I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
,
p
p
.
76
~
88
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
1
6
i
1
.
pp
76
-
88
76
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
O
ptima
l
inv
estme
nt
frame
wo
rk of s
tatic
V
Ar
co
mpe
n
sa
tors
in
distribut
io
n sy
ste
m ba
sed o
n lif
e cy
cle cost
Ng
uy
en
H
ien Trun
g
,
Vu V
a
n T
ha
ng
D
e
p
a
r
t
me
n
t
o
f
P
o
w
e
r
S
y
s
t
e
m,
F
a
c
u
l
t
y
o
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E
l
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
,
T
h
a
i
n
g
u
y
e
n
U
n
i
v
e
r
si
t
y
o
f
Te
c
h
n
o
l
o
g
y
,
T
h
a
i
n
g
u
y
e
n
C
i
t
y
,
V
i
e
t
n
a
m
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
2
7
,
2
0
2
4
R
ev
is
ed
Sep
1
7
,
2
0
2
5
Acc
ep
ted
No
v
2
3
,
2
0
2
5
Th
e
d
istri
b
u
ti
o
n
sy
ste
m
p
la
n
n
in
g
a
n
d
o
p
e
ra
ti
n
g
p
re
se
n
t
sig
n
ifi
c
a
n
t
c
h
a
ll
e
n
g
e
s
d
u
e
t
o
lo
w
v
o
lt
a
g
e
,
h
ig
h
imp
e
d
a
n
c
e
,
a
n
d
lar
g
e
lo
a
d
d
e
n
sit
y
,
wh
ich
lea
d
t
o
su
b
sta
n
ti
a
l
p
o
we
r
lo
ss
e
s
a
n
d
lo
w
v
o
lt
a
g
e
q
u
a
li
ty
.
T
o
a
d
d
re
ss
th
is
c
h
a
ll
e
n
g
e
,
t
h
e
p
a
p
e
r
p
r
o
p
o
se
s
a
n
o
p
ti
m
a
l
fra
m
e
wo
rk
fo
r
th
e
sim
u
lt
a
n
e
o
u
s
d
e
term
in
a
ti
o
n
o
f
th
e
p
lac
e
m
e
n
t
a
n
d
siz
i
n
g
o
f
st
a
ti
c
VA
r
c
o
m
p
e
n
sa
to
rs
(S
VCs
)
in
DSs.
Th
e
p
r
o
p
o
se
d
m
o
d
e
l
is
fo
rm
u
late
d
a
s
a
n
o
p
ti
m
iza
ti
o
n
p
r
o
b
lem
th
a
t
m
in
imi
z
e
s th
e
li
fe
c
y
c
le co
st,
wh
il
e
a
c
c
o
u
n
ti
n
g
f
o
r
th
e
v
a
r
y
in
g
l
ifes
p
a
n
s
a
n
d
in
v
e
stm
e
n
t
ti
m
e
s
o
f
S
VCs
.
Th
e
fr
a
m
e
wo
rk
in
c
o
rp
o
ra
tes
h
o
u
rly
l
o
a
d
v
a
riatio
n
a
n
d
e
m
p
lo
y
s
f
u
ll
a
lt
e
rn
a
ti
n
g
c
u
rre
n
t
(AC
)
p
o
we
r
fl
o
w
a
n
a
ly
sis
to
imp
ro
v
e
th
e
a
c
c
u
ra
c
y
o
f
re
su
lt
s.
A
d
d
i
ti
o
n
a
ll
y
,
it
c
o
n
sid
e
rs t
h
e
d
e
p
e
n
d
e
n
c
y
o
f
t
h
e
r
e
a
c
ti
v
e
p
o
we
r
in
jec
ted
b
y
S
VCs
o
n
th
e
DSs
a
n
d
i
n
c
o
rp
o
ra
tes
th
e
d
isc
re
te
ra
ted
c
a
p
a
c
it
ies
o
f
S
VCs
t
o
e
n
s
u
re
p
ra
c
ti
c
a
l
fe
a
sib
il
it
y
a
n
d
e
n
h
a
n
c
e
th
e
a
c
c
u
ra
c
y
o
f
c
o
m
p
e
n
sa
ti
o
n
p
o
we
r,
e
ffe
c
t
o
f
DSs.
Th
e
p
r
o
p
o
se
d
a
p
p
ro
a
c
h
is
v
a
li
d
a
ted
u
sin
g
a
m
o
d
ifi
e
d
3
3
-
b
u
s
I
EE
E
tes
t
sy
ste
m
imp
lem
e
n
ted
in
t
h
e
g
e
n
e
ra
l
a
lg
e
b
ra
ic
m
o
d
e
li
n
g
s
y
ste
m
(G
AMS
).
Nu
m
e
rica
l
re
su
lt
s
fro
m
m
u
lt
ip
le
c
a
se
stu
d
ies
c
o
n
firm
th
e
fe
a
sib
il
it
y
a
n
d
h
i
g
h
p
e
rfo
rm
a
n
c
e
o
f
t
h
e
p
r
o
p
o
se
d
m
o
d
e
l.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
tio
n
s
y
s
tem
s
Op
tim
izatio
n
Static
VAr
co
m
p
en
s
ato
r
s
L
if
e
cy
cle
co
s
t
Gen
er
al
alg
eb
r
aic
m
o
d
elin
g
s
y
s
tem
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Vu
Van
T
h
an
g
Dep
ar
tm
en
t o
f
Po
wer
Sy
s
tem
,
Facu
lty
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
,
T
h
ain
g
u
y
e
n
Un
iv
e
r
s
ity
o
f
T
ec
h
n
o
lo
g
y
No
.
6
6
6
,
3
/2
Stre
et,
T
h
ain
g
u
y
en
C
ity
,
Vietn
am
E
m
ail: th
an
g
v
v
h
td
@
tn
u
t.e
d
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Dis
tr
ib
u
tio
n
s
y
s
tem
s
(
D
Ss
)
ar
e
th
e
p
o
in
ts
o
f
co
n
tact
b
e
twee
n
th
e
elec
tr
icity
in
d
u
s
tr
y
an
d
th
e
co
n
s
u
m
er
s
,
ty
p
ically
o
p
er
ati
n
g
at
m
ed
iu
m
o
r
lo
w
v
o
lta
g
e
lev
els.
T
h
ey
in
clu
d
e
n
u
m
er
o
u
s
f
ee
d
e
r
s
an
d
d
is
tr
ib
u
tio
n
tr
an
s
f
o
r
m
er
s
ch
a
r
ac
ter
ized
b
y
h
ig
h
im
p
ed
a
n
ce
an
d
d
e
n
s
e
lo
ad
s
,
wh
ich
r
esu
lt
in
elev
ated
p
o
wer
lo
s
s
es
an
d
d
eg
r
a
d
ed
v
o
ltag
e
q
u
ality
[
1
]
,
[
2
]
.
T
h
ese
f
ac
to
r
s
s
ig
n
if
ican
tly
r
ed
u
ce
th
e
tec
h
n
ical
an
d
ec
o
n
o
m
ic
ef
f
icien
cy
o
f
DSs
,
r
eq
u
ir
i
n
g
co
s
tly
u
p
g
r
a
d
es
to
f
ee
d
er
s
,
tr
an
s
f
o
r
m
er
s
,
an
d
in
cr
ea
s
ed
elec
tr
icity
p
u
r
ch
ases
f
r
o
m
th
e
g
r
id
.
C
o
n
s
eq
u
en
tly
,
th
ese
is
s
u
es a
r
e
cr
itical
in
DS p
lan
n
in
g
,
d
esig
n
,
an
d
o
p
er
atio
n
[
3
]
.
Ad
d
itio
n
ally
,
m
o
d
er
n
DSs
f
ac
e
g
r
ea
t
ch
allen
g
es
d
u
e
t
o
t
h
e
in
cr
ea
s
in
g
p
en
etr
atio
n
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
a
n
d
th
e
in
te
g
r
atio
n
o
f
ad
v
an
ce
d
p
o
wer
elec
t
r
o
n
ic
d
ev
ices.
E
f
f
ec
tiv
e
p
lan
n
in
g
an
d
o
p
er
atio
n
al
s
tr
ateg
ies
ar
e
th
er
ef
o
r
e
n
ec
es
s
ar
y
to
en
h
an
ce
s
y
s
tem
p
er
f
o
r
m
an
ce
,
r
ed
u
ce
o
p
er
atio
n
al
co
s
ts
,
an
d
im
p
r
o
v
e
v
o
ltag
e
p
r
o
f
iles
[
3
]
,
[
4
]
.
As
a
r
esu
lt,
th
e
tr
ad
itio
n
al
p
ass
i
v
e
m
o
d
el
o
f
DSs
is
ev
o
lv
in
g
to
war
d
ac
tiv
e
DSs
,
wh
ich
in
teg
r
ate
d
is
tr
ib
u
ted
g
en
er
atio
n
(
DG)
,
en
er
g
y
s
to
r
a
g
e
s
y
s
tem
s
,
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
d
ev
ices,
allo
win
g
o
p
er
ato
r
s
to
m
an
ag
e
p
o
wer
f
lo
ws
d
y
n
am
i
ca
lly
th
r
o
u
g
h
f
le
x
ib
le
n
etwo
r
k
to
p
o
lo
g
ies
[
5
]
,
[
6
]
.
I
n
th
is
co
n
te
x
t,
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
b
ec
o
m
es
a
cr
u
cial
asp
ec
t
o
f
DS
p
lan
n
in
g
an
d
o
p
er
atio
n
.
Selectin
g
th
e
o
p
tim
al
ty
p
e,
s
ize,
an
d
lo
ca
tio
n
o
f
co
m
p
en
s
a
tio
n
d
ev
ices
is
es
s
en
tial
to
m
in
im
ize
lo
s
s
es
an
d
m
ain
tain
ac
ce
p
tab
le
v
o
ltag
e
p
r
o
f
iles
.
C
o
m
m
o
n
tech
n
iq
u
es
f
o
r
im
p
r
o
v
in
g
DS
p
er
f
o
r
m
a
n
ce
in
clu
d
e
f
e
ed
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l in
ve
s
tmen
t fra
mewo
r
k
o
f sta
tic
va
r
co
mp
en
s
a
to
r
s
in
d
is
tr
ib
u
tio
n
…
(
N
g
u
ye
n
Hien
Tr
u
n
g
)
77
u
p
g
r
a
d
es,
v
o
ltag
e
le
v
el
en
h
a
n
ce
m
en
t,
d
is
tr
ib
u
ted
g
en
er
atio
n
,
an
d
n
etwo
r
k
r
ec
o
n
f
ig
u
r
ati
o
n
[
7
]
,
[
8
]
.
Am
o
n
g
th
ese,
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
is
p
ar
ticu
lar
ly
attr
ac
tiv
e
d
u
e
to
its
co
s
t
-
ef
f
ec
tiv
en
ess
,
m
in
im
al
d
is
r
u
p
tio
n
to
th
e
ex
is
tin
g
n
etwo
r
k
,
a
n
d
r
e
lativ
ely
s
h
o
r
t im
p
lem
en
tatio
n
tim
elin
e
[
9
]
.
T
r
ad
itio
n
al
c
o
m
p
en
s
atio
n
d
e
v
ices
s
u
ch
as
s
y
n
c
h
r
o
n
o
u
s
c
o
n
d
en
s
er
s
,
ca
p
ac
it
o
r
s
,
an
d
r
ea
cto
r
s
h
av
e
lim
itatio
n
s
.
Sy
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
ar
e
less
co
m
m
o
n
to
d
a
y
d
u
e
to
th
eir
h
i
g
h
lo
s
s
es,
h
ig
h
co
s
ts
,
an
d
s
lo
wer
r
esp
o
n
s
e
tim
es.
C
ap
ac
ito
r
s
an
d
r
ea
cto
r
s
ar
e
m
o
r
e
co
m
m
o
n
l
y
u
s
ed
d
u
e
to
l
o
wer
co
s
t
an
d
s
im
p
licity
,
th
ey
lack
th
e
d
y
n
am
ic
r
esp
o
n
s
e
r
e
q
u
ir
e
d
b
y
m
o
d
er
n
DSs
with
v
ar
ia
b
l
e
lo
ad
p
r
o
f
iles
an
d
DG
[
6
]
,
[
1
0
]
.
Ov
e
r
co
m
in
g
th
e
ab
o
v
e
lim
itatio
n
s
,
SVC
s
o
f
f
er
s
ev
er
al
a
d
v
an
ta
g
es.
B
y
u
s
in
g
th
y
r
is
to
r
-
b
ased
s
witch
in
g
,
s
tatic
VAr
co
m
p
en
s
ato
r
s
(
SVC
s
)
p
r
o
v
i
d
e
f
ast,
co
n
tin
u
o
u
s
co
n
tr
o
l
o
f
r
ea
ctiv
e
p
o
we
r
with
o
u
t
i
n
cr
ea
s
in
g
f
au
lt
cu
r
r
en
t
lev
els.
T
h
ey
im
p
r
o
v
e
v
o
ltag
e
s
tab
ilit
y
,
r
ed
u
ce
s
y
s
tem
lo
s
s
es,
an
d
en
h
an
ce
p
o
wer
q
u
ality
b
y
m
itig
atin
g
v
o
ltag
e
f
lu
ctu
atio
n
s
a
n
d
lo
ad
im
b
alan
ce
[
9
]
,
[
1
1
]
,
[
1
2
]
.
T
h
e
r
ef
o
r
e,
SVC
s
h
av
e
b
ec
o
m
e
in
cr
ea
s
in
g
ly
r
ele
v
an
t
in
m
o
d
er
n
DS p
lan
n
i
n
g
an
d
o
p
er
atio
n
.
Var
io
u
s
o
p
tim
izatio
n
tech
n
i
q
u
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
d
e
ter
m
in
e
th
e
o
p
tim
al
l
o
ca
tio
n
an
d
s
ize
o
f
r
ea
ctiv
e
co
m
p
en
s
atio
n
d
ev
i
ce
s
,
in
clu
d
in
g
g
e
n
etic
alg
o
r
ith
m
s
,
d
r
a
g
o
n
f
ly
,
f
lo
wer
p
o
llin
atio
n
,
wh
ale
o
p
tim
izatio
n
,
an
d
o
t
h
er
s
[
1
3
]
–
[
1
9
]
.
Alth
o
u
g
h
th
ese
s
tu
d
ies
h
elp
r
ed
u
ce
lo
s
s
es
an
d
im
p
r
o
v
e
v
o
ltag
e
p
r
o
f
iles
,
th
ey
o
f
ten
ass
u
m
e
co
n
s
tan
t
lo
ad
s
,
ig
n
o
r
e
th
e
v
o
ltag
e
d
ep
en
d
en
cy
o
f
co
m
p
e
n
s
atio
n
p
o
wer
,
an
d
s
im
p
lify
o
b
jectiv
es
u
s
in
g
weig
h
tin
g
o
r
s
en
s
itiv
ity
f
ac
to
r
s
,
wh
ich
m
ay
ca
u
s
e
er
r
o
r
s
in
p
o
wer
f
lo
w
an
d
lo
s
s
ca
lcu
latio
n
s
.
T
o
o
v
er
co
m
e
th
e
lim
itatio
n
s
o
f
ca
p
ac
ito
r
s
,
SVC
s
h
av
e
b
ee
n
r
esear
ch
ed
d
u
e
to
th
eir
s
u
p
er
io
r
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
co
n
tr
o
l
f
lex
ib
il
ity
.
R
ec
en
t
s
tu
d
ies
h
av
e
em
p
lo
y
ed
m
u
lti
-
o
b
jectiv
e
m
o
d
els
to
o
p
tim
ize
SVC
p
lace
m
en
t
an
d
s
izin
g
,
tak
in
g
in
to
ac
co
u
n
t
v
o
ltag
e
d
e
v
iatio
n
,
s
y
s
tem
lo
s
s
e
s
,
an
d
in
v
estme
n
t
co
s
t
[
2
0
]
–
[
2
9
]
.
Ho
wev
er
,
m
o
s
t
o
f
th
ese
ap
p
r
o
ac
h
es
ass
u
m
e
a
f
ix
ed
lo
ad
a
n
d
o
v
er
lo
o
k
t
h
e
tim
e
-
v
a
r
y
in
g
o
p
er
atio
n
p
ar
am
eter
s
o
f
DSs
an
d
th
e
d
is
cr
ete
n
atu
r
e
o
f
SVC
r
ated
ca
p
ac
itie
s
.
T
h
ey
also
o
f
ten
ig
n
o
r
e
d
if
f
er
en
ce
s
in
in
v
estme
n
t
tim
e
an
d
life
s
p
an
s
o
f
SVC
s
,
wh
ich
ca
n
in
f
lu
en
ce
p
lan
n
i
n
g
an
d
o
p
er
atio
n
r
esu
lts
o
f
DSs
.
L
if
e
cy
cle
co
s
t
(
L
C
C
)
an
aly
s
is
is
a
co
m
p
r
eh
en
s
iv
e
m
eth
o
d
f
o
r
ev
alu
atin
g
th
e
t
o
tal
co
s
t
o
f
a
p
r
o
ject
o
v
er
its
en
tire
life
s
p
an
,
in
clu
d
in
g
in
v
estme
n
t,
o
p
er
atio
n
,
m
ain
ten
an
ce
,
a
n
d
e
n
d
-
of
-
life
co
s
ts
[
3
0
]
,
[
3
1
]
.
T
h
is
ap
p
r
o
ac
h
h
as
b
ee
n
wid
ely
ap
p
lied
in
p
o
wer
s
y
s
tem
s
f
o
r
o
p
tim
izin
g
d
is
tr
ib
u
tio
n
f
ee
d
er
s
o
r
r
ein
f
o
r
ce
th
e
DSs
[
3
2
]
.
I
t
h
as
also
b
ee
n
u
s
ed
to
ass
ess
th
e
ec
o
n
o
m
ic
p
er
f
o
r
m
an
ce
o
f
m
icr
o
g
r
id
s
[
3
3
]
,
e
n
er
g
y
h
u
b
s
,
r
e
n
ewa
b
le
r
eso
u
r
ce
s
[
3
4
]
,
[
3
5
]
,
an
d
tr
a
n
s
f
o
r
m
er
s
[
3
6
]
.
T
h
e
ab
o
v
em
en
tio
n
ed
s
tu
d
ies
h
av
e
s
h
o
wn
th
e
f
ea
s
ib
ilit
y
an
d
effec
tiv
en
ess
o
f
th
e
L
C
C
an
aly
s
is
m
eth
o
d
.
T
o
ad
d
r
ess
th
e
af
o
r
em
en
tio
n
e
d
ch
allen
g
es,
th
is
s
tu
d
y
p
r
o
p
o
s
es
an
o
p
tim
al
in
v
estme
n
t
f
r
a
m
ewo
r
k
f
o
r
th
e
s
im
u
ltan
eo
u
s
d
eter
m
in
atio
n
o
f
SVC
p
lace
m
en
t
an
d
s
izin
g
in
DSs
.
T
h
e
f
r
am
ewo
r
k
ai
m
s
to
m
in
im
ize
th
e
to
tal
L
C
C
wh
ile
in
co
r
p
o
r
atin
g
r
ea
lis
tic
o
p
er
atio
n
al
co
n
s
tr
ain
ts
,
in
clu
d
in
g
lo
ad
v
ar
iati
o
n
,
v
o
ltag
e
p
r
o
f
ile
lim
its
,
tr
an
s
f
o
r
m
er
an
d
f
ee
d
er
ca
p
ac
ities
,
an
d
th
e
d
is
cr
ete
r
at
ed
ca
p
ac
ities
o
f
SVC
s
.
T
h
e
n
o
v
elty
o
f
th
is
s
tu
d
y
lies
in
its
co
m
p
r
eh
en
s
iv
e
m
o
d
elin
g
o
f
in
v
estme
n
t
tim
e,
d
ev
i
ce
life
s
p
an
,
an
d
d
y
n
am
ic
s
y
s
tem
b
eh
av
io
r
,
wh
ich
en
ab
les
m
o
r
e
ac
cu
r
ate,
p
r
ac
tic
al,
an
d
ec
o
n
o
m
ically
ef
f
icien
t
p
lan
n
in
g
f
o
r
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
atio
n
u
s
in
g
SVC
s
in
DSs
.
T
h
e
m
ain
co
n
tr
i
b
u
tio
n
s
o
f
t
h
is
r
esear
ch
ar
e
as
f
o
llo
ws:
a.
A
n
o
v
el
in
v
estme
n
t
o
p
tim
iz
atio
n
m
o
d
el
is
f
o
r
m
u
lated
as
a
m
ix
ed
-
in
teg
er
n
o
n
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
NL
P)
p
r
o
b
lem
with
th
e
o
b
jectiv
e
o
f
m
in
im
izin
g
th
e
to
tal
L
C
C
.
T
h
e
m
o
d
el
in
te
g
r
at
es
v
ar
io
u
s
c
o
s
t
co
m
p
o
n
en
ts
as
in
v
estme
n
t,
o
p
er
atio
n
,
en
er
g
y
l
o
s
s
es,
r
ep
lace
m
en
t,
an
d
r
esid
u
al
v
alu
e
o
v
er
a
m
u
lti
-
y
ea
r
p
lan
n
in
g
h
o
r
iz
o
n
.
T
h
is
h
o
lis
tic
ap
p
r
o
ac
h
p
r
o
v
id
es
a
m
o
r
e
r
ea
lis
tic
ec
o
n
o
m
ic
ev
alu
ati
o
n
th
an
s
in
g
le
-
o
b
jectiv
e
f
o
r
m
u
latio
n
s
.
b.
T
h
e
p
r
o
p
o
s
e
d
f
r
a
m
e
w
o
r
k
a
c
c
o
u
n
t
s
f
o
r
h
o
u
r
l
y
l
o
a
d
v
a
r
i
a
t
i
o
n
,
d
i
f
f
e
r
e
n
t
i
n
v
e
s
t
m
e
n
t
s
c
h
e
d
u
l
e
s
,
a
n
d
v
a
r
y
i
n
g
l
i
f
e
s
p
a
n
s
o
f
S
VC
s
.
I
t
a
ls
o
c
o
n
s
i
d
e
r
s
t
h
e
d
e
p
e
n
d
e
n
c
y
o
f
o
u
t
p
u
t
r
e
a
c
ti
v
e
p
o
w
e
r
o
f
SV
C
o
n
o
p
e
r
a
t
i
o
n
v
o
l
t
a
g
e
a
n
d
r
e
f
l
e
c
ts
ac
t
u
a
l
d
e
v
i
c
e
s
p
ec
i
f
i
c
a
ti
o
n
s
b
y
i
n
t
e
g
r
a
ti
n
g
d
is
cr
e
t
e
r
a
te
d
c
a
p
a
ci
t
i
es
o
f
SV
C
s
.
T
h
e
s
e
f
e
a
t
u
r
es
s
i
g
n
i
f
i
c
a
n
t
l
y
e
n
h
a
n
c
e
t
h
e
f
i
d
el
it
y
a
n
d
p
r
a
c
t
i
c
a
l
r
el
e
v
a
n
c
e
o
f
t
h
e
o
p
t
i
m
i
z
a
ti
o
n
o
u
t
c
o
m
e
s
.
c.
T
h
i
s
s
t
u
d
y
e
m
p
l
o
y
s
t
h
e
b
as
i
c
o
p
e
n
-
s
o
u
r
c
e
n
o
n
l
i
n
e
a
r
m
i
x
e
d
in
t
e
g
e
r
p
r
o
g
r
a
m
m
i
n
g
s
o
l
v
e
r
(
B
O
N
M
I
N
)
s
o
l
v
e
r
i
n
t
h
e
g
e
n
e
r
a
l
a
l
g
e
b
r
a
i
c
m
o
d
e
l
in
g
s
y
s
t
e
m
(
G
AM
S
)
e
n
v
i
r
o
n
m
en
t
t
o
s
o
l
v
e
t
h
e
M
I
N
L
P
m
o
d
e
l
e
f
f
i
c
i
e
n
t
l
y
.
T
h
e
a
b
i
l
i
t
y
o
f
s
o
l
v
e
r
t
o
h
a
n
d
l
e
b
o
t
h
c
o
n
t
i
n
u
o
u
s
a
n
d
d
i
s
c
r
e
t
e
v
ar
i
a
b
l
e
s
al
l
o
ws
f
o
r
i
m
p
r
o
v
e
d
c
o
n
v
e
r
g
e
n
c
e
a
n
d
r
e
d
u
c
e
d
c
o
m
p
u
t
a
t
i
o
n
a
l
b
u
r
d
en
w
h
i
l
e
e
n
s
u
r
i
n
g
s
o
l
u
t
i
o
n
q
u
a
l
i
t
y
a
n
d
r
e
li
a
b
i
li
t
y
.
T
h
e
r
e
f
o
r
e
,
t
h
e
p
r
o
p
o
s
e
d
s
o
l
u
t
i
o
n
c
a
n
b
e
a
p
p
r
o
p
r
i
a
t
el
y
ap
p
l
i
e
d
t
o
r
e
a
l
-
w
o
r
l
d
,
l
a
r
g
e
-
s
c
ale
d
i
s
t
r
i
b
u
ti
o
n
s
y
s
t
e
m
s
.
Nex
t
s
ec
tio
n
s
o
f
th
e
p
ap
er
a
r
e
o
r
g
an
ized
as
f
o
llo
ws:
T
h
e
m
a
th
em
atic
m
o
d
el
o
f
SVC
is
in
tr
o
d
u
ce
d
i
n
s
ec
tio
n
2
.
An
o
p
tim
al
i
n
v
es
tm
en
t
f
r
a
m
ewo
r
k
with
o
b
jec
tiv
e
f
u
n
ctio
n
an
d
co
n
s
tr
ain
ts
ar
e
p
r
esen
ted
in
s
ec
tio
n
3
.
Sectio
n
4
s
h
o
ws
ca
lcu
lated
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
f
r
o
m
th
e
3
3
-
b
u
s
I
E
E
E
test
s
y
s
tem
.
Fin
ally
,
th
e
co
n
clu
s
io
n
is
d
em
o
n
s
tr
ated
in
s
ec
tio
n
5
.
2.
M
AT
H
E
M
AT
I
C
M
O
D
E
L
OF
SVC
SVC
is
d
ef
in
ed
as
a
th
y
r
is
to
r
-
co
n
t
r
o
lled
g
en
er
ato
r
o
f
r
e
ac
tiv
e
p
o
wer
w
h
o
s
e
o
u
t
p
u
t
v
ar
ies
to
ex
ch
an
g
e
ca
p
ac
itiv
e
o
r
in
d
u
ct
iv
e
cu
r
r
e
n
t
o
r
b
o
th
to
m
ain
tai
n
o
r
c
o
n
tr
o
l
s
p
ec
ific
p
ar
a
m
eter
s
o
f
th
e
elec
tr
ical
p
o
wer
s
y
s
tem
,
ty
p
ically
b
u
s
v
o
ltag
es.
SVC
i
s
a
h
ig
h
-
v
o
ltag
e
d
ev
ice
th
at
r
eg
u
lates
ef
f
ec
tiv
ely
th
e
v
o
ltag
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
76
-
88
78
r
ea
ctiv
e
p
o
wer
,
an
d
d
am
p
in
g
o
f
p
o
wer
a
n
d
v
o
ltag
e
o
s
cillatio
n
s
[
1
1
]
,
[
3
7
]
,
[
3
8
]
.
SVC
is
co
n
n
ec
ted
in
a
s
h
u
n
t
with
s
ev
er
al
d
if
f
er
en
t
cir
cu
it
s
tr
u
ctu
r
es.
T
h
e
g
e
n
er
al
ci
r
c
u
it
s
tr
u
ctu
r
e
o
f
an
SVC
in
cl
u
d
es
a
f
ix
ed
s
h
u
n
t
ca
p
ac
ito
r
an
d
th
y
r
is
to
r
-
c
o
n
tr
o
lled
r
ea
cto
r
as sh
o
wn
i
n
Fig
u
r
e
1
[
2
4
]
,
[
2
9
]
.
Fig
u
r
e
1
.
C
ir
cu
it st
r
u
ctu
r
e
an
d
eq
u
iv
alen
t m
o
d
el
o
f
SVC
As
s
ee
n
,
an
SVC
is
co
m
p
o
s
ed
o
f
a
fix
e
d
ca
p
ac
ito
r
an
d
t
h
y
r
is
to
r
-
co
n
tr
o
lled
r
ea
cto
r
.
T
h
e
r
ea
ctiv
e
p
o
wer
in
jecte
d
b
y
th
e
SVC
is
co
n
tr
o
lled
b
y
th
e
firin
g
d
ela
y
an
g
le
o
f
th
e
t
h
y
r
is
to
r
.
T
h
e
firin
g
d
elay
an
g
le
o
f
th
e
t
h
y
r
is
to
r
c
h
an
g
es
lead
to
a
ch
a
n
g
e
v
alu
e
o
f
eq
u
iv
alen
t
s
u
s
ce
p
tan
ce
o
f
SVC
ac
co
r
d
i
n
g
to
(
1
)
[
1
2
]
,
[
2
4
]
.
Hen
ce
,
th
e
r
ea
cti
v
e
p
o
wer
p
r
o
v
id
ed
b
y
SVC
d
ep
en
d
in
g
o
n
th
e
r
ated
v
o
ltag
e
p
r
o
f
ile
ca
n
b
e
ex
p
r
ess
ed
as
(
2
)
.
W
h
er
e
is
r
ea
ctiv
e
p
o
wer
in
je
cted
b
y
th
e
SVC
,
is
eq
u
i
v
ale
n
t
s
u
s
ce
p
tan
ce
o
f
SVC
,
is
th
e
r
ated
v
o
ltag
e
p
r
o
f
ile
o
f
SVC
,
an
d
L
an
d
C
ar
e
th
e
in
d
u
ctan
ce
o
f
th
e
r
ea
cto
r
an
d
th
e
ca
p
ac
itan
ce
o
f
t
h
e
ca
p
ac
ito
r
,
r
esp
ec
tiv
ely
.
=
(
)
+
(
)
=
−
1
(
1
−
2
)
=
(
1
)
=
−
2
.
(
2
)
I
f
th
e
lo
ad
o
f
th
e
elec
tr
ical
s
y
s
tem
is
ca
p
ac
itiv
e,
th
e
SVC
co
n
tr
o
ls
th
y
r
is
to
r
s
s
o
th
at
co
ils
g
en
e
r
ate
m
ax
i
m
u
m
p
o
wer
,
a
n
d
th
e
SVC
co
n
s
u
m
e
s
r
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
s
y
s
t
em
.
W
h
en
th
e
lo
ad
is
in
d
u
ctiv
e,
th
e
SVC
co
n
tr
o
ls
th
y
r
is
to
r
s
s
o
th
at
co
ils
g
en
er
ate
m
in
im
u
m
p
o
wer
,
a
n
d
r
ea
ct
iv
e
p
o
wer
is
in
jecte
d
in
to
th
e
s
y
s
tem
.
SV
C
ca
n
ac
h
iev
e
f
ast an
d
c
o
n
tin
u
o
u
s
co
n
tr
o
l a
n
d
th
u
s
o
p
er
atin
g
p
ar
am
eter
s
o
f
th
e
s
y
s
tem
ca
n
b
e
im
p
r
o
v
ed
[
1
0
]
,
[
3
8
]
.
3.
O
P
T
I
M
AL
I
N
VE
ST
M
E
NT
F
RAM
E
WO
RK
I
n
DS,
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
b
y
ca
p
ac
ito
r
s
o
r
SVC
s
ca
n
r
e
d
u
ce
p
o
we
r
lo
s
s
es
an
d
en
e
r
g
y
lo
s
s
es.
Ho
wev
er
,
wh
en
SVC
is
in
v
ested
in
DS,
th
e
co
s
t
o
f
th
e
s
y
s
tem
will
b
e
in
cr
ea
s
ed
alo
n
g
with
th
e
o
p
er
atin
g
p
ar
am
eter
s
o
f
DS
also
b
ein
g
ch
a
n
g
ed
.
T
h
er
e
f
o
r
e,
an
o
p
tim
al
in
v
estme
n
t
f
r
am
e
wo
r
k
is
p
r
o
p
o
s
ed
to
o
p
tim
ally
in
v
est
SVC
in
th
e
DS
d
escr
ib
ed
b
y
th
e
MI
NL
P
p
r
o
b
lem
with
o
b
jectiv
e
f
u
n
cti
o
n
an
d
c
o
n
s
tr
ain
ts
as
b
elo
w.
3
.
1
.
O
bje
c
t
iv
e
f
un
ct
io
n
I
n
th
is
s
tu
d
y
,
an
o
b
jectiv
e
f
u
n
ctio
n
m
in
im
izin
g
t
h
e
life
cy
cl
e
co
s
t
o
f
th
e
SVC
s
in
v
estme
n
t
p
r
o
ject
in
DS
d
u
r
in
g
p
lan
n
i
n
g
h
o
r
izo
n
is
p
r
o
p
o
s
ed
as
s
h
o
wn
in
(
3
)
[
3
2
]
,
[
3
4
]
.
W
h
er
e
th
e
life
cy
cle
co
s
t
is
ca
lcu
lated
to
th
e
p
r
esen
t
v
al
u
e
at
th
e
b
ase
y
ea
r
b
y
d
is
co
u
n
t
r
ate
,
.
is
th
e
en
er
g
y
lo
s
s
co
s
t
o
f
DS,
.
is
th
e
in
v
estme
n
t
co
s
t
o
f
SVC
s
,
.
is
th
e
o
p
er
atio
n
an
d
e
n
er
g
y
lo
s
s
co
s
t
in
th
e
SV
C
s
it
s
elf
,
an
d
is
th
e
r
ep
lace
d
an
d
r
esid
u
al
v
al
u
e
o
f
SVC
s
at
th
e
en
d
o
f
th
e
co
m
p
u
t
ed
p
er
io
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l in
ve
s
tmen
t fra
mewo
r
k
o
f sta
tic
va
r
co
mp
en
s
a
to
r
s
in
d
is
tr
ib
u
tio
n
…
(
N
g
u
ye
n
Hien
Tr
u
n
g
)
79
=
[
]
=
∑
1
(
1
+
)
=
1
(
.
+
.
+
.
−
)
(
3
)
T
h
e
en
e
r
g
y
lo
s
s
co
s
t
o
f
DS
i
s
co
m
p
u
te
d
b
y
(
4
)
as
f
o
llo
ws
[
2
4
]
,
[
2
5
]
.
T
h
e
ca
p
ital
co
s
t
p
er
k
VAr
o
f
SVC
d
ep
en
d
s
o
n
th
e
in
v
ested
ca
p
a
city
ca
lcu
lated
as
(
5
)
an
d
is
d
en
o
ted
as
0
.
,
.
So
,
th
e
to
tal
in
v
estme
n
t
co
s
t
f
o
r
SVC
s
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
o
f
th
e
p
r
o
ject
is
p
r
esen
t
in
(
6
)
.
.
=
∑
ℎ
.
∑
∑
(
,
,
ℎ
2
+
,
,
ℎ
2
+
2
,
,
ℎ
,
,
ℎ
(
,
,
ℎ
−
,
,
ℎ
)
)
=
1
,
≠
=
1
ℎ
=
1
∀
∈
(
4
)
0
.
,
=
0
,
0003
.
(
.
,
)
2
+
0
,
3051
.
.
,
+
127
,
38
∈
(
5
)
.
=
∑
,
.
0
.
,
.
.
,
=
1
∈
(
6
)
SVC
d
ev
ices
in
clu
d
e
th
e
ca
p
ac
ito
r
,
th
e
r
ea
cto
r
,
an
d
t
h
e
th
y
r
is
to
r
s
.
So
,
th
er
e
is
en
er
g
y
l
o
s
s
in
th
e
SVC
it
s
elf
.
T
h
e
ca
p
ac
ito
r
lo
s
s
es a
r
e
s
m
all
b
u
t c
o
n
s
tan
t,
wh
er
ea
s
th
e
r
ea
cto
r
an
d
t
h
y
r
is
to
r
l
o
s
s
es d
ep
en
d
o
n
th
e
o
p
er
atin
g
cu
r
r
en
t.
Hen
ce
,
th
e
o
p
er
atio
n
co
s
t
o
f
SVC
ca
n
b
e
co
m
p
u
ted
as
(
7
)
.
T
h
e
l
if
e
tim
e
o
f
SVC
s
is
n
o
r
m
al
ly
d
i
f
f
er
e
n
t
wit
h
p
l
a
n
n
i
n
g
h
o
r
i
z
o
n
s
,
a
n
d
t
h
e
y
a
r
e
n
o
t
c
o
n
c
u
r
r
e
n
t
ly
i
n
v
est
e
d
.
At
t
h
e
e
n
d
o
f
t
h
e
ca
lcu
latio
n
p
e
r
i
o
d
,
th
e
SVC
s
ca
n
c
o
n
ti
n
u
e
to
o
p
er
ate
i
f
t
h
e
ca
lc
u
l
ati
o
n
ti
m
e
is
s
h
o
r
t
e
r
t
h
a
n
th
e
li
f
et
im
e
o
f
t
h
e
S
VC
.
W
h
e
r
ea
s
t
h
e
SVC
s
n
ee
d
t
o
b
e
r
e
p
l
ac
ed
if
t
h
e
ca
l
cu
lat
io
n
tim
e
is
g
r
ea
te
r
t
h
a
n
th
e
li
f
e
tim
e
o
f
t
h
e
SVC
s
.
T
h
er
ef
o
r
e
,
t
h
e
r
e
p
la
ce
m
e
n
t
c
o
s
t
a
n
d
r
esi
d
u
al
v
al
u
e
ar
e
p
r
ese
n
te
d
in
(
8
)
a
n
d
ca
l
cu
lat
e
d
at
t
h
e
b
ase
y
e
ar
i
n
t
h
e
o
b
je
cti
v
e
f
u
n
c
ti
o
n
.
W
h
er
e,
a
n
d
a
r
e
in
s
tallatio
n
t
im
e
a
n
d
l
if
e
tim
e
o
f
SVC
s
[
3
0
]
,
[
3
2
]
.
.
=
∑
∑
0
.
ℎ
.
,
,
ℎ
ℎ
=
1
=
1
∀
∈
(
7
)
=
(
−
)
,
∀
∈
(
8
)
3
.
2
.
Co
ns
t
ra
ints
T
h
e
tech
n
ical
co
n
s
tr
ain
ts
ar
e
u
tili
ze
d
to
g
u
ar
a
n
tee
th
e
o
p
er
ab
ilit
y
o
f
th
e
DSs
an
d
SVC
s
,
wh
ich
in
clu
d
e
alter
n
atin
g
cu
r
r
en
t
p
o
wer
f
lo
w
co
n
s
tr
ain
ts
,
in
v
esti
n
g
an
d
s
izin
g
SVC
co
n
s
tr
ain
ts
,
an
d
lim
itatio
n
s
o
f
b
u
s
v
o
ltag
e
p
r
o
f
ile
a
n
d
tr
a
n
s
m
is
s
io
n
p
o
wer
o
f
f
ee
d
er
s
.
3
.
2
.
1
.
Co
ns
t
ra
ints f
o
r
po
wer
f
lo
w
T
o
r
ed
u
ce
th
e
er
r
o
r
o
f
co
m
p
u
ted
r
esu
lts
,
an
AC
n
o
n
lin
ea
r
p
o
wer
f
lo
w
m
o
d
el
co
n
s
id
er
in
g
to
ch
an
g
e
o
f
lo
ad
in
ea
ch
h
o
u
r
a
n
d
co
m
p
u
tin
g
y
ea
r
is
u
tili
ze
d
an
d
ex
p
r
ess
ed
in
(
9
)
[
2
3
]
,
[
2
4
]
.
T
h
e
e
f
f
ec
ts
o
f
b
o
t
h
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
we
r
o
n
th
e
ca
lcu
latio
n
o
f
p
o
we
r
an
d
v
o
ltag
e
lo
s
s
es
ar
e
co
n
s
id
er
ed
in
th
e
m
o
d
el
lead
in
g
to
im
p
r
o
v
e
d
ec
o
n
o
m
ic
ef
f
ec
t
o
f
th
e
p
r
o
ject
a
n
d
ac
cu
r
ac
y
o
f
o
p
er
atio
n
p
ar
a
m
eter
s
o
f
DSs
.
W
h
er
e
th
e
lo
ad
at
b
u
s
es in
ea
ch
h
o
u
r
h
an
d
co
m
p
u
tin
g
y
ea
r
t is an
aly
ze
d
as
(
1
0
)
f
o
llo
ws.
,
,
ℎ
−
,
,
ℎ
−
0
.
,
,
ℎ
=
∑
|
|
.
|
,
,
ℎ
|
.
|
,
,
ℎ
|
.
(
−
,
,
ℎ
−
,
,
ℎ
)
=
1
,
,
ℎ
−
,
,
ℎ
+
,
,
ℎ
=
−
∑
|
|
.
|
,
,
ℎ
|
.
|
,
,
ℎ
|
.
(
−
,
,
ℎ
−
,
,
ℎ
)
=
1
∀
∈
,
∈
,
ℎ
∈
(
9
)
,
,
ℎ
=
ℎ
.
,
,
=
,
−
1
(
1
+
)
,
,
ℎ
=
ℎ
.
,
,
=
,
−
1
(
1
+
)
(
1
0
)
3
.
2
.
2
.
L
im
it
s
o
f
SVC
ca
pa
cit
y
As
is
k
n
o
wn
,
th
e
p
ar
ticip
atio
n
o
f
SVC
in
DS
ch
an
g
es
th
e
p
o
wer
f
lo
w
an
d
af
f
ec
ts
th
e
tech
n
ical
an
d
ec
o
n
o
m
ic
p
ar
am
eter
s
o
f
s
y
s
te
m
s
.
T
h
er
ef
o
r
e,
t
o
en
s
u
r
e
th
e
e
f
f
ec
t
o
f
th
e
SVC
in
v
estme
n
t,
t
h
e
an
n
u
al
in
s
talled
ca
p
ac
ity
o
f
SVC
m
u
s
t b
e
s
elec
ted
to
o
p
tim
ize
co
s
t a
n
d
g
u
ar
a
n
tee
th
e
o
p
er
atio
n
tech
n
ic
p
ar
am
eter
s
o
f
DS.
T
h
e
b
in
ar
y
v
ar
iab
le
,
p
r
o
p
o
s
ed
in
(
1
1
)
lim
its
th
e
m
ax
im
u
m
an
d
m
in
im
u
m
i
n
v
ested
ca
p
ac
ity
o
f
SVC
f
o
r
ea
c
h
b
u
s
ea
ch
y
ea
r
.
B
esid
es,
th
e
p
l
an
n
in
g
h
o
r
iz
o
n
o
f
t
h
e
DS
is
s
h
o
r
t
-
ter
m
,
an
d
th
u
s
o
n
ly
an
S
VC
is
ch
o
s
en
at
ea
ch
lo
ad
b
u
s
i
n
th
e
o
v
er
all
p
lan
n
i
n
g
h
o
r
izo
n
to
r
e
d
u
ce
t
h
e
ca
p
it
al
co
s
t
as
co
n
s
tr
ain
ed
in
(
1
2
)
with
b
in
ar
y
v
ar
iab
le
,
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
76
-
88
80
.
,
−
∀
∈
,
∈
(
1
1
)
∑
∑
,
=
1
=
1
≤
1
(
1
2
)
SVC
s
ar
e
o
f
ten
m
ad
e
in
to
m
o
d
u
les
an
d
th
eir
r
ated
ca
p
ac
itie
s
ar
e
d
is
cr
ete
v
alu
es.
He
n
ce
,
t
h
e
b
in
a
r
y
v
ar
iab
les
,
,
ar
e
in
teg
r
ated
in
to
th
e
m
o
d
el
to
s
elec
t
o
p
tim
al
r
ated
ca
p
ac
it
y
ac
co
r
d
in
g
to
th
e
s
tan
d
ar
d
v
a
lu
e
o
f
SVC
a
s
p
r
esen
ted
in
(
1
3
)
wh
ich
.
is
th
e
r
ated
ca
p
ac
ity
o
f
m
o
d
u
le
k
.
.
,
=
.
,
−
1
+
,
,
.
.
∑
∑
∑
,
,
=
1
=
1
=
1
≤
1
∀
∈
,
∈
,
∈
(
1
3
)
Mo
r
eo
v
er
,
th
e
m
ax
im
u
m
ca
p
a
city
o
f
SVC
at
ea
ch
o
p
er
atio
n
tim
e
d
ep
en
d
s
o
n
th
e
r
ated
ca
p
ac
ity
an
d
o
p
er
atin
g
v
o
ltag
e
p
r
o
f
ile
at
b
u
s
-
c
o
n
n
ec
t
ed
SVC
.
T
h
e
o
p
er
atin
g
ca
p
ac
ity
o
f
SVC
ca
n
b
e
c
o
n
tr
o
lle
d
to
ch
an
g
e
to
m
ee
t
s
y
s
tem
r
eq
u
ir
em
en
ts
.
So
,
co
n
s
tr
ain
ts
f
o
r
SVC
ca
p
ac
ity
d
ep
en
d
o
n
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile
s
h
o
wn
in
(
1
4
)
with
th
e
r
ated
v
o
ltag
e
o
f
SVC
d
en
o
ted
[
2
4
]
,
[
2
5
]
.
,
,
ℎ
=
,
.
,
,
ℎ
2
,
=
(
.
,
÷
.
,
)
.
,
=
−
.
,
2
.
,
=
.
,
2
∀
∈
,
∈
,
ℎ
∈
(
1
4
)
3
.
2
.
3
.
Co
ns
t
ra
ints o
f
f
ee
der
T
h
e
p
o
wer
-
ca
r
r
y
in
g
ca
p
ab
ilit
y
o
f
f
ee
d
er
s
is
p
r
im
ar
ily
li
m
ited
b
y
t
h
eir
th
er
m
al
r
atin
g
s
,
wh
ich
p
r
ev
en
ts
o
v
er
h
ea
tin
g
an
d
p
o
te
n
tial
eq
u
ip
m
en
t
d
am
a
g
e.
T
h
er
ef
o
r
e,
it
is
ess
en
tial
to
im
p
o
s
e
co
n
s
tr
ain
ts
o
n
th
e
s
elec
tio
n
o
f
SVC
ca
p
ac
ity
to
en
s
u
r
e
s
af
e
s
y
s
tem
o
p
er
atio
n
.
T
h
ese
co
n
s
tr
ain
ts
ar
e
s
h
o
wn
in
(
1
5
)
.
Du
r
in
g
th
e
p
lan
n
in
g
an
d
o
p
er
atio
n
al
p
er
io
d
,
th
e
p
o
wer
f
lo
w
th
r
o
u
g
h
ea
ch
f
ee
d
er
m
u
s
t
r
em
ain
with
in
its
allo
wab
le
tr
an
s
m
is
s
io
n
lim
its
.
T
h
is
h
elp
s
m
ain
tain
s
y
s
tem
r
eliab
ilit
y
,
av
o
id
o
v
er
lo
a
d
in
g
,
an
d
ex
ten
d
th
e
life
s
p
an
o
f
d
is
tr
ib
u
tio
n
s
y
s
tem
.
,
,
ℎ
≤
.
max
∀
∈
,
∈
,
ℎ
∈
(
1
5
)
3
.
2
.
4
.
Co
ns
t
ra
ints o
f
t
ra
ns
f
o
rm
er
s
ub
s
t
a
t
io
n
Du
r
in
g
th
e
p
lan
n
in
g
tim
e,
th
e
DSs
r
ec
eiv
e
th
e
p
o
wer
th
r
o
u
g
h
th
e
u
tili
ty
g
r
id
-
co
n
n
ec
ted
t
r
an
s
f
o
r
m
er
s
u
b
s
tatio
n
.
T
h
e
tr
a
n
s
f
o
r
m
er
h
as
a
m
ax
im
u
m
tr
an
s
m
is
s
io
n
ca
p
ac
ity
th
at
m
u
s
t
n
o
t
b
e
e
x
ce
ed
ed
to
e
n
s
u
r
e
s
af
e
an
d
s
tab
le
o
p
e
r
atio
n
.
T
h
er
e
f
o
r
e,
th
e
tr
an
s
m
is
s
io
n
p
o
wer
t
h
r
o
u
g
h
tr
an
s
f
o
r
m
er
s
m
u
s
t
b
e
g
u
ar
an
teed
with
in
th
e
tr
an
s
m
is
s
io
n
lim
its
o
f
th
e
tr
an
s
f
o
r
m
er
s
s
h
o
wn
in
(
1
6
)
.
,
,
ℎ
≤
.
(
1
6
)
3
.
2
.
5
.
Co
ns
t
ra
ints o
n bus
v
o
lt
a
g
es
Fo
r
th
e
DSs
co
n
n
ec
ted
to
th
e
lar
g
e
g
r
i
d
,
th
e
v
o
ltag
es
at
t
h
e
co
n
n
ec
ted
b
u
s
ar
e
u
s
u
ally
s
ta
b
ilized
an
d
ass
u
m
ed
to
b
e
co
n
s
tan
t
.
Ho
we
v
er
,
a
v
o
ltag
e
lo
s
s
is
g
en
e
r
ate
d
o
n
th
e
f
ee
d
e
r
lead
in
g
to
a
d
r
o
p
in
v
o
ltag
e
at
t
h
e
lo
ad
b
u
s
.
T
h
e
v
o
ltag
e
p
r
o
f
ile
s
at
lo
ad
b
u
s
es
ar
e
c
h
an
g
e
d
a
cc
o
r
d
in
g
to
th
e
f
ee
d
er
p
ar
am
eter
s
an
d
th
e
p
o
wer
f
lo
w.
T
h
u
s
,
t
h
e
lim
its
o
n
lo
a
d
b
u
s
v
o
ltag
es
ar
e
s
h
o
wn
in
(
1
7
)
.
,
ar
e
m
ax
im
u
m
an
d
m
in
im
u
m
lim
it
o
f
lo
ad
b
u
s
v
o
lta
g
es.
≤
|
,
,
ℎ
|
≤
(
1
7
)
3
.
3
.
So
lutio
n
m
et
ho
d
T
h
e
ab
o
v
e
in
v
estme
n
t
f
r
am
ew
o
r
k
to
o
p
tim
ize
SVC
s
in
D
Ss
is
f
o
r
m
u
lated
with
n
o
n
lin
ea
r
c
o
n
s
tr
ain
ts
in
teg
r
ated
in
to
b
in
a
r
y
v
ar
iab
l
es.
Hen
ce
,
th
e
p
r
o
p
o
s
ed
m
o
d
el
is
a
m
ix
ed
i
n
teg
er
n
o
n
lin
ea
r
p
r
o
g
r
am
m
i
n
g
.
T
o
s
o
lv
e
th
e
MI
NL
P
p
r
o
b
lem
s
,
s
ev
er
al
s
o
lv
er
s
h
av
e
b
ee
n
in
t
r
o
d
u
ce
d
in
t
h
e
e
x
is
tin
g
liter
atu
r
e
[
3
9
]
.
I
n
p
ar
ticu
la
r
,
th
e
B
ONM
I
N
s
o
lv
er
is
th
e
m
o
s
t
s
u
itab
le
s
o
lu
tio
n
in
th
e
GA
MS
en
v
ir
o
n
m
e
n
t
to
s
o
lv
e
th
e
MI
NL
P
n
o
n
-
c
o
n
v
e
x
p
r
o
b
lem
s
.
I
t is a
h
ig
h
-
lev
el
m
o
d
elin
g
s
y
s
tem
f
o
r
m
ath
em
atic
al
p
r
o
g
r
am
m
in
g
an
d
o
p
tim
izat
io
n
o
f
t
h
e
DSs
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l in
ve
s
tmen
t fra
mewo
r
k
o
f sta
tic
va
r
co
mp
en
s
a
to
r
s
in
d
is
tr
ib
u
tio
n
…
(
N
g
u
ye
n
Hien
Tr
u
n
g
)
81
B
ONM
I
N
im
p
l
em
e
n
ts
t
h
r
ee
d
i
f
f
er
e
n
t
a
lg
o
r
it
h
m
s
t
o
s
o
lv
e
M
I
N
L
P
p
r
o
b
le
m
s
c
o
n
s
is
t
in
g
o
f
s
im
p
l
e
b
r
a
n
c
h
-
a
n
d
-
b
o
u
n
d
al
g
o
r
it
h
m
s
,
o
u
te
r
-
a
p
p
r
o
x
im
ati
o
n
-
b
ase
d
d
e
co
m
p
o
s
iti
o
n
al
g
o
r
it
h
m
s
,
a
n
d
o
u
te
r
-
a
p
p
r
o
x
i
m
at
io
n
b
as
ed
b
r
an
c
h
-
an
d
-
c
u
t
al
g
o
r
it
h
m
s
[
3
9
]
.
T
h
is
is
n
o
t
an
ex
ac
t
s
o
lv
er
o
n
ly
f
o
r
c
o
n
v
e
x
p
r
o
b
l
em
s
b
u
t
tak
es
in
to
co
n
s
id
er
atio
n
t
h
e
v
al
u
es
o
f
th
e
h
eu
r
is
tic
s
o
lu
tio
n
s
t
o
s
o
lv
e
th
e
p
r
o
b
lem
ef
f
icien
tly
f
o
r
co
n
v
er
g
en
ce
co
m
p
ar
ed
to
th
e
o
th
e
r
s
o
lv
er
s
m
en
tio
n
ed
o
r
m
eta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
.
Mo
r
eo
v
er
,
th
e
MI
NL
P
p
r
o
b
le
m
s
ar
e
s
u
cc
ess
f
u
lly
s
o
lv
ed
with
t
h
e
least
c
o
m
p
u
tat
io
n
al
b
u
r
d
e
n
.
Fo
r
th
e
ab
o
v
e
r
e
aso
n
s
,
th
is
s
tu
d
y
is
d
ir
ec
ted
to
war
d
th
e
u
s
e
o
f
th
e
B
ONM
I
N
s
o
lv
er
to
f
in
d
an
o
p
tim
al
s
o
lu
tio
n
to
th
e
p
r
o
p
o
s
ed
p
r
o
b
lem
.
4.
CALCU
L
A
T
I
O
NS
AND
DI
SCUSS
I
O
NS
4
.
1
.
Ana
ly
s
is
pa
ra
m
e
t
er
s
a
nd
a
s
s
um
ptio
ns
T
h
e
f
ea
s
ib
ilit
y
an
d
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
h
av
e
b
ee
n
in
v
esti
g
ated
o
n
a
m
o
d
if
i
ed
3
3
-
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
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atin
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V,
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r
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g
h
t
r
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s
f
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r
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er
s
,
as
s
h
o
wn
in
Fig
u
r
e
2
[
1
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]
,
[
4
0
]
.
Par
am
ete
r
s
o
f
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ad
s
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d
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ee
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er
s
ch
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g
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atch
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y
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e
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ted
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le
s
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d
2
.
T
h
e
lim
it
ca
p
ac
ity
o
f
t
h
e
tr
an
s
f
o
r
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e
r
is
ass
u
m
ed
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e
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t
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5
MV
A.
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h
e
h
o
u
r
l
y
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ad
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r
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m
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ted
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e
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r
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r
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n
ality
f
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to
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f
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d
e
m
an
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r
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ted
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Fig
u
r
e
3
.
Fig
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r
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2
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Diag
r
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ax
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y
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1
2
3
4
5
6
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9
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12
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15
16
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25
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
76
-
88
82
T
h
e
f
o
llo
win
g
ass
u
m
p
tio
n
s
ar
e
u
tili
ze
d
in
th
is
s
tu
d
y
in
clu
d
i
n
g
:
a.
T
h
e
h
o
u
r
ly
l
o
ad
c
u
r
v
e
o
f
Ds
i
s
s
et
to
b
e
th
e
s
am
e
as
in
Fig
u
r
e
3
.
Similar
ly
,
th
e
elec
tr
ical
p
r
ice
ac
co
r
d
in
g
to
tim
e
o
f
u
s
e
is
ass
u
m
ed
in
Fig
u
r
e
4
.
T
h
e
s
elec
ted
p
la
n
n
i
n
g
h
o
r
izo
n
is
5
y
ea
r
s
with
an
an
n
u
al
g
r
o
wth
f
ac
to
r
o
f
lo
ad
o
f
ab
o
u
t 1
0
% p
e
r
y
ea
r
.
b.
T
h
e
in
v
estme
n
t
co
s
t
o
f
SVC
s
is
co
m
p
u
ted
as
(
5
)
.
T
h
e
a
ctiv
e
p
o
wer
lo
s
s
f
ac
to
r
o
f
t
h
e
SVC
its
e
lf
i
s
d
eter
m
in
ed
at
ab
o
u
t
1
%
[
4
1
]
,
[
4
2
]
with
t
h
e
SVC
life
tim
e
o
f
ab
o
u
t
2
0
y
ea
r
s
[
1
1
]
,
[
4
3
]
.
T
h
e
SVC
ca
n
b
e
s
elec
ted
to
in
s
tall
at
all
lo
ad
b
u
s
es
b
ec
au
s
e
o
f
q
u
ick
in
s
t
allatio
n
an
d
s
m
all
s
p
ac
es
o
f
o
cc
u
p
atio
n
.
T
h
e
p
ar
am
eter
s
o
f
ca
n
d
id
ate
SVC
with
th
e
r
ated
p
o
wer
s
b
ein
g
d
i
s
cr
ete
v
alu
es a
r
e
p
r
esen
ted
i
n
T
ab
le
3
.
c.
T
h
e
v
o
ltag
e
at
lo
ad
b
u
s
es
is
al
lo
wed
to
ch
an
g
e
f
r
o
m
0
.
9
5
to
1
.
0
5
pu
in
o
r
d
er
to
g
u
a
r
an
tee
t
h
e
o
p
er
atio
n
o
f
d
ev
ices.
At
th
e
u
tili
ty
g
r
id
-
c
o
n
n
ec
ted
tr
a
n
s
f
o
r
m
er
s
u
b
s
tatio
n
b
u
s
,
th
e
v
o
ltag
e
u
s
u
ally
i
s
s
tab
ilized
an
d
ass
u
m
ed
to
b
e
1
.
0
5
pu.
Fig
u
r
e
3
.
T
h
e
h
o
u
r
ly
l
o
ad
cu
r
v
e
o
f
DS
Fig
u
r
e
4
.
E
lectr
ical
e
n
er
g
y
p
r
i
ce
s
T
ab
le
3
.
Par
am
eter
s
o
f
ca
n
d
i
d
ate
SVC
Ty
p
e
1
2
3
4
5
6
7
R
a
t
e
d
p
o
w
e
r
(
M
V
A
r
)
1
5
0
3
0
0
4
5
0
6
0
0
7
5
0
9
0
0
1
0
5
0
Ty
p
e
8
9
10
11
12
13
14
R
a
t
e
d
p
o
w
e
r
(
k
V
A
r
)
1
2
0
0
1
3
5
0
1
5
0
0
1
6
5
0
1
8
0
0
2
1
0
0
2
7
0
0
4
.
2
.
Resul
t
s
a
nd
dis
cu
s
s
io
n
s
T
o
ev
alu
ate
th
e
f
ea
s
ib
ilit
y
an
d
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
in
v
estme
n
t
f
r
am
ewo
r
k
,
th
e
te
s
t
DS
ar
e
in
v
esti
g
ated
an
d
co
m
p
ar
ed
i
n
th
e
f
o
llo
win
g
ca
s
es
.
C
ase
1
co
m
p
u
tes
th
e
DS
with
o
n
e
lo
ad
m
o
d
e
a
n
d
u
n
u
tili
ze
d
SVC
wh
ile
SV
C
i
s
s
elec
ted
to
co
m
p
en
s
ate
f
o
r
DS
with
co
n
s
tan
t
lo
ad
m
o
d
e
in
ca
s
e
2
d
u
r
in
g
ca
lcu
latin
g
tim
e
an
d
t
h
e
av
er
a
g
e
p
r
ice.
C
ase
3
d
o
es n
o
t u
tili
ze
SVC
to
co
m
p
en
s
ate
f
o
r
DS
with
an
h
o
u
r
ly
lo
ad
cu
r
v
e.
Fin
ally
,
o
p
tim
al
c
o
m
p
e
n
s
atio
n
b
y
SVC
f
o
r
DS
is
task
ed
in
ca
s
e
4
co
n
s
id
er
in
g
ec
o
n
o
m
ic
e
f
f
ec
tiv
en
ess
b
y
L
C
C
o
b
jectiv
e
f
u
n
ctio
n
,
lo
ad
v
ar
iatio
n
with
h
o
u
r
ly
lo
a
d
cu
r
v
e,
SVC
co
m
p
en
s
atin
g
p
o
wer
ac
co
r
d
in
g
t
o
b
u
s
v
o
ltag
e,
an
d
r
ated
ca
p
ac
ity
wit
h
d
is
cr
ete
v
alu
es a
s
o
p
tim
al
f
r
am
ewo
r
k
p
r
esen
ted
in
s
ec
tio
n
2
.
T
h
e
n
u
m
er
ical
r
esu
lts
with
th
e
ab
o
v
e
DS
d
eter
m
in
e
p
lace
m
en
t,
s
izin
g
,
a
n
d
tim
e
o
f
SVC
in
v
ested
in
ca
s
es a
s
s
h
o
wn
in
T
ab
le
4
.
B
o
th
ca
s
e
2
an
d
ca
s
e
4
s
elec
t th
e
in
s
talled
p
lace
m
en
t o
f
SVC
at
b
u
s
es a
t th
e
f
ee
d
er
en
d
b
ec
au
s
e
o
f
th
e
h
ig
h
er
co
m
p
en
s
atio
n
ef
f
ec
tiv
en
ess
o
f
SVC
co
m
p
ar
is
o
n
with
b
u
s
es a
t th
e
f
ee
d
er
b
eg
in
n
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l in
ve
s
tmen
t fra
mewo
r
k
o
f sta
tic
va
r
co
mp
en
s
a
to
r
s
in
d
is
tr
ib
u
tio
n
…
(
N
g
u
ye
n
Hien
Tr
u
n
g
)
83
SVC
is
s
elec
ted
in
th
e
f
ir
s
t
y
e
ar
to
m
ax
im
ize
its
ef
f
icien
c
y
b
y
r
ed
u
cin
g
p
o
wer
lo
s
s
an
d
i
m
p
r
o
v
i
n
g
o
p
er
ati
n
g
v
o
ltag
e
d
u
r
in
g
p
lan
n
i
n
g
h
o
r
iz
o
n
.
T
h
e
to
tal
in
v
ested
ca
p
ac
ity
o
f
ca
s
e
2
is
ab
o
u
t
3
0
k
VAr
an
d
b
ig
g
er
th
a
n
ca
s
e
4
b
y
1
5
0
k
VAr
,
eq
u
iv
ale
n
t
to
5
%.
B
ec
au
s
e
ca
s
e
2
is
co
m
p
u
ted
with
th
e
co
n
s
tan
t
lo
ad
b
ein
g
p
ea
k
lo
a
d
d
u
r
in
g
p
lan
n
in
g
h
o
r
iz
o
n
,
th
e
SVC
ca
p
ac
ity
s
elec
ted
is
lar
g
e.
Ho
we
v
er
,
th
er
e
is
a
s
ig
n
if
ican
t
er
r
o
r
in
th
is
ca
s
e
d
u
e
to
th
e
lo
ad
v
a
r
iatio
n
in
p
r
ac
tice.
Alth
o
u
g
h
t
h
er
e
ar
e
th
e
ab
o
v
e
d
is
ad
v
an
tag
es,
th
e
c
o
m
p
en
s
ati
o
n
b
y
SVC
in
ca
s
e
2
also
im
p
r
o
v
es
th
e
ef
f
ec
tiv
en
ess
o
f
DS
co
m
p
ar
ed
with
ca
s
e
1
,
with
o
u
t
SVC
,
in
clu
d
in
g
1
4
.
2
%
r
ed
u
ce
d
L
C
C
an
d
1
.
1
% r
ed
u
ce
d
lo
s
s
o
f
to
tal
elec
tr
ical
lo
s
s
o
f
DS a
s
s
h
o
wn
o
n
T
ab
le
5
.
T
ab
le
4
.
I
n
v
ested
ca
p
ac
ity
o
f
SVC
(
MV
Ar
)
B
u
s
I
n
v
e
st
e
d
t
i
me
(
y
e
a
r
)
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
C
a
se
1
C
a
se
2
C
a
se
1
C
a
se
4
13
7
5
0
7
5
0
18
7
5
0
7
5
0
27
7
5
0
7
5
0
33
7
5
0
6
0
0
T
ab
le
5
.
C
o
m
p
a
r
is
o
n
o
f
th
e
ec
o
n
o
m
ic
in
d
icato
r
s
No
C
o
s
t
C
a
se
1
C
a
se
2
C
a
se
3
C
a
se
4
1
LC
C
(
M
$
)
5
.
2
1
4
.
4
7
4
.
7
2
3
.
7
7
2
S
V
C
i
n
v
e
st
me
n
t
c
o
st
(
M
$
)
0
0
.
3
8
0
0
.
3
6
3
El
e
c
t
r
i
c
a
l
e
n
e
r
g
y
l
o
ss (
%)
6
.
8
8
5
.
7
8
5
.
9
7
4
.
6
6
I
n
ca
s
e
4
,
th
e
DS
ef
f
ec
tiv
en
ess
is
s
ig
n
if
ican
tly
im
p
r
o
v
e
d
wh
en
SVC
i
s
u
tili
ze
d
an
d
in
v
ested
p
lace
m
en
t,
s
izin
g
,
an
d
tim
e
o
f
SVC
ar
e
co
m
p
u
ted
ac
co
r
d
in
g
to
th
e
p
r
o
p
o
s
ed
in
v
estme
n
t f
r
am
ewo
r
k
.
T
h
e
to
tal
s
elec
ted
ca
p
ac
ity
o
f
SV
C
is
2
8
5
0
k
VAr
co
m
p
e
n
s
ated
at
b
u
s
1
3
,
1
8
an
d
2
7
ab
o
u
t
7
5
0
VAr
,
an
d
b
u
s
3
3
ab
o
u
t
6
0
0
k
VAr
.
Alth
o
u
g
h
th
e
to
tal
co
m
p
en
s
atio
n
ca
p
ac
ity
is
r
ed
u
ce
d
b
y
1
5
0
VAr
,
eq
u
iv
ale
n
t
to
5
%,
co
m
p
ar
ed
with
ca
s
e
2
,
elec
tr
ical
e
n
er
g
y
lo
s
s
is
r
ed
u
ce
d
b
y
1
.
3
1
%.
T
h
e
elec
tr
ical
en
er
g
y
lo
s
s
is
r
ed
u
ce
d
i
n
th
is
ca
s
e
b
ec
au
s
e
it
co
n
s
id
er
s
lo
a
d
v
a
r
iatio
n
with
th
e
h
o
u
r
l
y
lo
ad
c
u
r
v
e
a
n
d
c
o
m
p
en
s
ated
p
o
wer
d
ep
en
d
in
g
o
n
t
h
e
o
p
er
atio
n
v
o
ltag
e
o
f
SVC
.
Hen
ce
,
th
e
ac
cu
r
ac
y
o
f
n
u
m
er
i
ca
l
r
esu
lts
is
en
h
an
ce
d
an
d
m
o
r
e
s
u
itab
le
f
o
r
th
e
o
p
er
atin
g
p
r
ac
tices
o
f
SVC
.
T
h
e
to
tal
r
ated
ca
p
ac
ity
o
f
th
e
SVC
s
elec
ted
is
ab
o
u
t
3
2
%
o
f
th
e
p
ea
k
r
ea
ctiv
e
p
o
wer
o
f
DS
an
d
SVC
ca
n
b
e
co
n
tr
o
lled
to
c
h
an
g
e
co
m
p
en
s
atio
n
p
o
wer
a
n
d
r
esp
o
n
s
e
to
t
h
e
v
a
r
iatio
n
o
f
l
o
ad
d
u
r
in
g
c
o
m
p
u
te
d
tim
e.
T
h
er
e
f
o
r
e,
th
er
e
is
n
o
o
v
er
co
m
p
en
s
atio
n
,
an
d
th
e
n
u
m
b
er
o
f
SVC
s
in
th
e
s
y
s
tem
is
r
ed
u
ce
d
.
B
esid
es,
th
e
ef
f
ec
tiv
en
ess
o
f
o
p
tim
al
co
m
p
en
s
atio
n
b
y
SVC
in
DS
in
ca
s
e
4
is
also
s
h
o
wn
wh
en
co
m
p
ar
ed
t
o
ca
s
e
3
,
with
o
u
t S
VC
.
L
C
C
o
f
th
e
p
r
o
ject
d
ec
r
e
ases
b
y
ab
o
u
t 0
.
9
5
M$
,
f
r
o
m
4
.
7
2
M$
to
3
.
7
7
M$
,
eq
u
iv
alen
t
to
2
0
.
1
%,
alth
o
u
g
h
th
e
in
v
ested
c
o
s
t
o
f
SVC
in
cr
ea
s
es
ab
o
u
t
0
.
3
6
M$
in
th
e
f
ir
s
t
co
m
p
u
tin
g
y
ea
r
.
Similar
ly
,
th
e
e
n
er
g
y
lo
s
s
o
f
t
h
is
ca
s
e
is
r
ed
u
ce
d
b
y
1
.
3
1
%
o
f
th
e
to
tal
elec
tr
ical
lo
s
s
o
f
DS,
f
r
o
m
5
.
9
7
%
to
4
.
6
6
%.
I
n
an
aly
ze
d
ca
s
es,
th
e
f
ee
d
e
r
s
an
d
tr
an
s
f
o
r
m
er
s
u
b
s
tatio
n
s
ar
e
alwa
y
s
g
u
ar
an
teed
f
o
r
o
p
er
atio
n
d
u
r
in
g
p
lan
n
in
g
h
o
r
izo
n
b
y
c
o
n
s
tr
ain
ts
o
n
th
e
lim
ited
tr
an
s
m
is
s
io
n
p
o
wer
s
.
T
h
e
m
ax
im
u
m
p
o
wer
o
n
f
ee
d
er
s
an
d
tr
an
s
f
o
r
m
er
s
d
u
r
in
g
p
lan
n
in
g
h
o
r
izo
n
s
o
f
ca
s
e
4
p
r
esen
t
ed
in
Fig
u
r
e
s
5
a
n
d
6
s
h
o
ws
th
e
p
o
wer
o
f
all
o
f
th
e
d
ev
ices in
th
e
s
y
s
tem
is
a
l
way
s
lo
wer
th
an
lim
ited
p
o
wer
.
T
h
e
m
ax
im
u
m
p
o
wer
is
o
n
f
ee
d
er
1
.
2
in
th
e
5
th
y
ea
r
o
n
ly
1
5
.
7
7
MV
A,
eq
u
iv
a
len
t
to
7
8
.
9
%
o
f
lim
ited
p
o
w
er
,
an
d
d
ec
r
ea
s
es
1
5
.
6
%
co
m
p
ar
ed
with
ca
s
e
3
.
Similar
ly
,
th
e
m
ax
im
u
m
o
p
er
atio
n
p
o
wer
o
f
th
e
tr
a
n
s
f
o
r
m
e
r
is
1
5
.
7
MV
A
in
th
e
5
th
y
ea
r
,
eq
u
iv
alen
t
to
6
3
%
o
f
th
e
lim
ited
ca
p
ac
ity
o
f
th
e
t
r
an
s
f
o
r
m
er
.
T
h
is
p
o
wer
is
1
3
.
3
9
MV
A
an
d
is
3
.
1
% lar
g
er
t
h
an
th
e
lim
it c
ap
ac
ity
in
ca
s
e
3
an
d
th
u
s
m
u
s
t
u
p
g
r
a
d
e
th
e
tr
an
s
f
o
r
m
er
s
u
b
s
tatio
n
i
n
th
e
4
th
y
ea
r
.
T
h
e
p
o
wer
f
lo
w
in
th
e
f
ee
d
er
s
an
d
tr
an
s
f
o
r
m
er
s
d
ec
r
ea
s
es
d
u
e
t
o
b
ein
g
s
u
p
p
o
r
ted
b
y
in
s
talled
SVC
s
at
lo
ad
b
u
s
es.
As
a
r
esu
lt,
u
p
g
r
ad
es
o
f
f
ee
d
er
s
an
d
t
r
an
s
f
o
r
m
e
r
s
ar
e
d
ef
er
r
ed
,
lea
d
in
g
to
a
d
ec
r
ea
s
e
i
n
th
e
ca
p
ital c
o
s
ts
o
f
DS.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
a
s
p
ec
ts
o
f
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
is
to
r
ed
u
ce
v
o
ltag
e
lo
s
s
an
d
im
p
r
o
v
e
b
u
s
v
o
ltag
e
p
r
o
f
iles
.
T
h
is
is
also
g
u
ar
a
n
teed
b
y
t
h
e
co
n
s
tr
ain
ts
o
f
lim
ited
v
o
ltag
es
o
n
th
e
o
p
tim
al
m
o
d
el.
Ho
wev
er
,
th
e
p
o
wer
f
lo
w
in
th
e
f
ee
d
er
s
d
ec
r
ea
s
es
d
u
e
to
b
ein
g
s
u
p
p
o
r
ted
b
y
SVC
s
a
t
lo
ad
b
u
s
es.
Hen
ce
,
th
e
v
o
ltag
e
lo
s
s
less
e
n
s
,
an
d
v
o
ltag
e
p
r
o
f
iles
at
b
u
s
es
in
th
e
ca
s
e
with
SVC
ar
e
im
p
r
o
v
ed
d
u
r
in
g
p
lan
n
in
g
h
o
r
izo
n
s
h
o
wn
in
Fi
g
u
r
es
7
an
d
8
.
T
h
e
m
in
im
u
m
v
o
ltag
e
is
0
.
9
0
an
d
0
.
9
6
p
u
at
b
u
s
es
1
6
,
1
7
an
d
1
8
in
th
e
5
th
y
ea
r
o
f
ca
s
e
3
an
d
ca
s
e
4
,
r
esp
ec
tiv
ely
.
T
h
e
v
o
lt
ag
e
p
r
o
f
iles
im
p
r
o
v
e
b
y
ab
o
u
t
6
%,
eq
u
iv
ale
n
t
to
0
.
0
6
p
u
.
T
h
e
m
in
im
u
m
v
o
ltag
e
p
r
o
f
ile
at
b
u
s
es 1
4
,
1
5
an
d
3
3
is
im
p
r
o
v
e
d
b
y
ab
o
u
t 5
%,
eq
u
iv
alen
t to
0
.
0
5
p
u
,
wh
ile
th
e
v
o
ltag
e
p
r
o
f
ile
at
b
u
s
es
9
to
1
3
a
n
d
2
7
t
o
3
0
is
e
n
h
an
ce
d
b
y
ab
o
u
t
4
%,
eq
u
iv
a
len
t
to
0
.
0
5
p
u
.
T
h
e
v
o
ltag
e
o
f
b
u
s
es
n
ea
r
t
h
e
u
til
ity
g
r
id
also
im
p
r
o
v
es
b
y
0
t
o
3
%.
Similar
ly
,
th
e
m
a
x
im
u
m
v
o
ltag
e
p
r
o
f
ile
at
m
o
s
t
b
u
s
es
is
im
p
r
o
v
ed
f
r
o
m
1
%
to
4
%,
an
d
it
is
alwa
y
s
lo
wer
th
an
th
e
v
o
lta
g
e
p
r
o
f
ile
lim
ited
to
ab
o
u
t
1
.
0
5
p
u
.
M
o
r
eo
v
e
r
,
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile
d
u
r
in
g
c
o
m
p
u
tin
g
tim
e
in
ca
s
e
2
co
m
p
ar
e
d
with
ca
s
e
1
also
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
76
-
88
84
im
p
r
o
v
e
d
f
r
o
m
1
%
to
5
%.
T
h
e
ab
o
v
e
r
esu
lts
s
h
o
w
th
e
ef
f
ec
tiv
en
ess
o
f
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
b
y
SVC
at
DS in
im
p
r
o
v
in
g
b
u
s
v
o
ltag
e
p
r
o
f
iles
.
Fig
u
r
e
5
.
L
im
ited
an
d
m
ax
im
u
m
p
o
wer
o
f
f
ee
d
er
s
in
ca
s
e
4
Fig
u
r
e
6
.
L
im
ited
an
d
m
ax
im
u
m
p
o
wer
o
f
tr
an
s
f
o
r
m
er
i
n
ca
s
e
4
Fig
u
r
e
7
.
Min
im
u
m
v
o
ltag
e
p
r
o
f
ile
d
u
r
i
n
g
p
la
n
n
in
g
h
o
r
iz
o
n
Fig
u
r
e
8
.
Ma
x
im
u
m
v
o
ltag
e
p
r
o
f
ile
d
u
r
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g
p
lan
n
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g
h
o
r
izo
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
Op
tima
l in
ve
s
tmen
t fra
mewo
r
k
o
f sta
tic
va
r
co
mp
en
s
a
to
r
s
in
d
is
tr
ib
u
tio
n
…
(
N
g
u
ye
n
Hien
Tr
u
n
g
)
85
T
h
e
co
m
p
e
n
s
atio
n
p
o
wer
o
f
S
VC
in
ea
ch
o
p
er
atio
n
s
tate
is
co
n
tr
o
lled
to
c
h
an
g
e
a
n
d
r
esp
o
n
d
to
th
e
v
ar
iatio
n
o
f
lo
ad
o
r
p
ar
am
ete
r
s
o
f
DS.
Fig
u
r
e
s
9
(
a)
to
9
(
c
)
s
h
o
w
th
e
c
o
m
p
en
s
atio
n
p
o
wer
o
f
SVC
d
u
r
in
g
p
lan
n
in
g
h
o
r
iz
o
n
in
c
ase
4
at
b
u
s
es
1
3
,
1
8
,
2
7
an
d
3
3
th
at
a
r
e
th
e
f
ee
d
e
r
en
d
-
b
u
s
es.
T
h
e
c
o
m
p
en
s
atio
n
p
o
wer
is
eq
u
al
to
th
e
r
ated
p
o
wer
o
f
SVC
a
t
p
ea
k
h
o
u
r
s
at
th
e
en
d
y
ea
r
s
o
f
p
lan
n
in
g
h
o
r
izo
n
d
u
e
to
th
e
g
r
o
win
g
lo
ad
,
a
n
d
it
r
ed
u
ce
s
at
d
if
f
er
e
n
t
tim
es
b
ec
au
s
e
o
f
th
e
lo
ad
v
ar
iatio
n
.
At
b
u
s
1
8
,
co
m
p
en
s
atio
n
p
o
wer
eq
u
als
th
e
r
ated
p
o
wer
o
f
a
b
o
u
t
7
5
0
k
VAr
at
th
e
(
8
th
÷12
th
)
an
d
(
1
5
th
÷
2
4
th
)
h
o
u
r
s
o
f
th
e
5
th
y
ea
r
.
I
t
r
e
d
u
ce
s
at
d
if
f
er
en
t
h
o
u
r
s
wh
en
th
e
l
o
ad
is
r
ed
u
ce
d
,
an
d
th
e
m
in
im
u
m
p
o
wer
is
5
0
0
.
5
k
VAr
,
e
q
u
iv
ale
n
t
to
7
3
.
4
%
o
f
th
e
r
ated
p
o
wer
o
f
SVC
,
at
1
st
h
o
u
r
in
th
e
1
st
y
ea
r
.
Similar
ly
,
th
e
co
m
p
en
s
atio
n
p
o
wer
o
f
SVC
a
t
b
u
s
3
3
also
ch
an
g
es
f
r
o
m
th
e
r
ated
p
o
we
r
at
th
e
1
9
th
to
t
h
e
2
0
th
h
o
u
r
i
n
th
e
5
th
y
ea
r
t
o
m
in
im
u
m
p
o
wer
,
wh
ich
eq
u
als
3
0
2
.
2
k
VAr
,
eq
u
iv
alen
t
to
5
0
.
4
%
o
f
th
e
r
ated
p
o
wer
o
f
SV
C
,
at
th
e
2
nd
h
o
u
r
in
th
e
1
st
y
e
ar
.
On
b
u
s
es
1
3
an
d
2
7
,
th
e
r
ated
p
o
wer
o
f
SVC
o
n
ly
is
g
e
n
er
ated
at
t
h
e
1
9
th
an
d
2
0
th
h
o
u
r
s
in
t
h
e
5
th
y
ea
r
th
en
it
ch
a
n
g
es
an
d
d
ec
r
ea
s
es
at
d
if
f
er
en
t
o
p
er
at
io
n
s
tates.
T
h
e
co
m
p
en
s
atio
n
p
o
wer
is
m
in
im
u
m
an
d
eq
u
als
3
6
9
.
4
k
VAr
,
eq
u
iv
alen
t
to
4
9
.
7
%
o
f
th
e
r
at
ed
p
o
wer
o
f
SVC
,
at
th
e
3
rd
h
o
u
r
in
th
e
1
st
y
ea
r
.
T
h
is
is
an
ad
v
an
tag
e
o
f
SVC
b
ec
au
s
e
th
e
co
m
p
e
n
s
atio
n
p
o
wer
s
ca
n
b
e
co
n
tr
o
lled
ac
co
r
d
in
g
to
th
e
v
a
r
iatio
n
o
f
p
ar
am
e
ter
s
o
f
DS
an
d
th
u
s
in
cr
ea
s
e
th
e
co
m
p
e
n
s
atio
n
p
o
wer
at
p
ea
k
lo
a
d
with
o
u
t
o
v
er
co
m
p
en
s
atio
n
at
o
f
f
-
p
ea
k
lo
a
d
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
9
.
C
o
m
p
e
n
s
atio
n
p
o
wer
o
f
SVC
d
u
r
in
g
p
lan
n
in
g
h
o
r
i
zo
n
in
ca
s
e
4
(
a)
b
u
s
1
3
,
(
b
)
b
u
s
1
8
,
(
c)
b
u
s
2
7
,
an
d
(
d
)
b
u
s
3
3
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ts
an
o
p
tim
al
in
v
estme
n
t
f
r
am
ewo
r
k
f
o
r
s
im
u
ltan
eo
u
s
ly
d
eter
m
in
i
n
g
t
h
e
lo
ca
tio
n
an
d
s
izin
g
o
f
SVC
s
in
DSs
,
with
th
e
o
b
jectiv
e
o
f
m
in
i
m
izin
g
th
e
L
C
C
o
f
th
e
in
v
e
s
tm
en
t
p
r
o
ject.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
in
te
g
r
ates
c
r
itical
p
r
ac
tical
f
ac
to
r
s
s
u
ch
as
h
o
u
r
ly
lo
ad
v
ar
iatio
n
,
d
is
cr
ete
SVC
r
ated
ca
p
ac
ities
,
in
v
estme
n
t
tim
in
g
,
an
d
d
ev
ice
life
s
p
an
.
T
h
e
o
p
tim
al
f
r
am
ewo
r
k
is
f
o
r
m
u
lated
as
a
MI
NL
P
p
r
o
b
lem
a
n
d
s
o
lv
e
d
u
s
in
g
t
h
e
B
ONM
I
N
s
o
lv
er
in
GAM
S,
p
r
o
v
id
in
g
a
r
ig
o
r
o
u
s
an
d
ef
f
icie
n
t so
lu
tio
n
m
eth
o
d
.
T
o
ev
alu
ate
t
h
e
p
r
o
p
o
s
ed
f
r
a
m
ewo
r
k
,
s
im
u
latio
n
s
a
r
e
co
n
d
u
cted
o
n
a
m
o
d
if
ie
d
3
3
-
b
u
s
r
ad
ial
DS
with
tim
e
-
of
-
u
s
e
elec
tr
icity
p
r
icin
g
.
R
esu
lts
u
n
eq
u
iv
o
ca
lly
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
a
n
d
ap
p
licab
ilit
y
o
f
m
o
d
el.
T
h
e
o
p
tim
al
SVC
p
l
ac
em
en
t,
s
izin
g
,
an
d
in
v
estm
en
t
tim
in
g
ar
e
d
eter
m
in
ed
at
f
ee
d
er
en
d
-
b
u
s
es,
ac
h
iev
in
g
th
e
lo
west
L
C
C
.
S
p
ec
if
ically
,
th
e
m
o
d
el
y
ield
e
d
to
tal
en
er
g
y
lo
s
s
r
ed
u
ctio
n
s
o
f
ap
p
r
o
x
im
ately
0
.
9
9
%
an
d
1
.
4
8
%
co
m
p
ar
ed
to
ca
s
es
3
an
d
2
,
r
esp
ec
tiv
ely
,
r
ed
u
cin
g
o
v
er
all
s
y
s
tem
lo
s
s
es
f
r
o
m
6
.
0
3
%
to
5
.
0
4
%.
SVC
s
d
y
n
am
ically
a
d
j
u
s
ted
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t,
im
p
r
o
v
i
n
g
v
o
ltag
e
p
r
o
f
iles
f
r
o
m
1
%
to
2
%
ac
r
o
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.