I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
d
van
c
e
s
i
n
A
p
p
li
e
d
S
c
ie
n
c
e
s
(
I
JA
A
S
)
V
ol
.
15
, N
o.
1
,
M
a
r
c
h
20
26
, pp.
107
~
122
I
S
S
N
:
2252
-
8814
,
D
O
I
:
10.11591/
ij
a
a
s
.
v15.
i
1
.
pp
107
-
122
107
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
aas
.i
ae
s
c
or
e
.c
om
M
od
e
l
i
n
g of
sol
ar
an
d
w
i
n
d
e
n
e
r
gy u
si
n
g
M
A
T
L
A
B
/
S
i
m
u
l
i
n
k
:
a r
e
vi
e
w
N
ic
h
ol
as
P
r
an
at
a, F
ah
m
y R
in
an
d
a S
a
p
u
t
r
i
D
e
pa
r
t
m
e
nt
of
E
ngi
ne
e
r
i
ng P
hys
i
c
s
, F
a
c
ul
t
y of
E
ngi
ne
e
r
i
ng a
nd I
n
f
or
m
a
t
i
c
s
, U
ni
ve
r
s
i
t
a
s
M
ul
t
i
m
e
di
a
N
u
s
a
nt
a
r
a
, T
a
nge
r
a
ng, I
ndon
e
s
i
a
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
A
pr
30, 2025
R
e
vi
s
e
d
N
ov 20, 2025
A
c
c
e
pt
e
d
J
a
n 1, 2026
This
paper
presents
a
concise
review
of
solar
(photovoltaic
(PV)
)
an
d
wind
(horizontal
axis)
energy
systems,
focusing
on
their
modeling
and
sim
ulation
using
MATLAB)/Simulink.
The
advantages,
disadvantages,
strength
s,
and
weaknesses
of
each
system
are
discussed,
providing
a
compreh
ensive
overview
of
their
characteristics.
The
review
explores
the
mathematical
modeling
approac
hes
for
PV
cells
and
modules
spe
cific
for
singl
e
diode
model,
as
well
as
horizontal
-
axis
wind
turbine
systems,
highlighting
t
he
key
equa
tions
and
parameters
involved.
Furthermore,
the
paper
discuss
es
the
emerging
trend
of
hybrid
solar
-
wind
energy
systems
and
their
potent
ial
for
optimizing
power
output,
efficiency,
and
reliability.
The
review
emp
hasizes
the
importance
of
accurate
modeling
based
on
fundamental
kno
wledge
,
which
serves
as
a
practical
implication
for
readers
to
understa
nd
the
mechanism.
Future
resear
ch
directions
and
challenge
s
in
the
fi
eld
of
renewable
energy
modeling
and
simulati
on
are
also
outlined.
This
review
serves as a
va
luable re
source f
or rese
archer
s,
engineer
s, and dec
ision
-
makers
involved
in
the
developmen
t
and
implem
entation
of
solar
and
wind
energy
systems.
K
e
y
w
o
r
d
s
:
H
ybr
id
M
A
T
L
A
B
/S
im
ul
in
k
R
e
ne
w
a
bl
e
e
ne
r
gy
S
ol
a
r
W
in
d
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
F
a
hm
y R
in
a
nda
S
a
put
r
i
D
e
pa
r
tm
e
nt
of
E
ngi
ne
e
r
in
g P
hys
ic
s
, F
a
c
ul
ty
of
E
ngi
ne
e
r
in
g a
nd I
nf
or
m
a
ti
c
s
U
ni
ve
r
s
it
a
s
M
ul
ti
m
e
di
a
N
u
s
a
nt
a
r
a
S
c
ie
nt
ia
B
oul
e
va
r
d S
tr
e
e
t,
K
e
la
pa
D
ua
D
i
s
tr
ic
t,
T
a
nge
r
a
ng
R
e
g
e
nc
y, B
a
nt
e
n 15810
, I
ndone
s
ia
E
m
a
il
:
f
a
hm
y.r
in
a
nda
@
um
n.a
c
.i
d
1.
I
N
T
R
O
D
U
C
T
I
O
N
E
ne
r
gy
is
a
n
im
por
ta
nt
a
s
pe
c
t
f
or
li
vi
ng
be
in
gs
a
s
it
is
th
e
b
a
s
is
f
or
doi
ng
a
ll
ki
nds
of
a
c
ti
vi
ti
e
s
.
H
um
a
ns
,
e
s
pe
c
i
a
ll
y,
ha
ve
us
e
d
e
ne
r
gy
s
in
c
e
th
e
pr
e
hi
s
to
r
ic
e
r
a
f
or
he
a
ti
ng
a
nd
li
ght
in
g
us
in
g
f
i
r
e
s
our
c
e
s
.
A
f
te
r
th
e
te
c
hnol
ogi
c
a
l
r
e
vol
ut
io
n,
m
a
r
ke
d
by
th
e
us
e
of
th
e
s
t
e
a
m
e
ngi
ne
,
e
ne
r
gy
w
a
s
us
e
d
m
or
e
f
r
e
que
nt
ly
[
1]
.
N
ow
,
w
it
h
th
e
r
a
pi
d
de
m
a
nd
f
or
e
ne
r
gy
r
e
s
our
c
e
s
,
th
e
us
e
of
f
os
s
il
f
ue
ls
a
s
one
of
th
e
m
os
t
dom
in
a
nt
s
our
c
e
s
due
to
th
e
ir
out
put
c
ha
r
a
c
te
r
is
ti
c
s
h
a
s
b
e
c
o
m
e
de
pl
e
te
d
s
ig
ni
f
ic
a
nt
ly
[
2]
,
[
3]
.
H
e
nc
e
,
a
n
a
lt
e
r
na
ti
ve
is
pr
opos
e
d,
w
hi
c
h
is
u
s
in
g
r
e
ne
w
a
bl
e
e
ne
r
gy.
R
e
n
e
w
a
bl
e
e
ne
r
gy
i
s
a
n
e
f
f
ic
ie
nt
s
our
c
e
th
a
t
c
a
n
m
e
e
t
th
e
r
e
qui
r
e
m
e
nt
s
of
th
e
e
nvi
r
onm
e
nt
,
a
nd
e
n
e
r
gy
is
a
l
s
o
c
ons
id
e
r
e
d
c
l
e
a
n
by
r
e
du
c
in
g
C
O
2
e
m
is
s
io
n
s
onl
y
if
it
s
ur
pa
s
s
e
s
a
c
e
r
ta
in
th
r
e
s
hol
d
of
r
e
ne
w
a
bl
e
e
n
e
r
gy
c
on
s
um
pt
io
n
[
4]
–
[
6]
.
E
xa
m
pl
e
s
of
th
is
e
ne
r
gy
a
r
e
s
ol
a
r
e
ne
r
gy,
w
in
d
e
ne
r
gy,
hydr
opowe
r
e
ne
r
gy,
ge
ot
he
r
m
a
l
e
ne
r
gy,
bi
om
a
s
s
,
oc
e
a
n
th
e
r
m
a
l
e
ne
r
gy,
a
nd
ti
da
l
e
ne
r
gy.
T
he
s
ig
ni
f
ic
a
nc
e
of
r
e
ne
w
a
bl
e
e
ne
r
gy
is
th
a
t
it
pr
oduc
e
s
e
l
e
c
tr
ic
it
y
th
a
t
w
il
l
s
uppl
y
th
e
e
ne
r
gy
de
m
a
nd
ne
e
d
e
d.
T
he
ot
he
r
a
dva
nt
a
ge
s
of
r
e
n
e
w
a
bl
e
e
ne
r
gy
in
ge
ne
r
a
l
a
r
e
it
s
a
v
a
il
a
bi
li
ty
,
la
nd
u
s
a
ge
,
s
a
f
e
ty
(
m
in
im
iz
in
g
th
e
r
is
k
of
m
a
n
-
m
a
de
di
s
a
s
te
r
)
,
de
ve
lo
pm
e
nt
of
te
c
hnol
ogy,
e
m
pl
oy
m
e
nt
,
e
nvi
r
onm
e
nt
a
l
f
r
ie
ndl
in
e
s
s
,
a
nd
r
e
duc
in
g
f
os
s
il
f
ue
l
de
pe
nd
e
nc
y
[
4]
,
[
7]
,
[
8]
.
I
t
w
il
l
a
ls
o
he
lp
s
uppl
y
e
n
e
r
gy
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8814
I
nt
J
A
dv A
ppl
S
c
i
,
V
ol
. 15, No. 1, M
a
r
c
h 2026
:
107
-
122
108
unde
r
de
ve
lo
pe
d
a
r
e
a
s
[
4]
.
H
ow
e
ve
r
,
th
e
di
s
a
dv
a
nt
a
ge
of
th
e
s
e
s
our
c
e
s
li
e
s
in
po
w
e
r
pr
oduc
ti
on
due
to
w
e
a
th
e
r
c
ondi
ti
ons
(
unpr
e
di
c
ta
bi
li
ty
a
nd
vol
a
ti
li
ty
)
,
lo
w
e
f
f
ic
ie
nc
y,
a
nd/
or
th
e
pr
e
s
e
nc
e
of
r
e
s
e
r
ve
s
th
a
t
w
il
l
pr
ovi
de
e
ne
r
gy w
he
n e
ne
r
gy de
f
ic
ie
nc
y oc
c
ur
s
[
4
]
,
[
8
]
. T
he
l
im
it
a
ti
on c
a
n be
c
ount
e
r
e
d by c
a
r
e
f
ul
ly
pl
a
nni
ng
a
nd
s
e
le
c
ti
ng
s
p
e
c
if
ic
r
e
ne
w
a
bl
e
e
ne
r
gy
c
hoi
c
e
s
.
H
e
n
c
e
,
th
e
ph
a
s
e
of
r
e
s
e
a
r
c
h
a
nd
d
e
s
ig
n
be
c
om
e
s
one
of
th
e
im
por
ta
nt
pa
r
ts
due
t
o t
he
ne
e
d f
or
c
om
pl
e
m
e
nt
a
r
y s
tu
di
e
s
, de
s
ig
ni
ng, a
nd t
e
s
ti
ng.
A
s
tr
a
te
gi
c
w
a
y
to
s
u
ppo
r
t
t
he
de
ve
l
op
m
e
n
t
o
f
r
e
ne
w
a
bl
e
e
n
e
r
g
y
i
n
th
e
r
e
s
e
a
r
c
h
p
ha
s
e
is
to
us
e
e
ne
r
gy
m
o
de
ls
,
a
s
t
he
y
h
e
l
p
in
p
r
ov
id
in
g
s
ui
ta
bl
e
de
s
i
gns
f
o
r
de
c
is
io
n
-
m
a
k
in
g
[
9]
.
T
he
m
e
t
hod
us
e
d
,
na
m
e
ly
s
im
ul
a
ti
ons
,
ha
s
be
c
o
m
e
a
pow
e
r
f
u
l
to
o
l
t
o
c
r
e
a
te
v
i
r
tu
a
l
e
xpe
r
ie
nc
e
s
a
s
t
he
a
ns
w
e
r
t
o
r
e
a
l
-
phys
ic
a
l
pe
r
f
o
r
m
a
nc
e
[
1
0]
.
I
t
a
c
ts
a
s
a
r
e
p
li
c
a
ti
on
,
l
in
k
in
g
th
e
or
ie
s
a
nd
e
x
pe
r
i
m
e
n
ta
l
in
ve
s
t
ig
a
ti
on
ba
s
e
d
o
n
s
ys
te
m
s
,
p
r
oc
e
s
s
e
s
,
a
n
d
l
a
w
s
f
o
r
r
a
nd
om
kno
w
n
pa
r
a
m
e
te
r
s
[
10
]
.
I
n
th
e
c
a
s
e
o
f
r
e
ne
w
a
bl
e
e
ne
r
gy
,
s
im
ul
a
ti
on
e
na
bl
e
s
pe
op
le
t
o
a
na
ly
z
e
t
he
e
s
t
im
a
te
d
r
e
s
u
lt
s
be
f
or
e
d
i
r
e
c
t
ly
in
s
t
a
l
li
ng
s
ys
t
e
m
s
t
o
r
e
d
uc
e
l
os
s
e
s
s
uc
h
a
s
c
os
t
,
t
im
e
,
a
n
d
qua
l
it
y
,
a
s
w
e
ll
a
s
c
o
ns
e
que
nc
e
s
s
u
c
h
a
s
e
n
vi
r
o
nm
e
nt
a
l
da
m
a
ge
.
M
a
ny
ty
pe
s
of
r
e
ne
w
a
b
le
e
ne
r
gy
i
m
p
le
m
e
n
ta
t
io
n
s
us
e
s
i
m
u
la
t
io
n
be
f
o
r
e
i
m
p
le
m
e
nt
a
t
io
n
.
I
n
t
he
f
u
tu
r
e
,
th
e
e
r
a
w
h
e
r
e
r
e
ne
w
a
bl
e
e
n
e
r
gy
m
us
t
b
e
c
o
m
e
th
e
m
a
in
s
ou
r
c
e
,
s
ol
a
r
a
nd
w
in
d
e
ne
r
g
y
ha
v
e
be
c
o
m
e
t
he
t
op
c
hoi
c
e
s
f
o
r
u
ti
li
z
a
t
io
n.
T
h
is
is
d
ue
to
th
e
po
pu
la
r
it
y
o
f
bo
th
s
ou
r
c
e
s
th
a
t
ha
ve
be
e
n
im
pl
e
m
e
nt
e
d
a
n
d
th
e
ir
huge
p
ot
e
nt
ia
l
c
o
m
pa
r
e
d
to
ot
he
r
r
e
ne
w
a
b
le
e
ne
r
gy
s
o
ur
c
e
s
(
s
o
la
r
by
8
,
300
T
W
y
r
a
nd
W
i
nd
e
ne
r
g
y
by
1
,
5
00
T
W
y
r
)
[
11
]
.
W
i
th
t
he
c
a
pa
c
it
y
ge
ne
r
a
t
io
n
f
o
r
bo
t
h
t
ype
s
i
nc
r
e
a
s
i
ng,
u
nc
e
r
ta
in
ti
e
s
w
it
h
t
he
a
va
i
la
b
il
it
y
o
f
t
he
s
up
pl
y
m
us
t
be
c
a
r
e
f
ul
ly
c
ons
i
de
r
e
d
to
a
voi
d
s
ys
t
e
m
r
e
l
ia
b
i
li
ty
q
ua
l
it
y
l
os
s
or
e
ve
n
pow
e
r
ou
ta
ge
s
[
1
2
]
.
T
hus
,
de
t
a
i
le
d
p
la
n
ni
ng
m
us
t
be
don
e
t
o
a
s
s
e
s
s
h
ow
f
a
r
th
e
s
ys
te
m
s
c
a
n
r
e
a
c
h
t
he
de
s
i
r
e
d
o
ut
p
ut
c
o
m
pa
r
a
bl
e
t
o
th
e
po
te
n
ti
a
l.
S
in
c
e
s
im
ul
a
ti
on
a
c
t
s
a
s
th
e
ke
y
s
te
p
in
th
e
pl
a
nni
ng
s
t
a
ge
s
,
it
is
im
por
ta
nt
to
s
e
e
how
th
e
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy
im
pl
e
m
e
nt
a
ti
on
w
il
l
r
e
s
ul
t.
S
ol
a
r
e
ne
r
gy
s
ys
te
m
s
m
a
in
ly
c
on
s
is
t
of
s
e
ve
r
a
l
p
a
r
ts
,
in
c
lu
di
ng
m
ode
ls
of
phot
ovol
ta
ic
(
PV
)
c
e
ll
s
a
nd
m
odul
e
s
,
s
to
r
a
ge
s
ys
t
e
m
s
,
tr
a
c
ke
r
s
,
di
r
e
c
t
c
ur
r
e
nt
to
di
r
e
c
t
c
ur
r
e
nt
(
D
C
/DC
)
c
onve
r
te
r
s
,
a
nd
in
ve
r
te
r
s
.
S
e
ve
r
a
l
e
le
m
e
nt
s
th
a
t
a
f
f
e
c
t
th
e
f
in
a
l
out
put
of
th
e
s
ys
te
m
in
c
lu
de
r
a
te
d
pow
e
r
,
c
e
ll
in
te
r
na
l
r
e
s
is
ta
nc
e
,
ope
r
a
ti
ng
vol
ta
g
e
a
nd
c
ur
r
e
nt
,
s
hor
t
c
ir
c
ui
t
c
ur
r
e
nt
,
a
nd
ope
n
c
ir
c
ui
t
vol
ta
ge
[
10]
.
F
or
w
in
d
e
ne
r
gy,
th
e
w
hol
e
s
ys
te
m
m
a
y
c
ons
is
t
of
a
tu
r
bi
ne
s
ys
te
m
,
ge
ne
r
a
to
r
,
a
nd
e
le
c
tr
oni
c
pow
e
r
s
ys
te
m
.
N
ot
to
m
e
nt
io
n
th
a
t,
e
a
c
h
s
ys
te
m
ha
s
r
e
c
ip
r
oc
a
ti
ng
c
om
pl
e
x
s
ubs
ys
te
m
s
s
uc
h
a
s
bl
a
de
s
,
na
c
e
ll
e
,
a
nd
r
ot
or
.
W
it
h
uns
uppor
ti
ve
w
e
a
th
e
r
c
ondi
ti
ons
,
th
e
c
om
pl
e
xi
ty
of
bot
h
e
ne
r
gi
e
s
undoubte
dl
y
pos
e
s
th
e
pot
e
nt
ia
l
f
or
in
e
f
f
ic
ie
nc
ie
s
a
nd
lo
s
s
e
s
.
T
he
r
e
f
or
e
,
th
e
us
e
of
s
im
ul
a
ti
on
m
a
y
s
ig
ni
f
ic
a
nt
ly
he
lp
in
s
ugge
s
ti
ng t
he
out
c
om
e
und
e
r
s
im
ul
a
te
d c
ondi
ti
ons
ba
s
e
d on ph
ys
ic
a
l
w
or
ld
be
ha
vi
or
.
S
e
ve
r
a
l
s
im
ul
a
ti
on
s
of
twa
r
e
us
e
d
f
or
e
ne
r
gy
m
ode
li
ng
in
c
lu
d
e
s
r
e
ts
c
r
e
e
n
e
xpe
r
t
(
R
E
T
S
C
R
E
E
N
)
,
PV
s
ys
t
,
hybr
id
opt
im
iz
a
ti
on
of
m
ul
ti
pl
e
e
ne
r
gy
r
e
s
our
c
e
s
(
H
O
M
E
R
)
,
pow
e
r
s
y
s
te
m
s
c
om
put
e
r
a
id
e
d
de
s
ig
n
(
P
S
C
A
D
)
,
dyna
m
ic
m
ode
li
ng
la
bor
a
to
r
y
(
D
Y
M
O
L
A
)
,
pow
e
r
s
ys
te
m
s
im
ul
a
to
r
f
or
e
ngi
ne
e
r
in
g
(
P
S
S
/
E
)
,
th
e
r
m
a
l
li
br
a
r
y
(
T
he
r
m
o
L
ib
)
,
ope
n
a
na
ly
s
is
pl
a
tf
or
m
f
or
r
e
a
l
-
ti
m
e
la
bor
a
to
r
y
ve
r
i
f
ic
a
ti
on
(
O
P
A
L
-
RV
)
,
a
nd
M
A
T
L
A
B
.
M
A
T
L
A
B
is
pr
ogr
a
m
m
in
g,
a
na
ly
s
is
,
a
nd
c
om
put
a
ti
on
s
of
twa
r
e
f
or
m
a
th
e
m
a
ti
c
s
a
nd
e
ngi
ne
e
r
in
g
pur
pos
e
s
w
it
h
m
a
tr
i
ces
a
s
th
e
ba
s
i
s
[
13]
.
T
hi
s
s
of
twa
r
e
is
us
e
d
to
s
uppor
t
s
c
ie
nt
if
ic
pr
ogr
a
m
m
in
g
us
in
g
to
ol
boxe
s
s
uc
h a
s
S
im
ul
in
k.
S
e
ve
r
a
l
a
dva
nt
a
ge
s
of
th
is
s
of
twa
r
e
c
om
pa
r
e
d
to
ot
he
r
s
a
r
e
it
s
f
le
xi
bi
li
ty
a
nd
c
us
to
m
iz
a
ti
on
(
bl
oc
k
-
ba
s
e
d
e
nvi
r
onm
e
nt
)
,
a
dva
nc
e
d
c
ont
r
ol
s
ys
te
m
de
s
ig
n
,
ha
r
dw
a
r
e
-
in
-
th
e
-
lo
op
(
H
I
L
)
s
im
ul
a
ti
on
f
or
ha
r
dw
a
r
e
in
te
gr
a
ti
on,
a
nd
a
va
il
a
bi
li
ty
f
or
c
o
-
s
im
ul
a
ti
on.
S
im
ul
in
k
c
a
n
s
im
ul
a
te
th
e
e
ne
r
gy
s
ys
te
m
th
a
t
ha
s
be
e
n
de
s
ig
n
e
d
a
nd
e
s
ti
m
a
te
th
e
out
put
a
s
pa
r
t
of
th
e
c
on
s
id
e
r
a
ti
on
a
nd
pl
a
nni
ng
be
f
or
e
de
c
i
s
io
n
-
m
a
ki
ng
f
or
r
e
a
l
s
ys
te
m
in
s
ta
ll
a
ti
on.
F
or
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy,
s
e
ve
r
a
l
s
t
udi
e
s
ha
ve
c
onduc
te
d
e
xpe
r
im
e
nt
s
us
in
g
th
i
s
s
of
twa
r
e
.
H
ow
e
ve
r
,
m
os
t
a
r
ti
c
le
s
di
r
e
c
tl
y
s
how
m
a
th
e
m
a
ti
c
a
l
a
ppr
oa
c
he
s
a
nd
ju
m
p
in
to
r
e
s
ul
ts
a
nd
di
s
c
us
s
io
n
s
by only des
c
r
ib
in
g t
he
m
e
th
ods
na
r
r
a
ti
ve
ly
, w
it
hout
a
ny guide
f
or
r
e
a
de
r
s
t
o t
r
y.
T
hus
,
ba
s
e
d
on
th
is
,
th
e
us
e
of
s
im
ul
a
ti
ons
c
a
n
be
a
s
ol
ut
io
n
f
or
e
ne
r
gy
m
ode
ll
in
g,
s
pe
c
if
ic
a
ll
y
f
or
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy,
due
to
it
s
popula
r
it
y
in
th
e
m
id
dl
e
of
th
e
in
c
r
e
a
s
in
g
r
e
ne
w
a
bl
e
e
n
e
r
gy
c
a
pa
c
it
y
in
s
ta
ll
a
ti
on
a
s
th
e
a
ns
w
e
r
f
or
a
c
le
a
ne
r
tr
a
ns
it
io
n.
I
n
th
is
a
r
ti
c
le
,
a
br
ie
f
r
e
vi
e
w
of
r
e
la
te
d
a
r
ti
c
le
s
on
r
e
ne
w
a
bl
e
e
ne
r
gy
s
im
ul
a
ti
on
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k
is
pr
e
s
e
nt
e
d,
s
p
e
c
if
ic
a
ll
y
on
s
ol
a
r
(
PV
)
a
nd
w
in
d
(
hor
iz
ont
a
l
a
xi
s
)
e
ne
r
gy.
A
ddi
ti
ona
l
e
xpl
a
na
ti
ons
of
a
dva
nt
a
g
e
s
,
di
s
a
dv
a
nt
a
ge
s
,
s
tr
e
ngt
hs
,
w
e
a
kne
s
s
e
s
,
a
nd
hybr
id
m
ode
ls
w
il
l
a
ls
o
be
in
c
lu
d
e
d
to
s
e
r
ve
a
s
a
n
in
tr
oduc
ti
on
f
or
th
is
a
r
ti
c
le
in
th
e
c
ont
e
xt
of
s
ol
a
r
a
nd
w
in
d e
ne
r
gy.
T
he
s
c
ope
of
th
e
r
e
vi
e
w
w
il
l
be
li
m
it
e
d
to
s
ol
a
r
e
ne
r
gy
ba
s
e
d
on
a
s
in
gl
e
di
ode
a
nd
w
in
d
e
ne
r
g
y
ba
s
e
d
on
th
e
tu
r
bi
ne
s
ys
te
m
.
O
th
e
r
s
pe
c
if
ic
s
a
nd
a
ddi
ti
ona
l
s
y
s
te
m
s
w
il
l
not
be
e
la
bor
a
te
d.
T
he
pur
pos
e
of
th
e
r
e
vi
e
w
is
to
gi
ve
a
n
in
tr
oduc
ti
on
a
nd
ba
s
ic
gui
de
li
ne
s
f
o
r
r
e
s
e
a
r
c
he
r
s
w
ho
ne
e
d
a
qui
c
k
s
um
m
a
r
y
of
m
ode
li
ng
a
nd
s
im
ul
a
ti
on
f
o
r
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy
ba
s
e
d
on
M
A
T
L
A
B
/S
im
ul
in
k.
T
he
in
nova
ti
on
of
th
is
pa
pe
r
is
to
pr
e
s
e
nt
th
e
s
im
ul
a
ti
on
a
r
c
hi
te
c
tu
r
e
.
R
e
le
va
nt
r
e
vi
e
w
s
ha
d
s
how
n
c
a
s
e
by
c
a
s
e
f
or
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy
w
it
h
th
e
m
e
nt
io
ne
d
s
c
ope
,
pr
ovi
ng
th
e
us
e
of
M
A
T
L
A
B
/S
im
ul
in
k
a
s
a
s
our
c
e
f
o
r
e
ne
r
gy
m
ode
l
s
im
ul
a
ti
ons
w
hi
le
a
ls
o pr
oduc
in
g r
e
s
ul
t
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
dv A
ppl
S
c
i
I
S
S
N
:
2252
-
8814
M
ode
li
ng of s
ol
ar
and w
in
d e
ne
r
g
y
us
in
g m
at
r
i
x
l
abor
at
or
y
/
S
i
m
ul
in
k
:
a r
e
v
ie
w
(
N
ic
hol
a
s
P
r
anat
a)
109
2.
M
E
T
H
O
D
I
n
c
onduc
ti
ng
th
e
li
te
r
a
tu
r
e
r
e
vi
e
w
on
r
e
ne
w
a
bl
e
e
ne
r
gy
s
im
ul
a
ti
on
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k,
th
e
m
e
th
odol
ogi
c
a
l
s
te
ps
f
ol
lo
w
e
d
a
r
e
a
s
f
ol
lo
w
s
.
F
ir
s
t,
r
e
s
e
a
r
c
h
w
a
s
c
ondu
c
te
d
th
r
ough
va
r
io
us
a
c
a
de
m
ic
da
ta
ba
s
e
s
s
uc
h
a
s
I
E
E
E
X
pl
or
e
,
S
c
ie
nc
e
D
ir
e
c
t,
a
nd
G
oogl
e
S
c
hol
a
r
.
K
e
yw
or
ds
us
e
d
in
c
lu
de
d
"
r
e
ne
w
a
bl
e
e
ne
r
gy
s
im
ul
a
ti
on,"
"
M
A
T
L
A
B
/S
im
ul
in
k,"
"
s
ol
a
r
e
ne
r
gy
s
im
ul
a
ti
on,"
a
nd
"
w
in
d
e
ne
r
gy
s
im
ul
a
ti
on."
A
ddi
ti
ona
ll
y,
th
e
r
e
s
e
a
r
c
h
a
ls
o
in
vol
ve
d
r
e
la
te
d
a
r
ti
c
le
s
,
book
s
,
a
nd
c
onf
e
r
e
nc
e
s
r
e
le
va
nt
to
th
e
to
pi
c
.
N
e
xt
,
a
r
ti
c
le
s
f
ound
in
th
e
s
e
a
r
c
he
s
w
e
r
e
e
va
lu
a
t
e
d
to
e
ns
ur
e
th
e
ir
r
e
le
va
nc
e
to
r
e
ne
w
a
bl
e
e
ne
r
gy
s
im
ul
a
ti
on
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k,
w
it
h
a
s
p
e
c
if
ic
f
oc
us
on
s
ol
a
r
a
nd
w
i
nd
e
ne
r
gy.
A
r
ti
c
le
s
th
a
t
di
d
not
m
e
e
t
th
e
s
e
in
c
lu
s
io
n
c
r
it
e
r
ia
w
e
r
e
e
x
c
lu
de
d
f
r
om
th
e
r
e
vi
e
w
.
A
f
te
r
id
e
n
ti
f
yi
ng
r
e
le
va
nt
a
r
ti
c
le
s
,
th
e
a
n
a
ly
s
is
pr
oc
e
s
s
be
ga
n
by
e
xt
r
a
c
ti
ng
in
f
or
m
a
ti
on
on
th
e
a
dva
nt
a
ge
s
,
di
s
a
dva
nt
a
ge
s
,
s
tr
e
ngt
hs
,
w
e
a
kne
s
s
e
s
,
a
nd
hybr
id
m
ode
ls
in
th
e
c
ont
e
xt
of
s
ol
a
r
a
nd
w
in
d
e
ne
r
gy
f
r
o
m
e
a
c
h
a
r
ti
c
le
.
R
e
l
e
va
nt
in
f
or
m
a
ti
on
f
r
om
e
a
c
h
a
r
ti
c
le
w
a
s
th
e
n
s
ynt
he
s
iz
e
d
to
pr
ovi
de
a
c
om
pr
e
he
n
s
iv
e
ove
r
vi
e
w
of
s
ub
s
ys
te
m
m
ode
li
ng
a
nd
s
im
ul
a
ti
on
s
e
tu
p
de
ta
il
s
f
or
r
e
a
de
r
s
w
ho w
is
h t
o s
tu
dy
a
nd e
xpe
r
im
e
nt
w
it
h M
A
T
L
A
B
/S
im
ul
in
k on s
ol
a
r
a
nd w
in
d s
ys
te
m
s
.
3.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
3.1. Ad
van
t
age
s
an
d
d
is
ad
van
t
age
s
of
s
ol
ar
an
d
w
in
d
e
n
e
r
gy i
n
ge
n
e
r
al
B
e
f
or
e
c
hoos
in
g
th
e
r
ig
ht
r
e
ne
w
a
bl
e
e
ne
r
gy
s
our
c
e
s
,
s
e
ve
r
a
l
c
ons
id
e
r
a
ti
ons
m
us
t
be
ta
ke
n
a
nd
a
na
ly
z
e
d
be
f
or
e
de
c
i
s
io
n
-
m
a
ki
ng.
K
now
in
g
a
nd
a
s
s
e
s
s
in
g
th
e
a
dva
nt
a
ge
s
a
nd
di
s
a
dv
a
nt
a
ge
s
of
r
e
ne
w
a
bl
e
e
ne
r
gy
c
a
n
be
h
e
lp
f
ul
in
m
a
ki
ng
th
e
r
ig
ht
c
hoi
c
e
c
a
r
e
f
ul
ly
.
I
n
th
is
a
r
ti
c
le
,
th
e
a
dva
nt
a
g
e
s
a
nd
di
s
a
dva
nt
a
g
e
s
of
s
ol
a
r
a
nd
w
in
d
c
a
n
b
e
e
xpl
a
in
e
d
br
ie
f
ly
,
a
s
s
how
n
in
T
a
bl
e
1.
T
hus
,
b
a
s
e
d
on
th
e
pr
io
r
e
xpl
a
na
ti
on
of
th
e
a
dva
nt
a
ge
s
a
nd
di
s
a
dva
nt
a
ge
s
,
ge
ne
r
a
l
knowle
dge
r
e
ga
r
di
ng
th
e
r
e
f
e
r
e
nc
e
f
or
e
ne
r
gy
s
ui
ta
bi
li
ty
is
p
r
ovi
de
d
.
T
hus
,
b
a
s
e
d
on
th
e
pr
io
r
e
xpl
a
na
ti
on
of
th
e
a
dva
nt
a
ge
s
a
nd
di
s
a
dva
nt
a
ge
s
,
ge
n
e
r
a
l
knowle
dge
r
e
ga
r
di
ng
th
e
r
e
f
e
r
e
nc
e
f
or
e
ne
r
gy s
ui
ta
bi
li
ty
is
pr
ovi
de
d
.
T
a
bl
e
1. S
ol
a
r
e
ne
r
gy a
dva
nt
a
g
e
s
a
nd di
s
a
dva
nt
a
ge
s
T
ype
of
e
ne
r
gy
K
e
y c
ha
r
a
c
t
e
r
i
s
t
i
c
s
A
dva
nt
a
ge
s
D
i
s
a
dva
nt
a
ge
s
S
ol
a
r
S
ol
a
r
e
ne
r
gy
c
om
e
s
f
r
om
t
he
s
un'
s
r
a
di
a
t
i
on,
w
hi
c
h
i
s
ut
i
l
i
z
e
d
a
nd
c
onve
r
t
e
d
t
o
he
a
t
,
e
l
e
c
t
r
i
c
i
t
y,
a
nd
ot
he
r
e
ne
r
gy
f
or
m
s
us
i
ng
c
onve
r
s
i
on
t
e
c
hnol
ogy
[
14]
.
T
hi
s
e
ne
r
gy
,
i
n
ge
ne
r
a
l
,
i
s
di
vi
de
d
i
nt
o
s
ol
a
r
P
V
(
c
onve
r
t
s
a
bs
or
be
d
l
i
ght
t
ha
t
m
ove
s
e
l
e
c
t
r
ons
t
o
e
l
e
c
t
r
i
c
i
t
y)
a
nd
t
he
r
m
a
l
s
ol
a
r
e
ne
r
gy
(
c
ol
l
e
c
t
s
di
r
e
c
t
nor
m
a
l
i
r
r
a
di
a
nc
e
a
nd
t
r
a
ns
por
t
s
t
he
he
a
t
t
o s
t
or
a
ge
)
[
14]
,
[
15]
.
T
he
a
dva
nt
a
ge
s
of
s
ol
a
r
e
ne
r
gy
a
r
e
t
ha
t
i
t
c
a
n
c
onve
r
t
s
ol
a
r
e
ne
r
gy
di
r
e
c
t
l
y
t
o
e
l
e
c
t
r
i
c
i
t
y
w
i
t
hout
c
a
us
i
ng
pol
l
ut
i
on,
he
l
pi
ng
i
n
m
i
t
i
ga
t
i
ng
c
l
i
m
a
t
e
c
ha
nge
,
ha
s
l
ow
ope
r
a
t
i
ona
l
a
nd
m
a
i
nt
e
na
nc
e
c
os
t
s
,
a
nd
c
a
n
b
e
us
e
d
f
or
he
a
t
i
ng/
c
ool
i
ng
pur
pos
e
s
i
n
i
ndus
t
r
y
or
o
t
he
r
s
e
c
t
or
s
[
14]
,
[
16]
–
[
18]
.
D
e
s
pi
t
e
t
hos
e
be
ne
f
i
t
s
,
s
ol
a
r
e
ne
r
gy
a
l
s
o
h
a
s
m
a
ny
di
s
a
dva
nt
a
ge
s
,
s
uc
h
a
s
hi
gh
i
nve
s
t
m
e
nt
c
os
t
,
l
ow
e
f
f
i
c
i
e
nc
y,
t
he
ne
e
d
f
or
a
r
e
a
,
w
e
a
t
h
e
r
,
a
nd
l
a
t
i
t
ude
de
pe
nde
nc
y
,
a
s
w
e
l
l
a
s
c
om
pl
e
x
s
ys
t
e
m
s
(
s
pe
c
i
f
i
c
a
l
l
y
f
or
s
ol
a
r
t
he
r
m
a
l
t
e
c
hnol
ogy)
[
14]
,
[
16]
–
[
18]
.
W
i
nd
W
i
nd e
ne
r
gy i
s
a
s
our
c
e
of
e
n
e
r
gy
t
ha
t
r
e
s
ul
t
s
f
r
om
t
he
m
ove
m
e
nt
of
a
i
r
f
r
om
a
hi
ghe
r
t
e
m
pe
r
a
t
ur
e
r
e
gi
on
t
o
a
l
ow
e
r
one
due
t
o
pr
e
s
s
ur
e
di
f
f
e
r
e
nc
e
s
[
19]
,
[
20]
.
T
he
c
onve
r
s
i
on
of
w
i
nd
t
o
e
l
e
c
t
r
i
c
i
t
y
c
a
n
be
ba
s
e
d
on
t
w
o
di
f
f
e
r
e
nt
t
ype
s
of
t
ur
bi
ne
s
,
w
hi
c
h
a
r
e
hor
i
z
ont
a
l
a
xi
s
(
bl
a
de
pa
r
a
l
l
e
l
t
o
w
i
nd
f
l
ow
)
a
nd
ve
r
t
i
c
a
l
a
xi
s
(
bl
a
de
pe
r
pe
ndi
c
ul
a
r
t
o
w
i
nd
f
l
ow
)
[
21]
.
B
a
s
e
d
on
t
he
l
oc
a
t
i
on
t
ype
,
i
t
c
a
n
be
c
l
a
s
s
i
f
i
e
d
i
nt
o
ons
hor
e
a
nd of
f
s
hor
e
[
22]
.
T
he
a
dva
nt
a
ge
of
w
i
nd
e
ne
r
gy
i
s
t
ha
t
,
a
s
i
de
f
r
om
be
i
ng
e
nvi
r
onm
e
nt
a
l
l
y
f
r
i
e
ndl
y
s
i
nc
e
no
gr
e
e
nhous
e
ga
s
i
s
e
m
i
t
t
e
d
dur
i
ng
ope
r
a
t
i
on,
i
t
a
l
s
o
s
t
i
m
ul
a
t
e
s
j
ob
c
r
e
a
t
i
on
(
i
ns
t
a
l
l
a
t
i
on
a
nd
m
a
nuf
a
c
t
ur
i
ng)
,
a
nd
i
t
a
l
s
o
s
uppl
i
e
s
e
l
e
c
t
r
i
c
i
t
y
.
T
he
di
s
a
dva
nt
a
ge
s
of
t
hi
s
e
ne
r
gy
i
nc
l
ude
hi
gh
i
nve
s
t
m
e
nt
c
os
t
,
c
om
pl
e
x
m
a
i
nt
e
na
nc
e
,
di
f
f
i
c
ul
t
y
i
n
t
he
t
r
a
ns
por
t
a
t
i
on
of
c
om
pone
nt
s
,
noi
s
e
,
vi
s
ua
l
e
f
f
e
c
t
s
,
a
nd
t
e
m
pe
r
a
t
ur
e
r
i
s
e
a
r
ound
t
he
s
ur
r
oundi
ngs
,
w
hi
c
h
c
a
us
e
ha
bi
t
at
c
ha
nge
a
nd
a
ni
m
a
l
de
a
t
h
[
18]
,
[
21]
,
[
23]
.
3.2. S
t
r
e
n
gt
h
s
an
d
w
e
ak
n
e
s
s
e
s
of
P
V
s
ys
t
e
m
an
d
w
in
d
p
ow
e
r
s
ys
t
e
m
M
ovi
ng
on
f
r
om
ge
ne
r
a
l
a
dva
nt
a
ge
s
a
nd
di
s
a
dv
a
nt
a
ge
s
,
th
e
s
tr
e
ngt
hs
a
nd
w
e
a
kne
s
s
e
s
of
s
ol
a
r
(
P
V
)
a
nd w
in
d s
ys
te
m
s
c
a
n be
d
e
pi
c
te
d
a
s
f
ol
lo
w
s
[
24]
:
i)
S
t
r
e
n
gt
h:
r
e
ne
w
a
b
le
e
ne
r
g
y
s
ou
r
c
e
t
ha
t
h
a
s
a
r
e
l
a
t
iv
e
ly
p
r
e
d
i
c
ta
b
le
pa
tt
e
r
n
,
c
a
n
be
s
c
a
le
d
t
o
in
c
r
e
a
s
e
e
ne
r
gy
,
lo
w
ope
r
a
ti
ng
a
n
d
m
a
in
t
e
na
nc
e
c
os
ts
,
de
c
e
n
tr
a
li
z
e
d
g
e
ne
r
a
t
io
n
(
s
pe
c
i
f
ic
to
P
V
)
,
h
ig
h
e
ne
r
gy
yi
e
ld
(
s
pe
c
i
f
ic
to
w
in
d
e
ne
r
g
y
i
n
s
o
m
e
r
e
gi
o
ns
w
it
h
c
ons
t
a
nt
a
nd
s
t
r
on
g
w
in
d)
,
r
e
d
uc
e
s
g
r
e
e
nh
ous
e
ga
s
e
m
is
s
i
ons
a
nd
po
l
lu
t
io
n,
te
c
hno
lo
gi
c
a
l
a
dva
nc
e
m
e
n
ts
,
gr
id
s
upp
o
r
t
,
a
n
d
e
ne
r
gy
in
de
p
e
nde
nc
e
(
o
n
f
os
s
i
l
f
ue
ls
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
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I
nt
J
A
dv A
ppl
S
c
i
,
V
ol
. 15, No. 1, M
a
r
c
h 2026
:
107
-
122
110
ii)
W
e
a
kne
s
s
:
bot
h
e
ne
r
gi
e
s
a
r
e
li
m
it
e
d
(
P
V
by
w
e
a
th
e
r
a
nd
w
in
d
by
w
in
d
s
pe
e
d)
,
li
m
it
e
d
e
ne
r
gy
pr
oduc
ti
on
(
P
V
is
li
m
it
e
d
by
w
e
a
th
e
r
a
nd
doe
s
not
pr
oduc
e
a
t
ni
ght
/l
e
a
s
t
li
ght
c
ondi
ti
ons
w
he
r
e
a
s
w
in
d
c
a
us
e
s
lo
w
pr
oduc
ti
on
on
c
a
lm
c
ondi
ti
ons
)
,
s
ha
di
ng
im
pa
c
t
(
s
pe
c
if
ic
on
P
V
th
a
t
r
e
duc
e
e
ne
r
gy
pr
oduc
ti
on)
,
a
e
s
th
e
ti
c
c
ons
id
e
r
a
ti
ons
,
ge
ogr
a
phi
c
a
l
a
nd
la
nd
us
e
li
m
it
a
ti
ons
,
r
e
s
our
c
e
li
m
it
a
ti
ons
,
m
a
in
te
na
nc
e
c
ha
ll
e
nge
s
(
e
s
p
e
c
ia
ll
y
f
or
th
e
of
f
s
hor
e
s
ys
t
e
m
)
,
hi
gh
in
it
ia
l
c
os
t
s
,
vi
s
ua
l
im
pa
c
t
s
,
a
nd
e
ne
r
gy s
to
r
a
ge
r
e
qui
r
e
m
e
nt
s
.
H
e
nc
e
,
e
a
c
h
s
ys
te
m
pr
e
s
e
nt
s
s
im
il
a
r
s
tr
e
ngt
hs
a
nd
w
e
a
kne
s
s
e
s
th
a
t
m
us
t
be
c
on
s
id
e
r
e
d
b
e
f
or
e
de
s
ig
ni
ng,
pl
a
nni
ng,
a
nd
e
xe
c
ut
in
g
th
e
ove
r
a
ll
in
s
ta
ll
a
ti
on
of
t
he
s
ys
te
m
s
.
A
ddi
ti
ona
ll
y,
th
e
c
hoi
c
e
be
twe
e
n
s
ol
a
r
a
nd
w
in
d
s
y
s
te
m
s
of
te
n
de
pe
nd
s
on
lo
c
a
l
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
a
nd s
pe
c
if
ic
e
n
e
r
gy
ne
e
d
s
.
E
f
f
e
c
ti
ve
in
te
gr
a
ti
on of
t
he
s
e
s
ys
te
m
s
r
e
qui
r
e
s
a
ddr
e
s
s
in
g t
he
ir
r
e
s
pe
c
ti
ve
l
im
it
a
ti
ons
w
hi
le
m
a
xi
m
iz
in
g t
he
ir
be
ne
f
it
s
.
3.
3
. S
t
u
d
ie
s
on
s
ol
ar
an
d
w
in
d
e
n
e
r
gy m
od
e
ll
in
g u
s
in
g M
A
T
L
A
B
/S
im
u
li
n
k
R
e
c
e
nt
s
tu
di
e
s
f
r
om
th
e
la
s
t
5
ye
a
r
s
on
r
e
ne
w
a
bl
e
e
n
e
r
gy
in
te
gr
a
ti
on
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k
ha
ve
f
oc
us
e
d
on
c
r
e
a
ti
ng
m
or
e
a
c
c
ur
a
te
a
nd
e
f
f
ic
ie
nt
m
ode
l
s
f
or
P
V
a
nd
w
in
d
tu
r
b
in
e
s
ys
te
m
s
,
s
uc
h
a
s
de
ve
lo
pi
ng a
dva
nc
e
d c
ont
r
ol
s
tr
a
te
gi
e
s
l
ik
e
m
a
xi
m
um
pow
e
r
p
oi
nt
t
r
a
c
ki
ng
(
M
P
P
T
)
a
nd i
nve
r
te
r
s
t
o
i
m
pr
ov
e
gr
id
s
ta
bi
li
ty
a
nd
pow
e
r
qua
li
ty
.
F
or
P
V
a
r
r
a
ys
,
m
ode
ls
a
r
e
now
be
in
g
de
s
ig
ne
d
to
a
c
c
ur
a
te
ly
c
a
pt
ur
e
th
e
e
f
f
e
c
ts
of
r
e
a
l
-
w
or
ld
c
ondi
ti
ons
li
ke
pa
r
ti
a
l
s
ha
di
ng,
w
he
r
e
s
om
e
P
V
c
e
ll
s
a
r
e
e
xpo
s
e
d
to
le
s
s
s
unl
ig
ht
,
c
r
e
a
ti
ng
m
ul
ti
pl
e
pow
e
r
pe
a
ks
[
25]
.
T
he
s
e
m
ode
ls
a
r
e
c
r
uc
ia
l
f
or
de
ve
lo
pi
ng
e
f
f
e
c
ti
ve
c
ont
r
ol
a
lg
or
it
hm
s
.
S
im
il
a
r
ly
,
w
in
d
tu
r
bi
ne
m
ode
li
ng
ha
s
pr
ogr
e
s
s
e
d
to
in
c
lu
d
e
de
ta
il
e
d
r
e
pr
e
s
e
nt
a
ti
on
s
of
di
f
f
e
r
e
nt
ge
ne
r
a
to
r
te
c
hnol
ogi
e
s
,
li
ke
th
e
pe
r
m
a
ne
nt
m
a
gne
t
s
ync
hr
onous
ge
ne
r
a
to
r
(
P
M
S
G
)
a
nd
doubly
-
f
e
d
in
duc
ti
on
ge
ne
r
a
to
r
(
D
F
I
G
)
[
26]
,
[
27]
.
T
he
s
e
a
dva
n
c
e
d
m
ode
l
s
s
im
ul
a
te
c
om
pl
e
x
m
e
c
ha
ni
c
a
l
a
nd
e
le
c
tr
ic
a
l
dyn
a
m
ic
s
,
s
uc
h
a
s
bl
a
de
pi
tc
h c
ont
r
ol
a
nd r
ot
or
a
e
r
odyna
m
ic
s
, t
o pr
e
di
c
t
pe
r
f
or
m
a
nc
e
unde
r
va
r
yi
ng w
in
d s
pe
e
d
s
.
A
s
f
or
M
P
P
T
,
th
e
f
ie
ld
is
s
hi
f
ti
ng
f
r
om
tr
a
di
ti
ona
l
a
lg
or
it
hm
s
to
m
or
e
a
dva
nc
e
d
hybr
id
m
e
th
ods
,
pr
im
a
r
il
y
de
ve
lo
pe
d
a
nd
te
s
te
d
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k.
R
e
s
e
a
r
c
h
e
r
s
s
im
ul
a
te
a
lg
or
it
hm
pe
r
f
or
m
a
nc
e
unde
r
va
r
yi
ng
ir
r
a
di
a
nc
e
a
nd
te
m
pe
r
a
tu
r
e
c
ondi
ti
ons
to
v
a
li
da
te
th
e
ir
e
f
f
e
c
ti
ve
ne
s
s
be
f
or
e
ha
r
dw
a
r
e
im
pl
e
m
e
nt
a
ti
on.
W
hi
le
c
onve
nt
io
na
l
m
e
th
ods
li
ke
pe
r
tu
r
b
a
nd
obs
e
r
ve
(
P
&
O
)
a
nd
in
c
r
e
m
e
nt
a
l
c
onduc
ta
nc
e
(
I
N
C
)
a
r
e
s
ti
ll
c
om
m
on,
th
e
y
s
tr
uggl
e
w
it
h
r
a
pi
d
c
h
a
nge
s
a
nd
p
a
r
ti
a
l
s
ha
di
ng.
A
s
a
r
e
s
ul
t,
r
e
c
e
nt
r
e
s
e
a
r
c
h
ha
s
f
oc
us
e
d
on
e
nha
nc
in
g
P
&
O
m
e
th
ods
w
it
h
va
r
ia
bl
e
s
te
p
s
iz
e
s
to
r
e
duc
e
os
c
il
la
ti
ons
a
nd
im
pr
ove
tr
a
c
ki
ng
s
pe
e
d
[
25]
,
[
28]
.
M
or
e
ove
r
,
a
s
ig
ni
f
ic
a
nt
tr
e
nd
is
th
e
in
te
gr
a
t
io
n
of
in
te
ll
ig
e
nt
a
lg
or
it
hm
s
li
ke
f
uz
z
y
lo
gi
c
c
ont
r
ol
le
r
s
(
F
L
C
)
a
nd
ne
ur
a
l
ne
twor
ks
(
N
N
)
.
T
he
s
e
in
te
ll
ig
e
nt
c
ont
r
ol
le
r
s
a
r
e
pa
r
ti
c
ul
a
r
ly
e
f
f
e
c
ti
ve
i
n
ha
ndl
in
g
th
e
c
om
pl
e
x,
m
ul
ti
-
pe
a
k
pow
e
r
c
ur
ve
s
c
r
e
a
te
d
by
pa
r
ti
a
l
s
ha
di
ng,
a
s
th
e
y
c
a
n
a
da
pt
w
it
hout
r
e
qui
r
in
g
a
pr
e
c
is
e
s
ys
te
m
m
ode
l.
T
he
S
im
ul
in
k
e
nvi
r
onm
e
n
t
e
na
bl
e
s
a
s
id
e
-
by
-
s
id
e
c
om
pa
r
is
on
of
th
e
s
e
in
te
ll
ig
e
nt
c
ont
r
ol
le
r
s
w
it
h
c
onve
nt
io
na
l
m
e
th
od
s
,
de
m
ons
tr
a
ti
n
g
th
e
ir
s
upe
r
io
r
tr
a
c
ki
ng
s
pe
e
d
a
nd e
f
f
ic
ie
nc
y.
A
s
tu
dy
by
M
e
lh
a
oui
e
t
al
.
[
29]
us
e
d
S
im
ul
in
k
to
s
how
th
a
t
a
hybr
id
P
&
O
-
F
L
C
m
e
th
od
ha
d
a
f
a
s
te
r
tr
a
c
ki
ng
s
pe
e
d
a
nd
hi
ghe
r
e
f
f
ic
ie
nc
y,
w
hi
le
a
not
he
r
m
e
th
od
by
D
a
hm
a
ne
e
t
al
.
[
30]
ut
il
iz
e
d
th
e
pl
a
tf
or
m
to
te
s
t
a
hybr
id
P
&
O
a
nd ne
ur
a
l
ne
twor
k a
ppr
oa
c
h f
or
w
in
d e
ne
r
gy s
ys
te
m
s
.
T
he
in
te
gr
a
ti
on
of
r
e
ne
w
a
bl
e
e
ne
r
gy
s
our
c
e
s
in
to
th
e
po
w
e
r
gr
id
is
a
vi
ta
l
r
e
s
e
a
r
c
h
a
r
e
a
,
f
oc
us
in
g
on
in
ve
r
te
r
c
ont
r
ol
f
or
m
a
in
ta
in
in
g
pow
e
r
qua
li
ty
a
nd
s
ys
te
m
s
ta
bi
li
ty
.
M
A
T
L
A
B
/S
im
ul
in
k
is
a
n
e
s
s
e
nt
ia
l
to
ol
f
or
m
ode
li
ng
a
nd
te
s
ti
ng
a
dva
nc
e
d
in
ve
r
te
r
s
tr
a
te
gi
e
s
s
a
f
e
ly
.
A
ke
y
a
dva
nc
e
m
e
nt
is
th
e
s
hi
f
t
f
r
om
gr
id
-
f
ol
lo
w
in
g
to
gr
id
-
f
or
m
in
g
in
ve
r
te
r
s
.
W
hi
le
gr
id
-
f
ol
lo
w
in
g
in
ve
r
te
r
s
r
e
ly
on
th
e
gr
id
f
or
vol
ta
ge
a
nd
f
r
e
que
nc
y
r
e
f
e
r
e
nc
e
s
,
gr
id
-
f
o
r
m
in
g
in
ve
r
te
r
s
c
a
n
ge
ne
r
a
te
th
e
s
e
r
e
f
e
r
e
nc
e
s
a
ut
onomous
ly
.
T
hi
s
is
c
r
uc
ia
l
f
or
m
ic
r
ogr
id
s
a
nd
lo
w
-
in
e
r
ti
a
pow
e
r
s
ys
te
m
s
,
e
na
bl
in
g
th
e
m
to
pr
ovi
de
e
s
s
e
nt
ia
l
s
e
r
vi
c
e
s
li
ke
vol
ta
g
e
a
nd
f
r
e
que
nc
y
s
uppor
t.
R
e
s
e
a
r
c
he
r
s
u
s
e
S
im
ul
in
k
to
te
s
t
th
e
s
e
c
ont
r
ol
s
tr
a
te
gi
e
s
,
pa
r
ti
c
ul
a
r
ly
f
or
f
a
ul
t
r
id
e
-
th
r
ough
c
a
pa
bi
li
ti
e
s
,
e
ns
ur
in
g
in
ve
r
te
r
s
r
e
m
a
in
c
onne
c
te
d
dur
in
g
d
is
tu
r
ba
nc
e
s
[
31]
,
[
32
]
.
A
ddi
ti
ona
ll
y
,
S
im
ul
in
k'
s
a
dva
nc
e
d
a
na
ly
s
is
to
ol
s
a
r
e
ut
il
iz
e
d
to
de
s
ig
n
a
n
d
e
va
lu
a
te
f
il
te
r
s
th
a
t
r
e
duc
e
to
ta
l
ha
r
m
oni
c
di
s
to
r
ti
on
(
T
H
D
)
,
e
ns
ur
in
g
th
a
t
th
e
po
w
e
r
s
uppl
ie
d
to
th
e
gr
id
c
om
pl
ie
s
w
it
h
s
tr
ic
t
qua
li
ty
s
ta
nda
r
ds
.
S
tu
di
e
s
li
ke
th
a
t
b
y
N
guy
e
n
e
t
al
.
[
33]
a
nd
R
a
o
e
t
al
.
[
34]
u
s
e
d
S
im
ul
in
k
to
de
s
ig
n
a
nd
s
im
ul
a
te
c
ont
r
ol
s
ys
te
m
s
,
a
na
ly
z
in
g
th
e
dyna
m
ic
op
e
r
a
ti
on
of
m
ic
r
ogr
id
s
.
T
hi
s
d
e
m
ons
tr
a
te
s
th
e
pl
a
tf
or
m
'
s
vi
ta
l
r
ol
e
in
e
ns
ur
in
g
r
e
li
a
bl
e
a
nd high
-
qua
li
ty
pow
e
r
de
li
ve
r
y f
r
om
r
e
ne
w
a
bl
e
s
our
c
e
s
.
D
e
s
pi
te
a
dva
nc
e
m
e
nt
s
in
c
om
pl
e
x
a
nd
in
te
ll
ig
e
nt
s
ys
te
m
s
,
it
is
e
s
s
e
nt
ia
l
to
r
e
c
ogni
z
e
th
a
t
th
e
s
e
s
ys
te
m
s
a
r
e
bui
lt
on
f
unda
m
e
nt
a
l
m
ode
l
s
.
A
s
ol
id
und
e
r
s
ta
ndi
n
g
of
how
to
c
r
e
a
te
b
a
s
ic
P
V
a
nd
w
in
d
tu
r
bi
ne
m
ode
ls
i
n S
im
ul
in
k i
s
i
m
por
ta
nt
f
or
s
e
ve
r
a
l
r
e
a
s
ons
. T
he
s
e
f
ou
nda
ti
ona
l
m
ode
ls
, w
hi
c
h a
r
e
of
te
n ba
s
e
d on the
m
a
th
e
m
a
ti
c
a
l
e
qua
ti
ons
of
e
qui
va
le
nt
c
ir
c
ui
ts
a
nd a
e
r
odyna
m
ic
f
or
c
e
s
, pr
ovi
de
i
ns
ig
ht
i
nt
o t
he
c
or
e
pr
in
c
ip
le
s
of
r
e
ne
w
a
bl
e
e
ne
r
gy
c
onve
r
s
io
n.
T
h
e
y
s
e
r
ve
a
s
bui
ld
in
g
bl
oc
ks
f
or
m
or
e
c
om
pl
e
x
s
ys
te
m
s
,
e
na
bl
in
g
r
e
s
e
a
r
c
he
r
s
a
nd
s
tu
de
nt
s
to
pr
ogr
e
s
s
iv
e
ly
in
c
or
por
a
te
f
e
a
tu
r
e
s
s
uc
h
a
s
M
P
P
T
a
lg
or
it
hm
s
,
ba
tt
e
r
y
s
to
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im
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
A
dv A
ppl
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c
i
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S
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:
2252
-
8814
M
ode
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and w
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y
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N
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a
s
P
r
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111
3.
4
. S
ol
ar
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e
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gy
-
p
h
ot
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t
ai
c
c
e
ll
m
od
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ll
in
g u
s
in
g M
A
T
L
A
B
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S
im
u
li
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k
T
he
de
s
ig
n
of
PV
e
ne
r
gy s
ys
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m
s
de
pe
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p
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f
or
m
a
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th
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ir
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s
a
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ls
. T
he
c
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ll
c
a
n
be
r
e
pr
e
s
e
nt
e
d
us
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g
e
it
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a
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gl
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two
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it
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(
how
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,
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two
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s
c
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xi
ty
w
it
h
e
qua
ti
ons
a
nd
p
a
r
a
m
e
te
r
s
)
[
35]
.
T
he
s
in
gl
e
di
ode
c
ir
c
ui
t
m
ode
l
in
F
ig
ur
e
1
is
pr
e
f
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r
a
bl
e
in
m
os
t
r
e
le
va
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a
r
ti
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le
s
s
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c
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it
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s
f
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w
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r
c
om
pl
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x
c
a
lc
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la
ti
ons
w
hi
le
pr
ovi
di
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lo
w
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r
c
om
put
a
ti
ona
l
e
r
r
or
s
c
om
pa
r
e
d
to
th
e
two
di
ode
c
ir
c
ui
t
m
ode
ls
[
35]
,
[
36]
.
O
ve
r
a
ll
,
th
e
s
im
ul
a
ti
on
s
te
ps
in
vol
ve
f
in
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ng
ir
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di
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nc
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of
il
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s
ba
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on
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e
de
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lo
c
a
ti
on,
m
ode
ll
in
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b
a
s
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d
on
P
V
gove
r
ni
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e
qua
ti
on
s
,
de
te
r
m
in
in
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lo
a
d
c
ondi
ti
ons
,
a
nd
f
in
a
ll
y
in
te
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a
ti
ng
s
to
r
a
ge
,
pow
e
r
e
le
c
tr
oni
c
s
,
a
nd
c
ont
r
ol
lo
ops
.
H
ow
e
ve
r
,
th
is
pa
pe
r
w
il
l
di
s
c
us
s
l
im
it
e
d t
o P
V
m
ode
ll
in
g.
F
ig
ur
e
1. S
in
gl
e
di
ode
c
ir
c
ui
t
r
e
pr
e
s
e
nt
a
ti
on
f
or
P
V
c
e
ll
[
36]
T
he
gove
r
ni
ng e
qua
ti
on of
t
he
c
ur
r
e
nt
s
our
c
e
of
t
hi
s
m
ode
l
is
gi
ve
n a
s
(
1)
-
(
6)
[
35]
–
[
37]
.
=
ℎ
−
−
ℎ
(
1)
ℎ
=
[
+
(
−
)
]
(
2)
=
[
e
x
p
(
+
)
−
1
]
(
3)
ℎ
=
+
ℎ
(
4)
=
(
)
3
[
(
1
−
1
)
]
(
5)
=
e
x
p
(
)
−
1
(
6)
I
n
w
hi
c
h
I
is
out
pu
t
c
ur
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e
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,
ℎ
is
th
e
c
ur
r
e
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s
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c
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G
is
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s
ol
a
ti
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s
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ti
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pe
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t
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ic
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ℎ
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hr
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ℎ
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a
s
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r
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a
tu
r
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ti
on c
ur
r
e
nt
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ode
, V
a
s
t
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m
in
a
l
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li
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c
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ode
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m
a
l
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(
=
(
)
(
)
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f
or
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×
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C
a
nd
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by
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×
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J
/K
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B
ol
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m
a
nn’
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ons
ta
nt
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,
a
s
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nd
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t
S
T
C
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ope
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ta
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V
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R
s
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th
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V
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ll
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onne
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ti
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ll
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in
a
s
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nd
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r
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na
ti
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pow
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it
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to
a
to
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c
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ll
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d
m
odul
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(
36
or
72
c
om
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na
ti
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of
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ll
s
)
.
T
he
gove
r
ni
ng
e
qua
ti
on of
t
he
P
V
m
odul
e
i
s
a
s
(
7)
.
=
ℎ
−
[
e
x
p
(
+
−
1
)
]
−
+
ℎ
(
7)
I
n w
hi
c
h
is
a
n e
qui
va
le
nt
c
ir
c
ui
t
in
pa
r
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ll
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s
tr
in
gs
,
a
nd
is
f
or
s
e
r
ie
s
a
r
r
a
nge
m
e
nt
.
T
he
known
e
qua
ti
on
c
a
n
now
be
c
onve
r
te
d
to
a
n
e
ne
r
gy
s
ys
te
m
m
ode
l
in
S
im
ul
in
k.
F
or
a
s
im
pl
e
r
unde
r
s
ta
ndi
ng,
s
om
e
a
s
s
um
pt
io
n
s
a
r
e
m
a
de
.
F
ir
s
t,
ba
s
e
d
on
F
i
gur
e
1,
R
s
a
nd
R
sh
a
r
e
bot
h
r
e
s
is
ta
nt
f
or
s
e
r
ie
s
(
c
ur
r
e
nt
pa
th
a
nd
a
c
t
a
s
lo
s
s
e
s
by
J
oul
e
e
f
f
e
c
t)
a
nd
p
a
r
a
ll
e
l
(
c
o
r
r
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la
te
d
w
it
h
s
e
e
pa
g
e
of
c
ur
r
e
nt
)
a
s
p
e
c
ts
[
37]
.
A
lt
hough both var
ia
bl
e
s
m
us
t
not
be
ove
r
lo
oke
d, w
it
h t
he
pur
p
os
e
of
s
im
pl
ic
it
y, R
sh
c
a
n be
i
gnor
e
d
(
be
c
om
e
s
c
ons
pi
c
uous
if
m
a
ny
m
odul
e
s
a
r
e
c
on
s
id
e
r
e
d)
w
hi
le
R
s
is
s
ti
ll
ta
ke
n
in
to
a
c
c
ount
due
to
it
s
m
ul
ti
pl
ic
a
ti
on
e
f
f
e
c
t,
m
a
ki
ng i
t
m
or
e
pr
om
in
e
nt
[
37]
. T
hi
s
w
il
l
r
e
s
ul
t
in
a
ne
w
e
r
e
qua
ti
on, whic
h i
s
(
8)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
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8814
I
nt
J
A
dv A
ppl
S
c
i
,
V
ol
. 15, No. 1, M
a
r
c
h 2026
:
107
-
122
112
ℎ
−
[
e
x
p
(
(
+
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−
1
)
]
(
8)
T
he
n,
w
it
h
th
e
s
e
e
qua
ti
on
s
,
P
V
c
a
n
be
m
ode
le
d
ba
s
e
d
on
t
he
de
s
ir
e
d
c
a
ta
lo
gue
a
nd
ty
pe
.
A
s
a
r
e
f
e
r
e
nc
e
,
a
s
tu
dy
by
V
in
od
e
t
a
l
.
[
37
]
us
e
s
th
is
a
ppr
oa
c
h
to
m
ode
l
a
P
V
s
ys
te
m
ba
s
e
d
on
th
e
de
te
r
m
in
e
d
pa
r
a
m
e
te
r
s
of
J
A
P
6
-
72
-
320/
4B
B
. T
he
va
lu
e
s
of
t
he
pa
r
a
m
e
te
r
s
a
r
e
gi
ve
n i
n T
a
bl
e
2.
T
a
bl
e
2. J
A
P
6
-
72
-
320/
4B
B
P
V
m
odul
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pa
r
a
m
e
te
r
s
[
37]
V
a
r
i
a
bl
e
V
a
l
ue
s
V
a
r
i
a
bl
e
V
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l
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m
(
m
a
xi
m
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a
t
S
T
C
)
320 W
N
s
(
t
ot
a
l
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s
c
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l
l
s
)
72
V
mp
(
m
a
xi
m
um
pow
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r
vol
t
a
ge
)
37.38 V
N
p
(
t
ot
a
l
pa
r
a
l
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c
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l
s
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1
I
mp
(
m
a
xi
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r
c
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r
r
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nt
)
8.56 A
n (
i
de
a
l
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t
y f
a
c
t
or
)
1.3
V
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ope
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T
C
T
he
ne
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te
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m
a
ke
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ub
s
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m
s
ba
s
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d
on
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m
a
ll
e
r
e
qua
ti
ons
th
a
t
a
r
e
not
de
pe
nde
nt
on
ot
he
r
s
ubs
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te
m
e
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ti
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.
T
hi
s
c
a
n
be
done
f
ir
s
t
f
or
th
e
ope
r
a
ti
ng
te
m
pe
r
a
tu
r
e
c
onve
r
s
io
n
m
ode
l
a
s
s
how
n
in
F
ig
ur
e
2
a
nd
pr
oduc
ts
of
N
s
knT
op
a
s
s
how
n
in
F
ig
ur
e
3,
in
w
hi
c
h
th
e
va
r
ia
bl
e
n
is
e
qui
va
le
nt
to
A
[
37]
.
T
he
n
th
e
m
ode
li
ng
c
a
n
be
f
oc
us
e
d
on
obt
a
in
in
g
I
,
w
hi
c
h
de
pe
nds
on
I
ph
a
nd
I
d
(
G
a
in
f
r
o
m
I
s
a
t
in
(
5)
th
r
ough
I
Rs
)
.
H
e
nc
e
, us
in
g (
2)
a
nd (
6)
t
o
f
in
d I
ph
a
nd I
Rs
a
s
s
how
n i
n F
ig
ur
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s
4 a
nd 5, the
n us
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g I
Rs
to
f
in
d
I
s
(
o
r
I
s
a
t
)
s
how
n
in
F
ig
ur
e
6.
T
he
n,
I
c
a
n
be
p
r
oduc
e
d
ba
s
e
d
on
th
e
r
e
s
ul
t
in
g
va
l
ue
of
th
e
m
e
nt
io
ne
d
s
ubs
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te
m
s
ba
s
e
d
on
(
1)
,
w
hi
c
h i
s
s
how
n i
n F
ig
ur
e
7. T
he
f
in
a
l
s
ys
te
m
m
ode
ls
a
r
e
s
how
n
i
n F
ig
ur
e
s
8 a
nd 9.
S
e
ve
r
a
l
ot
he
r
s
tu
di
e
s
of
f
e
r
im
pr
ove
d
e
qua
ti
ons
ta
il
or
e
d
to
s
pe
c
if
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ne
e
ds
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nd
pur
pos
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s
.
T
he
s
e
ne
w
e
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ti
ons
r
e
s
ul
t
in
di
f
f
e
r
e
nt
m
a
th
e
m
a
ti
c
a
l
f
or
m
ul
a
ti
ons
de
pe
nd
in
g
on
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e
r
e
qui
r
e
m
e
nt
s
.
O
ne
e
xa
m
pl
e
is
f
r
om
th
e
B
e
r
li
ni
s
tu
di
e
s
(
s
e
e
n i
n F
ig
ur
e
10)
t
ha
t
s
how
s
t
he
a
ppr
oa
c
he
s
a
s
(
9)
-
(
15)
[
38]
–
[
40
]
.
=
[
1
−
1
(
e
x
p
2
−
1
)
]
(
9)
1
=
(
1
−
)
e
x
p
−
2
(
10)
2
=
(
−
1
ln
(
1
−
)
)
(
11)
(
,
)
=
.
[
1
+
(
−
)
]
(
12)
(
,
)
=
.
[
1
+
(
−
)
]
(
13)
(
)
=
[
1
+
(
−
)
]
(
14)
(
)
=
[
1
+
(
−
)
]
(
15)
I
n
w
hi
c
h
is
P
V
c
ur
r
e
nt
.
W
hi
le
1
a
nd
2
a
r
e
pa
r
a
m
e
te
r
s
de
pe
nd
e
n
t
on
ir
r
a
di
a
nc
e
a
nd
te
m
pe
r
a
tu
r
e
.
A
f
te
r
th
a
t,
,
,
, a
nd
a
r
e
va
lu
e
s
gi
ve
n i
n
th
e
d
a
ta
s
he
e
ts
of
P
V
m
odul
e
m
a
nuf
a
c
tu
r
e
r
s
.
F
ig
ur
e
2. S
ubs
ys
te
m
f
or
ope
r
a
ti
ng t
e
m
pe
r
a
tu
r
e
c
onve
r
s
io
n m
ode
l
[
37]
F
ig
ur
e
3. S
ubs
ys
te
m
f
or
N
s
knT
o
p
[
37]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
dv A
ppl
S
c
i
I
S
S
N
:
2252
-
8814
M
ode
li
ng of s
ol
ar
and w
in
d e
ne
r
g
y
us
in
g m
at
r
i
x
l
abor
at
or
y
/
S
i
m
ul
in
k
:
a r
e
v
ie
w
(
N
ic
hol
a
s
P
r
anat
a)
113
F
ig
ur
e
4. S
ubs
ys
te
m
f
or
I
ph
[
37]
F
ig
ur
e
5. S
ubs
ys
te
m
f
or
I
R
s
[
37]
F
ig
ur
e
6. S
ubs
ys
te
m
f
or
I
s
[
37]
F
ig
ur
e
7. S
ubs
ys
te
m
f
or
I
[
37]
F
ig
ur
e
8. F
in
a
l
s
ys
te
m
i
nt
e
gr
a
te
d ba
s
e
d on
de
s
ig
ne
d s
ub
s
ys
te
m
s
[
37]
F
ig
ur
e
9. S
im
pl
if
ie
d f
in
a
l
s
ys
te
m
[
37]
F
ig
ur
e
10. S
im
ul
in
k m
ode
l
by
M
öl
le
r
a
nd K
r
a
ut
e
r
[
40
]
,
ba
s
e
d on
A
ya
z
e
t
al
.
[
38]
a
nd
B
e
r
li
ni
e
t
al
.
[
39]
a
ppr
oa
c
he
s
C
or
r
e
s
ponding
to
th
e
r
e
vi
e
w
e
d
li
te
r
a
tu
r
e
pr
ovi
de
d,
it
c
a
n
be
hi
ghl
ig
ht
e
d
th
a
t
th
e
m
ode
ll
in
g
ba
s
e
d
on
th
e
S
im
ul
in
k
c
a
n
be
m
a
de
by
us
in
g
th
e
e
qua
ti
on
th
a
t
gove
r
ns
t
he
s
ol
a
r
c
e
ll
ope
r
a
ti
ons
.
H
ow
e
v
e
r
,
th
e
s
tu
di
e
s
gi
ve
n
ha
ve
s
e
v
e
r
a
l
li
m
it
a
ti
ons
,
w
hi
c
h
c
a
n
be
f
ur
th
e
r
pr
ogr
e
s
s
e
d
by
in
c
lu
di
ng
s
e
ve
r
a
l
ot
he
r
c
ons
id
e
r
a
ti
on
s
a
s
id
e
f
r
om
th
e
m
a
th
e
m
a
ti
c
a
l
m
ode
ls
of
P
V
c
e
ll
s
a
nd
m
odul
e
s
,
s
uc
h
a
s
s
to
r
a
ge
s
y
s
te
m
s
,
tr
a
c
ki
ng
a
lg
or
it
hm
s
(
ge
ne
r
a
ll
y
M
P
P
T
)
,
D
C
/DC
c
onv
e
r
te
r
s
,
in
ve
r
te
r
s
,
a
nd
ot
he
r
a
ddi
ti
ona
l
s
ys
te
m
s
,
s
uc
h
a
s
te
m
pe
r
a
tu
r
e
a
dj
us
tm
e
nt
s
ys
te
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8814
I
nt
J
A
dv A
ppl
S
c
i
,
V
ol
. 15, No. 1, M
a
r
c
h 2026
:
107
-
122
114
3.5.
Wi
n
d
e
n
e
r
gy
-
t
u
r
b
in
e
an
d
ge
n
e
r
at
or
m
od
e
ll
in
g u
s
in
g
M
A
T
L
A
B
/S
im
u
li
n
k
F
or
a
w
in
d
e
ne
r
gy
s
ys
te
m
,
th
e
s
im
ul
a
ti
on
s
te
ps
in
vol
ve
f
in
di
n
g
w
in
d
ve
lo
c
it
y
pr
o
f
il
e
s
ba
s
e
d
on
th
e
s
e
le
c
te
d
a
r
e
a
,
m
ode
ll
in
g
b
a
s
e
d
on
w
in
d
e
ne
r
gy
gove
r
ni
ng
e
qua
ti
ons
,
de
te
r
m
in
in
g
lo
a
d
c
ondi
ti
ons
,
a
nd
in
te
gr
a
ti
on w
it
h s
to
r
a
ge
, powe
r
e
le
c
tr
oni
c
s
, a
nd c
ont
r
ol
lo
ops
.
H
ow
e
ve
r
, s
im
il
a
r
t
o
th
e
P
V
s
e
c
ti
on, t
hi
s
a
r
ti
c
le
w
il
l
di
s
c
us
s
li
m
it
e
d
to
w
in
d
e
ne
r
gy
m
ode
ll
in
g.
T
he
m
a
in
c
om
pone
nt
s
of
w
in
d
e
ne
r
gy
s
ys
te
m
s
c
ons
i
s
t
of
a
bl
a
de
tu
r
bi
ne
,
ge
ne
r
a
to
r
,
pow
e
r
c
onve
r
te
r
,
a
nd
c
ont
r
ol
le
r
[
41]
.
W
in
d
e
ne
r
gy
tu
r
bi
ne
m
ode
le
d
in
M
A
T
L
A
B
/S
im
ul
in
k. I
t
c
a
n be
ba
s
e
d on
(
16)
.
=
1
2
2
3
(
,
)
(
16)
I
n
w
hi
c
h
is
m
e
c
ha
ni
c
a
l
pow
e
r
(
W
)
.
W
hi
le
R
is
th
e
r
a
di
us
of
th
e
tu
r
bi
ne
bl
a
de
(
m
)
,
v
is
th
e
w
in
d
ve
lo
c
it
y,
is
th
e
pow
e
r
c
oe
f
f
ic
ie
nt
,
λ
is
th
e
ti
p
s
pe
e
d
r
a
ti
o,
a
nd
β
is
t
he
pi
tc
h
a
ngl
e
.
O
bt
a
in
in
g
λ
w
il
l
be
b
a
s
e
d
on
(
17)
.
=
(
17)
T
he
λ
a
c
ts
a
s
t
he
r
a
ti
o of
t
a
nge
nt
ia
l
ve
lo
c
it
y t
o w
in
d s
pe
e
d
,
in
w
hi
c
h ω
i
s
t
he
a
ngul
a
r
s
pe
e
d
[
42]
. T
he
is
de
pe
nde
nt
on
s
e
ve
r
a
l
a
s
pe
c
t
s
.
F
or
th
e
hor
iz
ont
a
l
a
xi
s
ty
pe
,
f
a
c
to
r
s
th
a
t
a
r
e
a
f
f
e
c
ti
ng
c
ons
i
s
t
of
s
e
ve
r
a
l
bl
a
de
s
,
λ
,
a
nd
β
.
T
he
r
e
f
or
e
,
in
m
a
ki
ng
th
e
s
ys
te
m
of
w
in
d
e
ne
r
gy,
th
e
s
ig
ni
f
ic
a
nt
ly
im
pa
c
t
s
th
e
pow
e
r
out
put
ba
s
e
d on the
λ
a
nd
β.
S
e
ve
r
a
l
m
a
th
e
m
a
ti
c
a
l
a
ppr
oa
c
he
s
t
o
a
r
e
ba
s
e
d on thr
e
e
m
a
in
f
unc
ti
ons
, w
hi
c
h
a
r
e
pol
ynomi
a
l,
s
in
us
oi
da
l,
a
nd
e
xpone
nt
ia
l
f
unc
ti
ons
.
O
ne
of
th
e
m
os
t
ge
n
e
r
a
l
f
unc
ti
ons
us
e
d
to
de
s
ig
n
a
S
im
ul
in
k
m
ode
l
is
us
in
g
th
e
e
xpone
nt
ia
l
f
unc
ti
on
ba
s
e
d
on
O
va
ndo
e
t
al
.
e
qua
ti
ons
[
42]
,
[
43]
.
T
he
e
qua
ti
on
is
a
s
(
18)
a
nd (
19)
.
1
=
1
+
0
.
08
.
−
0
.
035
1
+
3
(
18)
=
0
.
5176
(
116
−
0
.
4
.
−
5
)
−
(
21
)
+
0
.
0068
(
19)
U
s
in
g
th
e
gi
ve
n
e
qua
ti
on
s
,
th
e
m
a
th
e
m
a
ti
c
a
l
m
od
e
l
c
a
n
be
d
e
s
ig
ne
d
in
S
im
ul
in
k.
F
ir
s
t,
s
ubs
y
s
te
m
s
m
us
t
be
c
r
e
a
te
d
f
or
(
18)
.
T
hi
s
pr
oc
e
s
s
is
il
lu
s
tr
a
te
d
in
F
ig
ur
e
1
1
,
in
w
hi
c
h
e
q1
r
e
pr
e
s
e
nt
s
1
+
0
.
08
.
−
0
.
035
1
+
3
a
nd
eq
2
a
s
0
.
5176
(
116
−
0
.
4
.
−
5
)
−
(
21
)
+
0
.
0068
.
N
ow
th
a
t
th
e
m
ode
l
f
or
(
18)
is
known,
a
pow
e
r
f
a
c
to
r
c
a
n
be
obt
a
in
e
d.
T
hi
s
pow
e
r
f
a
c
to
r
c
a
n
th
e
n
be
u
s
e
d
to
c
om
pl
e
te
th
e
c
a
lc
ul
a
ti
ons
ba
s
e
d
on
(
16)
,
a
s
s
how
n
in
F
ig
ur
e
12. T
hi
s
m
ode
l
c
a
n now be
s
im
pl
i
f
ie
d t
o
a
f
in
a
l
s
ys
te
m
,
a
s
s
how
n i
n F
ig
ur
e
13. T
he
pa
r
a
m
e
te
r
s
f
or
t
he
bl
a
de
r
a
di
us
,
w
in
d
ve
lo
c
it
y,
be
ta
,
a
nd
a
ngul
a
r
ve
lo
c
it
y
s
houl
d
m
a
tc
h
th
e
r
e
a
l
c
ondi
ti
ons
a
nd
p
r
e
f
e
r
e
nc
e
s
.
T
he
a
ngul
a
r
ve
lo
c
it
y c
a
n be
obt
a
in
e
d f
r
om
(
17)
.
M
a
ny
ot
he
r
m
a
th
e
m
a
ti
c
a
l
a
ppr
oa
c
he
s
a
r
e
pr
e
s
e
nt
e
d
to
s
how
di
f
f
e
r
e
nt
de
s
ig
ns
of
C
p
in
S
im
ul
in
k
s
uc
h
a
s
pol
ynomi
a
l
f
unc
ti
on
(
th
ir
d
or
de
r
,
f
our
th
or
de
r
,
f
if
th
o
r
d
e
r
,
a
nd
s
ix
th
or
de
r
[
44]
,
[
45]
–
[
47]
)
,
s
in
us
oi
da
l
f
unc
ti
on
(
[
44]
,
[
48
]
–
[
51]
)
a
s
w
e
ll
a
s
e
xpone
nt
ia
l
(
[
43]
,
[
52]
–
[
57]
)
.
T
he
s
te
ps
to
de
s
ig
n
th
e
m
ode
l
s
a
r
e
th
e
s
a
m
e
s
in
c
e
th
e
y
onl
y
r
e
ly
on
th
e
gi
ve
n
m
a
th
e
m
a
ti
c
a
l
m
ode
l
s
.
A
s
id
e
f
r
om
C
p
c
ons
id
e
r
a
ti
ons
,
c
hoos
in
g
th
e
r
ig
ht
tu
r
bi
ne
in
w
hi
c
h
th
e
d
a
ta
of
s
pe
e
d
in
a
s
e
le
c
t
e
d
a
r
e
a
is
s
ui
ta
bl
e
a
s
th
e
c
ut
-
in
s
pe
e
d
f
or
th
e
tu
r
bi
ne
.
I
n
a
ddi
ti
on
to
th
e
tu
r
bi
ne
s
e
le
c
ti
on
a
nd
m
a
th
e
m
a
ti
c
a
l
a
ppr
oa
c
he
s
, t
he
us
e
of
a
ge
ne
r
a
to
r
is
a
de
qua
te
ly
im
por
ta
nt
due
to
th
e
tu
r
bi
ne
s
e
le
c
ti
on,
w
hi
c
h
c
a
n
be
c
la
s
s
if
ie
d
in
to
f
ix
e
d
-
s
pe
e
d
w
in
d
tu
r
bi
ne
s
a
nd
va
r
ia
bl
e
-
s
pe
e
d
w
in
d
tu
r
bi
ne
s
.
F
or
f
ix
e
d
-
s
pe
e
d
tu
r
bi
ne
s
,
th
e
s
qui
r
r
e
l
c
a
ge
in
duc
ti
on
ge
ne
r
a
to
r
is
s
ui
ta
bl
e
,
w
he
r
e
a
s
th
e
doubly
f
e
d
in
duc
ti
on
ge
ne
r
a
to
r
s
a
nd
pe
r
m
a
ne
nt
m
a
gn
e
t
ge
ne
r
a
to
r
s
a
r
e
us
e
d
f
or
va
r
ia
bl
e
-
s
pe
e
d
tu
r
bi
ne
s
[
41]
.
T
he
ge
ne
r
a
to
r
c
a
n
be
c
la
s
s
if
ie
d
in
to
a
s
ync
hr
onous
a
nd
s
yn
c
hr
onous
ty
pe
s
ba
s
e
d
on
th
e
gr
id
s
uppl
y
r
e
qui
r
e
m
e
nt
f
or
th
e
a
s
ync
hr
onous
ty
pe
,
in
c
ont
r
a
s
t
to
s
ync
hr
onous
.
T
he
s
qu
ir
r
e
l
c
a
ge
in
duc
ti
on
ge
ne
r
a
to
r
a
nd
doubly
f
e
d
in
duc
ti
on
ge
ne
r
a
to
r
a
r
e
bot
h
c
a
te
gor
iz
e
d
a
s
a
s
ync
hr
onous
ty
pe
s
w
hi
le
th
e
pe
r
m
a
ne
nt
m
a
gne
t
is
c
la
s
s
if
ie
d
a
s
s
ync
hr
onous
.
A
c
c
or
di
ng
to
th
e
s
tu
dy
c
onduc
t
e
d
by
C
hong
e
t
al
.
[
41]
a
s
im
ul
a
ti
on
us
in
g
th
e
m
e
nt
io
ne
d
ge
ne
r
a
to
r
in
th
e
va
r
ia
ti
on
of
s
pe
e
d
(
0
-
9
m
/s
)
f
r
om
1
to
10
s
s
how
s
th
a
t
th
e
pe
r
m
a
ne
nt
m
a
gne
t
s
ync
hr
onous
ge
ne
r
a
to
r
pe
r
f
or
m
s
be
tt
e
r
a
t
lo
w
e
r
w
in
d
s
pe
e
d
(
w
hi
c
h
m
e
a
ns
be
tt
e
r
e
f
f
ic
ie
nc
y)
in
M
a
la
ys
ia
s
in
c
e
th
e
ot
he
r
two
ge
ne
r
a
to
r
s
m
us
t
dr
a
w
r
e
a
c
ti
ve
pow
e
r
f
r
om
th
r
e
e
-
pha
s
e
a
lt
e
r
na
ti
ng
c
ur
r
e
nt
(
A
C
)
s
our
c
e
,
w
hi
c
h
c
ons
um
e
s
e
ne
r
gy
be
f
or
e
th
e
ge
ne
r
a
to
r
s
ta
r
ts
w
or
k
in
g.
T
he
m
ode
l
of
e
a
c
h
ge
ne
r
a
to
r
ba
s
e
d
on
th
e
pr
io
r
s
tu
dy
c
a
n
be
s
how
n i
n F
ig
ur
e
s
14
-
16.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
dv A
ppl
S
c
i
I
S
S
N
:
2252
-
8814
M
ode
li
ng of s
ol
ar
and w
in
d e
ne
r
g
y
us
in
g m
at
r
i
x
l
abor
at
or
y
/
S
i
m
ul
in
k
:
a r
e
v
ie
w
(
N
ic
hol
a
s
P
r
anat
a)
115
F
ig
ur
e
11. S
ubs
ys
te
m
f
or
(
18)
pr
ov
id
e
d by r
e
s
e
a
r
c
he
r
F
ig
ur
e
12. S
ubs
ys
te
m
f
or
(
16)
pr
ov
id
e
d by r
e
s
e
a
r
c
he
r
F
ig
ur
e
13. W
in
d
tu
r
bi
ne
f
in
a
l
s
ys
te
m
pr
ovi
de
d by r
e
s
e
a
r
c
he
r
F
ig
ur
e
14. S
im
ul
in
k
m
ode
l
of
a
s
qui
r
r
e
l
c
a
ge
i
nduc
ti
on ge
ne
r
a
t
or
[
41]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8814
I
nt
J
A
dv A
ppl
S
c
i
,
V
ol
. 15, No. 1, M
a
r
c
h 2026
:
107
-
122
116
F
ig
ur
e
15. S
im
ul
in
k
m
ode
l
of
a
doubly
-
f
e
d i
nduc
ti
on ge
ne
r
a
to
r
[
41]
F
ig
ur
e
16. S
im
ul
in
k
m
ode
l
of
pe
r
m
a
ne
nt
m
a
gne
t
in
duc
ti
on ge
ne
r
a
to
r
[
41]
B
a
s
e
d
on
a
ll
th
os
e
c
ons
id
e
r
a
ti
ons
,
upon
de
s
ig
ni
ng
th
e
s
ys
t
e
m
of
w
in
d
e
n
e
r
gy,
de
s
ig
na
te
d
a
nd
w
e
ll
-
pl
a
nne
d
c
om
pone
nt
s
a
nd
s
e
le
c
ti
on
of
tu
r
bi
ne
s
a
nd
ge
ne
r
a
to
r
s
m
us
t
be
c
om
pa
ti
bl
e
w
it
h
th
e
w
in
d
s
pe
e
d
da
ta
of
th
e
c
hos
e
n
lo
c
a
ti
on,
in
w
hi
c
h
th
e
c
os
t
-
be
ne
f
it
a
na
l
ys
is
m
us
t
not
be
ove
r
lo
oke
d.
M
or
e
ove
r
,
th
e
c
ons
id
e
r
a
ti
on
f
or
a
gr
id
-
c
onne
c
te
d
s
ys
te
m
ba
s
e
d
on
th
e
os
c
i
ll
a
ti
on
f
a
c
to
r
s
th
a
t
m
a
y
ha
ppe
n
m
us
t
not
be
ove
r
lo
oke
d,
w
hi
c
h
is
a
ls
o
s
how
n
by
th
e
s
tu
dy
by
B
e
ha
bt
u
e
t
al
.
[
58]
c
om
pa
r
in
g
th
e
s
qui
r
r
e
l
c
a
ge
in
duc
ti
on
ge
ne
r
a
to
r
a
nd
a
doubly
f
e
d
in
duc
ti
on
ge
ne
r
a
to
r
in
F
ig
ur
e
s
17
a
nd
18.
T
he
r
e
s
ul
ts
of
th
e
s
tu
dy
s
how
th
a
t
th
e
pe
r
f
or
m
a
nc
e
of
a
doubly
f
e
d
in
duc
ti
on
ge
ne
r
a
to
r
is
be
tt
e
r
th
a
n
th
e
ot
he
r
dur
in
g
va
r
ia
bl
e
w
in
d
s
pe
e
d
s
w
e
ll
,
a
s
w
e
ll
a
s
a
c
ti
ve
-
r
e
a
c
ti
ve
po
w
e
r
c
ont
r
ol
c
a
pa
bi
li
ty
dur
in
g s
te
a
dy
-
s
ta
te
a
nd t
r
a
ns
ie
nt
ope
r
a
ti
ng c
ondi
ti
ons
.
3.6
.
M
od
e
l
e
val
u
at
io
n
T
he
e
va
lu
a
ti
on
of
P
V
a
nd
w
in
d
tu
r
bi
ne
m
ode
l
pe
r
f
or
m
a
nc
e
in
M
A
T
L
A
B
/S
im
ul
in
k
is
a
c
r
it
ic
a
l
pr
oc
e
s
s
th
a
t
f
oc
u
s
e
s
on
two
ke
y
a
s
pe
c
ts
:
a
c
c
ur
a
c
y a
nd
c
om
put
a
ti
ona
l
e
f
f
ic
ie
nc
y.
R
e
s
e
a
r
c
he
r
s
ha
v
e
de
ve
lo
pe
d
a
va
r
ie
ty
of
m
e
th
ods
to
e
ns
ur
e
th
a
t
th
e
ir
m
ode
ls
a
r
e
bot
h
r
e
li
a
bl
e
a
nd
pr
a
c
ti
c
a
l
f
or
a
w
id
e
r
a
nge
of
a
ppl
ic
a
ti
ons
, f
r
om
a
c
a
de
m
ic
r
e
s
e
a
r
c
h t
o r
e
a
l
-
ti
m
e
c
ont
r
ol
.
A
c
c
ur
a
c
y
is
th
e
pr
im
a
r
y
m
e
tr
ic
f
or
m
ode
l
va
li
da
ti
on
a
nd
is
ty
pi
c
a
ll
y
a
s
s
e
s
s
e
d
by
c
om
pa
r
in
g
s
im
ul
a
ti
on
r
e
s
ul
ts
w
it
h
r
e
a
l
-
w
or
ld
da
ta
.
T
h
e
m
os
t
c
om
m
on
a
p
pr
oa
c
h
is
e
xp
e
r
im
e
nt
a
l
va
li
da
ti
on,
w
he
r
e
th
e
out
put
of
a
S
im
ul
in
k
m
ode
l
is
c
om
pa
r
e
d
a
ga
in
s
t
da
ta
c
ol
le
c
te
d
f
r
om
a
phys
ic
a
l
P
V
a
r
r
a
y
or
w
in
d
tu
r
bi
ne
s
ys
te
m
und
e
r
th
e
s
a
m
e
ope
r
a
ti
ng
c
ondi
ti
ons
.
F
or
P
V
m
ode
l
s
,
th
is
in
vol
ve
s
u
s
in
g
m
e
a
s
ur
e
d
va
lu
e
s
of
s
ol
a
r
ir
r
a
di
a
nc
e
a
nd a
m
bi
e
nt
t
e
m
pe
r
a
tu
r
e
a
s
i
nput
s
a
nd c
om
pa
r
in
g t
h
e
s
im
ul
a
te
d volt
a
ge
, c
ur
r
e
nt
, a
nd powe
r
out
pu
t
a
ga
in
s
t
th
e
m
e
a
s
ur
e
d
va
lu
e
s
.
T
he
di
f
f
e
r
e
nc
e
i
s
of
te
n
qua
nt
if
ie
d
us
in
g
m
e
tr
ic
s
li
ke
r
oot
m
e
a
n
s
qu
a
r
e
e
r
r
or
(
R
M
S
E
)
or
pe
r
c
e
nt
a
ge
e
r
r
o
r
,
w
hi
c
h
pr
ovi
de
s
a
c
le
a
r
m
e
a
s
ur
e
of
th
e
m
ode
l'
s
f
id
e
li
ty
.
F
or
w
in
d
tu
r
bi
ne
s
,
m
ode
ls
a
r
e
va
li
da
te
d
by
c
om
pa
r
in
g
s
im
ul
a
te
d
pow
e
r
c
ur
ve
s
a
n
d
to
r
que
-
s
pe
e
d
c
ha
r
a
c
t
e
r
is
ti
c
s
w
it
h
da
t
a
f
r
om
r
e
a
l
tu
r
bi
ne
s
a
t
va
r
yi
ng w
in
d s
pe
e
ds
.
S
om
e
s
tu
di
e
s
a
l
s
o
us
e
th
e
or
e
ti
c
a
l
va
li
da
ti
on,
w
he
r
e
th
e
m
ode
l'
s
out
put
is
c
om
pa
r
e
d
a
ga
in
s
t
e
s
ta
bl
is
he
d
m
a
th
e
m
a
ti
c
a
l
pr
in
c
ip
le
s
or
e
xi
s
ti
ng,
hi
ghl
y
va
li
da
te
d
m
ode
ls
.
F
or
in
s
ta
nc
e
,
th
e
s
in
gl
e
-
di
ode
m
ode
l
f
or
P
V
c
e
ll
s
is
a
w
e
ll
-
unde
r
s
to
od
th
e
or
e
ti
c
a
l
ba
s
is
,
a
nd
ne
w
S
im
ul
in
k
m
ode
ls
a
r
e
of
te
n
va
li
da
te
d
by
s
how
in
g
th
a
t
th
e
ir
I
-
V
a
nd
P
-
V
c
ur
ve
s
m
a
tc
h
th
e
th
e
or
e
ti
c
a
l
c
u
r
ve
s
unde
r
s
ta
nda
r
d
te
s
t
c
ondi
ti
ons
[
59]
,
[
60]
.
T
hi
s
a
ppr
oa
c
h
i
s
pa
r
ti
c
ul
a
r
ly
us
e
f
ul
f
or
ve
r
if
yi
ng
th
e
f
unda
m
e
nt
a
l
phys
ic
s
of
th
e
m
ode
l
be
f
or
e
m
ovi
ng
on
to
m
or
e
c
om
pl
e
x
s
im
ul
a
ti
ons
.
W
hi
le
th
e
a
c
c
ur
a
c
y
of
in
di
vi
dua
l
c
om
pone
nt
s
,
s
uc
h
a
s
th
e
a
e
r
odyna
m
ic
bl
oc
k'
s
C
p or
t
he
e
le
c
tr
ic
a
l
ge
ne
r
a
to
r
'
s
out
put
, i
s
a
ls
o v
e
r
if
ie
d t
o e
ns
ur
e
th
e
ove
r
a
ll
m
ode
l'
s
c
or
r
e
c
tn
e
s
s
[
57]
.
Evaluation Warning : The document was created with Spire.PDF for Python.