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2
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in
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]
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I
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P
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E
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&
Dr
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Vo
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9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
377
–
3
8
9
378
tak
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ased
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cu
s
s
ed
b
y
Di
n
g
,
et
al
[
2
0
]
.
A
lta
s
,
et
al
[
2
1
]
h
av
e
d
es
cr
ib
ed
a
p
h
o
to
v
o
ltaic
ar
r
ay
s
i
m
u
latio
n
m
o
d
el
f
o
r
MA
T
L
A
B
S
i
m
u
li
n
k
GUI
e
n
v
ir
o
n
m
e
n
t.
Fu
r
t
h
er
,
Uzu
n
o
g
le,
et
al
[
2
2
]
h
av
e
p
r
ese
n
ted
a
s
tatic
V
AR
co
m
p
e
n
s
ato
r
b
ased
r
ea
ctiv
e
p
o
w
er
m
a
n
ag
e
m
e
n
t
s
c
h
e
m
e
f
o
r
SOFC
p
o
w
er
p
lan
ts
.
Gr
id
co
n
n
ec
ted
f
u
el
ce
ll
an
d
P
V
h
y
b
r
id
p
o
w
er
g
e
n
er
atin
g
s
y
s
te
m
d
esi
g
n
w
it
h
Ma
tlab
Si
m
u
lin
k
h
a
s
b
ee
n
p
r
esen
ted
b
y
B
ay
r
ak
,
et
al
[
2
3
]
.
R
ec
en
t
l
y
,
Mo
li
n
a,
et
al
[
2
4
]
h
av
e
d
ev
elo
p
ed
m
o
d
elin
g
a
n
d
s
i
m
u
lat
io
n
o
f
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
en
er
g
y
co
n
v
er
s
io
n
s
y
s
te
m
s
a
n
d
d
e
m
o
n
s
tr
ated
it
s
e
f
f
ec
ti
v
en
e
s
s
.
Als
o
a
co
n
tr
o
l
s
tr
ate
g
y
is
d
ev
elo
p
ed
f
o
r
th
e
w
i
n
d
an
d
f
u
e
l
ce
ll
co
n
n
ec
ted
to
g
r
id
a
s
w
ell
as
a
p
o
w
er
m
a
n
a
g
e
m
en
t
s
tr
ate
g
y
is
d
e
v
elo
p
ed
f
o
r
th
e
h
y
b
r
id
s
y
s
te
m
d
escr
ib
ed
in
[
2
5
]
an
d
[
2
6
]
.
T
h
e
q
u
alit
y
o
f
p
o
w
er
tr
an
s
f
er
ca
n
b
e
d
eter
m
in
ed
b
y
a
s
i
n
g
l
e
in
d
icato
r
r
an
g
i
n
g
f
r
o
m
ze
r
o
to
o
n
e
k
n
o
w
n
a
s
p
o
w
er
q
u
al
it
y
f
ac
to
r
(
P
QF)
f
o
r
th
e
3
-
Ø
s
u
p
p
l
y
a
n
d
th
is
s
u
p
p
l
y
is
co
n
n
ec
ted
to
th
e
lo
ad
as
d
escr
ib
ed
in
[
2
7
]
.
So
it
ca
n
b
e
m
en
t
io
n
ed
t
h
at
t
h
e
p
o
w
er
tr
an
s
f
er
q
u
alit
y
is
lo
w
d
u
e
to
th
e
h
ar
m
o
n
i
c
co
n
ten
t
i
n
s
u
p
p
l
y
v
o
lta
g
e,
n
o
n
li
n
ea
r
lo
ad
an
d
u
n
b
alan
ce
d
v
o
ltag
e
s
u
p
p
l
y
o
r
ca
u
s
ed
d
u
e
to
b
o
th
o
f
t
h
e
m
.
A
cc
o
r
d
in
g
to
th
e
r
ef
.
[
2
7
]
,
in
a
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
,
a
s
u
g
g
ested
P
QF
d
eter
m
in
e
s
t
h
e
q
u
a
lit
y
o
f
p
o
w
er
at
a
n
y
p
o
in
t b
y
t
h
e
h
elp
o
f
s
i
n
g
le
in
d
i
ca
to
r
w
it
h
o
u
t ta
k
i
n
g
m
a
n
y
f
ac
t
o
r
s
an
d
th
eir
v
al
u
es.
An
atte
m
p
t
h
as
b
ee
n
m
ad
e
in
th
is
p
ap
er
to
d
esig
n
an
d
a
n
al
y
ze
a
HGS
a
s
s
e
m
b
li
n
g
P
V,
w
i
n
d
,
SOF
C
,
elec
tr
o
l
y
ze
r
an
d
s
to
r
ag
e
tan
k
co
n
n
ec
ted
to
g
r
id
.
I
t
d
escr
ib
es
d
etailed
m
o
d
elin
g
o
f
ea
ch
co
m
p
o
n
en
t
in
cl
u
d
in
g
s
to
r
ag
e
ta
n
k
w
h
o
s
e
d
etai
led
m
o
d
eli
n
g
i
s
n
o
t
a
v
ail
ab
le
in
t
h
e
li
ter
atu
r
e
a
n
d
al
s
o
t
h
e
co
n
tr
o
l
s
tr
ateg
y
is
w
ell
ex
p
lain
ed
.
F
u
r
t
h
er
,
th
e
p
o
w
er
q
u
alit
y
an
a
l
y
s
is
i
s
d
o
n
e
b
r
ief
l
y
i
n
t
h
is
p
ap
er
.
Fi
n
all
y
t
h
e
e
f
f
ec
tiv
e
n
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
is
v
er
if
ied
u
n
d
er
s
ev
er
al
co
n
d
itio
n
s
a
n
d
s
i
m
u
latio
n
r
es
u
lt
s
ar
e
p
r
es
en
ted
.
2.
E
XP
L
A
NAT
I
O
N
O
F
G
R
I
D
CO
NNEC
T
E
D
H
YB
RID G
E
NE
RAT
I
O
N
SYS
T
E
M
T
h
e
d
etailed
m
o
d
el
o
f
HG
S
i
s
r
ep
r
esen
ted
in
Fi
g
u
r
e
1
.
A
h
y
b
r
id
m
o
d
el
h
a
v
in
g
P
V/
w
i
n
d
en
er
g
y
g
en
er
atio
n
s
y
s
te
m
i
s
d
esi
g
n
e
d
an
d
s
i
m
u
lated
a
n
d
co
n
n
ec
t
ed
w
it
h
t
h
e
SO
FC
f
o
r
th
e
b
a
ck
u
p
p
o
w
er
s
u
p
p
l
y
w
h
e
n
th
er
e
i
s
n
o
p
o
w
er
s
u
p
p
l
y
f
r
o
m
w
i
n
d
an
d
P
V.
I
n
th
e
HGS,
SOF
C
ta
k
es
t
h
e
H2
as
f
u
e
l
f
o
r
t
h
e
b
ac
k
u
p
p
o
w
er
g
en
er
atio
n
an
d
th
i
s
H2
is
p
r
o
d
u
ce
d
b
y
th
e
elec
tr
o
l
y
z
er
w
h
e
n
t
h
e
w
a
ter
is
d
iv
id
ed
in
to
t
w
o
h
alv
e
s
(
H2
an
d
Ox
y
g
e
n
)
th
r
o
u
g
h
t
h
e
ele
ctr
o
ly
s
is
p
r
o
ce
s
s
in
t
h
e
elec
tr
o
ly
ze
r
.
T
h
e
elec
tr
o
ly
ze
r
o
p
er
ates
b
y
tak
i
n
g
t
h
e
ex
ce
s
s
a
m
o
u
n
t
o
f
elec
tr
ical
p
o
w
er
f
r
o
m
th
e
P
V/
w
i
n
d
g
en
e
r
atio
n
.
T
h
e
a
m
o
u
n
t
o
f
H2
f
lo
w
to
t
h
e
SO
FC
is
co
n
tr
o
lled
b
y
t
h
e
f
u
el
ce
ll c
o
n
t
r
o
ller
an
d
th
e
r
est a
m
o
u
n
t o
f
H2
is
s
to
r
ed
in
th
e
s
to
r
ag
e
tan
k
.
Fig
u
r
e
1
.
Gr
id
co
n
n
ec
ted
H
y
b
r
id
Gen
er
atio
n
S
y
s
te
m
(
Deta
il
ed
Mo
d
el)
.
T
h
r
e
e
P
h
a
s
e
S
o
u
r
c
e
B
D
i
s
t
r
i
b
u
t
e
d
P
a
r
a
m
e
t
e
r
l
i
n
e
C
i
r
c
u
i
t
B
r
e
a
k
e
r
B
T
h
r
e
e
P
h
a
s
e
T
r
a
n
s
f
o
r
m
e
r
H
y
b
r
i
d
G
e
n
e
r
a
t
i
o
n
S
y
s
t
e
m
B
C
i
r
c
u
i
t
B
r
e
a
k
e
r
C
i
r
c
u
i
t
B
r
e
a
k
e
r
T
h
r
e
e
P
h
a
s
e
L
o
a
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
P
o
w
er Qu
a
lity A
n
a
lysi
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
S
o
l
a
r
/Wi
n
d
/Hyd
r
o
g
en
E
n
erg
y
Hyb
r
id
…
(
S
u
jit K
u
ma
r
B
h
u
ya
n
)
379
I
n
t
h
e
m
o
d
el
o
f
H
GS
m
a
x
i
m
u
m
en
er
g
y
ca
n
b
e
tr
ac
k
ed
b
y
th
e
h
e
lp
o
f
MP
P
T
f
r
o
m
t
h
e
P
V
an
d
W
E
C
S.
T
h
en
th
e
s
e
en
er
g
ies
a
r
e
s
u
p
p
lied
to
th
e
b
o
o
s
t
co
n
v
e
r
ter
to
en
h
an
ce
t
h
e
D
C
v
o
lta
g
e
lev
el.
Hen
ce
,
t
h
is
b
o
o
s
ted
DC
v
o
ltag
e
is
ap
p
lied
to
th
e
in
v
er
ter
(
DC
/
AC
C
o
n
v
er
ter
)
to
co
n
v
er
t D
C
v
o
lta
g
e
t
o
A
C
v
o
ltag
e.
T
h
e
s
tr
ateg
y
o
f
t
h
e
p
o
w
er
m
a
n
ag
e
m
e
n
t
o
f
t
h
e
HG
S
is
co
n
s
i
d
er
ed
to
m
ax
i
m
ize
th
e
p
o
w
er
d
eliv
er
y
to
th
e
lo
ad
at
th
e
ti
m
e
o
f
b
ad
w
ea
t
h
er
an
d
g
eo
g
r
ap
h
ical
co
n
d
itio
n
s
.
Hen
ce
,
th
e
p
r
o
p
o
s
ed
HGS
o
f
f
er
s
clea
n
o
u
tp
u
t p
o
w
er
t
h
at
co
m
p
e
n
s
ate
s
lo
ad
d
em
a
n
d
.
3.
DE
T
AI
L
E
D
E
XP
L
ANA
T
I
O
N
O
F
P
V
M
O
DE
L
Fo
r
d
esig
n
i
n
g
th
e
P
V
m
o
d
el
b
asicall
y
Si
n
g
le
-
d
io
d
e
o
r
t
w
o
-
d
io
d
e
m
o
d
els
ar
e
b
r
o
ad
ly
u
s
ed
.
Mo
s
tl
y
s
in
g
le
-
d
io
d
e
m
o
d
el
is
m
o
r
e
ap
p
r
o
p
r
iate
to
u
s
e
as
d
escr
ib
ed
in
[
1
9
-
2
1
]
.
T
h
e
d
esig
n
in
g
o
f
P
V
m
o
d
el
is
d
o
n
e
b
y
ap
p
ly
i
n
g
th
e
E
q
u
a
tio
n
(
1
)
.
T
a
b
le
1
s
h
o
w
s
th
e
p
ar
a
m
eter
s
o
f
th
e
P
V
m
o
d
u
le.
V
pv
=
N
s
akT
q
ln
[
I
sc
−
I
pv
+
N
p
N
p
I
o
]
−
N
s
N
p
R
s
I
pv
(
1
)
P
ar
am
eter
s
ar
e
ta
k
e
n
f
o
r
m
o
d
elin
g
o
f
t
h
e
P
V
s
y
s
te
m
s
u
ch
a
s
,
I
0
is
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t
o
f
P
V
m
o
d
el
in
[
A
]
,
I
SC
i
s
th
e
s
h
o
r
t
-
cir
cu
it P
V
ce
ll c
u
r
r
en
t in
[
A
]
,
I
P
V/I
p
h
is
th
e
o
u
tp
u
t
c
u
r
r
en
t
o
f
P
V
m
o
d
el
i
n
[
A
]
,
k
i
s
th
e
b
o
ltz
m
an
n
’
s
co
n
s
ta
n
t
in
[
J
/o
K]
,
a
is
th
e
co
m
p
letio
n
o
r
id
ea
lit
y
f
ac
t
o
r
,
q
is
th
e
e
lectr
o
n
ch
ar
g
e
in
[
C
]
,
R
P
i
n
t
h
e
p
ar
all
el
r
esis
ta
n
ce
o
f
t
h
e
P
V
m
o
d
el
in
[
Ω
]
,
R
S i
n
t
h
e
s
er
ies r
e
s
is
ta
n
ce
o
f
P
V
m
o
d
el
i
n
[
Ω
]
,
NS
is
th
e
n
o
.
o
f
ce
lls
ar
e
co
n
n
ec
ted
i
n
s
er
ie
s
in
a
s
tr
i
n
g
o
f
th
e
P
V
m
o
d
el,
NP
is
th
e
n
o
.
o
f
p
ar
allel
s
tr
i
n
g
s
,
T
is
th
e
te
m
p
er
at
u
r
e
i
n
[
K]
,
VP
V
is
t
h
e
ter
m
i
n
al
v
o
lta
g
e
o
f
th
e
P
V
m
o
d
el
in
v
o
lt
i
n
[
V]
,
VM
P
i
s
th
e
m
ax
i
m
u
m
p
o
w
er
o
f
t
h
e
P
V
ce
ll in
v
o
lt i
n
[
V]
,
VOC i
s
th
e
o
p
en
-
cir
c
u
it v
o
lta
g
e
o
f
t
h
e
P
V
ce
ll in
v
o
lt i
n
[
V]
I
n
th
e
P
V
s
y
s
te
m
m
a
x
i
m
u
m
p
o
w
er
o
u
tp
u
t
d
ep
en
d
s
u
p
o
n
t
h
e
lo
ad
cu
r
r
en
t
as
w
ell
as
s
o
lar
r
ad
iatio
n
.
So
a
co
n
tr
o
l
tech
n
iq
u
e
s
i
s
e
m
p
lo
y
ed
to
tr
ac
k
th
e
m
ax
i
m
u
m
a
m
o
u
n
t o
f
p
o
w
er
f
r
o
m
th
e
P
V
s
y
s
te
m
is
k
n
o
w
n
a
s
MP
PT
ac
c
o
r
d
in
g
to
[
1
4
-
1
6
]
.
I
n
th
i
s
liter
at
u
r
e
P
&
O
tech
n
iq
u
e
is
u
s
ed
f
o
r
th
e
MP
PT
.
T
ab
le
1
P
ar
am
eter
s
o
f
P
h
o
to
v
o
ltaic
(
P
V)
Sy
s
te
m
S
p
e
c
if
ica
ti
o
n
Va
lu
e
No
.
o
f
se
ries
c
o
n
n
e
c
ted
P
V ce
ll
96
No
.
o
f
M
o
d
u
les
in
p
a
ra
ll
e
l
66
No
.
o
f
M
o
d
u
les
in
se
ries
05
Op
e
n
c
ircu
it
v
o
lt
a
g
e
(V
OC
)
6
4
.
2
V
S
h
o
rt
c
ircu
it
c
u
rre
n
t(I
SC
)
5
.
9
6
A
M
a
x
i
m
u
m
P
o
w
e
r
o
f
P
V ce
ll
305W
T
e
m
p
e
r
a
tu
re
(T
)
25
Irra
d
ian
c
e
1
0
0
0
4.
DE
T
AI
L
E
D
R
E
A
L
I
Z
A
T
I
O
N
O
F
WE
CS
Kin
etic
E
n
er
g
y
(
KE
)
o
f
th
e
w
i
n
d
i
s
co
n
v
er
ted
i
n
to
m
ec
h
a
n
ical
e
n
er
g
y
b
y
m
ea
n
s
o
f
b
la
d
es
o
f
t
h
e
w
i
n
d
tu
r
b
in
e,
t
h
en
a
g
e
n
er
ato
r
is
co
n
n
ec
ted
to
th
e
w
i
n
d
tu
r
b
in
e
to
co
n
v
er
ts
m
ec
h
an
ical
en
er
g
y
to
elec
tr
ica
l
en
er
g
y
.
So
,
a
r
elatio
n
s
h
ip
is
e
s
tab
lis
h
ed
in
b
et
w
ee
n
th
e
w
i
n
d
s
p
ee
d
an
d
m
ec
h
a
n
ical
p
o
w
e
r
w
h
ic
h
is
d
escr
ib
ed
b
elo
w
:
P
M
=
1
2
ρ
A
V
w
3
C
P
(
2
)
P
ar
am
eter
s
ar
e
ta
k
e
n
f
o
r
m
o
d
elin
g
o
f
t
h
e
W
E
C
S
s
u
ch
a
s
,
P
M
is
t
h
e
m
ec
h
a
n
ical
p
o
w
er
in
[
W
]
,
ρ
is
th
e
air
d
en
s
it
y
i
n
[
kg
m
2
⁄
]
,
A
is
t
h
e
S
w
ep
t
ar
ea
in
[
m
2
]
,
V
w
is
t
h
e
w
i
n
d
s
p
ee
d
in
[
m
s
⁄
]
,
C
P
is
th
e
p
o
w
er
co
ef
f
icie
n
t o
f
w
in
d
t
u
r
b
in
e,
λ
T
is
th
e
s
p
ee
d
r
atio
,
β is
th
e
p
itch
an
g
le
o
f
t
h
e
b
lad
e
,
w
m
is
th
e
s
p
ee
d
o
f
th
e
tu
r
b
in
e,
R
T
is
t
h
e
b
lad
e
r
ad
iu
s
,
C
P
is
th
e
f
u
n
ctio
n
o
f
λ
T
an
d
β
an
d
c
an
b
e
r
ea
lized
as
C
P
(
λ
T
,
β
)
.
W
h
er
e
λ
T
=
w
m
R
T
V
w
.
T
h
e
co
ef
f
icie
n
t
o
f
p
o
w
er
C
p
d
ep
en
d
s
o
n
t
h
e
λ
T
.
T
o
ca
p
tu
r
e
m
a
x
i
m
u
m
p
o
w
er
,
w
i
n
d
tu
r
b
i
n
e
is
r
u
n
f
o
r
a
ce
r
tain
v
al
u
e
o
f
w
i
n
d
s
p
ee
d
.
T
h
e
m
a
x
i
m
u
m
v
al
u
e
o
f
t
h
e
C
P
is
0
.
5
9
ac
co
r
d
in
g
to
th
e
B
etz
li
m
it [
1
1
]
.
T
o
ex
tr
ac
t
th
e
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
W
E
C
S
a
co
n
tr
o
l
tech
n
iq
u
e
i
s
e
m
p
lo
y
ed
.
B
asic
all
y
,
P
&
O
tech
n
iq
u
e
is
u
s
ed
i
n
th
e
MP
P
T
f
o
r
th
e
W
E
C
S a
cc
o
r
d
in
g
to
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
377
–
3
8
9
380
5.
DE
T
AI
L
E
D
M
O
DE
L
O
F
E
L
E
C
T
RO
L
Y
Z
E
R
An
elec
tr
o
l
y
ze
r
co
n
s
i
s
ts
o
f
t
h
e
n
o
.
o
f
s
er
ies
-
co
n
n
ec
ted
ce
ll
s
.
T
w
o
elec
tr
o
d
es
ar
e
p
r
esen
t
ed
in
t
h
e
elec
tr
o
l
y
ze
r
an
d
s
ep
ar
ated
b
y
a
n
elec
tr
o
l
y
te.
W
ater
(
H2
O)
is
d
ec
o
m
p
o
s
ed
in
to
H2
an
d
o
x
y
g
en
i
n
t
h
e
elec
tr
o
l
y
ze
r
w
h
e
n
th
e
c
u
r
r
en
t i
s
p
ass
ed
th
r
o
u
g
h
it a
cc
o
r
d
in
g
t
o
[
2
,
1
8
]
.
T
h
e
elec
tr
o
ch
e
m
ical
r
ea
ctio
n
o
f
H2
O
is
g
i
v
e
n
b
elo
w
:
H
2
O
(
I
)
+
e
l
e
c
tr
ic
a
l
e
n
e
r
gy
=
H
2
(
g
)
+
1
2
O
2
(
g
)
(
3
)
P
ar
am
eter
s
ar
e
tak
e
n
f
o
r
m
o
d
elin
g
o
f
t
h
e
elec
tr
o
l
y
ze
r
s
u
c
h
as,
ie
i
s
t
h
e
c
u
r
r
en
t
o
f
a
n
elec
tr
o
ly
ze
r
i
n
[
A
]
,
n
c
is
t
h
e
n
o
.
o
f
elec
tr
o
l
y
ze
r
ce
ll
s
co
n
n
ec
ted
i
n
s
er
ies,
n
H2
i
s
th
e
h
y
d
r
o
g
en
g
e
n
er
atio
n
i
n
m
o
les
p
er
s
ec
o
n
d
in
t
h
e
[
m
o
l
s
−1
]
,
F is
t
h
e
f
ar
ad
a
y
co
n
s
ta
n
t i
n
th
e
[
C
k
m
o
l−1
]
,
η
F is
t
h
e
Far
ad
a
y
e
f
f
i
cien
c
y
.
H2
is
p
r
o
d
u
ce
d
b
y
th
e
elec
tr
o
l
y
ze
r
an
d
r
ate
o
f
it
s
p
r
o
d
u
ctio
n
d
ep
en
d
s
u
p
o
n
t
h
e
c
u
r
r
en
t
f
lo
w
t
h
r
o
u
g
h
it g
i
v
en
i
n
Far
ad
a
y
’
s
la
w
[
1
2
]
.
nH
2
=
n
F
n
c
i
e
2F
(
4
)
Far
ad
ay
e
f
f
icie
n
c
y
i
s
n
o
ted
as
th
e
r
atio
o
f
ac
tu
al
p
r
o
d
u
ctio
n
o
f
H2
to
its
th
eo
r
etica
l v
a
lu
e.
ƞ
F
=
96
.
5
e
(
0
.
09
i
e
−
75
.
5
i
e
2
)
(
5)
W
ith
th
e
h
elp
o
f
E
q
u
atio
n
(
4
)
an
d
(
5
)
an
elec
tr
o
ly
ze
r
is
d
esi
g
n
ed
b
y
u
s
i
n
g
Ma
tlab
-
Si
m
u
l
in
k
s
o
f
t
w
ar
e.
6.
DE
T
AI
L
E
D
M
O
DE
L
L
I
N
G
O
F
ST
O
RA
G
E
T
ANK
T
h
e
g
en
er
atio
n
o
f
H2
f
r
o
m
th
e
elec
tr
o
ly
ze
r
ca
n
b
e
k
ep
t
in
a
s
to
r
ag
e
tan
k
f
o
r
th
e
f
u
t
u
r
e
u
s
e.
B
asicall
y
th
r
ee
m
et
h
o
d
s
ar
e
ap
p
licab
le
t
o
s
to
r
e
th
e
H2
,
th
ese
ar
e
(
a)
h
ig
h
-
p
r
es
s
u
r
e
g
a
s
in
co
m
p
r
es
s
e
d
f
o
r
m
,
(
b
)
liq
u
id
s
to
r
ag
e
a
n
d
(
c)
h
y
d
r
o
g
en
ab
s
o
r
b
in
g
m
ater
ial
s
.
T
h
e
H2
is
s
to
r
ed
in
co
m
p
r
es
s
ed
h
ig
h
p
r
es
s
u
r
e
g
aseo
u
s
f
o
r
m
f
o
r
th
e
d
o
m
esti
c
ap
p
licatio
n
.
E
q
u
atio
n
(
6
)
is
co
n
s
id
er
ed
f
o
r
th
e
d
esig
n
i
n
g
o
f
h
y
d
r
o
g
e
n
s
to
r
ag
e
tan
k
ac
co
r
d
in
g
to
[
1
1
]
.
P
b
−
P
bi
=
z
NH
2
R
T
b
MH
2
V
b
(
6)
P
ar
am
eter
s
ar
e
tak
e
n
f
o
r
m
o
d
elin
g
o
f
th
e
SO
FC
s
u
c
h
as,
Z
is
t
h
e
p
r
ess
u
r
e
co
m
p
r
ess
ib
ilit
y
f
ac
to
r
,
NH2
is
th
e
a
m
o
u
n
t
o
f
h
y
d
r
o
g
en
s
to
r
ed
in
t
h
e
s
to
r
ag
e
ta
n
k
i
n
m
o
le
s
p
er
s
ec
o
n
d
in
th
e
[
k
m
o
l
s
−1
]
,
MH
2
is
th
e
H
y
d
r
o
g
en
m
o
lar
m
as
s
in
[
k
g
k
m
o
l−1
]
,
T
b
is
o
p
er
atin
g
te
m
p
e
r
atu
r
e
in
[
o
K]
,
P
b
i
is
th
e
s
to
r
a
g
e
tan
k
p
r
ess
u
r
e
at
in
itial
s
ta
g
e
in
[
P
a]
,
P
b
is
th
e
s
to
r
ag
e
tan
k
p
r
ess
u
r
e
i
n
[
P
a]
,
R
is
th
e
R
y
d
b
er
g
/U
n
i
v
er
s
al
g
as
co
n
s
ta
n
t
i
n
[
J
(
k
m
o
l o
K)
−1
]
,
Vb
is
th
e
s
to
r
ag
e
tan
k
v
o
l
u
m
e
in
[
m
3
]
.
7.
DE
T
AI
L
E
D
M
O
DE
L
L
I
N
G
O
F
SO
F
C
SOFC
is
u
s
ed
to
co
n
v
er
t
ch
e
m
ical
en
er
g
y
o
f
a
f
u
el
(
m
e
th
a
n
o
l,
h
y
d
r
o
g
e
n
,
g
a
s
o
lin
e,
n
a
tu
r
al
g
a
s
a
n
d
m
an
y
m
o
r
e)
i
n
to
an
elec
tr
ical
p
o
w
er
.
A
l
s
o
,
th
e
f
u
el
ce
ll
s
p
r
o
v
id
e
clea
n
e
n
er
g
y
an
d
n
o
e
m
is
s
io
n
s
.
P
ar
am
eter
s
o
f
th
e
SO
FC
w
h
ic
h
ar
e
u
s
ed
to
d
ev
elo
p
t
h
e
m
at
h
e
m
a
t
ical
m
o
d
el
ac
co
r
d
in
g
to
[
2
2
]
s
u
ch
as,
B
an
d
C
is
th
e
ac
tiv
atio
n
v
o
lta
g
e
co
n
s
ta
n
ts
i
n
SOF
C
s
y
s
te
m
in
[
V]
,
C
V
is
th
e
c
o
n
v
er
s
io
n
f
ac
to
r
in
[
Hy
d
r
o
g
en
(
km
o
h
)
Methen
(
km
o
h
)
]
,
E
0
is
th
e
n
o
r
m
al
n
o
lo
ad
v
o
ltag
e
in
[
V]
,
E
is
th
e
n
er
n
s
t
i
m
m
ed
iate
v
o
ltag
e
i
n
[
V]
,
F
is
t
h
e
Fa
r
ad
ay
’
s
co
n
s
ta
n
t
in
[
C
(
k
m
o
l
-
1
)
]
,
I
FC
is
th
e
f
ee
d
b
ac
k
cu
r
r
en
t
o
f
SOFC
i
n
[
A
]
,
k
1
is
th
e
g
ain
o
f
P
I
(
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al)
,
Kan
is
th
e
an
o
d
e
v
al
v
e
co
n
s
ta
n
t
in
[
√
k
mol
kg
(
a
tm
s
)
−
1
]
,
Kr
is
th
e
m
o
d
elin
g
co
n
s
ta
n
t
i
n
[
k
m
o
l
S
A
-
1
]
,
KH
2
O
is
t
h
e
m
o
lar
co
n
s
ta
n
t
o
f
wate
r
v
al
v
e
i
n
[
k
m
o
l
(
at
m
s
-
1
)
]
,
KH2
is
th
e
m
o
lar
co
n
s
ta
n
t
o
f
h
y
d
r
o
g
en
v
a
lv
e
in
[
k
m
o
l
(
at
m
s
-
1
)
]
,
KO2
is
t
h
e
m
o
lar
co
n
s
tan
t
o
f
o
x
y
g
e
n
v
al
v
e
i
n
[
k
m
o
l
(
at
m
s
-
1
)
]
,
MH
2
is
th
e
h
y
d
r
o
g
en
m
o
l
ar
m
a
s
s
i
n
[
k
g
k
m
o
l
-
1
]
,
P
H2
O
is
th
e
w
ater
f
r
ac
tio
n
al
p
r
ess
u
r
e
in
[
at
m
]
,
P
H2
is
th
e
h
y
d
r
o
g
e
n
f
r
ac
tio
n
a
l p
r
ess
u
r
e
in
[
at
m
]
,
P
O2
is
th
e
o
x
y
g
e
n
f
r
ac
tio
n
a
l p
r
ess
u
r
e
i
n
[
at
m
]
,
N0
is
t
h
e
n
o
.
o
f
f
u
el
ce
lls
ar
e
in
s
er
ie
s
in
a
s
tac
k
,
q
H2
is
th
e
m
o
lar
f
lo
w
o
f
h
y
d
r
o
g
en
i
n
[
k
m
o
ls
-
1
]
,
q
m
eth
a
n
e
is
th
e
m
et
h
a
n
e
f
lo
w
r
ate
in
[
k
m
o
ls
-
1
]
,
q
O2
in
th
e
i
n
p
u
t
m
o
lar
f
lo
w
o
f
o
x
y
g
en
,
[
k
m
o
l
s
-
1
]
,
q
H2
in
is
th
e
in
p
u
t
f
lo
w
o
f
h
y
d
r
o
g
e
n
in
[
k
m
o
l
s
-
1
]
,
q
H2
0
ut
is
th
e
h
y
d
r
o
g
en
o
u
tp
u
t
f
lo
w
in
[
k
m
o
ls
-
1
]
,
q
H2
r
is
th
e
h
y
d
r
o
g
en
f
lo
w
a
m
o
u
n
t
t
h
at
r
ea
cts in
[
K
m
o
l
s
-
1
]
,
q
H2
r
eq
is
th
e
h
y
d
r
o
g
en
f
lo
w
a
m
o
u
n
t th
a
t
m
ee
t
s
lo
ad
ch
an
g
e
i
n
[
k
m
o
l
s
-
1
]
,
R
is
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
P
o
w
er Qu
a
lity A
n
a
lysi
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
S
o
l
a
r
/Wi
n
d
/Hyd
r
o
g
en
E
n
erg
y
Hyb
r
id
…
(
S
u
jit K
u
ma
r
B
h
u
ya
n
)
381
r
y
d
b
er
g
(
U
n
i
v
er
s
al)
g
as
co
n
s
t
an
t
i
n
[
(
1
at
m
)
(
k
m
o
l
K)
−1
]
,
R
in
t
is
th
e
in
ter
n
al
r
es
is
ta
n
ce
o
f
SO
FC
i
n
[
Ω
]
,
T
is
th
e
ab
s
o
lu
te
te
m
p
er
atu
r
e
i
n
[
K
]
,
U
is
th
e
u
ti
lizatio
n
r
ate,
Va
n
is
th
e
v
o
lu
m
e
o
f
t
h
e
an
o
d
e
in
[
m
3
]
,
Vce
ll
is
th
e
SOF
C
d
c
o
u
tp
u
t
v
o
ltag
e
i
n
[
V]
,
τ
1
,
τ
2
is
th
e
r
ef
o
r
m
er
ti
m
e
c
o
n
s
ta
n
ts
i
n
[
s
]
,
τ
3
is
th
e
P
I
co
n
tr
o
ller
tim
e
co
n
s
ta
n
t in
[
s
]
,
τ
H2
in
t
h
e
h
y
d
r
o
g
e
n
ti
m
e
co
n
s
ta
n
t,
[
s
]
,
τ
H2
O
is
t
h
e
w
ater
t
i
m
e
co
n
s
tan
t
in
[
s
]
,
τ
O2
is
t
h
e
o
x
y
g
en
ti
m
e
co
n
s
tan
t
i
n
[
s
]
,
Z
ac
t
is
t
h
e
ac
tiv
atio
n
o
v
er
v
o
l
tag
e
in
[
V]
,
Z
o
h
m
ic
is
t
h
e
o
h
m
ic
o
v
er
v
o
lta
g
e
in
[
V]
.
T
h
e
r
atio
o
f
m
o
lar
f
lo
w
h
y
d
r
o
g
en
t
h
r
o
u
g
h
o
u
t
th
e
v
al
v
e
t
o
th
e
h
y
d
r
o
g
e
n
p
ar
tial
p
r
ess
u
r
e
i
n
t
h
e
ch
a
m
b
er
m
a
y
b
e
w
r
itte
n
as [
2
2
]
:
q
H2
P
H2
=
K
an
√
M
H2
=
K
H2
(
7
)
T
h
r
ee
m
aj
o
r
asp
ec
ts
ta
k
en
i
n
t
o
co
n
s
i
d
er
atio
n
f
o
r
t
h
e
m
o
lar
f
lo
w
o
f
h
y
d
r
o
g
en
ar
e
(
a)
i
n
p
u
t
f
lo
w
o
f
h
y
d
r
o
g
e
n
,
(
b
)
o
u
tp
u
t f
lo
w
o
f
h
y
d
r
o
g
e
n
a
n
d
(
c)
h
y
d
r
o
g
en
f
lo
w
d
u
r
i
n
g
th
e
r
ea
ctio
n
.
Hen
ce
,
th
e
E
q
u
a
tio
n
ca
n
b
e
w
r
itten
as
:
d
dt
p
H2
=
RT
V
an
(
q
H2
in
−
q
H2
o
ut
−
q
H2
r
)
(
8
)
T
h
e
r
ea
cted
h
y
d
r
o
g
en
f
lo
w
d
e
p
en
d
s
u
p
o
n
th
e
f
u
el
ce
ll
c
u
r
r
e
n
t
a
n
d
th
e
r
ate
o
f
f
lo
w
o
f
h
y
d
r
o
g
en
.
T
h
e
E
q
u
atio
n
o
f
r
ea
cted
h
y
d
r
o
g
e
n
f
lo
w
r
ate
is
s
h
o
w
n
b
elo
w
.
q
H2
r
=
N
0
I
FC
2F
=
2
K
r
I
FC
(
9)
B
y
co
n
s
id
er
in
g
th
e
E
q
u
at
io
n
s
(
7
)
an
d
(
9
)
an
d
tak
in
g
L
ap
la
ce
T
r
an
s
f
o
r
m
o
f
th
ese
E
q
u
a
ti
o
n
s
,
th
e
n
p
ar
tial p
r
ess
u
r
e
o
f
h
y
d
r
o
g
en
i
s
d
eter
m
i
n
ed
as:
P
H2
=
1
K
H2
⁄
1
+
τ
H2
s
(
q
H2
in
−
2
K
r
I
Fc
)
(
10)
W
he
r
e
,
τ
H2
=
V
an
K
H2
RT
(
11)
I
n
th
is
m
a
n
n
er
p
ar
tial
p
r
ess
u
r
es
o
f
w
ater
an
d
o
x
y
g
e
n
ar
e
d
eter
m
i
n
ed
.
Hen
ce
,
p
o
lar
izatio
n
c
u
r
v
e
o
f
th
e
SOF
C
is
f
o
u
n
d
o
u
t
f
r
o
m
th
e
s
u
m
m
atio
n
o
f
th
e
o
h
m
i
c
o
v
er
v
o
ltag
e,
ac
tiv
atio
n
o
v
er
v
o
ltag
e
an
d
th
e
Ner
n
s
t
’
s
v
o
lta
g
e.
A
co
n
s
ta
n
t
ass
u
m
p
tio
n
is
tak
e
n
f
o
r
th
e
o
x
y
g
e
n
co
n
ce
n
tr
atio
n
an
d
te
m
p
er
atu
r
e
an
d
h
e
n
ce
,
th
e
SO
FC
o
u
tp
u
t v
o
lta
g
e
ca
n
b
e
d
eter
m
i
n
ed
as:
V
cel
l
=
E
+
ƞ
act
+
(
12)
W
he
r
e
,
ƞ
act
=
−
B
l
n
(
C
I
FC
)
(
13)
A
n
d
ƞ
o
hm
i
c
=
−
R
i
n
t
I
FC
(
14)
Hen
ce
,
th
e
Ner
n
s
t
’
s
v
o
lta
g
e
can
b
e
s
tated
as
:
E
=
N
O
[
E
O
+
RT
2F
l
og
[
P
H2
√
P
O2
P
H
2
O
]
]
(
15)
T
o
co
n
tr
o
l
th
e
r
eq
u
ir
ed
a
m
o
u
n
t
o
f
H2
f
lo
w
to
th
e
SOF
C
ac
co
r
d
in
g
to
o
u
tp
u
t
p
o
w
er
o
f
S
OFC
,
a
P
I
D
co
n
tr
o
ller
is
tak
en
i
n
to
co
n
s
id
er
atio
n
.
A
f
ee
d
b
ac
k
co
n
tr
o
l
s
tr
ateg
y
i
s
ac
h
ie
v
ed
b
y
tak
i
n
g
S
OFC
o
u
tp
u
t
cu
r
r
en
t
f
ee
d
b
ac
k
to
th
e
cu
r
r
e
n
t
i
n
p
u
t
t
er
m
in
a
l
o
f
SO
FC
.
So
,
a
v
ailab
i
lit
y
o
f
h
y
d
r
o
g
en
in
a
h
y
d
r
o
g
e
n
ta
n
k
i
s
e
x
p
r
ess
ed
as [
2
2
]
:
q
H2
r
eq
=
N
O
I
FC
2
F
U
(
16)
A
5
KW
SOF
C
is
d
e
v
elo
p
ed
b
y
tak
in
g
t
h
e
p
ar
a
m
eter
s
as r
ep
r
esen
ted
in
T
ab
le
2
an
d
a
d
etailed
m
o
d
el
o
f
SO
FC
is
d
e
v
elo
p
ed
w
i
th
t
h
e
h
elp
o
f
Ma
tlab
/Si
m
u
li
n
k
a
cc
o
r
d
in
g
to
[
2
3
]
.
I
n
th
is
p
ap
e
r
f
o
u
r
n
o
.
o
f
5
KW
SOFC
ar
e
tak
en
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
377
–
3
8
9
382
T
ab
le
2
P
a
rti
c
u
lars
o
f
S
OFC
to
d
e
v
e
lo
p
th
e
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
li
n
g
S
p
e
c
if
ica
ti
o
n
s
Va
lu
e
A
c
ti
v
a
ti
o
n
v
o
lt
a
g
e
c
o
n
sta
n
t
(B)
0
.
0
4
7
7
7
[
A
-
1
]
A
c
ti
v
a
ti
o
n
v
o
lt
a
g
e
c
o
n
sta
n
t
(C)
0
.
0
1
3
6
[V]
Co
n
v
e
rsio
n
f
a
c
to
r
(C
V
)
2
F
a
ra
d
a
y
’s co
n
sta
n
t
(F
)
9
6
4
8
4
6
0
0
[
Ck
m
o
l
-
1
]
F
C
sy
st
e
m
in
tern
a
l
re
sista
n
c
e
(R
i
nt
)
0
.
2
6
6
6
4
[Ω
]
F
C
a
b
so
l
u
te t
e
m
p
e
ra
tu
re
(T
)
3
4
3
[
K
]
H
y
d
ro
g
e
n
ti
m
e
c
o
n
sta
n
t
(
2
)
3
.
3
7
[
s
]
H
y
d
ro
g
e
n
v
a
lv
e
c
o
n
sta
n
t
(K
H2
)
4
.
2
2
x
1
0
-
5
[
k
m
o
l
(s atm
)
-
1
]
H
y
d
ro
g
e
n
–
o
x
y
g
e
n
f
lo
w
r
a
ti
o
(r
H2O
)
1
.
1
6
8
Kr co
n
sta
n
t
=
N
0
/
4
F
2
.
2
8
0
2
x
1
0
-
7
[
k
m
o
l
(s A
)
-
1
L
in
e
re
a
c
tan
c
e
(X
)
0.
0
8
0
9
[
Ω
]
M
e
th
a
n
e
re
f
e
re
n
c
e
sig
n
a
l
(Q
m
e
t
h
r
e
f
)
0
.
0
0
0
0
1
5
[
k
m
o
l
s
-
1
]
No
lo
a
d
v
o
lt
a
g
e
(E
o
)
1
.
1
8
[V]
Nu
m
b
e
r
o
f
c
e
ll
s (N
o
)
88
Nu
m
b
e
r
o
f
sta
c
k
s (N
S
)
1
Ox
y
g
e
n
ti
m
e
c
o
n
sta
n
t
(
2
)
6
.
7
4
[
s
]
Ox
y
g
e
n
v
a
lv
e
c
o
n
sta
n
t,
(k
O2
)
2
.
1
1
x
1
0
-
5
[
k
m
o
l
(s atm
)
-
1
]
P
I
g
a
in
c
o
n
sta
n
t
(k
1
)
0
.
2
5
Re
f
o
r
m
e
r
ti
m
e
c
o
n
sta
n
t
(
1
,
2
,
3
)
1
5
[
s
]
Un
iv
e
rsa
l
g
a
s c
o
n
sta
n
t
(R)
8
3
1
4
.
4
7
[
J
k
m
o
lK
-
1
]
Util
iza
ti
o
n
f
a
c
to
r
(U)
0
.
8
W
a
ter t
i
m
e
c
o
n
sta
n
t
(
2
)
1
8
.
4
1
8
[
s
]
W
a
ter
v
a
lv
e
c
o
n
sta
n
t
(K
H2O
)
7
.
7
1
6
10
-
6
[
k
m
o
l
(s atm
)
-
1
]
8.
I
NT
E
RNA
L
ARR
AG
E
M
E
NT
O
F
H
YB
RID G
E
NE
RAT
I
O
N
SYST
E
M
T
h
e
d
etailed
m
o
d
el
o
f
p
r
o
p
o
s
ed
HGS
is
s
h
o
w
n
in
Fi
g
u
r
e
1
w
h
er
ea
s
;
t
h
e
i
n
ter
n
al
m
o
d
el
d
iag
r
a
m
i
s
r
ep
r
esen
ted
in
Fi
g
u
r
e
2
.
I
n
Fi
g
u
r
e
2
a
t
w
o
R
E
Ss
ar
e
s
h
o
w
n
,
o
n
e
o
f
t
h
e
m
is
P
V
s
y
s
te
m
an
d
an
o
t
h
er
o
n
e
is
W
E
C
S.
A
P
V
s
y
s
te
m
tr
ac
k
s
t
h
e
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
th
e
s
u
n
b
y
m
ea
n
s
o
f
MP
P
T
w
h
er
e
as,
W
E
C
S
u
til
izes
th
e
k
i
n
etic
en
er
g
y
o
f
t
h
e
w
i
n
d
an
d
co
n
v
er
ts
t
h
is
i
n
to
elec
t
r
ical
p
o
w
er
b
y
t
h
e
h
elp
o
f
M
P
PT.
T
h
e
elec
tr
ical
p
o
w
er
co
m
i
n
g
f
r
o
m
t
h
e
P
V
s
y
s
te
m
is
g
i
v
e
n
to
DC
-
D
C
b
o
o
s
t
co
n
v
er
ter
to
e
n
h
a
n
ce
th
e
v
o
ltag
e.
T
h
e
s
a
m
e
p
r
in
cip
le
is
h
ap
p
en
i
n
g
in
t
h
e
W
E
C
S.
I
n
W
E
C
S,
as
s
h
o
w
n
i
n
Fi
g
u
r
e
2
a,
V
w
i
n
d
_
ac
is
ap
p
lied
to
th
e
AC
-
D
C
co
n
v
er
ter
w
h
er
e,
AC
v
o
lta
g
e
i
s
co
n
v
er
ted
to
th
e
DC
v
o
lta
g
e
an
d
th
is
DC
v
o
ltag
e
is
ap
p
lie
d
to
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
to
en
h
a
n
ce
th
e
v
o
lta
g
e
lev
el.
T
h
e
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
s
e
m
p
lo
y
ed
in
W
E
C
S
an
d
P
V
s
y
s
te
m
ar
e
tr
ig
g
er
ed
b
y
th
e
p
u
l
s
es
g
e
n
er
ated
f
r
o
m
t
h
e
MP
PT
.
T
h
ese
MP
PT
s
a
r
e
u
s
ed
in
W
E
C
S
an
d
P
V
s
y
s
te
m
s
.
A
s
g
iv
e
n
in
Fi
g
u
r
e
2
a,
t
h
e
e
n
h
a
n
ce
d
v
o
ltag
e
s
o
f
t
h
e
b
o
t
h
D
C
-
DC
co
n
v
er
ter
s
o
f
th
e
W
E
C
S
an
d
P
V
s
y
s
te
m
ar
e
ap
p
lied
to
DC
-
A
C
co
n
v
er
ter
t
o
co
n
v
er
t D
C
v
o
ltag
e
to
AC
v
o
ltag
e.
T
h
is
DC
-
AC
co
n
v
er
ter
is
tr
ig
g
er
ed
b
y
g
ate
p
u
ls
e
g
en
er
ated
b
y
th
e
co
n
tr
o
l
tech
n
iq
u
e
o
f
t
h
e
v
o
ltag
e
s
o
u
r
ce
co
n
v
e
r
ter
(
VSC
)
.
T
h
is
c
o
n
tr
o
l
tech
n
iq
u
e
o
f
VSC
is
e
m
p
lo
y
ed
to
s
y
n
c
h
r
o
n
ize
th
e
v
o
lta
g
es
o
f
t
h
e
g
r
id
an
d
HGS.
T
h
e
ex
tr
a
am
o
u
n
t
o
f
p
o
w
er
f
r
o
m
th
e
W
E
C
S
an
d
P
V
i
s
u
tili
ze
d
f
o
r
th
e
H2
p
r
o
d
u
ctio
n
b
y
th
e
ele
ctr
o
ly
ze
r
a
n
d
t
h
e
H2
f
u
r
th
er
ac
ts
as
th
e
in
p
u
t
o
f
SOFC
a
s
a
f
u
el.
Ag
ai
n
a
D
C
-
DC
co
n
v
er
ter
is
co
n
n
ec
ted
to
t
h
e
SO
FC
to
e
n
h
a
n
ce
t
h
e
v
o
lta
g
e
lev
e
l o
f
SO
FC
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
2
b
.
A
VS
C
is
u
s
ed
to
s
y
n
c
h
r
o
n
ize
t
h
e
v
o
ltag
e
s
b
et
w
ee
n
g
r
id
an
d
s
y
s
te
m
.
T
h
e
co
n
tr
o
l
tech
n
iq
u
e
ap
p
lied
to
VSC
is
d
i
v
id
ed
in
to
t
w
o
p
ar
ts
a
s
d
escr
ib
ed
b
elo
w
.
DC
-
Lin
k
vo
lta
g
e
co
n
tr
o
ller
T
h
e
DC
-
li
n
k
v
o
lta
g
e
r
eg
u
la
te
s
th
e
d
esire
d
v
al
u
e
o
f
th
e
ac
ti
v
e
p
o
w
er
.
T
h
en
id
*
is
t
h
e
o
u
t
p
u
t
o
f
th
e
DC
-
li
n
k
P
I
co
n
tr
o
ller
ta
k
e
n
as
t
h
e
r
ef
er
e
n
ce
o
f
th
e
ac
ti
v
e
cu
r
r
en
t
co
n
tr
o
ller
(
cu
r
r
en
t
P
I
co
n
tr
o
ller
)
an
d
r
ep
r
esen
ted
in
Fi
g
u
r
e
2
c.
I
n
tern
a
l c
u
r
r
en
t lo
o
p
T
h
e
S
y
n
c
h
r
o
n
o
u
s
R
ef
er
e
n
ce
Fra
m
e
(
d
−q
co
n
tr
o
l)
tr
an
s
f
o
r
m
s
th
e
g
r
id
v
o
lta
g
e
s
(
Va,
Vb
,
Vc)
to
Vd
an
d
Vq
as
w
ell
a
s
g
r
id
c
u
r
r
en
t
s
(
ia,
ib
,
ic)
to
id
a
n
d
iq
r
e
f
er
e
n
ce
f
r
a
m
e
th
a
t
r
o
tates
s
y
n
c
h
r
o
n
o
u
s
l
y
alo
n
g
w
i
th
g
r
id
v
o
lta
g
e.
Vd
,
Vq
,
I
d
an
d
I
q
ar
e
th
e
DC
v
al
u
e
s
o
b
tain
ed
b
y
t
h
e
h
elp
o
f
d
-
q
co
n
tr
o
ller
,
also
th
e
s
e
DC
v
al
u
e
s
ar
e
ea
s
ier
f
o
r
d
esig
n
i
n
g
an
d
c
o
n
tr
o
llin
g
.
Gr
id
v
o
lt
a
g
e
(
Va,
Vb
,
Vc)
r
eg
u
late
s
P
L
L
(
P
h
ase
L
o
ck
L
o
o
p
)
,
h
en
ce
th
e
p
h
ase
a
n
g
le
is
o
b
tain
ed
an
d
u
s
ed
in
d
−q
co
n
tr
o
ller
f
o
r
ab
c
→
d
q
tr
an
s
f
o
r
m
atio
n
.
As
s
h
o
w
n
i
n
Fi
g
u
r
e
2
c,
th
e
r
ef
er
en
ce
r
ea
ctiv
e
c
u
r
r
en
t
iq
*
i
s
s
et
to
ze
r
o
an
d
ap
p
lied
t
o
cu
r
r
en
t
P
I
co
n
tr
o
ller
.
Hen
ce
,
p
f
(
p
o
w
er
f
ac
to
r
)
is
p
r
eser
v
ed
to
b
e
o
n
e
(
U
n
it
y
)
.
T
h
e
v
o
lta
g
e
o
u
tp
u
t
t
h
at
is
V
d
*
is
o
b
tain
ed
b
y
co
m
p
ar
i
n
g
i
d
*
an
d
id
,
also
Vq
*
is
o
b
tain
ed
b
y
co
m
p
ar
in
g
iq
*
an
d
iq
.
T
h
en
,
th
e
Vd
*
an
d
Vq
*
ar
e
ap
p
lied
to
P
W
M
g
en
er
ato
r
to
g
en
er
ate
th
e
p
u
ls
es
w
h
ic
h
ar
e
e
m
p
lo
y
ed
to
tr
ig
g
er
t
h
e
DC
-
AC
co
n
v
er
ter
as sh
o
w
n
i
n
Fi
g
u
r
e
2
a.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
P
o
w
er Qu
a
lity A
n
a
lysi
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
S
o
l
a
r
/Wi
n
d
/Hyd
r
o
g
en
E
n
erg
y
Hyb
r
id
…
(
S
u
jit K
u
ma
r
B
h
u
ya
n
)
383
As
s
h
o
w
n
i
n
th
e
Fi
g
u
r
e
2
b
,
a
b
u
ck
co
n
v
er
ter
is
co
n
n
ec
ted
ac
r
o
s
s
th
e
elec
tr
o
l
y
ze
r
w
h
ich
tak
es
t
h
e
ex
tr
a
a
m
o
u
n
t
o
f
p
o
w
er
f
r
o
m
t
h
e
W
E
C
S
a
n
d
p
r
o
v
id
es
t
h
at
e
x
tr
a
p
o
w
er
to
t
h
e
elec
tr
o
l
y
ze
r
to
co
n
v
er
t
th
e
w
ater
in
to
H2
an
d
o
x
y
g
e
n
.
T
h
is
H2
is
u
s
ed
as
t
h
e
i
n
p
u
t
f
u
el
o
f
S
OFC
a
n
d
th
e
r
est
a
m
o
u
n
t
o
f
f
u
el
is
s
to
r
ed
in
th
e
s
to
r
ag
e
ta
n
k
.
T
h
e
r
eq
u
ir
e
m
e
n
t
o
f
H2
f
lo
w
to
th
e
SOF
C
a
s
a
f
u
el
d
ep
en
d
s
u
p
o
n
th
e
lo
ad
d
em
a
n
d
.
Fi
g
u
r
e
2
d
s
h
o
w
s
t
h
e
g
r
ap
h
ical
s
tr
u
ct
u
r
e
o
f
th
e
f
u
e
l
ce
ll
f
lo
w
co
n
tr
o
lle
r
w
h
er
e
Vso
f
c_
b
o
o
s
t
is
t
h
e
o
u
tp
u
t
v
o
lta
g
e
o
f
t
h
e
b
o
o
s
t
co
n
v
er
ter
co
n
n
ec
ted
ac
r
o
s
s
th
e
SOF
C
.
P
I
D
co
n
tr
o
ller
tak
es
th
e
i
n
p
u
t
v
o
lta
g
e
o
f
t
h
e
b
o
o
s
t
co
n
v
er
ter
(
Vso
f
c_
b
o
o
s
t)
co
n
n
ec
ted
ac
r
o
s
s
t
h
e
SO
FC
an
d
g
i
v
es
t
h
e
c
o
n
tr
o
llin
g
s
i
g
n
al
to
t
h
e
v
a
lv
e
.
Hen
ce
,
th
e
v
a
lv
e
r
eg
u
late
s
t
h
e
a
m
o
u
n
t
o
f
H2
f
l
o
w
w
h
ic
h
is
g
i
v
e
n
to
t
h
e
SO
FC
ac
co
r
d
in
g
to
lo
ad
r
eq
u
ir
em
en
t.
T
h
e
v
alu
e
s
o
f
P
I
D
c
o
n
tr
o
ller
s
h
o
w
n
ar
e
ch
o
s
en
b
y
th
e
h
elp
o
f
s
el
f
-
tu
n
ed
m
o
d
e
o
f
th
e
Ma
tlab
/Si
m
u
lin
k
(
P
=
0
.
0
0
0
1
3
3
1
7
,
I
=
3
.
3
9
2
5
2
2
7
e
-
0
5
,
D
=
-
6
.
2
5
4
2
5
4
1
7
2
8
7
0
e
-
0
5
)
.
F
ig
u
re
2
a
.
Bl
o
c
k
d
iag
ra
m
Re
p
re
s
e
n
tatio
n
o
f
Hy
b
rid
G
e
n
e
r
a
ti
o
n
S
y
ste
m
(H
G
S
)
F
ig
u
re
2
c
.
G
ra
p
h
ica
l
d
iag
ra
m
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re
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im
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ig
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re
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ra
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NT
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T
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E
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P
a
t
h
1
[P
pv
< P
L
o
a
d
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P
a
t
h
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[
(
P
pv
=
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]
P
a
t
h
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[
P
pv
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o
a
d
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P
a
t
h
4
[
(
P
pv
+
P
W
E
CS
)
=
0
]
Fig
u
r
e
3
.
v
ar
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s
p
ath
d
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t
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d
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
377
–
3
8
9
384
Fig
u
r
e
3
s
h
o
w
s
th
e
o
p
er
atio
n
al
co
n
tr
o
l
s
tr
ate
g
y
(
OC
S)
o
f
t
h
e
HG
S.
T
h
e
u
s
ef
u
l
n
es
s
o
f
th
is
co
n
tr
o
l
s
tr
ateg
y
is
to
m
a
k
e
r
elatio
n
s
h
i
p
b
etw
ee
n
th
e
p
o
w
er
d
em
a
n
d
an
d
g
en
er
atio
n
o
f
HGS.
So
,
th
e
w
h
o
le
o
p
er
atio
n
is
co
n
d
u
cted
i
n
a
s
m
o
o
t
h
m
a
n
n
er
.
B
asicall
y
i
n
t
h
is
to
p
ic
th
e
r
eq
u
ir
ed
lo
ad
d
em
a
n
d
co
n
s
id
er
ed
is
g
r
ea
ter
th
a
n
P
V
p
o
w
er
.
B
u
t,
th
er
e
ar
e
f
o
u
r
p
o
s
s
ib
le
w
a
y
s
f
o
r
th
e
O
C
S to
r
eg
u
la
te
th
e
m
o
d
el
s
m
o
o
t
h
l
y
a
s
d
escr
ib
ed
b
el
o
w
.
a)
W
h
ile
P
V
p
o
w
er
(
P
p
v
)
is
les
s
th
a
n
th
e
d
e
m
an
d
p
o
w
er
(
P
d
em
a
n
d
)
i.e
.
,
P
p
v
<
Pd
em
a
n
d
,
th
en
p
ath
1
s
h
o
u
ld
b
e
f
o
llo
w
ed
.
T
o
tal
am
o
u
n
t
o
f
P
V
p
o
w
er
a
n
d
r
eq
u
ir
ed
am
o
u
n
t
o
f
W
E
C
S
p
o
w
er
(
P
W
E
C
S)
ar
e
s
u
p
p
lied
to
f
u
l
f
ill
t
h
e
lo
ad
d
em
an
d
.
T
h
en
t
h
e
r
es
t
a
m
o
u
n
t
W
E
C
S
p
o
w
er
is
g
i
v
e
n
to
th
e
elec
tr
o
l
y
ze
r
,
w
h
er
e
it d
is
s
o
lv
ed
t
h
e
w
ater
i
n
to
H2
an
d
o
x
y
g
e
n
an
d
t
h
i
s
H2
is
k
ep
t i
n
a
s
to
r
ag
e
ta
n
k
.
Fu
r
t
h
er
,
th
is
H2
i
s
tak
en
a
s
th
e
i
n
p
u
t f
u
el
o
f
S
OF
C
.
b)
W
h
ile
P
V
p
o
w
er
(
P
p
v
)
is
eq
u
a
l to
d
e
m
a
n
d
p
o
w
er
(
P
d
e
m
an
d
)
i.e
.
,
P
p
v
=
P
d
em
a
n
d
,
th
e
n
p
at
h
2
s
h
o
u
ld
b
e
f
o
llo
w
ed
.
A
t
th
a
t
ti
m
e
t
h
e
to
tal
P
V
p
o
w
er
is
u
s
ed
to
f
u
l
f
ill
th
e
d
em
a
n
d
o
f
th
e
lo
ad
an
d
W
E
C
S
p
o
w
er
(
P
W
E
C
S)
is
u
s
ed
to
s
u
p
p
l
y
t
h
e
elec
tr
o
ly
ze
r
.
c)
W
h
ile
P
V
p
o
w
er
(
P
p
v
)
is
eq
u
al
to
ze
r
o
i.e
.
,
P
p
v
=
0
,
th
e
n
p
ath
3
s
h
o
u
ld
b
e
f
o
llo
w
ed
.
T
o
f
u
lf
i
ll
t
h
e
p
o
w
er
d
e
m
an
d
th
e
r
eq
u
ir
ed
a
m
o
u
n
t
o
f
p
o
w
er
i
s
s
u
p
p
lied
f
r
o
m
SOF
C
alo
n
g
w
it
h
t
h
e
W
E
C
S
p
o
w
er
(
P
W
E
C
S)
to
th
e
lo
ad
.
Her
e
,
SOFC
g
ets
t
h
e
H2
as
f
u
el
f
r
o
m
t
h
e
s
to
r
ag
e
ta
n
k
to
g
e
n
er
ate
th
e
SOF
C
p
o
w
er
(
P
SOFC
)
.
d)
W
h
ile
P
V
p
o
w
er
(
P
p
v
)
as
w
e
ll
as
W
E
C
S
p
o
w
er
(
P
W
E
C
S)
is
eq
u
al
to
ze
r
o
i.e
.
,
(
P
p
v
+
P
W
E
C
S)
=
0
,
th
en
p
at
h
4
s
h
o
u
ld
b
e
f
o
llo
w
ed
.
Her
e,
n
o
W
E
C
S
an
d
PV
p
o
w
er
ar
e
s
u
p
p
lied
to
f
u
l
f
ill
t
h
e
p
o
w
er
d
em
a
n
d
,
o
n
l
y
SOF
C
p
o
w
er
(
P
SOFC
)
i
s
s
u
p
p
lied
to
f
u
l
f
ill t
h
e
d
em
a
n
d
r
eq
u
ir
e
m
e
n
t.
10.
ST
UDY
O
F
T
H
E
P
O
WE
R
Q
UA
L
I
T
Y
F
AC
T
O
R
T
h
e
th
r
ee
ess
en
t
ial
f
ea
t
u
r
es o
n
w
h
ic
h
P
QF d
ep
en
d
s
ar
e
d
escr
ib
ed
b
elo
w
.
1
0
.
1
V
o
lt
a
g
e
a
nd
Curre
nt
H
a
r
m
o
nic
s
Dis
t
o
rt
io
n lev
els
T
o
tal
h
ar
m
o
n
ic
s
d
is
to
r
tio
n
lev
el
o
f
th
e
v
o
lta
g
e
(
VT
HD)
an
d
to
tal
h
ar
m
o
n
ics
d
is
to
r
tio
n
l
ev
el
o
f
th
e
cu
r
r
en
t (
I
T
HD)
ar
e
th
e
d
is
to
r
tio
n
s
lev
e
ls
o
f
t
h
e
h
ar
m
o
n
ic
s
r
esp
ec
tiv
el
y
,
f
o
r
th
e
3
Ø
as
w
el
l a
s
1
Ø
cir
cu
its
.
[
V
T
HD
]
2
=
∑
V
h
2
h
≠
1
V
1
2
(
1
7
)
[
I
T
HD
]
2
=
∑
I
h
2
h
≠
1
I
1
2
(
18)
W
h
er
e,
V
an
d
I
ar
e
r
m
s
v
alu
e
s
,
h
=
h
ar
m
o
n
ic
o
r
d
er
,
1
=
f
u
n
d
a
m
en
tal
L
o
s
s
e
s
ar
e
less
i
n
lo
w
er
o
r
d
er
h
ar
m
o
n
ic
s
b
u
t
m
o
r
e
i
n
h
i
g
h
er
o
r
d
er
h
ar
m
o
n
ic
s
h
a
v
i
n
g
th
e
s
a
m
e
a
m
p
lit
u
d
e.
Hen
ce
,
to
tal
r
eg
u
la
ted
h
ar
m
o
n
ic
s
d
is
to
r
tio
n
o
f
t
h
e
cu
r
r
en
t a
n
d
v
o
lta
g
e
ar
e
r
ep
r
esen
ted
b
elo
w
.
[
V
T
HD
]
H
−
A
2
=
∑
(
C
h
V
h
)
2
k
≠
1
V
1
2
(
19)
[
I
T
HD
]
H
−
A
2
=
∑
(
D
h
I
h
)
2
k
≠
1
I
1
2
(
20)
W
h
er
e,
C
h
,
D
h
=
(
>1
)
k
n
o
w
n
a
s
w
ei
g
h
t
in
g
f
ac
to
r
s
.
Fu
r
t
h
er
,
E
q
u
atio
n
s
(
1
7
)
an
d
(
1
8
)
m
a
y
b
e
co
n
s
id
er
ed
in
a
3
Ø
n
et
w
o
r
k
ac
co
r
d
in
g
to
[
2
7
]
as:
V
eH
2
=
∑
V
ah
2
+
V
bh
2
+
V
ch
2
3
h
≠
1
(
21)
I
eH
2
=
∑
I
ah
2
+
I
bh
2
+
I
ch
2
3
h
≠
1
(
22)
W
h
er
e,
VeH
is
th
e
eq
u
i
v
ale
n
t
h
ar
m
o
n
ic
s
o
f
th
e
r
m
s
v
o
lt
ag
e
in
t
h
e
3
Ø
n
et
w
o
r
k
an
d
I
eH
is
th
e
eq
u
iv
ale
n
t
h
ar
m
o
n
ics
o
f
t
h
e
r
m
s
v
o
ltag
e
i
n
t
h
e
3
Ø
n
et
w
o
r
k
B
y
p
u
tt
in
g
t
h
e
E
q
u
atio
n
s
(
2
1
)
an
d
(
2
2
)
in
th
e
E
q
u
atio
n
s
(
1
9
)
an
d
(
2
0
)
,
th
e
eq
u
i
v
ale
n
t
cu
r
r
en
t
a
n
d
v
o
ltag
e
ad
j
u
s
ted
h
ar
m
o
n
ic
s
v
a
lu
es a
r
e
o
b
tain
ed
as s
h
o
w
n
b
el
o
w
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
P
o
w
er Qu
a
lity A
n
a
lysi
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
S
o
l
a
r
/Wi
n
d
/Hyd
r
o
g
en
E
n
erg
y
Hyb
r
id
…
(
S
u
jit K
u
ma
r
B
h
u
ya
n
)
385
V
eH
−
A
2
=
∑
C
h
2
V
ah
2
+
V
bh
2
+
V
ch
2
3
h
≠
1
(
2
3
)
I
eH
−
A
2
=
∑
D
h
2
I
ah
2
+
I
bh
2
+
I
ch
2
3
h
≠
1
(
24)
So
,
QA
1
is
th
e
q
u
alit
y
asp
ec
t o
f
V
T
HD
an
d
QA
2
is
t
h
e
q
u
alit
y
asp
ec
t
o
f
I
T
HD.
QA
1
=
VT
HD
=
V
eH
−
A
V
e1
(
25)
QA
2
=
ITHD
=
I
eH
−
A
I
e1
(
26)
W
h
er
e,
Ve1
is
th
e
3
Ø
n
et
w
o
r
k
eq
u
iv
ale
n
t
f
u
n
d
a
m
e
n
tal
p
h
ase
v
o
ltag
e
a
n
d
I
e1
is
th
e
3
Ø
n
et
w
o
r
k
eq
u
iv
ale
n
t
f
u
n
d
a
m
en
tal
p
h
ase
cu
r
r
en
t.
V
e1
2
=
V
a1
2
+
V
b1
2
+
V
c1
2
3
(
2
7
)
I
e1
2
=
I
a1
2
+
I
b1
2
+
I
c1
2
3
(
28)
E
q
u
atio
n
s
(
2
1
)
to
(
2
4
)
,
(
2
7
)
an
d
(
2
8
)
r
ep
r
esen
t
3
Ø
n
et
w
o
r
k
l
o
s
s
es
w
h
er
e
it
is
eq
u
al
to
th
o
s
e
o
f
ac
tu
al
s
y
s
te
m
s
ta
k
en
i
n
to
co
n
s
id
er
ati
o
n
.
So
,
a
f
e
w
a
s
s
u
m
p
t
io
n
s
ar
e
r
ep
r
esen
ted
b
elo
w
:
a)
T
h
e
lo
s
s
es o
f
th
e
l
in
e
eq
u
ip
m
e
n
t a
r
e
r
elate
d
to
th
e
s
q
u
ar
e
o
f
cu
r
r
en
t o
r
v
o
ltag
e
b)
P
ar
am
eter
s
o
f
t
h
e
eq
u
ip
m
e
n
t a
n
d
lin
e
ar
e
co
n
s
id
er
ed
as s
y
m
m
etr
ical
1
0
.
2
De
g
re
e
o
f
Unba
la
nce
T
h
e
tr
an
s
f
er
q
u
al
it
y
o
f
t
h
e
p
o
w
er
is
in
f
l
u
e
n
ce
d
b
y
th
e
u
n
b
alan
ce
v
o
lta
g
e
a
n
d
cu
r
r
en
t
i
n
a
p
o
ly
-
p
h
a
s
e
cir
cu
it.
Ma
n
y
r
ea
s
o
n
s
ar
e
tak
en
i
n
to
co
n
s
id
er
atio
n
f
o
r
t
h
e
ab
o
v
e
p
r
o
b
le
m
s
u
c
h
as
o
v
e
r
lo
ad
in
g
i
n
n
e
u
tr
al
co
n
d
u
cto
r
in
f
o
u
r
w
ir
e
s
y
s
te
m
o
f
d
is
tr
ib
u
t
io
n
n
et
w
o
r
k
,
i
n
cr
ea
s
ed
lo
s
s
es o
cc
u
r
r
ed
in
t
h
e
li
n
e
at
th
e
s
a
m
e
p
o
w
er
tr
an
s
f
er
le
v
el.
T
h
e
3
Ø
s
i
n
u
s
o
id
al
v
o
ltag
e
co
n
s
is
t
s
o
f
t
h
r
e
e
co
m
p
o
n
e
n
ts
:
P
o
s
itiv
e
-
s
eq
u
e
n
ce
V+
,
Neg
a
tiv
e
-
s
eq
u
en
ce
V−
a
n
d
Z
er
o
s
eq
u
e
n
ce
V0
as sh
o
w
n
b
elo
w
.
{
V
+
=
1
√
3
(
V
a
+
a
V
b
+
a
2
V
c
)
V
−
=
1
√
3
(
V
a
+
a
2
V
b
+
a
V
c
)
V
0
=
1
√
3
(
V
a
+
V
b
+
V
c
)
(
2
9
)
W
h
er
e,
V
=
p
h
aso
r
o
f
V
an
d
a
=
e
xp
(
j2
π
3
⁄
)
So
,
b
y
u
s
i
n
g
t
h
e
E
q
u
atio
n
s
(
2
7
)
to
(
2
9
)
th
e
eq
u
iv
ale
n
t v
o
lta
g
e
is
d
ev
elo
p
ed
as:
V
e1
2
=
V
+
2
+
V
−
2
+
V
0
2
(
30)
I
n
th
i
s
m
a
n
n
er
th
e
c
u
r
r
en
t E
q
u
atio
n
ca
n
b
e
w
r
itte
n
as:
I
e1
2
=
I
+
2
+
I
−
2
+
I
0
2
(
31)
So
,
q
u
alit
y
a
n
al
y
s
is
ca
n
b
e
f
o
u
n
d
o
u
t a
s
g
iv
e
n
b
elo
w
.
QA
3
=
[
V
e1
2
−
(
V
+
)
2
]
1
2
V
e1
(
32)
QA
4
=
[
I
e1
2
−
(
I
+
)
2
]
1
2
I
e1
(
33)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
377
–
3
8
9
386
1
0
.
3
P
ha
s
e
dis
pla
ce
m
e
nt
bet
w
ee
n t
he
v
o
lt
a
g
e
a
nd
curr
en
t
a
t
t
heir
f
un
da
m
ent
a
l f
re
qu
ency
P
h
ase
d
is
p
lace
m
e
n
t
b
et
w
ee
n
v
o
ltag
e
a
n
d
cu
r
r
en
t
at
g
iv
e
n
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
c
y
s
h
o
w
s
less
o
r
f
u
ll
u
tili
za
t
io
n
o
f
eq
u
ip
m
e
n
t
at
d
is
tr
ib
u
tio
n
o
r
g
en
er
atio
n
s
id
e.
T
r
a
d
itio
n
all
y
p
o
w
er
f
ac
to
r
(
p
f
)
ca
n
b
e
d
ef
in
ed
a
s
th
e
r
atio
b
et
w
ee
n
t
h
e
ac
ti
v
e
p
o
w
er
(
P
)
an
d
ap
p
ar
en
t
p
o
w
er
(
S)
w
h
ic
h
is
p
o
s
s
ib
le
f
o
r
s
in
u
s
o
id
al
s
itu
atio
n
.
B
u
t,
f
o
r
th
e
n
o
n
-
s
i
n
u
s
o
id
al
s
i
tu
ati
o
n
p
f
d
ef
i
n
itio
n
d
escr
ib
ed
ab
o
v
e
is
m
is
lead
i
n
g
.
So
,
in
s
tan
t
an
eo
u
s
v
o
lta
g
e
an
d
cu
r
r
en
t
g
iv
e
t
h
e
r
esu
lts
o
f
t
h
e
in
s
ta
n
ta
n
eo
u
s
p
o
w
er
as
g
i
v
e
n
in
[
2
7
]
.
C
o
n
v
e
n
tio
n
a
l
ac
tiv
e
p
o
w
er
is
t
h
e
ti
m
e
av
er
ag
e
v
al
u
es
o
f
t
h
e
in
s
tan
t
an
eo
u
s
p
o
w
er
w
i
th
r
esp
ec
t
to
ti
m
e
.
A
ls
o
,
t
h
e
i
n
s
tan
ta
n
eo
u
s
p
o
w
er
(
S)
h
a
s
n
o
p
h
y
s
ical
m
ea
n
i
n
g
.
So
,
at
ea
ch
in
s
ta
n
t
v
o
ltag
e
a
n
d
cu
r
r
en
t
v
al
u
es a
r
e
n
o
t ta
k
en
i
n
to
co
n
s
id
er
atio
n
.
A
ll
t
h
e
ab
o
v
e
s
aid
i
n
ad
eq
u
ac
i
es
m
a
y
b
e
cir
cu
m
v
e
n
ted
,
w
h
e
n
th
e
u
tili
za
tio
n
o
f
t
h
e
p
o
w
er
i
s
p
o
o
r
d
u
e
to
th
e
p
h
y
s
ical
en
tit
y
.
T
h
is
en
tit
y
is
k
n
o
w
n
a
s
p
h
ase
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
v
o
lt
ag
e
an
d
cu
r
r
en
t
at
f
u
n
d
a
m
en
ta
l
f
r
eq
u
e
n
c
y
eit
h
er
o
n
lo
ad
s
id
e
o
r
s
o
u
r
ce
s
id
e.
Hen
ce
,
to
r
ev
ea
l
th
is
a
s
p
ec
t
o
n
th
e
p
o
w
er
q
u
alit
y
a
n
e
w
f
ac
to
r
is
co
n
s
id
er
ed
n
a
m
e
d
as o
r
th
o
g
o
n
al
cu
r
r
en
t f
ac
to
r
(
OC
F)
as g
iv
e
n
i
n
[
2
7
]
.
OCF
=
I
1a
s
i
n
∅1
a
+
I
1b
s
i
n
∅1
b
+
I
1c
s
i
n
∅1
c
I
1a
+
I
1b
+
I
1c
(
3
4
)
QA
5
=
|
OCF
|
(
35)
QA
5
=
|
OCF
|
(
36)
P
QF
d
eter
m
i
n
es
t
h
e
p
o
w
er
q
u
alit
y
.
I
n
th
e
ab
o
v
e
E
q
u
atio
n
w
i
is
k
n
o
w
n
as
w
ei
g
h
ti
n
g
f
ac
t
o
r
(
≅
1
)
w
h
er
ea
s
,
QA
i
is
th
e
d
if
f
er
en
t q
u
ali
t
y
asp
ec
ts
.
11.
E
XP
E
R
I
M
E
NT
A
L
VE
R
I
F
I
CATI
O
N
R
E
S
UL
T
S W
I
T
H
T
H
E
H
E
L
P
O
F
SI
M
UL
AT
I
O
N
T
h
e
p
r
o
p
o
s
ed
HGS
is
d
esig
n
e
d
b
y
u
s
i
n
g
Ma
t
lab
Si
m
u
li
n
k
an
d
v
er
if
ied
u
n
d
er
d
if
f
er
en
t c
o
n
d
itio
n
s
.
Fig
u
r
e
4
a
r
ep
r
esen
ts
th
e
H2
f
l
o
w
f
r
o
m
elec
tr
o
l
y
ze
r
,
w
h
e
n
it
tak
es
t
h
e
e
x
tr
a
a
m
o
u
n
t
o
f
W
E
C
S
p
o
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er
w
h
ic
h
is
d
escr
ib
ed
in
p
ath
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an
d
p
ath
2
o
f
Fi
g
u
r
e
3
.
SOF
C
tak
e
s
th
e
a
m
o
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n
t
o
f
H2
f
lo
w
ac
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r
d
in
g
to
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e
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o
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er
d
e
m
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d
a
n
d
co
n
tr
o
lle
d
b
y
t
h
e
P
I
D
co
n
tr
o
ller
as
s
h
o
w
n
in
Fi
g
u
r
e
4
b
an
d
Fi
g
u
r
e
4
c.
Fig
u
r
e
4
d
r
ep
r
esen
ts
th
e
v
o
lta
g
e
o
u
tp
u
t o
f
b
o
o
s
t c
o
n
v
er
ter
o
f
t
h
e
SOF
C
,
w
h
ich
i
s
co
n
n
ec
ted
ac
r
o
s
s
th
e
SOFC
.
T
h
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
w
av
e
f
o
r
m
s
o
f
HGS
ar
e
s
h
o
w
n
i
n
Fig
u
r
e
5
a.
Fig
u
r
e
5
b
s
h
o
w
s
t
h
e
v
o
lta
g
e,
cu
r
r
en
t
an
d
p
o
w
er
w
av
e
f
o
r
m
s
o
f
th
e
3
Ø
lo
ad
as
s
h
o
w
n
i
n
Fig
u
r
e
1
h
av
i
n
g
t
h
e
ac
tiv
e
p
o
w
er
(
P
)
=
1
4
KW
,
in
d
u
cti
v
e
p
o
w
er
(
Q
L
)
=
2
KVAR a
n
d
ca
p
ac
iti
v
e
p
o
w
er
(
QC
)
=
1
0
0
VA
R
.
T
im
e
(
t)
Fig
u
r
e
4
a.
H2
g
en
er
atio
n
f
r
o
m
th
e
E
lectr
o
l
y
ze
r
T
im
e
(
t)
Fig
u
r
e
4
c.
Ou
tp
u
t o
f
th
e
P
I
D
C
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.