I
nte
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l J
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f
P
o
wer
E
lect
ro
nics
a
nd
Driv
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S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
,
p
p
.
1
5
2
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~
1
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3
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1
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1521
J
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:
h
ttp
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Sa
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De
p
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Co
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P
il
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ENS
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M
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Ism
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A
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ticle
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R
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22
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R
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2
7
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021
Acc
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ted
J
u
l
1
3
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2
0
21
S
u
p
e
rc
a
p
a
c
it
o
rs
a
re
e
lec
tri
c
a
l
e
n
e
rg
y
sto
ra
g
e
d
e
v
ice
s
with
a
h
ig
h
sp
e
c
ifi
c
p
o
we
r
d
e
n
sity
,
a
l
o
n
g
c
y
c
le
li
fe
a
n
d
a
g
o
o
d
e
fficie
n
c
y
,
w
h
ich
m
a
k
e
th
e
m
a
tt
ra
c
ti
v
e
a
lt
e
rn
a
ti
v
e
st
o
ra
g
e
d
e
v
ice
s
fo
r
v
a
rio
u
s
a
p
p
li
c
a
ti
o
n
s.
Ho
we
v
e
r,
su
p
e
rc
a
p
a
c
it
o
rs
a
re
su
b
jec
t
to
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ss
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ti
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n
o
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h
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ir
p
e
rfo
r
-
m
a
n
c
e
b
e
c
a
u
se
o
f
a
g
i
n
g
p
h
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n
o
m
e
n
o
n
.
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h
e
re
fo
re
,
it
is
v
e
ry
im
p
o
r
tan
t
t
o
b
e
a
b
le
to
e
stim
a
te
th
e
ir
S
tate
-
of
-
He
a
lt
h
d
u
ri
n
g
o
p
e
ra
ti
o
n
.
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e
c
tr
o
c
h
e
m
ica
l
Im
p
e
d
a
n
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e
S
p
e
c
tro
sc
o
p
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(EI
S
)
is
a
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ry
re
c
o
g
-
n
ize
d
tec
h
n
i
q
u
e
t
o
d
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term
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e
su
p
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rc
a
p
a
c
it
o
rs’
sta
te
-
of
-
h
e
a
lt
h
.
Ho
we
v
e
r,
it
re
q
u
ires
th
e
in
terr
u
p
-
ti
o
n
o
f
sy
ste
m
o
p
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ra
ti
o
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a
n
d
t
h
u
s
c
a
n
n
o
t
b
e
p
e
rfo
rm
e
d
in
re
a
l
ti
m
e
(
o
n
li
n
e
).
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th
is
p
a
p
e
r,
a
n
e
w
o
n
li
n
e
i
d
e
n
ti
f
ica
ti
o
n
m
e
th
o
d
is
p
r
o
p
o
se
d
b
a
se
d
o
n
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te
n
d
e
d
Ka
lma
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se
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e
r
c
o
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e
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o
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p
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tary
P
ID
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o
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to
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T
h
e
p
ro
p
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se
d
m
e
th
o
d
a
ll
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to
a
c
c
u
ra
tely
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a
ti
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g
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p
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p
a
c
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o
r
re
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n
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e
a
n
d
c
a
p
a
c
it
a
n
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e
,
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ich
a
re
t
h
e
m
a
in
in
d
ica
to
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o
f
su
p
e
rc
a
p
a
c
it
o
r
sta
te
-
of
-
h
e
a
lt
h
.
T
h
e
n
e
w
o
n
li
n
e
id
e
n
t
ifi
c
a
ti
o
n
m
e
th
o
d
wa
s
a
p
p
li
e
d
fo
r
two
v
o
lt
a
g
e
/cu
rre
n
t
p
ro
f
il
e
s
u
si
n
g
two
d
iffere
n
t
s
u
p
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rc
a
p
a
c
it
o
rs.
T
h
e
re
sista
n
c
e
/ca
p
a
c
it
a
n
c
e
e
stim
a
ted
b
y
th
e
n
e
w
m
e
th
o
d
a
n
d
th
e
c
o
n
v
e
n
t
io
n
a
l
EKF
we
re
c
o
m
p
a
re
d
with
th
o
se
o
b
tain
e
d
b
y
a
n
e
x
p
e
rime
n
tal
o
ff
li
n
e
m
e
th
o
d
.
In
c
o
m
p
a
riso
n
wit
h
c
o
n
v
e
n
ti
o
n
a
l
EKF
,
t
h
e
c
a
p
a
c
it
a
n
c
e
o
b
tain
e
d
b
y
th
e
n
e
w
m
e
th
o
d
is
si
g
n
ifi
c
a
n
tl
y
m
o
re
a
c
c
u
ra
te.
K
ey
w
o
r
d
s
:
C
ap
ac
itan
ce
E
x
ten
d
ed
Kalm
a
n
f
ilter
On
lin
e
id
en
tific
atio
n
PID
co
r
r
ec
to
r
R
esi
s
tan
ce
Su
p
er
ca
p
ac
ito
r
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
:
Z
o
u
b
id
a
B
o
u
o
u
c
h
m
a
Dep
ar
tm
en
t o
f
C
o
n
tr
o
l,
Pil
o
tin
g
an
d
Su
p
er
v
is
io
n
o
f
Sy
s
tem
s
E
NSAM
-
Me
k
n
es
Mo
u
lay
I
s
m
ail
Un
iv
er
s
ity
E
n
s
am
-
Me
k
n
ès
,
Ma
r
jan
e
2
B
.
P 1
5
2
9
0
,
Al
Ma
n
s
o
u
r
Me
k
n
ès,
Mo
r
o
cc
o
E
m
ail: z
o
u
b
id
a.
b
o
u
o
u
ch
m
a@
ed
u
.
u
m
i.a
c
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
Su
p
er
ca
p
ac
ito
r
s
(
SC
s
)
,
also
c
alled
u
ltra
ca
p
ac
ito
r
s
o
r
elec
tr
ic
d
o
u
b
le
lay
er
ca
p
ac
ito
r
s
,
ar
e
elec
tr
ical
en
er
g
y
s
to
r
ag
e
tech
n
o
lo
g
ies.
C
o
m
p
ar
ed
to
b
atter
ies,
th
ey
h
av
e
a
b
etter
s
p
ec
if
ic
p
o
we
r
d
e
n
s
ity
,
a
lo
n
g
er
cy
cle
life
(
o
v
er
1
0
4
cy
cles)
an
d
a
b
e
tter
ef
f
icien
cy
[
1
]
.
T
h
ey
ar
e
al
s
o
ch
ar
ac
ter
ized
b
y
lo
wer
s
er
i
es
r
esis
tan
ce
an
d
a
m
o
r
e
s
ig
n
if
ican
t e
q
u
i
v
alen
t c
a
p
ac
itan
ce
[
2
]
,
[
3
]
.
T
h
ese
s
tr
en
g
th
s
m
ak
e
th
em
attr
ac
tiv
e
f
o
r
s
ev
er
al
ap
p
licatio
n
s
s
u
ch
as
elec
tr
ic
o
r
h
y
b
r
id
v
eh
i
cles
f
o
r
p
ea
k
p
o
wer
[
4
]
-
[
6
]
,
win
d
p
o
wer
g
e
n
er
atio
n
[
7
]
,
s
o
la
r
p
o
wer
g
en
e
r
atio
n
[
7
]
,
[
8
]
,
o
r
s
im
p
ly
co
n
s
u
m
e
r
elec
tr
o
n
ics
[
9
]
-
[
1
2
]
.
T
h
ey
ca
n
b
e
u
s
ed
in
d
ep
e
n
d
en
tl
y
,
o
r
in
co
m
b
in
atio
n
with
o
th
er
en
er
g
y
s
to
r
ag
e
tech
n
o
lo
g
y
s
u
ch
as
lead
–
ac
id
b
atter
ies
[
1
3
]
,
lith
iu
m
b
atter
ies
[
5
]
,
[
1
4
]
o
r
h
y
d
r
o
g
en
f
u
el
ce
lls
[1
5
]
,
[
1
6
]
.
Du
r
in
g
th
eir
o
p
er
atio
n
,
s
u
p
er
c
ap
ac
ito
r
s
ar
e
s
u
b
ject
to
ag
in
g
,
wh
ich
ca
u
s
es
a
p
r
o
g
r
ess
iv
e
d
eg
r
ad
atio
n
o
f
th
eir
p
e
r
f
o
r
m
an
ce
s
.
T
h
er
e
ex
is
t
s
o
m
e
f
ac
to
r
s
th
at
ca
n
ac
ce
ler
ate
ag
in
g
m
ec
h
an
is
m
s
s
u
ch
as
h
ig
h
v
o
ltag
e,
h
ig
h
o
p
er
atin
g
tem
p
er
atu
r
e,
an
d
v
o
l
tag
e
im
b
alan
ce
s
th
at
tak
e
p
lace
wh
en
s
ev
er
al
s
u
p
er
ca
p
ac
ito
r
s
ar
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
:
152
1
–
153
4
1522
co
n
n
ec
ted
in
s
er
ies
[
1
7
]
.
T
h
e
in
d
u
s
tr
ial
ex
p
an
s
io
n
o
f
s
u
p
er
c
ap
ac
ito
r
s
r
eq
u
ir
es
a
d
ee
p
u
n
d
er
s
tan
d
in
g
o
f
a
g
in
g
m
ec
h
an
is
m
s
an
d
th
e
d
ev
elo
p
m
en
t
o
f
tech
n
i
q
u
es
f
o
r
th
e
e
s
tim
atio
n
o
f
t
h
eir
s
tate
-
of
-
h
e
alth
(
So
H)
d
u
r
in
g
o
p
er
atio
n
.
Su
ch
tech
n
iq
u
es a
r
e
v
er
y
im
p
o
r
tan
t t
o
p
r
e
d
ict
an
d
an
ticip
ate
s
u
p
er
ca
p
ac
ito
r
b
r
ea
k
d
o
wn
.
Du
r
in
g
SC
o
p
er
atio
n
,
th
e
o
n
li
n
e
id
en
tific
atio
n
o
f
its
in
ter
n
al
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
is
im
p
o
r
tan
t.
SC
d
eg
r
ad
atio
n
is
ch
a
r
ac
ter
iz
ed
b
y
a
n
in
c
r
ea
s
e
o
f
th
e
in
te
r
n
al
r
esis
tan
ce
o
r
a
d
ec
r
ea
s
e
o
f
th
e
eq
u
iv
ale
n
t
ca
p
ac
itan
ce
[
1
7
]
,
[
1
8
]
.
T
h
er
e
f
o
r
e,
t
h
ese
two
p
ar
am
eter
s
c
o
n
s
titu
te
g
o
o
d
in
d
icato
r
s
o
f
SC
s
tate
-
of
-
h
ea
lth
.
T
h
er
e
id
en
tific
atio
n
ca
n
f
ac
il
itate
th
e
p
lan
if
icatio
n
o
f
p
r
e
v
en
tiv
e
m
ain
ten
a
n
ce
task
s
an
d
im
p
r
o
v
e
s
y
s
tem
s
af
ety
.
SC
r
esis
tan
ce
an
d
ca
p
ac
ita
n
c
e
ca
n
b
e
d
eter
m
in
e
d
b
ased
o
n
th
e
im
p
ed
an
ce
m
ea
s
u
r
em
en
ts
u
s
in
g
elec
tr
o
ch
em
ica
l
im
p
ed
an
ce
s
p
ec
tr
o
s
co
p
y
(
E
I
S)
tech
n
i
q
u
e
[
1
9
]
,
[
2
0
]
.
Ho
wev
e
r
,
E
I
S
is
an
o
f
f
lin
e
m
ea
s
u
r
em
en
ts
tech
n
iq
u
e,
w
h
ich
m
ea
n
s
t
h
at
th
e
s
y
s
tem
’
s
o
p
er
atio
n
m
u
s
t
b
e
i
n
ter
r
u
p
ted
.
T
h
e
o
b
jectiv
e
o
f
th
e
p
r
esen
t p
ap
er
is
to
d
ev
elo
p
an
o
n
lin
e
(
r
ea
l
-
tim
e
)
id
en
tific
atio
n
tech
n
iq
u
e.
Gu
alo
u
s
et
a
l.
[
2
1
]
p
r
o
p
o
s
ed
an
id
en
tific
atio
n
alg
o
r
ith
m
b
a
s
ed
o
n
ex
ten
d
ed
Kalm
an
f
ilter
(
E
KF)
to
esti
m
ate
b
u
f
f
er
ed
e
n
er
g
y
o
f
a
SC
u
s
ed
f
o
r
a
s
o
lar
ap
p
licatio
n
.
T
h
e
SC
was
m
o
d
eled
b
y
th
r
ee
-
b
r
an
c
h
cir
cu
it.
T
h
ey
ass
u
m
ed
th
at
R
C
cir
cu
it
p
ar
am
eter
s
a
r
e
c
o
n
s
tan
ts
with
th
e
ag
in
g
tim
e.
In
[
2
2
]
also
p
r
o
p
o
s
ed
an
o
n
lin
e
id
en
tific
atio
n
tech
n
iq
u
e
b
ase
d
o
n
th
e
E
KF
to
esti
m
ate
th
e
tem
p
er
atu
r
e
an
d
th
e
s
tate
o
f
ch
a
r
g
e
o
f
a
s
u
p
er
ca
p
ac
ito
r
.
In
[
2
3
]
p
r
o
p
o
s
ed
two
r
ea
l
-
tim
e
o
b
s
er
v
er
s
f
o
r
th
e
p
r
ed
ictio
n
o
f
s
u
p
er
c
ap
ac
ito
r
s
’
ca
p
ac
itan
ce
an
d
th
e
r
esis
tan
ce
.
O
n
e
is
b
ased
o
n
E
KF
a
n
d
th
e
o
th
er
is
b
ased
o
n
in
ter
co
n
n
ec
ted
o
b
s
er
v
er
s
.
B
o
th
o
b
s
er
v
er
s
u
s
ed
R
C
c
ir
cu
it
to
m
o
d
el
s
u
p
er
ca
p
ac
ito
r
.
T
h
e
y
ass
u
m
ed
th
at
ca
p
ac
itan
ce
an
d
r
esis
tan
ce
r
em
ain
co
n
s
tan
t.
T
h
e
r
esu
lts
o
b
tain
ed
b
y
th
e
two
o
n
lin
e
o
b
s
er
v
er
s
ar
e
t
h
en
co
m
p
ar
ed
with
an
o
f
f
lin
e
ch
a
r
ac
ter
iza
tio
n
.
Nad
ea
u
et
a
l
.
[
2
4
]
d
ev
elo
p
e
d
a
tech
n
iq
u
e
f
o
r
th
e
r
ea
l
-
tim
e
id
en
tific
atio
n
o
f
SC
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
f
o
r
v
e
h
icu
lar
ap
p
licatio
n
s
.
I
n
o
r
d
e
r
to
m
o
d
el
SC
,
th
ey
ch
o
s
e
R
C
cir
cu
it
in
wh
ich
th
e
ca
p
ac
itan
ce
is
ass
u
m
ed
to
v
ar
y
lin
ea
r
ly
with
b
ias
v
o
ltag
e.
Sli
d
in
g
m
o
d
e
o
b
s
er
v
er
with
an
ad
a
p
tatio
n
g
ain
was
u
s
ed
t
o
id
en
tify
SC
in
ter
n
al
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
.
B
ased
o
n
a
L
y
ap
u
n
o
v
-
b
ased
ad
ap
tatio
n
law,
d
ev
elo
p
e
d
a
r
ea
l
-
tim
e
r
esis
tan
ce
/cap
ac
itan
ce
id
en
tific
atio
n
m
eth
o
d
f
o
r
s
u
p
er
ca
p
ac
ito
r
s
[
2
5
]
.
C
o
m
p
ar
e
d
to
o
th
er
m
eth
o
d
s
in
liter
atu
r
e,
th
e
s
tab
ilit
y
an
d
t
h
e
co
n
v
er
g
en
ce
o
f
th
eir
m
eth
o
d
is
g
u
ar
an
teed
b
y
L
y
ap
u
n
o
v
’
s
d
ir
ec
t
m
eth
o
d
.
In
[
2
6
]
p
r
o
p
o
s
ed
an
o
n
lin
e
id
en
tific
atio
n
s
ch
em
e
b
ased
o
n
p
ar
ticle
f
ilter
(
PF
)
f
o
r
th
e
esti
m
atio
n
o
f
s
tate
-
of
-
ch
ar
g
e
,
So
H
an
d
tem
p
er
atu
r
e
o
f
SC
b
y
co
m
b
in
in
g
elec
tr
ic
al
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
a
n
d
th
er
m
al
m
o
d
e
l.
T
h
ey
f
o
u
n
d
th
at
th
e
p
r
o
p
o
s
ed
esti
m
atio
n
s
ch
em
e
p
er
f
o
r
m
s
S
o
H
esti
m
atio
n
with
ac
ce
p
tab
le
ac
cu
r
ac
y
.
In
[
2
7
]
p
r
o
p
o
u
n
d
ed
a
n
o
n
lin
ea
r
s
tate
-
s
p
ac
e
m
o
d
el
f
o
r
t
h
e
o
n
lin
e
esti
m
atio
n
o
f
ca
p
ac
it
an
ce
a
n
d
r
e
s
is
tan
ce
o
f
SC
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
tak
es
th
e
ca
p
ac
itan
ce
v
ar
iatio
n
an
d
s
elf
-
d
is
ch
ar
g
e
e
f
f
ec
ts
in
to
ac
co
u
n
t.
T
h
e
esti
m
atio
n
er
r
o
r
ac
h
iev
ed
with
th
e
p
r
o
p
o
s
ed
m
o
d
el
is
ap
p
r
o
x
im
ately
5
%.
Ac
co
r
d
in
g
to
[
2
8
]
s
u
g
g
ested
a
p
r
o
ce
d
u
r
e
in
teg
r
atin
g
f
u
zz
y
lo
g
ic
an
d
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
(
ANN)
to
es
tim
ate
s
u
p
er
ca
p
ac
ito
r
s
’
in
ter
n
al
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
.
ANN
ca
n
b
e
a
p
o
wer
f
u
l
tech
n
iq
u
e
to
p
r
o
v
id
e
a
r
o
b
u
s
t
id
en
tific
atio
n
f
o
r
s
y
s
tem
s
th
at
ar
e
s
u
b
jecte
d
to
u
n
ce
r
tain
ties
[
2
9
]
.
Ho
wev
er
,
th
is
tech
n
iq
u
e
u
s
u
ally
r
e
q
u
ir
es
lo
n
g
o
f
f
lin
e
test
s
to
h
av
e
th
e
e
n
o
u
g
h
tr
ain
in
g
d
ata.
T
h
e
E
KF
b
ec
o
m
es
a
r
ec
o
g
n
ized
an
d
a
wid
ely
u
s
ed
tec
h
n
iq
u
e
f
o
r
s
tate
esti
m
atio
n
in
s
ev
er
al
n
o
n
lin
ea
r
d
y
n
a
m
ic
s
y
s
tem
s
.
On
e
o
f
th
e
ad
v
an
tag
es
o
f
E
KF
in
o
u
r
ca
s
e
is
th
at
it
o
n
ly
r
eq
u
ir
es
ter
m
i
n
al
m
ea
s
u
r
em
en
t
o
f
v
o
ltag
e
an
d
cu
r
r
en
t,
wh
ich
ca
n
b
e
d
o
n
e
d
u
r
in
g
SC
o
p
er
atio
n
.
H
o
wev
er
,
th
e
m
ain
d
if
f
icu
lt
y
u
s
in
g
E
KF
in
o
u
r
ca
s
e
co
n
s
is
t
s
in
s
ett
in
g
in
itial
v
alu
es
o
f
th
e
SC
p
ar
am
eter
s
.
T
h
ese
v
alu
e
s
m
u
s
t
b
e
clo
s
e
to
r
ea
l
v
alu
es.
Oth
er
wis
e,
th
e
E
KF
is
u
n
ab
le
to
ac
c
u
r
ately
id
en
tify
th
e
co
r
r
ec
t
v
alu
es
o
f
S
C
p
ar
am
eter
s
(
s
tate
v
ec
to
r
)
[
2
1
]
-
[
2
3
]
.
T
h
is
lim
ita
tio
n
was
also
h
ig
h
lig
h
ted
in
th
is
p
ap
er
(
s
ec
tio
n
5
)
.
Un
f
o
r
tu
n
ately
,
it
is
n
o
t
alwa
y
s
ea
s
y
to
ac
cu
r
atel
y
esti
m
ate
th
e
in
itial
s
y
s
tem
s
tate.
I
n
o
r
d
er
to
a
d
d
r
ess
th
is
li
m
itatio
n
,
a
co
m
p
lem
en
tar
y
PID
co
r
r
ec
to
r
was
in
teg
r
ated
to
E
KF
s
ch
em
e
in
th
e
p
r
esen
t
p
ap
er
.
I
n
liter
atu
r
e,
s
o
m
e
au
th
o
r
s
h
av
e
alr
ea
d
y
in
v
esti
g
ated
t
h
e
co
m
b
in
atio
n
b
etwe
en
E
KF
s
ch
em
e
an
d
PID
c
o
r
r
ec
to
r
in
o
r
d
er
to
im
p
r
o
v
e
s
y
s
tem
s
co
n
tr
o
l
[
3
0
]
-
[
3
2
]
.
T
h
is
co
m
b
in
atio
n
allo
ws
b
etter
s
tab
ilit
y
an
d
b
etter
co
n
v
e
r
g
e
n
ce
[
3
0
]
-
[
3
2
]
.
T
h
e
n
o
v
elty
o
f
th
e
p
r
esen
t
p
ap
er
is
to
in
v
esti
g
ate
th
e
u
s
e
o
f
E
KF
co
m
b
in
ed
with
PID
co
r
r
e
cto
r
to
id
en
tif
y
SC
p
ar
am
eter
s
.
Sectio
n
2
p
r
esen
ts
th
e
ex
p
er
im
en
tal
p
r
o
ce
d
u
r
e
u
s
ed
to
ch
a
r
ac
ter
ize
SC
.
I
n
s
ec
tio
n
3
,
th
e
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
u
s
ed
in
o
u
r
m
et
h
o
d
is
p
r
esen
ted
.
I
n
s
ec
tio
n
4
,
SC
s
tate
v
ec
to
r
is
d
eter
m
in
ed
b
ased
o
f
t
h
e
ch
o
s
en
eq
u
iv
alen
t
cir
cu
it
m
o
d
el.
I
n
s
ec
tio
n
5
th
e
e
x
ten
d
e
d
Kalm
a
n
f
ilter
s
ch
em
e
is
p
r
esen
ted
.
T
h
e
co
m
p
lem
e
n
tar
y
PID
co
r
r
ec
t
o
r
is
th
en
d
etaile
d
in
s
ec
tio
n
6
.
I
n
s
ec
tio
n
7
,
th
e
o
b
tain
e
d
r
esu
lts
ar
e
r
e
p
o
r
ted
an
d
d
is
cu
s
s
ed
.
Fin
ally
,
co
n
clu
s
io
n
a
n
d
s
o
m
e
f
u
tu
r
e
wo
r
k
s
ar
e
r
ec
o
m
m
en
d
e
d
in
s
ec
tio
n
8
.
2.
E
XP
E
R
I
M
E
N
T
A
L
ST
UDY
I
n
th
is
e
x
p
er
im
e
n
tal
s
tu
d
y
,
tw
o
s
u
p
er
ca
p
ac
ito
r
s
m
a
x
well
tec
h
n
o
lo
g
i
es
B
C
AP1
5
0
0
an
d
B
C
AP3
5
0
ar
e
s
u
b
jecte
d
to
ch
ar
g
in
g
a
n
d
d
is
ch
ar
g
in
g
cy
cles
u
n
d
er
th
e
tw
o
cu
r
r
e
n
t
p
r
o
f
iles
s
h
o
wn
in
Fi
g
u
r
e
1
.
T
h
e
a
p
p
lied
cu
r
r
en
ts
co
r
r
esp
o
n
d
t
o
th
e
r
e
al
cu
r
r
en
ts
d
u
r
i
n
g
SC
o
p
er
at
io
n
.
A
s
ch
em
atic
o
f
th
e
e
x
p
er
im
en
tal
b
en
ch
is
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
On
lin
e
d
ia
g
n
o
s
is
o
f su
p
erca
p
a
cito
r
s
u
s
in
g
ex
ten
d
ed
K
a
lma
n
fi
lter
…
(
Zo
u
b
id
a
B
o
u
o
u
ch
m
a
)
1523
p
r
esen
ted
in
Fig
u
r
e
2
.
B
o
th
b
ias
v
o
ltag
es
r
esp
o
n
s
e
(
Fig
u
r
e
3
)
an
d
ap
p
lied
cu
r
r
en
ts
ar
e
m
ea
s
u
r
ed
d
u
r
in
g
ex
p
er
im
en
t
a
n
d
s
av
ed
u
s
in
g
t
h
e
ac
q
u
is
itio
n
b
o
a
r
d
NI
cDA
Q
9
1
7
8
a
n
d
L
ab
View
s
o
f
twa
r
e.
Sam
p
lin
g
tim
e
u
s
ed
f
o
r
v
o
ltag
e/cu
r
r
en
t
m
ea
s
u
r
em
en
ts
is
s
et
to
0
.
0
1
s
.
T
h
e
ex
p
er
im
en
tal
b
e
n
ch
u
s
ed
is
p
r
esen
ted
in
Fig
u
r
e
4
.
I
n
th
e
s
ec
tio
n
s
th
at
f
o
llo
w,
th
e
p
r
o
p
o
s
ed
id
en
tific
atio
n
m
eth
o
d
is
ap
p
lied
to
th
e
two
s
u
p
er
ca
p
ac
ito
r
s
.
(
a)
(
b
)
Fig
u
r
e
1
.
C
u
r
r
e
n
t p
r
o
f
iles
ap
p
l
ied
to
th
e
two
SC
,
(
a)
B
C
AP1
5
0
0
; (
b
)
B
C
AP3
5
0
Fig
u
r
e
2
.
Sch
em
atic
o
f
ex
p
er
i
m
en
tal
b
en
ch
u
s
ed
f
o
r
SC
ch
a
r
ac
ter
izatio
n
(
a)
(
b
)
Fig
u
r
e
3
.
Vo
ltag
e
r
esp
o
n
s
e
p
r
o
f
iles
o
f
th
e
two
SC
,
(
a)
B
C
AP1
5
0
0
; (
b
)
B
C
AP3
5
0
T
h
e
in
ter
n
al
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
o
f
a
SC
ar
e
af
f
ec
ted
b
y
o
p
er
atin
g
tem
p
er
atu
r
e
as
d
em
o
n
s
tr
ated
in
[
2
4
]
.
I
t
is
th
u
s
im
p
o
r
tan
t
to
co
n
d
u
ct
th
e
ex
p
er
im
en
t
in
a
co
n
s
ta
n
t
tem
p
er
atu
r
e.
Fo
r
th
is
r
ea
s
o
n
,
th
e
two
SC
s
wer
e
p
lac
ed
in
s
id
e
a
tem
p
er
atu
r
e
-
co
n
t
r
o
lled
ch
am
b
er
in
wh
ich
th
e
tem
p
er
atu
r
e
is
s
et
to
a
co
n
s
tan
t v
alu
e
o
f
6
5
° C
.
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
:
152
1
–
153
4
1524
Fig
u
r
e
4
.
E
x
p
er
im
e
n
tal
b
en
ch
u
s
ed
f
o
r
SC
ch
ar
ac
ter
izatio
n
T
h
e
ex
p
er
im
e
n
tal
r
esu
lts
o
b
tain
ed
at
th
is
s
tag
e
will
b
e
u
s
e
d
to
id
en
tify
SC
p
ar
am
eter
s
f
o
r
th
e
two
SC
s
u
s
in
g
th
e
n
ew
o
n
lin
e
id
en
tific
atio
n
m
eth
o
d
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
I
t
is
wo
r
th
n
o
ticin
g
th
at
v
o
ltag
e/cu
r
r
e
n
t m
ea
s
u
r
em
e
n
ts
ca
n
b
e
d
o
n
e
in
r
ea
l tim
e
an
d
d
o
es n
o
t r
eq
u
ir
e
th
e
in
te
r
r
u
p
tio
n
o
f
SC
o
p
er
atio
n
.
I
n
th
e
s
ec
o
n
d
p
ar
t
o
f
th
is
ex
p
er
im
en
tal
s
tu
d
y
,
th
e
s
am
e
e
x
p
er
im
en
tal
b
en
c
h
d
escr
ib
e
d
in
th
e
p
r
esen
t
s
ec
tio
n
is
u
s
ed
t
o
ap
p
ly
Ma
x
w
ell
ch
ar
ac
ter
izatio
n
test
to
t
h
e
two
SC
s
.
Ma
x
well
test
is
an
o
f
f
lin
e
id
e
n
tific
atio
n
test
th
at
allo
ws
th
e
d
eter
m
in
atio
n
o
f
i
n
ter
n
al
r
esis
tan
ce
a
n
d
ca
p
ac
itan
ce
.
Alth
o
u
g
h
m
a
x
well
test
p
r
o
v
id
es
ac
cu
r
ate
an
d
r
eliab
le
r
esu
lts
[
3
3
]
,
it
r
eq
u
ir
es
th
e
in
ter
r
u
p
tio
n
o
f
s
y
s
tem
o
p
er
atio
n
an
d
th
er
ef
o
r
e
,
ca
n
n
o
t
b
e
p
er
f
o
r
m
ed
in
r
ea
l
tim
e.
I
n
th
e
p
r
esen
t
s
tu
d
y
,
th
e
v
al
u
es
o
f
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
o
b
tain
ed
b
y
m
a
x
well
test
ar
e
u
s
ed
as
r
ef
er
e
n
ce
v
al
u
es
to
co
m
p
ar
e
th
e
r
esu
lts
o
b
tain
ed
b
y
th
e
p
r
o
p
o
s
ed
r
ea
l
-
tim
e
id
en
tific
atio
n
m
eth
o
d
a
n
d
to
ass
ess
th
e
ac
cu
r
ac
y
o
f
th
is
m
eth
o
d
.
Fig
u
r
e
5
.
Ma
x
well
id
e
n
tific
atio
n
test
T
h
e
m
ax
well
ch
ar
ac
te
r
izatio
n
test
is
b
ased
o
n
th
e
ass
u
m
p
tio
n
th
at
th
e
SC
ca
n
b
e
m
o
d
eled
b
y
a
s
im
p
le
R
C
eq
u
iv
alen
t
cir
cu
it.
Mo
r
e
d
etails
o
n
th
is
m
o
d
el
ar
e
g
iv
e
n
in
s
ec
tio
n
3
.
B
ased
o
n
th
is
m
o
d
el,
th
e
v
o
lta
g
e
m
ea
s
u
r
e
d
o
n
th
e
ter
m
in
als
o
f
th
e
SC
ca
n
b
e
d
escr
ib
ed
as
th
e
s
u
m
o
f
th
e
v
o
ltag
e
o
n
th
e
ter
m
in
al
o
f
a
r
esis
to
r
an
d
a
ca
p
ac
ito
r
,
d
en
o
ted
r
esp
ec
tiv
ely
an
d
.
T
h
e
S
C
is
s
u
b
m
itted
to
th
e
cu
r
r
en
t
p
r
o
f
ile
s
h
o
wn
in
Fig
u
r
e
5
.
Acc
o
r
d
in
g
to
Ma
x
well
tes
t
p
r
o
ce
d
u
r
e
[
3
0
]
,
a
n
d
b
ased
o
n
v
o
ltag
e
r
esp
o
n
s
e
(
Fig
u
r
e
5
)
,
in
ter
n
al
r
esis
tan
ce
an
d
ca
p
ac
itan
ce
ar
e
d
eter
m
in
ed
u
s
in
g
(
1
)
an
d
(
2
)
:
=
(
1
)
=
.
(
2
)
T
h
e
d
if
f
e
r
en
t
p
ar
a
m
eter
s
u
s
e
d
in
(
1
)
an
d
(
2
)
ar
e
illu
s
tr
ated
in
Fig
u
r
e
5
.
T
h
e
in
ter
n
al
r
esis
tan
ce
s
o
b
tain
ed
u
s
in
g
m
ax
well
c
h
a
r
ac
ter
izatio
n
test
ar
e
r
esp
ec
t
iv
ely
=
6
.
67
×
10
−
4
ℎ
an
d
=
3
.
32
×
10
−
3
ℎ
f
o
r
s
u
p
er
ca
p
ac
ito
r
s
B
C
AP
1
5
0
0
a
n
d
B
C
AP3
5
0
.
T
h
e
c
ap
ac
itan
ce
s
o
b
tain
ed
u
s
in
g
Ma
x
well
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
On
lin
e
d
ia
g
n
o
s
is
o
f su
p
erca
p
a
cito
r
s
u
s
in
g
ex
ten
d
ed
K
a
lma
n
fi
lter
…
(
Zo
u
b
id
a
B
o
u
o
u
ch
m
a
)
1525
ch
ar
ac
ter
izatio
n
test
ar
e
=
1498
.
21
f
o
r
s
u
p
e
r
ca
p
ac
ito
r
B
C
AP1
5
0
0
an
d
=
349
.
56
f
o
r
th
e
s
u
p
er
ca
p
ac
ito
r
B
C
AP3
5
0
.
3.
SUPERC
AP
ACI
T
O
R
M
O
D
E
L
I
NG
I
n
o
r
d
er
to
m
o
d
el
th
e
elec
tr
ic
al
b
eh
av
io
r
o
f
a
SC
,
s
ev
er
al
e
q
u
iv
alen
t
elec
tr
ical
cir
cu
it
m
o
d
els
h
av
e
b
ee
n
p
r
o
p
o
s
ed
i
n
liter
atu
r
e
.
T
h
e
m
o
s
t
co
m
m
o
n
ar
e
s
im
p
le
R
C
m
o
d
el
[
2
4
]
,
[
3
4
]
,
Z
u
b
ieta
m
o
d
el
[
3
5
]
,
s
im
p
le
p
o
r
e
m
o
d
el
[
1
0
]
,
C
PE
m
o
d
el
[
3
6
]
,
m
u
lti
-
p
o
r
e
m
o
d
el
[
3
7
]
,
an
d
f
r
ac
tio
n
al
-
Or
d
er
Mo
d
el
[
3
8
]
.
I
n
cr
ea
s
in
g
cir
c
u
it
s
o
p
h
is
ticatio
n
alwa
y
s
lead
s
t
o
a
m
o
r
e
co
m
p
lex
f
o
r
m
u
lati
o
n
an
d
g
en
e
r
ally
r
eq
u
i
r
es
h
ig
h
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
m
a
k
in
g
it
m
o
r
e
d
i
f
f
icu
lt
to
id
en
tify
SC
p
ar
am
e
ter
s
in
r
ea
l
tim
e
[
3
9
]
,
[
4
0
]
.
Z
u
b
ieta
m
o
d
el
[
3
5
]
,
p
r
esen
ted
in
Fig
u
r
e
6
,
is
a
s
i
m
p
le
m
o
d
el
th
at
ev
alu
ates
th
e
o
v
er
all
r
ea
l
b
eh
a
v
io
r
o
f
t
h
e
s
u
p
er
ca
p
ac
ito
r
.
I
t
is
co
m
p
o
s
ed
o
f
a
s
er
ies
co
m
b
in
a
tio
n
o
f
a
r
esis
to
r
an
d
a
ca
p
ac
i
to
r
wh
ich
is
ch
ar
ac
ter
ized
b
y
v
ar
iab
le
ca
p
ac
ity
o
v
er
tim
e
.
T
h
e
ca
p
ac
ito
r
r
e
p
r
esen
ts
th
e
ca
n
o
n
ical
ca
p
a
citan
ce
ef
f
ec
t
o
f
SC
s
.
T
h
e
r
esis
to
r
b
asically
r
ep
r
esen
ts
th
e
elec
tr
o
ly
te
a
n
d
elec
tr
o
d
es r
esis
tan
ce
s
.
Fig
u
r
e
6
.
E
q
u
iv
alen
t e
lectr
ical
cir
cu
it m
o
d
el
i(
)
is
th
e
ch
ar
g
e/d
is
ch
ar
g
e
cu
r
r
en
t.
T
h
e
b
ias
v
o
ltag
e
U
s
(
t
)
o
n
th
e
ter
m
in
als
o
f
SC
ca
n
b
e
d
esc
r
ib
ed
in
(
3
)
:
(
)
=
(
)
+
(
)
=
.
(
)
+
∫
1
(
)
.
(
)
.
(
3
)
I
t
h
as
b
ee
n
p
r
o
v
e
n
th
at
th
e
ca
p
ac
itan
ce
(
)
v
ar
ies
lin
ea
r
ly
with
th
e
v
o
ltag
e
(
t
)
[
3
5
]
,
[
4
1
]
,
[
4
2
]
.
T
h
er
ef
o
r
e,
th
e
ca
p
ac
itan
ce
(
)
is
ex
p
r
ess
ed
as
a
f
u
n
ctio
n
o
f
v
o
ltag
e
(
t
)
u
s
in
g
th
e
f
o
llo
win
g
lin
ea
r
ex
p
r
ess
io
n
:
(
)
=
0
+
.
(
)
(
4
)
C
0
is
th
e
ca
p
ac
itan
ce
v
alu
e
wh
en
th
e
v
o
ltag
e
U
c
(
t)
is
n
u
ll a
n
d
α
is
th
e
p
r
o
p
o
r
tio
n
al
co
ef
f
icien
t.
I
n
th
e
r
est o
f
th
is
p
ap
er
,
C
0
an
d
α
ar
e
ass
u
m
ed
to
b
e
co
n
s
tan
t.
4.
E
XP
RE
SS
I
O
N
O
F
SC ST
A
T
E
V
E
C
T
O
R
E
x
ten
d
ed
Kalm
an
f
ilter
(
E
KF
)
allo
ws
s
tate
e
s
tim
atio
n
o
f
n
o
n
lin
ea
r
d
y
n
am
ic
s
y
s
tem
s
d
u
r
in
g
ea
ch
tim
e
p
er
io
d
.
I
n
o
u
r
s
tu
d
y
,
th
e
s
tate
v
ec
to
r
ch
o
s
en
in
o
u
r
wo
r
k
is
g
iv
en
in
(
5
)
.
=
[
1
2
3
4
]
=
[
]
(
5
)
E
KF
is
u
s
ed
to
esti
m
ate,
at
e
ac
h
tim
e
p
er
io
d
,
t
h
e
s
tate
v
ar
iab
les
o
f
a
co
n
tin
u
o
u
s
n
o
n
lin
ea
r
s
y
s
tem
d
ef
in
ed
b
y
(
6
)
:
{
̇
(
)
=
.
(
)
+
(
)
=
(
(
)
,
(
)
)
(
)
=
.
(
)
+
(
)
=
(
(
)
,
(
)
)
(
6
)
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
:
152
1
–
153
4
1526
Y
(
t
)
is
th
e
s
y
s
tem
o
u
tp
u
t,
wh
ich
co
r
r
esp
o
n
d
s
to
th
e
b
ias
v
o
ltag
e
U
s
(
t
)
in
o
u
r
s
tu
d
y
.
t
is
th
e
tim
e
in
d
ex
,
X
(
t
)
is
th
e
s
tate
v
ec
to
r
,
w
(
t
)
is
t
h
e
s
tate
n
o
is
e
an
d
v
(
t
)
is
th
e
m
ea
s
u
r
em
en
t n
o
is
e.
T
h
e
d
eter
m
i
n
at
io
n
o
f
w
(
t
)
an
d
v
(
t
)
ar
e
d
etailed
in
s
ec
tio
n
5
.
I
n
th
is
s
ec
tio
n
,
th
e
d
ete
r
m
in
ati
o
n
o
f
A
an
d
G
is
d
etailed
.
W
e
ass
u
m
e
th
at,
d
u
r
in
g
a
cy
cle
o
f
s
ev
er
al
c
h
ar
g
es/d
is
ch
ar
g
es,
th
e
v
a
r
iatio
n
in
r
e
s
is
tan
ce
is
n
eg
lig
ib
le.
W
e
also
co
n
s
id
er
t
h
at
th
e
ca
p
ac
itan
ce
in
cr
ea
s
es
with
an
alm
o
s
t
co
n
s
tan
t
r
is
in
g
s
lo
p
e
as
a
f
u
n
ctio
n
o
f
th
e
v
o
ltag
e,
with
a
p
r
o
p
o
r
t
io
n
al
co
ef
f
icien
t
α
.
W
e
ca
n
th
u
s
as
s
u
m
e
th
at
th
e
v
ar
iatio
n
s
o
f
r
esis
tan
ce
R
as
well
as o
f
th
e
p
r
o
p
o
r
ti
o
n
ality
f
ac
to
r
α
ar
e
ze
r
o
as a
f
u
n
ctio
n
o
f
tim
e:
=
0
(
7
)
=
0
(
8
)
T
h
e
d
er
iv
ativ
e
o
f
th
e
v
o
ltag
e
at
th
e
ter
m
in
als o
f
ca
p
ac
ito
r
is
d
escr
ib
ed
as
s
h
o
wn
in
(
9
)
:
=
.
−
(
2
.
2
−
²
)
.
(
9
)
B
ased
o
n
th
e
ex
p
r
ess
io
n
g
iv
en
in
(4
)
an
d
(
9
)
,
c
ap
ac
itan
ce
d
e
r
iv
ate
ca
n
b
e
d
escr
ib
ed
as
s
h
o
wn
in
(
1
0
)
:
=
.
=
.
(
.
−
)
(
²
.
²
−
²
)
.
(
1
0
)
Fin
ally
,
b
ased
o
n
p
r
ev
i
o
u
s
eq
u
atio
n
s
,
th
e
d
er
iv
ate
o
f
s
tate
v
e
cto
r
ca
n
b
e
ex
p
r
ess
ed
as
s
h
o
wn
in
(
1
1
)
:
̇
=
=
(
0
0
0
0
0
0
0
0
0
0
0
0
)
.
=
.
(
1
1
)
W
h
er
e:
{
=
−
(
)
4
²
.
1
²
−
3
²
=
1
.
(
)
4
²
.
1
²
−
3
²
=
4
2
.
(
)
4
²
.
1
²
−
3
²
=
−
4
.
(
)
4
²
.
1
²
−
3
²
(
1
2
)
T
h
e
esti
m
ated
s
y
s
tem
o
u
tp
u
t,
wh
ich
co
r
r
esp
o
n
d
s
to
t
h
e
v
o
lt
ag
e
at
th
e
ter
m
i
n
als
o
f
th
e
SC
,
is
d
en
o
ted
(
)
.
I
t
ca
n
b
e
ex
p
r
ess
ed
as a
f
u
n
ctio
n
o
f
s
tate
v
ec
to
r
as
s
h
o
wn
in
(
1
3
)
:
(
)
=
.
+
=
.
=
[
1
0
0
]
.
(
1
3
)
5.
E
XT
E
ND
E
D
K
A
L
M
A
N
F
I
L
T
E
R
SCH
E
M
E
On
e
o
f
th
e
ad
v
an
ta
g
es
o
f
u
s
in
g
ex
ten
d
e
d
Kalm
an
filt
er
(
E
KF)
is
i
ts
ab
ilit
y
to
d
ea
l
w
ith
n
o
n
lin
ea
r
s
y
s
tem
s
,
as
it
is
th
e
ca
s
e
ca
p
a
citan
ce
an
d
th
e
b
ias
v
o
lta
g
e
b
eh
av
io
r
o
f
SC
s
.
I
t
h
as
b
ee
n
u
s
ed
with
s
u
cc
ess
in
o
r
d
er
to
esti
m
ate
s
y
s
tem
s
s
tat
es
in
m
an
y
ap
p
licatio
n
s
[
1
6
]
,
[
1
8
]
,
[
1
9
]
,
[
2
9
]
.
I
ts
r
ec
u
r
s
iv
e
s
tr
u
ctu
r
e
an
d
lo
w
co
m
p
u
tatio
n
al
c
o
s
t
m
ak
e
it
s
u
itab
le
f
o
r
r
ea
l
-
tim
e
id
en
tific
atio
n
o
f
s
y
s
tem
s
tate
p
ar
am
eter
s
.
E
KF
allo
ws
th
e
esti
m
atio
n
o
f
s
y
s
tem
s
tate,
r
e
p
r
esen
ted
b
y
th
e
s
tate
v
ec
to
r
in
o
u
r
ca
s
e,
a
t
ea
ch
tim
e
s
tep
(
in
r
ea
l
-
tim
e)
.
I
n
ad
d
itio
n
,
E
KF
o
n
ly
r
eq
u
ir
es
ter
m
in
al
m
ea
s
u
r
e
m
en
t
o
f
v
o
ltag
e
an
d
cu
r
r
en
t,
wh
ich
ca
n
b
e
d
o
n
e
in
r
ea
l
-
tim
e.
A
f
u
n
ctio
n
al
d
iag
r
am
o
f
E
KF is p
r
esen
ted
in
Fig
u
r
e
7
.
T
h
e
E
KF
is
u
s
ed
to
esti
m
ate
th
e
s
tate
v
ec
to
r
X
o
f
a
s
y
s
tem
d
e
s
cr
ib
ed
b
y
(
6
)
.
I
n
th
is
eq
u
atio
n
,
Y
(
t
)
is
th
e
s
y
s
tem
o
u
tp
u
t
(
v
o
ltag
e
at
th
e
ter
m
in
als
o
f
th
e
SC
)
.
X
(
t
)
is
t
h
e
s
tate
v
ec
to
r
p
r
esen
ted
in
(
5
)
.
is
th
e
tim
e
v
ar
iab
le.
T
h
e
tim
e
in
cr
em
e
n
t
u
s
ed
f
o
r
o
u
r
s
im
u
latio
n
is
s
et
to
0
.
0
1
s
.
T
h
at
co
r
r
esp
o
n
d
s
to
s
am
p
lin
g
tim
e
u
s
ed
f
o
r
e
x
p
er
im
e
n
tal
v
o
ltag
e/c
u
r
r
e
n
t
m
ea
s
u
r
em
e
n
ts
.
w
(
t
)
an
d
v
(
t
)
r
ep
r
es
en
t
r
esp
ec
tiv
ely
s
tate
an
d
m
ea
s
u
r
em
en
t
n
o
is
e.
I
n
o
u
r
s
tu
d
y
,
it
is
a
s
s
u
m
ed
th
at
s
tate
an
d
m
ea
s
u
r
em
en
t
n
o
is
es
ar
e
wh
ite,
g
au
s
s
ian
,
u
n
c
o
r
r
elate
d
an
d
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
On
lin
e
d
ia
g
n
o
s
is
o
f su
p
erca
p
a
cito
r
s
u
s
in
g
ex
ten
d
ed
K
a
lma
n
fi
lter
…
(
Zo
u
b
id
a
B
o
u
o
u
ch
m
a
)
1527
ce
n
ter
ed
with
ze
r
o
ex
p
ec
tatio
n
.
I
t
is
also
ass
u
m
ed
t
h
at
th
e
n
o
is
es
w
(
t
)
an
d
v
(
t
)
ar
e
k
n
o
wn
r
esp
e
ctiv
ely
b
y
co
v
ar
ian
ce
m
atr
ices
W
an
d
V
.
T
h
e
ac
cu
r
ate
d
eter
m
in
atio
n
o
f
W
an
d
V
ter
m
s
is
d
if
f
icu
lt
s
in
ce
th
e
s
e
n
o
is
es
ar
e
r
elate
d
to
u
n
m
o
d
eled
d
y
n
am
i
cs
an
d
u
n
co
n
tr
o
lled
v
ar
iab
ilit
y
in
p
ar
a
m
eter
s
.
In
[
2
4
]
c
o
n
d
u
cted
an
em
p
ir
ical
s
tu
d
y
u
s
in
g
o
f
f
lin
e
d
atasets
to
esti
m
ate
th
e
v
ar
ian
ce
ter
m
s
,
wh
ich
allo
ws
th
e
esti
m
atio
n
th
e
ter
m
s
o
f
co
v
ar
ian
ce
m
atr
i
x
W
an
d
V
.
T
h
e
s
am
e
p
r
o
ce
d
u
r
e
is
u
s
ed
in
th
e
p
r
esen
t
s
tu
d
y
to
d
eter
m
in
e
W
an
d
V
.
T
h
er
ef
o
r
e,
th
e
c
o
v
ar
ian
ce
m
at
r
ix
o
f
n
o
is
e
co
n
d
itio
n
is
as
s
h
o
wn
in
(
1
4
)
an
d
(
1
5
)
:
=
(
0
.
1
2
0
.
0001
2
0
.
0001
2
0
.
1
2
)
(
1
4
)
=
0
.
01
(
1
5
)
T
h
e
E
KF
is
b
a
s
ed
o
n
two
im
p
o
r
tan
t
s
tep
s
:
p
r
ed
ictio
n
an
d
est
im
atio
n
.
T
h
e
f
ir
s
t
s
tep
co
n
s
is
t
s
o
n
p
r
ed
ictin
g
th
e
s
tate
v
ec
to
r
X
an
d
t
h
e
co
v
a
r
ian
c
e
m
atr
ix
o
f
th
e
esti
m
atio
n
er
r
o
r
P
(
t
)
,
wh
ich
s
atis
f
ies
as sh
o
wn
in
(
1
6
)
:
(
)
=
[
(
−
̃
)
.
(
−
̃
)
]
(
1
6
)
W
h
er
e,
X
̃
is
th
e
p
r
ed
icted
s
tate
v
ec
to
r
.
Fro
m
(
16
)
,
a
R
icca
ti d
i
f
f
er
en
tial e
q
u
ati
o
n
is
d
er
iv
e
d
t
o
co
m
p
u
te
P
(
t
)
:
̇
(
)
=
.
(
)
+
(
)
.
−
(
)
.
.
−
1
.
.
(
)
+
(
1
7
)
T
h
e
tr
an
s
itio
n
an
d
o
b
s
er
v
atio
n
m
atr
ices
u
s
ed
in
th
e
ex
ten
d
ed
k
alm
a
n
f
ilter
ar
e
d
ef
in
e
d
as
th
e
f
o
llo
win
g
J
ac
o
b
ian
s
(
th
e
f
ir
s
t o
r
d
er
p
a
r
tial d
er
iv
ativ
e
o
f
v
ec
to
r
f
u
n
ctio
n
s
)
:
=
|
(
18
)
=
|
(
19
)
T
h
e
s
ec
o
n
d
s
tep
o
f
th
e
e
x
ten
d
ed
Kalm
an
o
b
s
er
v
er
is
th
e
c
o
r
r
ec
tio
n
s
tep
,
w
h
er
e
th
e
Kal
m
an
f
ilter
g
ain
K
is
ca
lcu
lated
b
ased
o
n
th
e
co
v
ar
ian
ce
m
atr
ix
o
f
th
e
esti
m
atio
n
er
r
o
r
P
(
t
)
.
Usi
n
g
th
is
g
ain
,
th
e
p
r
ed
icted
s
tate
v
ec
to
r
X
̃
(
t
)
an
d
th
e
c
o
v
ar
ian
c
e
m
atr
ix
o
f
t
h
e
p
r
ed
icted
m
ea
s
u
r
em
en
t
e
r
r
o
r
P
̃
(
t
)
ar
e
u
p
d
at
ed
,
w
h
ich
lead
s
to
th
e
esti
m
ated
s
tate
X
̃
(
t
)
an
d
P
̃
(
t
)
.
Fig
u
r
e
7
s
h
o
ws th
e
f
u
n
ctio
n
al
d
i
ag
r
am
o
f
th
e
ex
te
n
d
ed
Kalm
a
n
f
ilter
.
Fig
u
r
e
7
.
Fu
n
ctio
n
al
d
iag
r
am
o
f
ex
ten
d
ed
Kalm
an
f
ilter
B
ef
o
r
e
u
s
in
g
th
e
p
r
o
p
o
s
ed
E
KF
s
ch
em
e,
it
i
s
im
p
o
r
tan
t
t
o
v
er
if
y
th
e
o
b
s
er
v
a
b
ilit
y
o
f
th
e
s
y
s
tem
.
B
ec
au
s
e
o
f
th
e
n
o
n
-
lin
ea
r
ity
o
f
o
u
r
s
y
s
tem
,
a
lin
ea
r
izatio
n
ar
o
u
n
d
an
o
p
er
atio
n
p
o
in
t
is
r
eq
u
ir
ed
[
4
3
]
,
[
4
4
]
.
T
h
e
o
b
s
er
v
a
b
ilit
y
is
th
en
v
er
i
f
ied
ar
o
u
n
d
an
eq
u
ilib
r
i
u
m
p
o
i
n
t
u
s
in
g
th
e
J
ac
o
b
ian
m
atr
ix
(
)
as
d
ef
in
ed
in
[
4
5
]
.
Af
ter
th
e
ca
lc
u
latio
n
o
f
(
)
,
we
f
o
u
n
d
t
h
at
(
(
)
)
=
4
,
wh
ich
co
r
r
e
s
p
o
n
d
to
th
e
o
r
d
e
r
o
f
o
u
r
s
y
s
tem
.
T
h
er
ef
o
r
e
,
o
u
r
s
y
s
t
em
is
o
b
s
er
v
ab
le
ar
o
u
n
d
its
eq
u
ilib
r
iu
m
p
o
in
t
[
4
5
]
.
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
:
152
1
–
153
4
1528
I
n
th
e
r
est
o
f
th
is
s
ec
tio
n
,
th
e
r
esu
lts
o
b
tain
ed
u
s
in
g
s
im
u
lati
o
n
ar
e
p
r
esen
ted
,
th
e
lim
itatio
n
o
f
u
s
in
g
E
KF
is
ex
p
lain
ed
to
h
ig
h
lig
h
t
th
e
n
ee
d
f
o
r
co
m
p
lem
en
tar
y
co
r
r
ec
tio
n
.
th
en
,
t
h
e
p
r
o
p
o
s
e
d
PID
co
r
r
ec
to
r
is
p
r
esen
ted
in
t
h
e
n
e
x
t
s
ec
tio
n
.
First,
s
im
u
latio
n
s
h
av
e
b
e
en
co
n
d
u
cted
u
s
in
g
c
o
n
v
e
n
tio
n
al
E
KF
s
ch
em
e
ex
p
lain
ed
in
th
e
p
r
esen
t
s
ec
ti
o
n
(
with
o
u
t
an
y
co
r
r
ec
tio
n
)
f
o
r
th
e
two
s
u
p
er
ca
p
ac
ito
r
s
an
d
u
s
in
g
th
e
cy
clic
cu
r
r
en
t
p
r
o
f
iles
d
escr
ib
ed
in
F
ig
u
r
e
3
.
I
n
o
r
d
er
to
esti
m
ate
t
h
e
r
esis
tan
c
e
an
d
ca
p
ac
itan
ce
u
s
in
g
co
n
v
en
tio
n
al
E
KF
alg
o
r
ith
m
,
ex
p
er
i
m
en
tal
b
ias
v
o
ltag
e
is
also
u
s
ed
(
Fig
u
r
e
4
)
with
th
e
s
am
e
tim
e
in
c
r
em
en
t
(
0
.
0
1
s
)
.
T
h
e
o
b
tain
ed
r
esis
tan
ce
an
d
ca
p
a
citan
ce
v
alu
es
u
s
in
g
c
o
n
v
e
n
tio
n
al
E
KF
alg
o
r
ith
m
wer
e
co
m
p
ar
ed
with
t
h
o
s
e
o
b
tain
ed
u
s
in
g
Ma
x
well
test
,
co
n
s
id
er
ed
as
th
e
r
ef
er
en
ce
v
alu
es.
Fig
u
r
e
8
an
d
Fig
u
r
e
9
s
h
o
w
th
e
o
b
tain
ed
r
esu
lts
.
As
s
h
o
wn
in
th
ese
f
ig
u
r
es,
s
im
u
latio
n
s
h
av
e
b
e
en
p
er
f
o
r
m
ed
u
s
in
g
d
if
f
e
r
en
t
in
itial
v
alu
es
o
f
ca
p
ac
itan
ce
an
d
r
esis
tan
ce
.
(
a)
(
b
)
Fig
u
r
e
8
.
E
s
tim
atio
n
o
f
s
u
p
e
r
c
ap
ac
ito
r
’
s
r
esis
tan
ce
u
s
in
g
d
if
f
er
en
t in
itial v
alu
es
f
o
r
two
SC
,
(
a)
B
C
AP1
5
0
0
; (
b
)
B
C
AP3
5
0
Fig
u
r
e
8
(
a)
an
d
Fig
u
r
e
8
(
b
)
s
h
o
ws
th
at,
r
eg
ar
d
less
o
f
th
e
in
itial
v
alu
e
ch
o
s
en
,
th
e
r
esis
tan
ce
co
n
v
er
g
es
to
war
d
v
alu
es
clo
s
e
to
ex
p
er
im
e
n
tal
r
esis
tan
ce
(
Ma
x
well
test
)
.
T
h
e
a
b
s
o
lu
te
er
r
o
r
s
b
etwe
en
s
im
u
lated
r
esis
tan
ce
an
d
Ma
x
well
test
r
esis
tan
ce
ar
e
r
esp
ec
tiv
ely
3
.
7
1
%
an
d
4
.
0
2
%
f
o
r
B
C
AP1
5
0
0
an
d
B
C
A
P3
5
0
.
Ho
wev
er
,
as
s
h
o
wn
in
Fig
u
r
e
9
(
a)
an
d
Fig
u
r
e
9
(
b
)
,
th
e
ca
p
ac
itan
ce
p
r
o
f
ile
is
h
ig
h
ly
d
ep
en
d
en
t
o
n
th
e
in
itial
v
alu
e.
W
h
en
th
i
s
later
is
f
ar
f
r
o
m
th
e
r
ea
l
v
a
lu
e
o
f
ca
p
ac
itan
ce
,
E
KF
is
u
n
ab
le
to
co
n
v
er
g
e
t
o
th
is
r
ea
l
v
alu
e.
As
th
e
ca
p
ac
itan
ce
is
o
n
e
o
f
th
e
k
ey
p
ar
a
m
eter
s
to
d
iag
n
o
s
is
s
u
p
er
ca
p
ac
i
to
r
s
s
tate
-
of
-
h
ea
lth
[
1
7
]
,
[
1
8
]
,
it
is
v
er
y
im
p
o
r
tan
t
to
ac
cu
r
ately
id
e
n
tify
th
is
p
ar
am
eter
d
u
r
in
g
SC
f
u
n
ctio
n
in
g
.
I
n
th
e
r
est
o
f
th
is
s
ec
tio
n
,
th
e
E
KF
s
ch
em
e
is
an
aly
ze
d
to
u
n
d
e
r
s
tan
d
wh
y
th
e
o
b
tai
n
ed
ca
p
ac
itan
ce
is
f
ar
f
r
o
m
th
e
c
o
r
r
ec
t
v
alu
e.
(
a)
(
b)
Fig
u
r
e
9
.
E
s
tim
atio
n
o
f
s
u
p
e
r
c
ap
ac
ito
r
’
s
ca
p
ac
itan
ce
u
s
in
g
d
if
f
er
en
t in
itial v
alu
es
f
o
r
two
SC
,
(
a)
B
C
A
P1
5
0
0
;
(
b
)
B
C
AP3
5
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
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lec
&
Dr
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N:
2
0
8
8
-
8
694
On
lin
e
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ia
g
n
o
s
is
o
f su
p
erca
p
a
cito
r
s
u
s
in
g
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ten
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a
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lter
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(
Zo
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id
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o
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o
u
ch
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a
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1529
As
ex
p
lain
ed
in
s
ec
tio
n
5
,
th
e
E
KF
d
eter
m
in
es
SC
s
tat
e
p
ar
am
eter
s
b
y
two
im
p
o
r
t
an
t
s
tep
s
:
p
r
ed
ictio
n
a
n
d
c
o
r
r
ec
tio
n
.
D
u
r
in
g
p
r
ed
ictio
n
s
tep
,
s
tate
p
ar
am
eter
s
ar
e
p
r
ed
icted
r
ec
u
r
s
iv
ely
as
s
h
o
wn
in
eq
u
atio
n
(
6
)
.
At
ea
ch
tim
e
in
c
r
em
en
t
t
n
,
th
e
d
er
iv
ate
X
̇
n
o
f
s
tate
p
ar
am
eter
s
is
f
ir
s
t
ca
lcu
lated
u
s
in
g
eq
u
atio
n
(
6
)
.
T
h
e
n
,
u
s
in
g
E
u
ler
'
s
m
eth
o
d
as
s
h
o
wn
in
(
2
0
)
,
th
e
s
tate
v
ec
to
r
X
n
at
tim
e
s
tep
t
n
is
p
r
ed
icted
u
s
in
g
th
e
d
er
iv
ate
X
̇
n
an
d
th
e
s
tate
v
ec
to
r
X
n
-
1
d
eter
m
in
ed
at
tim
e
s
tep
t
n
-
1
:
=
−
1
+
∆
×
̇
(
2
0
)
W
h
er
e
∆
t
is
th
e
tim
e
s
p
an
.
Sin
ce
s
tate
v
ec
to
r
is
ca
lcu
lated
r
ec
u
r
s
iv
ely
,
th
e
p
r
ed
icted
s
tate
v
alu
es
at
ea
ch
in
cr
em
e
n
t
ar
e
v
er
y
d
ep
en
d
e
n
t
o
n
th
e
i
n
itial
v
alu
es.
T
h
er
ef
o
r
e,
t
h
e
s
lig
h
test
er
r
o
r
in
in
itial
s
tate
v
ec
to
r
X
0
will
b
e
p
r
o
p
ag
ated
t
o
th
e
o
th
er
s
tate
v
ec
to
r
s
X
1
,
…,
X
n
.
Un
f
o
r
tu
n
ately
,
it
is
n
o
t
alwa
y
s
ea
s
y
to
ac
cu
r
ately
esti
m
ate
th
e
in
itial
s
y
s
tem
s
tate.
Mo
s
t
o
f
th
e
tim
e,
th
e
co
r
r
ec
tio
n
s
tep
p
r
o
p
o
s
ed
in
E
KF
s
ch
em
e
(
s
ec
tio
n
5
)
all
o
ws
to
co
r
r
ec
t
th
e
p
r
ed
ictio
n
e
r
r
o
r
s
ass
o
ciate
d
to
m
is
esti
m
atio
n
o
f
in
itial
s
tate
v
ec
to
r
.
T
h
is
is
o
n
e
o
f
th
e
b
en
ef
its
o
f
co
r
r
ec
tio
n
s
tep
,
p
r
o
p
o
s
ed
in
E
KF
s
ch
em
e.
Usi
n
g
th
e
g
ain
K
,
th
e
s
tate
v
ec
to
r
X
̂
P
p
r
ed
icted
at
th
e
f
ir
s
t
s
tep
o
f
E
KF
s
ch
em
e
ca
n
b
e
c
o
r
r
ec
ted
as
s
h
o
wn
in
(
2
1
)
.
T
h
is
in
clu
d
es
th
e
p
r
ed
ictio
n
er
r
o
r
s
ass
o
ciate
d
t
o
m
is
es
tim
atio
n
o
f
in
itial st
ate
v
ec
to
r
.
̂
=
̂
+
×
(
2
1
)
W
h
er
e
X
̂
C
is
th
e
co
r
r
ec
ted
s
tate
v
ec
to
r
an
d
E
r
r
is
th
e
er
r
o
r
b
etwe
en
s
im
u
lated
b
ias
v
o
ltag
e
U
s
an
d
ex
p
er
im
en
tal
b
ias v
o
ltag
e
Y
.
T
h
e
er
r
o
r
E
r
r
is
d
eter
m
in
ed
as
s
h
o
w
n
in
(
2
2
)
:
=
(
−
)
(
2
2
)
I
n
o
u
r
ca
s
e,
th
e
s
im
u
lated
b
ias v
o
ltag
e
U
s
is
o
b
tain
ed
b
y
:
=
.
=
[
1
0
0
]
.
[
]
=
+
.
(
2
3
)
As
ca
n
b
e
s
ee
n
in
(
2
3
)
,
a
m
o
n
g
th
e
f
o
u
r
s
tate
p
ar
am
eter
s
U
c
,
R
,
C
an
d
α
,
o
n
ly
s
u
p
er
ca
p
ac
ito
r
v
o
ltag
e
U
c
an
d
eq
u
iv
alen
t
r
esis
tan
ce
R
ar
e
u
s
e
d
to
esti
m
ate
b
ias
v
o
ltag
e
U
s
.
T
h
e
o
th
e
r
p
a
r
am
eter
s
C
an
d
α
ar
e
n
o
t
u
s
ed
.
C
o
n
s
eq
u
en
tly
,
th
e
co
r
r
ec
tio
n
ter
m
K
×
E
r
r
d
ep
en
d
s
o
n
l
y
o
n
U
c
an
d
R
.
On
ce
th
e
two
p
ar
a
m
eter
s
U
c
an
d
R
a
r
e
co
r
r
ec
ted
,
t
h
e
er
r
o
r
E
r
r
ten
d
s
to
war
d
s
ze
r
o
.
T
h
er
ef
o
r
e,
th
e
co
r
r
ec
tio
n
ter
m
K
×
E
r
r
also
ten
d
s
to
war
d
s
ze
r
o
.
As
a
co
n
s
eq
u
en
ce
,
th
e
p
ar
am
eter
s
C
an
d
α
ar
e
n
o
lo
n
g
er
c
o
r
r
ec
ted
.
T
h
is
ex
p
lain
s
wh
y
an
y
er
r
o
r
in
in
itial
v
alu
e
is
p
r
o
p
ag
ated
to
all
th
e
o
th
er
v
alu
es.
6.
CO
M
P
L
E
M
E
N
T
ARY
P
I
D
CO
R
RE
C
T
O
R
Fo
r
an
ef
f
ec
tiv
e
ca
p
ac
itan
ce
co
r
r
ec
tio
n
,
th
e
b
ias
v
o
ltag
e
s
im
u
lated
d
u
r
in
g
co
r
r
ec
tio
n
s
tep
m
u
s
t
b
e
d
eter
m
in
ed
co
n
s
id
er
in
g
th
e
v
alu
e
o
f
ca
p
ac
itan
ce
.
B
ased
o
n
Z
u
b
ieta
m
o
d
el
(
Fig
u
r
e
6
)
,
th
e
v
o
ltag
e
o
n
th
e
ter
m
in
als o
f
SC
ca
n
b
e
ex
p
r
es
s
ed
b
y
:
(
)
=
∫
1
(
)
.
0
+
0
+
.
(
2
4
)
W
h
er
e
U
0
is
th
e
v
o
ltag
e
o
n
th
e
ter
m
in
als
o
f
th
e
ca
p
ac
ito
r
wh
en
t
=
0s
.
C
o
n
s
id
er
in
g
tim
e
d
is
cr
etiza
tio
n
,
th
e
b
ias v
o
ltag
e
ca
n
b
e
ap
p
r
o
x
im
a
ted
b
y
:
(
)
=
∑
1
(
)
.
∆
=
0
,
…
,
+
0
+
.
(
)
(
2
5
)
Un
lik
e
th
e
b
ias
v
o
ltag
e
ex
p
r
ess
ed
in
(
2
3
)
,
as
s
h
o
wn
i
n
(
2
5
)
t
ak
es
in
to
ac
co
u
n
t
th
e
ca
p
ac
ita
n
ce
.
T
h
er
e
f
o
r
e,
th
e
b
ias v
o
ltag
e
ex
p
r
ess
ed
in
(
2
5
)
will b
e
u
s
ed
in
th
e
co
m
p
lem
en
tar
y
co
r
r
ec
tio
n
o
f
ca
p
ac
itan
ce
.
A
p
r
o
p
o
r
tio
n
al
–
in
teg
r
al
–
d
er
iv
ativ
e
co
r
r
ec
to
r
(
PID
c
o
r
r
ec
to
r
)
is
a
co
n
tr
o
l
l
o
o
p
th
at
u
s
e
f
ee
d
b
ac
k
r
esu
lts
to
co
r
r
ec
t
s
y
s
tem
o
u
tp
u
t.
B
ec
au
s
e
o
f
its
h
ig
h
ef
f
icie
n
cy
,
PID
is
a
wid
ely
u
s
ed
co
r
r
ec
to
r
in
in
d
u
s
tr
ial
ar
ea
.
I
t
is
v
er
y
ap
p
r
o
p
r
iate
to
s
y
s
tem
r
eq
u
ir
in
g
co
n
tin
u
o
u
s
co
r
r
ec
tio
n
,
wh
ich
co
r
r
esp
o
n
d
s
to
th
e
p
r
es
en
t
ca
s
e.
At
ea
ch
tim
e
in
cr
em
en
t,
th
e
e
r
r
o
r
v
alu
e
,
ex
p
r
ess
ed
in
(
2
6
)
,
is
ca
lcu
lated
as
th
e
d
if
f
er
en
ce
b
etwe
en
s
im
u
lated
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
:
152
1
–
153
4
1530
b
ias
v
o
ltag
e
U
sc
(
t
n
)
an
d
ex
p
e
r
im
en
t
al
b
ias
v
o
ltag
e
Y
(
t
n
)
.
I
t
is
wo
r
th
n
o
ticin
g
th
at
b
ias
v
o
ltag
e
U
sc
(
t
n
)
is
esti
m
ated
in
th
is
ca
s
e
u
s
in
g
(
2
5
)
.
T
h
e
r
ef
o
r
e
,
th
e
ca
p
ac
itan
c
e
is
co
n
s
id
er
ed
in
th
e
esti
m
ati
o
n
o
f
b
ias
v
o
ltag
e
.
B
ased
o
n
th
is
er
r
o
r
,
a
co
r
r
ec
ti
o
n
is
ap
p
lied
to
th
e
ca
p
ac
itan
ce
at
ea
ch
tim
e
in
cr
em
en
t
b
ased
o
n
p
r
o
p
o
r
ti
o
n
al
(
P
)
,
in
teg
r
al
(
I
)
an
d
d
e
r
iv
ate
(
D
)
as e
x
p
r
ess
ed
in
(
2
7
)
.
(
)
=
(
)
−
(
)
(
2
6
)
=
+
(
)
+
∑
(
)
.
∆
=
0
,
…
,
+
(
)
−
(
−
1
)
∆
(
2
7
)
C
pr
e
dict
e
d
r
ep
r
esen
ts
th
e
ca
p
ac
itan
ce
o
b
tain
ed
in
p
r
e
d
ictio
n
s
tep
o
f
E
KF.
C
c
or
r
e
c
ted
r
ep
r
esen
ts
th
e
co
r
r
ec
ted
ca
p
ac
itan
ce
.
K
P
,
K
I
an
d
K
D
d
en
o
te
th
e
co
e
f
f
icien
ts
f
o
r
t
h
e
p
r
o
p
o
r
tio
n
al,
in
te
g
r
al,
a
n
d
d
er
iv
ativ
e
co
r
r
ec
tio
n
ter
m
s
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
0
r
e
p
r
esen
ts
th
e
f
u
n
ctio
n
al
d
iag
r
am
o
f
ex
ten
d
ed
Kalm
a
n
f
ilter
co
m
b
in
ed
to
PID
co
r
r
ec
to
r
.
Fig
u
r
e
1
0
.
B
lo
ck
d
iag
r
a
m
o
f
e
x
ten
d
ed
Kalm
a
n
f
ilter
co
m
b
in
ed
to
PID
co
r
r
ec
to
r
7.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Usi
n
g
th
e
n
ew
al
g
o
r
ith
m
d
esc
r
ib
ed
in
Fig
u
r
e
1
0
(
E
KF
s
ch
e
m
e
co
m
b
i
n
ed
t
o
th
e
co
m
p
lem
en
tar
y
PID
)
an
d
th
e
cy
clic
cu
r
r
en
t/v
o
ltag
e
p
r
o
f
iles
p
r
esen
ted
ab
o
v
e,
s
im
u
latio
n
s
h
av
e
b
ee
n
e
x
ec
u
ted
f
o
r
th
e
two
d
if
f
e
r
en
t
s
u
p
er
ca
p
ac
ito
r
s
B
C
AP1
5
0
0
an
d
B
C
AP3
5
0
.
As
th
e
f
ir
s
t
s
im
u
latio
n
s
,
d
if
f
er
e
n
t
in
itial
v
alu
es
o
f
ca
p
ac
itan
ce
/r
esis
tan
ce
ar
e
test
ed
.
T
h
e
r
esu
lts
ar
e
p
r
esen
ted
an
d
d
is
cu
s
s
ed
in
th
e
p
r
esen
t
s
ec
tio
n
.
I
n
Fig
u
r
e
1
1
(
a)
an
d
Fig
u
r
e
1
1
(
b
)
,
a
c
o
m
p
ar
is
o
n
is
m
ad
e
b
etwe
en
t
h
e
s
im
u
lated
b
ias
v
o
ltag
e
o
b
tain
ed
b
y
th
e
n
ew
alg
o
r
ith
m
an
d
th
e
ex
p
er
im
en
tal
b
ias
v
o
ltag
e.
W
e
ca
n
clea
r
ly
s
ee
th
at
th
e
two
p
r
o
f
iles
r
em
ain
v
er
y
clo
s
e
th
r
o
u
g
h
o
u
t
th
e
s
im
u
latio
n
f
o
r
th
e
two
SC
.
T
h
e
m
ax
im
u
m
er
r
o
r
s
b
etwe
en
s
im
u
lated
an
d
ex
p
er
im
e
n
tal
b
ias
v
o
ltag
e
f
o
r
B
C
AP1
5
0
0
an
d
B
C
A
P3
5
0
ar
e
r
esp
ec
tiv
ely
0
.
0
0
7
V
(
0
.
3
%)
an
d
0
.
0
1
V
(
0
.
4
%).
T
h
ese
r
esu
lts
clea
r
ly
d
em
o
n
s
tr
ate
th
e
ab
ilit
y
o
f
th
e
n
ew
alg
o
r
ith
m
to
ac
cu
r
ately
s
im
u
late
th
e
b
ias v
o
ltag
e
.
T
h
e
r
ea
l
-
tim
e
ev
o
lu
tio
n
o
f
ca
p
ac
itan
ce
o
b
tain
ed
u
s
in
g
th
e
n
e
w
alg
o
r
ith
m
is
d
ep
icted
in
Fig
u
r
e
1
2
.
I
n
th
is
f
ig
u
r
e,
th
e
ca
p
ac
itan
ce
o
b
tain
ed
b
y
s
im
u
latio
n
is
co
m
p
ar
ed
to
th
e
ca
p
ac
itan
ce
o
b
tai
n
ed
u
s
in
g
Ma
x
well
test
,
co
n
s
id
er
ed
as
th
e
r
ef
er
en
ce
v
alu
e.
As
ca
n
b
e
s
ee
n
in
th
is
f
ig
u
r
e,
th
e
s
im
u
latio
n
was
p
er
f
o
r
m
ed
u
s
in
g
di
f
f
er
en
t
in
itial
v
alu
es
o
f
ca
p
ac
itan
ce
in
o
r
d
er
to
ass
ess
th
e
ab
ilit
y
o
f
th
e
n
ew
alg
o
r
ith
m
to
d
ea
l
with
er
r
o
r
s
ass
o
ciate
d
to
m
is
esti
m
atio
n
o
f
in
itial
ca
p
ac
itan
ce
.
Fro
m
Fig
u
r
e
1
2
(
a
)
a
n
d
Fig
u
r
e
1
2
(
b
)
,
it
ca
n
b
e
clea
r
ly
s
ee
n
E
x
p
e
ri
m
e
n
t
a
l
cu
r
re
n
t
in
t
e
n
s
ity
(I)
Ex
p
e
ri
m
e
n
t
a
l
bia
s
v
o
l
t
a
ge
(Y
)
+
+
+
-
Er
ro
r
be
t
w
e
e
n
a
n
d
+
+
+
∫
∫
+
+
÷
×
×
+
-
∫
+
+
̃
̇
̃
̃
̃
̃
Er
ro
r
be
t
w
e
e
n
a
n
d
̃
̃
̃
̃
Evaluation Warning : The document was created with Spire.PDF for Python.