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Vo
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[
4
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–
[
8
]
.
T
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f
ast
r
esp
o
n
s
e
ch
ar
ac
ter
is
tic
s
f
o
r
v
o
lta
g
e
an
d
f
r
eq
u
en
c
y
co
n
tr
o
l
as
co
m
p
ar
e
d
to
th
e
s
ec
o
n
d
ar
y
co
n
tr
o
l
co
n
s
id
er
ed
in
[
8
]
.
T
h
e
an
alo
g
y
b
et
w
ee
n
i
n
v
er
ter
co
n
t
r
o
l
an
d
th
e
s
y
n
c
h
r
o
n
o
u
s
g
e
n
e
r
ato
r
co
n
tr
o
l
in
an
is
lan
d
ed
m
icr
o
g
r
id
is
s
tu
d
ied
in
d
etail
in
[
9
]
.
I
n
t
h
e
i
s
la
n
d
ed
m
o
d
e,
t
h
er
e
is
th
e
n
ec
e
s
s
i
t
y
o
f
h
a
v
i
n
g
a
r
e
f
er
en
ce
v
o
ltag
e
an
d
f
r
eq
u
e
n
c
y
s
i
g
n
a
ls
in
th
e
m
icr
o
g
r
id
in
v
er
ter
co
n
tr
o
l
[
1
0
]
.
T
h
e
o
p
er
atio
n
an
d
co
n
tr
o
l
o
f
th
e
in
v
er
ter
in
ter
f
ac
e
o
f
r
en
e
w
ab
le
-
b
ased
d
is
t
r
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
(
DE
R
s
)
,
lik
e
So
lar
P
h
o
to
v
o
lt
aic
(
P
V)
in
a
m
icr
o
g
r
id
,
is
a
r
ea
l
ch
allen
g
e,
esp
ec
iall
y
w
h
e
n
it c
o
m
e
s
to
m
ain
tai
n
i
n
g
b
o
th
m
icr
o
g
r
id
v
o
l
tag
e
a
n
d
f
r
eq
u
en
c
y
w
i
th
in
an
ac
ce
p
tab
le
r
an
g
e.
A
v
o
ltag
e
co
n
tr
o
l
m
et
h
o
d
b
ased
o
n
tr
ad
itio
n
al
d
r
o
o
p
co
n
tr
o
l
f
o
r
v
o
ltag
e
s
a
g
m
iti
g
atio
n
alo
n
g
w
i
th
v
o
lta
g
e
r
id
e
th
r
o
u
g
h
ca
p
ab
ilit
y
i
s
p
r
o
p
o
s
e
d
in
[
1
1
]
.
A
d
y
n
a
m
ic
v
o
lta
g
e
r
eg
u
lat
io
n
b
ased
o
n
ad
ap
tiv
e
co
n
tr
o
l
is
p
r
o
p
o
s
ed
in
[
1
2
]
,
[
1
3
]
.
Ho
w
e
v
er
,
th
er
e
ar
e
n
o
t
m
a
n
y
r
esear
c
h
es
w
o
r
k
s
p
er
f
o
r
m
ed
o
n
V
-
f
o
r
P
-
Q
co
n
t
r
o
l
u
s
i
n
g
s
o
lar
P
V
in
cl
u
d
in
g
MP
PT
c
o
n
tr
o
l
an
d
b
atter
y
s
to
r
a
g
e
in
m
icr
o
g
r
id
s
.
I
n
[
1
4
]
,
f
r
eq
u
en
c
y
r
e
g
u
la
tio
n
w
ith
P
V
in
m
icr
o
g
r
id
s
is
s
tu
d
ied
;
h
o
w
e
v
er
,
th
is
w
o
r
k
d
o
es
n
o
t
co
n
s
id
er
th
e
v
o
ltag
e
co
n
tr
o
l
o
b
j
ec
tiv
e
an
d
lack
s
b
atter
y
s
to
r
ag
e
in
th
e
m
icr
o
g
r
id
.
I
n
[
1
5
]
,
a
s
m
al
l
s
ca
le
P
V
is
co
n
s
id
er
ed
in
a
g
r
id
-
co
n
n
ec
ted
m
o
d
e
to
co
n
tr
o
l
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
s
y
s
t
e
m
.
Her
e,
t
h
e
co
n
tr
o
l
m
et
h
o
d
s
co
n
s
id
er
ab
c
-
d
q
0
tr
an
s
f
o
r
m
at
io
n
a
n
d
v
ice
v
er
s
a
w
h
ic
h
i
s
a
v
o
id
ed
in
t
h
e
p
r
es
en
t
p
ap
er
.
I
n
[
1
6
]
,
p
o
w
er
m
o
d
u
lati
o
n
o
f
s
o
lar
P
V
g
en
er
at
o
r
s
w
ith
a
n
elec
tr
ic
d
o
u
b
le
la
y
er
ca
p
ac
ito
r
as
en
er
g
y
s
to
r
ag
e
is
co
n
s
id
er
ed
f
o
r
f
r
eq
u
en
c
y
co
n
tr
o
l.
I
n
[
1
7
]
,
lo
ad
f
r
eq
u
e
n
c
y
co
n
tr
o
l
is
i
m
p
le
m
e
n
ted
in
m
icr
o
g
r
id
w
it
h
P
V
an
d
s
to
r
ag
e
;
h
o
w
e
v
er
,
th
i
s
w
o
r
k
also
lac
k
s
t
h
e
co
n
s
id
er
atio
n
o
f
a
v
o
ltag
e
co
n
tr
o
l o
b
j
ec
tiv
e.
T
h
e
v
o
ltag
e
an
d
f
r
eq
u
en
c
y
co
n
tr
o
l
w
it
h
s
o
lar
P
V
an
d
b
atter
y
in
m
icr
o
g
r
id
w
it
h
an
in
d
u
ctio
n
m
ac
h
in
e
is
in
v
est
ig
ated
i
n
[
1
8
]
;
h
o
w
e
v
er
,
t
h
is
w
o
r
k
d
o
es
n
o
t
ex
p
lai
n
t
h
e
tr
an
s
f
er
m
ec
h
an
is
m
o
f
co
n
tr
o
ls
to
co
n
s
id
er
th
e
b
atter
y
SO
C
co
n
s
tr
ain
t.
I
n
s
u
m
m
ar
y
,
t
h
e
p
r
ev
io
u
s
w
o
r
k
s
i
n
th
i
s
to
p
ic
eith
er
lack
th
e
in
co
r
p
o
r
atio
n
o
f
an
en
er
g
y
s
t
o
r
ag
e
co
m
p
o
n
en
t
o
r
th
e
v
o
lta
g
e
co
n
tr
o
l
o
b
j
ec
tiv
e
alo
n
g
w
i
t
h
f
r
eq
u
en
c
y
co
n
tr
o
l
o
r
th
e
in
co
r
p
o
r
atio
n
o
f
co
n
tr
o
l
tr
an
s
itio
n
i
n
d
i
f
f
er
e
n
t
s
ce
n
ar
io
s
.
T
h
e
p
r
esen
t
w
o
r
k
f
u
l
f
ill
s
th
e
s
e
g
ap
s
b
y
co
n
s
id
er
in
g
all
o
f
t
h
ese
o
b
j
ec
tiv
es
[
1
9
]
.
T
h
e
co
o
r
d
in
ated
c
o
n
tr
o
l
an
d
m
an
a
g
e
m
en
t
o
f
d
is
tr
ib
u
ted
g
e
n
er
ato
r
s
an
d
r
en
e
w
ab
le
en
er
g
y
r
eso
u
r
ce
s
to
g
et
h
er
w
ith
co
n
tr
o
llab
le
lo
ad
s
an
d
s
to
r
ag
e
s
y
s
te
m
s
ar
e
th
e
m
o
s
t
i
m
p
o
r
ta
n
t
an
d
ch
al
len
g
i
n
g
tas
k
s
i
n
m
icr
o
g
r
id
o
p
er
atio
n
[
2
0
]
,
[
2
2
]
.
Mic
r
o
g
r
id
ca
n
b
e
o
p
er
ated
in
g
r
id
-
co
n
n
ec
ted
m
o
d
e
o
r
in
is
lan
d
ed
m
o
d
e
[
2
3
]
.
T
y
p
icall
y
,
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
s
ar
e
r
ep
ea
ted
l
y
p
r
o
p
o
s
ed
t
o
s
u
p
p
o
r
t
f
r
eq
u
en
c
y
an
d
v
o
ltag
e
co
n
tr
o
l
o
f
m
icr
o
g
r
id
s
.
Du
e
to
th
e
in
ter
m
itte
n
c
y
i
n
r
en
e
w
ab
le
p
o
w
er
g
e
n
er
at
io
n
an
d
co
n
s
ta
n
tl
y
ch
an
g
i
n
g
lo
ad
d
e
m
a
n
d
,
ch
ar
g
i
n
g
a
n
d
d
is
ch
ar
g
in
g
o
f
v
ar
io
u
s
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
s
in
a
m
icr
o
g
r
id
n
ee
d
s
to
b
e
ap
p
r
o
p
r
iately
co
o
r
d
in
ated
.
I
n
is
la
n
d
ed
m
o
d
e,
th
e
m
ai
n
r
esp
o
n
s
ib
ilit
y
o
f
th
e
s
to
r
ag
e
is
to
p
er
f
o
r
m
e
n
er
g
y
b
alan
ce
.
I
n
g
r
id
-
co
n
n
ec
ted
m
o
d
e,
t
h
e
m
ain
g
o
al
i
s
to
p
r
ev
en
t
p
r
o
p
ag
atio
n
o
f
th
e
r
en
e
w
ab
le
s
o
u
r
ce
in
ter
m
itte
n
c
y
a
n
d
lo
ad
f
l
u
ct
u
atio
n
s
to
t
h
e
g
r
id
.
I
n
a
r
en
e
wab
le
p
o
w
er
ed
m
icr
o
g
r
id
,
a
s
i
n
g
le
t
y
p
e
o
f
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
s
ca
n
n
o
t
p
er
f
o
r
m
all
t
h
ese
ta
s
k
s
ef
f
icie
n
tl
y
.
Hen
ce
,
in
i
n
ter
m
itte
n
t
n
atu
r
e
o
f
r
en
e
w
ab
le
en
er
g
y
s
o
u
r
ce
s
,
d
e
m
a
n
d
s
in
v
o
lv
e
u
s
a
g
e
o
f
s
to
r
ag
e
w
it
h
h
ig
h
e
n
er
g
y
d
en
s
it
y
.
A
t
t
h
e
s
a
m
e
ti
m
e,
q
u
ick
f
l
u
ct
u
atio
n
o
f
lo
ad
d
em
a
n
d
s
r
eq
u
ir
es
s
to
r
ag
e
w
ith
h
ig
h
p
o
w
er
d
en
s
it
y
.
T
h
is
p
r
o
j
ec
t
p
r
o
p
o
s
es
a
d
is
tr
ib
u
ted
en
er
g
y
s
to
r
a
g
e
s
y
s
te
m
t
h
at
co
n
tai
n
s
b
o
th
h
i
g
h
e
n
er
g
y
d
e
n
s
it
y
s
to
r
ag
e
s
y
s
te
m
s
as
w
ell
as
h
i
g
h
p
o
w
er
d
en
s
it
y
s
to
r
a
g
e
s
y
s
te
m
s
to
m
ee
t
t
h
e
ev
er
g
r
o
w
i
n
g
r
eq
u
ir
e
m
e
n
t
s
.
T
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
v
alid
ated
b
y
v
ar
io
u
s
s
i
m
u
lat
io
n
r
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u
lts
u
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L
o
ad
)
A
ct
u
al
g
en
er
ated
r
ea
ctiv
e
p
o
wer
Av
er
ag
e
ac
ti
v
e
p
o
w
er
r
ef
er
e
n
ce
(
A
cti
v
e
L
o
ad
)
A
ct
u
al
g
en
er
ated
ac
ti
v
e
p
o
w
er
2.
P
RO
P
O
SE
D
M
E
T
H
O
D
2
.
1
.
So
la
r
P
V
M
o
delin
g
a
nd
Va
lid
a
t
io
n
T
h
e
co
m
m
o
n
l
y
ac
ce
p
ted
s
o
lar
ce
ll
m
o
d
el
is
a
o
n
e
d
io
d
e
m
o
d
el
[
1
9
]
.
T
h
is
w
o
r
k
u
s
e
s
t
h
e
s
i
n
g
le
d
io
d
e
m
o
d
el
o
f
t
h
e
s
o
lar
ce
ll
to
m
o
d
el
th
e
K
y
o
ce
r
a
K
C
2
0
0
GT
s
o
lar
ar
r
ay
,
w
h
ich
i
s
s
h
o
w
n
in
Fig
u
r
e
1.
T
h
e
I
-
V
ch
ar
ac
ter
is
tic
s
o
f
a
s
o
lar
ar
r
a
y
,
as sh
o
w
n
in
Fig
u
r
e
2
,
ar
e
r
ep
r
esen
t
ed
b
y
(
1
)
.
Fig
u
r
e
1
.
On
e
d
io
d
e
eq
u
iv
alen
t c
ir
cu
it o
f
So
lar
P
V
(
(
)
)
(
1
)
w
h
er
e
an
d
ar
e
th
e
p
h
o
to
cu
r
r
en
t
an
d
th
e
d
io
d
e
s
atu
r
atio
n
c
u
r
r
en
ts
r
esp
ec
ti
v
el
y
.
T
h
e
p
h
o
to
cu
r
r
en
t
o
f
th
e
P
V
ar
r
ay
d
ep
en
d
s
lin
ea
r
l
y
o
n
th
e
s
o
lar
ir
r
ad
iatio
n
a
n
d
th
e
ce
ll
te
m
p
er
atu
r
e.
W
h
er
e
an
d
ar
e
th
e
p
h
o
to
cu
r
r
en
t
an
d
th
e
d
io
d
e
s
atu
r
ati
o
n
cu
r
r
en
ts
r
esp
ec
t
i
v
el
y
.
T
h
e
p
h
o
to
cu
r
r
en
t
o
f
th
e
P
V
ar
r
ay
d
ep
en
d
s
lin
ea
r
l
y
o
n
th
e
s
o
lar
ir
r
ad
iatio
n
an
d
th
e
ce
ll
te
m
p
er
atu
r
e.
Vth
er
m
(
=N
s
k
T
/q
)
is
th
e
th
er
m
al
v
o
ltag
e
o
f
th
e
ar
r
a
y
,
Ns
b
ein
g
th
e
ce
ll
s
co
n
n
ec
ted
in
s
er
ies
f
o
r
g
r
ea
ter
o
u
tp
u
t
v
o
lta
g
e,
K
i
s
th
e
B
o
ltz
m
a
n
n
co
n
s
tan
t
(
1
.
3
8
0
6
5
0
3
X1
0
-
23
J
/K)
,
T
is
th
e
te
m
p
er
atu
r
e
o
f
th
e
p
-
n
j
u
n
ct
io
n
o
f
t
h
e
d
io
d
e
q
(
1
.
6
0
2
1
7
6
4
6
X
1
0
-
1
9
)
is
th
e
elec
tr
o
n
ch
ar
g
e
R
s
an
d
R
s
h
ar
e
th
e
eq
u
i
v
alen
t
s
e
r
ies
an
d
s
h
u
n
t
r
esi
s
ta
n
ce
s
o
f
t
h
e
ar
r
a
y
r
esp
ec
ti
v
el
y
a
n
d
is
t
h
e
id
ea
lit
y
f
ac
to
r
u
s
u
all
y
ch
o
s
en
i
n
t
h
e
r
a
n
g
e
1
.
Her
e
i
s
ta
k
en
a
s
1
.
T
h
e
p
h
o
to
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r
r
en
t
o
f
t
h
e
P
V
ar
r
a
y
d
ep
en
d
s
lin
ea
r
l
y
o
n
th
e
s
o
lar
ir
r
ad
ian
ce
an
d
th
e
ce
ll te
m
p
er
at
u
r
e,
as s
h
o
w
n
b
y
(
2
)
.
(
)
(
2
)
Her
e,
is
th
e
p
h
o
to
cu
r
r
en
t
at
th
e
s
tan
d
ar
d
test
co
n
d
itio
n
(
ST
C
,
2
5
0
C
an
d
1
0
0
0
W
/m
2
)
,
is
t
h
e
s
h
o
r
t
cir
cu
i
t
cu
r
r
en
t/te
m
p
er
at
u
r
e
co
ef
f
icie
n
t,
is
th
e
d
i
f
f
er
en
c
e
b
et
w
ee
n
th
e
ac
tu
al
a
n
d
n
o
m
i
n
al
te
m
p
er
at
u
r
e
in
Kel
v
i
n
,
G
i
s
t
h
e
ir
r
ad
iatio
n
o
n
th
e
d
e
v
ice
s
u
r
f
ac
e
an
d
is
t
h
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n
o
m
i
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al
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,
b
o
th
i
n
W
/
.
C
an
b
e
ca
lcu
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b
ased
o
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(
3
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Usi
n
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t
h
ese
f
u
n
d
a
m
e
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tal
eq
u
a
tio
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ar
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m
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r
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m
t
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d
ata
s
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th
e
P
V
m
o
d
el
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d
v
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f
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w
it
h
t
h
e
p
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el
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atash
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t.
T
h
e
I
-
V
ch
ar
a
cter
i
s
ti
cs
o
f
K
C
2
0
0
GT
f
o
r
d
if
f
er
en
t
ir
r
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ce
lev
el
s
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
694
IJ
PEDS
Vo
l.
7
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3
,
Sep
tem
b
er
2
0
1
6
:
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th
e
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ll
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p
er
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Fi
g
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a)
an
d
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b
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h
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m
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o
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el
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el.
T
h
e
p
ar
am
eter
s
o
f
t
h
e
P
V
p
an
el
u
n
d
e
r
s
tu
d
y
ar
e
s
h
o
w
n
in
T
ab
le
1
.
T
ab
le
1
.
P
V
P
an
el
P
a
r
am
eter
s
at
1
0
0
0
W
/
M
an
d
2
5
C
M
o
d
e
l
K
yo
c
e
r
a
K
C
2
0
0
G
T
P
MPP
2
0
0
W
V
MPP
2
6
.
3
0
V
I
M
P
P
7
.
6
1
A
V
OC
3
2
.
9
0
V
I
SC
8
.
2
1
A
Fig
u
r
e
2.
T
h
e
-
ch
ar
ac
ter
is
tic
s
o
f
K
y
o
ce
r
a
KC
2
0
0
GT
f
r
o
m
s
i
m
u
latio
n
w
i
th
(
a)
v
ar
y
in
g
ir
r
a
d
ian
ce
at
a
ce
ll
te
m
p
er
atu
r
e
o
f
2
5
C
an
d
(
b
)
v
ar
y
in
g
ce
ll te
m
p
er
atu
r
e
at
1
0
0
0
W
/m
.
T
h
e
P
V
s
y
s
te
m
u
n
d
er
s
t
u
d
y
f
o
r
th
e
p
r
o
p
o
s
ed
V
-
f
an
d
P
-
Q
co
n
tr
o
l
h
as
1
2
5
s
tr
in
g
s
w
it
h
e
ac
h
s
tr
in
g
h
av
i
n
g
4
s
er
ies
co
n
n
ec
ted
p
an
els.
T
h
e
Ma
x
i
m
u
m
P
o
w
er
P
o
in
t
(
MP
P
)
f
o
r
a
s
i
n
g
le
p
an
el
o
f
KC
2
0
0
GT
at
1
0
0
0
W
/
m
2
an
d
2
5
0
C
(
ST
C
)
is
2
0
0
W
.
Hen
ce
,
th
e
m
a
x
i
m
u
m
p
o
w
er
o
f
th
e
P
V
g
en
er
ato
r
at
ST
C
is
1
2
5
X
4
X
2
0
0
=1
0
0
k
W
.
B
u
t
th
e
MP
P
v
ar
ies
ac
co
r
d
in
g
to
th
e
c
h
a
n
g
e
in
ir
r
ad
ia
n
ce
le
v
el
an
d
ce
l
l
te
m
p
er
atu
r
e.
3.
RE
S
E
ARCH
M
E
T
H
O
D
3
.
1
.
P
V
Sy
s
t
e
m
Co
nfig
ura
t
io
n a
nd
Sy
s
t
e
m
De
s
cr
i
ptio
n
3
.
1
.
1
.
P
V
Sy
s
t
e
m
Co
nfig
ura
t
io
n
Fig
u
r
e
3
s
h
o
w
s
th
e
P
V
s
y
s
te
m
co
n
f
ig
u
r
atio
n
f
o
r
V
-
f
a
n
d
P
-
Q
co
n
tr
o
l
w
it
h
P
V
o
p
er
ati
n
g
at
MP
P
in
cl
u
d
in
g
t
h
e
b
atter
y
s
to
r
ag
e
b
ac
k
u
p
.
I
t
is
a
t
w
o
-
s
ta
g
e
co
n
f
i
g
u
r
atio
n
w
h
er
e
a
D
C
-
D
C
b
o
o
s
t
co
n
v
er
ter
i
s
u
s
ed
f
o
r
MP
PT
co
n
tr
o
l.
T
h
e
s
y
s
te
m
also
co
n
s
id
er
s
a
b
atter
y
b
ac
k
-
u
p
in
ca
s
e
o
f
e
m
er
g
en
cie
s
wh
ile
m
ain
tain
i
n
g
th
e
v
o
ltag
e
a
n
d
f
r
eq
u
en
c
y
o
f
th
e
m
icr
o
g
r
id
o
r
w
h
ile
tr
y
in
g
to
s
u
p
p
l
y
th
e
cr
itical
lo
ad
s
.
A
b
at
ter
y
is
co
n
n
ec
ted
i
n
p
ar
allel
to
th
e
P
V
to
in
j
ec
t
o
r
ab
s
o
r
b
ac
tiv
e
p
o
w
er
t
h
r
o
u
g
h
a
b
id
ir
ec
tio
n
al
DC
-
D
C
c
o
n
v
er
ter
.
W
h
e
n
th
e
b
atter
y
i
s
ab
s
o
r
b
in
g
p
o
w
er
,
th
e
co
n
v
er
ter
o
p
er
ates
in
th
e
b
u
ck
m
o
d
e
an
d
w
h
en
b
atter
y
is
in
j
ec
tin
g
p
o
w
er
to
th
e
g
r
id
,
it
o
p
er
ates
i
n
th
e
b
o
o
s
t
m
o
d
e.
T
h
e
o
p
er
atio
n
m
o
d
e
is
m
ai
n
tai
n
ed
th
r
o
u
g
h
t
h
e
co
n
t
r
o
l
s
ig
n
al
p
r
o
v
id
ed
to
th
e
co
n
v
er
ter
s
w
itc
h
es.
T
h
e
P
V
s
y
s
te
m
is
co
n
n
ec
te
d
to
th
e
g
r
id
th
r
o
u
g
h
a
co
u
p
lin
g
i
n
d
u
cto
r
.
T
h
e
co
u
p
lin
g
i
n
d
u
c
to
r
f
ilter
s
o
u
t
t
h
e
r
ip
p
les
in
th
e
P
V
o
u
tp
u
t
cu
r
r
en
t.
T
h
e
co
n
n
ec
tio
n
p
o
in
t
is
ca
lled
th
e
p
o
i
n
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
an
d
th
e
P
C
C
v
o
ltag
e
i
s
d
en
o
ted
as
.
T
h
e
r
est
o
f
t
h
e
s
y
s
te
m
i
n
Fi
g
u
r
e
3
d
en
o
tes
th
e
I
E
E
E
1
3
-
b
u
s
d
is
t
r
ib
u
tio
n
f
ee
d
er
w
h
ic
h
is
s
i
m
p
lif
ied
as
a
s
u
b
s
ta
tio
n
w
it
h
th
e
f
ee
d
er
eq
u
iv
alen
t
i
m
p
ed
an
ce
,
R
+j
w
.
T
h
e
P
V
s
o
u
r
ce
is
co
n
n
ec
ted
to
th
e
DC
li
n
k
o
f
t
h
e
in
v
er
ter
w
i
th
a
ca
p
ac
ito
r
.
T
h
e
P
V
is
th
e
ac
t
iv
e
p
o
w
er
s
o
u
r
ce
,
an
d
th
e
ca
p
ac
ito
r
is
th
e
r
ea
cti
v
e
p
o
w
er
s
o
u
r
ce
o
f
t
h
e
P
V
s
y
s
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3
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1
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3.
Descript
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f
I
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E
E
1
3
-
B
us
Dis
t
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T
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u
s
d
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test
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g
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4
.
I
t
co
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s
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b
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1
3
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1
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tio
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d
8
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s
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I
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t
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1
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p
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4
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6
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V
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y
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s
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T
1
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h
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n
e
m
o
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tr
a
n
s
f
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er
(
T
2
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h
ic
h
s
tep
s
d
o
w
n
4
.
1
6
k
V
to
4
8
0
V.
I
n
th
e
g
r
id
co
n
n
ec
ted
m
o
d
e,
th
e
s
u
b
s
tatio
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lo
ca
ted
atB
u
s
6
5
0
at
1
1
5
k
V
lev
el
is
co
n
s
id
er
ed
as
a
s
o
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r
ce
.
I
n
an
is
la
n
d
ed
m
icr
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s
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a
d
iesel
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en
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r
co
n
n
ec
ted
at
th
e
s
a
m
e
b
u
s
s
u
p
p
lies
th
e
m
icr
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g
r
id
w
it
h
a
f
i
x
ed
a
m
o
u
n
t
o
f
ac
ti
v
e
p
o
w
er
a
s
r
ef
er
en
ce
d
b
y
t
h
e
ce
n
tr
al
co
n
tr
o
ller
(
C
C
)
o
f
t
h
e
m
icr
o
g
r
id
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Fig
u
r
e
4
.
IEEE
-
1
3
b
u
s
d
is
tr
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u
tio
n
f
ee
d
er
3
.
2
.
M
P
P
T
a
nd
B
a
t
t
er
y
I
nte
g
ra
t
ed
V
-
F
a
nd
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-
Q
Co
nro
l M
et
ho
ds
3
.
2
.
1
.
M
P
P
T
a
nd
B
a
t
t
er
y
I
nt
eg
ra
t
ed
V
-
f
Co
ntr
o
l
M
et
ho
d
T
h
e
MPPT
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d
b
atter
y
i
n
te
g
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ated
V
-
f
co
n
tr
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l
d
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r
a
m
s
ar
e
s
h
o
w
n
in
Fi
g
u
r
e
s
5
an
d
6
,
r
esp
ec
tiv
el
y
.
T
h
e
co
n
tr
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l
co
m
p
r
is
e
s
o
f
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n
e
lo
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p
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r
MPPT
co
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tr
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l,
t
w
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d
if
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t
lo
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p
s
f
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co
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tr
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l
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atter
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lo
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p
1
in
Fig
u
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5
is
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MP
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l.
T
h
e
ac
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P
V
p
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t,
is
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p
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w
it
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t
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e
MP
P
r
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,
f
r
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m
t
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p
T
ab
le
1
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ir
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a
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s
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d
th
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r
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r
is
f
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,
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w
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tp
u
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d
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T
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l
lo
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g
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.
Her
e,
K
an
d
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ar
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co
n
tr
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ller
p
r
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th
is
co
n
tr
o
l lo
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p
.
(
)
+
∫
(
)
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
S
o
la
r
P
h
o
to
vo
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ic
Gen
era
to
r
s
w
ith
MPP
T
a
n
d
B
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S
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r
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g
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in
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g
r
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s
(
B
V
R
a
ja
n
n
a
)
707
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ee
d
b
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h
o
w
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n
t
h
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co
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l
d
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r
a
m
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n
Fi
g
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5
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lo
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p
2
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t
h
e
P
C
C
v
o
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i
s
m
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as
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r
m
s
v
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f
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alcu
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e
r
m
s
v
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e
is
c
o
m
p
ar
ed
to
a
v
o
ltag
e
r
e
f
er
en
ce
w
h
ich
co
u
l
d
b
e
a
v
o
ltag
e
s
p
ec
if
ied
b
y
t
h
e
u
tili
t
y
,
an
d
th
e
er
r
o
r
is
f
ed
to
a
P
I
co
n
tr
o
ller
.
T
h
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
is
co
n
tr
o
lled
s
o
th
at
it
is
in
p
h
as
e
w
it
h
t
h
e
P
C
C
v
o
ltag
e,
a
n
d
th
e
m
ag
n
it
u
d
e
o
f
th
e
i
n
v
er
ter
o
u
t
p
u
t
v
o
lta
g
e
is
co
n
tr
o
lled
s
o
th
at
th
e
P
C
C
v
o
ltag
e
is
r
eg
u
l
ated
at
a
g
i
v
en
le
v
el
.
T
h
e
co
n
tr
o
l sch
e
m
e
ca
n
b
e
s
p
ec
if
icall
y
e
x
p
r
ess
ed
as e
q
u
atio
n
(
1
2
)
.
*
∫
(
(
)
)
+
(
1
2
)
w
h
er
e
an
d
ar
e
th
e
co
n
tr
o
ller
g
ain
s
f
o
r
th
is
lo
o
p
.
I
n
(
1
2
)
,
1
h
as
b
ee
n
ad
d
ed
to
th
e
r
ig
h
t
-
h
a
n
d
s
id
e
s
u
c
h
th
at
w
h
en
th
er
e
is
n
o
in
j
ec
tio
n
f
r
o
m
th
e
P
V
g
e
n
er
ato
r
,
th
e
P
V
o
u
tp
u
t
v
o
lta
g
e
is
e
x
ac
t
l
y
t
h
e
s
a
m
e
as
t
h
e
ter
m
i
n
al
v
o
lta
g
e.
T
h
e
f
r
eq
u
en
c
y
co
n
tr
o
l
i
s
ca
r
r
ied
o
u
t
b
y
c
o
n
tr
o
llin
g
t
h
e
ac
ti
v
e
p
o
w
er
o
u
tp
u
t
a
t
t
h
e
in
v
er
ter
s
id
e
as
s
h
o
w
n
i
n
t
h
e
o
u
ter
m
o
s
t
lo
o
p
3
.
T
h
e
r
ef
er
en
ce
d
m
ic
r
o
g
r
id
f
r
eq
u
en
c
y
o
f
6
0
Hz
is
co
m
p
ar
ed
w
it
h
th
e
m
ea
s
u
r
ed
v
alu
e
a
n
d
th
i
s
er
r
o
r
is
f
ed
to
th
e
P
I
c
o
n
tr
o
ller
th
at
p
r
o
v
id
es
th
e
p
h
ase
s
h
i
f
t
co
n
tr
ib
u
tio
n
w
h
ic
h
s
h
i
f
t
s
t
h
e
v
o
ltag
e
w
a
v
ef
o
r
m
i
n
ti
m
e
s
ca
le
s
u
c
h
t
h
at
th
e
ac
tiv
e
p
o
w
er
i
n
j
ec
ted
w
ill
b
e
e
n
o
u
g
h
to
m
ai
n
tai
n
th
e
f
r
eq
u
e
n
c
y
at
6
0
Hz
n
o
m
i
n
al
v
alu
e.
T
h
e
eq
u
ati
o
n
f
o
r
th
i
s
co
n
tr
o
l is g
iv
e
n
b
y
(
1
3
)
.
(
)
∫
(
)
(
1
3
)
T
h
er
e
is
an
o
th
er
co
n
tr
o
ller
u
s
ed
in
t
h
e
s
a
m
e
lo
o
p
3
.
T
h
i
s
co
n
tr
o
ller
m
ai
n
tai
n
s
ac
tiv
e
p
o
w
er
b
alan
ce
b
et
w
ee
n
th
e
A
C
an
d
DC
s
id
es
o
f
t
h
e
i
n
v
er
ter
.
T
h
e
r
ef
er
e
n
ce
s
ig
n
al
f
o
r
is
o
b
tain
ed
f
r
o
m
t
h
e
d
y
n
a
m
icall
y
c
h
a
n
g
i
n
g
ac
ti
v
e
p
o
w
er
in
j
ec
tio
n
f
r
o
m
t
h
e
i
n
v
er
ter
at
th
e
AC
s
id
e
as
d
eter
m
i
n
ed
b
y
t
h
e
o
u
tp
u
t
of
.
T
h
em
ea
s
u
r
ed
A
C
s
id
e
ac
tiv
e
p
o
w
er
is
m
u
ltip
lied
b
y
a
f
ac
to
r
o
f
1
.
0
2
co
n
s
id
er
in
g
th
e
ef
f
icien
c
y
o
f
i
n
v
er
ter
as
9
8
%
s
u
c
h
th
at
t
h
e
DC
s
id
e
ac
ti
v
e
p
o
w
er
is
1
0
2
%
o
f
th
e
A
C
s
id
e
ac
tiv
e
p
o
w
er
.
T
h
e
DC
s
id
e
ac
ti
v
e
p
o
w
er
i
s
co
m
p
ar
ed
w
it
h
th
i
s
v
alu
e
o
f
A
C
s
i
d
e
p
o
w
er
an
d
t
h
e
er
r
o
r
is
f
ed
to
to
o
b
tain
th
e
p
h
ase
s
h
i
f
t c
o
n
tr
ib
u
t
io
n
f
r
o
m
t
h
is
lo
o
p
as
.
T
h
e
eq
u
atio
n
f
o
r
t
h
is
co
n
tr
o
l is g
i
v
e
n
b
y
(
1
4
)
.
∫
(
1
4
)
T
h
e
p
h
ase
s
h
i
f
t
co
n
tr
ib
u
tio
n
s
f
r
o
m
DC
a
n
d
AC
s
id
es,
an
d
ar
e
th
en
av
er
a
g
ed
as
g
iv
e
n
b
y
(
1
5
)
to
o
b
tain
th
e
f
i
n
al
p
h
a
s
e
s
h
if
t,
o
f
th
e
v
o
lta
g
e
w
av
e
f
o
r
m
,
w
h
ich
,
th
e
n
,
g
e
n
er
ates
t
h
e
v
o
lta
g
e
r
ef
er
en
ce
s
ig
n
al
f
o
r
th
e
in
v
er
ter
P
W
M
.
⁄
(
1
5
)
Her
e,
th
e
r
ea
s
o
n
b
eh
in
d
co
n
s
id
er
in
g
p
h
ase
s
h
i
f
t
co
n
tr
ib
u
ti
o
n
s
f
r
o
m
b
o
th
D
C
an
d
A
C
s
id
e
ac
tiv
e
p
o
w
er
is
to
co
n
tr
o
l
th
e
D
C
s
i
d
e
v
o
ltag
e
an
d
ac
h
iev
e
t
h
e
d
esire
d
v
alu
e.
B
y
m
a
k
in
g
an
d
clo
s
e
in
r
an
g
e
th
r
o
u
g
h
t
h
e
co
n
tr
o
ller
g
ai
n
s
,
it
ca
n
b
e
ass
u
r
ed
th
at
th
e
ac
ti
v
e
p
o
w
er
at
th
e
DC
an
d
A
C
s
id
es
is
b
alan
ce
d
.
T
h
is
,
co
u
p
led
w
it
h
th
e
v
o
lta
g
e
co
n
t
r
o
l
lo
o
p
,
ass
u
r
es
th
at
th
e
D
C
s
id
e
v
o
ltag
e
is
m
ai
n
tai
n
ed
at
th
e
v
al
u
e
d
esire
d
b
y
t
h
e
AC
s
id
e
v
o
ltag
e.
T
h
e
co
n
t
r
o
ls
s
h
o
w
n
i
n
t
h
e
d
iag
r
a
m
o
f
Fig
u
r
e
5
an
d
d
escr
ib
ed
ab
o
v
e
ar
e
also
in
te
g
r
ated
w
it
h
th
e
b
atter
y
p
o
w
er
co
n
tr
o
l
s
h
o
w
n
in
Fi
g
u
r
e
6
.
T
h
e
b
atter
y
i
s
i
n
co
r
p
o
r
ated
in
t
h
e
P
V
s
y
s
te
m
co
n
f
i
g
u
r
at
io
n
in
o
r
d
er
to
s
u
p
p
l
y
o
r
ab
s
o
r
b
ac
tiv
e
p
o
w
er
a
n
d
s
u
p
p
o
r
t
th
e
f
r
eq
u
en
c
y
co
n
tr
o
l
o
b
j
ec
tiv
e
w
i
t
h
t
h
e
P
V
g
en
er
ato
r
.
I
f
th
er
e
is
ab
u
n
d
an
t
s
o
lar
p
o
w
er
an
d
t
h
e
ac
tiv
e
p
o
w
er
r
eq
u
ir
ed
f
o
r
f
r
eq
u
en
c
y
co
n
tr
o
l
is
less
th
a
n
P
V
MP
P
,
th
en
t
h
e
b
atter
y
w
i
ll
b
e
ch
ar
g
e
d
.
I
f
th
er
e
is
n
o
t
e
n
o
u
g
h
s
o
lar
p
o
w
er
av
ailab
le
an
d
i
f
th
e
ac
t
i
v
e
p
o
w
er
r
eq
u
ir
ed
f
o
r
f
r
eq
u
e
n
c
y
co
n
tr
o
l
is
m
o
r
e
th
a
n
P
V
MP
P
,
th
e
n
th
e
b
atter
y
w
i
ll
s
u
p
p
l
y
t
h
e
d
e
f
icit
p
o
w
er
i
n
o
r
d
er
to
m
ai
n
tai
n
th
e
m
icr
o
g
r
id
f
r
eq
u
e
n
c
y
at
6
0
Hz.
Hen
ce
,
t
h
e
co
n
t
r
o
l
m
et
h
o
d
f
o
r
th
e
b
atter
y
ch
a
r
g
e/d
is
ch
ar
g
e
t
h
at
d
ep
en
d
s
o
n
th
is
r
eq
u
ir
e
m
e
n
t
is
d
ev
elo
p
ed
as
s
h
o
w
n
in
Fi
g
u
r
e
6
.
I
t
also
s
h
o
w
s
t
h
e
s
elec
tio
n
o
f
ch
ar
g
e
an
d
d
is
ch
ar
g
e
m
o
d
e
s
w
h
ic
h
h
a
n
d
l
e
th
e
b
atter
y
S
OC
co
n
s
tr
ain
t
an
d
w
il
l
b
e
d
escr
ib
ed
later
in
th
e
P
ar
t
B
o
f
th
is
s
ec
tio
n
.
I
n
Fi
g
u
r
e
6
,
t
h
e
r
ef
er
en
ce
p
o
w
er
to
t
h
e
b
atter
y
is
g
en
er
ated
d
y
n
a
m
ical
l
y
b
y
s
u
b
tr
ac
tin
g
t
h
e
in
v
er
ter
ac
ti
v
e
p
o
w
er
i
n
j
ec
tio
n
,
f
r
o
m
th
e
p
o
w
er
g
e
n
er
ated
b
y
P
V,
.
T
h
e
co
n
tr
o
ller
co
m
p
r
is
ed
o
f
a
P
I
co
n
tr
o
ller
,
w
h
ic
h
r
ec
ei
v
es
th
e
er
r
o
r
s
ig
n
al
o
b
tai
n
ed
af
te
r
s
u
b
tr
ac
ti
n
g
th
e
ac
t
u
al
b
atter
y
p
o
w
er
,
f
r
o
m
t
h
e
b
atter
y
r
e
f
er
en
ce
,
.
T
h
e
s
ig
n
al
o
b
tain
ed
f
r
o
m
is
th
e
n
co
m
p
ar
ed
w
it
h
a
tr
ia
n
g
u
lar
w
a
v
e
f
o
r
m
o
f
u
n
it
y
m
a
g
n
i
tu
d
e
to
g
en
er
ate
th
e
s
ig
n
al,
.
T
h
is
is
s
i
m
ilar
to
co
m
m
o
n
P
u
ls
e
W
id
th
Mo
d
u
lati
on
(
P
W
M)
in
in
v
er
ter
co
n
tr
o
ls
.
an
d
ar
e
th
e
p
r
o
p
o
r
tio
n
al
an
d
in
t
eg
r
al
g
ain
s
r
esp
ec
ti
v
el
y
.
T
h
e
e
q
u
atio
n
f
o
r
th
is
co
n
tr
o
l is g
i
v
e
n
b
y
(
1
6
)
.
(
)
∫
(
)
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
701
-
7
1
2
708
On
e
m
o
r
e
s
tep
is
co
n
s
id
er
ed
to
d
if
f
er
en
tia
te
th
e
ch
ar
g
i
n
g
an
d
d
is
ch
ar
g
in
g
m
o
d
e
o
f
th
e
b
at
ter
y
.
T
h
is
is
u
n
d
er
tak
en
b
y
co
m
p
ar
i
n
g
w
ith
.
I
f
,
th
e
b
atter
y
is
i
n
ch
ar
g
in
g
m
o
d
e,
h
en
c
e
,
th
e
s
i
g
n
al
o
b
tain
ed
f
r
o
m
t
h
e
P
W
M,
an
d
th
e
r
esu
lt
o
f
th
is
co
m
p
ar
i
s
o
n
is
p
ass
ed
th
r
o
u
g
h
a
lo
g
ical
AND
to
g
en
er
ate
a
s
w
itc
h
in
g
s
i
g
n
al
w
h
ic
h
ac
tiv
a
tes
t
h
e
B
u
c
k
m
o
d
e
o
f
th
e
DC
-
D
C
co
n
v
er
ter
.
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f
th
e
co
n
d
it
io
n
is
f
alse,
(
i.e
.
,
)
,
th
e
o
p
p
o
s
ite
o
f
th
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s
ig
n
al
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d
is
p
ass
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r
o
u
g
h
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lo
g
ical
A
N
D
to
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e
n
er
ate
a
s
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u
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atter
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I
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4.
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CUSS
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er
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c
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atter
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te
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g
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r
e
7
.
Fig
u
r
e
7
.
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h
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li
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m
o
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h
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atter
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y
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te
m
f
o
r
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r
o
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n
4
.
1
.
1
.
T
est
o
f
V
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F
Co
ntr
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l
in M
icr
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g
rid
M
o
de:
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r
th
e
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ith
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ce
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ase
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ir
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1
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d
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tr
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ller
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ain
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iesel
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lled
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iesel
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ig
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r
e
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(
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ated
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iesel
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ated
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Fig
u
r
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s
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ip
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u
r
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8
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Fig
u
r
e
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(
h
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w
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ic
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s
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atter
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ase
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
694
IJ
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2
710
(a)
(b)
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c)
(
d)
(
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(
f
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(
g
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(
h
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F
ig
u
r
e
8.
R
esu
lts
o
f
co
o
r
d
in
at
ed
V
-
f
co
n
tr
o
l
w
it
h
So
lar
P
V
in
clu
d
i
n
g
MP
PT
co
n
tr
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l a
n
d
b
atter
y
co
n
tr
o
l
5.
CO
NCLU
SI
O
N
T
h
e
co
n
tr
ib
u
tio
n
o
f
t
h
is
p
ap
er
ca
n
b
e
s
u
m
m
ar
ized
as f
o
llo
w
s
:
a.
T
h
is
p
ap
er
p
r
o
p
o
s
es a
n
d
p
r
esen
ts
co
o
r
d
in
ated
s
tr
ate
g
ie
s
o
f
V
-
f
co
n
tr
o
l a
n
d
P
-
Q
co
n
tr
o
l,
r
es
p
ec
tiv
el
y
,
f
o
r
Mic
r
o
g
r
id
s
w
i
th
P
V
g
e
n
er
ato
r
an
d
b
atter
y
s
to
r
ag
e.
b.
I
n
th
e
co
n
tr
o
l
s
tr
ate
g
ie
s
,
th
e
P
V
g
en
er
ato
r
is
o
p
er
ated
at
MP
P
,
an
d
th
e
b
atter
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s
to
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ag
e
ac
ts
as
a
b
u
f
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er
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n
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er
to
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j
ec
t
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s
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r
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e
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h
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g
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o
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e
b
atter
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.
T
h
e
p
ap
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tr
ib
u
tes
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n
d
e
m
o
n
s
tr
ati
n
g
th
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co
n
tr
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l
s
tr
ateg
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es
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h
e
f
f
ec
ti
v
e
co
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d
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atio
n
b
et
w
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n
I
n
v
er
ter
V
-
f
(
Or
P
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Q)
co
n
tr
o
l,
MP
PT
c
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n
tr
o
l,
an
d
en
er
g
y
s
to
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ag
e
co
n
tr
o
l.
a.
T
h
e
p
r
o
p
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s
ed
co
n
tr
o
l
s
tr
ateg
y
also
p
r
o
v
id
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a
s
m
o
o
t
h
tr
a
n
s
it
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n
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f
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id
e
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Q
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tr
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l
in
g
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n
n
ec
ted
Mo
d
e
to
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f
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n
tr
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i
s
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d
ed
m
o
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e.
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h
is
i
s
t
h
e
m
o
s
t
es
s
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