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v
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1.
I
NT
RO
D
UCT
I
O
N
Mic
r
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g
r
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p
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r
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to
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s
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in
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ter
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to
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p
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AC
lo
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an
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co
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t
to
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Po
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in
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s
ar
e
co
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n
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ar
allel
[
1
]
,
[
2
]
.
C
u
r
r
en
tly
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th
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s
u
e
o
f
co
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tr
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llin
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allel
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ted
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ter
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id
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all
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[
3
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,
[
4
]
.
B
ased
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ter
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ies
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ch
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ter
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tr
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l
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tr
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allel
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ted
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co
r
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ter
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wev
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wer
s
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ar
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f
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r
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ter
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s
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if
ican
t
f
r
eq
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e
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cy
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n
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v
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d
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s
.
As
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em
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v
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wer
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r
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d
d
ec
r
ea
s
e
s
ig
n
if
ican
tly
[
3
]
,
[
4
]
.
R
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ch
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s
h
a
v
e
p
r
esen
ted
m
eth
o
d
s
to
im
p
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v
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s
lo
p
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ch
ar
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te
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tics
to
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n
ce
p
o
wer
-
s
h
ar
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g
ef
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cy
.
Ho
wev
e
r
,
th
e
im
p
r
o
v
em
e
n
ts
ar
e
n
o
t
aim
ed
a
t
r
ed
u
cin
g
v
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e
an
d
f
r
eq
u
en
cy
d
ev
iatio
n
s
to
im
p
r
o
v
e
p
o
wer
q
u
ality
[
5
]
-
[
7
]
.
I
n
ad
d
itio
n
,
s
o
m
e
r
esear
ch
wo
r
k
s
[
8
]
-
[
1
3
]
h
av
e
p
r
o
p
o
s
ed
m
eth
o
d
s
to
im
p
r
o
v
e
r
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an
d
s
av
e
c
o
s
ts
d
u
r
in
g
m
icr
o
g
r
id
o
p
er
atio
n
.
T
h
ese
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
s
m
ar
t
p
r
o
tectio
n
s
ch
em
es
f
o
r
m
icr
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g
r
id
s
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d
f
au
lt
id
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n
tific
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m
eth
o
d
s
d
u
r
in
g
o
p
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,
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m
e
a
d
ap
tiv
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r
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p
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tectio
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s
ch
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d
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t f
au
lts
an
d
is
o
late
f
au
lts
q
u
ick
ly
b
ased
o
n
wea
th
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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2088
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8
6
9
4
I
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v
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tive
fr
eq
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C
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r
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(
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Ho
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Th
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1487
Fu
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ly
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tain
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Fu
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co
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tr
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(
FLCs
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ased
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"
to
d
eter
m
in
e
th
e
o
p
tim
al
p
o
wer
allo
ca
tio
n
,
tak
in
g
in
t
o
ac
co
u
n
t
f
ac
t
o
r
s
s
u
ch
as
r
en
ewa
b
le
en
er
g
y
av
ailab
ilit
y
,
b
atter
y
s
t
ate
o
f
c
h
ar
g
e
(
SOC
)
,
an
d
lo
ad
d
em
a
n
d
.
FLC
is
r
o
b
u
s
t
t
o
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
an
ce
s
,
s
u
itab
le
f
o
r
p
r
ac
tical
m
icr
o
g
r
id
ap
p
licatio
n
s
,
FLC
ca
n
ad
ap
t
to
ch
an
g
in
g
co
n
d
itio
n
s
an
d
o
p
tim
ize
p
er
f
o
r
m
an
ce
b
ased
o
n
r
ea
l
-
tim
e
f
ee
d
b
ac
k
,
FLC
p
r
o
v
id
es
s
m
o
o
th
c
o
n
tr
o
l
r
esp
o
n
s
e,
s
im
p
le
d
esig
n
,
r
elativ
ely
f
ew
p
a
r
am
eter
s
an
d
r
u
les,
m
a
k
in
g
th
em
ea
s
ier
to
d
ep
lo
y
th
a
n
s
o
m
e
o
th
er
c
o
n
tr
o
l
s
tr
ateg
ies.
I
n
s
u
m
m
ar
y
,
f
u
zz
y
lo
g
ic
p
la
y
s
a
n
im
p
o
r
tan
t
r
o
le
i
n
p
o
wer
co
n
tr
o
l
f
o
r
m
icr
o
g
r
id
s
.
I
t
p
r
o
v
i
d
es
a
p
o
wer
f
u
l
an
d
f
lex
ib
le
ap
p
r
o
ac
h
to
m
an
ag
i
n
g
en
er
g
y
r
eso
u
r
ce
s
,
en
s
u
r
i
n
g
s
tab
ilit
y
an
d
o
p
tim
izin
g
p
er
f
o
r
m
an
ce
u
n
d
er
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
.
C
u
r
r
en
tly
,
th
er
e
h
av
e
b
ee
n
m
an
y
r
esear
ch
wo
r
k
s
ap
p
ly
in
g
FLC
to
m
icr
o
g
r
id
co
n
tr
o
l
.
R
esear
ch
[
1
4
]
,
[
1
5
]
h
av
e
a
d
d
r
ess
ed
th
e
im
p
r
o
v
em
en
t
o
f
th
e
co
n
tr
o
ller
f
o
r
t
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
co
n
n
ec
ted
to
t
h
e
b
atter
y
e
n
er
g
y
s
to
r
ag
e
s
y
s
tem
,
u
n
d
er
th
e
co
n
d
itio
n
s
o
f
s
o
lar
r
ad
iatio
n
,
tem
p
er
atu
r
e,
n
o
n
-
lin
ea
r
co
n
d
itio
n
s
,
an
d
lo
ad
.
R
esear
ch
[
1
6
]
,
[
1
7
]
h
av
e
p
r
o
p
o
s
ed
an
o
p
tim
al
DC
b
u
s
v
o
lta
g
e
r
eg
u
latio
n
m
eth
o
d
u
s
in
g
ad
a
p
tiv
e
FLC
an
d
a
n
ew
m
o
n
ito
r
i
n
g
p
o
wer
m
an
a
g
em
en
t
s
tr
ateg
y
f
o
r
PV
s
y
s
tem
s
.
T
h
e
g
o
al
is
to
m
ain
tain
a
s
tab
le
p
o
wer
f
lo
w
in
th
e
s
y
s
tem
.
Stu
d
ies
[
1
8
]
,
[
1
9
]
h
av
e
p
r
o
p
o
s
ed
a
n
en
er
g
y
m
an
ag
em
en
t
m
eth
o
d
f
o
r
m
icr
o
g
r
id
s
b
ased
o
n
f
u
zz
y
lo
g
ic
an
d
d
ata
an
aly
s
is
m
o
n
ito
r
in
g
to
ad
ju
s
t th
e
o
p
tim
al
p
o
w
er
o
f
o
b
jects in
th
e
m
icr
o
g
r
id
.
Ho
wev
e
r
,
m
o
s
t
o
f
th
e
r
esear
ch
is
o
n
ly
ap
p
lied
t
o
th
e
DC
s
u
b
g
r
id
o
f
th
e
m
icr
o
g
r
id
;
t
h
er
e
a
r
e
n
o
t
m
an
y
s
tu
d
ies ap
p
lied
to
th
e
A
C
g
r
id
o
f
th
e
m
icr
o
g
r
id
.
T
h
is
ar
ticle
p
r
o
p
o
s
es
a
co
n
tr
o
ller
f
o
r
in
v
e
r
ter
s
u
s
in
g
f
u
zz
y
lo
g
ic
to
s
tab
ly
ad
ju
s
t
th
e
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
f
o
r
th
e
AC
m
icr
o
g
r
id
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
will
o
f
f
er
th
e
f
o
llo
win
g
b
en
e
f
its
:
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
ca
n
au
to
m
atica
lly
ad
ju
s
t
th
e
f
r
eq
u
en
cy
an
d
v
o
l
tag
e
o
f
th
e
m
icr
o
g
r
id
.
I
n
a
d
d
itio
n
,
th
is
co
n
t
r
o
l
m
eth
o
d
also
m
ax
im
izes th
e
p
o
wer
d
is
tr
ib
u
tio
n
ef
f
icien
cy
f
o
r
th
e
in
v
er
ter
s
.
T
h
er
ef
o
r
e,
th
is
co
n
tr
o
ller
will k
ee
p
th
e
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
in
th
e
m
icr
o
g
r
id
s
tab
le,
o
n
ly
v
ar
y
in
g
with
in
th
e
p
er
m
is
s
ib
le
r
an
g
e,
e
n
s
u
r
e
th
e
ac
cu
r
ac
y
o
f
p
o
wer
s
h
ar
in
g
b
etwe
en
in
v
er
ter
s
,
an
d
also
elim
in
ate
th
e
b
alan
cin
g
c
u
r
r
en
t
f
lo
win
g
in
t
h
e
in
v
er
ter
s
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
is
ap
p
lied
to
p
o
wer
c
o
n
tr
o
l
f
o
r
a
co
m
m
o
n
m
icr
o
g
r
i
d
with
th
e
co
n
f
ig
u
r
atio
n
in
Fig
u
r
e
1
[
2
0
]
-
[
2
3
]
.
T
h
is
co
n
f
ig
u
r
atio
n
in
v
o
lv
es
in
ter
co
n
n
ec
ted
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
o
n
a
DC
b
u
s
.
T
h
is
ty
p
e
o
f
co
n
f
ig
u
r
atio
n
r
e
d
u
ce
s
th
e
n
u
m
b
er
o
f
in
v
er
ter
s
,
an
d
th
e
s
y
s
tem
ca
n
o
p
er
ate
f
le
x
ib
ly
d
ep
e
n
d
in
g
o
n
th
e
co
n
tr
o
l
m
eth
o
d
.
T
h
is
ar
ti
cle
f
o
cu
s
es
o
n
c
o
n
tr
o
l
m
eth
o
d
s
to
m
ain
tain
v
o
ltag
e
an
d
f
r
eq
u
en
c
y
s
tab
ilit
y
,
m
in
im
ize
f
r
eq
u
en
cy
a
n
d
v
o
lt
ag
e
d
ev
iatio
n
o
f
th
e
m
icr
o
g
r
i
d
,
an
d
s
h
a
r
e
th
e
p
o
wer
o
u
tp
u
t
p
r
ec
is
ely
with
th
e
in
v
er
ter
s
.
T
h
e
r
ef
o
r
e
,
th
e
r
en
e
wab
le
en
er
g
y
s
o
u
r
ce
s
c
o
n
ce
n
t
r
ated
o
n
th
e
DC
b
u
s
in
Fig
u
r
e
1
ar
e
ass
u
m
ed
to
alwa
y
s
p
r
o
v
id
e
s
u
f
f
icien
t p
o
w
er
to
th
e
lo
a
d
s
.
Fig
u
r
e
1
.
C
o
n
f
ig
u
r
atio
n
o
f
a
c
o
m
m
o
n
s
tan
d
alo
n
e
m
ic
r
o
g
r
i
d
2.
M
E
T
H
O
D
T
h
e
f
o
cu
s
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
is
:
i
)
m
ain
tain
in
g
v
o
ltag
e
a
n
d
f
r
e
q
u
en
c
y
s
tab
ilit
y
,
m
in
im
izin
g
f
r
eq
u
e
n
cy
an
d
v
o
ltag
e
d
e
v
iatio
n
s
o
f
th
e
m
icr
o
g
r
id
,
ii)
ac
c
u
r
ately
d
is
tr
ib
u
tin
g
p
o
we
r
to
th
e
in
v
er
ter
s
to
elim
in
ate
cir
cu
lati
n
g
cu
r
r
en
t a
n
d
n
o
is
e
cu
r
r
en
ts
g
en
er
ated
wh
e
n
th
e
in
v
er
ter
o
u
tp
u
t p
ar
a
m
eter
s
ar
e
in
co
n
s
is
ten
t.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l m
eth
o
d
is
im
p
lem
en
ted
a
s
f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
4
8
6
-
1498
1488
-
First,
b
ased
o
n
th
e
th
eo
r
etic
al
b
asis
o
f
th
e
co
n
v
en
tio
n
al
Dr
o
o
p
m
eth
o
d
f
o
r
p
o
wer
s
h
ar
in
g
am
o
n
g
in
v
er
ter
s
.
Stu
d
ies
[
3
]
-
[
5
]
p
r
es
en
ted
th
e
d
r
o
o
p
m
eth
o
d
f
o
r
l
o
w
-
v
o
ltag
e
n
etwo
r
k
s
,
th
e
d
r
o
o
p
m
eth
o
d
f
o
r
m
ed
iu
m
-
v
o
ltag
e
n
etwo
r
k
s
wa
s
p
r
esen
ted
i
n
s
tu
d
ies
[
6
]
-
[
8
]
,
an
d
s
tu
d
ies
[
9
]
-
[
1
3
]
p
r
esen
t
ed
th
e
d
r
o
o
p
m
eth
o
d
f
o
r
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
f
r
o
m
lo
w
to
m
ed
iu
m
v
o
ltag
e
to
ex
p
an
d
th
e
ap
p
licatio
n
s
co
p
e
o
f
th
e
d
r
o
o
p
m
eth
o
d
.
T
h
e
th
eo
r
etica
l
b
asis
o
f
th
e
co
n
v
en
tio
n
al
d
r
o
o
p
m
eth
o
d
is
p
r
esen
ted
i
n
s
ec
tio
n
2
.
1
.
-
Nex
t,
th
e
d
is
ad
v
an
tag
es
o
f
th
e
co
n
v
en
tio
n
al
Dr
o
o
p
m
eth
o
d
p
r
esen
ted
in
s
ec
tio
n
2
.
1
a
r
e
an
aly
s
ed
as
f
o
llo
ws:
i)
it
is
im
p
o
s
s
ib
le
to
ac
cu
r
ately
s
h
ar
e
p
o
wer
wh
e
n
th
e
o
u
tp
u
t
p
ar
am
eter
s
o
f
th
e
in
v
er
ter
ar
e
in
co
n
s
is
ten
t,
lead
in
g
t
o
th
e
ap
p
ea
r
an
ce
o
f
cir
c
u
latin
g
c
u
r
r
e
n
t
an
d
n
o
is
e
cu
r
r
en
t
th
at
d
am
ag
e
th
e
in
v
e
r
ter
;
ii)
wh
en
th
e
lo
ad
in
cr
ea
s
es
o
r
d
ec
r
ea
s
es
s
h
ar
p
ly
,
it
will
ca
u
s
e
v
er
y
lar
g
e
f
r
eq
u
en
cy
an
d
v
o
ltag
e
d
ev
iatio
n
s
,
wh
ich
m
a
y
ex
ce
e
d
th
e
p
er
m
is
s
ib
le
r
an
g
e
.
T
h
is
co
n
ten
t is p
r
esen
ted
in
s
ec
tio
n
2
.
2
.
-
Fin
ally
,
th
e
p
ap
er
p
r
o
p
o
s
es
a
m
eth
o
d
to
im
p
r
o
v
e
th
e
c
o
n
v
e
n
tio
n
al
Dr
o
o
p
c
o
n
tr
o
ller
b
y
:
i)
u
s
in
g
a
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
in
co
m
b
in
ati
o
n
with
th
e
co
n
v
e
n
tio
n
al
Dr
o
o
p
co
n
t
r
o
ller
.
T
h
e
f
u
zz
y
c
o
n
tr
o
ller
will
au
to
m
atica
lly
ad
ju
s
t
th
e
s
lip
c
o
ef
f
icien
t
to
s
h
if
t
th
e
Dr
o
o
p
g
r
ap
h
.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
will
r
esu
lt
in
:
ac
cu
r
ate
p
o
wer
s
h
a
r
in
g
am
o
n
g
th
e
in
v
er
ter
s
,
th
er
e
b
y
eli
m
in
atin
g
th
e
cy
clic
c
u
r
r
en
t;
an
d
r
ed
u
ce
d
f
r
eq
u
e
n
cy
an
d
v
o
ltag
e
d
ev
iati
o
n
s
o
f
th
e
m
icr
o
g
r
i
d
wh
en
th
e
lo
ad
ch
an
g
es.
T
h
is
is
p
r
esen
ted
in
s
ec
tio
n
2
.
3
.
ii)
On
th
e
o
th
er
h
an
d
,
to
m
ain
tain
th
e
s
tab
ilit
y
o
f
th
e
co
n
tr
o
l
s
y
s
tem
f
o
r
th
e
m
icr
o
g
r
id
,
th
e
p
ap
e
r
also
u
s
es
a
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
(
SMC
)
in
s
tead
o
f
th
e
co
n
v
en
tio
n
al
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
atin
g
(
PI)
co
n
tr
o
ller
.
T
h
e
SMC
will
s
tab
ilize
th
e
cu
r
r
en
t
a
n
d
v
o
ltag
e
a
t
th
e
in
v
er
ter
o
u
tp
u
t.
iii)
Simu
latio
n
r
esu
lts
in
s
ec
tio
n
3
will d
em
o
n
s
tr
ate
th
e
s
u
itab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
2
.
1
.
P
o
wer
co
ntr
o
l us
ing
t
he
t
ra
ditio
na
l D
ro
o
p
m
et
ho
d
Acc
o
r
d
in
g
to
s
tu
d
ies
[
1
]
–
[
4
]
,
th
e
tr
ad
itio
n
al
Dr
o
o
p
m
eth
o
d
f
o
r
p
o
we
r
d
is
tr
ib
u
tio
n
b
etw
ee
n
p
o
wer
s
o
u
r
ce
s
is
d
er
iv
ed
f
r
o
m
th
e
e
q
u
iv
alen
t
cir
cu
it
s
h
o
w
n
in
Fig
u
r
e
2
.
B
ased
o
n
Fig
u
r
e
2
,
s
tu
d
ies
[
1
]
-
[
4
]
h
a
v
e
ca
lcu
lated
th
e
p
o
wer
s
u
p
p
lied
b
y
th
e
p
o
wer
s
o
u
r
ce
to
th
e
l
o
a
d
as
(
1
)
.
S
̃
=
V
̇
.
I
*
=
V
̇
.
(
V
̇
-
V
̇
AC
Z
̇
)
*
=
V
.e
j
δ
1
(
V
e
j
δ
1
-
V
AC
e
j
δ
2
Z
e
j
θ
)
*
=
P
+
jQ
(
1
)
W
h
e
r
e
R
a
n
d
X
=
L
a
r
e
t
h
e
r
e
s
is
t
a
n
c
e
a
n
d
r
e
a
c
t
a
n
c
e
o
f
a
c
o
n
d
u
c
t
o
r
;
V
is
t
h
e
v
o
lt
a
g
e
a
t
t
h
e
s
o
u
r
c
e
;
V
AC
i
s
t
h
e
v
o
l
t
a
g
e
a
t
t
h
e
e
n
d
o
f
t
h
e
li
n
e
;
an
d
is
th
e
p
h
ase
an
g
le
d
if
f
er
e
n
ce
b
etwe
en
V
an
d
V
AC
:
=
1
−
δ
2
Z
̇
=
Z
e
j
θ
=R+jX
T
h
e
(
1
)
ca
n
b
e
tr
an
s
f
o
r
m
ed
in
t
o
:
s
in
δ =
XP
-
RQ
V
V
AC
(
2
)
.
V
-
V
AC
co
s
δ =
R
P
+
XQ
V
(
3
)
Acc
o
r
d
in
g
to
s
tu
d
ies
[
5
]
-
[
7
]
,
t
h
e
ac
tu
al
an
g
le
is
a
s
m
all
v
alu
e,
s
o
s
in
≈
an
d
co
s
=1
,
wh
en
X
>>
R
,
f
r
o
m
(
2
)
an
d
(
3
)
ca
n
b
e
wr
itten
(
4
)
an
d
(
5
)
.
δ=
XP
V
V
AC
(
4
)
V
-
V
AC
=
XQ
V
(
5
)
Acc
o
r
d
in
g
to
s
tu
d
ies
[
8
]
-
[
1
0
]
,
f
r
o
m
(
4
)
a
n
d
(
5
)
,
th
e
s
lo
p
e
co
n
tr
o
ller
s
P/f
an
d
Q/V
ca
n
b
e
s
et
u
p
to
co
n
tr
o
l
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
t
h
e
in
v
er
ter
s
as
(
6
)
an
d
(
7
)
.
f
=
f
0
-
m
p
P
(
6
)
V=
V
0
-
m
q
Q
(
7
)
m
p
c
h
a
r
a
c
t
e
r
i
ze
s
t
h
e
s
l
o
p
e
o
f
(
6
)
,
m
q
c
h
a
r
a
c
t
e
r
i
ze
s
t
h
e
s
l
o
p
e
o
f
(
7
)
,
a
n
d
t
h
e
y
a
r
e
c
a
l
c
u
l
a
t
e
d
as
(
8
)
.
m
p
=
f
0
-
f
min
P
max
;
m
q
=
V
0
-
V
min
Q
max
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
n
n
o
v
a
tive
fr
eq
u
en
cy
a
n
d
v
o
lta
g
e
co
n
tr
o
ller
fo
r
A
C
mic
r
o
g
r
id
…
(
X
u
a
n
Ho
a
Th
i P
h
a
m
)
1489
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it d
i
ag
r
am
o
f
a
p
o
wer
s
o
u
r
ce
s
u
p
p
ly
in
g
a
lo
a
d
2
.
2
.
Ana
ly
s
is
o
f
t
he
cha
r
a
ct
e
ristics o
f
t
he
t
ra
ditio
na
l D
ro
pp
er
m
et
ho
d
T
h
e
(
6
)
is
d
r
awn
i
n
Fig
u
r
e
3
(
Dr
o
o
p
P/f)
.
I
t
s
h
o
ws
th
at
if
th
e
lo
ad
i
n
cr
ea
s
es,
th
e
f
r
e
q
u
en
cy
will
d
ec
r
ea
s
e,
an
d
if
t
h
e
lo
a
d
in
cr
ea
s
es
s
ig
n
if
ican
tly
,
th
e
f
r
eq
u
en
cy
will
d
ec
r
ea
s
e
s
ig
n
if
ican
tly
.
T
h
er
e
f
o
r
e,
th
is
p
ap
er
will
p
r
esen
t
a
m
eth
o
d
to
s
h
if
t
th
e
Dr
o
o
p
P/f
c
h
ar
ac
ter
i
s
tic
cu
r
v
e
u
p
a
s
eg
m
e
n
t
to
b
ec
o
m
e
th
e
Dr
o
o
p
P/f'
ch
ar
ac
ter
is
tic
cu
r
v
e
to
r
ed
u
ce
th
e
f
r
eq
u
en
cy
d
ev
iatio
n
f
r
o
m
th
e
r
ated
v
al
u
e
wh
en
t
h
e
l
o
ad
in
cr
ea
s
es.
T
h
e
co
n
ten
t o
f
th
e
f
r
e
q
u
en
c
y
s
h
if
ti
n
g
m
eth
o
d
will b
e
p
r
esen
ted
i
n
s
ec
tio
n
2
.
3
.
T
h
e
(
7
)
is
d
r
awn
in
Fig
u
r
e
4
(
Dr
o
o
p
Q/V)
.
I
t
s
h
o
ws
th
at
if
th
e
lo
ad
in
cr
ea
s
es,
th
e
v
o
ltag
e
will
d
ec
r
ea
s
e,
an
d
if
th
e
lo
ad
in
cr
e
ases
s
ig
n
if
ican
tly
,
th
e
v
o
ltag
e
will
d
ec
r
ea
s
e
s
ig
n
if
ican
tly
.
T
h
er
ef
o
r
e,
th
is
p
ap
er
will
p
r
esen
t
a
m
eth
o
d
t
o
s
h
if
t
th
e
Dr
o
o
p
Q/V
ch
ar
ac
ter
is
tic
cu
r
v
e
u
p
a
s
eg
m
e
n
t
to
b
ec
o
m
e
th
e
Dr
o
o
p
Q/V’
ch
ar
ac
ter
is
tic
cu
r
v
e
to
r
e
d
u
ce
th
e
v
o
ltag
e
d
e
v
iatio
n
f
r
o
m
th
e
r
ated
v
alu
e
wh
e
n
th
e
lo
a
d
in
c
r
ea
s
es.
T
h
e
co
n
ten
t
o
f
th
e
f
r
eq
u
en
cy
s
h
if
tin
g
m
eth
o
d
will
b
e
p
r
esen
ted
in
s
ec
ti
o
n
2
.
3
.
I
n
Fig
u
r
e
3
,
V
0
an
d
f
0
r
ep
r
esen
t
th
e
r
ated
v
alu
es
o
f
v
o
ltag
e
an
d
f
r
e
q
u
en
cy
,
r
esp
ec
tiv
ely
,
wh
ile
V
an
d
f
d
en
o
te
th
e
ac
tu
al
o
p
er
atin
g
v
alu
es.
Fu
r
th
er
m
o
r
e
,
P
0
an
d
Q
0
in
d
icate
t
h
e
r
ated
v
alu
es
o
f
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
,
r
esp
ec
tiv
ely
.
Me
an
wh
il
e,
P
an
d
Q
r
ep
r
esen
t
th
e
ac
tu
al
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
co
n
d
itio
n
s
d
u
r
in
g
s
y
s
te
m
o
p
er
atio
n
.
(
a)
(
b
)
Fig
u
r
e
3
.
Dr
o
o
p
c
o
n
tr
o
ller
ch
a
r
ac
ter
is
tic
cu
r
v
es
:
(
a)
d
r
o
o
p
P/f
an
d
(
b
)
d
r
o
o
p
Q/V
Fig
u
r
e
4
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
in
p
u
t P
2
.
3
.
P
ro
po
s
ed
co
ntr
o
l
m
et
h
o
d
2
.
3
.
1
.
Desig
n o
f
t
he
f
uzzy
lo
g
ic
f
re
qu
ency
co
ntr
o
ller
T
h
i
s
p
a
p
e
r
a
i
m
s
t
o
r
e
d
u
c
e
f
r
e
q
u
e
n
c
y
d
e
v
i
a
t
i
o
n
w
h
e
n
t
h
e
l
o
a
d
c
h
a
n
g
e
s
.
T
h
e
r
e
f
o
r
e
,
t
h
i
s
p
a
p
e
r
p
r
o
p
o
s
e
s
a
m
e
t
h
o
d
t
o
s
h
i
f
t
t
h
e
f
r
e
q
u
e
n
c
y
o
f
t
h
e
P
/
f
d
r
o
o
p
c
h
a
r
a
c
t
e
r
is
t
ic
c
u
r
v
e
s
t
o
m
ai
n
t
a
i
n
t
h
e
s
t
a
b
i
li
t
y
o
f
f
r
e
q
u
e
n
c
y
w
i
t
h
i
n
t
h
e
a
l
l
o
w
a
b
le
r
a
n
g
e
u
s
i
n
g
f
u
z
z
y
l
o
g
i
c
.
T
h
e
t
h
e
o
r
e
t
i
c
a
l
b
a
s
i
s
o
f
f
u
z
z
y
l
o
g
i
c
i
s
r
e
f
e
r
r
e
d
t
o
i
n
t
h
e
d
o
c
u
m
e
n
t
[
1
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
4
8
6
-
1498
1490
S
p
e
c
i
f
i
ca
l
l
y
,
f
u
z
z
y
l
o
g
i
c
i
s
u
s
ed
t
o
s
h
i
f
t
t
h
e
P/
f
g
r
a
p
h
a
l
o
n
g
t
h
e
f
-
a
x
i
s
b
y
a
d
is
ta
n
c
e
f
(
t
h
e
P
/f
'
g
r
a
p
h
)
i
n
o
r
d
e
r
to
r
e
d
u
c
e
t
h
e
f
r
e
q
u
e
n
c
y
d
e
v
i
a
t
i
o
n
,
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
3
(
a
)
.
Fig
u
r
e
3
(
a
)
s
h
o
ws
th
at
w
h
e
n
P
=
P
1
th
e
n
f
1
<
f
0
,
wh
e
n
th
e
AC
lo
ad
in
cr
ea
s
es
P
=
P
2
th
e
n
f
r
e
q
u
en
c
y
d
ec
r
ea
s
es
(
f
2
<
f
1
<
f
0
)
.
T
h
e
f
u
zz
y
co
n
tr
o
ller
will
s
h
if
t
th
e
P/f
d
r
o
o
p
lin
e
u
p
b
y
a
d
i
s
t
a
n
c
e
f
.
T
h
e
n
(
6
)
i
s
i
m
p
r
o
v
e
d
a
s
(
9
)
.
f'
=
f
0
-
m
p
P+
f
(
9
)
W
h
er
e:
f
is
d
eter
m
in
ed
b
y
th
e
f
u
zz
y
lo
g
ic
f
r
e
q
u
en
c
y
b
lo
c
k
Fu
zz
y
lo
g
ic
f
r
eq
u
e
n
cy
co
n
t
r
o
ller
d
esig
n
:
T
h
e
f
u
zz
y
lo
g
ic
f
r
eq
u
e
n
cy
co
n
tr
o
ller
is
d
esig
n
ed
u
s
in
g
ac
tiv
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p
o
wer
(
P)
as
th
e
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u
t
v
ar
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an
d
f
r
eq
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e
n
cy
d
e
v
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atio
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(
Δ
f
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as
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e
o
u
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t
v
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ia
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le.
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h
e
lin
g
u
is
tic
v
ar
iab
les
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o
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th
e
i
n
p
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t
a
n
d
o
u
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t
s
ig
n
als
ar
e
d
ef
in
e
d
as
s
h
o
wn
in
Fig
u
r
es
4
an
d
5
,
r
esp
ec
t
iv
ely
.
B
ased
o
n
th
e
ac
tu
al
lo
ad
p
o
we
r
co
n
d
itio
n
s
,
th
e
in
p
u
t
p
o
wer
d
o
m
ain
f
o
r
P
is
s
elec
ted
with
in
th
e
r
a
n
g
e
o
f
[
0
,
3
5
0
0
]
.
Me
an
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ile,
b
ased
o
n
th
e
allo
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le
f
r
eq
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e
n
cy
d
e
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iatio
n
,
th
e
o
u
tp
u
t d
o
m
ain
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o
r
Δ
f
is
s
ele
cted
with
in
th
e
r
an
g
e
o
f
[
0
,
1
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.
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h
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
b
o
th
in
p
u
t a
n
d
o
u
t
p
u
t v
ar
iab
les ar
e
p
r
esen
ted
in
F
ig
u
r
es 4
an
d
5
.
T
h
e
f
u
zz
y
c
o
n
tr
o
l
r
u
les
ar
e
estab
lis
h
ed
ac
co
r
d
in
g
to
(
6
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an
d
Fig
u
r
e
3
(
a)
.
T
h
e
r
elatio
n
s
h
i
p
b
etwe
en
th
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in
p
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t
p
o
wer
an
d
f
r
eq
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en
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iatio
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is
r
ep
r
esen
ted
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s
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g
a
s
et
o
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lin
g
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is
tic
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T
h
e
co
r
r
esp
o
n
d
in
g
f
u
zz
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u
les ar
e
s
u
m
m
ar
ized
as f
o
llo
ws:
-
I
f
P
=
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th
en
f
=
a
1
; I
f
P
=
A2
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en
f
=
a2
; I
f
P
=
A3
th
e
n
f
=
a3
-
I
f
P
=
B
1
th
en
f
=
b
1
;
I
f
P
=
B
2
th
en
f
=
b
2
; I
f
P
=
B
3
th
e
n
f
=
b3
-
I
f
P
=
C
1
th
en
f
=
c1
; I
f
P
=
C
2
th
en
f
=
c
2
; I
f
P
=
C
3
th
e
n
f
=
c3
-
I
f
P
=
D1
th
en
f
=
d
1
; I
f
P
=
D2
th
en
f
=
d
2
; I
f
P
=
D3
th
e
n
f
=
d3
-
I
f
P
=
E
1
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e
n
f
=
e1
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f
P
=
E
2
th
en
f
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e2
; I
f
P
=
E
3
t
h
e
n
f
=
e3
2
.
3
.
2
.
Desig
n o
f
t
he
f
uzzy
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g
ic
v
o
lt
a
g
e
co
ntr
o
ller
T
h
i
s
p
a
p
e
r
a
i
m
s
t
o
r
e
d
u
c
e
v
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l
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g
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d
e
v
i
a
t
i
o
n
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h
e
n
t
h
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o
a
d
ch
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n
g
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s
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h
e
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f
o
r
e
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t
h
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r
p
r
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d
t
o
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h
i
f
t
t
h
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Q/
V
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r
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c
h
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r
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e
r
i
s
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c
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f
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s
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y
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d
i
s
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n
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e
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h
e
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r
a
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e
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c
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h
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a
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s
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g
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ll
y
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u
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s
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f
t
t
h
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r
a
p
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l
o
n
g
t
h
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V
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a
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s
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y
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d
i
s
t
a
n
c
e
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(
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h
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r
a
p
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n
o
r
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e
r
t
o
r
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d
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c
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t
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t
a
g
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i
a
t
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,
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
3
(
b
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.
Fig
u
r
e
3
(
b
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s
h
o
ws
th
at
wh
en
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1
th
en
V
1
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en
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ad
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cr
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s
es
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en
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o
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e
d
ec
r
ea
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<V
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T
h
e
f
u
zz
y
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n
tr
o
ller
will
s
h
if
t
th
e
Q/V
d
r
o
o
p
lin
e
u
p
b
y
a
d
i
s
t
an
c
e
V
.
T
h
e
n
(
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i
s
i
m
p
r
o
v
e
d
a
s
f
o
l
l
o
ws
:
V'
=
V
0
-
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p
Q+
V
(
1
0
)
W
h
er
e:
V
is
d
eter
m
in
ed
b
y
th
e
f
u
zz
y
lo
g
ic
v
o
ltag
e
b
lo
ck
Desig
n
o
f
f
u
zz
y
lo
g
ic
v
o
ltag
e
b
lo
ck
:
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h
e
f
u
zz
y
lo
g
ic
v
o
ltag
e
co
n
tr
o
ller
is
d
esig
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s
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r
ea
ctiv
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p
o
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(
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as
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in
p
u
t v
ar
iab
l
e
an
d
v
o
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e
d
e
v
iatio
n
(
Δ
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as
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o
u
tp
u
t v
ar
iab
le.
T
h
e
lin
g
u
is
tic
v
ar
iab
les
f
o
r
th
e
in
p
u
t
an
d
o
u
tp
u
t
s
ig
n
als
a
r
e
d
ef
in
e
d
as
s
h
o
wn
in
Fig
u
r
e
s
6
an
d
7
,
r
esp
ec
tiv
ely
.
B
ased
o
n
th
e
ac
tu
al
l
o
ad
p
o
wer
,
t
h
e
in
p
u
t
v
alu
e
d
o
m
a
in
f
o
r
Q
is
s
elec
ted
with
in
t
h
e
r
an
g
e
o
f
[
0
,
3
5
0
0
]
.
Me
an
wh
ile,
b
ased
o
n
th
e
allo
wab
le
v
o
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e
d
e
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iatio
n
,
th
e
o
u
t
p
u
t
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d
o
m
ain
f
o
r
Δ
V
is
s
elec
ted
with
in
th
e
r
a
n
g
e
o
f
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0
,
5
]
.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
b
o
t
h
in
p
u
t a
n
d
o
u
tp
u
t
v
ar
iab
les ar
e
p
r
esen
ted
in
Fig
u
r
es 6
an
d
7
.
T
h
e
f
u
zz
y
c
o
n
tr
o
l
r
u
les
ar
e
estab
lis
h
ed
ac
co
r
d
i
n
g
t
o
(
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)
a
n
d
Fig
u
r
e
4
.
T
h
e
r
elatio
n
s
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i
p
b
e
twee
n
th
e
r
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ctiv
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p
o
wer
in
p
u
t
an
d
v
o
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ag
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d
ev
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is
r
ep
r
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g
a
s
et
o
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lin
g
u
is
tic
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u
les.
T
h
e
co
r
r
esp
o
n
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g
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u
zz
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r
u
les ar
e
s
u
m
m
ar
ized
as f
o
llo
ws:
-
I
f
Q
=
A1
th
e
n
V
=
a1
;
I
f
Q
=
A2
th
en
V
=
a
2
; I
f
Q
=
A
3
th
en
V
=
a3
-
I
f
Q
=
B
1
th
en
V
=
b
1
; I
f
Q
=
B
2
th
en
V
=
b
2
; I
f
Q
=
B
3
th
en
V
=
b3
-
I
f
Q
=
C
1
th
en
V
=
c1
; I
f
Q
=
C
2
th
en
V
=
c2
;
I
f
Q
=
C
3
th
en
V
=
c3
-
I
f
Q
=
D1
th
e
n
V
=
d
1
; I
f
Q
=
D2
th
en
V
=
d
2
; I
f
Q
=
D3
th
en
V
=
d3
-
I
f
Q
=
E
1
t
h
en
V
=
e
1
; I
f
Q
=
E
2
th
en
V
=
e2
; I
f
Q
=
E
3
th
en
V
=
e3
Use th
e
Su
m
-
Pro
d
u
ct
p
r
in
cip
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e
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d
th
e
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n
tr
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eth
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h
e
b
lo
ck
d
iag
r
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o
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r
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s
h
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Fig
u
r
e
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.
T
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p
r
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p
o
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s
lid
in
g
m
o
d
e
co
n
t
r
o
ll
er
(
SMC
)
to
im
p
r
o
v
e
th
e
r
o
b
u
s
tn
ess
an
d
s
tab
ilit
y
o
f
th
e
s
y
s
tem
d
u
r
in
g
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
s
h
if
ts
,
th
e
SMC
is
p
r
esen
ted
as
f
o
l
lo
ws:
T
h
e
p
u
r
p
o
s
e
o
f
th
e
SMC
is
to
m
ak
e
th
e
s
ig
n
als
at
th
e
in
v
er
ter
o
u
tp
u
t
clo
s
ely
tr
ac
k
th
e
r
ef
er
en
ce
v
a
lu
e
o
f
th
e
in
v
er
ter
in
p
u
t.
T
h
e
th
eo
r
etica
l
b
asis
o
f
th
e
SMC
is
r
ef
er
en
ce
d
in
s
tu
d
i
e
s
[
2
4
]
,
[
2
5
]
.
Fro
m
Fig
u
r
e
9
,
we
h
av
e
(
1
1
).
d
v
c
dt
=
1
C
i
1
−
1
C
i
2
d
i
1
dt
=
1
L
f
v
i
n
v
−
1
L
f
v
c
−
R
f
L
f
i
1
d
i
2
dt
=
1
L
v
c
−
1
L
v
p
cc
−
R
L
i
2
(
1
1
)
T
r
an
s
f
o
r
m
in
g
s
y
s
tem
(
1
1
)
to
t
h
e
d
q
0
co
o
r
d
in
ate
s
y
s
tem
,
we
h
av
e
th
e
f
o
llo
win
g
s
y
s
tem
s
(
1
2
)
an
d
(
1
3
)
.
v
̇
Cd
=
1
C
i
1d
−
1
C
i
2d
+
ω
v
cq
i
̇
̇
1d
=
v
inv
d
L
f
−
1
L
f
v
cd
−
R
f
L
f
i
1d
+
ω
i
1q
(
1
2
)
i
̇
̇
2d
=
v
cd
L
−
1
L
v
p
ccd
−
R
L
i
2d
+
ω
i
2q
v
̇
Cq
=
1
C
i
1q
−
1
C
i
2q
−
ω
v
cd
i
̇
̇
1q
=
v
inv
q
L
f
−
1
L
f
v
cq
−
R
f
L
f
i
1q
−
ω
i
1d
i
̇
̇
2q
=
v
cq
L
−
1
L
v
p
ccq
−
R
L
i
2q
−
ω
i
2d
(
1
3
)
T
h
e
p
u
r
p
o
s
e
o
f
th
e
SMC
is
to
en
s
u
r
e
th
at
th
e
v
o
ltag
e
V
C
clo
s
ely
f
o
llo
ws V
ref
,
s
o
we
d
ef
in
e
th
e
d
ev
iatio
n
s
:
e
d
=
v
Cd
−
v
Cd
∗
e
q
=
v
Cq
−
v
Cq
∗
(
1
4
)
W
h
er
e
:
v
Cd
∗
=
v
r
ef
d
;
v
Cq
∗
=
v
r
ef
q
.
C
h
o
o
s
e
th
e
s
lid
in
g
s
u
r
f
ac
es f
o
r
(
1
4
)
:
S
d
=
e
̇
d
+
a
e
d
=
(
v
̇
Cd
−
v
̇
Cd
∗
)
+
a
(
v
Cd
−
v
Cd
∗
)
S
q
=
e
̇
q
+
a
e
q
=
(
v
̇
Cq
−
v
̇
Cq
∗
)
+
a
(
v
Cq
−
v
Cq
∗
)
(
1
5
)
S
d
̇
=
e
̈
d
+
a
e
̇
d
=
(
v
̈
Cd
−
v
̈
Cd
∗
)
+
a
(
v
̇
Cd
−
v
̇
Cd
∗
)
S
q
̇
=
e
̈
q
+
a
e
̇
q
=
(
v
̈
Cq
−
v
̈
Cq
∗
)
+
a
(
v
̇
Cq
−
v
̇
Cq
∗
)
(
1
6
)
W
h
er
e:
a
=
co
n
s
tan
t; a
>
0
.
Usi
n
g
th
e
L
y
a
p
u
n
o
v
s
tab
ilit
y
p
r
i
n
cip
le:
=
1
2
2
.
T
h
er
e
f
o
r
e,
we
ch
o
o
s
e:
S
̇
d
=
−
k
s
ign
(
S
d
)
S
̇
q
=
−
k
s
ign
(
S
q
)
(
1
7
)
W
h
er
e:
k
=
co
n
s
tan
t; k
>0
.
Fro
m
th
e
s
y
s
tem
s
o
f
(
1
2
)
to
(
1
7
)
,
we
ca
n
d
er
iv
e
(
1
8
)
an
d
(
1
9
)
.
=
v
i
n
v
d
=
C
L
f
[
−
k
s
ign
(
S
d
)
+
A
i
1d
+
B
v
Cd
+
D
i
2d
+
2ω
C
i
2q
−
2ω
C
i
1q
−
ω
a
v
Cq
+
v
̈
Cd
∗
−
1
CL
v
p
ccd
+
a
v
̇
Cd
∗
]
(
1
8
)
=
v
i
n
v
q
=
C
L
f
[
−
k
s
ign
(
S
q
)
+
A
i
1q
+
B
v
Cq
+
D
i
2q
−
2ω
C
i
2d
+
2ω
C
i
1d
+
ω
a
v
Cd
+
v
̈
Cq
∗
−
1
CL
v
p
ccq
+
a
v
̇
Cq
∗
]
(
1
9
)
W
h
er
e:
A=
(
R
f
C
L
f
-
a
C
)
;
B=
(
1
C
L
f
+
1
CL
+
ω
2
)
;
D=
(
a
C
-
R
LC
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
n
n
o
v
a
tive
fr
eq
u
en
cy
a
n
d
v
o
lta
g
e
co
n
tr
o
ller
fo
r
A
C
mic
r
o
g
r
id
…
(
X
u
a
n
Ho
a
Th
i P
h
a
m
)
1493
T
h
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
im
p
lem
en
ted
ac
co
r
d
i
n
g
to
(
1
8
)
an
d
(
1
9
)
.
I
n
wh
ich
v
*
Cd
an
d
v
*
Cq
ar
e
r
ef
er
en
ce
v
o
ltag
es,
u
is
th
e
in
v
er
ter
co
n
t
r
o
l sig
n
al,
wh
ich
is
th
e
v
o
ltag
e
s
ig
n
al
to
m
o
d
u
late
th
e
in
v
er
te
r
.
F
i
g
u
r
e
9
.
E
q
u
i
v
a
l
e
n
t
s
c
h
e
m
a
ti
c
o
f
a
n
i
n
v
e
r
t
e
r
c
o
n
n
e
c
t
e
d
t
o
l
o
ad
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Per
f
o
r
m
a
s
im
u
latio
n
f
o
r
th
e
m
icr
o
g
r
id
c
o
n
f
ig
u
r
ed
as
s
h
o
wn
in
Fig
u
r
e
1
,
w
h
ich
co
n
s
is
t
s
o
f
3
in
v
er
ter
s
co
n
n
ec
ted
in
p
a
r
allel.
Use
b
o
th
co
n
tr
o
ller
s
:
th
e
co
n
v
en
tio
n
al
co
n
tr
o
ller
an
d
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
.
T
h
e
d
ata
u
s
ed
f
o
r
t
h
e
s
im
u
latio
n
ar
e
g
iv
en
in
T
ab
le
1
.
T
ab
le
1
.
Data
u
s
ed
f
o
r
s
im
u
lat
io
n
P
a
r
a
me
t
e
r
s
n
a
m
e
V
a
l
u
e
P
a
r
a
me
t
e
r
s
n
a
m
e
V
a
l
u
e
D
C
l
i
n
k
v
o
l
t
a
g
e
V
cd
(V)
6
0
0
f
0
(
H
z
)
f
m
a
x
(
H
z
)
f
m
i
n
(
H
z
)
50
51
4
9
.
5
L
f
(
mH
)
4
.
2
S
(
k
V
A
)
4
R
f
(
)
0
.
1
V
A
C,
0
(V)
V
A
C,
m
a
x
(V)
V
A
C,
m
i
n
(V)
3
1
1
3
1
5
3
0
5
C (
F)
2
.
2
S
o
p
e
c
o
e
f
f
i
c
i
e
n
t
m
q
(
V
/
V
a
r
)
0
.
0
0
0
1
0
5
f
z
(
k
H
z
)
5
S
o
p
e
c
o
e
f
f
i
c
i
e
n
t
m
p
(
r
a
d
/
s
/
W
)
0
.
0
0
0
1
Li
n
e
i
mp
e
d
a
n
c
e
p
a
r
a
m
e
t
e
r
s
L
(
H
)
0
.
0
0
3
R (
)
1
3
.
1
.
Ca
s
e
1
Po
wer
s
h
ar
in
g
s
im
u
latio
n
f
o
r
a
s
tan
d
alo
n
e
m
icr
o
g
r
id
with
two
in
v
er
ter
s
co
n
n
ec
ted
in
p
a
r
allel,
th
e
s
im
u
latio
n
is
p
er
f
o
r
m
ed
u
s
in
g
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
an
d
t
h
e
co
n
v
e
n
tio
n
al
co
n
tr
o
ller
.
T
h
e
two
in
v
er
ter
s
ar
e
ass
u
m
ed
to
h
a
v
e
th
e
s
am
e
r
at
ed
p
o
we
r
P
1đm
:
P
2đm
=
1
:1
.
At
tim
e
t
=
10
s
,
t
h
e
p
o
wer
co
n
s
u
m
p
tio
n
o
f
th
e
lo
a
d
in
cr
ea
s
es.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
es
1
0
an
d
1
1
.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
g
iv
es
th
e
r
esu
lt
o
f
d
iv
id
i
n
g
ac
tiv
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
ex
a
ctly
in
th
e
r
atio
o
f
1
:1
,
as
s
h
o
wn
in
Fig
u
r
e
s
10
(
a
)
an
d
1
0
(
b
)
.
T
h
e
s
ettlin
g
tim
e
is
r
elativ
ely
ea
r
ly
,
an
d
th
e
r
esp
o
n
s
e
is
s
tab
le
ev
en
wh
en
th
e
lo
ad
ch
an
g
es
s
h
ar
p
ly
.
Fig
u
r
es
1
1
(
a
)
an
d
1
1
(
b
)
s
h
o
w
th
at
th
e
co
n
v
en
tio
n
al
co
n
tr
o
ller
g
iv
es
less
ac
cu
r
ate
p
o
wer
d
iv
i
s
io
n
r
esu
lts
th
an
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
an
d
wo
r
s
e
s
tab
ilit
y
th
an
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
d
u
r
in
g
th
e
p
e
r
io
d
o
f
s
tr
o
n
g
lo
ad
ch
an
g
es.
Fig
u
r
es
1
0
(
c
)
a
n
d
1
1
(
c
)
ar
e
t
h
e
s
in
g
le
-
p
h
ase
cu
r
r
en
ts
o
f
in
v
er
ter
s
1
an
d
2
.
Fig
u
r
e
1
0
(
c)
s
h
o
ws
th
at
th
e
two
wav
ef
o
r
m
s
m
atch
e
x
ac
tly
,
wh
ile
Fig
u
r
e
1
1
(
c)
s
h
o
ws
th
at
th
e
two
wav
ef
o
r
m
s
h
av
e
d
if
f
er
en
t
am
p
litu
d
es
d
u
r
in
g
th
e
lo
a
d
ch
an
g
e
p
er
i
o
d
.
Fig
u
r
es
1
0
(
d
)
an
d
1
1
(
d
)
ar
e
v
o
ltag
e
at
th
e
lo
a
d
.
I
n
th
e
p
e
r
io
d
f
r
o
m
0
s
to
1
0
s
,
th
e
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t
o
f
ea
ch
in
v
er
ter
is
Q
1
=
Q
2
=
9
9
0
Var
,
s
o
ac
co
r
d
in
g
to
Fig
u
r
es
6
an
d
7
,
th
e
Q/V
d
r
o
o
p
lin
e
will
s
h
if
t
u
p
a
d
is
tan
ce
o
f
V=
1
.
4
(
V)
alo
n
g
th
e
v
er
tical
ax
is
,
th
e
Q/V
d
r
o
o
p
lin
e
b
ec
o
m
es
th
e
Q/V'
d
r
o
o
p
lin
e
as
in
Fig
u
r
e
3
(
b
)
o
r
(
1
0
)
,
s
o
th
e
AC
b
u
s
v
o
ltag
e
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
(
3
0
9
.
5
V)
is
r
aised
h
ig
h
er
th
an
th
e
tr
a
d
itio
n
al
m
eth
o
d
(
3
0
7
V)
.
T
h
e
V
s
h
if
t
o
f
th
e
Q/V
d
r
o
o
p
d
e
p
en
d
s
o
n
th
e
v
al
u
e
d
o
m
ain
o
f
th
e
o
u
t
p
u
t
o
f
th
e
f
u
zz
y
lo
g
ic
s
et
s
elec
ted
a
b
o
v
e
.
I
n
th
e
p
er
i
o
d
f
r
o
m
1
0
s
to
2
0
s
,
th
e
r
ea
ctiv
e
p
o
we
r
o
u
tp
u
t
o
f
ea
ch
in
v
er
ter
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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r
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(
a)
(
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(
c)
(
d
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(
e)
Fig
u
r
e
1
0
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im
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th
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a)
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(
b
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(
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r
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en
t,
(
d
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v
o
ltag
e,
an
d
(
e
)
f
r
eq
u
en
cy
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
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2
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Ca
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e
2
Simu
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ee
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ter
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o
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p
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tly
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r
atio
o
f
1
:1
:1
,
as
s
h
o
wn
in
Fig
u
r
e
s
12
(
a
)
an
d
1
2
(
b
)
.
T
h
e
s
ettlin
g
tim
e
is
r
elativ
ely
ea
r
ly
,
an
d
th
e
r
esp
o
n
s
e
is
s
tab
le
ev
en
wh
en
th
e
lo
ad
ch
an
g
es
s
h
ar
p
ly
.
Fig
u
r
e
1
2
(
c
)
s
h
o
ws
th
e
s
in
g
le
-
p
h
ase
cu
r
r
en
ts
o
f
in
v
er
ter
s
1
a
n
d
2
.
Fig
u
r
e
1
2
(
c
)
s
h
o
ws
th
at
th
e
two
wav
ef
o
r
m
s
m
atch
ex
ac
tly
,
an
d
Fig
u
r
e
12
(
d
)
is
v
o
ltag
e
at
th
e
lo
a
d
.
I
n
th
e
p
er
io
d
f
r
o
m
0
s
to
1
0
s
,
th
e
r
ea
ctiv
e
p
o
wer
o
u
t
p
u
t
o
f
ea
ch
in
v
er
te
r
is
Q
3
=
Q
1
=
Q
2
=
990
Var
,
s
o
ac
co
r
d
i
n
g
to
Fig
u
r
es 6
a
n
d
7
,
th
e
g
r
ap
h
Q/V
will
s
h
if
t
u
p
a
d
is
tan
ce
o
f
V=
1
.
4
(
V)
alo
n
g
th
e
v
er
tical
ax
is
,
th
e
g
r
ap
h
Q/V
b
ec
o
m
es
th
e
g
r
ap
h
Q/V'
as
in
Fig
u
r
e
3
(
b
)
o
r
(
1
0
)
,
s
o
th
e
v
o
ltag
e
at
lo
ad
is
3
0
9
.
5
V.
T
h
e
V
s
h
if
t
o
f
th
e
Q/V
d
r
o
o
p
d
ep
en
d
s
o
n
t
h
e
v
alu
e
d
o
m
ain
o
f
th
e
o
u
tp
u
t
o
f
th
e
f
u
zz
y
lo
g
ic
s
et
s
elec
ted
ab
o
v
e.
I
n
th
e
p
er
io
d
f
r
o
m
1
0
s
to
20
s
,
th
e
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t
o
f
ea
ch
in
v
er
ter
is
Q
1
=
Q
2
=
Q
3
=1
9
0
0
Var
,
s
o
ac
co
r
d
in
g
to
Fig
u
r
es
6
an
d
7
,
th
e
g
r
ap
h
Q/V
will
s
h
if
t
u
p
a
d
is
tan
ce
o
f
V
=
2
.
8
(
V)
al
o
n
g
th
e
v
er
tical
ax
is
,
th
e
Q/V
d
r
o
o
p
lin
e
b
ec
o
m
es
th
e
g
r
a
p
h
Q/V'
d
r
o
o
p
as
i
n
Fig
u
r
e
3
(
b
)
o
r
(
1
0
)
,
s
o
th
e
AC
b
u
s
v
o
ltag
e
is
3
0
8
V.
T
h
e
V
s
h
if
t
o
f
th
e
g
r
ap
h
Q/V
d
ep
en
d
s
o
n
th
e
v
alu
e
d
o
m
ain
o
f
th
e
o
u
t
p
u
t
o
f
th
e
f
u
zz
y
lo
g
ic
s
et
s
elec
ted
ab
o
v
e.
T
h
ese
r
esu
lts
ar
e
in
f
u
l
l
ag
r
ee
m
en
t
with
th
e
estab
lis
h
ed
f
u
zz
y
c
o
n
tr
o
l
law,
co
n
s
is
ten
t
with
(
1
0
)
a
n
d
th
e
g
r
ap
h
d
r
o
o
p
in
Fig
u
r
e
3
(
b
)
.
T
h
er
ef
o
r
e,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
will sh
if
t th
e
tr
ad
itio
n
al
d
r
o
o
p
lin
e
u
p
war
d
,
aim
in
g
to
r
e
s
to
r
e
v
o
ltag
e
at
th
e
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