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C
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p
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A
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Vin
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Sin
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C
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I
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titu
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T
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New
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I
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d
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g
h
v
in
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@
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m
1.
I
NT
RO
D
UCT
I
O
N
R
en
ewa
b
le
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g
y
g
en
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eq
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d
d
ec
r
ea
s
e
d
ep
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d
en
cy
o
n
th
er
m
al
[
1
]
.
I
n
t
h
is
p
ap
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d
y
n
am
ic
s
tab
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y
s
tu
d
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s
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v
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m
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with
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ased
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Su
ch
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eq
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Use
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also
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m
W
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S/P
VS [
2
]
.
T
h
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co
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tr
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d
o
p
tim
izatio
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o
f
a
h
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/d
c
n
etwo
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k
ar
e
s
till
an
o
p
en
p
r
o
b
lem
[
3
]
-
[
5
]
.
T
h
e
co
o
r
d
in
ate
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co
n
tr
o
l
ar
ch
it
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tu
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p
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d
ev
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h
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o
l
th
e
s
y
s
te
m
f
r
eq
u
en
cy
an
d
v
o
ltag
e
[
6
]
,
[
7
]
.
I
n
v
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r
ter
s
f
o
r
m
cr
itical
eq
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ip
m
en
t
i
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co
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tr
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a
r
ch
itectu
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f
co
n
tr
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llin
g
p
o
w
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f
r
o
m
r
en
ewa
b
les
[
8
]
.
Ma
n
y
s
tu
d
ies
h
av
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b
ee
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ca
r
r
ied
o
u
t
in
ac
tiv
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d
r
ea
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p
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wer
co
n
tr
o
l
o
f
h
y
b
r
id
p
o
wer
s
y
s
tem
[
9
]
-
[
1
1
]
.
T
h
er
ef
o
r
e,
g
en
e
r
atio
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m
ix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
Micr
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terco
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etw
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k
(
V
in
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u
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in
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)
327
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win
d
-
s
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lar
-
b
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g
as
co
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ld
b
e
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ev
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p
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h
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m
all
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s
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s
e
o
f
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ab
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Var
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k
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T
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PMSG
with
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a
n
y
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tag
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[
1
2
]
,
[
1
3
]
.
W
in
d
tu
r
b
in
e
with
I
n
d
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Gen
er
ato
r
r
eq
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ir
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tiv
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o
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is
s
u
p
p
lied
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p
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cito
r
b
a
n
k
o
r
s
tatic
co
m
p
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s
ato
r
[
1
4
]
.
PVS
d
c
p
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u
tp
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t
d
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p
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e
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ts
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ax
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tr
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k
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(
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s
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tial.
T
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m
o
s
t
two
c
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m
o
n
m
a
x
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m
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m
p
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wer
p
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s
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P&
O)
an
d
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
(
I
C
)
[
1
5
]
,
[
1
6
]
.
Mic
r
o
g
r
id
is
en
er
g
y
s
y
s
tem
wh
ich
is
lo
ca
lly
co
n
tr
o
lled
a
n
d
u
s
es
v
ar
io
u
s
ca
teg
o
r
ies
o
f
r
en
ewa
b
le
en
er
g
y
ass
ets
(
s
o
lar
,
win
d
,
b
io
m
ass
,
h
y
d
r
o
an
d
o
ce
an
)
,
g
en
er
ato
r
s
(
b
io
g
as,
d
iesel
an
d
g
aso
lin
e
)
,
en
er
g
y
s
to
r
ag
e
s
y
s
tem
s
(
b
atter
ies,
f
l
y
wh
ee
l,
f
u
el
ce
ll
an
d
th
er
m
a
l)
,
lo
ad
s
(
r
esid
en
tial
an
d
in
d
u
s
tr
ial)
an
d
co
n
t
r
o
l
eq
u
ip
m
en
t
[
1
7
]
.
A
m
icr
o
g
r
i
d
m
o
d
el
o
p
tim
izin
g
lo
ca
l
r
en
ewa
b
le
en
er
g
y
r
eso
u
r
ce
s
f
o
r
o
n
-
g
r
id
ar
ea
was
in
v
esti
g
ated
f
o
r
e
n
er
g
y
c
o
s
t
s
av
in
g
an
d
r
e
d
u
ctio
n
i
n
C
O
2
em
is
s
io
n
[
1
8
]
.
T
h
e
p
r
o
b
lem
o
f
in
ter
co
n
n
ec
tin
g
m
icr
o
g
r
id
s
is
m
ajo
r
ar
ea
o
f
c
o
n
ce
r
n
b
ec
au
s
e
b
ein
g
s
m
all
s
y
s
tem
,
f
r
eq
u
e
n
cy
,
v
o
ltag
e
an
d
p
h
ase
an
g
le
m
ay
v
ar
y
with
n
o
m
in
al
d
is
tu
r
b
an
c
e.
Sin
ce
th
e
m
icr
o
g
r
id
c
o
n
s
is
t
o
f
v
ar
i
o
u
s
g
en
e
r
atin
g
s
o
u
r
c
es,
d
u
e
to
d
if
f
er
en
t
p
o
wer
s
h
ar
in
g
ca
p
ac
ity
th
e
ch
an
ce
s
o
f
m
icr
o
g
r
id
f
ailu
r
e
ar
e
h
ig
h
er
in
ca
s
e
o
f
f
au
lt
o
r
h
ea
v
y
ch
a
n
g
e
in
lo
ad
o
r
in
d
r
o
p
i
n
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
[
1
9
]
,
[
2
0
]
.
Ma
in
ca
u
s
e
o
f
co
llap
s
e
is
v
er
y
f
ast
r
esp
o
n
s
e
o
f
in
v
er
ter
-
b
ased
s
y
s
tem
an
d
s
lo
w
r
esp
o
n
s
e
o
f
p
r
im
e
m
o
v
er
b
ased
r
ec
ip
r
o
ca
tin
g
en
g
in
e.
I
n
s
u
ch
ca
s
e
co
n
tr
o
ll
er
is
d
esig
n
ed
an
d
tu
n
ed
in
s
u
ch
a
way
s
o
th
at
ef
f
ec
t
is
n
u
llified
v
er
y
f
ast.
Fra
ctio
n
al
o
r
d
er
p
r
o
p
o
r
ti
o
n
a
l
in
teg
r
al
co
n
tr
o
ller
(
FOPI
)
(
PI
α
)
b
ased
co
n
tr
o
ller
is
o
n
e
o
f
th
e
s
o
lu
tio
n
s
.
Mo
r
e
f
lex
ib
ilit
y
was
ex
ten
d
ed
i
n
tr
ad
itio
n
al
n
o
tio
n
o
f
PID
co
n
tr
o
ller
s
with
th
e
c
o
n
t
r
o
ller
g
ai
n
s
d
ef
in
e
th
e
f
r
ac
tio
n
al
d
if
f
e
r
en
tial
an
d
in
te
g
r
als
as
d
esig
n
v
a
r
iab
les
[
2
1
]
-
[
2
3
]
.
T
h
e
f
r
ac
tio
n
al
-
o
r
d
e
r
s
y
s
tem
ca
n
b
e
ap
p
r
o
x
im
ate
d
b
y
m
an
y
m
eth
o
d
s
[
2
4
]
.
B
ased
o
n
ap
p
r
o
x
im
atio
n
,
th
e
FOMCON to
o
lb
o
x
was u
s
ed
f
o
r
cr
ea
tin
g
th
e
f
r
ac
tio
n
al
-
o
r
d
er
s
y
s
tem
[
2
5
]
,
[
2
6
]
.
T
h
e
r
est
o
f
th
e
p
a
p
er
is
o
r
g
an
i
ze
d
as
f
o
llo
ws:
Sectio
n
-
2
g
iv
e
s
th
e
d
etail
o
f
t
h
e
s
y
s
tem
co
n
s
id
er
ed
f
o
r
in
v
esti
g
atio
n
.
Sectio
n
3
co
m
p
r
is
es
o
f
d
escr
ip
tio
n
r
eg
a
r
d
in
g
m
o
d
elin
g
o
f
m
icr
o
g
r
id
s
an
d
its
as
s
o
ciate
d
lin
e.
Sectio
n
4
d
is
cu
s
s
ab
o
u
t
th
e
s
im
u
latio
n
o
f
th
e
s
y
s
tem
an
d
r
esu
lt
s
.
Fin
ally
,
s
ec
tio
n
-
5
is
th
e
co
n
clu
s
io
n
o
f
t
h
e
p
ap
er
u
n
d
er
co
n
s
id
er
atio
n
.
2.
SYST
E
M
CO
NS
I
DE
R
E
D
F
O
R
I
NVE
ST
I
G
AT
I
O
N
I
n
th
e
s
y
s
tem
m
o
d
elin
g
two
cl
u
s
ter
s
v
iz.
MG
-
1
a
n
d
MG
-
2
ar
e
co
n
s
id
er
ed
f
o
r
s
tab
ilit
y
s
tu
d
y
.
Sy
s
tem
d
etails
with
FOPI
tu
n
ed
p
ar
a
m
eter
s
,
lo
w
v
o
ltag
e
AC
(
L
VA
C
)
lin
e
d
ata,
MG
-
1
d
ata
a
n
d
MG
-
2
d
ata
ar
e
g
iv
e
n
in
T
ab
le
1
,
T
ab
le
2
,
T
ab
le
3
a
n
d
T
ab
le
4
.
B
o
th
th
e
clu
s
ter
s
ar
e
r
ated
at
1
5
0
0
k
W
.
I
t
is
ass
u
m
ed
th
at
th
e
p
o
we
r
is
f
lo
win
g
f
r
o
m
MG
-
1
t
o
MG
-
2
.
MG
-
1
co
n
s
is
ts
o
f
W
E
S
r
ated
at
1
0
0
0
k
W
an
d
b
io
g
as
g
en
er
atio
n
s
y
s
tem
(
B
G1
)
with
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
r
ated
at
5
0
0
k
W
.
Data
o
f
B
G1
an
d
W
E
S
ar
e
g
iv
en
in
T
ab
le
5
an
d
T
ab
le
6
.
MG
-
1
h
as
lo
ca
l
lo
ad
o
f
1
0
0
0
k
W
an
d
also
tr
a
n
s
m
itt
in
g
1
0
0
k
W
to
MG
-
2
co
n
s
id
er
in
g
l
o
s
s
o
f
5
k
W
th
r
o
u
g
h
L
VAC
n
etwo
r
k
i.e
to
tal
g
e
n
e
r
atio
n
o
f
MG
-
1
is
1
1
0
5
k
W
.
MG
-
2
co
n
s
is
ts
o
f
PVS
r
ated
at
6
5
0
k
W
,
B
io
g
as
g
en
er
atio
n
s
y
s
tem
(
B
G2
)
r
ate
d
at
5
0
0
k
W
an
d
g
r
id
r
ated
at
3
5
0
k
W
.
Data
o
f
B
G2
,
PVS
an
d
g
r
id
ar
e
g
iv
e
n
in
T
ab
le
7
,
T
a
b
le
8
a
n
d
T
a
b
le
9
.
L
VAC
n
etwo
r
k
co
n
s
is
ts
o
f
3
-
p
h
ase
o
v
er
h
ea
d
Ar
iel
B
u
n
c
h
e
d
ca
b
le
(
AB
C
)
.
T
h
e
s
ize
o
f
ca
b
le
co
n
s
id
er
ed
is
1
5
0
m
m
2
alu
m
in
u
m
co
n
d
u
cto
r
r
ated
at
4
1
5
Vo
lts
.
T
h
e
o
b
je
ctiv
e
o
f
th
e
L
VAC
n
etwo
r
k
is
to
s
u
p
p
ly
c
o
n
s
tan
t
p
o
wer
o
f
1
0
0
k
W
to
MG
-
2
.
Su
p
p
ly
f
r
o
m
lim
ited
g
r
id
is
c
o
n
s
id
er
ed
co
n
s
tan
t
an
d
is
s
u
p
p
ly
i
n
g
to
p
r
io
r
ity
lo
ad
s
o
n
ly
.
I
n
th
e
lim
ited
g
r
i
d
t
h
e
v
o
ltag
e
as
well
as
th
e
an
g
l
e
at
th
at
b
u
s
is
k
e
p
t
co
n
s
tan
t.
T
ab
le
1
.
FOPI
d
ata
C
o
n
t
r
o
l
l
e
r
MG
-
1
MG
-
2
P(K
p
)
I
(
K
i
)
α
P(K
p
)
I
(
K
i
)
α
F
O
P
I
1
6
.
9
8
7
2
.
5
7
8
0
.
4
5
2
.
7
4
5
4
.
5
7
2
0
.
8
F
O
P
I
2
-
6
.
2
9
6
-
8
.
5
7
8
0
.
5
-
1
.
4
2
5
-
7
.
8
8
7
0
.
7
1
F
O
P
I
3
1
.
9
4
5
1
0
.
6
7
6
0
.
8
1
0
.
3
5
5
2
.
7
6
5
0
.
2
F
O
P
I
4
-
2
.
3
7
8
-
5
6
4
7
0
.
7
9
.
5
6
7
-
3
0
9
7
0
.
9
Th
e
M
G
-
1
a
n
d
M
G
-
2
mi
c
r
o
g
r
i
d
h
a
s
b
e
e
n
m
o
d
e
l
e
d
c
o
n
s
i
d
e
r
i
n
g
t
o
t
a
l
c
o
n
t
r
a
c
t
d
e
ma
n
d
=
1
7
2
5
k
W
.
M
a
x
i
m
u
m
d
i
f
f
e
r
e
n
t
i
a
t
e
d
d
e
ma
n
d
a
t
d
i
v
e
r
si
t
y
f
a
c
t
o
r
o
f
0
.
5
8
=
1
7
2
5
*
0
.
5
8
=
1
0
0
0
k
W
(
a
p
p
r
o
x
.
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
2
6
–
336
328
T
ab
le
2
.
L
VAC
d
ata
v
a
l
u
e
v
a
l
u
e
v
a
l
u
e
v
a
l
u
e
R
=
0
.
5
6
2
p
u
X
=
0
.
2
6
8
p
u
K
1
a
c
=
1
.
7
5
8
K
2
a
c
=
-
1
.
1
3
7
K
3
a
c
=
1
.
1
3
2
K
4
a
c
=
0
.
2
5
2
K
5
a
c
=
-
1
.
1
3
2
K
6
a
c
=
-
1
.
1
3
7
K
7
a
c
=
1
.
5
1
4
K
8
a
c
=
-
1
.
3
8
1
K
9
a
c
=
0
.
5
3
1
K
10
a
c
=
0
.
5
3
1
K
11
a
c
=
-
1
.
7
3
3
K
12
a
c
=
-
1
.
5
1
4
T
ab
le
3
.
Gen
e
r
atio
n
p
a
r
am
eter
s
o
f
MG
-
1
S
o
u
r
c
e
s
R
a
t
e
d
C
a
p
a
c
i
t
y
(
k
W
)
G
e
n
e
r
a
t
i
o
n
(
k
W
)
P
a
r
t
i
c
i
p
a
t
i
o
n
F
a
c
t
o
r
B
i
o
g
a
s
5
0
0
3
5
0
0
.
2
3
3
3
W
ES
1
0
0
0
7
5
5
0
.
5
0
2
0
To
t
a
l
1
5
0
0
1
1
0
5
D
FS1
=
∂
∂
f
=
∗
=
0
.
0
1
3
3
3
p
u
k
W
/
H
z
.
K
FS1
=
1
/
1
=
7
5
H
z
/
p
u
k
W
.
T
FS1
=
1
8
s
e
c
.
D
VS1
=
∂
∂
V
=
∗
=
∗
=
0
.
6
7
7
7
p
u
k
V
A
R
/
p
u
k
V
.
K
VS1
=
1
/
1
=
1
.
5
p
u
k
V
/
p
u
k
V
A
R
.
T
VS1
=
0
.
0
0
4
se
c
.
p
f
=
0
.
8
6
6
,
P
L
1
=
0
.
6
6
6
7
p
u
T
ab
le
4
.
Gen
e
r
atio
n
p
a
r
am
eter
s
o
f
MG
-
2
S
o
u
r
c
e
s
R
a
t
e
d
C
a
p
a
c
i
t
y
(
k
W
)
G
e
n
e
r
a
t
i
o
n
(
k
W
)
P
a
r
t
i
c
i
p
a
t
i
o
n
F
a
c
t
o
r
G
r
i
d
3
5
0
3
0
0
0
.
2
B
i
o
g
a
s
5
0
0
3
0
0
0
.
2
PV
6
5
0
3
0
0
0
.
2
To
t
a
l
1
5
0
0
9
0
0
+
1
0
0
(
L
i
n
e
)
D
FS2
=
∂
∂
f
=
∗
=
0
.
0
1
3
3
p
u
k
W
/
H
z
.
K
FS2
=
1
/
2
=
7
5
H
z
/
p
u
k
W
.
T
FS2
=
6
sec
.
D
V2
=
∂
∂
V
=
∗
=
∗
=
0
.
6
6
6
7
p
u
k
V
A
R
/
p
u
k
V
.
K
V2
=
1
/
2
=
1
.
5
p
u
k
V
/
p
u
k
V
A
R
.
T
V2
=
0
.
0
0
4
s
e
c
.
p
f
=
0
.
8
6
6
,
P
L2
=
0
.
6
6
6
7
p
u
T
ab
le
5
.
B
io
g
as (
B
G1
)
d
ata
v
a
l
u
e
v
a
l
u
e
P
BG
1
=
0
.
2
3
3
3
p
u
k
W
Q
BG
1
=
0
.
1
3
4
6
p
u
k
V
A
R
X
d
=
1
p
u
X
d
’
=
0
.
1
5
p
u
T
BG
1
=
0
.
0
1
sec
T
BG
2
=
0
.
0
2
sec
T
BG
5
=
0
.
0
1
4
s
e
c
T
BG
6
=
0
.
0
4
sec
T
BG
7
=
0
.
0
3
6
s
e
c
K
AB
=
2
0
0
T
EB
=
2
.
0
s
e
c
K
FB
=
0
.
5
T
AB
=
0
.
0
5
s
e
c
K
EB
=
1
T
FB
=
1
.
0
se
c
K
1BG
1
=
0
.
1
5
K
2BG
1
=
0
.
8
3
1
K
3BG
1
=
6
.
5
1
5
K
4BG
1
=
-
6
.
8
4
4
T
d0
‘
=
5
.
0
se
c
T
G
BG
1
=
0
.
7
5
sec
T
ab
le
6
.
W
E
S
d
ata
v
a
l
u
e
v
a
l
u
e
P
WES
=
0
.
5
0
3
p
u
Q
WES
=
0
.
2
9
0
p
u
X
T
IN
V
=
0
.
5
p
u
T
d
=
0
.
0
0
5
s
e
c
K
W
E
S
1
=
2
.
2
6
5
K
W
E
S
2
=
2
.
2
6
5
K
W
E
S
3
=
0
.
4
3
3
K
W
E
S
4
=
0
.
5
K
W
E
S
5
=
-
0
.
5
K
W
E
S
6
=
-
0
.
5
K
W
E
S
7
=
1
.
9
5
3
K
W
E
S
8
=
-
1
.
7
3
5
T
ab
le
7
.
B
io
g
as (
B
G2
)
d
ata
v
a
l
u
e
v
a
l
u
e
P
BG
1
=
0
.
2
p
u
k
W
Q
B
G
1
=
0
.
1
1
5
4
p
u
k
V
A
R
X
d
=
1
p
u
X
d
’
=
0
.
1
5
p
u
T
BG
1
=
0
.
0
1
sec
T
BG
2
=
0
.
0
2
sec
T
BG
5
=
0
.
0
1
4
s
e
c
T
BG
6
=
0
.
0
4
sec
T
BG
7
=
0
.
0
3
6
s
e
c
K
AB
=
2
0
0
T
EB
=
2
.
0
s
e
c
K
FB
=
0
.
5
T
AB
=
0
.
0
5
s
e
c
K
EB
=
1
T
FB
=
1
.
0
se
c
K
1BG
1
=
0
.
1
5
K
2BG
1
=
0
.
8
3
1
K
3BG
1
=
6
.
5
1
5
K
4BG
1
=
-
6
.
8
4
4
T
d0
‘
=
5
.
0
se
c
T
G
BG
1
=
0
.
7
5
sec
T
ab
le
8
.
PVS
d
ata
v
a
l
u
e
v
a
l
u
e
P
PV1
=
0
.
2
p
u
Q
PV1
=
0
.
1
1
5
4
p
u
X
T
P
V
=
0
.
8
p
u
T
PV1
=
0
.
0
0
5
se
c
K
PV1
=
1
.
4
6
7
K
PV2
=
1
.
4
6
7
K
PV3
=
0
.
1
6
9
K
PV4
=
0
.
2
K
PV5
=
-
0
.
2
K
PV6
=
-
0
.
2
K
PV7
=
1
.
2
3
8
K
PV8
=
-
1
.
0
3
T
ab
le
9
.
Gr
id
d
ata
v
a
l
u
e
v
a
l
u
e
P
G
=
0
.
2
p
u
Q
G
=
0
.
1
1
5
4
p
u
K
1G
=
-
2
.
8
7
5
K
2G
=
0
.
2
K
3G
=
0
.
2
K
4G
=
-
2
.
6
8
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Micr
o
g
r
id
s
d
yn
a
mic
s
ta
b
ilit
y
i
n
terco
n
n
ec
ted
th
r
o
u
g
h
l
o
w
vo
lta
g
e
A
C
n
etw
o
r
k
(
V
in
it K
u
ma
r
S
in
g
h
)
329
3.
M
O
DE
L
I
NG
O
F
I
N
T
E
RCO
NNEC
T
E
D
M
I
CRO
G
RID
S WIT
H
L
VAC
N
E
T
WO
RK
At
s
tead
y
s
tate,
th
e
p
o
we
r
tr
a
n
s
f
er
r
ed
th
r
o
u
g
h
th
e
in
ter
co
n
n
ec
tio
n
r
em
ain
s
s
am
e
at
all
c
o
n
d
itio
n
s
.
An
y
ch
an
g
e
in
d
em
an
d
o
r
g
e
n
er
atio
n
is
tak
en
ca
r
e
lo
ca
lly
b
y
th
e
r
esp
ec
tiv
e
m
icr
o
g
r
id
s
y
s
tem
.
T
h
e
s
y
s
tem
lin
e
d
iag
r
am
is
s
h
o
wn
i
n
Fig
u
r
e
1
.
Fig
u
r
e
1
.
L
i
n
e
d
iag
r
a
m
o
f
MG
-
1
an
d
MG
-
2
co
n
n
ec
ted
t
h
r
o
u
g
h
AC
lin
e
T
h
e
p
o
wer
b
alan
ce
e
q
u
atio
n
s
ar
e
g
iv
en
as (
1
)
(
2
)
(
3
)
an
d
(
4
)
.
PB
G1
+
P
W
E
S
=
PL1
+Ps
(
1
)
QB
G1
+
QW
E
S
=
QL
1
+Q
S
(
2
)
PB
G2
+
PP
V
S+PG+
Pr
=
PL2
(
3
)
QB
G2
+
QPVS+
QG+
Qr
=
PL2
(
4
)
Fo
r
s
m
all
ch
an
g
e
in
p
o
wer
(
1
)
(
2
)
(
3
)
an
d
(
4
)
ca
n
b
e
r
ewr
itte
n
as (
5
)
(
6
)
(
7
)
a
n
d
(
8
)
.
∆PB
G1
+
∆P
W
E
S
=
∆PL
1
+∆
Ps
(
5
)
∆Q
B
G1
+
∆Q
W
E
S
=
∆
QL
1
+∆
Qs
(
6
)
∆PB
G2
+
∆PPV
S+∆Pr
=
∆
PL2
(
7
)
∆Q
B
G2
+
∆Q
PVS+∆
QG
-
∆Q
r
=
∆
PL2
(
8
)
T
h
e
ch
an
g
e
in
ac
tiv
e
p
o
wer
g
en
er
ated
a
n
d
ab
s
o
r
b
ed
b
y
lo
ad
will
r
esu
lt
in
th
e
s
y
s
tem
f
r
eq
u
en
c
y
d
ev
ia
n
ce
wh
ich
ca
n
b
e
ex
p
r
ess
ed
in
s
d
o
m
ain
as
(
9
)
an
d
(
1
0
)
.
∆F1
(
s
)
=
K
p
1
1
+
1
[
PB
G1
(
s
)
+
PW
E
S (
s
)
−
Ps
(
s
)
-
PL1
(
s
)
]
(
9
)
∆F2
(
s
)
=
K
p
2
1
+
2
[
PB
G2
(
s
)
+
PP
VS
(
s
)
+
PG(
s
)
+
Pr(
s
)
-
PL2
(
s
)
]
(
1
0
)
Similar
ly
,
f
o
r
r
ea
ctiv
e
p
o
wer
t
h
e
eq
u
atio
n
ca
n
b
e
wr
itten
as
(
1
1
)
an
d
(
1
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
2
6
–
336
330
∆V
1
(
s
)
=
K
v
1
1
+
1
[
QB
G1
(
s
)
+
QW
E
S
(
s
)
−
QS(
s
)
-
QL
1
(
s
)
]
(
1
1
)
∆V
2
(
s
)
=
K
v
2
1
+
2
[
QB
G2
(
s
)
+
QPVS(
s
)
+
QG(
s
)
+
Qr
(
s
)
-
QL
2
(
s
)
]
(
1
2
)
P
BG
,
P
WES
,
P
PV
S
,
P
G
,
P
S
,
P
r
an
d
P
L
ar
e
ac
tiv
e
p
o
wer
o
f
b
io
g
as,
win
d
,
s
o
lar
,
g
r
i
d
,
lin
e
s
e
n
d
in
g
e
n
d
p
o
wer
,
lin
e
r
ec
eiv
in
g
en
d
p
o
wer
an
d
lo
ad
.
Q
BG
,
Q
WES,
Q
P
VS
,
Q
G
,
Q
S
,
Q
r
an
d
Q
L
ar
e
r
ea
ctiv
e
p
o
wer
b
io
g
as,
win
d
,
s
o
lar
,
g
r
id
,
lin
e
s
en
d
in
g
en
d
p
o
wer
,
lin
e
r
ec
eiv
i
n
g
e
n
d
p
o
wer
an
d
lo
ad
.
∆F1
an
d
∆F2
ar
e
ch
an
g
e
in
f
r
eq
u
e
n
cy
o
f
MG
-
1
an
d
MG
-
2
r
esp
ec
tiv
ely
.
K
p
,
T
p
,
K
v
an
d
T
v
ar
e
p
o
wer
s
y
s
tem
g
ain
an
d
tim
e
co
n
s
tan
t
f
o
r
ch
an
g
e
in
ac
tiv
e
p
o
wer
an
d
r
e
ac
tiv
e
p
o
wer
.
3
.
1
.
M
o
delin
g
o
f
WE
S a
nd
P
VS
co
nn
ec
t
ed
inv
er
t
er
T
h
e
W
E
S
in
clu
d
es
tu
r
b
in
e
t
o
g
eth
er
with
PMSG
wh
ich
g
en
er
ates
p
o
wer
h
a
v
in
g
f
r
eq
u
en
cy
a
n
d
v
o
ltag
e
v
ar
iab
le
in
n
atu
r
e
d
ep
en
d
in
g
u
p
o
n
win
d
s
p
ee
d
.
T
h
e
g
en
e
r
ato
r
s
id
e
AC
-
DC
p
o
wer
elec
tr
o
n
ics
co
n
v
er
ter
tr
a
n
s
m
its
th
e
p
o
wer
o
f
th
e
PMSG to
th
e
lo
ad
s
id
e
DC
-
AC
co
n
v
er
ter
th
r
o
u
g
h
a
c
o
u
p
lin
g
ca
p
ac
ito
r
in
b
etwe
en
th
e
co
n
v
er
ter
s
.
T
h
e
PVS
co
m
p
r
is
es
Ph
o
to
v
o
ltaic
C
ell
co
u
p
led
with
B
u
ck
B
o
o
s
t
C
o
n
v
er
ter
.
T
h
e
PV
s
id
e
DC
-
DC
co
n
v
er
ter
tr
an
s
m
its
th
e
p
o
wer
o
f
th
e
PV
c
ell
to
th
e
lo
ad
s
id
e
DC
-
AC
co
n
v
er
ter
th
r
o
u
g
h
a
co
u
p
lin
g
ca
p
ac
ito
r
in
b
etwe
e
n
.
T
h
e
co
u
p
lin
g
ca
p
ac
ito
r
h
e
lp
s
in
m
ain
tain
in
g
co
n
s
tan
t
v
o
ltag
e
ac
r
o
s
s
th
e
co
n
v
er
to
r
s
.
Sm
all
s
ig
n
al
m
o
d
el
o
f
t
h
e
W
E
S
an
d
PVS
is
estab
lis
h
ed
u
s
in
g
p
o
wer
o
u
t
p
u
t
eq
u
atio
n
s
f
r
o
m
th
e
I
n
v
er
ter
m
o
d
el
g
iv
en
as
(
1
3
)
a
n
d
(
1
4
)
.
=
(
+
)
(
1
3
)
=
(
+
)
−
(
1
4
)
Fo
r
s
m
all
v
ar
iatio
n
in
th
e
o
u
tp
u
t p
o
wer
o
f
th
e
I
n
v
er
te
r
(
1
3
)
a
n
d
(
1
4
)
ca
n
b
e
wr
itten
as (
1
5
)
an
d
(
1
6
)
I
N
V
in
v
1
in
v
2
in
v
3
in
v
+
in
v
4
Δ
P
(
s
)
=
K
Δ
δ
(
s
)
+
K
Δ
θ
(
s
)
+
K
Δ
V
(
s
)
K
Δ
V
(
s
)
(
1
5
)
I
N
V
in
v
5
in
in
v
6
in
v
7
in
+
in
v
8
Δ
Q
(
s
)
=
K
Δ
δ
(
s
)
+
K
Δ
θ(
s
)
+
K
Δ
V
(
s
)
K
Δ
V
(
s
)
(
1
6
)
T
h
e
p
ar
am
eter
s
/co
n
s
tan
ts
P
in
,
V
inv
∠
δ
an
d
X
TINV
ar
e
in
p
u
t
p
o
wer
,
in
v
er
ter
v
o
ltag
e
an
d
r
e
ac
tan
ce
o
f
co
u
p
lin
g
tr
a
n
s
f
o
r
m
er
.
T
d
is
s
y
s
tem
tim
e
d
elay
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n
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e
o
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S
T
d
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5
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an
d
f
o
r
PVS
T
d
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0
0
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s
.
K
inv1
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K
inv2
--
--
K
inv8
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e
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n
s
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t
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th
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o
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ciate
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ar
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les.
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h
e
b
lo
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d
iag
r
am
o
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ter
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d
r
e
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o
l
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h
o
w
n
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Fig
u
r
e
2
.
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h
e
f
u
n
ctio
n
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th
e
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r
o
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r
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o
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ter
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n
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er
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n
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itio
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Data
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e
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tain
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E
S a
n
d
PVS ar
e
g
iv
en
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T
a
b
le
6
a
nd
T
ab
le
8
.
Fig
u
r
e
2
.
T
r
an
s
f
er
f
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n
ctio
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el
o
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n
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ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Micr
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2
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o
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o
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ic
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u
r
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3
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BG
1
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BG
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e
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G2
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r
e
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iv
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n
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5
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T
ab
le
7
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h
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u
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io
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lated
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ich
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ig
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ee
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ig
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ated
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e
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h
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t
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io
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en
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iv
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y
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1
7
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an
d
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1
8
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(
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=
1
1
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17
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(
)
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1
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h
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it
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1
2
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An
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E
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E
ty
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e
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citatio
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o
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as
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h
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u
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e
4
is
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n
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id
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ed
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e
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lectin
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at
u
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atio
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h
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s
m
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o
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eh
in
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tr
a
n
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ien
t r
ea
ctan
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,
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B
,
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iv
en
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y
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E
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B
G
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d
B
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s
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K
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V
(
s
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]
(
2
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r
s
m
all
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ce
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e
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et
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V
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s
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(
21
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Ass
u
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th
at
SG
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atin
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at
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n
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t
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ac
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r
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e
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n
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e
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iv
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2
2
)
.
∆Q
′
BG
(
s
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=K
rb
∆P
BG
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s
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(
22
)
Fig
u
r
e
3
.
T
r
an
s
f
er
f
u
n
ctio
n
m
o
d
el
o
f
b
io
g
as
-
g
e
n
s
et
f
o
r
r
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l
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o
wer
co
n
tr
o
l
Fig
u
r
e
4
.
Mo
d
el
o
f
I
E
E
E
T
y
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e
-
I
ex
citatio
n
c
o
n
tr
o
l sy
s
tem
f
o
r
b
io
g
as
-
g
e
n
s
et
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
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g
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Vo
l.
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4
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er
2
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1
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2
6
–
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332
3
.
3
.
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r
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r
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f
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e
g
r
id
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n
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e
wr
itten
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tate
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ar
iab
les as
(
2
3
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a
n
d
(
2
4
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.
12
(
)
(
)
(
)
G
G
G
P
s
K
s
K
V
s
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+
(
2
3
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34
(
)
(
)
(
)
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G
G
Q
s
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s
K
V
s
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2
4
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T
h
e
ch
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g
e
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tem
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u
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ag
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r
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n
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y
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2
5
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.
2
()
Fs
s
=
(
25
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3
.
4
.
AC
net
wo
r
k
Fig
u
r
e
5
s
h
o
ws
th
e
m
o
d
el
o
f
AC
n
etwo
r
k
.
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h
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AC
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ter
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le
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ter
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t
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s
ter
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ar
e
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n
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er
in
g
,
i.e
.
,
MG
-
1
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d
MG
-
2.
T
r
an
s
f
er
f
u
n
ctio
n
m
o
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el
AC
Netwo
r
k
i
n
ter
m
s
o
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lo
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g
i
v
e
n
in
Fig
u
r
e
6
.
Ps
an
d
Qs
ar
e
s
en
d
in
g
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n
d
ac
tiv
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d
r
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ctiv
e
p
o
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r
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d
Pr
a
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ar
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r
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eiv
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d
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.
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ein
g
a
s
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o
r
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n
s
id
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e
d
9
5
%
an
d
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o
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at
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d
is
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k
W
,
th
er
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o
r
e,
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e
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Netwo
r
k
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ee
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d
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f
5
k
W
.
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h
e
im
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ed
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e
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n
e
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g
i
v
en
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y
Z
∠
Ψ
=0
.
6
2
3
∠
2
5
.
5
5
˚
.
I
n
cr
em
en
tal
ch
an
g
e
in
p
o
wer
f
lo
w
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e
to
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h
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l
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ad
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ch
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n
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e
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er
atio
n
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g
iv
en
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y
(
2
6
)
,
(
2
7
)
,
(
2
8
)
,
(
2
9
)
,
(
3
0
)
,
(
3
1
)
,
(
3
2
)
an
d
(
3
3
)
.
=
1
2
−
1
2
(
Ψ
+
12
)
(
26
)
=
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2
−
1
2
(
Ψ
+
12
)
(
27
)
=
1
2
(
Ψ
+
12
)
−
1
2
(
28
)
=
1
2
(
Ψ
+
12
)
−
1
2
(
29
)
=
1
1
+
2
2
+
3
12
(
30
)
=
4
1
+
5
2
+
6
12
(
31
)
=
7
1
+
8
2
+
9
12
(
32
)
=
10
1
+
11
2
+
12
12
(
33
)
W
h
er
e
K1
ac
,
K2
ac
,
-
-
-
-
K
1
2
ac
ar
e
co
n
s
tan
t
o
f
th
e
ab
o
v
e
-
m
en
tio
n
e
d
e
q
u
atio
n
s
,
ass
o
ciate
d
with
s
tate
v
ar
iab
les.
T
h
e
v
al
u
es o
f
th
e
c
o
n
s
tan
ts
ar
e
g
iv
en
in
T
ab
le
2
.
3
.
5
.
F
r
a
ct
io
na
l
o
rder
pro
po
rt
io
na
l int
eg
ra
l c
o
ntr
o
ller
I
n
th
is
p
ap
er
,
th
e
s
im
u
latio
n
h
as
b
ee
n
ca
r
r
ied
o
u
t
u
s
in
g
f
r
ac
ti
o
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
a
l
in
teg
r
al
co
n
tr
o
ller
.
Fo
r
FOPI
FOMCON
to
o
lb
o
x
in
MA
T
L
AB
/Si
m
u
lin
k
is
u
s
ed
.
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h
e
im
p
r
o
v
e
m
en
t/tu
n
in
g
o
f
co
n
tr
o
l
s
y
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tem
p
er
f
o
r
m
an
ce
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t
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ti
m
e
d
o
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ain
is
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r
r
ied
o
u
t
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y
m
in
im
izin
g
e
r
r
o
r
s
ig
n
al
e(
t)
u
s
in
g
in
teg
r
al
s
q
u
ar
e
er
r
o
r
(
I
SE)
.
T
h
e
f
r
ac
tio
n
al
o
r
d
er
PI
co
n
tr
o
ller
tr
an
s
f
er
f
u
n
cti
o
n
is
g
iv
en
b
y
(
3
4
)
.
(
)
=
+
(
3
4
)
W
h
er
e
α
is
n
o
n
-
in
teg
er
.
I
n
ca
s
e
o
f
FOPI
t
h
r
ee
v
ar
iab
les
i.e
.
Kp
,
Ki
an
d
α
n
ee
d
to
b
e
tu
n
ed
in
s
tead
o
f
tw
o
v
ar
iab
les in
ca
s
e
o
f
c
o
n
v
e
n
tio
n
al
PI
C
o
n
tr
o
ller
.
T
h
e
v
alu
es
o
f
Kp
,
Ki
an
d
α
a
r
e
g
iv
e
n
at
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Micr
o
g
r
id
s
d
yn
a
mic
s
ta
b
ilit
y
i
n
terco
n
n
ec
ted
th
r
o
u
g
h
l
o
w
vo
lta
g
e
A
C
n
etw
o
r
k
(
V
in
it K
u
ma
r
S
in
g
h
)
333
Fig
u
r
e
5
.
Mo
d
el
o
f
AC
n
etwo
r
k
4.
SYST
E
M
SI
M
U
L
A
T
I
O
N
A
ND
R
E
S
UL
T
S
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
m
o
d
el
o
f
th
e
m
icr
o
g
r
id
s
y
s
tem
MG
-
1
an
d
MG
-
2
u
s
in
g
PVS
-
b
io
g
as
an
d
PVS
-
b
io
g
as
-
lim
ited
g
r
id
is
s
h
o
wn
in
Fig
u
r
e
s
7
(
a)
a
n
d
(
b
)
r
esp
ec
tiv
ely
.
I
n
th
is
p
ap
e
r
o
n
l
y
o
n
e
ty
p
ical
ex
am
p
le
is
co
n
s
id
er
ed
i.e
.
in
b
o
th
th
e
C
lu
s
ter
s
MG
-
1
an
d
MG
-
2
,
s
tep
lo
ad
is
in
cr
ea
s
ed
b
y
1
%.
Fu
r
th
er
,
it
is
as
s
u
m
ed
th
at
in
p
u
t
p
o
wer
to
W
E
S
in
MG
-
1
in
cr
ea
s
es
b
y
1
%
a
n
d
in
p
u
t
s
o
lar
p
o
wer
to
PVS
d
ec
r
ea
s
es
b
y
1
%.
Fig
u
r
e
7
(
c)
s
h
o
ws
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
(
MG
-
1
)
d
u
e
to
1
%
i
n
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
lo
ad
an
d
1
% in
cr
ea
s
e
in
win
d
in
p
u
t p
o
wer
,
tim
e
(
s
ec
o
n
d
)
v
er
s
u
s
ch
a
n
g
e
in
v
o
ltag
e.
I
n
MG
-
1
d
u
e
to
s
tep
in
cr
ea
s
e
in
lo
ad
an
d
in
cr
ea
s
e
in
i
n
p
u
t
win
d
p
o
wer
b
y
1
%,
th
e
win
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t
i
n
cr
ea
s
es
g
r
ad
u
ally
alo
n
g
with
d
ec
r
ea
s
e
in
o
u
tp
u
t
o
f
b
io
g
as.
I
t
t
ak
es
ar
o
u
n
d
9
s
f
o
r
o
u
tp
u
t
p
o
wer
to
r
ea
ch
s
tead
y
s
tate
in
MG
-
1
in
Fig
u
r
e
s
7
(
d
)
an
d
(
e)
.
T
h
is
is
d
u
e
to
th
e
s
lo
w
r
esp
o
n
s
e
o
f
win
d
tu
r
b
in
e.
Ho
wev
er
,
f
r
eq
u
e
n
cy
an
d
v
o
ltag
e
an
g
le
r
ea
ch
s
tea
d
y
s
tate
with
in
5
s
i
n
Fig
u
r
e
s
7
(
a)
an
d
(
b
)
.
T
h
e
v
o
ltag
e
r
ea
c
h
es
s
tead
y
s
tate
with
in
6
0
m
s
ec
i
n
Fig
u
r
e
7
(
c)
.
Fig
u
r
e
s
8
(
a)
,
(
b
)
,
(
c)
s
h
o
ws
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
(
MG
-
2
)
d
u
e
to
1
%
in
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
lo
a
d
an
d
1
%
d
e
cr
ea
s
e
in
s
o
lar
in
p
u
t
p
o
wer
,
tim
e
(
s
ec
o
n
d
)
v
er
s
u
s
c
h
an
g
e
in
f
r
eq
u
en
cy
,
ch
an
g
e
in
v
o
ltag
e
an
g
le
an
d
c
h
an
g
e
in
v
o
ltag
e.
I
n
MG
-
2
d
u
e
t
o
s
tep
in
cr
ea
s
e
in
lo
ad
b
y
1
%
an
d
d
ec
r
ea
s
e
in
s
o
lar
p
o
wer
,
ac
tiv
e
p
o
wer
o
u
tp
u
t
o
f
PV
S
in
v
er
ter
d
ec
r
ea
s
es
im
m
ed
iately
in
Fig
u
r
e
8
(
d
)
.
T
o
c
o
m
p
en
s
ate,
in
itially
p
o
wer
is
d
r
awn
f
r
o
m
th
e
g
r
id
wh
ich
s
lo
wly
d
ec
r
ea
s
es
as
th
e
o
u
tp
u
t
p
o
wer
f
r
o
m
th
e
b
i
o
g
as
in
cr
ea
s
es.
T
h
e
s
tead
y
s
tate
o
f
ac
tiv
e
p
o
wer
is
ac
h
iev
ed
with
in
5
s
ec
.
Als
o
,
th
e
ac
tiv
e
p
o
wer
d
r
awin
g
f
r
o
m
th
e
g
r
id
b
ec
o
m
es
ze
r
o
.
Ho
wev
er
,
th
e
ca
s
e
o
f
r
ea
ctiv
e
p
o
we
r
in
MG
-
2
is
d
if
f
er
en
t
in
Fig
u
r
e
8
(
e
)
.
E
v
en
t
h
o
u
g
h
t
h
e
s
o
lar
in
p
u
t
p
o
we
r
d
ec
r
ea
s
es
th
e
co
u
p
lin
g
ca
p
ac
ito
r
attac
h
ed
with
PVS
in
v
er
ter
p
r
o
v
id
es
r
ea
ctiv
e
p
o
wer
in
itially
an
d
f
in
ally
ta
k
en
u
p
b
y
b
io
g
as
r
ea
ch
in
g
s
tead
y
s
tate
with
in
5
s
.
As
s
ee
n
f
r
o
m
th
e
g
r
ap
h
t
h
e
f
r
eq
u
e
n
cy
,
Fig
u
r
e
s
7
(
a
)
an
d
8
(
a)
an
d
v
o
ltag
e
an
g
le,
Fig
u
r
e
s
7
(
b
)
a
n
d
8
(
c)
s
ettles
with
in
5
s
ec
an
d
v
o
lta
g
e,
Fig
u
r
e
s
7
(
c)
an
d
8
(
c)
s
ettles
with
in
6
0
m
s
ec
in
b
o
th
th
e
m
ic
r
o
g
r
i
d
as
an
ticip
a
ted
.
Fu
r
th
er
,
f
r
o
m
th
e
f
r
e
q
u
en
cy
g
r
ap
h
o
f
b
o
th
th
e
m
icr
o
g
r
id
it
ca
n
b
e
in
ter
p
r
eted
th
at
f
r
eq
u
en
cy
o
s
cillatio
n
is
m
o
r
e
in
MG
-
2
as
co
m
p
ar
e
d
to
MG
-
1
;
th
is
is
b
ec
au
s
e
o
f
p
r
esen
ce
W
E
S
in
er
tia
in
MG
-
1
wh
ich
s
u
p
p
o
r
ts
th
e
s
y
s
tem
wo
r
k
in
g
as
s
h
o
ck
ab
s
o
r
b
er
.
Oscill
a
t
io
n
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
PVS
an
d
B
io
g
as
in
MG
-
2
ca
n
b
e
in
te
r
p
r
et
ed
as
s
y
s
tem
in
ter
ac
tio
n
with
th
e
g
r
id
.
C
o
u
p
lin
g
ca
p
ac
ito
r
attac
h
e
d
with
th
e
in
v
er
ter
p
r
o
v
id
e
t
h
e
r
ea
ctiv
e
p
o
wer
in
itially
th
r
o
u
g
h
t
h
e
s
to
r
e
d
en
e
r
g
y
th
er
e
f
o
r
e,
v
o
ltag
e
p
r
o
f
ile
is
m
ain
t
ain
ed
q
u
ick
ly
.
As
d
esire
d
n
o
ex
tr
a
p
o
wer
is
d
r
awn
f
r
o
m
t
h
e
g
r
id
as
well
as
AC
n
etwo
r
k
.
Fro
m
th
e
ab
o
v
e,
it
is
o
p
in
ed
th
at
co
n
tr
o
ller
s
ar
e
tu
n
ed
to
o
v
er
c
o
m
e
th
e
s
m
all
d
is
tu
r
b
an
ce
in
t
h
e
s
y
s
tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
2
6
–
336
334
(
a)
(
b
)
Fig
u
r
e
6
.
T
r
an
s
f
er
f
u
n
ctio
n
m
o
d
el
o
f
:
(
a)
MG
-
1
,
(
b
)
MG
-
2
(
a)
(
b
)
(
c
)
(
d
)
(
e)
Fig
u
r
e
7
.
Dy
n
am
ic
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
(
MG
-
1
)
d
u
e
to
1
% in
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
lo
a
d
an
d
1
% in
cr
ea
s
e
in
win
d
in
p
u
t
p
o
wer
,
tim
e
(
s
ec
o
n
d
)
v
er
s
u
s
:
(
a)
C
h
an
g
e
in
f
r
eq
u
en
cy
,
(
b
)
C
h
an
g
e
in
v
o
ltag
e
an
g
le
,
(
c)
C
h
an
g
e
in
v
o
ltag
e
,
(
d
)
C
h
an
g
e
i
n
ac
tiv
e
p
o
wer
o
f
B
G1
an
d
W
E
S
,
(
e)
C
h
an
g
e
in
r
ea
ctiv
e
p
o
wer
o
f
B
G1
an
d
W
E
S
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Micr
o
g
r
id
s
d
yn
a
mic
s
ta
b
ilit
y
i
n
terco
n
n
ec
ted
th
r
o
u
g
h
l
o
w
vo
lta
g
e
A
C
n
etw
o
r
k
(
V
in
it K
u
ma
r
S
in
g
h
)
335
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
8
.
Dy
n
am
ic
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
(
MG
-
2
)
d
u
e
to
1
% in
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
lo
a
d
an
d
1
% d
ec
r
ea
s
e
in
s
o
lar
in
p
u
t p
o
wer
,
tim
e
(
s
ec
o
n
d
)
v
er
s
u
s
:
(
a)
C
h
an
g
e
in
f
r
eq
u
en
cy
,
(
b
)
C
h
an
g
e
in
v
o
ltag
e
an
g
le
,
(
c)
C
h
an
g
e
in
v
o
ltag
e
,
(
d
)
C
h
an
g
e
i
n
ac
tiv
e
p
o
wer
o
f
B
G2
,
PVS
an
d
g
r
id
,
(
e
)
C
h
an
g
e
in
r
ea
ctiv
e
p
o
wer
o
f
B
G2
,
PVS
an
d
g
r
id
5.
CO
NCLU
SI
O
N
I
n
ter
co
n
n
ec
ted
m
icr
o
g
r
id
h
a
v
e
m
o
d
eled
u
s
in
g
win
d
en
er
g
y
s
y
s
tem
an
d
p
h
o
to
v
o
lta
ic
s
y
s
tem
ac
co
m
p
an
ied
with
b
io
g
as
b
as
ed
s
y
s
tem
.
On
e
o
f
th
e
m
icr
o
g
r
id
is
also
co
n
n
ec
ted
to
m
ain
g
r
id
.
T
h
e
co
m
p
lete
s
y
s
tem
is
test
ed
with
1
%
s
tep
ch
an
g
e
in
in
p
u
t
p
o
wer
t
o
r
en
e
wab
le
en
er
g
y
s
o
u
r
ce
s
an
d
lo
a
d
.
As
p
er
th
e
r
esu
lt
th
e
s
y
s
tem
b
ec
o
m
es
s
tab
le
i.e
.
f
r
eq
u
en
c
y
an
d
a
n
g
le
s
ettles
w
ith
in
5
s
an
d
v
o
ltag
e
with
in
6
0
m
s
.
As
d
esire
d
n
o
ex
tr
a
p
o
wer
is
d
r
awn
f
r
o
m
th
e
m
ain
g
r
id
as
well
ac
in
ter
c
o
n
n
ec
tin
g
lin
e.
E
ac
h
m
icr
o
g
r
id
g
ets
s
u
p
p
o
r
t f
r
o
m
its
o
wn
s
y
s
tem
to
o
v
er
r
id
e
th
e
d
is
tu
r
b
an
ce
ca
u
s
ed
b
y
ch
a
n
g
e
in
lo
ad
an
d
in
p
u
t
p
o
wer
t
o
r
en
ewa
b
le
s
o
u
r
ce
s
.
Fro
m
th
e
s
tu
d
y
it
ca
n
b
e
i
n
ter
p
r
etate
d
th
at
if
th
e
in
d
i
v
id
u
al
co
n
t
r
o
l
o
f
th
e
clu
s
ter
is
ac
h
iev
ed
th
en
in
ter
co
n
n
ec
tio
n
o
f
m
icr
o
g
r
id
s
co
u
ld
b
e
s
o
lu
tio
n
f
o
r
v
al
id
o
p
tim
izatio
n
o
f
r
eso
u
r
ce
s
.
T
h
e
b
e
n
ef
it
o
f
in
eter
co
n
n
ec
tio
n
is
th
at
at
tim
e
co
n
tig
en
c
y
th
e
p
o
wer
tr
an
s
f
er
ca
n
g
et
r
ev
er
s
ed
as
p
e
r
th
e
r
eq
u
ir
em
e
n
t.
Als
o
th
e
lin
e
s
u
p
p
o
r
ts
in
itially
wh
en
th
er
e
is
s
tep
ch
an
g
e
in
lo
a
d
o
r
in
p
u
t to
th
e
g
en
er
atin
g
r
eso
u
ce
s
.
RE
F
E
R
E
NC
E
S
[1
]
Ov
e
rv
iew
o
f
I
n
d
ia
n
P
o
we
r
S
c
e
n
a
rio
.
[O
n
li
n
e
].
Av
a
il
a
b
le:
h
tt
p
s://p
o
we
rm
in
.
n
ic.i
n
.
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[8
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