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an
ex
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ex
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[
1
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cr
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P
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s
u
es
in
th
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p
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y
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[
2
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.
I
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al
-
tim
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life
tim
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e
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q
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m
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[
3
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.
T
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is
s
u
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s
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s
in
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Vs
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f
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r
E
Vs
[
4
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.
Mo
s
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th
e
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V
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ar
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in
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tr
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s
f
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ailu
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f
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r
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L
ian
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a
l.
[
5
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ex
p
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a
v
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if
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b
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m
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PtV)
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Qu
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[
6
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p
r
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p
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s
ed
a
ch
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g
in
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s
tr
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f
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B
o
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p
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als
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s
s
ed
in
[
5
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an
d
[
6
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wer
e
n
o
t
a
b
le
to
ad
d
r
ess
th
e
o
p
tim
izatio
n
o
b
jectiv
es
lik
e
v
o
ltag
e
u
n
b
alan
ce
(
VU
)
,
v
o
ltag
e
d
e
v
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n
(
VD
)
,
an
d
v
o
ltag
e
h
ar
m
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n
ics
(
VH
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cr
ea
te
d
b
y
E
Vs
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n
n
ec
ted
to
PDN.
Ad
v
an
cin
g
th
e
v
o
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e
d
is
tr
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u
tio
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a
lg
o
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with
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p
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al
o
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in
ter
c
o
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ec
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d
wi
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ec
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n
o
m
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a
d
d
is
p
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is
p
r
esen
te
d
in
[
7
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f
o
r
m
in
im
izi
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th
e
ef
f
ec
t
o
f
E
V
lo
a
d
s
in
a
p
a
r
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lar
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.
Ho
wev
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th
e
au
th
o
r
s
f
ailed
in
a
d
d
r
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in
g
th
e
is
s
u
es
lik
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o
p
tim
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n
o
b
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es
VU,
VD
&
VH.
A
s
im
ilar
ty
p
e
o
f
r
esear
ch
is
p
r
esen
te
d
in
[
8
]
,
wh
er
e
a
d
y
n
a
m
ic
p
r
icin
g
s
y
s
tem
ac
co
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in
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to
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All
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ed
s
o
f
ar
co
n
s
id
er
ed
t
h
e
p
a
r
am
eter
s
o
f
a
PDN
as
th
e
s
am
e
an
d
esti
m
ated
t
h
e
v
alu
es
b
ased
o
n
E
Vs
d
is
tr
ib
u
ted
eq
u
ally
t
o
ea
c
h
p
h
ase
,
m
ak
i
n
g
t
h
em
u
n
s
u
ita
b
le
f
o
r
b
alan
cin
g
th
e
th
r
ee
-
p
h
ase
g
r
id
s
y
s
tem
an
d
r
ed
u
cin
g
th
e
h
a
r
m
o
n
ics o
f
v
o
lt
ag
e.
Mo
s
t
o
f
th
e
v
o
ltag
e
q
u
ality
p
r
o
b
lem
s
ca
n
b
e
s
o
lv
ed
b
y
h
av
in
g
ac
ce
s
s
to
co
n
tr
o
l
d
ev
ices
o
f
th
e
ch
ar
g
in
g
n
etwo
r
k
th
r
o
u
g
h
a
co
n
tr
o
ller
[
9
]
;
h
o
wev
er
co
u
n
tr
ies
lik
e
I
n
d
ia,
it’s
d
if
f
icu
lt
to
ac
h
iev
e
an
d
im
p
lem
en
t
in
p
r
ac
tical
co
n
d
itio
n
s
[
1
0
]
.
R
esear
ch
is
th
en
s
h
if
ted
to
th
e
d
esig
n
o
f
co
n
tr
o
ller
s
in
[
1
1
]
.
A
v
o
ltag
e
s
ag
co
n
tr
o
ller
is
p
r
o
p
o
s
ed
f
o
r
m
itig
atin
g
th
e
im
b
alan
ce
s
i
n
v
o
ltag
e,
b
u
t
th
is
m
o
d
el
f
ai
led
to
ad
d
r
ess
th
e
v
o
ltag
e
o
s
cillatio
n
s
an
d
o
p
tim
izatio
n
o
b
jectiv
es
lik
e
VD
&
VH.
A
n
alg
o
r
ith
m
f
o
r
a
co
n
t
r
o
ller
is
d
esig
n
ed
o
n
th
e
b
asis
o
f
ad
ap
tiv
e
n
o
tch
f
il
ter
s
(
ANFs
)
to
ad
d
r
ess
th
e
is
s
u
es
o
f
cu
r
r
en
t
h
a
r
m
o
n
ics
an
d
p
r
o
v
id
es
a
s
u
p
p
o
r
t
co
n
d
itio
n
in
th
e
alg
o
r
ith
m
f
o
r
im
p
r
o
v
in
g
th
e
r
ea
ctiv
e
p
o
we
r
co
m
p
o
n
en
t
o
f
PDN
,
as
p
r
o
p
o
s
ed
in
[
1
2
]
.
T
h
e
ap
p
r
o
ac
h
in
[
1
3
]
p
r
o
p
o
s
ed
p
h
ase
s
wi
tch
in
g
m
eth
o
d
is
em
p
lo
y
ed
f
o
r
b
alan
cin
g
th
e
VU
;
h
o
wev
er
,
wh
en
th
er
e
is
m
o
r
e
f
r
eq
u
e
n
t
co
n
n
ec
tio
n
o
f
E
V
lo
ad
s
,
th
en
it
s
u
f
f
er
s
f
r
o
m
o
s
cillatin
g
f
r
eq
u
en
cies
,
wh
i
ch
is
n
o
t
d
esira
b
le
f
o
r
t
h
e
PDN
s
y
s
tem
.
An
im
p
r
o
v
e
d
v
e
r
s
io
n
is
p
r
o
p
o
s
ed
i
n
[
1
4
]
,
s
im
ilar
to
[
1
5
]
,
b
u
t
t
h
is
m
o
d
el
f
ails
in
ad
d
r
ess
in
g
th
e
co
m
m
u
tatio
n
f
ailu
r
es
th
at
o
cc
u
r
d
u
r
in
g
th
e
p
h
ase
s
h
if
tin
g
p
r
o
ce
s
s
.
So
f
ar
,
th
e
liter
atu
r
e
h
as
ad
d
r
ess
ed
r
ef
er
en
cin
g
th
e
VU
,
b
u
t
v
er
y
less
m
o
d
els
h
av
e
f
o
cu
s
ed
o
n
VD
an
d
VD
wh
en
o
p
er
atin
g
th
e
Sp
lit
-
p
h
ase
v
o
ltag
e
q
u
ality
im
p
r
o
v
e
m
en
t.
T
o
ad
d
r
ess
th
e
ab
o
v
e
-
m
e
n
tio
n
ed
p
r
o
b
lem
s
,
th
is
ar
ticle
p
r
o
p
o
s
es
VU,
VD
,
an
d
VH
co
n
s
tr
ain
ts
f
o
r
allo
ca
tin
g
th
e
o
p
tim
al
ch
ar
g
in
g
f
o
r
E
V
lo
ad
s
s
o
th
at
lo
s
s
es
an
d
e
f
f
ec
tiv
e
u
tili
za
tio
n
o
f
a
v
ai
lab
le
p
o
wer
ca
n
b
e
ac
h
iev
ed
,
r
esp
ec
tiv
el
y
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
t
h
is
ar
ticle
ar
e
as
f
o
llo
ws:
a.
I
m
p
r
o
v
ed
v
o
ltag
e
q
u
ality
wit
h
s
p
lit
-
p
h
ase
ch
ar
g
in
g
:
T
h
e
ar
ticle
d
em
o
n
s
tr
ates
th
at
s
p
lit
-
p
h
ase
co
n
n
ec
tio
n
o
f
E
Vs s
ig
n
if
ican
tly
en
h
an
ce
s
v
o
ltag
e
q
u
ality
b
y
r
ed
u
cin
g
th
r
ee
-
p
h
ase
VU,
VD
,
an
d
VH.
b.
Op
tim
izatio
n
u
s
in
g
NSGA
-
II
a
lg
o
r
ith
m
:
T
h
e
s
tu
d
y
em
p
lo
y
s
th
e
NSGA
-
I
I
alg
o
r
ith
m
to
o
p
tim
ize
th
e
s
p
lit
-
p
h
ase
ch
ar
g
in
g
s
tr
ateg
y
,
p
r
o
v
id
in
g
ef
f
ec
tiv
e
s
o
lu
tio
n
s
f
o
r
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
s
with
f
aster
co
n
v
er
g
en
ce
a
n
d
im
p
r
o
v
ed
r
esu
lts
co
m
p
a
r
ed
to
tr
a
d
itio
n
al
m
eth
o
d
s
.
c.
E
f
f
ec
tiv
e
in
teg
r
atio
n
o
f
r
en
e
wab
le
en
er
g
y
:
B
y
c
o
o
r
d
in
atin
g
E
V
ch
ar
g
i
n
g
with
win
d
p
o
wer
o
u
tp
u
t,
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
b
alan
ce
s
th
e
lo
ad
d
is
tr
ib
u
tio
n
,
en
s
u
r
in
g
o
p
tim
al
u
tili
za
tio
n
o
f
r
en
ewa
b
l
e
en
er
g
y
s
o
u
r
ce
s
an
d
r
ed
u
cin
g
v
o
ltag
e
q
u
ality
i
s
s
u
es.
d.
Scalab
ilit
y
an
d
r
o
b
u
s
tn
ess
:
T
h
e
ar
ticle
v
alid
ates
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
s
p
lit
-
p
h
ase
ch
ar
g
in
g
s
tr
ateg
y
ac
r
o
s
s
v
ar
y
in
g
n
u
m
b
er
s
o
f
E
Vs
(
1
,
0
0
0
to
5
,
0
0
0
)
,
co
n
f
ir
m
i
n
g
its
s
ca
lab
ilit
y
an
d
r
o
b
u
s
tn
e
s
s
in
m
ain
tain
in
g
v
o
ltag
e
q
u
ality
with
in
n
atio
n
al
s
tan
d
ar
d
s
,
ev
en
with
in
cr
ea
s
in
g
E
V
ad
o
p
tio
n
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
:
i)
S
ec
tio
n
2
d
escr
ib
es
th
e
ch
ar
g
i
n
g
s
tr
ateg
y
;
ii)
Sectio
n
p
r
o
v
id
es
in
s
ig
h
t
in
to
m
ath
em
atica
l
m
o
d
ellin
g
;
iii)
S
ec
tio
n
4
d
escr
ib
es
th
e
alg
o
r
ith
m
s
u
p
p
o
r
tin
g
m
u
lti
lay
er
co
n
tr
o
l
;
an
d
iv
)
S
ec
tio
n
5
with
v
alid
atio
n
o
f
s
im
u
latio
n
r
esu
lts
an
d
co
n
clu
d
es
.
2.
CH
ARG
I
NG
ST
RAT
E
G
Y
O
UT
L
I
NE
W
ith
th
e
g
r
o
win
g
p
r
ev
ale
n
ce
o
f
E
Vs,
th
e
u
n
p
r
e
d
ictab
ilit
y
ass
o
ciate
d
with
s
in
g
le
-
p
h
ase
c
h
ar
g
in
g
is
also
in
cr
ea
s
in
g
[
1
6
]
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
s
in
g
le
-
p
h
ase
lo
ad
s
f
u
r
th
er
in
ten
s
if
ies
th
e
ex
is
tin
g
im
b
alan
ce
with
i
n
th
e
o
r
ig
in
ally
u
n
b
alan
ce
d
PD
N
[
1
7
]
.
At
th
e
s
am
e
tim
e,
th
e
d
is
tr
ib
u
tio
n
g
r
id
is
p
r
o
g
r
ess
iv
ely
in
co
r
p
o
r
atin
g
m
o
r
e
s
in
g
le
-
p
h
ase
co
n
n
ec
tio
n
s
f
o
r
d
is
tr
ib
u
ted
win
d
en
er
g
y
.
Giv
en
th
at
win
d
p
o
wer
g
en
e
r
atio
n
ten
d
s
to
p
ea
k
d
u
r
in
g
n
ig
h
ttime
an
d
d
ec
r
ea
s
e
d
u
r
in
g
d
ay
lig
h
t
h
o
u
r
s
,
it
alig
n
s
well
with
th
e
s
ig
n
if
ican
t
s
i
n
g
le
-
p
h
ase
ch
a
r
g
in
g
d
em
an
d
s
o
f
p
r
iv
ate
v
e
h
icles
at
n
ig
h
t.
C
o
n
s
eq
u
en
tly
,
wh
en
d
ev
elo
p
in
g
an
E
V
ch
ar
g
in
g
s
tr
ateg
y
,
it
is
ess
en
tial
to
tak
e
in
to
ac
co
u
n
t
th
e
s
p
lit
-
p
h
ase
co
n
n
ec
tio
n
s
a
n
d
th
e
s
y
n
er
g
is
tic
r
elatio
n
s
h
ip
b
etw
ee
n
E
Vs
an
d
win
d
en
er
g
y
[
1
8
]
.
C
o
n
n
ec
tin
g
m
o
r
e
E
V
lo
a
d
s
to
th
e
n
etwo
r
k
d
u
r
in
g
p
ea
k
win
d
p
o
wer
o
u
tp
u
t
p
h
ases
h
el
p
s
m
ee
t
ch
ar
g
in
g
d
em
an
d
s
wh
ile
b
al
an
cin
g
win
d
p
o
wer
o
u
tp
u
t
[
1
9
]
.
Ad
d
itio
n
ally
,
t
h
e
s
tr
ateg
y
m
u
s
t
ac
co
u
n
t
f
o
r
h
ar
m
o
n
ics
in
tr
o
d
u
ce
d
in
to
t
h
e
s
y
s
tem
b
y
win
d
p
o
wer
an
d
E
Vs
v
ia
p
o
wer
elec
tr
o
n
ic
co
n
v
e
r
ter
s
,
en
s
u
r
in
g
ea
c
h
p
h
ase'
s
h
ar
m
o
n
ic
lev
els r
em
ain
with
in
ac
ce
p
tab
le
lim
its
.
Giv
en
th
e
PDN’
s
h
ea
v
y
lo
a
d
,
co
n
n
ec
tin
g
an
E
V
lo
ad
ca
n
r
esu
lt
in
l
o
w
n
o
d
e
v
o
ltag
e
,
lead
in
g
to
VU,
VD
,
a
n
d
VHs
.
T
h
is
r
esear
ch
i
n
v
esti
g
ates
elec
tr
ic
v
eh
icle
(
E
V)
ch
ar
g
in
g
tech
n
iq
u
es
d
esig
n
ed
to
en
h
a
n
ce
th
e
v
o
ltag
e
q
u
ali
ty
at
PDN
n
o
d
es,
wh
ile
tak
in
g
in
to
ac
c
o
u
n
t
th
e
o
p
tim
al
an
d
u
n
co
n
tr
o
llab
le
u
ti
lizatio
n
o
f
d
is
tr
ib
u
ted
win
d
en
er
g
y
g
en
er
atio
n
[
2
0
]
.
B
y
r
eg
u
latin
g
th
e
p
h
ase
o
f
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1472
-
1
4
8
3
1474
s
in
g
le
-
p
h
ase
E
V
lo
ad
co
n
n
ec
t
io
n
s
,
we
ca
n
m
itig
ate
v
o
ltag
e
q
u
ality
ch
allen
g
es
ar
is
in
g
f
r
o
m
th
e
in
teg
r
atio
n
o
f
E
Vs an
d
win
d
p
o
wer
,
as we
ll a
s
r
ec
tify
th
e
im
b
alan
ce
is
s
u
es
s
tem
m
in
g
f
r
o
m
PDN
b
ase
lo
ad
s
[
2
1
]
.
Fig
u
r
e
1
(
a)
d
ep
icts
th
e
s
p
lit
-
p
h
ase
ch
ar
g
in
g
p
r
o
ce
s
s
f
o
r
E
Vs.
T
h
e
p
o
wer
s
y
s
tem
co
n
tr
o
l
ce
n
te
r
co
llects
th
e
to
tal
s
ch
ed
u
led
ch
ar
g
in
g
l
o
ad
f
r
o
m
ea
ch
s
tatio
n
an
d
u
tili
ze
s
th
is
in
f
o
r
m
atio
n
to
d
ev
el
o
p
a
p
h
ase
-
o
r
ien
ted
ch
a
r
g
in
g
m
o
d
el
b
a
s
ed
o
n
th
e
o
v
e
r
all
ch
ar
g
in
g
r
eq
u
ir
em
e
n
ts
an
d
win
d
e
n
er
g
y
p
r
o
d
u
ctio
n
.
Su
b
s
eq
u
en
tly
,
t
h
e
co
n
t
r
o
l
ce
n
ter
co
m
m
u
n
icate
s
th
e
ch
a
r
g
in
g
p
lan
to
ea
ch
s
tatio
n
,
d
ir
ec
tin
g
E
V
u
s
er
s
to
ch
ar
g
e
th
eir
v
eh
icles a
cc
o
r
d
in
g
to
th
e
d
esig
n
ated
lo
ad
s
o
u
tlin
ed
in
th
e
ch
ar
g
i
n
g
s
ch
em
e.
3.
M
AT
H
E
M
AT
I
CA
L
M
O
D
E
L
L
I
NG
O
F
E
V
CH
ARG
I
N
G
ST
RA
T
E
G
Y
Mo
r
e
d
ec
en
tr
aliza
tio
n
o
f
lo
a
d
d
em
an
d
m
ak
es
it
d
if
f
icu
lt
to
esti
m
ate
th
e
v
o
ltag
e
q
u
ality
in
s
in
g
le
-
p
h
ase
[
2
2
]
.
So
m
o
r
e
r
o
b
u
s
t
m
ath
em
atica
l
d
ev
elo
p
e
d
in
t
h
e
p
r
esen
t
s
tu
d
y
f
o
r
m
a
k
in
g
th
e
s
y
s
tem
m
o
r
e
ef
f
icien
t.
3
.
1
.
Vo
lt
a
g
e
qu
a
lity
a
na
ly
s
is
E
V
co
n
n
ec
ted
to
PDN
h
as
b
ee
n
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
I
n
o
r
d
er
to
ea
s
e
th
e
m
a
th
em
atica
l
co
m
p
u
tatio
n
,
th
e
E
V
co
n
n
ec
t
ed
to
th
e
g
r
id
is
co
n
s
id
er
ed
as
n
o
d
e
k
,
an
d
th
e
lin
e
co
n
s
tr
ai
n
ts
lik
e
lo
s
s
e
s
wer
e
n
eg
lecte
d
,
a
n
d
th
e
p
o
wer
f
ac
to
r
is
h
ig
h
f
o
r
E
V
lo
ad
s
,
s
o
r
ea
ctiv
e
p
o
we
r
is
n
e
g
lecte
d
.
T
h
en
th
e
r
esu
ltan
t
v
o
ltag
e
eq
u
atio
n
at
n
o
d
e
k
is
wr
itten
as
(
1
)
.
=
(
ℎ
−
∑
(
,
+
)
+
∑
,
=
=
ℎ
)
<
(
ℎ
−
∑
,
+
∑
,
=
=
ℎ
)
(
1
)
U
h
is
th
e
v
o
ltag
e
at
k
, P
,
an
d
Q
wer
e
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
c
o
m
p
o
n
en
ts
o
f
th
e
s
y
s
tem
,
P
ev
i
s
th
e
lo
ad
,
R
is
th
e
lin
e
r
esis
tan
ce
,
an
d
X
is
th
e
r
e
ac
tan
ce
.
(
a)
(
b
)
Fig
u
r
e
1
.
Sch
em
atic
o
f
(
a
)
E
V
p
h
ase
s
elec
tio
n
f
lo
wch
ar
t
a
n
d
(
b
)
E
V
c
h
ar
g
in
g
co
n
n
ec
tio
n
d
iag
r
am
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
Op
timiz
in
g
s
lo
w
-
ch
a
r
g
in
g
E
V
lo
a
d
s
w
ith
a
tw
o
-
la
ye
r
s
tr
a
teg
y
to
en
h
a
n
ce
…
(
A
tta
d
a
Du
r
g
a
P
r
a
s
a
d
)
1475
Fu
r
th
er
,
f
o
r
th
e
ab
o
v
e
-
d
e
r
iv
ed
eq
u
atio
n
,
th
e
o
p
tim
izab
le
v
ar
iab
les
lik
e
VU,
VD
,
an
d
V
H
co
m
p
o
n
en
ts
ar
e
ch
o
s
en
s
o
th
at
th
e
f
in
al
s
y
s
tem
wil
l
b
e
r
o
b
u
s
t.
First
ly
,
let
u
s
co
n
s
id
er
th
e
t
h
r
ee
-
p
h
ase
v
o
ltag
e
u
n
b
alan
ce
VU
c
o
n
d
itio
n
,
b
y
ass
u
m
in
g
th
e
s
y
m
m
etr
ical
c
o
m
p
o
n
e
n
t
ap
p
r
o
ac
h
f
o
r
re
-
tr
a
n
s
f
o
r
m
in
g
t
h
e
p
h
ase
v
o
ltag
es in
+v
e,
-
v
e
a
n
d
0
co
m
p
o
n
e
n
ts
s
u
ch
th
at
th
e
f
u
n
ctio
n
ca
n
b
e
d
ef
in
e
d
as
(
2
)
an
d
(
3
)
.
1
=
∑
∑
,
,
(
2
)
,
,
=
|
2
,
,
1
,
,
|
=
|
,
,
+
2
,
,
+
,
,
,
,
+
,
,
+
2
,
,
|
(
3
)
W
h
e
r
e
,
,
i
s
VU
a
t
n
o
d
e
i
,
a
n
d
t
im
e
t
,
f
u
r
t
h
e
r
m
a
n
d
n
r
e
p
r
e
s
e
n
t
t
h
e
n
o
.
o
f
n
o
d
e
s
h
e
r
e
c
o
n
s
t
a
n
t
=
12
0
0
.
N
ow
,
t
h
e
c
h
a
r
a
ct
e
r
i
z
at
i
o
n
e
q
u
at
i
o
n
f
o
r
t
h
e
V
D
c
o
n
d
i
ti
o
n
f
o
r
a
p
h
a
s
e
s
y
s
t
e
m
c
a
n
b
e
d
e
f
i
n
e
d
as
(
4
)
.
2
=
,
=
∑
∑
|
,
,
−
∗
,
,
|
∗
,
,
×
100%
(
4
)
Her
e,
U
&
U
*
r
ep
r
esen
t
th
e
p
ar
ticu
lar
p
h
ase’
s
r
ea
l
-
tim
e
an
d
n
o
m
in
al
v
o
ltag
es
at
th
at
p
ar
ticu
lar
n
o
d
e
a
n
d
in
s
tan
t o
f
tim
e.
C
o
n
s
id
er
in
g
th
e
f
in
al
o
b
jectiv
e
o
f
h
ar
m
o
n
ics
in
v
o
ltag
e
V
H,
th
e
d
is
to
r
tio
n
r
ate
is
p
r
ese
n
ted
in
(
5
)
an
d
(
6
)
.
C
o
n
s
id
er
in
g
th
e
eq
u
a
tio
n
s
s
u
g
g
ested
b
y
C
iu
ce
an
u
e
t
a
l.
[
2
1
]
s
am
e
wer
e
i
n
co
r
p
o
r
a
ted
f
o
r
th
e
p
r
esen
t
m
o
d
el
f
o
r
ca
lcu
latin
g
h
ar
m
o
n
i
c
cu
r
r
en
t
.
H
en
ce
,
a
d
etailed
ex
p
lan
atio
n
f
o
r
th
e
d
er
iv
atio
n
is
n
o
t
p
r
o
v
id
ed
h
er
e.
3
=
=
∑
∑
∑
,
,
1
,
,
×
100%
(
5
)
,
,
=
√
∑
(
ℎ
,
,
)
∞
ℎ
=
2
2
(
6
)
Her
e,
,
,
r
ep
r
esen
ts
th
e
VH
o
f
th
e
th
r
ee
-
p
h
ase
s
y
s
tem
at
a
p
ar
ticu
lar
n
o
d
e
an
d
tim
e.
T
h
e
p
h
ase
s
elec
tio
n
f
o
r
th
e
E
V
in
s
id
e
th
e
g
r
id
ca
n
r
esu
lt
i
n
q
u
ality
is
s
u
es
;
h
en
ce
,
th
r
o
u
g
h
a
n
aly
s
is
p
er
f
o
r
m
ed
with
t
h
e
h
elp
o
f
Par
eto
an
aly
s
is
,
th
e
h
ig
h
est
d
e
g
r
ee
f
u
n
ctio
n
i
n
m
em
b
er
s
h
ip
will
lead
to
a
b
ette
r
o
u
tco
m
e
.
m
in
,
m
a
x
,
m
in
m
a
x
,,
m
a
x
m
in
m
in
,
1,
0
i
j
j
j
i
j
i
j
j
i
j
j
jj
i
j
j
=
−
=
−
=
(
7
)
Her
e,
th
e
b
eta
f
u
n
ctio
n
s
wer
e
th
e
s
o
lu
tio
n
v
ar
iab
les,
m
in
a
n
d
m
ax
f
u
n
ctio
n
s
o
f
b
eta
ar
e
v
alu
es
o
f
j
o
n
th
e
Par
eto
f
r
o
n
t.
Fu
r
t
h
er
,
f
o
r
d
e
r
iv
in
g
th
e
o
p
tim
al
s
o
lu
tio
n
,
th
e
f
o
r
m
u
la
is
r
ed
e
f
in
ed
,
a
n
d
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
is
r
e
p
r
esen
ted
with
(
8
)
.
,
=
(
∑
,
=
1
)
⇒
,
(
8
)
3
.
2
.
Co
ns
t
ra
int
c
o
nd
it
io
ns
T
h
r
ee
ty
p
es
o
f
lim
itatio
n
s
m
u
s
t
b
e
in
co
r
p
o
r
ated
in
o
r
d
er
t
o
en
s
u
r
e
th
e
p
r
ac
ticality
o
f
a
ctu
al
g
r
id
-
co
n
n
ec
ted
E
V
ch
ar
g
i
n
g
:
r
estrictio
n
s
ab
o
u
t
E
V
ch
ar
g
in
g
,
p
o
wer
f
lo
w
m
ath
em
atica
l
b
alan
ce
,
alo
n
g
ad
d
itio
n
al
co
n
s
tr
ain
ts
[
2
3
]
.
Firstl
y
,
th
e
p
o
wer
f
lo
w
b
alan
ce
co
n
s
tr
ain
ts
p
er
tain
in
g
to
ac
tiv
e
an
d
r
ea
ct
iv
e
p
o
wer
b
alan
ce
eq
u
atio
n
s
wer
e
d
e
f
in
ed
as
(
9
)
.
{
=
⬚
∑
(
+
)
=
1
=
⬚
∑
(
+
)
=
1
(
9
)
Her
e,
th
e
U
f
u
n
ctio
n
r
ep
r
esen
ts
th
e
v
o
ltag
e
am
p
litu
d
e
,
an
d
th
e
G
f
u
n
ctio
n
r
ep
r
esen
ts
th
e
lin
e
co
n
d
u
ctan
ce
.
P &
Q
r
ep
r
esen
t
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
o
n
en
ts
.
Seco
n
d
ly
,
t
h
e
E
V
c
h
ar
g
i
n
g
c
o
n
s
tr
ain
ts
,
wh
ich
h
av
e
s
u
b
-
c
o
n
s
tr
ain
ts
lik
e
ch
ar
g
in
g
p
o
w
er
,
b
atter
y
ca
p
ac
ity
,
an
d
p
o
wer
b
alan
ce
[
2
4
]
.
T
h
e
ch
ar
g
in
g
p
o
wer
c
o
n
s
tr
ain
t c
an
b
e
d
ef
in
e
d
as
(
1
0
)
.
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1472
-
1
4
8
3
1476
0
≤
(
,
)
≤
(
,
)
(
1
0
)
(
,
)
=
{
,
,
∈
[
,
]
0
,
∉
[
,
]
,
∈
(
1
1
)
I
n
th
e
ab
o
v
e
eq
u
atio
n
,
P
+v
e
an
d
p
-
v
e
co
m
p
o
n
en
ts
wer
e
th
e
p
o
wer
tak
en
f
o
r
ch
ar
g
in
g
an
d
its
m
ax
im
u
m
lim
it.
No
w
th
e
b
atter
y
co
n
s
tr
ain
t h
as th
e
is
s
u
es in
clu
d
ed
f
o
r
t
h
e
SOC
s
tatu
s
an
d
lev
els o
f
SOC
as p
er
(
1
2
)
.
(
1
2
)
L
astl
y
,
th
e
p
o
wer
b
alan
cin
g
c
o
n
s
tr
ain
t
is
d
ef
in
ed
as
p
er
(
1
3
)
,
wh
er
e
th
e
s
u
b
-
c
o
n
s
tr
ain
ts
o
f
th
e
E
V
m
ix
ed
an
d
f
in
alize
d
th
e
o
p
tim
al
eq
u
atio
n
.
,
∑
(
,
)
=
,
=
−
(
(
,
)
−
(
,
)
)
(
1
3
)
Fu
r
th
er
,
th
e
o
th
er
a
d
d
itio
n
al
c
o
n
s
tr
ain
ts
wer
e
d
ef
in
ed
f
o
r
v
o
ltag
e
as
p
er
(
1
4
)
an
d
c
u
r
r
en
t
a
s
p
er
(
1
5
)
,
th
e
to
tal
n
u
m
b
er
o
f
c
h
ar
g
in
g
p
iles
in
th
e
s
y
s
tem
is
s
h
o
wn
in
(
1
7
)
.
(
)
(
1
4
)
(
)
≤
(
1
5
)
0
≤
≤
(
1
6
)
4.
DE
S
I
G
N
O
F
A
M
UL
T
I
L
AYER
A
L
G
O
RI
T
H
M
F
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R
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V
CH
ARG
I
NG
S
T
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l
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F
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g
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2
(
a
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a
n
d
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is
p
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v
i
d
e
d
i
n
F
i
g
u
r
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2
(
b
)
.
4
.
1
.
T
he
f
un
ct
io
na
litie
s
o
f
t
h
e
o
ute
r
la
y
er
T
h
e
o
u
ter
lay
er
o
f
th
e
alg
o
r
ith
m
co
n
s
o
lid
ates
th
e
E
V
lo
ad
s
f
r
o
m
th
e
in
n
er
la
y
er
an
d
em
p
lo
y
s
p
o
wer
f
lo
w
an
aly
s
is
to
ass
ess
th
e
v
o
l
tag
e
q
u
ality
o
f
th
e
PDN
ac
r
o
s
s
v
ar
io
u
s
ch
a
r
g
in
g
s
ce
n
ar
io
s
.
Du
e
to
th
e
in
h
e
r
en
t
ch
ar
ac
ter
is
tics
o
f
th
e
im
b
ala
n
c
ed
PDN
[
2
2
]
-
[
2
4
]
,
in
cl
u
d
in
g
t
h
r
ee
-
p
h
ase
lo
ad
im
b
alan
ce
an
d
asy
m
m
etr
y
in
th
e
th
r
ee
-
p
h
ase
f
ac
to
r
s
,
alo
n
g
with
th
e
u
n
co
o
r
d
in
ated
g
r
id
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co
n
n
ec
ted
ch
ar
g
in
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o
f
s
in
g
le
-
p
h
ase
E
Vs
an
d
win
d
en
er
g
y
,
d
ir
ec
tly
ap
p
ly
i
n
g
th
e
eq
u
iv
alen
t
s
in
g
le
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p
h
ase
tr
e
n
d
ca
lcu
latio
n
m
eth
o
d
to
th
e
t
h
r
ee
-
p
h
ase
n
etwo
r
k
p
r
o
v
es
im
p
r
ac
tical
[
2
5
]
.
I
n
th
is
s
tu
d
y
,
th
e
f
o
r
war
d
-
b
ac
k
wa
r
d
g
en
e
r
atio
n
tech
n
iq
u
e
[
2
6
]
is
im
p
lem
en
ted
to
ev
alu
ate
b
o
th
v
o
ltag
e
q
u
ality
a
n
d
th
r
ee
-
p
h
ase
p
o
wer
f
lo
w.
E
s
tab
lis
h
in
g
th
e
s
y
s
tem
in
itia
lizatio
n
s
tate
,
wh
ich
co
n
s
is
t
s
o
f
p
ar
am
eter
s
lik
e
g
r
id
s
tate
,
E
V
lo
ad
s
tate,
win
d
p
o
wer
o
u
tp
u
t,
an
d
g
r
id
co
n
n
ec
tio
n
d
ia
g
r
am
.
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r
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te
ad
m
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m
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f
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2
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ith
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MA
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Evaluation Warning : The document was created with Spire.PDF for Python.
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16
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H
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u
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(
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,
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+
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,
,
,
(
2
0
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Her
e
,
th
e
eq
u
atio
n
is
a
m
er
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e
r
o
f
lo
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ce
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r
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en
ts
.
,
1
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2
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=
∑
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,
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+
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,
,
,
(
2
1
)
I
te
r
a
ti
o
n
s
p
er
f
o
r
m
a
n
ce
f
o
r
v
o
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ag
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o
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u
s
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s
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-
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e
f
o
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wa
r
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b
ac
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r
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ti
o
n
,
n
o
d
al
v
o
l
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g
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te
c
h
n
iq
u
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[
2
4
]
,
s
u
c
h
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h
at
t
h
e
t
h
r
ee
-
p
h
ase
v
o
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d
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as
(
2
2
)
.
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=
−
1
+
1
1
,
2
,
0
(
2
2
)
No
w
th
e
co
n
v
er
g
en
ce
s
f
o
r
th
e
m
ax
im
u
m
p
o
in
t
o
f
v
o
ltag
e
d
if
f
er
en
ce
a
r
e
d
o
n
e
,
an
d
i
f
s
atis
f
ac
to
r
y
lev
els
ar
e
n
o
t a
ch
iev
e
d
,
th
en
s
tep
s
3
to
6
ar
e
r
ep
ea
ted
to
ac
h
iev
e
m
ax
i
m
u
m
co
n
v
er
g
e
n
ce
.
=
|
+
1
,
,
−
,
,
|
<
(
2
3
)
No
w
,
f
in
ally
,
th
e
v
o
ltag
e
q
u
ali
ty
is
ass
es
s
ed
an
d
f
ed
in
t
o
th
e
in
n
er
lay
er
.
4
.
2
.
F
un
ct
io
na
litie
s
o
f
t
he
in
ner
la
y
er
T
h
e
in
n
er
lay
er
o
f
th
e
alg
o
r
ith
m
o
p
tim
izes
th
e
s
p
lit
-
p
h
ase
ch
ar
g
in
g
s
tr
ateg
y
u
s
in
g
th
e
NSGA
-
I
I
alg
o
r
ith
m
,
wh
ich
en
h
a
n
ce
s
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
[
2
0
]
with
b
etter
s
p
ee
d
an
d
c
o
n
v
er
g
en
ce
th
an
th
e
tr
ad
itio
n
al
GA
m
eth
o
d
[
2
2
]
.
T
h
e
p
r
o
ce
s
s
in
v
o
lv
es:
i)
I
n
itializatio
n
:
Ass
es
s
th
e
f
itn
e
s
s
o
f
th
e
m
u
lti
-
o
b
jectiv
e
f
u
n
c
tio
n
u
tili
zin
g
in
itial
d
ata
o
n
E
V
ac
ce
s
s
ib
ilit
y
an
d
v
o
lta
g
e
q
u
ality
f
r
o
m
th
e
o
u
ter
lay
er
.
ii)
Gen
etic
E
v
o
lu
tio
n
:
C
alcu
late
cr
o
wd
ed
an
d
n
o
n
-
d
o
m
in
ated
o
r
d
er
i
n
g
d
is
tan
ce
s
,
co
m
b
in
e
o
f
f
s
p
r
in
g
with
p
ar
en
ts
,
an
d
g
en
er
ate
n
ew
p
o
p
u
latio
n
s
th
r
o
u
g
h
p
r
o
ce
s
s
es su
ch
as c
r
o
s
s
o
v
er
,
m
u
tatio
n
,
a
n
d
elite
s
elec
tio
n
.
iii)
Selectio
n
:
Pre
s
er
v
e
in
d
iv
id
u
a
ls
r
an
k
ed
b
y
q
u
ality
i
n
d
esc
en
d
in
g
o
r
d
e
r
,
c
h
o
o
s
in
g
th
e
f
in
al
s
u
b
s
et
with
h
ig
h
er
c
r
o
wd
in
g
d
is
tan
ce
to
es
tab
lis
h
a
n
ew
p
ar
en
t
p
o
p
u
latio
n
.
iv
)
I
ter
atio
n
:
C
o
n
f
ir
m
th
e
c
o
m
p
le
tio
n
o
f
iter
atio
n
s
;
if
th
e
cr
iter
i
a
ar
e
n
o
t
m
et,
r
etu
r
n
E
V
ch
ar
g
in
g
s
tr
ateg
ies
to
th
e
o
u
ter
lay
e
r
an
d
r
ep
ea
t t
h
e
p
r
o
ce
d
u
r
e
u
n
til th
e
r
eq
u
ir
em
e
n
ts
ar
e
f
u
lf
illed
.
v)
Fin
al
Op
tim
izatio
n
:
E
m
p
lo
y
t
h
e
af
f
iliatio
n
f
u
n
ctio
n
t
o
d
ete
r
m
in
e
th
e
o
p
tim
al
p
h
ase
s
tr
ateg
y
with
in
th
e
Par
eto
s
o
lu
tio
n
s
et.
5.
VALI
DAT
I
O
N
AND
R
E
SU
L
T
AN
AL
Y
SI
S
T
h
e
s
im
u
latio
n
v
alid
atio
n
is
p
r
esen
ted
i
n
th
is
s
ec
tio
n
,
a
n
d
f
o
r
s
im
u
latio
n
v
alid
atio
n
MA
T
L
AB
en
v
ir
o
n
m
en
t
is
u
s
ed
,
a
n
d
f
o
r
alg
o
r
ith
m
im
p
lem
en
tatio
n
c
o
n
v
er
g
en
ce
MA
T
L
AB
s
cr
ip
t
h
as
b
ee
n
u
s
ed
,
as
s
h
o
wn
in
Fig
u
r
e
3
(
a
)
.
T
h
e
v
a
r
io
u
s
ca
s
es
co
n
s
id
er
ed
f
o
r
th
e
p
er
f
o
r
m
an
ce
v
alid
atio
n
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ar
e
as f
o
llo
ws
:
5
.
1
.
A
s
t
a
nd
a
rd
ba
s
ic
po
wer
g
rid lo
a
d t
esting
T
o
v
alid
ate
th
e
ef
f
icac
y
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
to
war
d
s
s
o
m
e
b
asic
s
tan
d
ar
d
s
,
th
e
I
E
E
E
-
33
s
tan
d
ar
d
n
o
d
e
ar
c
h
itectu
r
e
is
u
tili
ze
d
.
An
im
p
r
o
v
is
ed
I
E
E
E
-
3
3
s
tan
d
a
r
d
n
o
d
e
ar
c
h
itectu
r
e
is
u
s
ed
f
o
r
th
e
s
u
g
g
ested
ca
s
e
s
tu
d
y
to
wa
r
d
s
th
e
win
d
p
o
wer
s
y
s
tem
.
T
h
e
1
2
n
o
d
es
o
f
PDN
h
a
v
e
a
p
o
wer
in
p
u
t
o
f
3
.
3
6
MW
co
m
b
in
ed
f
r
o
m
v
ar
io
u
s
win
d
t
u
r
b
in
es.
No
d
es
1
7
to
3
1
h
a
v
e
an
ap
p
r
o
x
im
ate
lo
ad
f
r
o
m
E
V
s
r
an
g
in
g
f
r
o
m
8
0
0
to
1
2
0
0
.
T
h
ese
n
o
d
es
h
av
e
ac
c
ess
to
co
m
m
u
n
icatio
n
s
to
th
e
co
n
n
ec
ted
lo
ad
,
an
d
a
r
atio
o
f
6
:4
:5
is
m
ain
tain
ed
to
war
d
s
th
e
ca
p
ac
ity
lev
els.
T
h
e
p
h
ase
-
wis
e
ac
ce
s
s
f
o
r
th
e
lo
ad
co
n
n
ec
ted
at
th
e
p
a
r
allel
p
o
in
ts
in
Fig
u
r
e
3
(
b
)
p
r
esen
ts
th
e
lo
ad
ac
ce
s
s
with
o
u
t
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
an
d
Fig
u
r
e
3
(
c)
p
r
esen
ts
th
e
r
esu
lts
with
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
5
.
2
.
P
er
f
o
rma
nce
a
na
ly
s
is
o
f
ph
a
s
e
s
elec
t
io
n
Fig
u
r
es
4
(
a)
an
d
4
(
b
)
illu
s
tr
ate
th
e
p
h
ase
-
wis
e
lo
ad
ac
c
ess
at
th
e
p
ar
allel
co
n
n
ec
tio
n
p
o
in
ts
.
Sp
ec
if
ically
,
Fig
u
r
e
4
(
a)
p
r
esen
ts
th
e
s
y
s
tem
b
e
h
av
io
r
with
o
u
t
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
wh
er
ea
s
Fig
u
r
e
4
(
b
)
d
em
o
n
s
tr
ates
th
e
im
p
r
o
v
em
en
t
ac
h
iev
ed
wh
en
th
e
alg
o
r
ith
m
is
ap
p
lied
.
Fro
m
th
e
r
esu
lts
,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
with
o
u
t
a
n
alg
o
r
ith
m
,
th
e
lo
ad
is
d
is
o
r
d
e
r
ed
as
Ph
ase
C
r
ec
eiv
ed
m
o
r
e
l
o
ad
a
n
d
c
r
ea
te
d
th
e
u
n
b
ala
n
ce
in
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
Op
timiz
in
g
s
lo
w
-
ch
a
r
g
in
g
E
V
lo
a
d
s
w
ith
a
tw
o
-
la
ye
r
s
tr
a
teg
y
to
en
h
a
n
ce
…
(
A
tta
d
a
Du
r
g
a
P
r
a
s
a
d
)
1479
th
e
s
y
s
tem
.
I
n
co
n
tr
ast
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ef
f
ec
tiv
ely
d
is
tr
ib
u
ted
th
e
lo
ad
t
o
all
p
h
a
s
es
eq
u
ally
with
th
e
s
p
lit
-
p
h
ase
alg
o
r
ith
m
.
Fu
r
th
er
win
d
p
o
wer
was
g
en
e
r
ated
,
an
d
th
e
lo
a
d
lin
e
o
f
E
V
s
was
s
h
o
wn
in
Fig
u
r
e
4
(
a)
.
T
h
e
3
3
-
n
o
d
e
b
ase
lo
ad
,
alo
n
g
with
th
e
co
n
n
ec
ted
s
ites
o
f
t
h
e
g
r
id
,
is
s
h
o
wn
in
Fig
u
r
es
4
(
b
)
an
d
4
(
c
)
.
T
h
e
PDN
d
escr
ib
ed
ab
o
v
e
h
as th
e
f
o
llo
win
g
r
atin
g
:
a
ca
p
ac
ity
o
f
1
0
0
MV
A
p
o
w
er
an
d
a
m
ax
im
u
m
v
o
ltag
e
r
atin
g
o
f
1
2
.
6
6
KV.
Fu
r
th
er
,
a
to
tal
o
f
s
ix
s
ce
n
ar
i
o
s
wer
e
p
r
o
p
o
s
ed
to
ass
ess
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
an
d
h
o
w
ef
f
ec
tiv
ely
th
e
ch
ar
g
in
g
tech
n
i
q
u
e
is
im
p
lem
en
ted
to
en
h
an
ce
t
h
e
s
y
s
tem
'
s
v
o
ltag
e
q
u
ality
.
Fu
r
th
e
r
p
r
o
p
o
s
ed
s
ce
n
ar
io
s
wer
e
lis
ted
in
T
ab
le
1
.
W
h
er
e
th
e
av
er
ag
e
an
d
m
ax
im
u
m
v
al
u
es
ar
e
tak
en
in
to
co
n
s
id
er
atio
n
f
o
r
ass
ess
in
g
th
e
v
o
ltag
e
q
u
ality
u
n
d
er
v
a
r
io
u
s
co
n
d
itio
n
s
o
f
th
e
s
y
s
tem
E
x
am
in
atio
n
o
f
T
a
b
le
2
s
h
o
ws
th
at
in
C
ase
Stu
d
ies
1
,
2
,
an
d
3
,
th
e
in
d
icato
r
s
in
cr
ea
s
e
wh
e
n
E
Vs
ar
e
ass
o
ciate
d
with
av
er
ag
e
an
d
d
is
o
r
d
er
ed
ac
ce
s
s
.
T
h
is
is
b
ec
a
u
s
e
lack
o
f
o
f
f
s
et
f
o
r
in
cr
ea
s
e
d
en
er
g
y
p
r
o
d
u
ctio
n
an
d
th
e
ex
ac
er
b
atio
n
o
f
th
r
ee
-
p
h
ase
lo
ad
d
if
f
er
e
n
ce
s
b
y
th
e
b
ase
g
r
id
lo
ad
.
Sp
lit
-
p
h
ase
ch
ar
g
in
g
im
p
r
o
v
es
v
o
ltag
e
q
u
ality
,
r
e
d
u
cin
g
s
y
s
tem
VU
b
y
a
p
er
ce
n
tag
e
o
f
2
4
.
5
6
%
co
m
p
ar
e
d
with
av
er
ag
e
ac
ce
s
s
f
o
r
E
Vs
an
d
3
2
.
8
1
%
c
o
m
p
ar
e
d
to
d
is
o
r
d
e
r
ed
ac
ce
s
s
.
T
h
e
m
a
x
.
SP
-
VD
d
ec
r
ea
s
es
b
y
4
.
8
9
%
wh
e
n
c
o
m
p
ar
ed
with
th
e
av
er
ag
e
ac
ce
s
s
an
d
9
.
1
1
%
wh
en
co
m
p
a
r
ed
with
d
is
o
r
d
er
ed
ac
ce
s
s
.
VH
at
th
e
g
r
id
p
o
in
t
is
r
ed
u
ce
d
b
y
6
.
2
5
%
wh
en
co
m
p
ar
ed
with
d
is
o
r
d
er
ed
ac
ce
s
s
.
In
av
e
r
ag
e
a
n
d
d
is
o
r
d
er
e
d
ac
ce
s
s
s
ce
n
ar
io
s
,
t
h
r
e
e
-
p
h
ase
u
n
b
alan
c
e
an
d
VD
ex
ce
ed
n
atio
n
al
s
tan
d
ar
d
s
b
y
m
o
r
e
t
h
an
2
%
an
d
7
%,
r
esp
ec
tiv
ely
.
T
h
e
ch
a
r
g
in
g
s
tr
ateg
y
i
n
th
is
w
o
r
k
en
s
u
r
es
v
o
ltag
e
q
u
ality
m
ee
t
s
n
atio
n
al
s
tan
d
ar
d
s
.
C
ar
eless
s
elec
tio
n
o
f
ch
a
r
g
in
g
p
iles
lead
s
to
s
ig
n
if
ican
t
v
o
ltag
e
q
u
ality
o
v
er
r
u
n
s
,
h
ig
h
l
ig
h
tin
g
th
e
n
ee
d
f
o
r
s
p
lit
-
p
h
ase
ch
ar
g
in
g
to
m
ee
t
v
o
ltag
e
q
u
ality
s
tan
d
ar
d
s
.
T
h
e
m
ax
.
3
-
p
h
ase
VU,
VD,
an
d
VH
o
b
s
er
v
e
d
r
ates
ar
e
1
.
7
7
8
%,
6
.
5
2
8
%,
an
d
0
.
2
8
6
%,
r
e
s
p
ec
tiv
ely
.
Ho
wev
er
,
o
p
tim
izin
g
f
o
r
a
s
in
g
le
v
o
ltag
e
q
u
ality
in
cr
ea
s
es
th
e
o
th
er
two
t
o
v
ar
y
in
g
d
e
g
r
ee
s
.
T
h
is
p
ap
er
'
s
ch
ar
g
in
g
tech
n
i
q
u
e
m
in
im
izes
th
e
o
v
er
all
tar
g
et
wh
ile
ac
h
ie
v
in
g
t
h
e
b
est
p
o
s
s
ib
le
eq
u
ilib
r
iu
m
f
o
r
all
t
h
r
ee
o
f
th
e
v
o
ltag
e
attr
ib
u
tes.
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
Stru
ctu
r
al
v
iew
o
f
(
a
)
I
E
E
E
-
3
3
s
tan
d
ar
d
n
o
d
e
s
y
s
tem
an
d
3
-
p
h
ase
h
ar
m
o
n
ics
,
(
b
)
lo
a
d
ac
ce
s
s
with
o
u
t th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
a
n
d
(
c
)
lo
ad
ac
ce
s
s
with
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1472
-
1
4
8
3
1480
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
R
ep
r
esen
tatio
n
o
f
(
a
)
g
en
er
ate
d
w
in
d
p
o
wer
an
d
lo
ad
o
f
E
Vs
,
(
b
)
3
-
ph
b
ase
lo
ad
f
o
r
I
E
E
E
-
3
3
s
y
s
tem
s
,
an
d
(
c)
3
-
p
h
b
ase
lo
a
d
at
n
o
d
es 1
7
an
d
3
1
T
ab
le
1
.
PDN
v
o
ltag
e
q
u
ality
u
n
d
er
d
if
f
er
e
n
t scen
ar
io
s
S
c
e
n
a
r
i
o
3
-
p
h
a
s
e
V
U
%
V
D
p
e
r
p
h
a
se
%
V
H
a
t
g
r
i
d
n
o
d
e
p
o
i
n
t
s
%
A
v
g
.
v
a
l
u
e
M
a
x
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