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[
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T
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r
ea
cti
v
e
p
o
w
er
r
eq
u
ir
em
e
n
t
.
T
h
e
n
at
u
r
al
d
r
o
o
p
m
eth
o
d
is
n
o
t
s
u
itab
le
w
h
e
n
t
h
e
MG
h
as
n
o
n
li
n
ea
r
lo
ad
s
d
u
e
to
th
e
h
ar
m
o
n
ic
cu
r
r
en
t
[
6
]
-
[
9
]
.
A
n
o
t
h
er
i
s
s
u
e
r
elatin
g
to
t
h
e
co
n
v
e
n
tio
n
al
d
r
o
o
p
is
th
at
th
e
f
r
eq
u
e
n
c
y
an
d
v
o
lta
g
e
ar
e
r
esp
ec
tiv
el
y
r
elate
d
to
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
w
h
e
n
t
h
e
o
u
tp
u
t
i
m
p
ed
an
ce
o
f
th
e
g
e
n
er
ato
r
is
m
ai
n
l
y
i
n
d
u
ct
iv
e,
e.
g
.
,
in
d
u
ctio
n
g
e
n
er
ato
r
s
.
Hen
ce
,
t
h
e
p
o
w
er
s
h
ar
i
n
g
p
er
f
o
r
m
an
ce
i
s
a
f
f
ec
t
ed
b
y
t
h
e
o
u
tp
u
t
i
m
p
ed
an
ce
o
f
th
e
d
is
tr
ib
u
ted
g
e
n
er
atio
n
u
n
i
ts
a
n
d
th
e
li
n
e
i
m
p
ed
an
ce
s
.
I
t
in
f
er
s
t
h
at,
th
e
ac
tiv
e
p
o
w
er
-
v
o
lta
g
e
(
P
-
V
)
d
r
o
o
p
c
o
n
tr
o
l
n
ee
d
s
to
b
e
u
s
ed
in
s
tead
o
f
th
e
co
n
v
e
n
tio
n
al
ac
ti
v
e
p
o
w
er
-
f
r
eq
u
en
c
y
(
P
-
f
)
d
r
o
o
p
co
n
tr
o
l,
w
h
ich
is
co
n
tr
ar
y
to
th
e
co
n
v
e
n
tio
n
al
elec
tr
ical
tr
an
s
m
is
s
io
n
s
y
s
te
m
s
o
r
in
d
u
c
tio
n
g
e
n
er
atio
n
d
o
m
i
n
ated
s
y
s
te
m
s
.
A
(
Q
-
V)
d
r
o
o
p
co
n
tr
o
l
m
et
h
o
d
is
m
o
s
tl
y
u
s
ed
to
i
m
p
r
o
v
e
r
ea
ctiv
e
p
o
w
er
s
h
ar
i
n
g
[
1
0
]
.
T
h
e
v
o
ltag
e
an
d
f
r
eq
u
en
c
y
(
V
-
f
)
co
n
tr
o
l
was i
m
p
le
m
e
n
ted
to
co
n
tr
o
l D
G
s
i
n
a
n
i
s
la
n
d
ed
m
o
d
e
b
y
m
ai
n
tain
i
n
g
v
o
ltag
e
an
d
f
r
eq
u
en
c
y
at
r
ef
er
en
ce
s
.
Ho
w
e
v
er
,
p
u
r
e
(
V
-
f
)
co
n
tr
o
ller
f
o
r
DGs
in
is
lan
d
ed
m
o
d
e
is
n
o
t
ab
le
to
r
esp
o
n
d
to
lo
ad
ch
an
g
es
;
a
m
a
s
ter
-
s
la
v
e
co
n
tr
o
l
co
n
f
ig
u
r
atio
n
o
f
a
M
G
is
b
u
ilt
[
1
1
]
,
[
1
2
]
.
I
n
g
r
id
-
c
o
n
n
ec
ted
m
o
d
e,
all
DGs
ar
e
eq
u
ip
p
ed
w
it
h
P
Q
co
n
tr
o
ller
s
,
an
d
d
u
r
in
g
is
la
n
d
e
d
m
o
d
e
o
n
l
y
th
e
m
aster
i
n
v
er
ter
s
w
i
tch
e
s
to
(
V
-
f
)
co
n
tr
o
l
to
m
ai
n
tai
n
th
e
MG
v
o
ltag
e
lev
el
an
d
f
r
eq
u
e
n
c
y
.
T
h
e
d
r
aw
b
ac
k
o
f
m
aster
–
s
la
v
e
m
e
th
o
d
is
th
at
it
also
tak
es
lar
g
e
a
m
o
u
n
t
o
f
co
m
m
u
n
icatio
n
.
B
y
r
etr
ie
v
in
g
th
e
g
r
i
d
p
ar
am
eter
s
s
u
c
h
as
th
e
v
o
lta
g
e,
f
r
eq
u
en
c
y
,
g
r
id
i
m
p
ed
an
ce
,
t
h
e
in
v
er
ter
s
b
ase
d
o
n
t
h
e
d
r
o
o
p
co
n
tr
o
l
m
et
h
o
d
ar
e
ab
le
to
in
j
ec
t
r
ea
l
a
n
d
r
e
ac
tiv
e
p
o
w
er
to
t
h
e
g
r
id
[
1
3
]
,
[
1
4
]
.
I
n
o
r
d
er
to
en
h
a
n
ce
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
te
m
b
y
u
tili
zin
g
th
e
lo
ca
ll
y
m
ea
s
u
r
ab
le
f
ee
d
b
ac
k
s
ig
n
al,
t
h
e
e
f
f
ec
t
iv
e
co
n
tr
o
l
te
ch
n
iq
u
e
f
o
r
in
ter
co
n
n
ec
tio
n
o
f
DG
to
p
o
w
er
g
r
id
t
h
r
o
u
g
h
i
n
t
er
f
ac
in
g
co
n
v
er
ter
s
is
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
Sin
ce
t
h
e
n
et
w
o
r
k
s
y
s
te
m
i
s
m
o
r
e
co
m
p
lex
,
a
lo
ad
s
h
ar
in
g
w
it
h
m
i
n
i
m
a
l
co
m
m
u
n
icatio
n
is
to
b
e
i
m
p
le
m
e
n
ted
.
Hen
ce
,
an
i
m
p
r
o
v
ed
d
r
o
o
p
co
n
tr
o
l
m
et
h
o
d
wh
ich
is
ca
p
ab
le
o
f
ef
f
icien
tl
y
m
a
n
a
g
in
g
p
o
w
er
b
et
w
ee
n
DG
s
an
d
g
r
id
is
ad
o
p
ted
.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
tech
n
iq
u
e
d
ep
en
d
s
o
n
r
esh
ap
in
g
t
h
e
i
n
p
u
t
i
m
p
ed
an
c
e
o
f
th
e
i
n
ter
f
ac
ed
co
n
v
er
ter
b
y
i
n
j
ec
tin
g
an
ac
tiv
e
s
tab
iliz
atio
n
s
i
g
n
a
l
at
th
e
co
n
tr
o
l
lo
o
p
o
f
t
h
e
co
n
v
er
ter
.
T
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
th
e
s
t
u
d
y
i
n
t
h
e
s
y
s
te
m
is
v
al
id
ated
b
y
MA
T
L
A
B
/S
i
m
u
li
n
k
s
o
f
t
w
ar
e
d
u
r
in
g
s
e
v
er
al
o
p
er
atin
g
co
n
d
i
tio
n
s
.
2.
M
I
CRO
G
RID AR
CH
I
T
E
C
T
UR
E
D
G
1
V
S
I
P
W
M
D
G
n
V
S
I
P
W
M
L
f
1
C
f
1
L
f
n
C
f
n
R
1
L
1
R
n
L
n
L
o
a
d
1
L
o
a
d
n
T
r
a
n
s
f
o
r
m
e
r
B
r
e
a
k
e
r
R
g
L
g
P
C
C
G
r
i
d
Fig
u
r
e
1
.
A
r
ch
itech
t
u
r
e
o
f
Mi
cr
o
-
Gr
id
A
s
i
m
p
le
MG
s
tr
u
ct
u
r
e
is
d
ev
elo
p
ed
in
o
r
d
er
to
test
t
h
e
e
f
f
ec
tiv
e
n
ess
a
n
d
e
f
f
ic
ien
c
y
o
f
c
o
n
tr
o
ller
s
,
as
s
h
o
w
n
i
n
Fig
u
r
e
1
.
DG
1
,
…,
DG
n
ar
e
co
n
n
ec
ted
to
t
h
e
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
s
(
V
SI)
c
o
n
tr
o
lled
b
y
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
P
W
M)
co
n
tr
o
ller
f
o
llo
w
ed
b
y
t
h
e
f
ilter
s
a
n
d
lo
ad
1
,
…,
lo
an
d
n
.
A
ll t
h
ese
DGS
ar
e
co
n
n
ec
ted
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
an
d
th
en
,
DG
s
ar
e
co
n
n
ec
ted
to
th
e
m
ai
n
g
r
id
th
r
o
u
g
h
t
h
e
tr
an
s
m
is
s
io
n
l
in
e,
cir
c
u
it
b
r
ea
k
er
s
,
an
d
tr
an
s
f
o
r
m
er
s
.
DG
s
a
r
e
i
m
p
le
m
e
n
ted
t
h
r
o
u
g
h
P
Q
co
n
tr
o
ller
u
n
d
er
g
r
id
-
co
n
n
ec
ted
m
o
d
e
an
d
d
r
o
o
p
co
n
tr
o
ller
ca
n
b
e
i
m
p
le
m
en
ted
u
n
d
er
eith
er
g
r
id
-
co
n
n
ec
ted
o
r
is
lan
d
ed
m
o
d
e
[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
ew s
t
r
a
teg
y
fo
r
o
n
-
L
in
e
D
r
o
o
p
a
d
j
u
s
tmen
t fo
r
Micr
o
g
r
i
d
co
n
n
ec
ted
DGs
..
(
S
a
th
ya
p
r
a
b
a
ka
r
a
n
B
)
141
2
.
1
.
P
V
M
o
del
A
P
V
ce
ll
ca
n
b
e
m
o
d
eled
as
a
cu
r
r
en
t
s
o
u
r
ce
co
n
n
ec
ted
w
i
th
o
n
e
d
io
d
e
an
d
t
w
o
r
esis
to
r
s
as
s
h
o
w
n
in
f
i
g
u
r
e
2
.
A
P
V
m
o
d
u
le
is
b
u
i
lt
b
y
s
i
m
p
l
y
co
n
n
ec
ti
n
g
m
a
n
y
P
V
ce
ll
s
i
n
s
er
ie
s
an
d
p
ar
allel.
T
h
e
ch
ar
ac
ter
is
tic
eq
u
at
io
n
f
o
r
a
s
in
g
le
P
V
ce
ll is
g
i
v
en
a
s
=
ℎ
−
{
[
(
+
)
]
−
1
}
−
+
ℎ
(
1
)
w
h
er
e
V
is
o
u
tp
u
t
v
o
ltag
e,
I
is
o
u
tp
u
t
cu
r
r
en
t,
I
0
is
ce
ll
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t,
I
ph
is
lig
h
t
-
g
e
n
er
ated
cu
r
r
en
t,
q
is
elec
tr
o
n
c
h
ar
g
e
1
.
6
×
10
−
23
(
C
)
,
T
is
ce
ll
te
m
p
er
atu
r
e
i
n
C
el
s
i
u
s
,
k
is
B
o
ltz
m
an
n
'
s
co
n
s
ta
n
t
1
.
38
×
10
−
19
(
J
/k
)
,
R
sh
is
s
h
u
n
t
r
esis
ta
n
ce
,
R
s
is
s
er
ies
r
esis
tan
ce
,
id
ea
lit
y
f
ac
to
r
n
is
in
tr
o
d
u
ce
d
in
th
e
d
en
o
m
i
n
ato
r
o
f
th
e
e
x
p
o
n
en
t,
w
h
ic
h
r
an
g
es
f
r
o
m
1
to
2
,
r
ep
r
esen
ti
n
g
th
e
d
e
f
ec
ts
f
r
o
m
id
ea
l
d
io
d
e.
I
D
I
p
h
D
R
s
h
I
s
h
R
s
V
p
v
I
p
v
+
-
Fig
u
r
e
2
.
Sin
g
le
Dio
d
e
Mo
d
el
o
f
P
V
ce
ll
3.
M
O
DE
L
I
N
G
O
F
T
H
E
T
H
R
E
E
-
P
H
AS
E
G
RID
-
CO
NN
E
CT
E
D
VSI
SYS
T
E
M
A
t
y
p
ical
m
o
d
el
o
f
a
t
h
r
ee
-
p
h
ase
g
r
id
co
n
n
ec
ted
VSI
w
it
h
an
L
C
f
ilter
i
s
d
ep
icted
in
Fig
u
r
e
3
,
w
h
er
ea
s
Rf
,
Lf,
C
f,
r
ep
r
esen
t
t
h
e
eq
u
i
v
ale
n
t
l
u
m
p
ed
r
esis
tan
ce
,
an
in
d
u
ctan
ce
o
f
th
e
f
il
ter
an
d
ca
p
ac
itan
ce
o
f
th
e
f
ilter
,
r
esp
ec
tiv
el
y
.
I
ab
c
is
th
e
g
r
id
cu
r
r
e
n
t a
n
d
V
abc
is
th
e
g
r
id
v
o
ltag
e
[
1
3
]
.
S
I
X
P
U
L
S
E
C
O
N
V
E
R
T
E
R
R
f
L
f
G
R
I
D
D
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s
t
r
i
b
u
t
e
d
G
e
n
e
r
a
t
i
o
n
V
d
c
V
a
V
b
V
c
I
a
I
b
I
c
I
d
c
I
i
n
C
d
c
S
1
S
3
S
5
S
2
S
4
S
6
E
a
E
c
E
b
C
f
Fig
u
r
e
3
.
Sch
e
m
atic
cir
cu
it o
f
T
h
r
ee
-
p
h
ase
g
r
id
-
co
n
n
ec
ted
in
v
er
ter
I
n
th
e
abc
r
ef
er
en
ce
f
r
a
m
e,
t
h
e
s
tate
s
p
ac
e
eq
u
atio
n
s
o
f
t
h
e
s
y
s
te
m
eq
u
i
v
ale
n
t c
ir
cu
it a
r
e
g
i
v
en
a
s
[
]
=
[
]
+
1
(
[
]
−
[
]
)
(
2
)
Usi
n
g
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
,
(
2
)
ca
n
b
e
ex
p
r
ess
ed
in
th
e
dq
r
ef
er
en
ce
f
r
a
m
e
a
s
[
]
=
[
−
−
−
]
[
]
+
1
(
[
]
−
[
]
)
(
3
)
w
h
er
e
is
t
h
e
co
o
r
d
in
ate
an
g
u
l
ar
f
r
eq
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en
c
y
,
an
d
th
e
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
ca
n
b
e
d
ef
i
n
ed
as
=
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
139
–
1
4
9
142
w
h
er
e,
=
[
0
]
,
I
=
[
]
,
=
2
3
[
(
−
2
3
)
(
+
2
3
)
−
(
−
2
3
)
−
(
+
2
3
)
1
2
1
2
1
2
]
an
d
=
+
0
is
th
e
s
y
n
ch
r
o
n
o
u
s
r
o
tatin
g
an
g
le,
0
r
ep
r
esen
ts
th
e
i
n
i
tial v
al
u
e.
3
.
1
.
P
ha
s
e
L
o
ck
ed
L
o
o
p(P
L
L
)
T
h
e
s
y
n
ch
r
o
n
izatio
n
alg
o
r
it
h
m
f
o
r
attai
n
i
n
g
a
co
n
tr
o
llab
le
p
o
w
er
f
ac
to
r
m
u
s
t
d
etec
t
t
h
e
p
h
ase
a
n
g
le
o
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t
h
e
t
h
r
ee
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p
h
ase
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t
ilit
y
g
r
id
v
o
lta
g
e
w
i
th
o
p
ti
m
al
d
y
n
a
m
i
c
r
esp
o
n
s
e
a
n
d
r
eliab
ili
t
y
in
o
r
d
er
to
o
b
tain
th
e
s
y
n
ch
r
o
n
izatio
n
o
f
t
h
e
co
n
tr
o
lled
th
r
ee
-
p
h
ase
i
n
v
er
ter
cu
r
r
en
t
an
d
to
en
s
u
r
e
th
e
p
r
o
p
er
b
eh
av
io
r
o
f
th
e
in
v
er
ter
co
n
tr
o
l
s
tr
ate
g
y
.
A
t
h
r
ee
-
p
h
ase
P
L
L
s
tr
u
ct
u
r
e
is
s
h
o
w
n
i
n
F
ig
u
r
e
4
,
co
n
s
i
s
ti
n
g
o
f
C
lar
k
’
s
an
d
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
s
(
also
k
n
o
w
n
as
abc
to
dq
tr
an
s
f
o
r
m
at
io
n
)
,
th
e
P
I
r
eg
u
lato
r
as
t
h
e
lo
o
p
f
ilter
,
an
d
an
in
te
g
r
ato
r
as
th
e
v
o
ltag
e
-
co
n
tr
o
ller
o
s
cillato
r
(
VC
O)
.
T
h
is
P
L
L
s
tr
u
ct
u
r
e
is
also
k
n
o
w
n
a
s
S
y
n
c
h
r
o
n
o
u
s
R
ef
er
e
n
ce
Fra
m
e(
S
R
F)
P
L
L
o
r
dq
P
L
L
.
T
h
e
in
p
u
t
v
ar
iab
les
ar
e
t
h
r
ee
p
h
ase
u
t
ilit
y
g
r
i
d
v
o
ltag
e
s
(
V
a
,
V
b
,
V
c
)
an
d
o
u
tp
u
t v
ar
iab
le
is
t
h
e
p
h
ase
a
n
g
le(
θ
)
.
[
1
6
]
,
[
1
7
]
P
I
1
/
s
a
b
c
d
q
o
α
β
α
β
V
α
V
β
V
d
V
q
L
o
o
p
f
i
l
t
e
r
V
*
q
=
0
ω
r
e
f
=
3
1
4
ω
θ
V
a
b
c
+
-
+
+
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
dq
P
L
L
s
y
n
ch
r
o
n
izatio
n
al
g
o
r
ith
m
3
.
2
.
VSI
co
ntr
o
l st
ra
t
e
g
ies
VSI
is
n
ee
d
ed
to
in
ter
f
ac
e
th
e
DG
u
n
it
to
th
e
g
r
id
an
d
p
r
o
v
id
e
f
lex
ib
le
o
p
er
atio
n
.
A
s
s
h
o
w
n
i
n
Fig
u
r
e
5
,
th
e
p
o
w
er
cir
c
u
it o
f
t
h
e
VSI
b
ased
DG
u
n
i
t is
as
s
o
ciate
d
w
ith
th
e
co
n
tr
o
l str
u
ct
u
r
e,
s
o
th
e
co
n
tr
o
lled
o
p
er
atio
n
o
f
th
e
DG
u
n
it
r
elie
s
o
n
th
e
i
n
v
er
ter
co
n
tr
o
l
m
o
d
e.
Fo
r
in
s
tan
ce
,
i
n
t
h
e
g
r
id
-
co
n
n
ec
ted
m
o
d
e,
D
G
u
n
i
t
o
p
er
ates
as
a
P
Q
g
en
er
ato
r
an
d
th
e
in
v
er
ter
s
h
o
u
ld
f
o
llo
w
th
e
P
Q
co
n
tr
o
l
m
o
d
e,
w
h
ile
v
o
lta
g
e
an
d
f
r
eq
u
en
c
y
r
e
g
u
latio
n
ar
e
n
o
t
r
eq
u
ir
ed
b
ec
au
s
e
t
h
e
g
r
id
v
o
lt
ag
e
is
f
i
x
ed
.
Ho
w
ev
er
,
i
n
t
h
e
is
lan
d
ed
m
o
d
e,
t
h
e
DG
u
n
it
s
ar
e
e
x
p
ec
ted
to
m
ee
t
th
e
lo
ad
d
e
m
a
n
d
w
it
h
r
esp
ec
t
to
th
e
q
u
ali
t
y
o
f
p
o
w
er
s
u
p
p
l
y
.
I
n
t
h
is
ca
s
e,
t
h
e
v
o
ltag
e
a
n
d
f
r
eq
u
en
c
y
ar
e
n
o
t
f
i
x
ed
an
d
th
e
in
v
er
ter
s
h
o
u
ld
f
o
llo
w
th
e
(
V
-
f)
co
n
tr
o
l
m
o
d
e
t
ak
in
g
i
n
to
ac
co
u
n
t
th
e
in
v
er
ter
p
o
w
er
r
atin
g
f
o
r
s
h
ar
in
g
p
o
w
er
is
s
u
e
[
1
5
]
,
[
1
6
]
.
P
W
M
a
b
c
d
q
o
P
I
C
U
R
R
E
N
T
C
O
N
T
R
O
L
P
O
W
E
R
C
O
N
T
R
O
L
d
q
o
a
b
c
P
L
L
a
b
c
d
q
o
G
r
i
d
ω
V
d
V
q
P
r
e
f
Q
r
e
f
I
d
*
I
q
*
I
d
I
q
V
d
*
V
q
*
V
r
e
f
*
T
h
r
e
e
P
h
a
s
e
I
n
v
e
r
t
e
r
S
1
S
2
S
5
S
6
S
4
S
3
+
-
V
a
b
c
L
g
R
g
L
f
C
f
I
a
b
c
I
L
V
d
c
Fig
u
r
e
5
.
C
o
n
tr
o
l Str
u
ct
u
r
e
o
f
Gr
id
-
co
n
n
ec
ted
VSI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
ew s
t
r
a
teg
y
fo
r
o
n
-
L
in
e
D
r
o
o
p
a
d
j
u
s
tmen
t fo
r
Micr
o
g
r
i
d
co
n
n
ec
ted
DGs
..
(
S
a
th
ya
p
r
a
b
a
ka
r
a
n
B
)
143
3
.
3
.
P
Q
Co
ntr
o
l St
ra
t
e
g
y
V
a
b
c
I
a
b
c
I
d
*
ω
L
ω
L
P
I
P
I
P
L
L
d
q
o
a
b
c
P
*
Q
*
I
d
*
I
q
*
a
b
c
d
q
o
a
b
c
d
q
o
I
q
*
I
q
I
d
V
q
V
d
V
d
V
q
θ
θ
V
d
*
V
q
*
+
-
+
+
+
+
P
W
M
E
q
u
a
t
i
o
n
.
(
5
-
8
)
+
-
+
-
P
I
P
I
d
q
0
a
b
c
V
*
r
e
f
S
i
n
θ
V
a
b
c
a
b
c
d
q
0
θ
V
d
V
q
-
+
-
+
-
+
-
+
+
Q
r
e
f
Q
m
e
a
s
V
r
e
f
V
*
r
e
f
n
1
θ
I
d
*
I
q
*
V
q
*
V
d
*
I
a
b
c
a
b
c
d
q
0
+
-
+
-
I
d
I
q
I
*
d
r
e
f
I
*
q
r
e
f
Fig
u
r
e
6
.
Stru
ct
u
r
e
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
co
n
tr
o
l
Fig
u
r
e
7
.
Stru
ct
u
r
e
o
f
v
o
lta
g
e
an
d
f
r
eq
u
e
n
c
y
co
n
tr
o
l
Fo
r
b
o
th
m
icr
o
g
r
id
o
p
er
atio
n
m
o
d
e
s
,
as
lo
n
g
as
th
e
v
o
lta
g
e
an
d
f
r
eq
u
en
c
y
ar
e
in
s
tab
le
co
n
d
itio
n
,
th
e
P
Q
co
n
tr
o
l
m
o
d
e
ca
n
b
e
u
s
ed
eith
er
to
i
m
p
o
r
t
less
p
o
w
er
f
r
o
m
th
e
u
tili
t
y
(
P
ea
k
Sh
av
i
n
g
)
in
g
r
id
-
co
n
n
ec
ted
m
o
d
e
o
r
to
in
j
ec
t
a
s
tab
le
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
in
a
s
tan
d
alo
n
e
m
o
d
e.
T
h
e
P
Q
m
o
d
e
is
u
s
u
all
y
ap
p
lied
to
th
e
DG
u
n
it
s
w
h
ic
h
s
u
p
p
l
y
a
co
n
s
ta
n
t
p
o
w
er
.
I
n
th
is
ca
s
e,
t
h
e
a
m
p
li
tu
d
e
an
d
p
h
ase
an
g
le
o
f
t
h
e
in
v
er
ter
cu
r
r
en
t
i
s
co
n
tr
o
lled
in
o
r
d
er
to
i
n
j
ec
t
th
e
p
r
e
-
s
e
t
ac
tiv
e
a
n
d
r
ea
cti
v
e
p
o
w
er
v
al
u
es
w
h
ich
ca
n
b
e
d
ef
in
ed
lo
ca
ll
y
o
r
b
y
t
h
e
Mic
r
o
g
r
id
C
o
n
tr
o
l
C
en
tr
e
(
MG
C
C
)
.
[
1
8
]
-
[
2
0
]
.
Fig
u
r
e
6
s
h
o
w
s
th
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
P
Q
co
n
tr
o
l stra
teg
y
.
T
h
e
m
ea
s
u
r
ed
v
al
u
es o
f
t
h
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
ca
n
b
e
ex
p
r
ess
ed
as
=
3
2
(
∗
+
∗
)
(
5
)
=
3
2
(
∗
−
∗
)
(
6
)
T
h
e
v
ar
iatio
n
in
f
r
eq
u
e
n
c
y
a
n
d
v
o
ltag
e
ar
e
co
n
s
id
er
ed
to
ad
j
u
s
t
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
.
T
h
e
eq
u
atio
n
s
(
7
)
an
d
(
8
)
p
r
o
v
id
e
th
e
d
etails
o
f
d
r
o
o
p
ad
j
u
s
t
m
e
n
t
in
v
o
lta
g
e
an
d
f
r
eq
u
e
n
c
y
to
co
n
tr
o
l
th
e
cu
r
r
en
t
lo
o
p
an
d
v
o
ltag
e
lo
o
p
(
s
ee
Fig
u
r
e
6
)
=
∗
−
(
+
)
(
−
∗
)
(
7
)
=
∗
−
(
+
)
(
−
∗
)
(
8
)
3
.
4
.
V
-
f
Co
ntr
o
l st
ra
t
eg
y
Fo
r
a
r
eliab
le
o
p
er
atio
n
o
f
th
e
m
icr
o
g
r
id
,
it
is
n
ec
es
s
ar
y
to
en
s
u
r
e
th
e
co
n
ti
n
u
o
u
s
tr
an
s
i
tio
n
b
et
w
ee
n
th
e
m
icr
o
g
r
id
m
o
d
es
an
d
k
e
ep
a
s
tab
le
o
p
er
atio
n
d
u
r
in
g
th
e
is
la
n
d
in
g
m
o
d
e
i
n
ter
m
s
o
f
r
eg
u
lati
n
g
t
h
e
m
icr
o
g
r
id
v
o
ltag
e
a
n
d
f
r
eq
u
en
c
y
w
it
h
r
esp
ec
t
to
th
e
lo
ad
d
em
an
d
.
I
n
t
h
is
ca
s
e,
t
h
e
DG
u
n
its
m
u
s
t
f
o
llo
w
t
h
e
lo
ad
d
em
a
n
d
an
d
m
ai
n
tai
n
t
h
e
v
o
ltag
e
an
d
f
r
eq
u
e
n
c
y
w
i
th
in
th
r
es
h
o
ld
li
m
its
,
s
o
th
at
V
-
f
c
o
n
tr
o
l
m
o
d
e
h
a
s
to
be
ad
o
p
ted
b
y
o
n
e
o
r
m
o
r
e
DG
u
n
its
i
n
o
r
d
er
to
s
atis
f
y
th
e
ab
o
v
e
r
eq
u
ir
e
m
en
t
s
[
9
]
.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
ap
p
licatio
n
is
s
h
o
w
n
i
n
Fi
g
u
r
e
7
.
Sin
ce
th
e
r
ef
er
e
n
ce
v
o
lta
g
e
an
d
f
r
eq
u
e
n
c
y
v
al
u
es
ca
n
b
e
d
ef
in
ed
lo
ca
ll
y
,
t
h
e
f
r
eq
u
en
c
y
ca
n
b
e
m
ea
s
u
r
ed
b
y
th
e
P
L
L
as
∗
=
∗
−
+
(
9
)
∗
=
∗
−
+
(
10
)
T
h
e
s
y
s
te
m
t
u
r
n
s
in
to
g
r
id
-
co
n
n
ec
ted
m
o
d
e
w
h
e
n
th
er
e
is
d
r
o
p
in
f
r
eq
u
en
c
y
an
d
v
o
lta
g
e,
th
e
r
ea
s
o
n
b
eh
in
d
i
s
t
h
e
c
h
a
n
g
e
in
i
m
p
ed
an
ce
v
alu
e
an
d
th
e
d
is
t
u
r
b
an
c
e
in
th
e
P
L
L
.
T
h
e
m
ea
s
u
r
ed
r
ea
ctiv
e
i
s
co
m
p
ar
ed
w
it
h
r
e
f
er
en
ce
r
ea
ctiv
e
p
o
w
e
r
to
r
eg
u
la
te
t
h
e
v
o
ltag
e.
T
h
e
m
ea
s
u
r
ed
d
i
f
f
er
e
n
ce
co
m
b
i
n
ed
w
it
h
d
r
o
o
p
co
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
139
–
1
4
9
144
ef
f
icien
t
p
r
o
d
u
ce
s
d
ir
ec
t
ax
is
an
d
q
u
ad
r
atu
r
e
ax
is
v
o
ltag
e.
T
h
e
d
an
d
q
v
o
ltag
es
ar
e
co
m
p
ar
ed
an
d
r
eg
u
lated
th
r
o
u
g
h
P
I
co
n
tr
o
ller
in
o
r
d
er
to
o
b
tain
th
e
n
e
w
d
an
d
q
cu
r
r
en
t
r
ef
er
e
n
ce
v
al
u
e
s
.
T
h
e
ch
an
g
es
o
f
d
a
n
d
q
ax
i
s
cu
r
r
en
ts
ar
e
r
ep
r
esen
ted
b
y
(
1
1
)
an
d
(
1
2
)
r
esp
ec
tiv
el
y
.
∗
=
(
+
/
)
(
∗
−
)
(
11
)
∗
=
(
+
/
)
(
∗
−
(
12
)
4.
P
O
WE
R
SH
AR
I
N
G
F
O
R
P
ARAL
L
E
L
CO
NN
E
CT
E
D
CO
NVER
T
E
R
O
P
E
RA
T
I
O
NS
T
h
e
d
r
o
o
p
tech
n
iq
u
e
h
as
b
ee
n
w
id
el
y
u
s
ed
as
a
p
o
w
er
s
h
ar
i
n
g
s
c
h
e
m
e
in
co
n
v
e
n
tio
n
a
l
p
o
w
er
s
y
s
te
m
w
it
h
m
u
ltip
le
g
e
n
er
ato
r
s
.
I
n
t
h
is
m
eth
o
d
,
t
h
e
g
e
n
er
ato
r
s
s
h
ar
e
th
e
s
y
s
te
m
lo
ad
b
y
d
r
o
o
p
in
g
w
i
th
th
e
f
r
eq
u
e
n
c
y
o
f
ea
ch
g
e
n
er
ato
r
w
ith
t
h
e
r
ea
l
p
o
w
er
(
P
)
d
eliv
er
e
d
b
y
th
e
g
en
er
ato
r
.
T
h
is
allo
w
s
ea
c
h
g
e
n
er
ato
r
to
s
h
ar
e
th
e
ch
an
g
es
i
n
to
tal
lo
ad
in
a
m
a
n
n
er
d
eter
m
in
ed
b
y
its
f
r
eq
u
en
c
y
d
r
o
o
p
ch
ar
ac
ter
is
tic
an
d
es
s
en
tia
ll
y
u
tili
ze
s
th
e
s
y
s
te
m
f
r
eq
u
en
c
y
a
s
a
co
m
m
u
n
ica
tio
n
lin
k
b
et
w
ee
n
th
e
g
e
n
er
ato
r
co
n
tr
o
l
s
y
s
te
m
s
.
Si
m
i
lar
l
y
,
a
d
r
o
p
in
th
e
v
o
ltag
e
a
m
p
lit
u
d
e
w
ith
r
ea
cti
v
e
p
o
w
er
(
Q
)
is
u
s
ed
to
en
s
u
r
e
r
ea
ctiv
e
p
o
w
er
s
h
ar
in
g
.
1
1
V
2
2
V
L
o
a
d
I
1
I
2
V
1
1
1
L
j
R
Z
2
2
2
L
j
R
Z
Φ
V
1
V
2
I
R
V
2
j
X
.
I
(
a)
(
b
)
Fig
u
r
e
8
.
(
a)
Sin
g
le
P
h
ase
eq
u
iv
ale
n
t c
ir
cu
it (
b
)
its
r
esp
ec
ti
v
e
p
h
aso
r
d
iag
r
a
m
Sin
ce
t
h
is
lo
ad
s
h
ar
in
g
tech
n
i
q
u
e
is
b
ased
o
n
th
e
p
o
w
er
f
lo
w
t
h
eo
r
y
i
n
an
AC
s
y
s
te
m
,
wh
ich
s
tates
th
at
th
e
f
lo
w
o
f
th
e
ac
tiv
e
p
o
w
er
(
P
)
an
d
r
ea
ctiv
e
p
o
w
er
(
Q)
b
et
w
ee
n
t
w
o
s
o
u
r
ce
s
ca
n
b
e
co
n
tr
o
lled
b
y
ad
j
u
s
tin
g
th
e
p
o
w
er
a
n
g
le
a
n
d
th
e
v
o
ltag
e
m
a
g
n
i
tu
d
e
o
f
e
ac
h
s
y
s
te
m
.
T
h
e
ac
tiv
e
p
o
w
er
f
lo
w
(
P
)
is
m
ain
l
y
co
n
tr
o
lled
b
y
th
e
p
o
w
er
a
n
g
le
,
w
h
i
le
th
e
r
ea
ctiv
e
p
o
w
er
(
Q
)
is
m
ai
n
l
y
co
n
tr
o
lled
b
y
th
e
v
o
ltag
es
m
ag
n
it
u
d
e,
in
d
icate
s
cr
it
ical
v
ar
iab
les
f
o
r
lo
ad
-
s
h
ar
i
n
g
co
n
tr
o
l
o
f
p
ar
alleled
p
o
w
er
co
n
v
er
ter
s
as
g
i
v
e
n
in
Fig
u
r
e.
8
(
a
-
b
)
.
As
it
s
h
o
w
s
,
th
e
s
u
p
p
l
y
f
r
o
m
i
n
v
er
ted
s
o
u
r
ce
(V
1
)
an
d
s
u
p
p
l
y
f
r
o
m
g
r
id
s
id
e
(V
2
)
r
ep
r
esen
ted
b
y
t
w
o
v
o
lta
g
e
s
o
u
r
ce
s
ar
e
co
n
n
ec
ted
to
a
lo
ad
th
r
o
u
g
h
l
in
e
i
m
p
ed
an
ce
Z
r
ep
r
esen
ted
b
y
p
u
r
e
in
d
u
c
t
an
ce
s
L
1
an
d
L
2
f
o
r
s
i
m
p
li
f
ied
an
al
y
s
is
p
u
r
p
o
s
e.
No
te
th
at
=
+
;
=
an
d
=
2
.
I
n
g
en
er
al,
th
e
co
m
p
lex
p
o
w
er
at
th
e
lo
ad
d
u
e
to
th
e
in
v
er
ter
m
e
asu
r
ed
at
an
y
n
et
w
o
r
k
is
g
iv
e
n
b
y
=
+
=
.
∗
(
13
)
w
h
er
e,
i
: 1
,
2
.
∗
is
th
e
co
m
p
le
x
co
n
j
u
g
ate
o
f
th
e
i
n
v
er
ter
cu
r
r
en
t a
n
d
it c
an
b
e
ex
p
r
es
s
ed
as
∗
=
[
+
−
+
]
∗
(
14
)
=
2
[
1
+
2
−
2
+
]
∗
(
15
)
B
ased
o
n
th
e
s
i
n
g
le
p
h
ase
e
q
u
iv
ale
n
t
cir
c
u
it
o
f
t
h
e
n
et
wo
r
k
(
Fig
u
r
e
8
(
a)
)
an
d
th
e
cu
r
r
en
t
an
d
co
m
p
le
x
p
o
w
er
eq
u
a
tio
n
s
(
1
4
)
an
d
(
1
5
)
,
th
e
p
h
aso
r
d
iag
r
am
is
o
b
tai
n
ed
as
g
i
v
e
n
in
Fi
g
u
r
e
8
(
b
)
.
Fu
r
th
er
,
co
n
s
id
er
ed
th
e
p
o
w
er
co
n
v
er
t
er
as
an
id
ea
l
v
o
lta
g
e
s
o
u
r
ce
co
n
n
ec
ted
to
th
e
m
ai
n
g
r
id
t
h
r
o
u
g
h
a
g
i
v
en
l
in
e
i
m
p
ed
an
ce
,
th
e
ac
t
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
i
s
d
eliv
er
ed
to
th
e
g
r
id
as g
i
v
en
b
y
1
=
1
2
+
2
[
(
1
−
2
)
+
2
]
(
16
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
ew s
t
r
a
teg
y
fo
r
o
n
-
L
in
e
D
r
o
o
p
a
d
j
u
s
tmen
t fo
r
Micr
o
g
r
i
d
co
n
n
ec
ted
DGs
..
(
S
a
th
ya
p
r
a
b
a
ka
r
a
n
B
)
145
1
=
1
2
+
2
[
−
2
+
(
1
−
2
)
]
(
17
)
w
h
er
e
P
1
an
d
Q
1
ar
e
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
s
r
esp
ec
ti
v
el
y
f
lo
w
in
g
f
r
o
m
th
e
s
o
u
r
ce
1
(
p
o
w
er
co
n
v
er
ter
)
to
th
e
s
o
u
r
ce
2
(
g
r
id
)
,
V
1
an
d
V
2
ar
e
th
e
v
o
ltag
e
v
al
u
es
o
f
th
ese
s
o
u
r
ce
s
,
co
r
r
esp
o
n
d
s
to
th
e
p
h
ase
-
a
n
g
le
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
t
w
o
v
o
ltag
es a
n
d
∅
is
th
e
i
m
p
ed
an
ce
a
n
g
le.
Ass
u
m
in
g
s
i
n
≈
an
d
co
s
≈
1
,
(
1
6
)
an
d
(
1
7
)
ca
n
b
e
r
e
w
r
itte
n
as,
1
=
1
(
2
)
⇒
=
1
1
2
(
18
)
1
=
1
(
1
−
2
)
⇒
1
−
2
=
1
1
(
19
)
T
h
e
d
ir
ec
t
r
elatio
n
s
h
ip
b
et
w
e
en
th
e
p
o
w
er
a
n
g
le
an
d
th
e
ac
tiv
e
p
o
w
er
P
as
w
ell
as
th
e
v
o
ltag
e
d
if
f
er
e
n
ce
V
1
–
V
2
an
d
th
e
r
ea
ctiv
e
p
o
w
er
Q
ca
n
b
e
o
b
s
er
v
ed
f
r
o
m
eq
u
atio
n
s
(
1
8
)
an
d
(
1
9
)
.
T
h
ese
r
elatio
n
s
h
ip
s
p
er
m
it
r
e
g
u
la
tin
g
th
e
g
r
id
f
r
eq
u
e
n
c
y
a
n
d
v
o
ltag
e
at
t
h
e
p
o
in
t
o
f
co
n
n
ec
t
io
n
o
f
th
e
p
o
w
er
co
n
v
er
ter
,
b
y
co
n
tr
o
llin
g
t
h
e
v
alu
e
o
f
th
e
ac
ti
v
e
a
n
d
r
ea
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ev
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ip
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r
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ch
ar
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as s
h
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g
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r
e
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.
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0
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V
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u
r
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.
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o
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ter
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tics
o
f
v
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g
e
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u
r
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ltag
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d
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p
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s
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y
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as
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g
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r
e
9
,
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ch
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t
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[
1
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p
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iv
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n
i
n
T
ab
le
1
.
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I
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N
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8
8
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I
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&
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9
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1
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r
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139
–
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
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[2
]
KT
T
a
n
,
X
Y
P
e
n
g
,
P
L
S
o
,
YC
C
h
u
.
Ce
n
tralize
d
c
o
n
tro
l
f
o
r
P
a
ra
ll
e
l
Op
e
ra
ti
o
n
o
f
Distrib
u
te
d
G
e
n
e
ra
ti
o
n
I
n
v
e
rters
in
M
icr
o
g
rid
s.
IEE
E
T
r
a
n
s.
S
ma
rt
Gr
id
.
2
0
1
2
;
3
(4
):
1
9
7
7
-
1
9
8
.
[3
]
Ng
u
y
e
n
T
ien
Ha
i,
K
y
e
o
n
g
-
H
w
a
Kim
.
A
n
A
d
a
p
ti
v
e
V
irt
u
a
l
Im
p
e
d
a
n
c
e
Ba
se
d
Dro
o
p
Co
n
tr
o
l
S
c
h
e
m
e
f
o
r
P
a
ra
ll
e
l
In
v
e
rter
Op
e
ra
ti
o
n
in
L
o
w
V
o
lt
a
g
e
M
icro
g
rid
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m.
2
0
1
6
;
7
(4
):
1
3
0
9
-
1
3
1
9
.
[4
]
W
e
n
lei
Ba
i
M
,
Re
z
a
A
b
e
d
i
,
K
w
a
n
g
Y.L
e
e
.
Distrib
u
ted
g
e
n
e
ra
ti
o
n
s
y
ste
m
c
o
n
tro
l
stra
teg
ies
w
it
h
P
V an
d
f
u
e
l
c
e
ll
in
m
icro
g
rid
o
p
e
ra
ti
o
n
.
Co
n
tro
l
En
g
in
e
e
rin
g
Pr
a
c
ti
c
e
.
2
0
1
6
;
5
3
:
1
8
4
-
1
9
3
.
[5
]
A
sh
ish
k
u
m
a
r
S
o
lan
k
i,
A
d
e
l
Na
siri
,
e
t
a
l,
A
Ne
w
F
ra
m
e
w
o
rk
f
o
r
M
icro
g
rid
M
a
n
a
g
e
m
e
n
t:
V
irt
u
a
l
Dro
o
p
Co
n
tro
l
.
IEE
E
T
ra
n
s.
S
ma
rt Gri
d
.
2
0
1
6
;
7
(
2
):5
5
4
-
5
6
6
.
[6
]
Zh
ik
a
n
g
S
h
u
a
i,
S
h
a
n
g
li
m
M
o
,
Ju
n
Wan
g
,
e
t
a
l.
Dro
o
p
c
o
n
tro
l
m
e
th
o
d
f
o
r
lo
a
d
sh
a
re
a
n
d
v
o
lt
a
g
e
re
g
u
latio
n
in
h
ig
h
-
v
o
lt
a
g
e
m
icro
g
rid
s.
J
o
u
rn
a
l
o
f
M
o
d
e
rn
P
o
we
r S
y
st.
a
n
d
Clea
n
E
n
e
rg
y
.
2
0
1
6
;
4
(
1
):7
6
–
8
6
.
[7
]
L
u
X
iao
n
a
n
,
Jo
se
p
G
u
e
rre
ro
,
e
t
a
l.
Co
n
tro
l
o
f
p
a
ra
ll
e
l
-
c
o
n
n
e
c
te
d
b
i
d
irec
ti
o
n
a
l
A
C
-
DC
c
o
n
v
e
rte
rs
in
sta
ti
o
n
a
ry
f
ra
m
e
f
o
r
m
icro
g
rid
a
p
p
li
c
a
ti
o
n
.
3
rd
IEE
E
En
e
rg
y
C
o
n
v
.
C
o
n
g
re
ss
a
n
d
Ex
p
o
siti
o
n
.
2
0
1
1
;
1
:4
1
5
3
-
4
1
6
0
.
[8
]
V
Ra
v
ik
u
m
a
r
P
a
n
d
i,
A
L
A
l
-
Hin
a
i,
A
li
F
e
li
a
c
h
i
.
Co
o
r
d
in
a
te
d
c
o
n
tr
o
l
o
f
d
istri
b
u
ted
e
n
e
rg
y
re
so
u
rc
e
s
to
su
p
p
o
rt
lo
a
d
f
re
q
u
e
n
c
y
c
o
n
tro
l.
En
e
rg
y
C
o
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
.
2
0
1
5
;
1
0
5
:9
1
8
–
9
2
8
.
[9
]
M
o
h
a
m
m
a
d
A
A
b
u
sa
ra
,
S
u
leim
a
n
n
M
S
h
re
k
h
,
J
o
se
p
h
M
G
u
e
rre
ro
.
Im
p
ro
v
e
d
d
ro
o
p
c
o
n
tr
o
l
str
a
teg
y
f
o
r
g
rid
-
c
o
n
n
e
c
ted
i
n
v
e
rters
.
S
u
st
a
in
a
b
le
En
e
rg
y
,
Gr
id
s
a
n
d
Ne
two
rk
s
.
2
0
1
5
;
1
:1
0
–
19.
[1
0
]
Ya
ju
a
n
G
u
a
n
,
Jo
se
p
h
M
G
u
e
rre
r
o
,
Xin
Z
h
a
o
,
e
t
a
l.
A
n
e
w
wa
y
o
f
c
o
n
tro
l
li
n
g
p
a
ra
ll
e
l
-
c
o
n
n
e
c
ted
in
v
e
rters
b
y
u
sin
g
s
y
n
c
h
ro
n
o
u
s
re
f
e
re
n
c
e
f
ra
m
e
v
irt
u
a
l
im
p
e
d
a
n
c
e
lo
o
p
–
P
a
rt
I:
Co
n
tro
l
P
rin
c
i
p
le.
IEE
E
T
ra
n
s.
P
o
we
r
El
e
c
tro
n
ics
.
2
0
1
6
;
3
1
(
6
):
4
5
7
6
–
4
5
9
3
.
[1
1
]
Us
m
a
n
Ba
sh
ir
T
a
y
a
b
a
,
M
o
h
d
A
z
ri
k
Bin
Ro
sla
m
,
e
t
a
l
.
A
re
v
i
e
w
o
f
d
ro
o
p
c
o
n
tr
o
l
tec
h
n
iq
u
e
s
f
o
r
m
icro
g
rid
.
Ren
e
wa
b
le
a
n
d
S
u
sta
in
a
b
le E
n
e
rg
y
Rev
iews
.
2
0
1
7
;
7
6
:7
1
7
–
7
2
7
.
[1
2
]
A
ll
a
l
M
Bo
u
z
id
,
A
h
m
e
d
Ch
a
rit
i
,
e
t
a
l
.
A
su
rv
e
y
o
n
c
o
n
tro
l
o
f
e
lec
tri
c
p
o
w
e
r
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
sy
ste
m
s
f
o
r
m
icro
g
rid
A
p
p
li
c
a
ti
o
n
s
.
Ren
e
wa
b
le a
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
Rev
iews
.
2
0
1
5
;
4
4
:7
5
1
–
7
6
6
.
[1
3
]
W
a
le
e
d
A
l
-
S
a
e
d
i,
S
tefa
n
W
L
a
c
h
o
w
icz
,
e
t
a
l
.
P
o
w
e
r
q
u
a
li
ty
e
n
h
a
n
c
e
m
e
n
t
in
a
u
to
n
o
m
o
u
s m
icro
g
rid
o
p
e
ra
ti
o
n
u
si
n
g
P
a
rti
c
le S
w
a
rm
Op
ti
m
iz
a
ti
o
n
.
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
ste
ms
.
2
0
1
2
:
4
2
(
1
):1
3
9
–
1
4
9
.
[1
4
]
A
li
Bid
ra
m
,
A
li
Da
v
o
u
d
i,
F
ra
n
k
L
L
e
w
is.
Distrb
u
ted
c
o
o
p
e
ra
ti
v
e
se
c
o
n
d
a
ry
c
o
n
tro
l
o
f
M
icro
g
rid
u
sin
g
F
e
e
d
b
a
c
k
li
n
e
a
riza
ti
o
n
.
IEE
E
T
ra
n
s.
P
o
we
r S
y
ste
ms
.
2
0
1
3
;2
8
(3
)
:3
4
6
2
-
3
4
7
0
.
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
0
5
10
15
20
25
30
35
40
D
i
r
e
c
t
axi
s
c
u
r
r
e
n
t
(
I
d
)
(
A
m
p
)
T
i
m
e
(
s
e
c
)
I
d
-
w
i
t
h
o
u
t
d
r
o
o
p
I
d
-
w
i
t
h
d
r
o
o
p
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-
100
0
100
200
300
400
500
T
i
m
e
(
s
e
c
)
V
d
,
V
q
(
vol
t
)
0.
22
0.
24
0.
26
0.
28
0.
3
400
420
440
0.
25
0.
3
0
20
40
60
V
d m
e
as
V
q re
f
V
q m
e
as
w
itho
ut
droop
w
ith d
roop
V
d re
f
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