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NT
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D
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T
h
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ex
p
an
d
in
g
d
ep
lo
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en
t
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tr
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icles
an
d
s
u
s
tain
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en
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m
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o
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(
L
iFePO₄)
b
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h
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m
e
p
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m
in
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n
t
ch
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s
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p
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r
f
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m
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n
d
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life
r
elativ
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to
alter
n
ativ
e
lith
iu
m
-
io
n
c
h
em
is
tr
ies
[
1
]
,
[
2
]
.
E
v
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n
s
o
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ch
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tly
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d
s
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f
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t
y
[
3
]
-
[
5
]
.
C
o
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v
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l
C
C
-
C
V
s
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h
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l
o
a
d
b
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h
a
v
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o
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s
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d
t
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p
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e
,
v
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r
r
o
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s
,
o
s
c
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la
t
o
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y
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h
a
v
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o
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s
a
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f
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ct
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t
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s
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ti
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f
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C
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p
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.
DC
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DC
co
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ter
s
,
p
ar
ticu
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ly
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u
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c
o
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v
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ter
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,
ar
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ess
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tial
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atter
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ch
a
r
g
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b
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ca
u
s
e
th
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u
late
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tp
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ac
co
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d
in
g
to
b
atter
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r
e
q
u
ir
em
en
ts
[
6
]
-
[
9
]
.
T
o
im
p
r
o
v
e
co
n
v
er
ter
c
o
n
tr
o
l
p
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f
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ce
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in
tellig
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t
c
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tr
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l
m
eth
o
d
s
s
u
ch
as
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
(
FLCs
)
h
av
e
b
ee
n
wid
ely
in
v
esti
g
ated
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
C
o
mb
in
a
tio
n
w
h
a
le
o
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timiz
a
tio
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lg
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r
ith
m
a
n
d
f
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tima
l
…
(
I
n
d
h
a
n
a
S
u
d
ih
a
r
to
)
1995
FLCs
ar
e
s
u
itab
le
f
o
r
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o
n
lin
e
ar
s
y
s
tem
s
an
d
u
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ce
r
tain
o
p
e
r
atin
g
co
n
d
itio
n
s
b
ec
a
u
s
e
th
ey
d
o
n
o
t
r
e
q
u
ir
e
an
ex
ac
t
m
ath
em
atica
l
m
o
d
el
o
f
th
e
p
la
n
t
[
1
0
]
-
[
1
3
]
.
Sev
er
al
f
u
zz
y
-
b
ased
ch
ar
g
in
g
ap
p
r
o
ac
h
es
h
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e
also
b
ee
n
r
ep
o
r
ted
f
o
r
lith
iu
m
b
atter
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ap
p
licatio
n
s
[
1
1
]
,
[
1
4
]
.
Desp
ite
th
ese
ad
v
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tag
es,
FLC
p
er
f
o
r
m
an
ce
s
tr
o
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ly
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em
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er
s
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ip
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e
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le
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ase,
an
d
s
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lin
g
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ac
to
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s
,
wh
ich
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e
co
m
m
o
n
ly
estab
lis
h
ed
u
s
in
g
ex
p
er
t j
u
d
g
m
en
t o
r
iter
ativ
e
t
r
ial
-
an
d
-
e
r
r
o
r
m
eth
o
d
s
d
u
r
in
g
co
n
t
r
o
ller
d
e
v
elo
p
m
en
t stag
es.
T
o
r
e
d
u
c
e
t
h
i
s
d
e
p
e
n
d
e
n
c
e
o
n
m
a
n
u
a
l
t
u
n
i
n
g
,
m
e
t
a
h
e
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r
is
t
i
c
o
p
t
i
m
i
z
at
i
o
n
a
l
g
o
r
it
h
m
s
h
a
v
e
b
e
e
n
i
n
t
r
o
d
u
c
e
d
t
o
d
e
t
e
r
m
i
n
e
c
o
n
t
r
o
l
l
e
r
p
a
r
a
m
e
te
r
s
a
u
t
o
m
a
t
i
ca
l
l
y
.
I
n
s
p
i
r
e
d
b
y
h
u
m
p
b
a
c
k
w
h
a
l
es
’
b
u
b
b
l
e
-
n
e
t
f
e
e
d
i
n
g
s
t
r
a
t
e
g
y
,
t
h
e
w
h
a
l
e
o
p
t
i
m
i
za
t
i
o
n
a
l
g
o
r
i
t
h
m
(
W
OA
)
h
as
g
ai
n
e
d
c
o
n
s
i
d
e
r
a
b
le
i
n
t
e
r
e
s
t
o
wi
n
g
t
o
i
ts
s
t
r
ai
g
h
t
f
o
r
w
a
r
d
a
r
c
h
i
t
e
c
t
u
r
e
a
n
d
e
f
f
e
c
t
i
v
e
g
l
o
b
al
e
x
p
l
o
r
a
t
i
o
n
c
a
p
a
b
i
l
i
t
y
i
n
o
p
t
im
i
z
a
t
i
o
n
p
r
o
b
l
e
m
s
[
1
5
]
-
[
1
8
]
.
P
r
e
v
i
o
u
s
s
t
u
d
i
es
h
a
v
e
s
h
o
w
n
t
h
a
t
W
O
A
c
a
n
i
m
p
r
o
v
e
t
h
e
t
u
n
i
n
g
o
f
c
o
n
t
r
o
l
s
t
r
a
t
e
g
i
es
i
n
p
o
w
e
r
-
e
l
e
c
t
r
o
n
i
c
a
n
d
m
o
t
o
r
-
d
r
i
v
e
a
p
p
l
i
c
a
t
i
o
n
s
[
1
9
]
-
[
2
1
]
.
H
o
w
e
v
e
r
,
t
h
e
u
s
e
o
f
W
O
A
t
o
o
p
t
i
m
i
ze
f
u
z
z
y
-
c
o
n
t
r
o
l
p
a
r
a
m
e
t
e
r
s
f
o
r
L
i
F
eP
O
₄
b
a
t
te
r
y
c
h
a
r
g
i
n
g
w
i
t
h
a
b
u
c
k
c
o
n
v
e
r
t
e
r
u
n
d
e
r
t
h
e
C
C
-
C
V
c
h
a
r
g
i
n
g
p
r
o
f
i
l
e
i
s
s
ti
l
l
l
i
m
ite
d
a
n
d
r
e
q
u
i
r
e
s
f
u
r
t
h
e
r
i
n
v
e
s
t
i
g
a
t
i
o
n
.
B
ased
o
n
th
is
g
ap
,
th
is
r
esear
ch
p
r
o
p
o
s
es
a
h
y
b
r
i
d
W
OA
-
f
u
zz
y
c
o
n
tr
o
l
s
tr
ateg
y
f
o
r
an
o
p
tim
ized
L
iFePO₄
b
atter
y
-
ch
ar
g
in
g
s
y
s
tem
.
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
W
OA
i
s
u
s
ed
to
o
p
tim
ize
th
e
s
ca
lin
g
f
ac
to
r
s
o
f
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
s
o
th
at
th
e
b
u
ck
c
o
n
v
e
r
ter
ca
n
r
eg
u
la
te
ch
ar
g
in
g
v
o
ltag
e
a
n
d
c
u
r
r
e
n
t
m
o
r
e
ac
c
u
r
ately
d
u
r
in
g
C
C
-
C
V
o
p
er
atio
n
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
em
e
is
ev
alu
ated
u
s
in
g
PS
I
M
s
im
u
latio
n
s
an
d
co
m
p
ar
e
d
with
f
u
zz
y
,
PI,
a
n
d
W
OA
-
PI
c
o
n
tr
o
l m
eth
o
d
s
u
n
d
er
s
ev
er
al
SOC
co
n
d
itio
n
s
r
an
g
in
g
f
r
o
m
3
0
% to
9
7
%.
T
h
is
s
t
u
d
y
p
r
o
v
i
d
es
th
r
ee
p
r
in
cip
al
co
n
t
r
i
b
u
ti
o
n
s
:
f
i
r
s
t,
it
f
o
r
m
u
lat
es
a
f
u
zz
y
co
n
t
r
o
ll
er
o
p
t
im
i
ze
d
b
y
W
OA
f
o
r
c
h
a
r
g
i
n
g
L
iF
ePO₄
b
atte
r
i
es;
s
e
co
n
d
,
i
t
in
c
o
r
p
o
r
ate
s
t
h
e
d
e
v
el
o
p
e
d
c
o
n
t
r
o
lle
r
i
n
t
o
a
b
u
ck
-
c
o
n
v
e
r
te
r
-
b
as
ed
C
C
-
C
V
ch
ar
g
i
n
g
a
r
c
h
it
ec
t
u
r
e;
a
n
d
t
h
ir
d
,
it
ass
ess
es
th
e
p
r
o
p
o
s
e
d
a
p
p
r
o
a
c
h
r
e
g
ar
d
in
g
o
u
t
p
u
t
-
v
o
l
ta
g
e
p
r
ec
is
i
o
n
,
tr
an
s
ie
n
t
b
eh
a
v
i
o
r
,
a
n
d
o
p
er
ati
o
n
al
s
t
ab
ilit
y
u
n
d
e
r
v
a
r
y
i
n
g
SOC
c
o
n
d
iti
o
n
s
.
T
h
es
e
f
i
n
d
in
g
s
a
r
e
an
t
ici
p
ate
d
t
o
f
a
cil
itat
e
t
h
e
d
esi
g
n
o
f
i
n
cr
ea
s
i
n
g
l
y
a
d
ap
ti
v
e
an
d
d
e
p
e
n
d
a
b
l
e
b
at
te
r
y
-
ch
ar
g
i
n
g
s
y
s
te
m
s
f
o
r
ele
ct
r
ic
-
v
e
h
i
cle
a
n
d
e
n
e
r
g
y
-
s
t
o
r
a
g
e
a
p
p
lica
ti
o
n
s
i
n
b
o
th
ac
a
d
e
m
ic
r
ese
ar
ch
a
n
d
p
r
a
cti
ca
l
i
n
d
u
s
tr
i
al
d
e
p
l
o
y
m
en
t
c
o
n
te
x
ts
.
2.
P
RO
P
O
SE
D
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
r
es
ea
r
ch
d
esig
n
,
m
ater
ials
an
d
d
ata
s
o
u
r
ce
s
,
im
p
lem
en
tatio
n
p
r
o
ce
d
u
r
e,
co
n
tr
o
l
alg
o
r
ith
m
s
,
an
d
v
alid
a
tio
n
s
tr
ateg
y
u
s
ed
t
o
d
ev
el
o
p
th
e
p
r
o
p
o
s
ed
L
iFePO4
b
atter
y
ch
ar
g
i
n
g
s
y
s
tem
.
T
h
e
m
eth
o
d
is
ar
r
an
g
ed
t
o
s
u
p
p
o
r
t
r
e
p
r
o
d
u
cib
ilit
y
an
d
to
d
ir
ec
tly
ad
d
r
ess
th
e
n
ee
d
f
o
r
a
n
ad
ap
tiv
e
C
C
-
C
V
ch
ar
g
in
g
co
n
tr
o
ller
id
en
tifie
d
in
th
e
I
n
t
r
o
d
u
ctio
n
s
ec
tio
n
.
2
.
1
.
Resea
rc
h desi
g
n/a
pp
ro
a
ch
T
h
is
r
esear
ch
em
p
lo
y
ed
a
s
im
u
latio
n
-
b
ased
e
x
p
er
im
e
n
tal
d
e
s
ig
n
.
A
b
u
c
k
co
n
v
er
te
r
-
b
ased
c
h
ar
g
er
was
m
o
d
eled
an
d
co
n
tr
o
lled
u
s
in
g
f
o
u
r
co
n
tr
o
l
ap
p
r
o
ac
h
es,
n
a
m
ely
f
u
zz
y
,
PI
,
W
OA
-
PI,
an
d
W
OA
-
f
u
zz
y
.
T
h
is
d
esig
n
was
s
elec
ted
b
ec
au
s
e
it
allo
ws
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
to
b
e
test
ed
u
n
d
er
r
ep
ea
ta
b
le
o
p
er
atin
g
c
o
n
d
itio
n
s
,
d
if
f
er
en
t
s
tate
-
of
-
ch
a
r
g
e
(
SOC
)
lev
els,
an
d
id
e
n
tical
c
o
n
v
er
ter
p
ar
a
m
eter
s
b
ef
o
r
e
p
r
ac
tical
h
ar
d
war
e
im
p
lem
en
tatio
n
.
2
.
2
.
Sy
s
t
e
m
a
rc
hite
ct
ure
a
n
d m
a
t
er
ia
ls
Fig
u
r
e
1
illu
s
tr
ates
th
e
co
m
p
lete
co
n
f
ig
u
r
atio
n
o
f
th
e
d
ev
elo
p
ed
b
atter
y
-
ch
ar
g
in
g
s
y
s
tem
.
T
h
e
2
2
0
VAC
in
p
u
t
is
co
n
v
er
ted
in
to
DC
v
o
ltag
e
u
s
in
g
an
SMPS
an
d
s
u
p
p
lied
t
o
th
e
b
u
ck
c
o
n
v
er
ter
,
w
h
ich
is
th
e
m
ain
p
o
wer
s
tag
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
an
d
c
u
r
r
e
n
t
ar
e
m
ea
s
u
r
ed
u
s
in
g
v
o
ltag
e
an
d
cu
r
r
en
t
s
en
s
o
r
s
,
th
en
f
ed
b
ac
k
to
th
e
STM
3
2
F4
m
icr
o
c
o
n
tr
o
ller
.
A
PW
M
d
u
ty
r
atio
is
p
r
o
d
u
ce
d
b
y
th
e
co
n
tr
o
ller
to
ad
ju
s
t
co
n
v
er
ter
o
u
tp
u
t a
cc
o
r
d
in
g
to
th
e
L
iFePO₄ b
atter
y
’
s
C
C
-
C
V
ch
ar
g
in
g
s
p
ec
if
icatio
n
s
d
u
r
in
g
o
p
er
atio
n
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
c
o
n
tr
o
ller
ch
ar
g
e
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
:
1994
-
2
0
0
3
1996
2
.
3
.
B
uck
c
o
nv
er
t
er
m
o
dellin
g
T
h
e
b
u
ck
co
n
v
er
ter
r
ed
u
ce
s
th
e
s
u
p
p
lied
DC
v
o
ltag
e
to
th
e
l
ev
el
n
ee
d
e
d
f
o
r
b
atter
y
ch
a
r
g
i
n
g
.
PW
M
s
witch
in
g
g
o
v
er
n
s
co
n
v
er
ter
o
p
er
atio
n
,
wh
ile
its
d
u
ty
r
atio
estab
lis
h
es
th
e
r
elatio
n
s
h
ip
am
o
n
g
in
p
u
t
v
o
ltag
e
,
o
u
tp
u
t v
o
ltag
e,
in
d
u
cto
r
c
u
r
r
e
n
t,
an
d
th
e
r
esu
lti
n
g
r
ip
p
le
ac
r
o
s
s
th
e
ca
p
ac
ito
r
.
B
y
ap
p
ly
in
g
Kir
ch
h
o
f
f
'
s
v
o
ltag
e
law
(
KVL
)
,
th
e
co
n
v
e
r
ter
d
esi
g
n
eq
u
atio
n
s
wer
e
d
er
iv
e
d
,
an
d
th
e
cir
cu
it
to
p
o
l
o
g
y
u
s
ed
in
th
i
s
r
esear
ch
is
s
h
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
B
u
ck
c
o
n
v
e
r
ter
cir
cu
it to
p
o
lo
g
y
T
h
e
(
1
)
-
(
5
)
wer
e
u
s
ed
to
ca
lcu
l
ate
th
e
m
ain
co
n
v
er
ter
p
a
r
am
et
er
s
,
in
clu
d
in
g
d
u
t
y
cy
cle,
in
d
u
cto
r
v
alu
e,
ca
p
ac
ito
r
v
alu
e,
a
n
d
o
u
tp
u
t
c
h
a
r
ac
ter
is
tics
.
T
h
e
d
esig
n
p
ar
am
eter
s
wer
e
s
elec
ted
b
ased
o
n
th
e
r
eq
u
ir
ed
c
h
ar
g
i
n
g
v
o
ltag
e
an
d
cu
r
r
en
t,
as su
m
m
a
r
ized
in
T
ab
le
1.
D
=
V
out
V
in
(
1
)
∆
i
L
=
2
0
% ×
i
L
(
a
vg)
(
2
)
L
=
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5
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W
h
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e
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Vs
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th
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V)
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t
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g
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(
V)
;
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is
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d
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ty
c
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cle
(
%)
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f
r
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q
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m
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r
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A
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ip
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n
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2
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esti
m
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ely
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ay
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ce
d
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r
all
ac
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r
ac
y
[
2
2
]
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Simu
latio
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ata
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en
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f
r
o
m
th
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PS
I
M
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tp
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esp
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in
cl
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SOC
,
s
tead
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-
s
tate
v
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a
n
d
s
ettlin
g
tim
e.
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
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le
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if
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et
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d
co
m
b
i
n
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a
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
with
th
e
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
.
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h
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FLC
u
s
ed
ca
n
h
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d
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th
e
n
o
n
lin
ea
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ity
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f
th
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ter
a
n
d
b
atter
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with
o
u
t
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eq
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ir
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n
g
a
m
ath
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atica
l
m
o
d
el.
Ho
wev
er
,
FLC p
er
f
o
r
m
an
ce
d
ep
en
d
s
o
n
t
h
e
s
elec
tio
n
o
f
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
,
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u
le
b
ase,
an
d
s
ca
lin
g
f
ac
to
r
s
.
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h
er
ef
o
r
e,
W
OA
is
ap
p
lied
to
o
p
tim
ize
th
e
FLC p
ar
am
eter
s
an
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r
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ce
th
e
d
ep
en
d
en
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o
n
m
an
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al
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n
in
g
.
2
.
5
.
1
.
WO
A
a
lg
o
ri
t
hm
Dev
elo
p
ed
b
y
T
o
m
aszewsk
a
et
a
l.
[
2
3
]
,
t
h
e
wh
ale
o
p
tim
i
za
tio
n
alg
o
r
ith
m
is
a
p
o
p
u
lat
io
n
-
d
r
i
v
en
m
etah
eu
r
is
tic
tech
n
iq
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e
d
er
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ed
f
r
o
m
th
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b
u
b
b
le
-
n
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f
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r
ag
i
n
g
s
tr
ateg
y
o
f
h
u
m
p
b
ac
k
wh
a
les,
as
d
ep
icted
in
Fig
u
r
e
3
.
W
ith
in
th
is
s
tu
d
y
,
each
wh
ale
d
en
o
tes
o
n
e
p
o
s
s
ib
le
co
m
b
in
atio
n
o
f
co
n
tr
o
lle
r
p
ar
am
eter
s
.
E
ac
h
s
o
lu
tio
n
ca
n
d
id
ate
is
ass
ess
ed
ac
co
r
d
in
g
to
th
e
ch
a
r
g
er
’
s
v
o
ltag
e
-
tr
ac
k
in
g
ca
p
ab
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,
ai
m
in
g
to
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e
d
u
ce
th
e
d
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iatio
n
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etwe
en
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e
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im
u
lat
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ter
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u
tp
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t
v
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an
d
th
e
s
p
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if
ied
r
e
f
er
en
ce
le
v
el
o
f
7
3
V.
T
h
e
p
r
in
cip
al
W
OA
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ett
in
g
s
c
o
n
s
id
er
ed
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er
e
f
o
r
th
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im
p
lem
en
tatio
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co
m
p
r
is
e
th
e
p
o
p
u
l
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n
co
u
n
t,
iter
atio
n
lim
it,
an
d
s
to
p
p
in
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c
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.
A
p
o
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u
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n
o
f
1
0
0
w
h
ales
is
ad
o
p
ted
,
as
f
o
r
m
u
lated
in
(
7
)
,
wh
er
ea
s
th
e
m
ax
im
u
m
iter
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n
co
u
n
t
is
f
i
x
ed
at
1
0
d
u
r
in
g
th
e
o
p
tim
iza
tio
n
p
r
o
ce
s
s
,
as
d
ef
in
ed
in
(
8
)
.
T
h
e
c
o
n
v
e
r
g
en
ce
cr
iter
io
n
is
d
eter
m
in
ed
b
ased
o
n
th
e
m
in
im
u
m
f
itn
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v
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e
an
d
th
e
m
ax
im
u
m
iter
atio
n
lim
it,
as
ex
p
r
ess
ed
in
(
9
)
.
T
h
ese
p
ar
am
eter
s
ar
e
s
elec
ted
to
b
alan
ce
co
n
v
er
g
en
ce
s
p
ee
d
,
o
p
tim
izatio
n
ac
cu
r
ac
y
,
c
o
m
p
u
tatio
n
al
e
f
f
o
r
t,
an
d
co
n
tr
o
ller
p
e
r
f
o
r
m
an
ce
.
T
h
e
W
OA
o
p
tim
izatio
n
p
r
o
c
ed
u
r
e
co
m
p
r
is
es
th
r
ee
m
ec
h
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is
m
s
:
ex
p
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atio
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,
e
n
cir
cle
m
en
t,
an
d
s
p
ir
al
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b
ased
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o
s
itio
n
u
p
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atin
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.
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x
p
lo
r
atio
n
is
p
er
f
o
r
m
ed
wh
en
|
A|
>
1
b
y
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elec
tin
g
a
r
an
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o
m
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ale
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itio
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,
wh
ile
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p
lo
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d
wh
en
|
A|
<
1
b
y
m
o
v
i
n
g
th
e
s
ea
r
ch
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en
t
t
o
war
d
th
e
b
est
ca
n
d
id
ate
s
o
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tio
n
.
T
h
e
co
ef
f
icien
t
v
ec
to
r
s
A
an
d
C
co
n
tr
o
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th
e
b
alan
ce
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etwe
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lo
b
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s
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ch
an
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l
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n
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g
en
ce
,
as
ex
p
r
ess
ed
in
(
6
)
a
n
d
(
7
)
.
{
+
1
=
−
.
|
.
−
|
|
|
>
1
+
1
=
∗
−
.
|
.
∗
−
|
|
|
<
1
(
6
)
[
X
=
{
1
,
2
,
3
,
…
,
}
]
(
7
)
(
)
=
2
−
2
(
8
)
=
a
r
g
(
)
,
=
(
9
)
T
h
e
(
6
)
a
n
d
(
7
)
d
e
f
in
e
t
as
th
e
p
r
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t
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,
as
th
e
p
er
m
itted
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lim
it,
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d
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ated
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wit
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in
[
0
,
1
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.
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h
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s
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ir
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u
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ate
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,
with
l
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ep
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ar
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f
r
o
m
t
h
e
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ter
v
al
[
-
1
,
1
]
.
T
h
ese
m
ec
h
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is
m
s
allo
w
th
e
alg
o
r
ith
m
to
s
ea
r
ch
f
o
r
s
u
itab
le
co
n
tr
o
ller
p
ar
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eter
s
an
d
g
r
a
d
u
ally
c
o
n
v
er
g
e
t
o
war
d
th
e
b
est s
o
lu
tio
n
.
+
1
=
∗
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|
∗
−
|
.
.
(
2
)
(
1
0
)
W
h
er
e
l is a
r
an
d
o
m
n
u
m
b
er
i
n
[
−1
,
1
]
.
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
:
1994
-
2
0
0
3
1998
Fig
u
r
e
3
.
Sp
ir
al
b
u
b
b
le
-
n
et
b
e
h
av
io
r
o
f
h
u
m
p
b
ac
k
wh
ales [
2
3
]
2
.
5
.
2
.
M
et
a
-
heuris
t
ic
t
un
ing
v
ia
wha
le
o
ptim
iza
t
io
n a
lg
o
rit
hm
(
WO
A)
Fig
u
r
e
4
s
h
o
ws
th
e
p
o
s
itio
n
u
p
d
ate
m
ec
h
a
n
is
m
o
f
th
e
W
OA
,
wh
ich
to
g
g
les
b
etwe
en
t
wo
p
r
im
ar
y
b
eh
av
io
r
s
b
ased
o
n
a
p
r
o
b
ab
ili
ty
f
ac
to
r
p
:
i)
S
h
r
in
k
in
g
en
cir
clin
g
m
ec
h
a
n
is
m
(
<
0
.
5
)
T
h
is
p
h
ase
m
o
d
els
th
e
p
r
ey
e
n
tr
ap
m
en
t
.
T
h
e
p
o
s
itio
n
is
u
p
d
ated
b
ased
o
n
th
e
d
is
tan
ce
v
ec
to
r
=
|
.
∗
(
)
−
(
)
|
,
wh
er
e
∗
is
th
e
cu
r
r
en
t
b
est
s
o
lu
tio
n
.
T
h
e
n
ew
p
o
s
itio
n
is
g
iv
e
n
b
y
(
+
1
)
=
∗
(
)
−
.
.
T
h
e
co
ef
f
icien
t
v
ec
to
r
s
A
an
d
C
f
ac
ilit
ate
th
e
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
lo
ita
tio
n
,
wh
ich
is
|
|
≥
1
f
o
r
ce
s
th
e
s
ea
r
ch
ag
en
t
to
m
o
v
e
awa
y
f
r
o
m
th
e
r
ef
e
r
en
ce
wh
a
le
(
ex
p
lo
r
atio
n
)
,
also
|
|
<
1
en
co
u
r
ag
es
co
n
v
er
g
en
ce
to
war
d
th
e
b
est s
o
lu
tio
n
(
e
x
p
lo
itatio
n
)
.
ii)
Sp
ir
al
u
p
d
atin
g
p
o
s
itio
n
(
≥
0
.
5
)
T
h
is
p
h
ase
m
im
ics
th
e
h
elix
-
s
h
ap
ed
m
o
v
e
m
en
t
o
f
wh
ales.
I
t
is
m
ath
em
atica
lly
m
o
d
elled
u
s
in
g
a
lo
g
ar
ith
m
ic
s
p
ir
al
eq
u
atio
n
:
(
+
1
)
=
′
⋅
⋅
c
os
(
2
)
+
∗
(
)
(
1
1
)
I
n
(
1
1
)
,
th
e
d
is
tan
ce
p
a
r
am
et
er
q
u
an
tifie
s
th
e
s
ep
ar
atio
n
b
etwe
en
ea
ch
cu
r
r
e
n
t
ca
n
d
id
at
e
an
d
th
e
o
p
tim
al
s
o
lu
tio
n
,
wh
ile
b
d
eter
m
in
es t
h
e
s
p
ir
al
g
eo
m
etr
y
,
an
d
l d
e
n
o
tes a
r
an
d
o
m
v
alu
e
d
r
awn
with
in
[
-
1
,
1
]
.
iii)
Pro
ce
d
u
r
es st
ep
s
˗
Def
in
e
th
e
ch
ar
g
in
g
b
atter
y
L
i
FePO
4
tar
g
et,
in
clu
d
in
g
t
h
e
7
3
V
o
u
tp
u
t v
o
ltag
e
r
ef
er
e
n
ce
an
d
9
A
ch
a
r
g
in
g
cu
r
r
en
t,
a
n
d
SOC
test
p
o
in
ts
:
3
0
%,
6
0
%,
9
0
%,
an
d
9
7
%.
˗
C
alcu
late
th
e
b
u
ck
co
n
v
e
r
ter
p
ar
am
eter
s
u
s
in
g
(
1
)
-
(
5
)
,
th
en
b
u
ild
th
e
co
n
v
er
ter
cir
c
u
it
in
PS
I
M
u
s
in
g
th
e
p
ar
am
eter
s
in
T
ab
le
1
.
˗
Dev
elo
p
th
e
L
iFePO4
b
atter
y
m
o
d
el
u
s
in
g
t
h
e
s
p
ec
if
icatio
n
s
in
T
ab
le
2
.
˗
Me
th
o
d
im
p
lem
e
n
t
v
ar
iatio
n
s
o
f
th
e
f
u
zz
y
,
PI,
W
OA
-
PI,
an
d
W
OA
-
Fu
zz
y
co
n
tr
o
ller
s
th
e
s
am
e
co
n
v
er
ter
an
d
b
atter
y
co
n
d
itio
n
s
.
˗
R
u
n
clo
s
ed
-
lo
o
p
s
im
u
latio
n
s
f
o
r
ea
ch
SOC
co
n
d
itio
n
,
th
e
n
r
e
co
r
d
o
u
tp
u
t
v
o
ltag
e,
c
u
r
r
e
n
t
r
e
s
p
o
n
s
e,
tr
ac
k
in
g
er
r
o
r
,
s
ettlin
g
tim
e,
a
n
d
th
e
C
C
-
C
V
tr
an
s
itio
n
.
iv
)
Valid
atio
n
T
h
e
m
eth
o
d
was
v
alid
ated
u
s
i
n
g
PS
I
M
s
im
u
latio
n
s
u
s
in
g
clo
s
e
lo
o
p
test
s
.
T
h
e
r
esear
ch
d
a
ta
in
clu
d
es
o
u
tp
u
t
-
v
o
ltag
e
ac
cu
r
ac
y
,
p
er
c
en
tag
e
er
r
o
r
,
av
er
ag
e
er
r
o
r
,
s
et
tlin
g
tim
e,
o
v
er
s
h
o
o
t,
an
d
s
tab
ilit
y
d
u
r
in
g
th
e
C
C
-
C
V
tr
an
s
itio
n
.
T
h
e
v
o
ltag
e
er
r
o
r
was c
alcu
lated
as
e
r
r
o
r
(
%)
=
|
Vo
u
t th
eo
r
y
-
Vo
u
t simu
lati
o
n
|
/ V
o
u
t th
eo
r
y
x
1
0
0
%.
T
h
e
W
OA
-
Fu
zz
y
m
eth
o
d
was
co
n
s
id
er
e
d
ef
f
ec
ti
v
e
;
it
r
ed
u
ce
d
v
o
ltag
e
e
r
r
o
r
an
d
im
p
r
o
v
e
d
d
y
n
am
ic
r
esp
o
n
s
e
co
m
p
a
r
ed
with
th
e
o
t
h
er
im
p
lem
en
t
m
eth
o
d
(
f
u
zz
y
,
PI,
an
d
W
OA
-
PI)
[
2
4
]
-
[
3
0
]
.
2
.
5
.
3
.
F
uzzy
des
ig
n
Fo
r
th
is
r
esear
ch
,
t
h
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
r
ec
eiv
es
two
i
n
p
u
ts
,
er
r
o
r
(
E
)
an
d
ch
an
g
e
in
er
r
o
r
(
Δ
E
)
,
wh
ile
p
r
o
d
u
ci
n
g
th
e
d
u
ty
c
y
cle
as
its
s
in
g
le
o
u
tp
u
t.
W
ith
in
t
h
e
co
n
v
e
r
ter
,
th
e
d
u
ty
-
c
y
cle
c
o
m
m
an
d
is
cr
u
cial
s
in
ce
it
estab
lis
h
es
th
e
s
witch
in
g
p
r
o
p
o
r
tio
n
an
d
co
n
s
eq
u
en
tly
in
f
lu
en
ce
s
o
u
tp
u
t
v
o
ltag
e.
T
h
e
m
em
b
er
s
h
i
p
-
f
u
n
ctio
n
d
ef
in
itio
n
s
ass
ig
n
ed
t
o
E
,
Δ
E
,
an
d
th
e
d
u
ty
-
cy
cle
o
u
tp
u
t a
r
e
p
r
esen
ted
in
Fig
u
r
e
5
.
As
s
h
o
wn
in
Fig
u
r
e
5
,
th
e
er
r
o
r
an
d
d
elta
er
r
o
r
v
ar
iab
les
ar
e
r
ep
r
esen
ted
b
y
s
ev
en
lin
g
u
i
s
tic
ter
m
s
:
NB
,
NM
,
N
S,
Z
,
P
S,
PM,
an
d
PB
.
T
h
e
d
u
ty
cy
cle
o
u
tp
u
t
is
d
ef
in
ed
with
in
th
e
r
an
g
e
o
f
0
.
7
2
to
0
.
9
0
a
n
d
u
s
es
th
e
s
am
e
s
ev
en
lin
g
u
is
tic
ter
m
s
.
T
r
ian
g
u
lar
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
ar
e
ap
p
lied
to
p
r
o
v
id
e
s
m
o
o
th
tr
an
s
itio
n
s
b
etwe
en
ad
jace
n
t
r
eg
io
n
s
,
en
a
b
lin
g
th
e
f
u
zz
y
co
n
tr
o
ller
to
d
eter
m
in
e
th
e
ap
p
r
o
p
r
iate
d
u
ty
cy
cle
b
ased
o
n
th
e
in
f
er
en
ce
p
r
o
ce
s
s
.
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
C
o
mb
in
a
tio
n
w
h
a
le
o
p
timiz
a
tio
n
a
lg
o
r
ith
m
a
n
d
f
u
z
z
y
lo
g
ic
fo
r
o
p
tima
l
…
(
I
n
d
h
a
n
a
S
u
d
ih
a
r
to
)
1999
Fig
u
r
e
4
.
Po
s
itio
n
u
p
d
ate
in
a
s
p
ir
al
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
p
lo
ts
f
o
r
th
e
f
u
zz
y
lo
g
ic
co
n
t
r
o
ller
in
p
u
ts
:
(
a)
er
r
o
r
(
E
)
,
(
b
)
d
elta
er
r
o
r
(
Δ
E
)
,
an
d
(
c)
d
u
ty
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Simu
latio
n
r
esu
lts
o
b
tain
ed
f
r
o
m
PS
I
M
ar
e
u
s
ed
to
test
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
W
OA
–
f
u
zz
y
-
b
ased
ch
ar
g
in
g
s
y
s
tem
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
c
o
n
d
itio
n
s
.
T
h
i
s
an
aly
ze
em
p
h
asize
th
e
s
etp
o
in
t
an
d
ac
cu
r
ate
r
eg
u
latio
n
o
f
ch
ar
g
in
g
in
c
o
n
s
tan
t
cu
r
r
en
t
(
C
C
)
m
o
d
e,
co
n
s
tan
t
v
o
ltag
e
(
C
V)
m
o
d
e,
an
d
SOC
test
p
o
in
ts
o
f
3
0
%,
6
0
%,
9
0
%,
an
d
9
7
%.
T
h
e
o
b
s
er
v
ed
s
m
o
o
th
tr
an
s
itio
n
b
etwe
en
th
e
C
C
an
d
C
V
s
tag
es
d
em
o
n
s
tr
ates
s
tab
le
s
y
s
tem
b
eh
av
io
r
with
m
in
im
al
o
v
er
s
h
o
o
t.
T
h
is
u
s
es
PS
I
M
with
ex
am
p
le
d
ata
illu
s
tr
atin
g
f
o
u
r
m
eth
o
d
s
:
i)
f
u
zz
y
,
ii)
PI
,
iii)
W
OA
–
PI
,
an
d
W
OA
-
f
u
zz
y
.
Fig
u
r
e
6
illu
s
tr
ates
a
clo
s
ed
-
lo
o
p
L
iFePO₄
b
atter
y
ch
ar
g
in
g
c
ir
cu
it
em
p
lo
y
in
g
f
o
u
r
co
n
tr
o
l stra
teg
ies:
f
u
zz
y
,
PI,
W
OA
-
PI,
an
d
W
O
A
-
f
u
zz
y
.
T
h
e
co
n
v
er
te
r
r
eg
u
la
tes
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
d
eliv
er
ed
to
th
e
b
atter
y
.
I
t
co
n
tin
u
o
u
s
ly
m
o
n
i
to
r
s
k
ey
p
ar
am
eter
s
,
in
cl
u
d
in
g
o
u
tp
u
t
c
u
r
r
en
t
a
n
d
v
o
ltag
e
,
an
d
f
ee
d
s
th
ese
m
ea
s
u
r
em
en
ts
b
ac
k
to
th
e
co
n
tr
o
ller
s
to
r
eliab
ly
m
ain
tain
o
p
tim
al
L
iFePO₄
b
atter
y
c
h
ar
g
in
g
co
n
d
itio
n
s
.
T
ab
le
3
p
r
esen
ts
th
e
o
p
en
-
lo
o
p
b
u
ck
co
n
v
er
ter
with
o
u
t
th
e
f
o
u
r
c
o
n
tr
o
l
m
eth
o
d
s
,
u
s
in
g
a
L
iFePO₄
b
atter
y
,
wh
ich
g
en
er
ates
o
u
tp
u
t
v
o
ltag
es
n
ea
r
th
e
th
eo
r
etica
l
7
3
V
ac
r
o
s
s
SO
C
lev
els
o
f
3
0
%,
6
0
%,
9
0
%,
an
d
9
7
%,
with
an
av
er
ag
e
er
r
o
r
o
f
1
.
2
9
%.
Fig
u
r
e
7
s
h
o
ws
th
e
ex
p
er
im
en
tal
d
ata
o
f
clo
s
ed
-
lo
o
p
b
atter
y
ch
ar
g
in
g
with
f
o
u
r
co
n
tr
o
l
m
e
th
o
d
s
(
PI,
f
u
zz
y
,
W
OA
-
PI,
an
d
W
OA
-
f
u
zz
y
)
.
T
h
e
r
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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
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s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
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20
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[
8
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M
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7
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B
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G
RAP
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S O
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AUTH
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RS
Ind
h
a
n
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S
u
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is a l
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tu
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r
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t
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c
h
n
ic In
stit
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te o
f
S
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ra
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a
y
a
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EP
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).
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h
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s fr
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m
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sti
tu
t
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o
lo
g
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S
e
p
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l
u
h
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p
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m
b
e
r
(IT
S
)
.
His res
e
a
rc
h
in
tere
sts in
c
l
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p
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tem
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h
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li
ty
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c
a
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b
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c
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tac
ted
a
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m
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d
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ra
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a
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EP
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).
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h
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l
d
s a
b
a
c
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l
o
r'
s d
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in
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tri
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d
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m
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fro
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l
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p
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m
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r
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S
).
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a
re
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o
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x
p
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in
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p
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,
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m
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o
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,
a
rti
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telli
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n
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,
c
o
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l
sy
ste
m
s,
a
n
d
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g
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g
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e
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tern
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a
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Au
to
d
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in
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ircu
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c
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c
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d
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m
a
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m
rifad
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m
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m
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c
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tac
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m
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7
3
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c
o
m
.
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