
m
p
o
wer
o
f
PV
an
d
r
eg
u
late
th
e
o
u
tp
u
t v
o
ltag
e.
Fu
r
th
er
m
o
r
e,
(
1
)
s
h
o
ws th
e
s
tate
-
s
p
ac
e
m
o
d
el
o
f
s
y
s
tem
s
.
L
1
d
i
L1
dt
=
−
r
1
i
L1
+
(
V
1
+
V
C
)
d
1
+
(
V
1
−
V
O
)
(
1
−
d
1
)
,
C
d
V
c
dt
=
(
i
L2
−
i
L1
)
(
d
1
−
d
2
)
−
i
L1
d
2
+
i
L2
(
1
-
d
2
)
L
2
d
i
L2
dt
=
−
r
2
i
L2
+
V
2
d
2
−
V
C
(
1
-
d
2
)
,
C
o
d
V
o
dt
=
i
L1
(
1
-
d
1
)
−
Vo
R
L
(1
)
T
h
e
(
1
)
is
d
r
iv
en
f
r
o
m
th
e
p
r
i
n
cip
le
o
f
th
e
v
o
ltag
e
b
alan
ce
an
d
cu
r
r
e
n
t
b
alan
ce
in
th
e
in
d
u
cto
r
an
d
ca
p
ac
ito
r
in
th
e
s
tead
y
-
s
tate,
r
esp
ec
tiv
ely
.
Mo
r
eo
v
er
,
(
1
)
r
ev
ea
ls
th
at
r
ea
ch
in
g
th
e
tr
an
s
f
er
f
u
n
ctio
n
m
atr
ix
is
im
p
o
s
s
ib
le
b
ec
au
s
e
th
e
d
u
ty
cy
cle
o
f
s
w
itch
es
is
d
ir
ec
tly
r
elate
d
to
s
t
ate
v
ar
iab
les.
T
h
e
lin
ea
r
izatio
n
tech
n
iq
u
e
at
th
e
o
p
er
atin
g
p
o
in
t
is
a
well
-
k
n
o
wn
tech
n
iq
u
e
f
o
r
s
o
lv
in
g
th
i
s
p
r
o
b
lem
.
I
n
th
is
m
eth
o
d
,
s
t
ate
v
ar
iab
les,
d
u
ty
cy
cles,
an
d
in
p
u
ts
ar
e
d
iv
id
ed
in
t
o
two
co
m
p
o
n
e
n
t
DC
v
alu
es
(
X
,
V
,
D
)
an
d
p
er
tu
r
b
atio
n
(
x
,
v
,
d
):
x
=
X
̄
+
x
̃
,
v
=
V
̄
+
v
̃
,
d
=
D
̄
+
d
̃
(
2
)
I
f
it
is
as
s
u
m
ed
th
at
th
e
p
er
tu
r
b
atio
n
is
s
m
all
an
d
d
o
es
n
o
t
s
ig
n
if
ican
tly
v
ar
y
d
u
r
in
g
t
h
e
s
witch
in
g
p
er
io
d
(
x
<
<
X
,
v
<
<
V
,
d
<
<
D
)
,
b
y
s
u
b
s
titu
tin
g
(
2
)
in
t
o
(
1
)
an
d
n
eg
lectin
g
th
e
s
ec
o
n
d
ter
m
s
,
s
m
all
-
s
ig
n
al
m
o
d
els
ar
e
r
ep
r
esen
ted
in
t
h
e
m
atr
ix
f
o
r
m
as
(
3
)
:
̃
•
=A
x
̃
+B
u
̃
̃
=C
x
̃
+Du
(
3
)
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:
2
0
8
8
-
8
694
Mo
d
elin
g
a
n
d
co
n
tr
o
l o
f a
h
yb
r
id
DC
/D
C
/AC c
o
n
ve
r
te
r
to
tr
a
n
s
fer p
o
w
er u
n
d
er
… (
A
min
A
liz
a
d
eh
A
s
l
)
1623
w
h
er
e
x
,
u
,
an
d
y
ar
e
s
tate
v
ar
iab
les
'
v
ec
to
r
,
co
n
tr
o
l
v
ar
iab
les
'
v
ec
to
r
,
an
d
th
e
o
u
tp
u
t
s
y
s
tem
,
r
esp
ec
tiv
ely
.
T
h
er
ef
o
r
e,
th
e
m
atr
i
x
f
o
r
m
o
f
th
e
s
m
all
-
s
ig
n
al
m
o
d
el
f
o
r
th
e
f
ir
s
t
mode
is
o
b
tain
e
d
as (
4
)
:
[
d
i
̃
L1
dt
d
i
̃
L2
dt
d
v
̃
c
dt
d
v
̃
o
dt
]
=
[
-
r
1
L
1
0
D
̄
1
L
1
-
1+
D
̄
1
L
1
0
-
r
2
L
2
-
1+
D
̄
2
L
2
0
-
D
̄
1
C
1
-
D
̄
2
C
00
1
-
D
̄
1
C
O
00
-
1
R
L
C
O
]
[
i
̃
L1
i
̃
L2
v
̃
c
v
̃
o
]
+
[
V
̄
O
+
V
̄
C
L
1
0
0
V
̄
2
+
V
̄
C
L
2
-
I
̄
L1
C
-
I
̄
L2
C
-
I
̄
L1
C
O
0
]
[
d
̃
1
d
̃
2
]
,
y
=
[
0100
0001
]
[
i
̃
L1
i
̃
L2
v
̃
c
v
̃
o
]
;
D
=
0
(
4
)
2
.
2
.
Seco
nd
o
pera
t
io
n m
o
de
(
Su
pp
ly
ing
t
he
lo
a
d wit
h dis
cha
r
g
ing
t
he
ba
t
t
er
y
)
In
th
is
m
o
d
e
,
th
e
m
a
x
im
u
m
p
o
wer
o
f
PV
an
d
FC
m
u
s
t
b
e
e
x
tr
ac
ted
,
an
d
th
e
b
atter
y
is
co
n
n
ec
ted
to
th
e
s
y
s
tem
to
r
eg
u
late
th
e
o
u
t
p
u
t
v
o
ltag
e.
S4
m
u
s
t
b
e
k
ep
t
t
u
r
n
ed
o
n
to
d
is
ch
ar
g
e
th
e
b
att
er
y
.
M
o
r
eo
v
er
,
th
e
p
o
wer
f
lo
w
to
th
e
b
atter
y
is
co
n
tr
o
lled
b
y
tu
r
n
in
g
o
n
an
d
tu
r
n
in
g
o
f
f
S3
.
Fu
r
th
er
m
o
r
e,
(
5
)
ex
p
r
ess
es
th
e
s
tate
-
s
p
ac
e
m
o
d
el
o
f
s
y
s
tem
s
.
L
1
d
i
L1
dt
=
-
r
1
i
L1
+
(
V
1
+
V
C
+
V
B
)
d
3
+
(
V
1
+
V
C
)
(
d
1
−
d
3
)
+
(
V
1
−
V
O
)
(
1
-
d
1
)
,
C
dV
dt
=
-
i
L1
d
2
+
(
i
L2
−
i
L1
)
(
d
1
−
d
2
)
+
i
L2
(
1
-
d
1
)
L
2
d
i
L2
dt
=
-
r
2
i
L2
+
(
V
2
+
V
B
)
d
3
+
V
2
(
d
2
−
d
3
)
-
V
C
(
1
-
d
2
)
,
C
o
d
V
o
dt
=
i
L1
(
1
-
d
1
)
−
V
o
R
L
(5
)
Similar
to
th
e
f
ir
s
t m
o
d
e,
th
e
d
y
n
am
ic
m
o
d
el
is
o
b
tain
ed
as
(
6
)
:
[
̃
L1
̃
L2
̃
̃
]
=
[
-
r
1
1
0
̄
1
1
-
1+
D
̄
1
1
0
-
r
2
2
-
1+
D
̄
2
2
0
-
D
̄
1
1
-
D
̄
2
00
1
-
D
̄
1
00
-
1
]
[
̃
L1
̃
L2
̃
̃
]
+
[
̄
+
V
̄
1
0
̄
1
0
̄
2
+
V
̄
2
̄
2
-
I
̄
L1
-
I
̄
L2
0
-
I
̄
L1
00
]
[
̃
1
̃
2
̃
3
]
,
y=
[
1000
0100
0001
]
[
̃
L1
̃
L2
̃
̃
]
;
D=0
(6
)
2
.
3
.
T
hird o
pera
t
io
n m
o
de
(
Su
pp
ly
ing
t
he
lo
a
d wit
h c
ha
rg
ing
t
he
ba
t
t
er
y
)
T
h
e
ch
a
r
g
e
p
ath
is
estab
lis
h
ed
b
y
tu
r
n
i
n
g
o
f
f
th
e
S4
,
a
n
d
t
h
e
cu
r
r
en
t
o
f
th
e
b
atter
y
is
co
n
tr
o
lled
b
y
tu
r
n
in
g
o
n
a
n
d
o
f
f
th
e
S3
.
Mo
r
eo
v
er
,
(
7
)
s
h
o
ws th
e
s
tate
-
s
p
a
ce
m
o
d
el
o
f
s
y
s
tem
s
.
L
1
d
i
L1
dt
=
-
r
1
i
L1
+
(
V
1
+
V
C
)
d
3
+
(
V
1
+
V
C
−
V
)
(
d
1
−
d
3
)
+
(
V
1
−
V
O
)
(
1
-
d
1
)
,
C
dV
dt
=
-
i
L1
d
2
+
(
i
L2
−
i
L1
)
(
d
1
−
d
2
)
+
i
L2
(
1
-
d
1
)
L
2
d
i
L2
dt
=
-
r
2
i
L2
+
V
2
d
3
+
(V
2
−
V
B
)
(
d
2
−
d
3
)
-
V
C
(
1
-
d
2
)
,
C
o
d
V
o
dt
=
i
L1
(
1
-
d
1
)
−
V
o
R
L
(7
)
Similar
to
th
e
p
r
ev
i
o
u
s
m
o
d
e
,
th
e
d
y
n
a
m
ic
m
o
d
el
is
o
b
tain
ed
as
(
8
)
:
[
d
i
̃
L1
dt
d
i
̃
L2
dt
d
v
̃
c
dt
d
v
̃
o
dt
]
=
[
−
r
1
L
1
0
D
̄
1
L
1
−
1
+
D
̄
1
L
1
0
−
r
2
L
2
−
1
+
D
̄
2
L
2
0
−
D
̄
1
C
1
-
D
̄
2
C
00
1
-
D
̄
1
C
O
00
−
1
R
L
C
O
]
[
i
̃
L1
i
̃
L2
v
̃
c
v
̃
o
]
+
[
V
̄
O
+
V
̄
C
-
V
̄
B
L
1
0
V
̄
B
L
1
0
V
̄
2
+
V
̄
C
-
V
̄
B
L
2
V
̄
B
L
2
-
I
̄
L1
C
-
I
̄
L2
C
0
-
I
̄
L1
C
O
00
]
[
d
̃
1
d
̃
2
d
̃
3
]
,
y=
[
1000
0100
0001
]
[
i
̃
L1
i
̃
L2
v
̃
c
v
̃
o
]
;
D=
0
(
8
)
3.
DE
S
I
G
NING
T
H
E
CL
O
SE
D
-
L
O
O
P
CO
NT
RO
L
L
E
R
A
ND
E
XA
M
I
N
I
NG
I
T
S P
E
R
F
O
RM
ANC
E
I
n
th
e
f
ir
s
t
m
o
d
e
,
th
e
m
ain
c
o
n
tr
o
l
o
b
jectiv
es
wer
e
s
p
ec
if
i
ed
.
I
L2
is
co
n
tr
o
lled
to
PV
w
o
r
k
in
g
at
m
ax
im
u
m
p
o
wer
,
an
d
th
e
o
u
t
p
u
t
ca
p
ac
ito
r
v
o
ltag
e
is
co
n
tr
o
lled
to
ad
ju
s
t
th
e
o
u
tp
u
t
v
o
l
tag
e.
As
ex
p
lain
ed
b
ef
o
r
e
,
i
n
th
e
f
ir
s
t
m
o
d
e,
th
e
d
u
ty
cy
cle
o
f
S3
a
n
d
S4
is
m
is
s
ed
as
co
n
tr
o
l
s
ig
n
als,
an
d
o
n
ly
d
1
a
n
d
d
2
ar
e
av
ailab
le
a
s
co
n
tr
o
l
s
ig
n
als
d
u
e
to
b
y
p
ass
in
g
th
e
b
atter
y
.
No
w
,
o
n
e
m
u
s
t
co
n
tr
o
l
s
tate
v
ar
i
ab
les
(
I
L2
,
V
O
)
with
d
1
o
r
d
2
.
I
n
m
u
ltiv
ar
iab
le
c
o
n
t
r
o
l,
co
n
tr
o
l
s
ig
n
als
f
o
r
ea
c
h
o
u
tp
u
t
(
s
tate
v
ar
ia
b
les)
ar
e
s
ele
cted
b
y
th
e
r
elativ
e
g
ain
ar
r
ay
(
R
GA
)
m
atr
ix
.
T
h
e
R
GA
i
s
a
wi
d
ely
-
u
s
ed
class
i
ca
l
m
eth
o
d
f
o
r
d
eter
m
in
in
g
th
e
b
est
in
p
u
t
-
o
u
tp
u
t
p
ar
in
g
f
o
r
th
e
m
u
ltiv
ar
iab
le
p
r
o
ce
s
s
co
n
tr
o
l sy
s
tem
.
I
n
its
g
e
n
er
al
f
o
r
m
, t
h
e
R
GA
m
atr
ix
is
d
ef
in
ed
as
(
9
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
162
0
–
163
1
1624
Λ
(
G
(
j
ω
)
)
=G
(
j
ω
)
.*
G
(
j
ω
)
-
T
(
9
)
T
h
e
R
GA
m
atr
ix
is
ca
lcu
lated
in
th
e
s
tead
y
s
tate
as:
Λ
(
G
(
0
)
)
=G
(
0
)
.*
G
-
T
(
0
)
=
(
2
.
39
−
1
.
39
−
1
.
39
2
.
39
)
(
1
0
)
Λ
(
G
(
0
)
)
=G
(
0
)
.*
G
-
T
(
0
)
=
(
2
.
1365
−
3
.
2139
2
.
0774
0
3
.
3333
−
2
.
3333
−
1
.
1365
0
.
8806
1
.
2559
)
(
1
1
)
Λ
(
G
(
0
)
)
=G
(
0
)
.*
G
-
T
(
0
)
=
(
2
.
2656
−
1
.
4350
0
.
1694
0
1
.
8224
−
0
.
8224
−
1
.
2656
0
.
6126
1
.
6530
)
(
1
2
)
(
1
0
)
,
(
1
1
)
,
an
d
(
1
2
)
ar
e
th
e
R
GA
m
atr
ix
f
o
r
th
e
f
ir
s
t,
s
ec
o
n
d
,
an
d
th
ir
d
m
o
d
es,
r
esp
ec
tiv
ely
.
T
h
e
R
GA
m
atr
ix
s
h
o
ws
th
e
d
ep
en
d
e
n
cy
o
f
th
e
co
n
tr
o
l
s
ig
n
al
to
th
e
o
u
tp
u
t.
I
n
(
1
0
)
-
(
1
2
)
,
d
iag
o
n
al
elem
en
ts
h
av
e
s
ig
n
if
ican
t
v
alu
es
co
m
p
a
r
ed
t
o
o
t
h
er
elem
e
n
ts
,
s
o
it
ca
n
b
e
c
o
n
clu
d
ed
t
h
at
,
in
(
1
0
)
,
d
1
an
d
d
2
h
av
e
th
e
m
o
s
t
im
p
ac
t
o
n
I
L2
an
d
V
O
,
r
esp
ec
tiv
ely
.
H
o
wev
er
,
b
ein
g
p
o
s
itiv
e
h
as
a
p
r
io
r
ity
to
th
e
v
alu
e
in
th
e
R
GA
m
atr
ix
.
T
h
er
ef
o
r
e,
p
air
in
g
th
e
in
p
u
t
-
o
u
t
p
u
t set is d
ef
in
e
d
as f
o
llo
w:
First m
o
d
e:
2
1
2
LO
I
d
V
d
→→
Seco
n
d
an
d
T
h
ir
d
m
o
d
es:
1
1
2
2
3
L
L
O
I
d
I
d
V
d
→
→
→
Fig
u
r
es
3
an
d
4
illu
s
tr
ate
th
e
clo
s
ed
-
lo
o
p
c
o
n
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ig
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atio
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i
n
th
e
f
ir
s
t,
s
ec
o
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d
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an
d
th
ir
d
m
o
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e.
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h
e
m
o
s
t im
p
o
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tan
t p
ar
t o
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th
e
m
u
l
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ar
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le
s
y
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is
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s
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co
u
p
lin
g
.
I
n
th
ese
s
ch
em
es,
th
e
C
P m
atr
ix
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s
p
l
ac
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to
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ec
o
u
p
le
th
e
s
y
s
tem
,
a
n
d
PI
co
n
tr
o
ller
s
u
n
d
e
r
tak
e
r
ef
er
en
ce
tr
ac
k
in
g
.
T
h
er
e
ar
e
s
ev
er
al
o
p
tio
n
s
f
o
r
d
esig
n
in
g
th
e
C
P
m
atr
ix
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b
u
t
in
g
en
er
al
f
o
r
m
,
C
P
d
ep
e
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d
s
o
n
s
y
s
tem
s
an
d
th
e
co
n
tr
o
l
o
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jectiv
e.
T
h
e
C
P
is
ch
o
s
en
as f
o
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ws f
o
r
d
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o
u
p
li
n
g
th
e
s
y
s
tem
in
th
e
s
tead
y
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tate
:
C
P=
[
(
0
)
]
-
1
(
1
3
)
Fig
u
r
e
3
.
Sch
em
e
o
f
cl
o
s
ed
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lo
o
p
f
o
r
f
ir
s
t m
o
d
e
Fig
u
r
e
4
.
T
h
e
clo
s
ed
-
lo
o
p
s
ch
em
e
f
o
r
s
ec
o
n
d
an
d
th
ir
d
m
o
d
es
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:
2
0
8
8
-
8
694
Mo
d
elin
g
a
n
d
co
n
tr
o
l o
f a
h
yb
r
id
DC
/D
C
/AC c
o
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ve
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te
r
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n
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fer p
o
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n
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er
… (
A
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a
d
eh
A
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1625
T
h
e
c
lo
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ed
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o
p
p
er
f
o
r
m
an
ce
is
s
im
u
lated
with
th
e
h
elp
o
f
MA
T
L
AB
/SIM
UL
I
NK
.
Fig
u
r
e
5
s
h
o
ws
th
e
clo
s
ed
-
lo
o
p
p
er
f
o
r
m
an
ce
i
n
th
e
f
ir
s
t
m
o
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e.
I
n
Fig
u
r
e
5
,
U
=
[
4
0
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T
is
ap
p
lied
to
t
h
e
s
y
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th
e
s
ec
o
n
d
m
o
m
en
t.
I
t
is
ex
p
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ted
t
h
at
Y
1
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d
Y
2
s
h
o
u
ld
h
av
e
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al
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e
d
u
e
t
o
th
e
in
h
er
en
t
c
o
u
p
lin
g
in
m
u
lti
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in
p
u
t
s
y
s
tem
s
.
T
h
e
C
P
m
atr
ix
m
ak
es
th
e
s
y
s
t
em
d
ec
o
u
p
le
in
t
h
e
s
tead
y
s
tate,
an
d
th
e
PI
co
n
tr
o
ller
ca
u
s
es
r
ef
er
en
ce
tr
ac
k
i
n
g
to
o
cc
u
r
.
T
h
e
ac
cu
r
ate
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
n
tr
o
ller
is
ev
i
d
en
t
b
ec
a
u
s
e
it
m
a
n
ag
ed
to
el
im
in
ate
th
e
i
n
tr
in
s
ic
co
u
p
lin
g
i
n
th
e
s
y
s
tem
,
an
d
r
e
f
er
en
ce
tr
ac
k
i
n
g
h
a
p
p
en
e
d
s
im
u
ltan
eo
u
s
ly
.
All
th
ese
f
ea
tu
r
es
ar
e
ac
h
iev
ed
b
y
a
s
im
p
le
C
P
m
atr
ix
an
d
d
iag
o
n
al
PI
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n
tr
o
ller
.
Fig
u
r
es
6
an
d
7
d
em
o
n
s
tr
ate
clo
s
ed
-
l
o
o
p
p
er
f
o
r
m
an
ce
in
th
e
s
ec
o
n
d
an
d
th
ir
d
m
o
d
es.
Similar
to
th
e
f
ir
s
t m
o
d
e,
g
o
o
d
p
er
f
o
r
m
an
ce
h
as b
ee
n
ac
h
iev
ed
.
Fig
u
r
e
5
.
C
lo
s
ed
-
lo
o
p
p
e
r
f
o
r
m
an
ce
in
th
e
f
i
r
s
t m
o
d
e
Fig
u
r
e
6
.
C
lo
s
ed
-
lo
o
p
p
e
r
f
o
r
m
an
ce
in
th
e
s
ec
o
n
d
mode
Fig
u
r
e
7
.
C
lo
s
ed
-
lo
o
p
p
e
r
f
o
r
m
an
ce
in
th
e
th
ir
d
m
o
d
e
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
clo
s
ed
-
lo
o
p
c
o
n
tr
o
ller
w
as
d
esig
n
ed
in
p
r
ev
io
u
s
s
ec
tio
n
s
.
I
n
th
is
s
ec
tio
n
,
th
e
h
y
b
r
id
DC
-
D
C
co
n
v
er
ter
is
co
n
n
ec
ted
to
a
th
r
ee
-
p
h
ase
in
v
er
ter
to
tr
an
s
f
e
r
th
e
p
o
wer
o
f
PV,
FC
,
an
d
b
atter
y
to
th
e
g
r
id
.
All
m
o
d
es
ar
e
s
im
u
lated
b
y
M
AT
L
AB
/
Simu
lin
k
.
Fig
u
r
es
8
an
d
9
d
is
p
lay
PV
an
d
FC
ch
ar
ac
ter
is
tics
,
r
esp
ec
tiv
ely
.
T
h
e
r
ea
d
y
b
lo
ck
o
f
PEM
FC
is
a
p
r
eset
m
o
d
el
f
o
r
f
u
el
ce
lls
in
MA
T
L
AB
/
Simu
lin
k
a
n
d
h
as
b
ee
n
em
p
lo
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ed
in
th
is
p
ap
e
r
.
T
h
e
s
im
u
latio
n
co
n
s
is
ts
o
f
th
r
ee
m
o
d
es.
I
n
th
e
f
ir
s
t
m
o
d
e,
t
h
e
s
u
n
ir
r
ad
iatio
n
o
f
PV
is
S=
5
0
0
W
/m
2
,
an
d
u
n
d
er
th
is
c
o
n
d
itio
n
,
th
e
m
ax
im
u
m
g
en
e
r
atio
n
p
o
wer
o
f
PV
is
ab
o
u
t
1
0
8
0
0
W
,
an
d
i
t
o
cc
u
r
s
at
3
0
0
V.
Mo
r
eo
v
er
,
in
th
is
m
o
d
e,
th
e
m
ax
im
u
m
p
o
we
r
o
f
FC
eq
u
als
8
3
2
5
W
,
an
d
it
h
ap
p
en
s
at
ar
o
u
n
d
2
2
5
A.
T
h
e
b
atter
y
is
b
y
p
ass
ed
in
th
is
m
o
d
e,
an
d
th
e
to
t
al
g
en
e
r
atio
n
a
n
d
tr
an
s
m
is
s
io
n
p
o
wer
s
ar
e
ass
u
m
ed
to
b
e
eq
u
al
(
1
0
8
0
0
+8
3
2
5
=
1
9
1
2
5
W
)
.
I
n
th
e
s
ec
o
n
d
m
o
d
e,
t
h
e
s
u
n
i
r
r
ad
iatio
n
o
f
PV
is
S=6
0
0
W
/m
2
,
an
d
th
e
m
ax
im
u
m
p
o
wer
u
n
d
er
th
is
ir
r
ad
iatio
n
is
1
2
9
5
0
W
an
d
ta
k
es
p
lace
at
3
0
0
V.
FC
h
as
6
0
0
0
W
in
t
h
e
s
ec
o
n
d
m
o
d
e,
a
n
d
u
n
d
er
t
h
is
p
o
wer
,
FC
ca
n
g
iv
e
n
ea
r
ly
1
3
3
A.
T
h
e
s
u
m
m
atio
n
o
f
p
o
wer
s
f
r
o
m
b
o
th
s
o
u
r
ce
s
eq
u
als
1
2
9
5
0
+6
0
0
0
=1
8
9
5
0
W
;
th
er
ef
o
r
e,
in
co
m
p
ar
i
s
o
n
to
t
h
e
f
ir
s
t
m
o
d
e
,
th
e
to
tal
g
en
e
r
atio
n
p
o
wer
h
as
d
ec
r
ea
s
ed
.
C
o
n
s
eq
u
en
tly
,
th
e
b
atter
y
m
u
s
t b
e
a
d
d
ed
to
th
e
s
y
s
tem
to
r
eso
lv
e
th
e
lack
o
f
p
o
wer
an
d
co
n
v
er
ter
lo
s
s
es
.
I
n
th
e
th
ir
d
m
o
d
e,
th
e
ir
r
ad
iat
io
n
o
f
PV
is
S=
750
W
/m
2
,
th
e
m
ax
im
u
m
p
o
wer
o
f
PV
r
ea
ch
es
ab
o
u
t
1
6
1
0
2
W
,
a
n
d
th
e
v
o
ltag
e
o
f
P
V
is
clo
s
e
to
2
8
5
V.
T
h
e
p
o
wer
o
f
FC
is
ap
p
r
o
x
im
ately
4
2
8
4
W
,
an
d
u
n
d
er
th
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
162
0
–
163
1
1626
p
o
wer
,
FC
ca
n
g
iv
e
8
6
A.
T
h
e
to
tal
g
e
n
er
atio
n
p
o
wer
f
r
o
m
b
o
th
s
o
u
r
ce
s
eq
u
als
1
6
1
0
2
+4
2
8
4
=
2
0
3
8
6
W
,
wh
ich
is
lar
g
er
th
an
th
e
d
em
an
d
ed
p
o
wer
f
o
r
tr
an
s
f
e
r
r
in
g
.
As
a
r
esu
lt,
th
e
b
atter
y
m
u
s
t
b
e
ch
ar
g
ed
to
s
av
e
s
u
r
p
lu
s
en
er
g
y
in
th
e
t
h
ir
d
m
o
d
e.
T
h
e
s
tate
v
ar
iab
les
o
f
th
e
h
y
b
r
id
DC
-
DC
co
n
v
er
ter
ar
e
co
n
tr
o
llab
le.
Hen
ce
,
I
L1
,
I
L2
,
an
d
V
O
m
u
s
t
b
e
co
n
tr
o
lled
to
e
x
tr
ac
t
th
e
m
ax
i
m
u
m
p
o
wer
o
f
r
eso
u
r
ce
s
b
esid
e
s
r
eg
u
latin
g
th
e
DC
-
lin
k
v
o
ltag
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
er
ter
d
ep
e
n
d
s
o
n
t
h
e
DC
-
lin
k
v
o
ltag
e
.
T
h
e
r
ef
o
r
e,
th
e
in
v
er
te
r
d
o
es
n
o
t
n
ee
d
to
b
e
co
n
tr
o
lled
in
a
co
n
v
en
tio
n
al
way
s
u
ch
as
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
.
Fu
r
th
e
r
m
o
r
e
,
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
er
ter
ca
n
b
e
co
n
tr
o
lled
b
y
ch
an
g
in
g
th
e
DC
-
lin
k
v
o
ltag
e
(
V
an
=2
V
dc
/π)
.
T
h
e
o
n
ly
p
ar
a
m
eter
th
at
m
u
s
t
b
e
co
n
tr
o
lled
in
th
e
in
v
er
te
r
is
th
e
p
h
ase
d
i
f
f
er
en
ce
.
I
n
all
th
r
e
e
m
o
d
es,
t
h
e
in
v
er
ter
m
u
s
t
b
e
ab
le
to
p
r
o
d
u
ce
a
+9
0
o
p
h
ase
d
if
f
er
en
ce
(
90
o
=
)
;
in
th
is
ca
s
e,
m
ax
im
u
m
ac
tiv
e
p
o
w
er
is
tr
an
s
f
er
r
ed
f
r
o
m
th
e
DC
s
id
e
to
th
e
AC
s
id
e.
Fig
u
r
e
8
.
PV c
h
ar
ac
te
r
is
tics
Fig
u
r
e
9
.
Fu
el
ce
ll c
h
a
r
ac
ter
is
tics
A
6
-
s
s
im
u
latio
n
with
th
r
ee
p
o
wer
m
a
n
ag
em
e
n
t
s
tr
ateg
ie
s
is
p
r
o
v
id
e
d
to
ev
alu
ate
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
y
s
tem
in
ea
ch
o
p
er
ati
o
n
m
o
d
e.
Fig
u
r
e
1
0
a
n
d
Fig
u
r
e
1
1
d
e
p
ict
th
e
d
u
t
y
c
y
cles
o
f
S1
,
S2
,
S3
,
a
n
d
S4
,
r
esp
ec
tiv
ely
,
an
d
s
h
o
w
th
e
co
n
tr
o
l
s
ig
n
als
th
at
v
a
r
y
t
o
e
x
tr
ac
t
th
e
m
a
x
im
u
m
p
o
wer
o
f
r
e
s
o
u
r
ce
s
.
Fig
u
r
e
1
2
r
ep
r
esen
ts
th
e
h
y
b
r
id
DC
-
DC
co
n
v
e
r
ter
o
u
tp
u
ts
.
T
h
e
m
o
s
t
im
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I
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I
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1
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.
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5
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is
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r
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1
5
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a)
an
d
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r
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1
5
(
b
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12
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3
φ
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1
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2
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=
1
0
0
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64
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12
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3
φ
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th
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h
an
d
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FF
T
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ase
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b
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t a
n
d
v
o
ltag
e:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
162
0
–
163
1
1628
S
in
v
(
3
φ
)
=
3
2
V
I
∗
V
=
300
.
3
∠
+
9
0
o
I
=
120
∠
18
.
4
o
→
S
in
v
(
3
φ
)
=
3
2
×
(
300
.
3
)
×
(
120
)
∠
9
0
o
−
(
180
+
18
.
4
)
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S
in
v
(
3
φ
)
=
−
17063
−
j51290
.
5
P
12
co
n
f
ir
m
s
S
inv
,
wh
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m
ea
n
s
th
at
th
e
in
v
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ter
tr
an
s
f
er
s
1
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0
6
3
W
o
f
ac
tiv
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p
o
we
r
to
t
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r
id
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n
ly
a
6
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d
if
f
er
en
ce
b
etwe
en
S
inv
an
d
P
12
is
o
r
ig
in
ated
f
r
o
m
n
u
m
er
ical
er
r
o
r
s
,
wh
ich
is
ac
ce
p
ta
b
le
in
th
is
r
an
g
e
o
f
p
o
wer
.
(
a)
(
a)
(
b
)
(
b
)
Fig
u
r
e
1
5
.
FF
T
an
aly
s
is
o
f
V
an
in
th
e
f
ir
s
t m
o
d
e
,
(
a)
in
v
er
te
r
o
u
t
p
u
t
v
o
ltag
e;
(
b
)
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t a
m
p
litu
d
e
Fig
u
r
e
1
6
.
FF
T
an
aly
s
is
o
f
I
an
in
th
e
f
ir
s
t m
o
d
e
,
(
a)
in
v
er
te
r
o
u
t
p
u
t c
u
r
r
en
t; (
b
)
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t a
m
p
litu
d
e
Seco
n
d
-
m
o
d
e
s
im
u
latio
n
2
≤
≤
4
;
Fi
g
u
r
e
1
7
(
a
)
an
d
Fig
u
r
e
1
7
(
b
)
p
r
esen
ts
an
FF
T
a
n
aly
s
is
o
f
V
an
.
I
t
v
er
if
ies
th
at
th
e
in
v
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te
r
p
r
o
d
u
ce
s
a
+9
0
o
p
h
ase
d
i
f
f
er
en
ce
.
Similar
to
th
e
f
i
r
s
t
m
o
d
e
,
Fig
u
r
e
1
8
(
a)
a
n
d
Fig
u
r
e
1
8
(
b
)
s
h
o
ws th
e
FF
T
an
aly
s
is
o
f
th
e
cu
r
r
en
t o
f
in
v
er
t
er
(
I
an
).
12
(
3
)
=
3
2
1
2
1
=
325
.
3
∠
+
9
0
2
=
100
∠
0
=
2
.
64
→
12
(
3
)
=
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.
4
S
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n
b
e
ca
lcu
lated
f
r
o
m
th
e
FF
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in
th
e
s
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n
d
m
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co
r
d
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g
t
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u
r
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1
7
a
n
d
Fig
u
r
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1
8
:
S
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v
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3
φ
)
=
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2
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I
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=
325
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3
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0
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an
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1
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1
o
→
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v
(
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φ
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3
×
129
.
1
∠
−
107
.
1
o
S
in
v
(
3
φ
)
=
−
18523
−
j60209
.
56
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:
2
0
8
8
-
8
694
Mo
d
elin
g
a
n
d
co
n
tr
o
l o
f a
h
yb
r
id
DC
/D
C
/AC c
o
n
ve
r
te
r
to
tr
a
n
s
fer p
o
w
er u
n
d
er
… (
A
min
A
liz
a
d
eh
A
s
l
)
1629
S
inv
an
d
P
12
co
n
f
ir
m
ea
ch
o
t
h
er
well.
A
3
2
W
d
if
f
er
e
n
ce
is
o
r
ig
in
ated
f
r
o
m
n
u
m
er
ic
al
er
r
o
r
s
,
w
h
ich
is
ac
ce
p
tab
le
in
th
is
r
an
g
e
o
f
p
o
wer
.
I
n
all
th
e
e
q
u
atio
n
s
,
V
1
=V
an
(
th
e
in
v
e
r
ter
v
o
ltag
e
)
an
d
V
2
=V
gird
.
(
a)
(
a)
(
b
)
(
b
)
Fig
u
r
e
1
7
.
FF
T
an
aly
s
is
o
f
V
an
in
th
e
s
ec
o
n
d
m
o
d
e
,
(
a)
in
v
er
te
r
o
u
t
p
u
t v
o
ltag
e;
(
b
)
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t a
m
p
litu
d
e
Fig
u
r
e
1
8
.
FF
T
an
aly
s
is
o
f
I
an
in
th
e
s
ec
o
n
d
m
o
d
e
,
(
a)
in
v
er
te
r
o
u
t
p
u
t c
u
r
r
en
t; (
b
)
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t a
m
p
litu
d
e
T
h
ir
d
-
m
o
d
e
s
im
u
latio
n
46
t
;
Fig
u
r
e
1
9
in
d
icate
s
th
e
p
o
wer
o
f
t
h
e
b
atter
y
in
th
r
ee
m
o
d
es.
Similar
to
th
e
f
ir
s
t
an
d
s
ec
o
n
d
m
o
d
es
Fig
u
r
e
s
20
(
a)
,
(
b
)
a
n
d
Fig
u
r
e
s
21
(
a
)
,
(
b
)
d
e
p
ict
th
e
FF
T
an
aly
s
is
in
th
e
th
ir
d
m
o
d
e
.
Fig
u
r
e
2
0
p
r
o
v
es th
at
th
e
in
v
e
r
ter
cr
ea
tes a
+9
0
o
p
h
ase
d
if
f
e
r
en
ce
.
Fro
m
FF
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aly
s
is
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inv
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d
P
12
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atch
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ch
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t
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er
.
1
3
1
4
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3
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0
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1
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0
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1
2
(
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)
1
2
(
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2
.
6
4
3
s
in
1
7
8
6
5
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XL
L
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P
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X
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+
=
=
=
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→
=
3
1
4
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3
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0
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2
5
1
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7
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(
3
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2
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6
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(
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(
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3
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5
10
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7
2
S
17
91
7.
05
56
14
1.
53
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L
V
a
n
ia
n
v
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o
v
v
VI
j
=
+
=
=
=
⎯
⎯
⎯
⎯
⎯
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⎯
⎯
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