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well
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s
tem
b
y
u
s
in
g
p
o
wer
elec
tr
o
n
ic
cir
cu
its
.
T
h
e
DC
v
o
ltag
e
m
u
s
t
b
e
lim
ited
with
in
a
n
ac
c
ep
tab
le
r
an
g
e
d
u
r
in
g
s
tead
y
s
tate
an
d
d
y
n
am
ic
co
n
d
itio
n
s
b
y
u
s
in
g
s
u
itab
le
co
n
tr
o
l
s
tr
ateg
ies.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
co
m
b
in
ed
o
p
er
atio
n
s
y
s
tem
o
f
SAP
F
an
d
f
u
el
ce
ll,
wh
ich
is
co
n
n
e
c
ted
to
th
e
d
c
lin
k
.
T
h
e
ad
v
an
t
ag
e
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
o
v
er
th
e
SAPF
is
to
co
m
p
en
s
ate
th
e
v
o
ltag
e
in
ter
r
u
p
tio
n
,
as
well
as
th
e
v
o
ltag
e
s
ag
,
h
ar
m
o
n
ics.
T
h
e
o
p
e
r
atio
n
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
was v
er
if
ied
th
r
o
u
g
h
s
i
m
u
latio
n
s
with
MA
T
L
AB
/Si
m
u
lin
k
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
T
h
e
o
b
jectiv
e
o
f
th
is
s
tu
d
y
is
to
s
u
p
p
ly
th
e
SA
PF
w
ith
a
SOF
C
s
o
u
r
ce
th
r
o
u
g
h
d
c
-
d
c
b
o
o
s
t
co
n
v
er
ter
s
to
ex
tr
ac
t
th
e
m
ax
i
m
u
m
p
o
wer
o
f
th
e
FC
an
d
s
ta
b
ilize
th
e
o
u
tp
u
t
o
p
e
r
atin
g
v
o
l
tag
e
o
f
th
e
DC
lin
k
,
wh
ile
co
m
p
en
s
atin
g
v
o
ltag
e
f
lu
ctu
atio
n
s
.
T
h
e
m
o
d
u
le
f
r
am
ewo
r
k
is
s
h
o
wn
in
F
ig
u
r
e
1
,
wh
er
e
a
s
en
s
itiv
e
th
r
ee
-
p
h
ase
l
o
ad
is
s
u
p
p
lied
b
y
a
t
h
r
ee
-
p
h
ase
s
o
u
r
ce
th
r
o
u
g
h
a
t
h
r
ee
-
p
h
ase
im
p
e
d
an
ce
.
T
h
e
in
jectio
n
m
o
d
e
o
f
th
e
SAPF
is
ac
h
iev
ed
th
r
o
u
g
h
a
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
,
w
h
er
e
lin
e
v
o
ltag
es
o
f
th
e
lo
ad
ar
e
r
esto
r
ed
a
r
o
u
n
d
its
r
ef
er
en
ce
v
alu
es
d
u
r
in
g
th
e
ap
p
lied
v
o
ltag
e
d
is
tu
r
b
an
ce
at
th
e
g
r
id
s
id
e.
T
h
e
s
to
r
ag
e
u
n
it
ca
n
b
e
r
ep
lace
d
b
y
th
e
SOFC
with
its
co
n
v
er
s
io
n
ch
ain
as v
iewe
d
in
th
e
Fig
u
r
e
1
.
L
O
A
D
Vs
S
o
u
r
c
e
V
o
l
t
a
g
e
I
n
j
e
c
t
i
n
g
t
r
a
n
s
f
o
r
m
e
r
AC
V
i
n
j
V
_
L
oa
d
C
f
R
f
L
f
C
1
C
2
S
1
S
2
S
t
o
r
a
g
e
u
n
i
t
Fig
u
r
e
1
.
Ge
n
e
r
al
co
n
f
ig
u
r
atio
n
o
f
th
e
SAPF
-
FC
s
y
s
tem
2
.
1
.
M
o
delin
g
a
nd
cha
ra
ct
er
is
t
ics o
f
SO
F
C
T
h
e
o
p
er
atin
g
p
r
in
ci
p
al
o
f
t
h
e
FOFC
d
ev
ice
is
b
ased
o
n
th
e
elec
tr
o
ch
em
ical
r
ea
ctio
n
b
etwe
en
h
y
d
r
o
g
en
a
n
d
o
x
y
g
en
ac
r
o
s
s
a
s
o
lid
elec
tr
o
ly
te,
in
o
r
d
e
r
to
g
en
er
a
te
e
lectr
icity
.
E
x
ac
tl
y
,
th
e
O²
io
n
s
ar
e
co
n
s
tr
u
cted
at
th
e
ca
th
o
d
e
s
id
e,
wh
er
e
th
e
o
x
y
g
en
ac
ce
p
ts
e
lectr
o
n
s
f
r
o
m
th
e
lo
a
d
cir
cu
it.
T
h
e
p
r
o
d
u
ce
d
io
n
s
ar
e
tr
an
s
f
er
r
ed
af
ter
war
d
to
th
e
an
o
d
e
th
r
o
u
g
h
th
e
elec
tr
o
ly
te,
an
d
th
en
co
m
b
in
ed
with
h
y
d
r
o
g
en
to
f
o
r
m
wa
ter
.
T
h
e
r
esu
lts
o
f
th
is
r
ea
c
tio
n
ar
e
t
r
an
s
f
er
r
e
d
th
r
o
u
g
h
t
h
e
lo
ad
cir
cu
it
to
th
e
ca
th
o
d
e
[
1
3
]
.
T
h
e
ess
en
tial
r
ea
ctio
n
s
o
f
th
e
SOFC
ar
e
th
e
f
o
llo
wi
n
g
,
at
th
e
ca
th
o
d
e:
2
+
4
−
1
→
2
−
2
(
1
)
at
th
e
an
o
d
e:
2
+
−
2
1
→
2
+
2
−
2
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
eries
a
ctive
p
o
w
er
filt
e
r
s
u
p
p
lied
b
y
fu
el
ce
ll fo
r
mitig
a
tin
g
p
o
w
er q
u
a
lity
… (
A
b
d
a
lla
h
B
e
n
A
b
d
elka
d
er
)
175
th
e
o
v
er
all
r
ea
ctio
n
is
:
2
+
1
/
2
2
1
→
2
(
3
)
th
e
d
y
n
a
m
ic
m
o
d
el
o
f
th
e
SO
FC
is
d
etailed
in
r
ef
er
en
ce
s
[
1
3
-
1
8
]
.
Fo
llo
win
g
ex
p
r
ess
io
n
r
e
p
r
esen
ts
th
e
o
u
tp
u
t v
o
ltag
e
o
f
th
e
s
tack
d
ev
ice:
=
(
−
ℎ
−
−
)
(
4
)
T
h
e
o
h
m
ic
lo
s
s
es
V
o
h
m
is
ca
u
s
ed
b
y
elec
tr
ical
r
esis
tan
ce
o
f
elec
tr
o
d
es,
th
e
r
esis
tan
ce
to
t
h
e
f
lo
w
o
f
io
n
s
in
th
e
elec
tr
o
ly
te,
wh
ich
c
an
b
e
d
e
d
u
ce
d
b
y
O
h
m
’
s
law.
2
.
1
.
1
.
O
hm
ic
lo
s
s
es
T
h
ese
lo
s
s
es
ar
e
d
u
e
to
th
e
o
p
p
o
s
itio
n
o
f
elec
tr
o
n
s
th
r
o
u
g
h
th
e
a
n
o
d
es
a
n
d
t
o
th
e
r
elo
ca
tio
n
o
f
p
ar
ticles th
r
o
u
g
h
th
e
elec
tr
o
l
y
te.
I
n
ad
d
itio
n
,
th
e
in
te
r
co
n
n
ec
tio
n
s
o
r
b
ip
o
lar
p
lates o
f
th
e
F
C
s
o
u
r
ce
ar
e
ad
d
ed
to
th
e
o
h
m
ic
lo
s
s
es [
1
3
-
1
5
]
.
ℎ
=
(
5
)
wh
er
e
r
is
th
e
in
ter
n
al
r
esis
tan
ce
an
d
i
fc
is
th
e
f
u
el
ce
ll st
ac
k
cu
r
r
en
t.
2
.
1
.
2
.
Act
iv
a
t
i
o
n lo
s
s
es
T
h
is
lo
s
s
is
ca
u
s
ed
b
y
th
e
s
lu
g
g
is
h
n
ess
o
f
ch
e
m
ical
r
ea
ct
io
n
th
at
tak
es
p
lace
o
n
th
e
s
u
r
f
ac
e
o
f
elec
tr
o
d
es.
A
d
r
o
p
v
o
ltag
e
p
r
o
d
u
ce
d
b
y
th
e
f
u
el
ce
ll
is
ca
r
r
y
i
n
g
th
e
r
ea
ctio
n
f
o
r
wa
r
d
,
wh
ic
h
tr
a
n
s
f
er
s
th
e
elec
tr
o
n
s
to
o
r
f
r
o
m
th
e
ele
ctr
o
d
e
[
1
3
]
.
T
h
e
ac
tiv
at
io
n
lo
s
s
v
act
is
g
iv
en
b
y
:
=
2
ln
(
)
(
6
)
wh
er
e
R
is
th
e
id
ea
l
g
as
co
n
s
tan
t,
T
i
s
th
e
tem
p
er
atu
r
e,
an
d
F
is
th
e
Far
ad
ay
co
n
s
tan
t.
T
h
e
co
ef
f
icien
t
α
r
ep
r
esen
ts
th
e
elec
tr
o
n
tr
an
s
f
er
o
f
t
h
e
r
ea
ctio
n
at
th
e
elec
t
r
o
d
e,
a
n
d
i
fc0
is
th
e
e
x
ch
an
g
e
cu
r
r
en
t
o
f
t
h
e
f
u
el
ce
ll st
ac
k
.
2
.
1
.
3
.
Co
ncent
ra
t
io
n lo
s
s
es
T
h
ese
lo
s
s
es
ar
e
k
n
o
w
n
as
m
ass
tr
an
s
p
o
r
t
l
o
s
s
es
an
d
ar
e
ca
u
s
ed
d
u
e
to
th
e
r
e
d
u
ctio
n
i
n
th
e
co
n
ce
n
tr
at
io
n
o
f
r
ea
ctan
ts
in
th
e
r
eg
io
n
o
f
th
e
elec
tr
o
d
e
wh
en
th
e
f
u
el
is
co
n
s
u
m
ed
.
T
h
e
co
n
s
u
m
p
tio
n
o
f
r
ea
ctan
ts
at
r
esp
ec
tiv
e
elec
tr
o
d
es,
i.e
.
h
y
d
r
o
g
e
n
at
th
e
a
n
o
d
e
an
d
o
x
y
g
en
at
th
e
ca
th
o
d
e
lead
s
to
a
s
lig
h
t
r
ed
u
ctio
n
in
th
e
r
ea
ctan
ts
co
n
ce
n
tr
atio
n
s
,
wh
ich
ca
u
s
e
a
d
r
o
p
in
p
ar
tial
p
r
ess
u
r
e
o
f
g
ases
r
esu
ltin
g
in
a
d
r
o
p
v
o
ltag
e
th
at
p
o
r
tio
n
o
f
th
e
elec
tr
o
d
e
ca
n
p
r
o
d
u
ce
[
1
3
]
.
T
h
e
c
o
n
ce
n
t
r
atio
n
lo
s
s
v
conc
is
d
ef
in
ed
b
y
(
7
)
:
=
2
ln
(
1
−
)
(
7
)
wh
er
e
if
cl
is
th
e
lim
itin
g
cu
r
r
e
n
t.
T
h
e
Ner
n
s
t
eq
u
atio
n
is
:
=
−
2
ln
(
2
√
2
2
)
(
8
)
wh
er
e
v
s
tan
d
ar
d
is
th
e
o
p
en
-
cir
cu
it
p
o
te
n
t
ial
at
th
e
s
tan
d
ar
d
p
r
ess
u
r
es.
p
H2
,
p
O2
an
d
p
H2O
ar
e
th
e
p
ar
tial
p
r
ess
u
r
e
o
f
h
y
d
r
o
g
e
n
,
o
x
y
g
en
an
d
wate
r
r
esp
ec
tiv
ely
.
T
h
u
s
,
th
ese
p
r
ess
u
r
es
ar
e
d
ef
in
ed
in
(
5
)
,
wh
ich
ar
e
as
f
o
llo
w:
2
=
−
1
2
2
+
1
2
2
(
2
−
2
)
(
9
)
2
=
−
1
2
2
+
1
2
2
(
2
−
2
)
(
1
0
)
2
=
−
1
2
2
+
1
2
2
2
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
9
,
No
.
2
,
Au
g
u
s
t 2
0
2
0
:
1
7
3
–
1
9
2
176
wh
er
e
τ
H2
,
τ
O2
an
d
τ
H2O
a
r
e
f
u
e
l,
air
an
d
f
u
el
ex
h
au
s
t
v
alv
es
t
im
e
co
n
s
tan
ts
r
esp
ec
tiv
ely
.
Qin
H2
,
q
in
H
2
O
ar
e
th
e
in
p
u
t
m
o
lar
f
lo
ws
o
f
h
y
d
r
o
g
e
n
an
d
wate
r
ac
r
o
s
s
th
e
an
o
d
e
v
alv
e
[
k
m
o
l/s
]
.
T
h
e
co
n
s
tan
ts
KH
2
,
KO
2
an
d
KH
2
O
a
r
e
th
e
v
al
v
e
m
o
l
ar
f
o
r
h
y
d
r
o
g
e
n
,
o
x
y
g
e
n
an
d
wate
r
r
esp
ec
tiv
ely
[
k
m
o
l/
(
s
at
m
)
]
.
Fo
r
m
o
d
elin
g
p
u
r
p
o
s
e,
a
co
n
s
tan
t is d
ef
in
e
d
b
y
Kr=
N
/4
F
.
T
h
e
to
tal
g
en
er
a
tio
n
o
f
th
e
f
u
el
ce
ll is
:
=
2
.
2
.
M
o
delin
g
a
nd
cha
ra
ct
er
is
t
ics o
f
SAPF
T
h
e
co
n
t
r
o
l
s
tr
ateg
y
u
s
ed
to
ex
tr
ac
t
th
e
r
e
f
er
en
ce
v
o
ltag
es
o
f
s
er
ies
ac
tiv
e
p
o
wer
f
ilter
(
SAPF
)
i
s
b
ased
o
n
th
e
PQ m
eth
o
d
[
1
5
,
19
]
,
a
n
d
th
e
c
o
n
tr
o
l sch
em
e
is
s
h
o
w
n
in
Fig
u
r
e
2
.
C
32
P
q
L
P
F
u
α
,
u
β
C
32
u
a
u
b
u
c
i
α
,
u
α
i
β
,
u
β
P
q
P
*
q
*
u
α
*
u
β
*
u
af
u
bf
u
cf
*
*
*
u
ac
u
bc
u
cc
*
*
*
+
-
-
-
+
+
C
u
r
r
e
n
t
Fig
u
r
e
2
.
Ser
ies ac
tiv
e
p
o
wer
f
ilter
s
tr
ateg
y
co
n
tr
o
l
T
h
e
g
r
id
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
is
ass
u
m
ed
to
b
e
s
y
m
m
e
tr
ic
an
d
n
o
t d
is
to
r
ted
:
[
]
=
[
∑
√
2
(
+
)
∞
=
1
∑
√
2
(
(
−
2
3
)
+
)
∞
=
1
∑
√
2
(
(
+
2
3
)
+
)
∞
=
1
]
(
1
2
)
wh
er
e
Un
an
d
θn
ar
e
r
esp
e
ctiv
ely
th
e
r
o
o
t
m
ea
n
s
q
u
ar
e
(
r
m
s
)
v
o
ltag
e
an
d
in
itial
p
h
ase
an
g
le,
n
is
th
e
h
ar
m
o
n
ic
o
r
d
er
.
W
h
en
n
=
1
,
it m
ea
n
s
th
r
ee
-
p
h
ase
f
u
n
d
a
m
en
tal
v
o
ltag
e
s
o
u
r
ce
.
[
]
=
[
√
2
1
(
+
1
)
√
2
1
(
(
−
2
3
)
+
1
)
√
2
1
(
(
+
2
3
)
+
1
)
]
(
1
3
)
T
h
e
(1
2)
is
tr
an
s
f
o
r
m
ed
in
to
(α
-
β)
r
ef
er
e
n
ce
f
r
a
m
e
,
[
]
=
32
[
]
=
√
3
[
∑
(
+
)
∞
=
1
∑
±
(
+
)
∞
=
1
]
(
1
4
)
32
=
√
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
(
1
5
)
T
h
e
th
r
ee
-
p
h
ase
p
o
s
itiv
e
f
u
n
d
am
en
tal
cu
r
r
e
n
t te
m
p
late
is
co
n
s
tr
u
cted
as
:
[
]
=
√
2
3
[
(
)
(
−
2
3
)
(
+
2
3
)
]
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
eries
a
ctive
p
o
w
er
filt
e
r
s
u
p
p
lied
b
y
fu
el
ce
ll fo
r
mitig
a
tin
g
p
o
w
er q
u
a
lity
… (
A
b
d
a
lla
h
B
e
n
A
b
d
elka
d
er
)
177
T
he
(
1
6
)
is
tr
an
s
f
o
r
m
ed
to
(α
-
β)
r
ef
er
en
ce
f
r
am
e
:
[
]
=
32
[
]
=
[
(
)
−
(
)
]
(
1
7
)
A
cc
o
r
d
in
g
t
o
th
e
in
s
tan
tan
e
o
u
s
r
ea
ctiv
e
p
o
wer
th
e
o
r
y
[
1
3
]
,
t
h
en
:
[
]
=
[
−
]
[
]
(
1
8
)
wh
er
e
AC
an
d
DC
co
m
p
o
n
en
t
s
ar
e
in
clu
d
ed
:
[
]
=
[
̅
+
̃
̅
+
̃
]
(
1
9
)
wh
er
e
p
an
d
q
a
r
e
p
ass
ed
th
r
o
u
g
h
lo
w
p
ass
-
f
ilter
(
L
PF
)
an
d
DC
co
m
p
o
n
en
t is g
o
tte
n
b
y
:
[
̅
̅
]
=
√
3
[
1
(
1
)
1
(
1
)
]
(
2
0
)
A
cc
o
r
d
in
g
t
o
[
1
5
]
,
tr
a
n
s
f
o
r
m
at
io
n
is
m
ad
e
:
[
]
=
[
−
]
[
]
=
[
−
]
[
]
(
2
1
)
T
h
e
DC
co
m
p
o
n
en
ts
o
f
an
d
:
[
̅
̅
]
=
[
−
]
[
]
=
[
−
]
[
]
(
2
2
)
T
h
e
f
u
n
d
am
en
tal
v
o
ltag
es in
(α
-
β)
r
ef
er
e
n
ce
f
r
a
m
e
ar
e:
[
]
=
[
−
]
−
1
[
̅
̅
]
=
[
−
]
[
̅
̅
]
(
2
3
)
T
h
e
th
r
ee
-
p
h
ase
f
u
n
d
am
en
tal
v
o
ltag
es a
r
e
s
p
ec
if
ied
b
y
:
[
u
af
u
bf
u
c
f
]
=
C
23
[
u
α
f
u
β
f
]
=
√
2
U
1
[
s
in
(
ω
t
+
θ
1
)
s
in
(
ω
t
+
θ
1
−
2π
3
)
s
in
(
ω
t
+
θ
1
+
2π
3
)
]
(
2
4
)
wh
er
e;
C
23
=
[
1
0
−
1
2
⁄
√
3
2
⁄
−
1
2
⁄
√
3
2
⁄
]
(
2
5
)
2
.
3
.
M
o
delin
g
o
f
DC
-
DC
bo
o
s
t
co
nv
er
t
er
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
o
r
s
tep
-
u
p
v
o
ltag
e
co
n
v
er
ter
,
s
tep
s
u
p
i
n
p
u
t
v
o
ltag
es,
s
tep
d
o
wn
in
p
u
t
cu
r
r
en
ts
o
f
th
e
DE
R
s
th
r
o
u
g
h
th
e
cir
cu
it
as
s
h
o
wn
in
Fig
u
r
e
3
.
V
low
an
d
V
high
ar
e
th
e
v
o
lta
g
e
at
lo
w
a
n
d
h
ig
h
v
o
ltag
e
s
id
es
r
esp
ec
tiv
ely
an
d
d
(
t)
is
th
e
s
witch
in
g
d
u
ty
cy
cl
e.
Gen
er
alize
d
eq
u
atio
n
s
o
f
th
e
p
o
wer
co
n
v
er
ter
s
ca
n
b
e
d
er
i
v
ed
f
o
r
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
C
C
M
d
u
e
to
its
s
im
p
licity
,
wh
er
e
two
s
tates
ar
e
u
s
ed
.
Star
tin
g
f
r
o
m
t
h
e
s
tate
s
p
ac
e
eq
u
atio
n
s
d
u
r
in
g
th
e
ON
-
O
FF
s
witch
in
g
s
tate
s
,
th
e
co
n
v
er
ter
m
o
d
el
ca
n
b
e
lin
ea
r
ized
u
s
in
g
an
av
er
a
g
in
g
m
eth
o
d
.
Fo
r
th
e
u
s
ed
d
c
-
d
c
co
n
v
er
ter
s
,
wh
en
th
e
s
witch
in
g
d
ev
ice
is
tu
r
n
ed
o
n
,
it
co
n
d
u
cts
f
o
r
a
r
atio
D
o
f
a
p
er
io
d
(
2
6
)
,
an
d
wh
en
t
h
e
s
witch
in
g
d
e
v
ice
is
tu
r
n
ed
o
f
f
,
th
e
d
io
d
e
co
n
d
u
cts
f
o
r
a
r
atio
o
f
(
1
-
D)
o
f
th
e
s
am
e
p
e
r
io
d
(
2
7
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
9
,
No
.
2
,
Au
g
u
s
t 2
0
2
0
:
1
7
3
–
1
9
2
178
{
̇
=
+
[
̇
]
=
[
0
0
0
−
1
]
[
]
+
[
1
0
]
(
2
6
)
{
̇
=
+
[
̇
]
=
[
0
−
1
1
−
1
]
[
]
+
[
0
0
]
(
2
7
)
T
h
e
(
2
8
)
is
u
s
ed
to
lin
ea
r
ize
th
e
ab
o
v
e
s
tate
-
s
p
ac
e
eq
u
ati
o
n
s
o
f
th
e
b
u
ck
co
n
v
er
ter
,
wh
er
e
X
is
th
e
s
tead
y
-
s
tate
co
m
p
o
n
en
t a
n
d
D
is
th
e
s
tead
y
s
tate
o
r
DC
co
m
p
o
n
en
t d
u
ty
-
r
atio
.
̇
=
[
+
(
1
−
)
]
+
[
+
(
1
−
)
]
(
2
8
)
{
[
̇
]
=
[
0
−
1
−
1
−
−
1
]
[
]
+
[
−
]
(
2
9
)
V
H
C
u
r
r
e
n
t
r
e
g
u
l
a
t
o
r
V
o
l
t
a
g
e
r
e
g
u
l
a
t
o
r
I
L
(
m
a
x
)
*
I
L
*
D
+
-
V
L
L
C
s
I
L
(
a
)
Fig
u
r
e
3
.
C
lo
s
ed
lo
o
p
b
o
o
s
t c
o
n
v
er
ter
cir
c
u
it
2
.
3
.
1
.
P
er
t
urb a
nd
o
bs
er
v
e
P&
O
T
h
is
MPPT
m
eth
o
d
is
th
e
wid
ely
co
m
m
o
n
an
d
u
s
ed
d
u
e
to
its
s
im
p
licity
an
d
it
s
ea
s
e
o
f
im
p
lem
en
tatio
n
.
T
h
u
s
,
th
is
MPPT
m
eth
o
d
p
er
t
u
r
b
s
th
e
s
y
s
tem
v
ar
iab
les
(
v
o
lt
ag
e
an
d
c
u
r
r
e
n
t)
,
an
d
co
n
s
eq
u
en
tly
o
b
s
er
v
es
th
e
o
u
tp
u
t
g
e
n
er
atio
n
o
f
th
e
FC
s
o
u
r
ce
.
T
h
e
p
r
in
ci
p
a
l
o
f
th
is
te
ch
n
iq
u
e
is
to
ad
ju
s
t
th
e
o
p
er
atin
g
v
o
ltag
e
o
f
th
e
s
y
s
tem
ar
o
u
n
d
th
e
m
ax
im
u
m
p
o
wer
p
o
i
n
t
(
∆P=∆
V>
0
)
,
(
∆P=∆
V
<0
)
.
T
h
e
m
ath
em
atica
l
ex
p
r
ess
io
n
th
at
r
esu
m
es
th
e
o
p
e
r
atin
g
p
r
in
cip
al
o
f
th
e
P&
O
alg
o
r
ith
m
is
:
(
)
=
(
−
1
)
+
∆
.
(
|
=
−
1
)
(
3
0
)
T
h
e
f
o
llo
win
g
T
a
b
le
1
ca
n
ill
u
s
tr
ate
th
e
v
ar
iatio
n
o
f
th
is
M
PP
T
tech
n
iq
u
e
ar
o
u
n
d
th
e
MPP
o
p
er
atin
g
p
o
i
n
t
o
f
th
e
s
y
s
tem
.
T
ab
le.
1
Dis
tu
r
b
an
ce
s
o
f
V
-
P
cu
r
v
e
(
∆P/∆V
)
o
f
P&
O
MPPT
tech
n
iq
u
e
D
i
st
u
r
b
a
n
c
e
C
h
a
n
g
e
i
n
t
h
e
p
o
w
e
r
N
e
x
t
d
i
st
u
r
b
a
n
c
e
P
o
si
t
i
v
e
P
o
si
t
i
v
e
P
o
si
t
i
v
e
P
o
si
t
i
v
e
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
P
o
si
t
i
v
e
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
N
e
g
a
t
i
v
e
P
o
si
t
i
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
eries
a
ctive
p
o
w
er
filt
e
r
s
u
p
p
lied
b
y
fu
el
ce
ll fo
r
mitig
a
tin
g
p
o
w
er q
u
a
lity
… (
A
b
d
a
lla
h
B
e
n
A
b
d
elka
d
er
)
179
3.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
I
n
th
is
s
ec
tio
n
,
MA
T
L
AB
/S
im
u
lin
k
s
im
u
latio
n
r
esu
lts
a
r
e
p
r
e
s
en
ted
an
d
d
is
cu
s
s
ed
in
d
etails.
T
h
e
p
r
o
p
o
s
ed
SAPF
-
FC
m
o
d
el
is
s
im
u
lated
b
y
MA
T
L
AB
/
Simu
lin
k
as
s
h
o
wn
in
F
ig
u
r
e
4
.
T
h
u
s
,
f
iv
e
p
h
en
o
m
en
a
ar
e
s
tu
d
ied
in
th
is
p
ap
er
,
wh
er
e
th
e
SAPF
with
t
h
e
SOFC
co
m
p
e
n
s
ate
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