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d
e
v
e
l
o
p
e
d
d
y
n
a
m
i
c
m
o
d
e
l
s
,
i
n
c
l
u
d
i
n
g
s
t
a
t
e
-
s
p
a
c
e
r
e
p
r
e
s
e
n
t
a
t
i
o
n
s
,
w
h
i
c
h
d
e
s
c
r
i
b
e
t
r
a
n
s
i
e
n
t
r
e
s
p
o
n
s
e
s
a
n
d
o
p
e
r
a
t
i
o
n
a
l
d
y
n
a
m
i
c
s
m
o
r
e
e
f
f
i
c
i
e
n
t
l
y
[
9
]
-
[
1
3
]
.
H
o
w
e
v
e
r
,
s
t
a
t
e
-
s
p
a
c
e
m
o
d
e
l
s
a
r
e
h
i
g
h
l
y
n
o
n
l
i
n
e
a
r
,
r
e
q
u
i
r
i
n
g
t
h
e
i
d
e
n
t
i
f
i
c
a
t
i
o
n
o
f
n
u
m
e
r
o
u
s
p
a
r
a
m
e
t
e
r
s
,
w
h
i
c
h
c
o
m
p
l
i
c
a
t
e
s
t
h
e
i
r
p
r
a
c
t
i
c
a
l
i
m
p
l
e
m
e
n
t
a
t
i
o
n
.
E
q
u
iv
alen
t
elec
tr
ical
cir
cu
it
m
o
d
els
p
r
o
v
id
e
a
s
im
p
lifie
d
y
et
ef
f
ec
tiv
e
r
e
p
r
esen
tatio
n
o
f
t
h
e
elec
tr
ical
b
eh
av
io
r
o
f
PEM
FC
s
u
s
in
g
s
tan
d
ar
d
co
m
p
o
n
e
n
ts
s
u
ch
as
r
esis
t
o
r
s
,
ca
p
ac
ito
r
s
,
an
d
in
d
u
c
to
r
s
.
Am
o
n
g
th
ese,
th
e
R
C
eq
u
iv
alen
t
cir
cu
it
is
wid
ely
u
s
ed
to
m
o
d
el
ch
ar
g
e
ac
cu
m
u
latio
n
a
n
d
tr
a
n
s
p
o
r
t
p
r
o
ce
s
s
es
d
u
e
to
its
s
im
p
licity
an
d
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
Ho
wev
er
,
R
C
m
o
d
els
o
f
ten
f
ail
to
ac
cu
r
ately
d
escr
ib
e
tr
an
s
ien
t
be
h
av
io
r
,
ag
in
g
ef
f
ec
ts
,
an
d
d
y
n
am
ic
lo
ad
v
ar
iatio
n
s
.
T
o
im
p
r
o
v
e
r
e
p
r
esen
tatio
n
,
alter
n
ati
v
e
f
r
am
ewo
r
k
s
s
u
ch
as
th
e
en
er
g
etic
m
ac
r
o
s
co
p
ic
r
ep
r
esen
tatio
n
(
EMR
)
h
a
v
e
b
e
en
d
ev
elo
p
ed
,
o
f
f
e
r
in
g
a
g
r
ap
h
ical
an
d
s
tr
u
ctu
r
e
d
m
eth
o
d
f
o
r
an
aly
zi
n
g
e
n
er
g
y
i
n
ter
ac
tio
n
s
i
n
PEM
FC
s
.
Desp
ite
th
eir
ad
v
an
tag
es,
t
h
ese
m
o
d
els
r
ely
h
ea
v
il
y
o
n
p
r
ec
is
e
p
ar
am
eter
esti
m
atio
n
,
wh
ich
r
em
ain
s
a
s
ig
n
if
ican
t c
h
allen
g
e
in
eq
u
iv
alen
t c
ir
cu
it m
o
d
elin
g
.
On
e
o
f
th
e
m
ajo
r
d
if
f
icu
lti
es
in
eq
u
iv
alen
t
cir
c
u
it
m
o
d
els
is
ac
cu
r
ately
d
eter
m
in
i
n
g
m
o
d
el
p
ar
am
eter
s
.
T
r
a
d
itio
n
al
p
ar
a
m
eter
esti
m
atio
n
tech
n
i
q
u
es,
s
u
ch
as
elec
tr
o
ch
e
m
ical
im
p
e
d
an
ce
s
p
ec
tr
o
s
co
p
y
(
E
I
S)
an
d
least
-
s
q
u
ar
es
o
p
tim
izatio
n
,
r
e
q
u
ir
e
lar
g
e
am
o
u
n
ts
o
f
ex
p
er
im
en
tal
d
ata
a
n
d
ar
e
h
ig
h
ly
s
en
s
itiv
e
to
m
ea
s
u
r
em
en
t
n
o
is
e
an
d
m
o
d
el
ass
u
m
p
tio
n
s
[
1
3
]
-
[
1
9
]
.
T
o
o
v
er
co
m
e
th
ese
c
h
allen
g
es,
m
ac
h
in
e
lear
n
i
n
g
-
b
ased
tech
n
iq
u
es
h
a
v
e
em
er
g
ed
as
p
o
wer
f
u
l
to
o
ls
f
o
r
d
ata
-
d
r
iv
en
p
ar
am
ete
r
esti
m
atio
n
.
I
n
p
ar
ticu
lar
,
p
h
y
s
ics
-
in
f
o
r
m
e
d
n
eu
r
al
n
etwo
r
k
s
(
PIN
Ns)
h
av
e
g
ain
ed
i
n
cr
ea
s
in
g
atten
tio
n
d
u
e
t
o
th
eir
ab
ilit
y
t
o
in
teg
r
ate
p
h
y
s
ical
co
n
s
tr
ain
ts
in
to
n
e
u
r
al
n
etwo
r
k
tr
ain
in
g
,
e
n
s
u
r
in
g
t
h
at
esti
m
ated
p
ar
am
ete
r
s
r
em
ain
p
h
y
s
ically
m
ea
n
in
g
f
u
l
wh
ile
im
p
r
o
v
in
g
g
en
e
r
aliza
tio
n
ac
r
o
s
s
d
if
f
er
e
n
t
o
p
e
r
atin
g
co
n
d
itio
n
s
.
T
h
is
m
ak
es
PIN
Ns
a
p
r
o
m
is
in
g
ap
p
r
o
ac
h
f
o
r
p
ar
a
m
eter
esti
m
atio
n
in
f
u
el
ce
ll
m
o
d
elin
g
[
2
0
]
-
[
2
5
]
.
I
n
th
is
s
tu
d
y
,
a
n
o
v
el
eq
u
iv
a
len
t
elec
tr
ical
cir
cu
it
f
o
r
PEM
FC
s
is
p
r
o
p
o
s
ed
,
in
teg
r
atin
g
a
PIN
N
-
b
ased
alg
o
r
ith
m
f
o
r
p
a
r
am
ete
r
id
en
tific
atio
n
.
T
h
e
n
ew
cir
c
u
it
is
d
esig
n
ed
to
en
h
a
n
ce
m
o
d
elin
g
ac
cu
r
ac
y
b
y
p
r
o
v
id
i
n
g
a
m
o
r
e
r
e
f
in
ed
r
ep
r
esen
tatio
n
o
f
b
o
th
d
y
n
a
m
ic
an
d
s
tead
y
-
s
tate
b
eh
a
v
i
o
r
s
,
wh
ile
en
s
u
r
in
g
co
m
p
u
tatio
n
al
e
f
f
icien
cy
.
T
o
ev
alu
ate
its
ef
f
ec
tiv
en
ess
,
th
e
p
r
o
p
o
s
ed
m
o
d
el
is
co
m
p
ar
ed
with
ex
is
tin
g
ap
p
r
o
ac
h
es,
in
clu
d
in
g
th
e
R
C
eq
u
iv
alen
t
cir
cu
it,
th
e
R
E
M
f
r
am
ewo
r
k
,
an
d
a
g
en
e
r
ic
PEM
FC
m
o
d
el.
E
x
p
er
im
en
tal
v
alid
atio
n
is
p
e
r
f
o
r
m
ed
u
s
in
g
a
1
.
2
k
W
PEM
FC
test
b
en
ch
,
allo
win
g
f
o
r
a
d
etailed
ass
ess
m
en
t
o
f
th
e
m
o
d
el’
s
ac
cu
r
ac
y
a
n
d
ad
ap
tab
ilit
y
ac
r
o
s
s
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
.
B
y
in
teg
r
atin
g
p
h
y
s
ics
-
in
f
o
r
m
e
d
m
ac
h
i
n
e
lear
n
i
n
g
i
n
to
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
elin
g
,
th
is
r
esear
ch
aim
s
to
b
r
id
g
e
th
e
g
a
p
b
etwe
e
n
tr
ad
itio
n
al
an
aly
tical
m
o
d
els
an
d
m
o
d
er
n
d
ata
-
d
r
i
v
en
tech
n
iq
u
es,
u
ltima
tely
p
r
o
v
id
in
g
v
alu
ab
le
in
s
ig
h
ts
f
o
r
p
er
f
o
r
m
an
ce
o
p
tim
izatio
n
,
r
ea
l
-
tim
e
co
n
tr
o
l,
a
n
d
p
r
ed
ictiv
e
d
iag
n
o
s
tic
s
o
f
PEM
FC
s
y
s
tem
s
.
T
h
is
p
ap
er
is
s
tr
u
ctu
r
e
d
as
f
o
llo
ws
:
i)
Sectio
n
2
o
u
tlin
es
th
e
th
eo
r
etica
l
p
r
in
cip
les
o
f
f
u
el
ce
lls
,
estab
lis
h
in
g
th
e
n
ec
ess
ar
y
b
ac
k
g
r
o
u
n
d
;
ii)
Sectio
n
3
p
r
esen
t
s
th
e
p
r
o
p
o
s
ed
eq
u
iv
alen
t
elec
tr
ical
cir
cu
it
m
o
d
el
;
iii)
Sectio
n
4
d
etails
th
e
PI
NN
-
b
ased
ap
p
r
o
ac
h
f
o
r
p
ar
a
m
eter
id
en
tific
atio
n
;
iv
)
Sect
io
n
5
d
escr
ib
es
th
e
ex
p
er
im
en
tal
s
etu
p
a
n
d
v
alid
a
tio
n
m
eth
o
d
o
lo
g
y
;
v
)
Sectio
n
6
a
n
aly
ze
s
th
e
r
esu
lts
,
co
m
p
ar
in
g
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
with
ex
is
tin
g
o
n
es
a
n
d
ex
p
e
r
im
en
tal
f
in
d
i
n
g
s
;
an
d
v
i)
F
in
ally
s
ec
tio
n
7
s
u
m
m
ar
izes
th
e
m
ain
co
n
clu
s
io
n
s
an
d
s
u
g
g
ests
p
o
te
n
tial d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
ese
ar
ch
.
2.
T
H
E
O
R
E
T
I
CA
L
P
RINC
I
P
L
E
S O
F
F
UE
L
C
E
L
L
F
u
e
l
c
el
l
s
g
e
n
e
r
a
t
e
el
e
c
t
r
i
c
i
t
y
t
h
r
o
u
g
h
e
l
e
c
t
r
o
c
h
e
m
i
c
al
c
o
n
v
e
r
s
i
o
n
,
d
i
r
e
c
tl
y
t
r
a
n
s
f
o
r
m
i
n
g
c
h
e
m
i
c
al
e
n
e
r
g
y
i
n
t
o
e
l
e
c
t
r
i
c
al
e
n
e
r
g
y
w
i
t
h
o
u
t
c
o
m
b
u
s
ti
o
n
.
I
n
t
h
i
s
r
e
g
a
r
d
,
f
u
e
l
c
e
l
l
s
s
h
a
r
e
s
i
m
i
l
a
r
it
ie
s
w
it
h
c
o
n
v
e
n
t
i
o
n
a
l
b
a
t
t
e
r
i
es
i
n
t
h
e
i
r
a
b
il
i
t
y
t
o
p
r
o
d
u
c
e
e
l
e
c
t
r
ic
a
l
p
o
w
e
r
.
H
o
w
e
v
e
r
,
t
h
e
f
u
n
d
a
m
e
n
t
a
l
d
is
ti
n
c
t
i
o
n
l
i
es
i
n
t
h
e
f
a
c
t
t
h
a
t
f
u
e
l
c
e
l
l
s
d
o
n
o
t
s
t
o
r
e
e
n
e
r
g
y
i
n
t
e
r
n
a
l
l
y
;
i
n
s
t
e
a
d
,
t
h
e
y
c
o
n
t
i
n
u
o
u
s
l
y
g
e
n
e
r
a
t
e
e
l
e
c
t
r
i
c
i
t
y
as
l
o
n
g
a
s
f
u
e
l
a
n
d
o
x
i
d
a
n
t
a
r
e
s
u
p
p
l
i
e
d
.
T
h
i
s
m
a
k
e
s
f
u
e
l
c
el
ls
s
u
i
t
a
b
l
e
f
o
r
a
p
p
li
ca
t
i
o
n
s
r
e
q
u
i
r
i
n
g
s
u
s
t
a
i
n
e
d
p
o
we
r
g
e
n
e
r
a
t
i
o
n
,
s
u
c
h
a
s
t
r
a
n
s
p
o
r
t
a
t
i
o
n
,
s
t
a
ti
o
n
a
r
y
p
o
w
e
r
p
l
a
n
t
s
,
a
n
d
p
o
r
t
a
b
l
e
e
n
e
r
g
y
s
y
s
te
m
s
.
2
.
1
.
St
ruct
ure
a
nd
o
pera
t
in
g
princip
le
o
f
a
P
E
M
F
C
T
h
e
s
tr
u
ctu
r
e
o
f
a
h
y
d
r
o
g
en
f
u
el
ce
ll c
o
m
p
r
is
es sev
er
al
k
ey
co
m
p
o
n
en
ts
,
in
clu
d
in
g
a
p
o
r
o
u
s
an
o
d
e,
a
ca
th
o
d
e,
an
d
a
s
o
lid
elec
tr
o
ly
t
e
m
em
b
r
a
n
e
th
at
s
ep
ar
ates
th
e
two
elec
tr
o
d
es,
as
s
h
o
wn
in
F
ig
u
r
e
1
.
T
h
e
an
o
d
e
s
er
v
es
as
th
e
s
ite
f
o
r
f
u
el
in
je
ctio
n
,
wh
er
e
elec
tr
o
c
h
em
ical
o
x
id
atio
n
o
f
h
y
d
r
o
g
en
o
cc
u
r
s
,
wh
ile
th
e
ca
t
h
o
d
e
f
ac
ilit
ates
th
e
r
ed
u
ctio
n
o
f
o
x
y
g
en
,
c
o
m
p
letin
g
th
e
r
ed
o
x
r
e
ac
tio
n
.
T
h
is
elec
tr
o
ch
em
ical
p
r
o
ce
s
s
g
en
er
ates
an
elec
tr
ic
cu
r
r
en
t
th
at
f
lo
ws
th
r
o
u
g
h
an
e
x
ter
n
al
cir
c
u
it,
d
eli
v
er
in
g
p
o
wer
to
a
c
o
n
n
ec
te
d
lo
ad
.
As
p
ar
t
o
f
t
h
e
ch
em
ical
r
ea
ctio
n
,
h
y
d
r
o
g
en
m
o
lecu
les
en
ter
in
g
th
e
an
o
d
e
ar
e
d
is
s
o
ciate
d
in
to
p
r
o
to
n
s
an
d
elec
tr
o
n
s
.
T
h
e
p
r
o
to
n
s
m
ig
r
ate
th
r
o
u
g
h
th
e
e
lectr
o
ly
te
m
em
b
r
an
e,
wh
er
ea
s
th
e
el
ec
tr
o
n
s
tr
a
v
el
th
r
o
u
g
h
t
h
e
ex
ter
n
al
cir
c
u
it,
th
er
eb
y
g
e
n
er
atin
g
u
s
ab
le
elec
tr
ical
en
er
g
y
.
At
th
e
ca
th
o
d
e,
t
h
e
elec
tr
o
n
s
r
ec
o
m
b
in
e
with
p
r
o
to
n
s
an
d
o
x
y
g
e
n
m
o
lecu
les to
f
o
r
m
wate
r
,
wh
ic
h
is
ex
p
elled
as a
h
ar
m
less
b
y
p
r
o
d
u
ct
[
2
0
]
.
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2804
-
2
8
1
8
2806
Pro
to
n
ex
c
h
an
g
e
m
em
b
r
a
n
e
f
u
el
ce
lls
(
PEM
FC
s
)
u
tili
z
e
a
s
o
lid
p
o
ly
m
er
m
em
b
r
a
n
e
as
th
e
elec
tr
o
ly
te,
wh
ich
allo
ws
th
e
s
elec
tiv
e
p
ass
ag
e
o
f
p
r
o
to
n
s
wh
ile
b
lo
ck
in
g
elec
tr
o
n
f
lo
w.
T
h
e
elec
tr
o
ch
e
m
ical
r
ea
ctio
n
s
o
cc
u
r
r
in
g
at
th
e
elec
tr
o
d
es a
r
e
g
o
v
er
n
ed
b
y
(
1
)
an
d
(
2
)
.
2
→
2
+
+
2
_
+
2
(
1
)
1
2
2
+
2
+
+
2
_
→
2
(
2
)
T
h
e
ef
f
icien
cy
o
f
PEM
FC
s
d
ep
en
d
s
o
n
t
h
e
o
p
e
r
atin
g
tem
p
e
r
atu
r
e,
p
r
ess
u
r
e,
a
n
d
r
ea
ctan
t c
o
n
ce
n
tr
atio
n
,
wh
ich
in
f
lu
en
ce
th
e
o
v
er
all
v
o
ltag
e
o
u
tp
u
t.
T
h
e
h
i
g
h
est
v
o
ltag
e
i
s
o
b
s
er
v
ed
u
n
d
er
o
p
e
n
-
cir
cu
it
co
n
d
itio
n
s
,
b
u
t
as
cu
r
r
en
t in
c
r
ea
s
es,
th
e
f
u
el
ce
ll
ex
p
er
ien
ce
s
v
ar
i
o
u
s
v
o
ltag
e
lo
s
s
es.
2
.
2
.
F
uel c
ell
po
la
riza
t
io
n c
urv
e
a
nd
perf
o
rm
a
nce
lo
s
s
es
T
h
e
ac
tu
al
o
p
e
r
atin
g
v
o
ltag
e
o
f
a
f
u
el
ce
ll
is
l
o
wer
th
a
n
it
s
th
eo
r
etica
l
m
a
x
im
u
m
d
u
e
t
o
in
h
e
r
en
t
lo
s
s
es
th
at
o
cc
u
r
d
u
r
in
g
o
p
er
a
t
io
n
.
T
h
ese
lo
s
s
es
d
ef
in
e
t
h
e
ch
ar
ac
ter
is
tic
p
o
lar
izatio
n
c
u
r
v
e
s
h
o
wn
in
Fig
u
r
e
2
an
d
ca
n
b
e
ca
teg
o
r
ized
in
t
o
ac
tiv
atio
n
lo
s
s
,
o
h
m
ic
lo
s
s
,
an
d
co
n
ce
n
tr
atio
n
lo
s
s
,
ea
ch
af
f
ec
tin
g
p
er
f
o
r
m
a
n
ce
at
d
if
f
er
en
t c
u
r
r
en
t
d
en
s
ities
.
Fig
u
r
e
1
.
Fu
el
ce
ll
s
ch
em
atic
Fig
u
r
e
2
.
Po
lar
izatio
n
cu
r
v
e
o
f
a
p
r
o
to
n
ex
c
h
an
g
e
m
em
b
r
an
e
f
u
el
ce
ll (
PEM
FC
)
2
.
2
.
1
.
Act
iv
a
t
i
o
n lo
s
s
es
T
h
ese
lo
s
s
es
co
r
r
esp
o
n
d
to
th
e
v
o
ltag
e
d
r
o
p
ca
u
s
ed
b
y
th
e
i
n
tr
in
s
ic
s
lu
g
g
is
h
n
ess
o
f
elec
tr
o
ch
em
ical
r
ea
ctio
n
s
at
th
e
elec
tr
o
d
es.
I
t
is
m
o
s
t
p
r
o
n
o
u
n
ce
d
at
lo
w
cu
r
r
e
n
t
d
e
n
s
ities
,
wh
er
e
en
e
r
g
y
is
r
eq
u
ir
e
d
to
o
v
er
co
m
e
th
e
ac
tiv
atio
n
b
ar
r
i
er
,
p
ar
tic
u
lar
ly
f
o
r
th
e
o
x
y
g
en
r
ed
u
ctio
n
r
ea
cti
o
n
(
OR
R
)
at
th
e
ca
th
o
d
e
[
5
]
.
T
h
e
u
s
e
o
f
h
ig
h
-
ef
f
icien
cy
ca
taly
s
ts
,
s
u
ch
as
p
latin
u
m
,
h
el
p
s
to
r
ed
u
ce
th
ese
lo
s
s
es.
T
h
ey
a
r
e
m
o
d
eled
u
s
in
g
th
e
T
af
el
eq
u
atio
n
as (
3
)
.
=
ln
(
0
)
(
3
)
0
is
th
e
ex
ch
an
g
e
cu
r
r
e
n
t d
en
s
it
y
,
wh
ich
r
e
f
lects th
e
ac
tiv
ity
o
f
th
e
ca
taly
s
t.
2
.
2
.
2
.
O
hm
ic
lo
s
s
es
Oh
m
ic
lo
s
s
es
ar
e
ass
o
ciate
d
with
r
esis
tiv
e
lo
s
s
e
s
d
u
e
to
th
e
elec
tr
o
n
ic
r
esis
tan
ce
in
th
e
elec
tr
o
d
es
an
d
th
e
io
n
ic
r
esis
tan
ce
in
th
e
elec
tr
o
ly
te.
Un
lik
e
ac
tiv
at
io
n
lo
s
s
es,
o
h
m
ic
lo
s
s
es
in
cr
ea
s
e
lin
ea
r
ly
with
cu
r
r
en
t
d
en
s
ity
,
lead
in
g
to
a
s
tead
y
v
o
ltag
e
d
r
o
p
[
5
]
.
Usi
n
g
lo
w
-
r
esis
tan
ce
m
ater
ials
an
d
h
ig
h
ly
c
o
n
d
u
ctiv
e
m
em
b
r
an
es m
in
im
izes th
ese
l
o
s
s
es.
T
h
ey
ar
e
g
iv
e
n
b
y
(
4
)
.
ℎ
=
(
4
)
T
h
e
m
em
b
r
an
e
r
esis
tan
ce
(
)
d
ep
en
d
s
o
n
m
em
b
r
an
e
th
ick
n
ess
,
co
n
d
u
ctiv
ity
,
an
d
tem
p
er
atu
r
e
,
as (
5
)
.
=
,
=
0
(
−
)
(
5
)
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
Dev
elo
p
men
t o
f a
P
E
M fu
el
ce
ll e
q
u
iva
len
t c
ir
cu
it mo
d
el
w
ith
…
(
I
s
ma
il A
it
T
a
leb
)
2807
2
.
2
.
3
.
Co
ncent
ra
t
io
n lo
s
s
es
At
h
ig
h
cu
r
r
e
n
t
d
en
s
ities
,
co
n
ce
n
tr
atio
n
lo
s
s
es
o
cc
u
r
d
u
e
to
m
ass
tr
an
s
p
o
r
t
lim
itatio
n
s
,
wh
er
e
r
ea
ctan
ts
b
ec
o
m
e
d
ep
lete
d
at
t
h
e
elec
tr
o
d
e
s
u
r
f
ac
e
,
r
e
d
u
cin
g
r
ea
ctio
n
r
ates
an
d
ca
u
s
in
g
a
s
h
ar
p
v
o
ltag
e
d
r
o
p
.
Pro
p
er
g
as
d
if
f
u
s
io
n
lay
er
s
(
GDL
s
)
an
d
o
p
tim
ized
f
lo
w
ch
an
n
els
h
elp
m
itig
ate
t
h
ese
ef
f
ec
ts
,
en
s
u
r
i
n
g
ef
f
icien
t
r
ea
ctan
t
s
u
p
p
ly
.
Min
im
izin
g
th
ese
lo
s
s
es
i
s
es
s
en
t
ial
f
o
r
im
p
r
o
v
in
g
f
u
el
ce
ll
ef
f
icien
cy
,
d
u
r
a
b
ilit
y
,
an
d
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
[
5
]
.
T
h
ey
a
r
e
ex
p
r
ess
ed
as
(
6
)
.
=
−
ln
(
1
−
)
(
6
)
T
h
e
lim
itin
g
cu
r
r
e
n
t
d
e
n
s
ity
(
)
d
e
f
in
es
th
e
m
ax
im
u
m
cu
r
r
en
t
th
e
ce
ll
ca
n
s
u
p
p
o
r
t,
b
as
ed
o
n
r
ea
ctan
t
d
if
f
u
s
io
n
r
ates.
3.
E
Q
UIVA
L
E
NT
E
L
E
C
T
RI
C
AL
CIR
CUI
T
3
.
1
.
P
r
o
po
s
ed
circ
uit
T
h
e
p
r
o
p
o
s
e
d
eq
u
i
v
a
le
n
t
ci
r
c
u
it
m
o
d
el
,
s
h
o
w
n
i
n
F
ig
u
r
e
3
,
c
ap
t
u
r
es
t
h
e
t
r
a
n
s
ie
n
t
el
ec
tr
o
c
h
e
m
i
ca
l
b
e
h
a
v
i
o
r
o
f
a
P
E
MFC
i
n
t
h
e
t
im
e
d
o
m
a
in
b
y
i
n
c
o
r
p
o
r
a
ti
n
g
k
e
y
r
esis
ti
v
e
,
ca
p
ac
i
ti
v
e
,
an
d
i
n
d
u
cti
v
e
e
le
m
e
n
ts
th
a
t
d
esc
r
i
b
e
its
d
y
n
am
ic
r
es
p
o
n
s
e.
T
h
e
o
h
m
ic
r
esis
ta
n
c
e
(
ℎ
)
ac
c
o
u
n
ts
f
o
r
i
o
n
ic
c
o
n
d
u
c
ti
o
n
lo
s
s
es
wit
h
i
n
th
e
ele
ct
r
o
ly
te
m
em
b
r
a
n
e
a
n
d
th
e
ele
ct
r
o
n
i
c
r
esis
ta
n
ce
o
f
t
h
e
el
ec
t
r
o
d
es
a
n
d
in
te
r
c
o
n
n
ec
ts
,
d
i
r
e
ctl
y
in
f
l
u
en
ci
n
g
th
e
i
n
s
t
a
n
ta
n
e
o
u
s
v
o
l
ta
g
e
d
r
o
p
.
T
h
e
ac
t
iv
ati
o
n
r
esis
t
an
c
e
(
)
ch
ar
ac
te
r
iz
es
t
h
e
k
in
eti
c
o
v
e
r
p
o
t
e
n
ti
al
ass
o
cia
te
d
wit
h
t
h
e
o
x
y
g
en
r
e
d
u
ct
io
n
r
e
ac
t
io
n
(
OR
R
)
a
t
t
h
e
c
ath
o
d
e
,
w
h
ic
h
d
o
m
i
n
ates
at
l
o
w
cu
r
r
e
n
t
d
e
n
s
it
ies
.
T
h
e
p
ar
all
el
b
r
an
c
h
c
o
n
s
is
ti
n
g
o
f
0
a
n
d
L
d
e
f
i
n
es
t
h
e
tr
a
n
s
ie
n
t
ef
f
e
cts
r
el
ate
d
t
o
t
h
e
a
d
s
o
r
p
ti
o
n
/
d
es
o
r
p
t
io
n
o
f
r
e
ac
ti
o
n
in
te
r
m
ed
iat
es,
i
n
t
r
o
d
u
cin
g
a
n
i
n
d
u
ct
iv
e
r
es
p
o
n
s
e
t
h
a
t
a
f
f
ec
ts
t
h
e
f
u
el
ce
l
l’
s
v
o
l
ta
g
e
r
e
co
v
e
r
y
f
o
ll
o
wi
n
g
v
a
r
i
ati
o
n
s
i
n
c
u
r
r
e
n
t
d
em
a
n
d
.
T
h
e
c
h
a
r
g
e
tr
a
n
s
f
er
r
esis
ta
n
c
e
(
1
)
r
e
p
r
ese
n
ts
t
h
e
d
i
r
ec
t
f
a
r
ad
a
ic
p
r
o
ce
s
s
es
th
at
co
n
t
r
i
b
u
te
t
o
t
h
e
o
v
e
r
a
ll
r
e
ac
t
io
n
r
at
e
w
it
h
o
u
t
b
ei
n
g
i
n
f
lu
e
n
ce
d
b
y
s
u
r
f
ac
e
co
v
er
ag
e
d
y
n
a
m
i
cs
.
A
d
d
it
io
n
all
y
,
th
e
d
o
u
b
l
e
-
la
y
e
r
ca
p
ac
i
ta
n
c
e
(
)
d
es
cr
ib
es
th
e
c
h
a
r
g
e
ac
c
u
m
u
lat
io
n
at
t
h
e
ele
ct
r
o
d
e/e
lec
tr
o
l
y
te
i
n
t
er
f
a
ce
,
wh
i
ch
s
i
g
n
i
f
ic
an
tl
y
i
m
p
a
cts
t
h
e
v
o
l
ta
g
e
r
es
p
o
n
s
e
t
o
r
ap
id
c
u
r
r
e
n
t
c
h
an
g
es
.
T
h
is
c
o
m
p
r
e
h
e
n
s
i
v
e
a
p
p
r
o
ac
h
y
ie
ld
s
a
n
u
an
ce
d
v
iew
o
f
PE
MFC
b
e
h
a
v
i
o
r
.
I
t
p
r
o
v
es
esp
e
cial
ly
v
a
lu
a
b
le
u
n
d
e
r
d
y
n
a
m
ic
l
o
a
d
c
o
n
d
iti
o
n
s
.
I
n
s
u
c
h
c
o
n
te
x
ts
,
tr
an
s
ie
n
t
p
h
en
o
m
e
n
a
p
la
y
a
d
e
cisi
v
e
r
o
le
.
Su
c
h
p
h
e
n
o
m
e
n
a
i
n
cl
u
d
e
c
h
a
r
g
e
r
ed
is
tr
ib
u
t
io
n
,
ele
ctr
o
ch
em
ic
al
r
ea
c
ti
o
n
k
i
n
etics
,
a
n
d
m
ass
t
r
a
n
s
p
o
r
t
d
ela
y
s
.
T
h
ei
r
i
n
c
l
u
s
i
o
n
e
n
h
a
n
ce
s
t
h
e
f
id
eli
ty
o
f
tim
e
-
d
o
m
ai
n
s
i
m
u
la
ti
o
n
s
.
C
o
n
s
eq
u
e
n
t
ly
,
th
e
s
i
m
u
la
ti
o
n
f
r
am
ewo
r
k
s
er
v
es
as
a
r
o
b
u
s
t
a
n
a
l
y
tica
l
t
o
o
l f
o
r
d
esi
g
n
o
p
ti
m
iz
ati
o
n
.
I
t
f
a
cil
itat
es
t
h
e
d
e
v
e
lo
p
m
e
n
t
o
f
a
d
v
a
n
ce
d
co
n
tr
o
l
s
t
r
a
te
g
ies
.
T
h
e
p
r
i
m
a
r
y
ai
m
s
a
r
e
t
o
m
iti
g
ate
tr
a
n
s
i
e
n
t
lo
s
s
es,
a
cc
ele
r
a
te
s
y
s
t
em
r
esp
o
n
s
e
,
a
n
d
i
m
p
r
o
v
e
o
v
e
r
al
l
en
er
g
y
c
o
n
v
er
s
io
n
e
f
f
ici
e
n
cy
.
Fig
u
r
e
3.
Pro
p
o
s
ed
e
q
u
iv
alen
t
elec
tr
ical
cir
cu
it m
o
d
el
f
o
r
PE
MFC
3
.
2
.
Det
er
m
ina
t
io
n o
f
mo
del pa
ra
m
et
er
s
Dev
elo
p
in
g
an
eq
u
iv
ale
n
t
cir
c
u
it
m
o
d
el
f
o
r
f
u
el
ce
lls
d
em
a
n
d
s
th
e
id
e
n
tific
atio
n
o
f
c
o
r
e
p
ar
am
eter
s
.
T
h
ese
in
clu
d
e
r
esis
tan
ce
s
,
ca
p
ac
itan
ce
s
,
an
d
in
d
u
ctan
ce
s
th
a
t
d
eter
m
in
e
th
e
s
y
s
tem
’
s
d
y
n
a
m
ic
r
esp
o
n
s
e
u
n
d
e
r
d
if
f
er
en
t
o
p
e
r
atin
g
c
o
n
d
itio
n
s
.
T
o
ac
cu
r
ately
d
escr
ib
e
th
e
f
u
el
ce
ll’s
elec
tr
ical
b
e
h
av
io
r
,
a
s
et
o
f
g
o
v
e
r
n
in
g
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2804
-
2
8
1
8
2808
eq
u
atio
n
s
is
estab
lis
h
ed
.
T
h
ese
eq
u
atio
n
s
ca
p
tu
r
e
in
ter
ac
t
io
n
s
am
o
n
g
th
e
cir
c
u
it
elem
en
ts
.
T
h
ey
d
ef
in
e
v
o
ltag
e
–
cu
r
r
en
t
r
elatio
n
s
h
ip
s
an
d
in
co
r
p
o
r
ate
b
o
t
h
s
tead
y
-
s
tate
an
d
tr
an
s
ien
t
ef
f
ec
ts
.
Su
c
h
f
o
r
m
u
latio
n
s
ar
e
ess
en
tial
f
o
r
ac
cu
r
ate
p
ar
am
eter
id
en
tific
atio
n
an
d
en
a
b
l
e
ef
f
ec
tiv
e
s
y
s
tem
o
p
tim
izatio
n
.
T
h
e
g
o
v
er
n
in
g
eq
u
atio
n
s
o
f
th
e
p
r
o
p
o
s
ed
eq
u
i
v
alen
t c
ir
cu
it m
o
d
el
ar
e
ex
p
r
e
s
s
ed
as (
7
)
-
(
1
3
)
.
=
−
−
ℎ
1
(
7
)
2
=
.
(
8
)
5
+
0
5
=
1
4
(
9
)
1
=
2
+
3
(
1
0
)
3
=
4
+
5
(
1
1
)
=
3
+
5
+
0
5
(
1
2
)
=
−
(
+
ℎ
)
1
+
−
5
+
0
5
(
1
3
)
4.
P
H
YSI
CS
-
I
NF
O
RM
E
D
N
E
URAL N
E
T
WO
RK
S (
P
I
NN
S)
4
.
1
.
I
ntr
o
du
ct
i
o
n t
o
P
I
NNs
Ph
y
s
ics
-
in
f
o
r
m
ed
n
eu
r
al
n
et
wo
r
k
s
(
PIN
Ns)
ar
e
a
class
o
f
d
ee
p
lear
n
in
g
m
o
d
els
th
a
t
in
teg
r
at
e
p
h
y
s
ical
laws
in
to
th
e
tr
ain
in
g
p
r
o
c
ess
.
T
h
ese
laws
ar
e
ex
p
r
ess
ed
as
p
ar
tial
d
if
f
er
en
tial
e
q
u
atio
n
s
(
PDEs)
o
r
o
r
d
in
ar
y
d
if
f
e
r
en
tial
eq
u
atio
n
s
(
ODE
s
)
.
Un
lik
e
tr
ad
itio
n
al
d
ata
-
d
r
iv
e
n
n
etwo
r
k
s
,
PIN
Ns
lev
er
ag
e
k
n
o
wn
p
h
y
s
ics
to
g
u
id
e
lear
n
in
g
,
r
ed
u
cin
g
th
e
n
ee
d
f
o
r
lar
g
e
la
b
eled
d
atasets
.
I
t
also
im
p
r
o
v
es
m
o
d
el
g
en
er
aliza
tio
n
.
PIN
Ns
ar
e
p
ar
ticu
lar
ly
v
alu
a
b
le
in
s
cien
tific
co
m
p
u
tin
g
.
T
h
ey
ca
n
s
o
lv
e
in
v
er
s
e
p
r
o
b
l
em
s
,
s
u
p
p
o
r
t
s
y
s
tem
id
en
tific
atio
n
,
an
d
s
er
v
e
as su
r
r
o
g
ate
m
o
d
els f
o
r
c
o
m
p
lex
p
h
y
s
ical
s
y
s
tem
s
[
2
0
]
-
[
2
5
]
.
4
.
2
.
P
I
NN
a
rc
hite
ct
ure
a
nd
f
o
rm
ula
t
io
n
T
h
e
f
o
r
m
u
latio
n
o
f
a
PIN
N
in
v
o
lv
es
in
teg
r
atin
g
p
h
y
s
ics
in
to
th
e
lo
s
s
f
u
n
ctio
n
,
wh
ich
co
n
s
tr
ain
s
th
e
n
etwo
r
k
to
s
atis
f
y
b
o
th
d
ata
-
d
r
iv
en
co
n
s
tr
ain
ts
an
d
g
o
v
er
n
in
g
eq
u
atio
n
s
.
4
.
2
.
1
.
Neura
l net
wo
rk
a
pp
ro
x
im
a
t
i
o
n
A
PIN
N
is
s
tr
u
ctu
r
ed
as
a
d
e
ep
n
eu
r
al
n
etwo
r
k
(
DNN)
p
ar
am
eter
ized
b
y
weig
h
ts
W
an
d
b
iases
b
,
m
ap
p
in
g
an
in
p
u
t x
t
o
an
o
u
tp
u
t
̂
,
as
(
1
4
)
.
̂
=
=
(
,
,
)
(
1
4
)
W
h
er
e
r
ep
r
esen
ts
th
e
f
in
al
lay
er
o
f
th
e
n
eu
r
al
n
etwo
r
k
.
T
h
e
n
etwo
r
k
is
co
m
p
o
s
ed
o
f
m
u
ltip
le
h
id
d
en
l
ay
er
s
with
ac
tiv
atio
n
f
u
n
ctio
n
s
g
,
wh
ich
in
tr
o
d
u
ce
n
o
n
-
lin
ea
r
ity
in
to
th
e
m
o
d
el.
4
.
2
.
2
.
P
hy
s
ics
-
info
rm
ed
lo
s
s
f
un
ct
io
n
T
h
e
f
u
n
d
am
en
tal
asp
ec
t
o
f
P
I
NNs
is
th
eir
p
h
y
s
ics
-
in
f
o
r
m
ed
lo
s
s
f
u
n
ctio
n
,
wh
ich
c
o
n
s
is
ts
o
f
two
m
ajo
r
ter
m
s
:
−
R
es
i
d
u
a
l
l
o
s
s
f
r
o
m
g
o
v
e
r
n
i
n
g
e
q
u
a
t
i
o
n
s
:
P
I
N
Ns
e
n
f
o
r
c
e
t
h
e
p
h
y
s
i
c
s
b
y
i
n
c
o
r
p
o
r
a
t
i
n
g
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
s
in
to
th
e
tr
ain
in
g
p
r
o
ce
s
s
.
Giv
en
a
d
if
f
e
r
en
tial o
p
e
r
ato
r
ℒ
,
th
e
n
etwo
r
k
m
in
im
izes th
e
r
esid
u
al
er
r
o
r
as (
1
5
)
.
=
1
∑
‖
ℒ
[
(
)
]
−
(
)
‖
2
=
1
(
1
5
)
W
h
er
e
ℒ
[
(
)
]
is
th
e
g
o
v
er
n
i
n
g
d
if
f
er
en
tial
eq
u
atio
n
a
p
p
lied
to
t
h
e
p
r
ed
icted
f
u
n
ctio
n
(
)
,
an
d
(
)
r
ep
r
esen
ts
th
e
k
n
o
wn
s
o
u
r
ce
t
er
m
.
d
en
o
tes
th
e
n
u
m
b
e
r
o
f
c
o
llo
ca
tio
n
p
o
in
ts
wh
er
e
th
e
PDE
r
esid
u
al
is
en
f
o
r
ce
d
.
−
B
o
u
n
d
ar
y
/
in
itial
c
o
n
d
itio
n
lo
s
s
:
T
o
en
s
u
r
e
t
h
at
th
e
p
r
e
d
icted
f
u
n
ctio
n
s
atis
f
ies
b
o
u
n
d
ar
y
o
r
in
itial
co
n
d
itio
n
s
,
an
ad
d
itio
n
al
te
r
m
is
in
tr
o
d
u
ce
d
,
as (
1
6
)
.
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
Dev
elo
p
men
t o
f a
P
E
M fu
el
ce
ll e
q
u
iva
len
t c
ir
cu
it mo
d
el
w
ith
…
(
I
s
ma
il A
it
T
a
leb
)
2809
=
1
∑
‖
[
(
)
]
−
(
)
‖
2
=
1
(
1
6
)
W
h
er
e
r
e
p
r
esen
ts
th
e
b
o
u
n
d
a
r
y
co
n
d
itio
n
o
p
e
r
ato
r
,
an
d
(
)
is
th
e
ex
p
ec
ted
b
o
u
n
d
ar
y
/in
itial
c
o
n
d
itio
n
v
alu
e.
−
Data
lo
s
s
:
I
n
ca
s
es
wh
er
e
o
b
s
er
v
atio
n
al
o
r
ex
p
er
im
en
tal
d
at
a
is
av
ailab
le,
an
ad
d
itio
n
al
d
ata
lo
s
s
ter
m
is
in
tr
o
d
u
ce
d
to
alig
n
th
e
m
o
d
el
with
k
n
o
wn
m
ea
s
u
r
em
en
ts
,
as (
1
7
)
.
=
1
∑
‖
(
)
−
‖
2
=
1
(1
7)
W
h
er
e
is
th
e
n
u
m
b
er
o
f
d
ata
p
o
in
ts
,
r
ep
r
esen
ts
th
e
o
b
s
e
r
v
ed
v
alu
es,
a
n
d
(
)
is
th
e
n
etw
o
r
k
'
s
p
r
ed
ictio
n
at
th
o
s
e
p
o
i
n
ts
.
T
h
is
ter
m
en
s
u
r
es
t
h
at
th
e
m
o
d
e
l
r
em
ain
s
co
n
s
is
ten
t
with
av
ai
lab
le
em
p
ir
ical
d
ata.
4
.
2
.
3
.
T
o
t
a
l lo
s
s
f
un
ct
io
n
T
h
e
to
tal
lo
s
s
f
u
n
ctio
n
is
d
e
f
in
ed
as
th
e
s
u
m
o
f
th
e
in
d
iv
id
u
al
co
n
t
r
ib
u
tio
n
s
f
r
o
m
th
e
p
h
y
s
ics
r
esid
u
als,
th
e
d
ata
f
id
elity
,
an
d
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
T
h
is
f
o
r
m
u
latio
n
allo
ws
th
e
PIN
N
to
in
co
r
p
o
r
ate
b
o
th
ex
p
er
im
en
tal
in
f
o
r
m
ati
o
n
an
d
p
h
y
s
ical
co
n
s
tr
ain
ts
d
u
r
in
g
tr
ai
n
in
g
.
B
y
b
alan
cin
g
th
ese
th
r
e
e
co
m
p
o
n
en
ts
,
th
e
n
etwo
r
k
ac
h
i
ev
es
p
h
y
s
ical
co
n
s
is
ten
cy
wh
i
le
m
ain
tain
in
g
p
r
ed
ictiv
e
ac
cu
r
ac
y
,
an
d
it
ca
n
b
e
ex
p
r
ess
ed
as
(
1
8
)
.
=
+
+
(
1
8
)
4
.
2
.
4
.
P
I
NN
t
ra
ini
ng
pro
ce
s
s
T
h
e
tr
ain
in
g
p
r
o
ce
s
s
o
f
a
PI
NN
f
o
llo
ws
th
ese
s
tep
s
:
i)
I
n
itialize
th
e
n
eu
r
al
n
etwo
r
k
with
r
an
d
o
m
weig
h
ts
an
d
b
iases
;
ii)
C
o
m
p
u
te
th
e
o
u
t
p
u
t
̂
f
o
r
g
iv
en
in
p
u
t
x
;
iii)
C
alcu
late
d
er
iv
ativ
es
o
f
̂
u
s
in
g
au
to
m
atic
d
if
f
er
en
tiatio
n
to
en
f
o
r
ce
PD
E
co
n
s
tr
ain
ts
;
iv
)
C
o
m
p
u
te
t
h
e
to
tal
lo
s
s
f
u
n
ctio
n
L
b
y
s
u
m
m
in
g
th
e
r
esid
u
als
f
r
o
m
th
e
g
o
v
er
n
in
g
eq
u
atio
n
s
an
d
b
o
u
n
d
a
r
y
c
o
n
d
itio
n
s
; a
n
d
v
)
C
h
ec
k
f
o
r
co
n
v
er
g
en
ce
:
-
C
h
ec
k
f
o
r
c
o
n
v
er
g
en
ce
:
I
f
th
e
lo
s
s
f
u
n
cti
o
n
f
alls
b
elo
w
t
h
e
p
r
ed
ef
in
e
d
e
r
r
o
r
to
ler
a
n
ce
ϵ
,
th
e
tr
ain
i
n
g
s
to
p
s
.
-
Oth
er
wis
e
,
p
ar
am
eter
s
(
W
,
b
)
ar
e
u
p
d
ate
d
u
s
in
g
a
n
o
p
tim
izatio
n
alg
o
r
ith
m
,
an
d
th
e
p
r
o
ce
s
s
r
ep
ea
ts
.
Fig
u
r
e
4
s
u
m
m
ar
izes
th
e
s
tep
s
d
escr
ib
ed
ea
r
lier
an
d
p
r
o
v
id
es
a
s
ch
em
atic
o
f
a
p
h
y
s
ics
-
in
f
o
r
m
ed
n
eu
r
al
n
etwo
r
k
(
PIN
N)
.
T
h
e
s
ch
e
m
a
tic
illu
s
tr
ates
h
o
w
p
h
y
s
ical
co
n
s
tr
ain
ts
in
teg
r
ate
in
to
t
h
e
lea
r
n
in
g
p
r
o
ce
s
s
.
T
h
is
iter
ativ
e
p
r
o
ce
s
s
en
s
u
r
es
th
at
th
e
tr
ain
ed
m
o
d
el
lear
n
s
a
s
o
l
u
tio
n
th
at
s
atis
f
ies
b
o
th
p
h
y
s
ical
co
n
s
tr
ain
ts
an
d
o
b
s
er
v
ed
d
ata.
4
.
3
.
Set
t
ing
up
t
he
P
I
NNs f
ra
m
ewo
r
k
B
u
ild
in
g
o
n
t
h
e
ea
r
lier
in
tr
o
d
u
ctio
n
o
f
Ph
y
s
ics
-
I
n
f
o
r
m
e
d
Neu
r
al
Netwo
r
k
s
(
PIN
Ns
)
an
d
t
h
e
g
o
v
er
n
in
g
eq
u
atio
n
s
o
f
t
h
e
p
r
o
p
o
s
ed
elec
tr
ical
eq
u
iv
ale
n
t
cir
cu
it,
th
is
s
ec
tio
n
p
r
esen
ts
a
PIN
N
-
b
ased
p
ar
am
eter
id
e
n
tific
atio
n
a
p
p
r
o
ac
h
.
T
h
e
f
r
am
ewo
r
k
lev
er
a
g
es
a
n
eu
r
al
n
etwo
r
k
to
a
p
p
r
o
x
im
at
e
k
ey
cir
cu
it
v
ar
iab
les.
I
t
e
n
f
o
r
ce
s
th
e
o
r
d
in
ar
y
d
if
f
er
en
tial
e
q
u
atio
n
s
g
o
v
er
n
in
g
th
e
f
u
el
ce
ll’s
d
y
n
a
m
ic
b
eh
av
i
o
r
.
T
h
is
d
esig
n
allo
ws
th
e
s
im
u
ltan
eo
u
s
lear
n
in
g
o
f
s
tate
v
ar
iab
les
an
d
cir
cu
it
p
ar
am
ete
r
s
.
I
t
ac
h
ie
v
es
ac
cu
r
ate
r
esu
lts
in
a
d
ata
-
ef
f
icie
n
t m
a
n
n
e
r
.
4
.
3
.
1
.
Neura
l net
wo
rk
a
pp
ro
x
im
a
t
i
o
n
A
n
eu
r
al
n
etwo
r
k
(
)
is
d
ef
in
ed
with
tr
ain
ab
le
p
a
r
am
eter
s
,
wh
er
e
th
e
n
etwo
r
k
o
u
t
p
u
ts
two
k
ey
q
u
an
titi
es f
o
r
ea
ch
tim
e
t
,
as in
(
1
9
)
.
[
̂
(
)
,
5
̂
(
)
]
=
(
)
(
1
9
)
Ad
d
itio
n
ally
,
th
e
p
h
y
s
ical
p
ar
am
eter
s
o
f
th
e
eq
u
iv
alen
t
cir
c
u
it
m
o
d
el,
s
u
ch
as:
{
,
ℎ
,
,
0
,
1
,
,
}
ar
e
tr
ea
ted
as tr
ain
ab
le
p
ar
am
e
ter
s
,
d
en
o
ted
as
.
T
h
u
s
,
th
e
o
v
er
all
tr
ain
ab
le
p
ar
a
m
eter
s
et
is
as (
2
0
)
.
=
∪
(
2
0
)
W
h
er
e
r
ep
r
esen
ts
th
e
n
e
u
r
al
n
etwo
r
k
weig
h
ts
an
d
b
iases
,
wh
ile
in
clu
d
es th
e
cir
cu
it p
a
r
am
eter
s
.
4
.
3
.
2
.
P
hy
s
ics
-
info
rm
ed
re
s
idu
a
ls
(
O
DE
c
o
ns
t
ra
int
s
)
T
o
en
f
o
r
ce
th
e
g
o
v
er
n
i
n
g
p
h
y
s
ical
eq
u
atio
n
s
,
th
e
d
er
iv
ativ
e
s
o
f
̂
(
)
an
d
5
̂
(
)
with
r
esp
ec
t
to
tim
e
ar
e
co
m
p
u
ted
u
s
in
g
au
to
m
atic
d
if
f
er
en
tiatio
n
.
T
h
ese
d
er
iv
ativ
es a
r
e
th
en
s
u
b
s
titu
ted
in
to
th
e
ODE
s
o
f
th
e
f
u
el
ce
ll e
q
u
iv
alen
t c
ir
cu
it:
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2804
-
2
8
1
8
2810
−
Vo
ltag
e
r
esid
u
al
1
(
)
=
̂
(
)
−
(
−
̂
(
)
−
ℎ
1
(
)
)
(
2
1
)
−
C
ap
ac
ito
r
cu
r
r
en
t
r
esid
u
al
2
(
)
=
2
(
)
−
̂
(
)
=
0
(
2
2
)
−
I
n
d
u
cto
r
cu
r
r
en
t r
esid
u
al
3
(
)
=
5
̂
(
)
−
0
5
̂
(
)
−
(
1
(
)
−
2
(
)
)
=
0
(
2
3
)
T
h
e
r
esid
u
als
r
ep
r
esen
t
th
e
d
if
f
er
en
ce
s
b
etwe
en
th
e
lef
t
-
h
an
d
an
d
r
i
g
h
t
-
h
a
n
d
s
id
es
o
f
th
e
ODE
s
.
T
h
ese
r
esid
u
als ar
e
m
in
im
ized
d
u
r
in
g
tr
ain
in
g
t
o
en
s
u
r
e
t
h
at
th
e
p
r
ed
icted
o
u
tp
u
ts
s
atis
f
y
th
e
p
h
y
s
ical
eq
u
atio
n
s
.
4
.
3
.
3
.
Da
t
a
lo
s
s
(
m
ea
s
urem
e
nt
co
ns
t
ra
ints)
T
h
e
m
o
d
el
in
co
r
p
o
r
ates
ex
p
er
i
m
en
tal
m
ea
s
u
r
em
en
ts
o
f
th
e
f
u
el
ce
ll
v
o
ltag
e
an
d
in
p
u
t
cu
r
r
en
t
{
(
)
,
1
(
)
}
.
T
y
p
ically
,
1
(
)
is
tr
ea
ted
as
an
i
n
p
u
t
(
o
r
b
o
u
n
d
ar
y
co
n
d
itio
n
)
,
wh
ile
(
)
is
u
s
ed
as
a
d
ata
co
n
s
tr
ain
t.
T
h
e
d
ata
lo
s
s
f
u
n
ctio
n
is
d
ef
i
n
ed
as (
2
4
)
.
=
1
∑
‖
̂
(
)
−
,
(
)
‖
2
=
1
(
2
4
)
T
h
is
en
s
u
r
es th
at
th
e
p
r
e
d
icted
v
o
ltag
e
̂
(
)
alig
n
s
with
th
e
o
b
s
er
v
ed
ex
p
er
im
en
tal
d
ata.
Fig
u
r
e
4
.
Sch
em
atic
r
ep
r
esen
t
atio
n
o
f
PIN
N
4
.
3
.
4
.
I
nitia
l a
nd
bo
un
da
ry
co
nd
it
io
ns
I
n
itial
co
n
d
itio
n
s
m
a
y
b
e
a
v
ailab
le
f
o
r
ce
r
tain
v
a
r
iab
les,
s
u
ch
as
(
)
an
d
5
(
)
.
I
f
t
h
ese
v
alu
es
ar
e
k
n
o
wn
,
t
h
ey
ca
n
b
e
d
i
r
ec
tly
e
n
f
o
r
ce
d
.
Oth
er
wis
e,
th
ey
ca
n
b
e
tr
ea
ted
as
tr
ain
ab
le
p
ar
am
et
er
s
o
r
ap
p
r
o
x
im
ate
d
u
s
in
g
i
n
itial g
u
ess
es.
A
lo
s
s
te
r
m
is
ad
d
ed
t
o
en
s
u
r
e
c
o
n
s
is
ten
cy
with
in
itial c
o
n
d
itio
n
s
:
=
|
̂
(
0
)
−
,
0
|
2
+
|
5
̂
(
0
)
−
5
,
0
|
2
(
2
5
)
4
.
3
.
5
.
T
o
t
a
l lo
s
s
f
un
ct
io
n
T
h
e
o
v
er
all
lo
s
s
f
u
n
ctio
n
co
m
b
in
es
th
e
p
h
y
s
ics
r
esid
u
als,
d
ata
co
n
s
tr
ain
ts
,
an
d
in
itial
co
n
d
itio
n
en
f
o
r
ce
m
e
n
t:
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
Dev
elo
p
men
t o
f a
P
E
M fu
el
ce
ll e
q
u
iva
len
t c
ir
cu
it mo
d
el
w
ith
…
(
I
s
ma
il A
it
T
a
leb
)
2811
(
,
)
=
1
+
2
+
3
(
2
6
)
T
h
e
p
ar
am
ete
r
s
1
,
2
,
an
d
3
in
th
e
to
tal
lo
s
s
f
u
n
ctio
n
,
th
e
y
s
er
v
e
as
weig
h
tin
g
co
ef
f
icien
ts
th
at
b
alan
ce
th
e
co
n
tr
ib
u
tio
n
s
o
f
d
i
f
f
er
en
t l
o
s
s
ter
m
s
in
th
e
PIN
N
f
r
am
ewo
r
k
.
5.
M
AT
E
R
I
AL
S AN
D
M
E
T
H
O
DS
5
.
1
.
E
x
perim
ent
a
l set
up
T
o
v
alid
ate
th
e
d
ev
elo
p
e
d
m
o
d
el,
ex
p
er
im
en
ts
wer
e
co
n
d
u
cted
u
s
in
g
th
e
B
AHI
A
d
i
d
a
ctic
b
en
ch
.
T
h
is
p
latf
o
r
m
f
ea
tu
r
es
2
4
P
E
MFC
s
with
a
co
m
b
in
ed
m
ax
im
u
m
p
o
wer
o
u
tp
u
t
o
f
1
.
2
k
W
an
d
an
o
u
tp
u
t
v
o
ltag
e
r
an
g
e
o
f
1
4
to
2
2
V,
with
a
n
o
m
in
al
cu
r
r
en
t
o
f
6
5
A.
T
h
e
B
AHI
A
b
en
ch
,
as
s
h
o
wn
in
Fig
u
r
e
5
,
is
eq
u
ip
p
e
d
with
a
h
u
m
a
n
-
m
ac
h
in
e
in
ter
f
ac
e
(
HM
I
)
,
wh
ich
allo
ws
f
o
r
th
e
p
r
ec
is
e
co
n
f
ig
u
r
atio
n
o
f
th
e
lo
ad
cu
r
r
en
t
an
d
en
ab
les
th
e
m
o
n
ito
r
in
g
o
f
t
h
e
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
th
e
f
u
el
ce
ll.
T
h
is
s
etu
p
f
ac
ilit
ates
a
d
ir
ec
t
co
m
p
ar
is
o
n
b
etwe
en
th
e
e
x
p
er
im
en
tal
d
ata
an
d
t
h
e
r
esu
lts
p
r
ed
icted
b
y
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
.
Fig
u
r
e
5
.
T
h
e
PEM
FC
test
b
en
ch
5
.
2
.
Sim
ula
t
i
o
n t
o
o
ls
T
o
v
alid
ate
th
e
p
r
o
p
o
s
ed
eq
u
iv
ale
n
t
cir
cu
it
m
o
d
el,
s
im
u
latio
n
s
wer
e
p
er
f
o
r
m
ed
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
,
wh
ile
Py
th
o
n
was
u
s
ed
to
r
u
n
th
e
PI
NNs
f
o
r
p
ar
am
eter
id
en
tific
at
io
n
,
esti
m
atin
g
th
e
f
u
el
ce
ll'
s
elec
tr
ical
an
d
p
ar
am
eter
s
.
5
.
2
.
1
M
AT
L
AB
/
Sim
uli
nk
f
o
r
f
uel c
ell
m
o
delin
g
:
T
wo
d
if
f
er
e
n
t M
AT
L
AB
/Si
m
u
lin
k
-
b
ased
m
o
d
els we
r
e
u
tili
ze
d
f
o
r
co
m
p
a
r
is
o
n
:
−
Gen
er
ic
MA
T
L
AB
PE
MFC
m
o
d
el:
A
Si
m
s
ca
p
e
-
b
as
e
d
g
e
n
e
r
ic
PE
M
f
u
e
l
c
ell
(
PE
MFC
)
m
o
d
el
was
u
s
e
d
t
o
s
im
u
la
te
f
u
el
ce
ll
b
e
h
a
v
i
o
r
u
n
d
e
r
v
a
r
i
o
u
s
o
p
er
ati
n
g
c
o
n
d
iti
o
n
s
.
T
h
is
m
o
d
el
p
r
o
v
i
d
es
a
d
e
ta
ile
d
,
d
ata
-
d
r
iv
e
n
s
im
u
la
ti
o
n
,
i
n
co
r
p
o
r
ati
n
g
e
lec
t
r
o
c
h
e
m
ic
al
an
d
th
e
r
m
al
d
y
n
a
m
ics
.
T
h
e
s
p
e
ci
f
ic
c
o
n
f
i
g
u
r
ati
o
n
a
n
d
p
a
r
a
m
et
e
r
v
al
u
es
ar
e
s
u
m
m
ar
ize
d
i
n
T
a
b
l
e
1
,
w
h
il
e
Fi
g
u
r
e
6
d
e
p
i
cts
t
h
e
s
tr
u
ct
u
r
e
o
f
t
h
is
MA
T
L
AB
m
o
d
el
.
−
E
q
u
i
v
a
le
n
t
RC
cir
cu
it
m
o
d
el
:
A
s
im
p
lifie
d
r
esis
to
r
-
ca
p
ac
ito
r
(
R
C
)
eq
u
iv
alen
t
cir
cu
it
wa
s
em
p
lo
y
ed
f
o
r
co
m
p
ar
is
o
n
,
as
illu
s
tr
ated
in
Fig
u
r
e
7
.
T
h
is
m
o
d
el
ca
p
tu
r
e
s
th
e
elec
tr
ical
d
y
n
am
ics
o
f
th
e
f
u
el
ce
ll.
I
n
p
ar
ticu
lar
,
it
r
ep
r
esen
ts
ch
ar
g
e
tr
an
s
f
er
r
esis
tan
ce
an
d
d
o
u
b
le
-
lay
e
r
ca
p
ac
itan
ce
.
T
h
i
s
co
n
f
ig
u
r
atio
n
en
ab
les
a
d
ir
ec
t
ev
alu
atio
n
o
f
tr
an
s
ien
t
r
esp
o
n
s
es.
C
o
n
s
eq
u
en
tly
,
th
e
R
C
m
o
d
el
p
r
o
v
id
es
a
s
im
p
lifie
d
y
et
in
s
ig
h
tf
u
l v
alid
atio
n
o
f
d
y
n
am
ic
ef
f
ec
ts
[
1
6
]
.
Op
er
atin
g
c
o
n
d
iti
o
n
s
wer
e
h
eld
co
n
s
tan
t
ac
r
o
s
s
all
s
im
u
latio
n
s
.
T
h
e
o
u
tp
u
ts
f
r
o
m
t
h
ese
m
o
d
els
wer
e
co
m
p
ar
ed
s
y
s
tem
atica
lly
with
ex
p
er
im
en
tal
d
ata.
T
h
ey
wer
e
also
ev
alu
ated
ag
ain
s
t
th
e
p
r
o
p
o
s
ed
eq
u
iv
alen
t
cir
cu
it m
o
d
el.
T
h
is
p
r
o
ce
s
s
p
r
o
v
id
ed
a
co
m
p
r
eh
en
s
iv
e
v
alid
atio
n
ap
p
r
o
ac
h
.
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2804
-
2
8
1
8
2812
T
ab
le
1
.
Par
am
eter
s
o
f
th
e
g
e
n
er
ic
Simscap
e
MA
T
L
AB
/Si
m
u
lin
k
f
u
el
ce
ll m
o
d
el
D
e
si
g
n
a
t
i
o
n
V
a
l
u
e
D
e
si
g
n
a
t
i
o
n
V
a
l
u
e
V
o
l
t
a
g
e
a
t
0
A
a
n
d
1
A
V
0
=
2
2
.
6
5
V
V
1
=
2
1
V
N
u
mb
e
r
o
f
c
e
l
l
s
N
=
2
4
N
o
mi
n
a
l
o
p
e
r
a
t
i
n
g
p
o
i
n
t
V
no
m
=
1
5
V
I
no
m
=
6
0
A
N
o
mi
n
a
l
s
u
p
p
l
y
p
r
e
s
su
r
e
P
O
=
1
b
a
r
P
H
=
1
.
3
b
a
r
M
a
x
i
m
u
m
o
p
e
r
a
t
i
n
g
p
o
i
n
t
I
e
nd
=
7
0
A
V
e
nd
=
1
4
.
4
V
O
p
e
r
a
t
i
n
g
t
e
mp
e
r
a
t
u
r
e
T
=
7
5
C
Fig
u
r
e
6
.
T
h
e
g
e
n
er
ic
MA
T
L
AB
/Si
m
u
lin
k
Simscap
e
m
o
d
el
o
f
a
PEM
FC
Fig
u
r
e
7
.
R
C
m
o
d
el
5
.
2
.
2
.
P
y
t
ho
n
I
n
th
is
s
tu
d
y
,
Py
th
o
n
was
e
m
p
lo
y
ed
f
o
r
p
a
r
am
eter
id
en
t
if
icatio
n
u
s
in
g
p
h
y
s
ics
-
in
f
o
r
m
ed
n
eu
r
al
n
etwo
r
k
s
(
PIN
Ns).
I
t
esti
m
ated
th
e
f
u
el
ce
ll’s
elec
tr
ical
an
d
elec
tr
o
ch
em
ical
p
a
r
am
eter
s
.
Py
th
o
n
p
r
o
v
id
es
h
ig
h
co
m
p
u
tatio
n
al
e
f
f
icien
cy
.
I
t
also
o
f
f
er
s
a
d
v
an
ce
d
o
p
ti
m
izatio
n
lib
r
ar
ies.
T
h
ese
f
ea
tu
r
es
en
ab
led
ac
cu
r
ate
f
itti
n
g
o
f
th
e
e
q
u
iv
alen
t
cir
c
u
i
t
m
o
d
el
to
ex
p
er
im
en
tal
d
ata.
T
h
is
,
in
tu
r
n
,
e
n
s
u
r
ed
a
r
eliab
le
r
ep
r
esen
tatio
n
o
f
th
e
f
u
el
ce
ll’s b
eh
a
v
io
r
.
5
.
2
.
3
.
Va
lid
a
t
io
n pa
ra
m
et
er
s
T
h
e
ac
cu
r
ac
y
o
f
th
e
p
r
o
p
o
s
ed
eq
u
iv
alen
t
cir
c
u
it
m
o
d
el
was
ass
e
s
s
ed
u
n
d
er
s
tatic
an
d
d
y
n
a
m
ic
co
n
d
itio
n
s
.
T
h
ese
ev
alu
atio
n
s
en
s
u
r
ed
its
r
eliab
ilit
y
f
o
r
PEM
FC
p
er
f
o
r
m
an
ce
a
n
aly
s
is
:
-
Static
t
est
in
g
: T
h
e
m
o
d
el
’
s
p
r
e
d
ictio
n
s
wer
e
co
m
p
a
r
ed
with
s
tead
y
-
s
tate
p
o
lar
izatio
n
c
u
r
v
es
to
ev
a
lu
ate
its
ab
ilit
y
to
ac
cu
r
ately
esti
m
ate
v
o
ltag
e
ac
r
o
s
s
d
if
f
er
e
n
t c
u
r
r
en
t
d
en
s
ities
.
-
Dy
n
am
ic
t
esti
n
g
:
Step
ch
an
g
e
s
in
lo
ad
cu
r
r
e
n
t
wer
e
ap
p
lied
.
T
h
is
test
ed
th
e
m
o
d
el’
s
ca
p
a
city
to
ca
p
tu
r
e
tr
an
s
ien
t
v
o
ltag
e
r
esp
o
n
s
es.
T
h
e
an
aly
s
is
in
clu
d
ed
th
e
ch
ar
g
e
d
o
u
b
l
e
-
lay
er
p
h
en
o
m
en
o
n
an
d
th
er
m
al
d
y
n
am
ics.
T
h
e
r
esu
lts
f
r
o
m
s
im
u
latio
n
s
an
d
ex
p
e
r
im
en
tal
m
ea
s
u
r
em
e
n
ts
wer
e
u
s
ed
to
v
alid
ate
th
e
m
o
d
el’
s
p
r
ed
ictiv
e
ca
p
ab
ilit
y
an
d
e
n
s
u
r
e
its
r
o
b
u
s
tn
ess
u
n
d
er
v
ar
y
in
g
c
o
n
d
itio
n
s
.
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
v
alid
atio
n
r
esu
lts
f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
el.
T
h
e
m
o
d
el’
s
o
u
tp
u
ts
wer
e
co
m
p
ar
ed
with
ex
p
er
im
en
tal
test
-
b
en
ch
d
ata
an
d
with
s
im
u
latio
n
s
f
r
o
m
th
e
g
en
er
ic
MA
T
L
AB
PEM
FC
m
o
d
el.
A
f
u
r
th
er
co
m
p
ar
is
o
n
was
m
ad
e
ag
ain
s
t
th
e
R
C
cir
cu
it
m
o
d
el.
T
h
e
an
aly
s
is
ev
alu
ates
b
o
th
s
tatic
an
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
T
h
ese
ev
alu
atio
n
s
o
f
f
er
in
s
ig
h
ts
in
to
th
e
m
o
d
el’
s
ac
cu
r
ac
y
an
d
its
ab
ilit
y
to
p
r
ed
ict
f
u
el
-
ce
ll
b
eh
av
io
r
ac
r
o
s
s
v
ar
io
u
s
co
n
d
it
io
n
s
.
6
.
1
.
P
a
ra
m
et
er
identif
ica
t
io
n u
s
ing
P
I
NNs
T
h
e
id
en
tific
atio
n
p
r
o
ce
s
s
aim
ed
to
r
ep
r
esen
t
th
e
f
u
el
ce
ll’s
elec
tr
ical
b
eh
av
io
r
ac
cu
r
ate
ly
.
I
t
r
elied
o
n
a
d
y
n
am
ic
s
tate
r
esp
o
n
s
e
d
r
iv
en
b
y
a
p
u
ls
e
in
p
u
t
cu
r
r
e
n
t
p
r
o
f
ile.
T
h
e
c
u
r
r
e
n
t
v
ar
ied
b
etwe
en
2
0
A
an
d
6
0
A,
as
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
PIN
N
f
r
am
ewo
r
k
lev
er
a
g
e
d
b
o
th
ex
p
e
r
im
en
tal
d
ata
a
n
d
g
o
v
er
n
in
g
e
q
u
atio
n
s
to
esti
m
ate
th
e
cir
cu
it
p
ar
am
e
ter
s
.
T
h
ese
p
ar
am
eter
s
wer
e
u
s
ed
to
r
ef
in
e
th
e
m
o
d
el,
alig
n
in
g
it
clo
s
ely
with
r
ea
l
-
wo
r
ld
b
e
h
av
io
r
.
T
h
e
i
d
e
n
tifie
d
p
ar
am
eter
s
ar
e
p
r
ese
n
ted
in
T
ab
le
2
,
ca
p
t
u
r
in
g
t
h
e
k
ey
r
esis
tan
ce
s
,
in
d
u
ctan
ce
,
a
n
d
ca
p
ac
i
tan
ce
in
f
lu
en
cin
g
t
h
e
f
u
el
ce
ll’s e
lectr
i
ca
l d
y
n
am
ics.
T
h
e
d
is
tr
ib
u
tio
n
o
f
p
r
ed
icti
o
n
er
r
o
r
s
is
s
h
o
wn
in
Fig
u
r
e
9
,
in
d
icatin
g
th
at
m
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Evaluation Warning : The document was created with Spire.PDF for Python.