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1
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1411
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O
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ATLAB
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T
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CC B
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C
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Am
al
Satif
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ab
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Ad
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s
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in
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n
al
Sch
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o
l o
f
A
p
p
lied
Scien
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s
(
E
NSA)
Ken
itra
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Mo
r
o
cc
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m
ail: a
m
al.
s
atif
@
u
it.a
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m
a
1.
I
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T
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t
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m
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tal
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atm
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p
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p
o
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ee
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allen
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r
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clim
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,
h
u
m
an
h
ea
lth
,
an
d
ec
o
n
o
m
ic
s
tab
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y
[
1
]
.
Fu
r
th
er
m
o
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th
e
d
e
p
letio
n
o
f
f
o
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is
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s
u
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tain
ab
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s
o
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s
[
2
]
.
T
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t
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ch
allen
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r
en
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le
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in
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n
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ter
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Ho
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ter
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tin
u
o
u
s
an
d
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p
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s
u
p
p
ly
[
2
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.
Ad
d
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in
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th
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eq
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ir
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atin
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ies in
to
r
en
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le
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y
s
y
s
t
em
s
[
3
]
.
Hy
b
r
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r
id
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co
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m
s
p
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m
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to
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eg
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late
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tab
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s
u
p
p
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.
T
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r
esear
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f
o
cu
s
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th
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p
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f
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p
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if
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,
wh
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ch
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s
to
r
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Hy
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o
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en
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
1
1
-
1
4
2
3
1412
is
ab
u
n
d
a
n
t,
clea
n
,
an
d
,
wh
e
n
u
s
ed
i
n
f
u
el
ce
lls
(
FC
s
)
,
p
r
o
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ce
s
n
o
p
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ts
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m
ak
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ca
r
r
ier
f
o
r
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
[
4
]
.
Am
o
n
g
v
a
r
io
u
s
h
y
d
r
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en
p
r
o
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s
s
tan
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t
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e
to
th
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d
esig
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,
ab
s
en
ce
o
f
h
ar
m
f
u
l
ch
em
icals,
an
d
ab
ilit
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to
g
en
er
ate
h
ig
h
-
p
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ity
h
y
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r
o
g
en
s
u
itab
le
f
o
r
d
ir
ec
t u
s
e
in
FC
s
[
5
]
.
W
h
ile
n
u
m
er
o
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s
s
tu
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ies
h
av
e
ex
p
lo
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ed
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e
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f
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m
an
ce
o
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id
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al
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o
n
en
ts
,
s
u
ch
as
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tr
o
ly
ze
r
s
,
p
h
o
to
v
o
ltaic
(
P
V)
p
an
els,
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d
FC
s
,
th
er
e
is
a
s
ig
n
if
ican
t
g
ap
in
th
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liter
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r
e
wh
en
it
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m
es
to
in
teg
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atin
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th
ese
c
o
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p
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to
a
u
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r
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cted
h
y
b
r
id
s
y
s
tem
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R
esear
ch
s
u
ch
as
[
6
]
–
[
1
0
]
h
as
p
r
im
ar
ily
f
o
cu
s
ed
o
n
e
v
alu
ati
n
g
s
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e
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en
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m
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lex
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o
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with
in
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Oth
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o
n
th
e
p
h
y
s
ical
b
eh
av
i
o
r
o
f
ce
lls
o
r
s
tack
s
[
1
1
]
,
[
1
2
]
,
y
et
d
o
n
o
t
f
u
lly
co
n
s
id
er
th
e
d
y
n
a
m
ic
in
ter
ac
tio
n
s
b
et
wee
n
PV
s
y
s
tem
s
,
elec
tr
o
ly
ze
r
s
,
an
d
FC
s
r
eq
u
ir
e
d
f
o
r
o
p
tim
al
p
er
f
o
r
m
an
ce
in
h
y
b
r
id
s
y
s
tem
s
.
Ad
d
itio
n
ally
,
th
e
r
o
le
o
f
p
o
wer
elec
tr
o
n
ics
—
s
u
ch
as
DC
/D
C
co
n
v
er
ter
s
,
th
r
ee
-
p
h
ase
in
v
er
ter
s
,
f
ilter
s
,
an
d
tr
an
s
f
o
r
m
er
s
—
is
cr
u
cial
in
en
h
an
cin
g
s
y
s
tem
ef
f
icien
cy
a
n
d
d
eser
v
es m
o
r
e
atten
tio
n
[
1
3
]
,
[
1
4
]
.
O
u
r
s
t
u
d
y
b
r
i
d
g
es
k
e
y
g
a
p
s
b
y
p
r
e
s
e
n
t
i
n
g
a
c
o
m
p
r
e
h
e
n
s
iv
e
i
n
t
e
g
r
a
ti
o
n
o
f
P
V
a
n
d
h
y
d
r
o
g
e
n
F
C
s
y
s
te
m
s
i
n
a
g
r
i
d
-
c
o
n
n
e
c
t
e
d
f
r
a
m
e
w
o
r
k
.
W
e
e
m
p
h
a
s
i
ze
h
o
l
i
s
ti
c
d
es
i
g
n
,
i
n
c
o
r
p
o
r
a
t
i
n
g
ad
v
a
n
c
e
d
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
M
P
P
T
)
f
o
r
P
V
o
p
t
i
m
i
z
a
ti
o
n
,
e
f
f
e
c
t
i
v
e
P
E
M
e
l
e
ct
r
o
l
y
z
e
r
m
a
n
a
g
e
m
e
n
t,
s
p
a
c
e
v
e
c
t
o
r
p
u
l
s
e
w
i
d
t
h
m
o
d
u
l
a
t
i
o
n
(
S
VP
W
M
)
f
o
r
p
r
e
c
i
s
e
i
n
v
e
r
t
e
r
c
o
n
t
r
o
l
,
a
n
d
p
h
a
s
e
-
l
o
c
k
e
d
l
o
o
p
(
P
L
L
)
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
f
o
r
s
e
a
m
l
ess
g
r
i
d
o
p
e
r
a
t
i
o
n
.
T
h
i
s
ap
p
r
o
a
c
h
e
n
h
a
n
c
e
s
s
y
s
t
e
m
r
e
li
ab
i
l
i
t
y
,
e
n
e
r
g
y
e
f
f
i
c
i
e
n
c
y
,
a
n
d
a
d
a
p
t
a
b
i
l
i
t
y
,
o
f
f
e
r
i
n
g
a
r
o
b
u
s
t
s
o
l
u
ti
o
n
f
o
r
s
u
s
ta
i
n
a
b
le
h
y
b
r
i
d
e
n
e
r
g
y
s
y
s
t
e
m
s
i
n
r
e
a
l
-
w
o
r
l
d
a
p
p
l
i
c
a
ti
o
n
s
[
1
5
]
.
T
h
e
p
r
im
a
r
y
o
b
jectiv
es
o
f
th
i
s
s
tu
d
y
ar
e
as
f
o
llo
ws:
i)
Des
ig
n
an
d
in
teg
r
atio
n
o
f
a
h
y
b
r
id
s
y
s
tem
d
ev
elo
p
a
g
r
i
d
-
co
n
n
ec
ted
h
y
b
r
id
p
o
wer
s
y
s
tem
th
at
i
n
teg
r
ates
PV
p
an
els
an
d
h
y
d
r
o
g
en
FC
g
en
er
at
o
r
s
;
ii)
Op
tim
izatio
n
o
f
c
o
n
tr
o
l
s
t
r
ateg
ies
im
p
lem
en
t
ad
v
a
n
ce
d
co
n
tr
o
l
s
tr
ateg
ies
to
o
p
tim
iz
e
th
e
p
o
wer
o
u
tp
u
t
f
r
o
m
b
o
th
th
e
PV
p
a
n
els
an
d
th
e
FC
g
en
er
ato
r
,
e
n
s
u
r
in
g
e
f
f
icien
t
g
r
id
s
y
n
ch
r
o
n
izatio
n
;
an
d
iii)
Simu
latio
n
an
d
v
alid
atio
n
co
n
d
u
ct
ex
ten
s
iv
e
s
im
u
latio
n
s
to
ev
alu
ate
th
e
h
y
b
r
id
s
y
s
tem
’
s
p
er
f
o
r
m
an
ce
u
n
d
er
v
a
r
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
an
d
v
ali
d
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
ies.
B
y
ad
d
r
ess
in
g
th
ese
o
b
jectiv
es,
th
is
s
tu
d
y
aim
s
t
o
ad
v
a
n
ce
th
e
s
tate
o
f
k
n
o
wled
g
e
in
h
y
b
r
i
d
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
an
d
p
r
o
v
id
e
s
o
lu
tio
n
s
f
o
r
in
teg
r
ati
n
g
clea
n
e
n
er
g
y
tech
n
o
l
o
g
ies in
to
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
.
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
is
wo
r
k
is
as
f
o
llo
ws:
s
ec
tio
n
2
p
r
esen
ts
an
o
v
er
v
iew
o
f
th
e
p
o
wer
s
y
s
tem
an
d
its
co
m
p
o
n
en
ts
.
Sectio
n
3
f
o
cu
s
es
o
n
th
e
co
m
p
r
eh
en
s
iv
e
im
p
lem
en
tatio
n
o
f
th
e
PV/F
C
h
y
b
r
id
g
r
id
-
c
o
n
n
ec
te
d
s
y
s
tem
,
co
v
er
in
g
th
e
c
o
n
tr
o
l
t
ec
h
n
iq
u
es
an
d
c
o
m
p
o
n
en
ts
u
ti
lized
.
Sectio
n
4
d
etails
th
e
o
b
t
ain
ed
r
esu
lts
,
wh
ile
s
ec
tio
n
5
co
n
clu
d
es th
e
p
a
p
er
an
d
ex
p
lo
r
es p
o
te
n
tial a
v
en
u
e
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
P
O
WE
R
SY
ST
E
M
O
V
E
RV
I
E
W
A
ND
CO
M
P
O
N
E
N
T
S
T
h
is
s
tu
d
y
ev
al
u
ates
th
e
p
e
r
f
o
r
m
an
ce
o
f
a
g
r
id
-
c
o
n
n
ec
te
d
h
y
b
r
id
PV
an
d
h
y
d
r
o
g
en
FC
s
y
s
tem
th
r
o
u
g
h
s
im
u
latio
n
s
.
T
h
e
s
etu
p
co
m
p
r
is
es
a
5
k
W
PV
ar
r
ay
,
a
1
k
W
PEM
elec
tr
o
ly
ze
r
,
an
d
a
1
k
W
h
y
d
r
o
g
en
FC
,
m
an
ag
ed
b
y
a
n
en
h
an
ce
d
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
MPPT
co
n
tr
o
l
alg
o
r
ith
m
.
MA
T
L
AB
-
Simu
lin
k
m
o
d
els
th
e
co
m
p
o
n
e
n
ts
u
n
d
er
v
ar
y
in
g
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e,
s
im
u
latin
g
r
e
al
-
wo
r
ld
co
n
d
itio
n
s
.
E
x
p
er
im
en
tal
d
ata,
in
clu
d
in
g
v
o
ltag
e,
cu
r
r
e
n
t,
an
d
p
o
wer
o
u
tp
u
t,
ar
e
an
aly
ze
d
to
ass
es
s
en
er
g
y
ef
f
icien
cy
,
s
y
s
tem
s
tab
ilit
y
,
an
d
lo
ad
r
esp
o
n
s
e.
Fig
u
r
e
1
o
u
tlin
es
th
e
s
y
s
tem
's
in
ter
co
n
n
ec
ted
co
m
p
o
n
en
ts
,
with
s
u
b
s
eq
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en
t su
b
s
ec
tio
n
s
d
etailin
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th
eir
f
u
n
ctio
n
alities
.
Fig
u
r
e
1
.
PV/F
C
p
r
o
p
o
s
ed
s
y
s
tem
co
n
n
ec
ted
to
g
r
i
d
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I
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-
8
7
0
8
Op
timiz
ed
co
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o
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n
d
s
imu
la
tio
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o
f a
g
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A
ma
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a
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1413
2
.
1
.
P
ho
t
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v
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ic
pa
nel m
o
del
Fig
u
r
e
2
illu
s
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ates
a
s
o
lar
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ell
m
o
d
el.
T
h
e
s
o
lar
p
an
el
is
co
n
f
ig
u
r
ed
with
ce
lls
in
s
er
ies
to
in
cr
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s
e
v
o
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e
an
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p
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h
e
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to
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e
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o
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-
lin
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r
(
1
)
[
1
6
]
.
=
ℎ
−
[
(
+
)
−
1
]
−
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ℎ
(
1
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wh
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o
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is
B
o
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v
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2
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d
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)
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ll tem
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Fig
u
r
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2
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So
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2
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n
d
(
3
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[
1
7
]
:
ℎ
=
(
+
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(
2
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=
+
[
+
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−
1
(
3
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wh
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h
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le
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t
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n
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e
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d
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T
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le
1
[
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7
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le
1
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E
lectr
ical
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ter
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r
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(A)
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2
O
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r
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(V)
3
2
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9
C
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e
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54
(
A
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°
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3
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1
2
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N
o
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n
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e
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e
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°
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25
2
.
2
.
B
o
o
s
t
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er
T
h
e
s
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lar
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tp
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t
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o
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f
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s
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m
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izin
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y
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n
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er
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io
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f
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c
y
r
eq
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ir
es
o
p
er
atin
g
n
ea
r
th
e
PV
s
o
u
r
ce
'
s
m
ax
im
u
m
p
o
wer
p
o
in
t.
Ho
wev
er
,
o
u
tp
u
t
p
o
wer
f
lu
ctu
ates
d
u
e
to
v
ar
iatio
n
s
in
s
o
lar
r
ad
iatio
n
,
t
em
p
er
atu
r
e,
a
n
d
lo
ad
c
h
ar
ac
te
r
is
tics
,
r
esu
ltin
g
in
in
co
n
s
is
ten
t
p
o
wer
d
eliv
er
y
.
T
o
m
itig
ate
th
is
,
a
DC
/DC
co
n
v
er
ter
,
r
eg
u
lated
b
y
an
MPPT
alg
o
r
ith
m
[
1
8
]
,
is
im
p
lem
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ted
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etwe
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th
e
r
en
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b
le
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o
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d
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Fig
u
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3
illu
s
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ates
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e
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ed
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tem
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o
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m
to
o
p
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ize
p
o
we
r
tr
ac
k
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
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p
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g
,
Vo
l.
15
,
No
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2
,
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r
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25
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1
4
1
1
-
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4
2
3
1414
Fig
u
r
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3
.
B
lo
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iag
r
am
o
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o
o
s
t c
o
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te
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2
.
3
.
P
E
M
elec
t
ro
ly
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m
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W
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h
e
e
l
e
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t
r
o
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c
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n
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h
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PE
M
el
e
c
t
r
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e
r
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r
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y
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a
p
p
l
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e
d
p
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te
n
t
i
a
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a
r
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h
o
w
n
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4
)
a
n
d
(
5
)
.
F
i
g
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r
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4
i
ll
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s
t
r
at
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s
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w
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t
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r
[
1
9
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.
An
o
d
e:
2
→
2
+
+
1
2
2
+
2
−
(
4
)
C
ath
o
d
e:
2
+
+
2
−
→
2
(
5
)
I
n
th
e
elec
tr
o
l
y
ze
r
,
wate
r
at
th
e
an
o
d
e
is
s
p
lit
in
to
o
x
y
g
en
g
as,
elec
tr
o
n
s
,
an
d
p
r
o
to
n
s
.
T
h
e
p
r
o
t
o
n
s
m
o
v
e
t
o
th
e
ca
th
o
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e
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g
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,
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ile
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tr
av
el
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ia
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t
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al
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it,
d
r
iv
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n
g
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e
ca
th
o
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e
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tr
o
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d
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r
o
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s
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ec
o
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i
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e
to
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o
r
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y
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n
g
as.
C
o
n
tin
u
o
u
s
wate
r
s
u
p
p
ly
to
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h
e
m
em
b
r
an
e
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tr
o
d
e
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en
tial,
as
i
s
th
e
r
em
o
v
al
o
f
h
y
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r
o
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en
an
d
o
x
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en
.
T
h
e
r
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n
s
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u
r
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e
m
em
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r
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e
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elec
tr
o
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e
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ter
f
ac
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n
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g
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e
p
o
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u
s
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e
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r
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t la
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em
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m
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ites
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tr
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ly
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r
ce
ll
m
o
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co
m
p
r
is
es
f
o
u
r
p
r
i
n
cip
al
co
m
p
o
n
e
n
ts
:
an
o
d
e,
ca
th
o
d
e,
m
em
b
r
an
e,
an
d
v
o
ltag
e
[
2
0
]
.
Fig
u
r
e
4
.
PEM
f
u
el
ce
ll r
ep
r
es
en
tatio
n
2
.
3
.
1
.
Ano
de
a
ncilla
ry
T
h
e
an
o
d
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n
cillar
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m
an
a
g
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th
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lcu
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n
o
f
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x
y
g
e
n
an
d
wate
r
f
lo
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d
th
eir
p
ar
tial
p
r
ess
u
r
es.
At
th
e
an
o
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e,
ac
c
o
r
d
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g
to
(
4
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,
wate
r
is
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ize
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to
p
r
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u
ce
o
x
y
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en
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as,
p
r
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to
n
s
,
an
d
elec
tr
o
n
s
.
T
h
e
eq
u
atio
n
s
f
o
r
th
ese
r
ea
ctio
n
s
a
r
e
p
r
o
v
id
ed
[
2
1
]
.
2
=
Ṅ
2
−
Ṅ
2
+
Ṅ
2
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
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Op
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(
A
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1415
dN
H
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ai
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H
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wh
er
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Ṅ
2
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2
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2
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2
(
m
o
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e
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let
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tlet
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d
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r
esp
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d
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tr
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atic
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th
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m
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o
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y
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atio
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a
n
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e.
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e
n
m
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Far
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y
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[
2
1
]
.
2
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Ṅ
2
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=
4
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A
(
8
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2
.
3
.
2
.
Ca
t
ho
de
a
ncilla
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T
h
e
ca
th
o
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cillar
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d
eter
m
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th
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w
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ates
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d
p
a
r
tial
p
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r
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ter
ac
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with
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lied
b
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p
o
we
r
s
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r
ce
to
p
r
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u
ce
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y
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e
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q
u
atio
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th
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e
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(
1
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[
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2
dt
=
Ṅ
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2
(
9
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2
dt
=
Ṅ
2
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2
(
1
0
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T
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e
m
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lu
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o
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en
at
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th
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e
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p
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s
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Far
ad
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as in
(
1
1
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.
2
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1
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2
.
3
.
3
.
M
em
bra
ne
a
ncilla
ry
T
h
e
m
em
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r
an
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tr
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d
e
ass
em
b
ly
is
t
h
e
c
o
r
e
o
f
th
e
PEM
e
lectr
o
ly
ze
r
,
in
v
o
l
v
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if
f
u
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,
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tr
o
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o
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m
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ag
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d
h
y
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r
au
lic
p
r
ess
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r
e
ef
f
ec
ts
[
1
9
]
.
Ṅ
2
=
Ṅ
2
−
Ṅ
2
+
Ṅ
2
ℎ
(
1
2
)
T
h
e
r
ate
o
f
wate
r
tr
an
s
p
o
r
t d
u
e
to
d
if
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ca
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Fick
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d
if
f
u
s
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[
2
1
]
.
Ṅ
2
=
(
2
,
,
−
2
,
,
)
(
1
3
)
wh
er
e
,
is
th
e
m
em
b
r
an
e
d
if
f
u
s
io
n
co
ef
f
icien
t
o
f
wate
r
,
is
th
e
m
em
b
r
an
e
t
h
ick
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ess
,
2
,
,
,
an
d
2
,
,
r
ep
r
esen
t th
e
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n
ce
n
tr
atio
n
s
o
f
wate
r
at
th
e
m
em
b
r
an
e
s
id
es.
E
lectr
o
-
o
s
m
o
tic
d
r
a
g
is
d
ep
e
n
d
en
t o
n
th
e
f
lo
w
o
f
h
y
d
r
ated
p
r
o
to
n
s
:
Ṅ
2
=
(
1
4
)
wh
er
e
is
th
e
elec
tr
o
-
o
s
m
o
tic
d
r
ag
c
o
ef
f
icien
t.
E
x
p
er
im
e
n
tally
,
v
ar
ies
with
ca
th
o
d
e
p
r
e
s
s
u
r
e,
cu
r
r
en
t
d
en
s
ity
,
an
d
tem
p
er
atu
r
e.
W
ater
tr
an
s
p
o
r
t
f
r
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m
ca
th
o
d
e
t
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an
o
d
e
th
r
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g
h
th
e
m
em
b
r
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n
e
is
d
escr
ib
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b
y
Dar
cy
'
s
law
[
2
1
]
:
Ṅ
2
ℎ
=
(
−
)
2
(
1
5
)
wh
er
e
,
is
th
e
m
em
b
r
an
e
p
er
m
ea
b
ilit
y
to
wate
r
,
is
th
e
v
is
co
s
ity
o
f
wate
r
,
an
d
is
th
e
wate
r
d
en
s
ity
.
T
h
e
n
et
m
o
la
r
f
lo
w
r
ate
o
f
wat
er
b
ec
o
m
es:
Ṅ
2
=
[
(
2
,
ℎ
,
−
2
Ṅ
2
)
−
(
2
,
ℎ
,
+
2
)
]
+
+
(
−
)
2
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
1
1
-
1
4
2
3
1416
E
lectr
o
ly
ze
r
s
ca
n
o
p
e
r
ate
in
eith
er
cu
r
r
en
t
m
o
d
e
o
r
v
o
ltag
e
m
o
d
e.
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n
v
o
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m
o
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e,
th
e
el
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tr
o
ly
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a
p
p
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d
d
r
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r
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n
t
ac
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g
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s
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s
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ter
tr
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ien
t
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Ho
wev
er
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t
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m
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cial
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tr
o
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r
s
ar
e
d
esig
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o
p
er
ate
in
cu
r
r
e
n
t
m
o
d
e.
T
h
e
o
p
er
atin
g
ce
ll
v
o
ltag
e
is
th
e
s
u
m
o
f
th
e
o
p
en
-
cir
c
u
it
v
o
ltag
e
,
o
h
m
ic
o
v
er
p
o
te
n
tial
ℎ
,
ac
tiv
atio
n
o
v
er
p
o
ten
tial
,
an
d
co
n
ce
n
tr
atio
n
o
v
e
r
p
o
ten
tial
,
as
(
1
7
)
[
2
0
]
.
=
+
ℎ
+
+
(
1
7
)
T
h
ese
p
ar
am
eter
s
co
u
l
d
b
e
r
ep
r
esen
ted
b
y
(
1
7
a
)
to
(
1
7
d
)
:
=
E
0
+
2
(
ln
(
2
√
2
2
)
)
(
17a
)
wh
er
e
,
is
th
e
u
n
iv
e
r
s
al
g
as
co
n
s
tan
t,
is
th
e
ce
ll
tem
p
er
atu
r
e
,
an
d
2
is
th
e
wate
r
ac
tiv
ity
b
et
wee
n
a
n
o
d
e
an
d
elec
tr
o
ly
te,
f
o
r
s
im
p
licity
it
is
ass
u
m
ed
h
er
e
to
b
e
1
.
T
h
e
s
tan
d
ar
d
v
o
ltag
e
E
0
i
s
0
=
1
.
229
−
0
.
9
−
3
(
−
298
)
.
=
ℎ
(
2
0
)
+
ℎ
(
2
0
)
(
1
7
b
)
wh
er
e
an
d
ar
e
th
e
ch
ar
g
e
tr
an
s
f
er
co
ef
f
icien
ts
,
is
th
e
cu
r
r
en
t d
en
s
ity
,
an
d
0
an
d
0
ar
e
th
e
ex
ch
an
g
e
cu
r
r
en
t
d
en
s
ities
f
o
r
th
e
an
o
d
e
an
d
ca
th
o
d
e,
r
esp
ec
tiv
el
y
.
=
4
2
2
,
0
+
2
2
2
,
0
(
1
7
c)
2
an
d
2
ar
e
th
e
o
x
y
g
e
n
an
d
h
y
d
r
o
g
en
c
o
n
ce
n
tr
atio
n
s
at
th
e
m
e
m
b
r
an
e
-
elec
tr
o
d
e
in
ter
f
ac
e.
ℎ
=
=
ℎ
+
ℎ
+
ℎ
(
1
7
d
)
wh
er
e
is
th
e
to
tal
r
esis
tan
ce
(
i
n
clu
d
in
g
elec
tr
o
d
es,
b
i
p
o
lar
p
l
ates,
an
d
m
em
b
r
an
e
r
esis
tan
ce
s
)
.
2
.
3
.
4
.
Sto
ra
g
e
a
ncilla
ry
T
h
e
h
y
d
r
o
g
e
n
p
r
o
d
u
ce
d
b
y
t
h
e
e
l
e
c
tr
o
ly
z
er
i
s
s
t
o
r
e
d
i
n
an
₂
s
t
o
r
a
g
e
b
o
t
t
l
e
.
T
h
i
s
s
to
r
ag
e
p
r
o
c
e
s
s
i
n
v
o
l
v
e
s
f
i
l
l
in
g
t
h
e
cy
l
i
n
d
e
r
w
i
t
h
a
co
n
s
t
an
t
f
l
o
w
o
f
h
y
d
r
o
g
en
u
n
t
i
l
th
e
p
r
e
s
s
u
r
e
i
n
s
i
d
e
t
h
e
cy
l
i
n
d
e
r
eq
u
a
l
s
t
h
e
c
a
th
o
d
i
c
p
r
e
s
s
u
r
e
o
f
t
h
e
el
e
c
t
r
o
ly
z
er
.
T
h
e
c
h
ar
a
c
t
er
i
s
t
ic
s
o
f
t
h
e
s
t
o
r
ag
e
p
r
o
c
e
s
s
ar
e
d
e
t
e
r
m
i
n
ed
a
s
(
1
8
)
[
2
0
]
:
−
=
2
2
(
1
8
)
wh
er
e
,
is
th
e
in
itial
h
y
d
r
o
g
e
n
p
r
ess
u
r
e
in
th
e
b
o
ttle,
is
th
e
co
m
p
r
ess
ib
ilit
y
f
ac
to
r
o
f
th
e
h
y
d
r
o
g
en
,
is
th
e
b
o
ttle te
m
p
er
at
u
r
e
,
an
d
is
th
e
b
o
ttle v
o
l
u
m
e.
D
u
r
i
n
g
t
h
e
s
to
r
ag
e
p
r
o
c
e
s
s
,
i
t
i
s
a
s
s
u
m
e
d
t
h
a
t
th
e
t
e
m
p
e
r
a
tu
r
e
o
f
t
h
e
b
o
t
t
le
r
e
m
a
in
s
c
o
n
s
t
a
n
t
.
T
h
i
s
a
s
s
u
m
p
t
i
o
n
i
s
v
a
l
id
b
e
ca
u
s
e
th
e
h
y
d
r
o
g
e
n
f
i
l
l
in
g
p
r
o
c
e
s
s
i
s
r
e
l
a
t
i
v
e
ly
s
l
o
w
,
a
l
lo
w
i
n
g
t
h
e
r
m
a
l
eq
u
i
l
ib
r
iu
m
t
o
b
e
m
a
in
t
a
i
n
ed
.
T
h
e
c
o
m
p
r
e
s
s
i
b
i
l
i
ty
f
a
c
to
r
a
c
c
o
u
n
t
s
f
o
r
t
h
e
n
o
n
-
i
d
e
a
l
b
eh
a
v
io
r
o
f
h
y
d
r
o
g
en
g
a
s
,
e
s
p
e
c
i
a
l
l
y
a
t
h
i
g
h
e
r
p
r
e
s
s
u
r
e
s
,
e
n
s
u
r
i
n
g
ac
c
u
r
a
t
e
d
e
t
er
m
i
n
at
i
o
n
o
f
t
h
e
p
r
e
s
s
u
r
e
c
h
an
g
e
s
w
i
t
h
i
n
th
e
s
to
r
ag
e
s
y
s
t
e
m
.
2
.
4
.
T
hree
-
ph
a
s
e
i
nv
er
t
er
T
h
e
in
v
er
ter
,
s
h
o
wn
in
Fig
u
r
e
5
,
u
s
es
s
em
ico
n
d
u
cto
r
d
ev
ic
es
lik
e
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
s
(
I
GB
T
s
)
o
r
m
etal
-
o
x
id
e
-
s
em
i
co
n
d
u
ct
o
r
f
iel
d
-
ef
f
ec
t
tr
an
s
is
to
r
s
(
MO
SF
E
T
s
)
to
co
n
v
er
t
DC
v
o
ltag
e
f
r
o
m
th
e
PV
-
h
y
d
r
o
g
en
s
y
s
tem
in
to
AC
cu
r
r
en
ts
s
u
itab
le
f
o
r
th
e
u
tili
ty
g
r
id
.
I
t
p
lay
s
a
cr
u
cial
r
o
le
in
en
s
u
r
in
g
e
f
f
icien
t
in
teg
r
atio
n
b
y
em
p
lo
y
in
g
s
u
p
p
o
r
t
v
ec
to
r
m
ac
h
in
es
(
SV
M)
,
ch
o
s
en
f
o
r
b
en
e
f
its
lik
e
co
n
s
tan
t
s
witch
in
g
f
r
eq
u
e
n
cy
,
well
-
d
ef
in
e
d
o
u
t
p
u
t
h
ar
m
o
n
ics,
o
p
tim
al
s
witch
in
g
p
atter
n
s
,
an
d
e
f
f
icien
t
u
s
e
o
f
cir
cu
it
v
o
ltag
e.
SVM
en
h
an
ce
s
s
y
s
tem
p
er
f
o
r
m
an
ce
,
s
tab
ilit
y
,
a
n
d
r
eliab
ilit
y
,
cr
u
cial
f
o
r
s
ea
m
less
g
r
id
co
n
n
ec
tiv
ity
o
f
t
h
e
h
y
b
r
id
s
y
s
tem
[
2
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
ed
co
n
tr
o
l a
n
d
s
imu
la
tio
n
o
f a
g
r
id
-
in
teg
r
a
ted
p
h
o
to
vo
lta
ic
a
n
d
fu
el
ce
ll
…
(
A
ma
l
S
a
tif
)
1417
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
o
f
th
r
ee
-
p
h
ase
two
-
lev
el
in
v
er
ter
2
.
5
.
F
ilte
r
R
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
m
u
s
t
m
ee
t
s
tr
in
g
e
n
t
en
e
r
g
y
q
u
a
lity
s
tan
d
ar
d
s
t
o
en
s
u
r
e
r
eliab
le
p
o
wer
d
eliv
er
y
to
th
e
g
r
id
.
R
esear
ch
in
d
icate
s
th
at
m
ax
im
u
m
allo
wab
le
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
in
th
r
ee
-
p
h
ase
cu
r
r
en
ts
is
ty
p
ically
5
%.
No
n
-
lin
ea
r
lo
ad
s
co
n
tr
ib
u
te
s
ig
n
if
ican
tly
to
lo
wer
-
o
r
d
e
r
h
ar
m
o
n
ics,
ex
ac
er
b
ated
b
y
h
ig
h
-
f
r
eq
u
en
c
y
r
ip
p
les
f
r
o
m
I
GB
T
s
witch
in
g
in
in
v
er
ter
s
.
Ad
d
r
ess
in
g
th
ese
ch
allen
g
es,
th
e
u
s
e
o
f
an
L
C
L
f
ilter
,
illu
s
tr
ated
in
Fig
u
r
e
5
,
o
n
th
e
in
v
er
ter
-
g
r
id
s
id
e
ef
f
ec
tiv
ely
r
ed
u
ce
s
h
ig
h
-
f
r
e
q
u
en
c
y
r
ip
p
les,
en
s
u
r
in
g
co
m
p
lian
ce
with
T
HD
s
tan
d
ar
d
s
an
d
en
h
a
n
cin
g
s
y
s
tem
ef
f
icien
c
y
[
2
3
]
.
3.
CO
NT
RO
L
SYS
T
E
M
3
.
1
.
M
P
P
T
T
h
e
MPPT
alg
o
r
ith
m
is
cr
itical
in
PV
s
y
s
tem
s
to
m
ax
im
ize
p
o
wer
g
en
e
r
atio
n
b
y
co
n
tin
u
o
u
s
ly
ad
ju
s
tin
g
o
p
e
r
atin
g
c
o
n
d
itio
n
s
.
Nu
m
er
o
u
s
MPPT
alg
o
r
ith
m
s
in
th
e
liter
atu
r
e
aim
to
e
n
h
an
ce
e
f
f
icien
cy
in
p
o
wer
tr
ac
k
in
g
.
A
r
ec
e
n
t
s
tu
d
y
in
tr
o
d
u
ce
d
an
alg
o
r
ith
m
s
u
r
p
ass
in
g
th
e
tr
ad
itio
n
al
P&
O
t
ec
h
n
iq
u
e,
o
f
f
e
r
in
g
im
p
r
o
v
e
d
p
o
wer
tr
ac
k
i
n
g
a
n
d
o
s
cillatio
n
elim
in
atio
n
c
ap
ab
ilit
ies.
T
h
is
alg
o
r
ith
m
i
n
teg
r
ates
a
v
o
ltag
e
r
eg
u
lato
r
to
m
in
im
ize
v
o
ltag
e
er
r
o
r
s
b
etwe
en
th
e
PV
p
an
el
an
d
th
e
MPPT
b
lo
ck
.
Fo
r
f
u
r
th
er
d
etails
o
n
t
h
is
ad
v
an
ce
m
e
n
t,
r
ef
er
to
[
2
4
]
.
Fi
g
u
r
e
6
illu
s
tr
ates th
e
p
r
in
cip
le
o
f
th
is
s
tr
ateg
y
.
Fig
u
r
e
6
.
MPPT
P&
O
-
b
ased
P
I
co
n
tr
o
ller
3
.
2
.
SVPWM c
o
ntr
o
l t
ec
hn
i
qu
e
SVP
W
M
is
em
p
lo
y
ed
to
c
o
n
t
r
o
l
th
e
in
d
iv
id
u
al
s
witch
es
o
f
th
e
th
r
ee
-
p
h
ase
in
v
e
r
ter
b
y
g
en
er
atin
g
p
r
ec
is
e
co
n
tr
o
l
p
u
ls
es.
Un
lik
e
s
in
u
s
o
id
al
PW
M,
wh
er
e
d
u
ty
cy
cles
ar
e
d
eter
m
in
ed
b
y
s
im
p
le
co
m
p
ar
is
o
n
s
,
SVP
W
M
ca
lcu
lates
d
u
ty
c
y
cle
r
atio
s
,
o
f
f
er
in
g
s
ev
er
al
ad
v
a
n
tag
es
as
p
r
e
v
io
u
s
ly
m
en
tio
n
e
d
.
Fo
r
a
th
r
ee
-
p
h
ase
two
-
lev
el
in
v
er
ter
,
SVPW
M
u
tili
ze
s
eig
h
t
d
is
tin
ct
s
tates,
ea
ch
co
r
r
esp
o
n
d
in
g
to
a
s
p
ec
if
ic
v
o
ltag
e
s
p
ac
e
v
ec
to
r
.
I
n
th
is
m
o
d
u
latio
n
tech
n
iq
u
e,
th
e
th
r
ee
-
p
h
ase
r
ef
er
e
n
ce
v
o
ltag
es
∗
,
∗
,
an
d
∗
ar
e
tr
an
s
f
o
r
m
ed
i
n
to
th
e
α
β p
lan
e
u
s
in
g
C
lar
k
e'
s
tr
an
s
f
o
r
m
atio
n
,
c
o
m
p
u
te
d
as sh
o
wn
in
(
2
2
)
.
T
h
e
SVM
ac
h
iev
e
s
its
r
esu
lts
th
r
o
u
g
h
th
e
s
tep
s
o
u
tlin
ed
in
[
1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
1
1
-
1
4
2
3
1418
[
]
=
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
∗
∗
∗
]
(
2
2
)
3
.
3
.
Sy
nchro
niza
t
io
n a
lg
o
rit
hm
I
n
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
s
,
s
y
n
ch
r
o
n
izin
g
th
e
in
v
er
ter
o
u
tp
u
t
with
th
e
g
r
id
v
o
ltag
e
i
s
ess
en
tial
f
o
r
s
tab
le
o
p
e
r
atio
n
.
T
h
is
s
tu
d
y
u
tili
ze
s
th
e
d
q
PLL
m
eth
o
d
f
o
r
ac
c
u
r
ate
f
r
eq
u
e
n
cy
an
d
p
h
a
s
e
d
etec
tio
n
,
ev
en
in
n
o
is
y
co
n
d
itio
n
s
.
Fig
u
r
e
7
illu
s
tr
ates
th
e
im
p
lem
en
tatio
n
o
f
th
e
d
q
PLL
,
wh
ich
in
v
o
lv
es
th
e
Par
k
tr
an
s
f
o
r
m
atio
n
(
−
)
,
a
p
r
o
p
o
r
tio
n
al
in
teg
r
ato
r
(
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u
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ates
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Evaluation Warning : The document was created with Spire.PDF for Python.