I
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l J
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Adv
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I
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Vo
l.
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J
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0
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~
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h
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ce
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th
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th
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lar
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th
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ter
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p
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th
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wea
th
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tim
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f
d
a
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wh
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t
win
d
en
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g
y
f
lu
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with
th
e
en
v
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o
n
m
en
t.
T
h
e
p
r
o
d
u
ctio
n
o
f
elec
tr
icity
v
ar
ie
s
as
a
r
esu
lt,
wh
ich
m
a
y
lea
d
to
p
o
wer
s
u
p
p
ly
in
s
tab
ilit
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.
T
h
e
in
ter
m
itten
t
n
atu
r
e
o
f
s
o
lar
an
d
win
d
en
e
r
g
y
r
esu
lts
in
f
lu
c
tu
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s
in
s
u
p
p
ly
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d
d
em
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d
,
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r
eq
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cy
,
an
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v
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wh
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ca
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lead
to
g
r
id
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s
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T
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v
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c
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s
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cy
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s
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lu
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s
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m
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t,
en
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g
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to
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ag
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an
d
f
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I
n
th
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wo
r
k
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a
n
o
v
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h
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b
r
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co
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tr
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o
s
ed
to
en
h
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n
ce
th
e
g
r
id
s
tab
ilit
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
2
5
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I
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t J Ad
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Ap
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Vo
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14
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2
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2
5
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61
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T
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o
d
elin
g
an
d
c
o
n
tr
o
l
m
eth
o
d
s
f
o
r
a
g
r
id
-
co
n
n
ec
ted
win
d
-
p
h
o
to
v
o
ltaic
h
y
b
r
id
s
y
s
tem
[
4
]
.
T
o
ac
h
iev
e
o
p
tim
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
an
d
h
i
g
h
tr
a
ck
in
g
ef
f
icien
c
y
d
u
r
in
g
p
r
o
b
l
em
atic
o
p
er
atio
n
al
in
s
tan
ce
s
,
a
m
ax
im
u
m
p
o
we
r
p
o
in
t
tr
ac
k
in
g
(
MPPT)
ap
p
r
o
ac
h
b
ased
o
n
h
y
b
r
id
f
r
ac
ti
o
n
al
-
o
r
d
er
p
a
r
ticle
s
war
m
o
p
tim
i
z
atio
n
(
FP
SO)
[
5
]
h
as
b
ee
n
em
p
l
o
y
ed
.
Ag
r
awa
l
et.
a
l
[
6
]
A
g
r
id
-
co
n
n
ec
ted
s
o
lar
PV/win
d
h
y
b
r
id
i
n
Ku
m
asi,
Gh
an
a
t
h
e
tech
n
o
-
ec
o
n
o
m
ic
v
iab
ilit
y
o
f
a
s
y
s
tem
th
at
ca
n
m
an
ag
e
a
ty
p
ical
co
m
m
er
cial
lo
ad
m
u
s
t
b
e
ass
ess
ed
.
I
n
v
esti
g
atio
n
s
in
to
th
e
d
y
n
am
ic
m
o
d
elin
g
,
c
o
n
tr
o
l,
an
d
s
im
u
latio
n
o
f
elec
tr
ical
g
r
id
-
co
n
n
ec
ted
R
E
S
ar
e
ca
r
r
ied
o
u
t
in
[
7
]
.
Utilizin
g
a
n
ac
tiv
e
p
o
wer
f
ilter
(
APF
)
ca
n
r
aise
th
e
p
o
wer
s
tan
d
ar
d
an
d
m
itig
ate
r
ea
ctiv
e
p
o
wer
.
I
n
lo
w
an
d
m
ed
iu
m
-
v
o
ltag
e
elec
tr
i
ca
l
s
y
s
tem
s
,
a
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
(
SAPF
)
is
p
r
im
ar
ily
u
s
ed
to
lo
wer
th
e
h
ar
m
o
n
ics
a
n
d
co
r
r
ec
t
f
o
r
v
o
ltag
e
d
is
to
r
tio
n
s
lik
e
s
ag
s
.
Fli
ck
er
s
an
d
n
o
tc
h
es
SAPF
ca
n
lo
wer
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
b
y
in
f
u
s
in
g
th
e
lin
e'
s
v
o
ltag
e
to
r
ed
u
ce
in
ac
c
u
r
ate
in
f
o
r
m
atio
n
[
8
]
.
Sawle
et.
a
l
[
9
]
Of
f
er
a
r
ev
iew
o
f
th
e
s
o
f
twa
r
e
u
s
ed
f
o
r
ac
cu
r
ate
s
izin
g
,
co
n
tr
o
l
,
an
d
o
p
tim
izatio
n
g
u
id
elin
es f
o
r
h
y
b
r
id
s
y
s
tem
co
n
f
i
g
u
r
atio
n
,
m
o
d
elin
g
,
R
E
S,
an
d
c
o
m
b
in
atio
n
s
y
s
tem
s
.
T
h
e
h
y
b
r
id
f
u
zz
y
-
n
eu
r
al
co
n
tr
o
ller
[
1
0
]
is
ab
le
t
o
s
u
p
p
ly
u
n
iq
u
e
d
y
n
am
ical
s
tab
ilit
y
,
an
e
ar
lier
r
ate
o
f
co
n
v
er
g
en
ce
,
an
d
f
ewe
r
o
s
cillatio
n
s
in
th
e
lo
ca
tio
n
a
r
o
u
n
d
th
e
f
u
n
ctio
n
in
g
lo
ca
tio
n
M
PP
.
I
t
is
also
m
o
r
e
ef
f
ec
tiv
e
th
an
co
n
v
en
tio
n
al
tech
n
iq
u
es
at
tr
ac
k
in
g
g
lo
b
al
m
ax
im
a
u
n
d
er
a
v
ar
iety
o
f
s
ce
n
ar
io
s
.
I
n
d
if
f
e
r
en
t
cir
cu
m
s
tan
ce
s
an
d
with
d
if
f
er
en
t
q
u
a
n
titi
es
o
f
s
o
lar
r
ad
iatio
n
,
a
g
r
id
-
co
n
n
ec
ted
MA
T
L
A
B
m
o
d
el
is
s
tu
d
ied
[
1
1
]
.
Ultr
a
-
lift
co
n
v
er
ter
s
g
en
er
ate
an
in
cr
ed
ib
ly
h
ig
h
tr
an
s
f
er
o
f
o
u
tp
u
t g
ai
n
s
lev
er
ag
in
g
g
eo
m
etr
ic
ex
p
an
s
io
n
in
co
n
tr
ast
to
ea
r
lier
v
o
ltag
e
elev
ate
tech
n
iq
u
es
lik
e
class
ical
b
o
o
s
t
co
n
v
er
ter
s
an
d
s
u
p
e
r
lift
co
n
v
e
r
ter
s
.
I
n
ad
d
itio
n
,
it
is
s
m
aller
a
n
d
m
o
r
e
ef
f
ec
tiv
e
th
a
n
o
th
er
o
p
tio
n
s
.
T
h
e
o
p
er
atio
n
o
f
th
e
c
o
n
v
e
r
ter
is
ex
a
m
in
ed
in
u
ltra
-
lift
c
o
n
tin
u
o
u
s
c
o
n
d
u
ctio
n
m
o
d
e
[
1
2
]
.
D
escr
ib
es
a
w
ell
-
th
o
u
g
h
t
-
o
u
t
h
y
b
r
id
r
e
n
ewa
b
le
en
er
g
y
s
y
s
tem
th
at
co
m
b
in
es
win
d
an
d
s
o
lar
en
er
g
y
with
a
c
o
n
v
e
r
ter
an
d
b
atter
ies.
T
h
e
s
y
s
tem
h
as
b
ee
n
o
p
tim
ally
s
im
u
lated
b
y
em
p
lo
y
in
g
t
h
e
iter
ativ
e
h
e
u
r
is
tic
o
p
tim
izatio
n
g
en
etic
al
g
o
r
ith
m
(
I
HOGA
)
t
o
o
ls
.
Mo
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
f
o
r
d
r
i
v
es
an
d
p
o
we
r
co
n
v
er
ter
s
is
o
n
e
c
o
n
tr
o
l
t
ec
h
n
iq
u
e
t
h
at
h
as
d
r
awn
f
o
c
u
s
f
r
o
m
s
cien
tis
ts
th
r
o
u
g
h
o
u
t t
h
e
wo
r
ld
[
1
3
]
,
[
1
4
]
.
M
PC
a
n
d
a
n
i
n
v
e
r
t
e
r
'
s
f
i
n
it
e
c
o
n
t
r
o
l
s
e
t
m
o
d
el
p
r
e
d
i
c
ti
v
e
cu
r
r
e
n
t
c
o
n
t
r
o
l
(
FC
S
-
MPC
C
)
ar
e
t
h
e
c
o
r
e
c
o
m
p
o
n
e
n
t
s
o
f
a
n
o
v
e
l
M
P
PT
p
r
o
t
o
c
o
l
f
o
r
P
V
m
o
d
u
l
e
s
t
h
at
h
a
ve
b
e
e
n
r
e
l
e
a
s
e
d
[
1
5
]
.
R
ai
e
t
.
a
l
[
1
6
]
f
o
c
u
s
o
n
d
e
v
e
l
o
p
i
n
g
a
n
d
s
i
m
u
l
a
t
i
n
g
a
n
e
f
f
i
c
i
e
n
t
MP
P
T
s
o
l
a
r
p
h
o
t
o
v
o
l
t
a
i
c
s
y
s
t
e
m
.
I
n
o
r
d
e
r
t
o
i
n
c
r
e
a
s
e
t
h
e
p
o
w
e
r
l
e
v
e
l,
[
1
7
]
r
e
c
o
m
m
e
n
d
P
V
p
o
w
e
r
co
n
n
e
c
t
i
o
n
s
t
o
t
h
e
g
r
i
d
-
p
r
o
d
u
c
i
n
g
s
y
s
t
e
m
wi
t
h
A
PF
c
a
p
a
b
il
it
y
.
G
a
d
a
et
.
a
l
[
18]
p
r
o
v
i
d
e
s
a
d
e
t
a
il
e
d
o
v
e
r
v
i
e
w
o
f
t
h
e
c
o
m
p
o
n
e
n
t
s
o
f
t
h
e
s
y
s
te
m
,
i
n
c
l
u
d
i
n
g
t
h
e
i
n
c
r
e
m
e
n
t
a
l
c
o
n
d
u
c
t
a
n
c
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
IC
-
M
PP
T
)
a
l
g
o
r
i
t
h
m
,
t
h
e
in
v
e
r
t
e
r
,
t
h
e
s
o
l
a
r
g
e
n
e
r
at
o
r
,
an
d
t
h
e
p
r
o
p
o
r
t
i
o
n
a
l
-
i
n
t
e
g
r
a
l
(
PI
)
r
e
g
u
l
a
t
o
r
f
o
r
d
i
r
e
c
t
c
u
r
r
e
n
t
(
DC
)
b
u
s
v
o
l
t
a
g
e
c
o
n
t
r
o
l
.
U
t
i
l
i
zi
n
g
a
PI
a
s
a
d
i
s
t
r
i
b
u
t
i
o
n
s
t
a
t
ic
c
o
m
p
e
n
s
a
t
o
r
(
DS
T
A
T
C
O
M
)
,
c
a
s
c
a
d
e
d
h
-
b
r
i
d
g
e
m
u
lt
i
l
e
v
el
in
v
e
r
t
e
r
(
C
HB
M
L
I
)
t
o
m
i
n
i
m
i
ze
s
o
u
r
c
e
h
a
r
m
o
n
i
cs
o
f
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
s
y
s
t
e
m
P
I
c
o
n
t
r
o
l
l
e
r
'
s
s
o
u
r
c
e
c
u
r
r
e
n
t
i
s
ad
d
r
e
s
s
e
d
[
1
9
]
.
T
h
e
P
I
c
o
n
t
r
o
l
le
r
h
o
l
d
s
t
h
e
p
o
w
e
r
f
a
c
t
o
r
o
f
t
h
e
d
i
s
t
r
i
b
u
t
i
o
n
s
y
s
tem
a
t
u
n
i
t
y
,
m
i
n
i
m
i
z
e
s
t
h
e
o
r
ig
i
n
a
l
c
u
r
r
e
n
t
'
s
h
a
r
m
o
n
i
c
s
,
a
n
d
s
u
b
s
t
i
t
u
t
e
s
r
e
a
ct
i
v
e
p
o
w
e
r
.
I
n
[
2
0
]
,
th
r
ee
-
p
h
ase,
two
-
lev
el
DC
-
AC
in
v
er
ter
s
,
a
b
o
o
s
t
co
n
v
er
ter
c
o
n
v
e
r
tin
g
DC
to
DC
,
a
n
d
a
n
AC
lo
ad
s
y
s
tem
h
o
o
k
ed
u
p
to
th
e
g
r
id
au
th
o
r
ity
m
ec
h
an
is
m
h
av
e
b
ee
n
s
tu
d
ied
an
d
s
h
o
wn
.
I
n
o
r
d
er
to
ass
ess
tr
ait
s
a
g
r
id
-
c
o
n
n
ec
te
d
two
-
s
tag
e
p
h
o
to
v
o
ltaic
a
r
r
ay
with
an
ex
t
en
d
ed
K
alm
a
n
f
ilter
(
E
KF)
c
ap
ab
ilit
y
h
as
b
ee
n
r
ec
o
m
m
en
d
ed
in
[
2
1
]
.
Ah
m
ed
et.
a
l
[
2
2
]
d
is
cu
s
s
f
in
ite
s
et
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
FS
-
MPC
)
,
b
ased
MP
PT
f
o
r
PV
s
y
s
tem
s
.
Par
ticle
s
w
ar
m
o
p
tim
izatio
n
m
o
d
el
p
r
e
d
ictiv
e
co
n
t
r
o
l
(
PS
O
-
MPC
)
is
a
n
o
v
el
h
y
b
r
id
in
cr
em
en
tal
co
n
d
u
ctan
ce
-
b
a
s
ed
MPPT
co
n
tr
o
l
alg
o
r
it
h
m
f
o
r
g
r
id
-
co
n
n
ec
ted
s
o
lar
s
y
s
tem
s
[
2
3
]
.
L
ek
o
u
ag
h
et
et.
a
l
[
2
4
]
a
d
d
r
es
s
ed
th
e
ch
ain
o
f
PV
p
o
wer
g
en
er
atio
n
'
s
co
n
tr
o
l
p
r
o
b
lem
s
o
th
at
th
e
g
r
id
-
co
n
n
ec
t
ed
s
y
s
tem
g
ets
th
e
m
o
s
t
p
o
wer
with
o
u
t
b
ein
g
o
b
lig
ed
f
o
r
ex
t
r
a
s
tep
s
o
f
t
h
e
m
o
d
u
le.
I
n
[
2
5
]
,
a
p
r
ed
ictiv
e
m
o
d
el
is
th
e
co
n
tr
o
ller
.
Ad
v
is
ed
to
u
s
e
a
co
n
tr
o
l
-
b
ased
m
eth
o
d
to
o
p
tim
ize
e
n
e
r
g
y
co
n
s
er
v
atio
n
i
n
th
e
PV
p
o
wer
p
r
o
ce
s
s
.
B
y
m
o
d
if
y
in
g
t
h
e
d
ef
a
u
lt
co
s
t
f
u
n
cti
o
n
,
MPC
s
elec
ts
th
e
o
p
tim
al
co
n
tr
o
l
ac
tio
n
f
o
r
th
e
DC
/A
C
co
n
v
er
ter
at
ea
ch
s
am
p
le
m
o
m
en
t.
W
e
ca
n
in
cr
ea
s
e
g
r
id
p
o
wer
s
tab
ilit
y
an
d
ac
h
iev
e
p
r
ec
is
e
r
esu
lts
b
y
u
s
in
g
m
o
d
el
p
r
e
d
ictiv
e
an
d
p
r
o
p
o
r
tio
n
al
r
eso
n
a
n
t
co
n
t
r
o
l
s
tr
ateg
ies
in
s
im
u
latio
n
.
E
n
h
a
n
cin
g
g
r
id
s
tab
ilit
y
d
u
r
in
g
b
o
th
s
ea
s
o
n
al
an
d
n
o
n
-
s
ea
s
o
n
al
s
ea
s
o
n
s
b
y
u
s
in
g
a
m
u
ltit
u
d
e
o
f
en
e
r
g
y
s
o
u
r
ce
s
t
h
at
in
v
o
l
v
e
win
d
an
d
s
o
lar
en
er
g
y
s
y
s
tem
s
.
2.
H
YB
RID
O
F
P
H
O
T
O
VO
L
T
AIC
A
ND
WI
ND
A
h
y
b
r
i
d
en
e
r
g
y
s
y
s
tem
m
ad
e
u
p
o
f
a
win
d
tu
r
b
in
e
(
WT
)
an
d
PV
a
r
r
ay
is
d
ep
icted
i
n
Fig
u
r
e
1
.
C
o
n
s
eq
u
en
tly
,
th
e
s
o
lar
p
an
el
s
wo
u
ld
p
r
o
v
id
e
th
e
h
ig
h
est
p
r
o
d
u
ctio
n
th
r
o
u
g
h
o
u
t
th
e
s
u
m
m
er
,
wh
ile
th
e
WT
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Op
timiz
ed
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
d
s
ta
b
ilit
y
in
g
r
id
-
c
o
n
n
ec
ted
p
v
-
w
in
d
…
(
Ma
d
h
u
B
a
b
u
Th
ir
u
ve
ed
u
la
)
611
wo
u
ld
g
en
er
ate
m
o
r
e
in
th
e
win
ter
.
A
h
y
b
r
id
s
o
lar
PV
W
T
s
y
s
tem
i
s
th
e
m
o
s
t
s
u
cc
ess
f
u
l
lead
to
lev
er
ag
e
m
an
y
R
E
S
in
s
tead
o
f
ju
s
t
o
n
e
lo
ca
lly
ac
ce
s
s
ib
le
r
eso
u
r
ce
.
A
tin
y
elec
tr
ic
"h
y
b
r
id
"
s
y
s
tem
th
at
co
n
n
ec
ts
h
o
m
e
s
o
lar
PV
an
d
r
esid
en
ce
win
d
T
ec
h
n
o
lo
g
y
f
o
r
elec
tr
icity
h
as
m
an
y
b
en
ef
its
o
v
er
eit
h
er
s
y
s
tem
alo
n
e,
ac
co
r
d
in
g
to
m
an
y
r
e
n
ewa
b
le
en
er
g
y
(
RE
)
s
p
ec
ialis
ts
.
Fig
u
r
e
1
.
T
h
e
Hy
b
r
id
o
f
p
h
o
to
v
o
ltaic
an
d
win
d
s
y
s
tem
b
lo
ck
d
iag
r
am
3.
M
O
DE
L
P
RE
DIC
T
I
V
E
CO
NT
RO
L
A
s
o
p
h
is
ticated
co
n
tr
o
l
ap
p
r
o
ac
h
th
at
f
o
r
ec
asts
an
d
o
p
tim
iz
es
f
u
tu
r
e
b
eh
av
i
o
r
ac
r
o
s
s
a
f
in
ite
h
o
r
izo
n
u
s
in
g
a
m
o
d
el
o
f
th
e
s
y
s
tem
.
B
ec
au
s
e
it
ca
n
m
an
ag
e
m
u
lti
-
v
ar
iab
le
s
y
s
tem
s
with
r
estrictio
n
s
,
it
is
f
r
eq
u
en
tly
u
tili
ze
d
in
p
o
wer
s
y
s
tem
s
,
r
o
b
o
tics
,
p
r
o
ce
s
s
co
n
tr
o
l,
an
d
h
y
b
r
id
e
n
er
g
y
s
y
s
tem
s
.
T
h
is
is
a
s
u
m
m
ar
y
o
f
h
o
w
th
e
m
o
d
el
wo
u
ld
d
escr
ib
e
th
e
d
y
n
am
ics
o
f
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
,
WT
,
co
n
v
er
ter
s
,
a
n
d
g
r
id
in
ter
f
ac
e
with
in
th
e
s
ce
n
ar
io
o
f
a
h
y
b
r
i
d
p
h
o
t
o
v
o
ltaic
win
d
p
o
wer
s
y
s
tem
.
T
h
e
MPC
T
o
d
eter
m
in
e
th
e
o
p
tim
al
s
et
o
f
co
n
tr
o
l
ac
tio
n
s
o
v
er
th
e
p
r
ed
ictio
n
h
o
r
izo
n
,
th
e
MPC
s
o
lv
es
an
o
p
ti
m
izatio
n
p
r
o
b
lem
a
f
ter
d
ef
in
in
g
an
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
th
e
co
n
tr
o
l
in
p
u
t o
p
tim
izatio
n
.
T
o
g
u
ar
an
tee
th
e
s
y
s
tem
r
u
n
s
s
ec
u
r
ely
an
d
ef
f
ec
tiv
ely
,
lim
itatio
n
s
s
u
ch
as p
o
wer
r
estrictio
n
s
,
v
o
l
tag
e,
cu
r
r
e
n
t,
o
r
s
tate
b
o
u
n
d
s
ar
e
in
co
r
p
o
r
ated
.
4.
P
RO
P
O
RT
I
O
NA
L
RE
SO
N
ANT CO
N
T
RO
L
E
s
p
ec
ially
in
g
r
id
-
co
n
n
ec
ted
a
p
p
licatio
n
s
lik
e
win
d
an
d
PV
s
y
s
tem
s
,
b
ec
au
s
e
o
f
its
ef
f
icie
n
t
tr
ac
k
in
g
o
f
AC
s
ig
n
als.
T
h
e
p
r
o
p
o
r
tio
n
al
r
eso
n
a
n
t
(
PR
)
co
n
tr
o
ller
is
v
er
y
g
o
o
d
f
o
r
lo
wer
in
g
s
tead
y
er
r
o
r
s
i
n
AC
r
ef
er
en
ce
tr
ac
k
in
g
b
ec
a
u
s
e
it
ca
n
m
a
n
ag
e
t
h
e
p
e
r
io
d
ic
n
atu
r
e
o
f
AC
s
ig
n
als,
u
n
lik
e
a
co
n
v
e
n
tio
n
al
PI
co
n
tr
o
ller
,
wh
ic
h
is
b
etter
s
u
ited
f
o
r
DC
ap
p
licatio
n
s
.
T
h
e
p
r
o
p
o
r
tio
n
al
co
m
p
o
n
en
t
s
p
ee
d
s
u
p
th
e
s
y
s
tem
's
r
esp
o
n
s
e
to
d
is
r
u
p
tio
n
s
b
y
p
r
o
v
id
in
g
a
r
esp
o
n
s
e
p
r
o
p
o
r
tio
n
ate
to
th
e
d
is
cr
ep
an
c
y
b
et
wee
n
th
e
r
ea
l
an
d
r
ef
er
en
ce
s
ig
n
als.
I
n
p
a
r
ticu
lar
,
th
e
r
eso
n
an
t
ter
m
is
m
ad
e
to
m
o
n
ito
r
s
in
u
s
o
id
al
r
ef
e
r
en
ce
s
ig
n
als
at
a
s
et
f
r
eq
u
e
n
cy
,
u
s
u
ally
th
e
g
r
i
d
f
r
e
q
u
en
cy
,
s
u
ch
as
50
o
r
6
0
Hz.
F
ig
u
r
e
2
r
e
p
r
esen
ts
t
h
e
MA
T
L
AB
/Si
m
u
latio
n
o
f
a
p
r
o
p
o
r
tio
n
al
r
eso
n
an
t c
o
n
tr
o
ll
er
b
lo
ck
d
iag
r
am
.
4
.
1
.
M
a
t
hema
t
ica
l
r
epre
s
ent
a
t
io
n
A
PR
co
n
tr
o
ller
'
s
tr
an
s
f
er
f
u
n
c
tio
n
is
p
r
o
v
i
d
ed
b
y
(
1
)
.
(
)
=
+
.
2
+
0
2
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
:
60
9
-
61
7
612
W
h
er
e
is
th
e
p
r
o
p
o
r
tio
n
al
g
ain
,
is
th
e
r
eso
n
a
n
t
g
ain
,
a
n
d
ω
0
is
th
e
r
eso
n
a
n
t
f
r
e
q
u
en
c
y
(
u
s
u
ally
th
e
g
r
id
f
r
eq
u
e
n
cy
,
s
u
ch
as 2
π×
5
0
o
r
2
π×
6
0
r
ad
/s
)
.
Fig
u
r
e
2
.
Pro
p
o
r
tio
n
al
r
eso
n
a
n
t c
o
n
tr
o
ller
5.
SI
M
UL
A
T
I
O
N
O
U
T
C
O
MES
A
N
D
D
ISC
U
SS
IO
N
MA
T
L
AB
/S
im
u
lin
k
is
u
s
ed
to
m
o
d
el
th
e
e
n
tire
PV
an
d
wi
n
d
en
er
g
y
h
y
b
r
id
p
o
wer
s
y
s
te
m
with
an
au
to
n
o
m
o
u
s
r
ec
tifie
r
.
T
h
e
b
l
o
ck
s
ets
f
o
r
th
e
s
im
p
o
wer
s
y
s
tem
ar
e
u
s
ed
to
m
o
d
el
th
e
co
n
tr
o
l
tech
n
iq
u
es
r
eq
u
ir
ed
in
th
e
MA
T
L
AB
/Si
m
u
lin
k
s
u
r
r
o
u
n
d
in
g
s
to
g
en
er
ate
th
e
s
ig
n
al
-
en
ab
lin
g
tr
ac
k
in
g
.
I
n
th
is
,
we
co
n
tr
o
l
th
e
MPC
to
co
m
b
in
e
th
e
w
in
d
-
p
o
wer
e
d
p
o
wer
s
o
u
r
ce
a
n
d
p
h
o
to
v
o
ltaic
ass
ets.
R
u
n
t
im
e
in
s
ec
o
n
d
s
is
d
is
p
lay
ed
o
n
th
e
X
-
ax
is
in
Fig
u
r
e
3
,
wh
ile
th
e
Y
-
ax
is
d
is
p
la
y
s
th
e
v
o
ltag
e
o
f
th
e
g
r
id
s
u
p
p
ly
.
I
n
Fig
u
r
e
3
,
T
h
e
v
o
ltag
e
r
an
g
es
f
r
o
m
p
ea
k
to
s
u
m
m
it
at
2
5
,
0
0
0
V.
Ph
ase
s
h
if
ts
b
etwe
en
th
r
ee
p
h
ases
s
h
o
u
ld
b
e
1
2
0
d
e
g
r
ee
s
ac
r
o
s
s
.
R
u
n
tim
e
in
s
ec
o
n
d
s
is
d
is
p
lay
ed
o
n
th
e
X
-
ax
is
in
Fig
u
r
e
4
,
wh
ile
th
e
Y
-
a
x
is
d
is
p
lay
s
th
e
cu
r
r
en
t
o
f
th
e
g
r
id
s
u
p
p
ly
.
Fu
r
th
er
m
o
r
e,
t
h
e
g
r
id
'
s
s
u
p
p
ly
h
as
r
em
ain
e
d
u
n
ch
an
g
e
d
,
as
s
ee
n
b
y
th
e
v
o
lt
ag
e
s
o
u
r
ce
in
v
er
te
r
(
VSI
)
co
n
tr
o
ller
'
s
s
u
p
p
lied
cu
r
r
en
t
v
alu
e
is
th
e
s
o
le
way
t
o
s
witch
th
e
co
n
tr
o
ller
s
f
o
r
t
h
e
MPC
co
n
tr
o
ller
,
wh
ich
u
s
es win
d
an
d
p
h
o
t
o
v
o
l
taic
h
y
b
r
id
e
n
er
g
y
.
Fig
u
r
e
3
.
S
u
p
p
ly
v
o
ltag
e
f
r
o
m
g
r
id
Fig
u
r
e
4
.
S
u
p
p
ly
c
u
r
r
en
t
f
r
o
m
g
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Op
timiz
ed
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
d
s
ta
b
ilit
y
in
g
r
id
-
c
o
n
n
ec
ted
p
v
-
w
in
d
…
(
Ma
d
h
u
B
a
b
u
Th
ir
u
ve
ed
u
la
)
613
T
h
e
cu
r
r
en
t
an
d
v
o
ltag
e
o
f
tr
ain
s
1
an
d
3
as
d
eter
m
i
n
ed
b
y
th
e
MPC
co
n
tr
o
ller
a
r
e
d
is
p
lay
ed
in
Fig
u
r
es
5
an
d
6
.
B
u
s
1
'
s
v
o
lta
g
e
an
d
cu
r
r
en
t
ar
e
s
h
o
wn
in
F
ig
u
r
e
s
5
an
d
6
.
C
o
n
s
eq
u
e
n
tly
,
b
u
s
3
'
s
v
o
ltag
e
an
d
cu
r
r
en
t
ar
e
s
h
o
wn
in
Fig
u
r
es
7
an
d
8.
Fig
u
r
e
5
d
is
p
lay
s
o
s
cillatin
g
v
o
ltag
e
an
d
n
ea
r
ly
ze
r
o
cu
r
r
en
t
o
v
er
a
0
-
to
-
0
.
1
-
tim
e
i
n
ter
v
al.
Ad
d
itio
n
al
v
o
ltag
e
v
ar
iatio
n
s
f
r
o
m
0
to
0
.
0
0
1
ar
e
s
h
o
w
n
in
Fig
u
r
e
6
.
T
h
e
am
p
litu
d
e
o
f
th
e
v
o
ltag
e
ch
an
g
es
with
tim
e.
Similar
to
th
is
,
th
e
cu
r
r
en
t
v
ar
ies
f
r
o
m
0
to
0
.
0
0
1
.
T
h
e
MPC
co
n
tr
o
ller
will
m
o
v
e
h
ig
h
er
a
n
d
s
tay
f
ir
m
till
th
e
v
er
y
e
n
d
,
r
ea
ch
in
g
its
m
ax
im
u
m
d
u
r
in
g
th
e
R
an
d
Y
p
h
a
s
es,
b
ec
au
s
e
it d
o
es
n
o
t ta
k
e
in
to
co
n
s
id
er
atio
n
ch
a
n
g
es in
p
h
o
to
v
o
ltaic
-
win
d
(
P
V
-
win
d
)
in
teg
r
atio
n
.
Fig
u
r
e
5
.
B
u
s
1
in
v
o
ltag
e
u
s
in
g
MPC
co
n
tr
o
ller
Fig
u
r
e
6
.
B
u
s
1
in
cu
r
r
e
n
t u
s
in
g
MPC
co
n
tr
o
ller
Fig
u
r
e
7
.
B
u
s
3
v
o
ltag
e
u
s
in
g
MPC
co
n
tr
o
ller
Fig
u
r
e
8
.
B
u
s
3
c
u
r
r
en
t
u
s
in
g
MPC
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
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v
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,
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14
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2
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2
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s
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s
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v
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n
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u
s
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ized
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o
n
tr
o
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.
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h
er
e
ar
e
n
o
f
l
u
ctu
atio
n
s
o
r
c
h
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g
es
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am
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litu
d
e.
An
y
lo
a
d
ca
n
b
e
ef
f
icien
tly
h
an
d
led
b
y
it.
B
etwe
en
0
an
d
0
.
0
0
1
,
th
e
tim
e
v
ar
iatio
n
h
as
im
p
r
o
v
e
d
.
I
n
p
u
ts
an
d
o
u
tp
u
ts
ar
e
ef
f
icien
tly
ar
r
a
n
g
ed
b
y
t
h
e
o
p
tim
ized
m
o
d
el
p
r
ed
ictiv
e
an
d
p
r
o
p
o
r
tio
n
al
r
eso
n
an
t
co
n
tr
o
ller
,
wh
ich
also
g
en
er
ates
r
ef
in
e
m
en
ts
to
alter
iter
atio
n
s
an
d
ac
h
iev
e
th
e
b
est
p
o
s
s
ib
le
r
esu
lt.
B
o
th
co
n
tr
o
ller
s
will
h
av
e
co
m
p
ar
ab
le
ci
r
cu
it
b
r
ea
k
er
ti
m
es.
An
y
n
o
n
lin
ea
r
r
eq
u
ir
em
e
n
t is ac
co
m
m
o
d
ated
.
F
ig
u
re
9
.
B
u
s 3
v
o
lt
a
g
e
u
sin
g
o
p
ti
m
ize
d
M
P
C
with
P
R
c
o
n
tr
o
ll
e
rs
F
ig
u
re
1
0
.
Bu
s
3
c
u
rre
n
t
u
sin
g
o
p
ti
m
ize
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M
P
C
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h
P
R
c
o
n
tr
o
ll
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rs
T
h
r
o
u
g
h
a
n
u
m
b
er
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f
in
ter
f
ac
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,
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d
tr
ain
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g
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s
,
th
e
o
p
tim
ized
MPC
an
d
PR
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n
tr
o
ller
will
b
e
s
et
u
p
to
p
r
o
d
u
ce
th
e
in
ten
d
e
d
o
u
tco
m
es,
b
o
o
s
t
s
tab
ilit
y
,
an
d
h
an
d
le
q
u
ality
in
p
o
wer
is
s
u
es
t
h
e
v
o
ltag
e
o
f
th
e
DC
o
f
th
e
c
o
m
b
in
ed
win
d
an
d
p
h
o
to
v
o
lta
ic
s
y
s
tem
s
i
s
d
is
p
lay
ed
in
Fig
u
r
e
1
1
.
T
h
e
g
r
id
ca
n
b
e
co
n
n
ec
ted
an
d
in
teg
r
ated
with
th
is
co
m
b
in
atio
n
.
I
t
will
b
e
ab
le
to
in
cr
ea
s
e
g
r
id
v
o
ltag
e
wh
ile
m
ain
tain
in
g
p
o
wer
.
PR
an
d
o
p
tim
ized
MPC
co
n
tr
o
ller
s
ar
e
co
m
p
ar
ab
le
to
th
e
co
m
p
licated
co
n
tr
o
ller
an
d
alter
t
h
e
o
u
tco
m
es wh
en
a
b
lo
ck
th
at
c
o
n
tr
o
ls
cu
r
r
en
t is em
p
lo
y
e
d
.
Fig
u
r
e
1
1
.
P
air
ed
o
u
t
p
u
ts
o
f
w
in
d
an
d
PV (
DC
v
o
ltag
e)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Op
timiz
ed
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
d
s
ta
b
ilit
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in
g
r
id
-
c
o
n
n
ec
ted
p
v
-
w
in
d
…
(
Ma
d
h
u
B
a
b
u
Th
ir
u
ve
ed
u
la
)
615
6.
CO
NCLU
SI
O
N
T
h
is
r
esear
ch
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n
v
ey
s
h
o
w
well
th
e
o
p
tim
ized
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
ller
with
p
r
o
p
o
r
tio
n
al
r
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n
an
ce
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PR
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k
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cr
ea
s
e
th
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e
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f
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ical
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h
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n
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o
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a
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x
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za
tio
n
o
f
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E
S
wh
ile
m
ain
tain
in
g
r
eliab
le
g
r
id
in
te
g
r
atio
n
.
I
t
is
p
r
o
v
en
t
o
b
e
f
l
ex
ib
le,
ac
cu
r
ate,
a
n
d
ef
f
ec
tiv
e.
I
n
co
m
p
ar
is
o
n
,
tr
ad
itio
n
al
MPC
-
PR
co
n
tr
o
ll
er
s
s
tr
u
g
g
le
with
co
n
s
is
ten
t
p
er
f
o
r
m
a
n
ce
,
esp
ec
ially
wh
en
f
ac
e
d
with
th
e
s
y
s
tem
'
s
n
o
n
-
lin
ea
r
ity
an
d
u
n
p
r
ed
ictab
ilit
y
.
T
h
is
co
n
s
tr
ain
t
ca
n
r
esu
lt
in
in
ef
f
ec
tiv
e
co
n
tr
o
l,
p
o
ten
tially
d
estab
ilizin
g
th
e
g
r
id
.
Fu
tu
r
e
r
esear
ch
s
h
o
u
ld
f
o
cu
s
o
n
im
p
r
o
v
i
n
g
th
e
o
p
tim
ized
MPC
-
P
R
co
n
tr
o
ller
'
s
in
co
r
p
o
r
atio
n
o
f
R
E
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th
at
p
r
o
v
id
e
s
p
o
wer
to
t
h
e
g
r
i
d
,
ad
d
r
e
s
s
in
g
s
y
s
tem
d
y
n
am
ics an
d
ch
an
g
in
g
c
o
n
d
itio
n
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
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in
g
in
v
o
lv
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r
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DATA AV
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[
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]
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ttp
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[
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.
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a
so
k
a
n
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e
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m
a
il
.
c
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
Op
timiz
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co
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tr
o
l str
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teg
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ta
b
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p
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w
in
d
…
(
Ma
d
h
u
B
a
b
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Th
ir
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ve
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la
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617
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o
sa
r
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lo
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lec
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m
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.
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d
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ra
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a
d
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d
ia.
Sh
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
k
o
sa
ra
sra
v
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m
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il
.
c
o
m
.
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g
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c
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m
sh
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c
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k
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p
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In
d
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c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ro
u
t
h
u
a
k
a
sh
9
@g
m
a
il
.
c
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.