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I
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u
ality
[
1
3
]
.
E
n
er
g
y
s
y
s
t
em
s
ca
n
b
e
d
ev
elo
p
e
d
b
y
in
s
tallin
g
HVDC
tr
an
s
m
is
s
io
n
lin
es
[
1
7
]
–
[
2
0
]
,
wh
ich
r
eso
lv
e
t
h
e
p
r
o
b
lem
s
o
f
l
o
w
im
p
ed
an
ce
a
n
d
u
n
b
alan
ce
d
p
o
wer
f
lo
w
b
e
ca
u
s
e
th
ey
co
n
tr
o
l
p
o
wer
b
ased
o
n
elec
tr
o
n
ic
p
o
wer
d
ev
ices
[
1
3
]
.
A
co
m
b
in
atio
n
o
f
s
er
ies
an
d
p
ar
allel
co
n
tr
o
ller
s
with
lin
e
im
p
ed
an
ce
co
n
tr
o
l
an
d
v
o
ltag
e
r
eg
u
lato
r
m
an
a
g
e
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
wer
in
th
e
s
y
s
tem
[
1
3
]
.
Hig
h
-
v
o
ltag
e
d
ir
ec
t
cu
r
r
en
t
s
y
s
tem
s
ar
e
o
f
p
ar
ticu
lar
im
p
o
r
tan
ce
d
u
e
to
th
e
ac
cu
m
u
latio
n
o
f
e
n
er
g
y
r
eso
u
r
ce
s
in
s
p
ec
if
ic
lo
ca
tio
n
s
,
wid
e
d
is
tr
i
b
u
tio
n
o
f
co
n
s
u
m
p
tio
n
ce
n
te
r
s
,
th
e
n
ee
d
to
co
n
n
ec
t
to
ad
jace
n
t
n
etwo
r
k
s
,
th
e
n
ee
d
f
o
r
tr
an
s
m
is
s
io
n
b
y
u
n
d
er
g
r
o
u
n
d
a
n
d
s
ea
r
o
u
tes
an
d
t
h
e
ec
o
n
o
m
ic
b
en
e
f
its
o
f
h
ig
h
-
p
o
wer
tr
an
s
m
is
s
io
n
o
v
er
lo
n
g
d
is
tan
ce
s
[
1
3
]
,
[
2
1
]
.
T
h
e
d
is
ad
v
an
ta
g
es
o
f
HVDC
lin
es,
o
n
th
e
o
th
er
h
an
d
,
in
c
lu
d
e
h
ig
h
en
er
g
y
co
n
v
er
s
io
n
co
s
ts
an
d
r
ea
ctiv
e
p
o
wer
r
eq
u
ir
em
en
ts
o
f
co
n
v
er
t
er
s
[
1
7
]
.
Flex
ib
le
al
ter
n
atin
g
cu
r
r
en
t
tr
an
s
m
is
s
io
n
s
y
s
tem
co
n
tr
o
ller
s
u
s
ed
in
th
is
p
ap
e
r
in
clu
d
ed
s
tatic
v
ar
c
o
m
p
e
n
s
ato
r
o
r
s
tatic
v
ar
co
m
p
en
s
ato
r
(
SVC
)
an
d
HVDC
lin
k
was
also
u
s
ed
in
th
e
tr
a
n
s
m
is
s
io
n
lin
e.
Hig
h
-
v
o
ltag
e
d
ir
ec
t
c
u
r
r
e
n
t
s
y
s
tem
s
ar
e
co
m
p
r
is
ed
o
f
t
wo
co
n
v
e
r
ter
s
,
o
n
e
ca
p
ab
le
o
f
r
eg
u
latin
g
v
o
ltag
e
an
d
th
e
o
t
h
er
ca
p
a
b
le
o
f
q
u
ic
k
ly
tr
an
s
m
itti
n
g
an
d
co
n
tr
o
llin
g
ac
tiv
e
p
o
wer
[
9
]
.
Pro
v
id
ed
t
h
at
d
ir
ec
t
c
u
r
r
en
t
(
DC
)
co
n
v
er
ter
s
in
h
e
r
en
tly
a
b
s
o
r
b
r
ea
ctiv
e
p
o
we
r
,
a
r
ea
ctiv
e
p
o
wer
s
o
u
r
ce
s
u
ch
as
an
SVC
ca
n
b
e
u
s
ed
n
ea
r
t
h
e
co
n
v
er
ter
[
1
0
]
.
SVC
is
u
s
ed
to
g
en
er
ate
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
in
p
ar
allel
in
th
e
n
etwo
r
k
to
co
n
tr
o
l
th
e
b
u
s
v
o
ltag
e
[
1
3
]
.
Mu
ch
r
ese
ar
ch
h
as
b
ee
n
ca
r
r
ied
o
u
t
o
n
th
e
u
s
e
o
f
FAC
T
S
d
ev
ices
an
d
HVDC
lin
es,
in
cl
u
d
ed
p
r
o
p
o
s
in
g
two
s
u
itab
le
m
u
lti
-
ter
m
in
al
VSC
-
HVDC
m
o
d
els
f
o
r
lo
ad
f
lo
w
s
tu
d
y
u
s
in
g
th
e
New
to
n
-
R
ap
h
s
o
n
al
g
o
r
ith
m
[
2
2
]
,
New
to
n
-
R
ap
h
s
o
n
HVDC
p
o
wer
f
lo
w
m
o
d
elin
g
[
2
3
]
–
[
2
5
]
,
an
d
m
u
lti
-
ter
m
in
al
VSC
-
HVDC
lo
ad
f
lo
w
was
m
o
d
ele
d
u
s
i
n
g
th
e
AC
/DC
lo
ad
f
lo
w
al
g
o
r
ith
m
b
y
MA
T
L
AB
an
d
MA
T
POW
E
R
s
o
f
twar
e
p
r
o
g
r
am
s
[
2
6
]
,
[
2
7
]
.
I
n
Vi
n
k
o
v
ic
a
n
d
Mih
alic
[
2
8
]
,
th
e
g
en
er
al
m
eth
o
d
f
o
r
d
u
al
m
o
d
elin
g
o
f
FAC
T
S
d
ev
ices
an
d
th
eir
s
er
ies
an
d
p
ar
allel
m
o
d
elin
g
wer
e
s
tu
d
ied
.
SVC
h
as
b
ee
n
u
s
ed
to
o
p
tim
ize
th
e
New
to
n
-
R
ap
h
s
o
n
p
o
wer
f
l
o
w
m
o
d
elin
g
[
2
9
]
,
[
3
0
]
.
I
n
[
3
1
]
,
a
co
n
tr
o
l
m
eth
o
d
f
o
r
th
e
c
o
o
r
d
i
n
atio
n
o
f
HVDC
an
d
FAC
T
S
was
p
r
o
p
o
s
ed
with
th
e
aim
o
f
o
b
tain
in
g
s
m
all
s
ig
n
al
s
tab
ilit
y
o
f
th
e
p
o
wer
s
y
s
tem
,
wh
ich
in
d
icate
d
th
at
b
y
ch
an
g
in
g
th
e
p
ar
am
eter
s
,
th
e
o
s
cillatio
n
b
e
twee
n
ad
jace
n
t
ar
ea
s
f
o
r
p
r
o
d
u
ctio
n
was
r
ed
u
ce
d
.
I
n
[
3
2
]
,
a
m
u
ltip
le
o
p
tim
al
p
o
wer
f
lo
w
(
OPF)
s
o
lu
tio
n
m
eth
o
d
was
p
r
esen
ted
with
t
h
e
p
r
esen
ce
o
f
FAC
T
S
d
ev
ic
es,
wh
ich
wer
e
v
e
r
y
p
o
wer
f
u
l
an
d
f
in
e
-
t
u
n
ed
th
e
u
n
eq
u
al
co
n
s
tr
ain
ts
o
f
th
e
s
y
s
tem
.
T
h
e
o
p
tim
al
m
u
lti
-
o
b
je
ctiv
e
p
lace
m
en
t
o
f
FAC
T
S
co
n
tr
o
ller
s
in
clu
d
in
g
SVC
,
t
h
y
r
is
to
r
-
co
n
tr
o
lled
s
er
ies
co
m
p
en
s
atio
n
(
T
C
SC
)
,
an
d
u
n
if
ied
p
o
wer
f
lo
w
co
n
tr
o
ller
(
UPFC
)
f
o
r
p
o
wer
s
y
s
tem
o
p
er
atio
n
al
p
lan
n
i
n
g
h
as
b
ee
n
i
n
v
esti
g
ated
in
[
3
3
]
–
[
3
7
]
.
T
h
e
o
p
tim
a
l
p
o
wer
f
lo
w
o
f
th
e
HVDC
two
-
ter
m
in
al
s
y
s
tem
was
o
b
tain
ed
with
th
e
h
elp
o
f
a
g
en
e
tic
alg
o
r
ith
m
an
d
a
b
ac
k
tr
ac
k
in
g
s
ea
r
ch
alg
o
r
ith
m
in
[
1
7
]
,
[
3
8
]
.
T
h
e
in
te
g
r
atio
n
o
f
an
SVC
in
to
th
e
d
is
tr
ib
u
ti
o
n
g
e
n
er
ato
r
i
n
th
e
n
etwo
r
k
,
le
d
to
an
im
p
r
o
v
em
e
n
t
in
v
o
ltag
e
r
eg
u
latio
n
an
d
a
r
ed
u
ctio
n
in
d
is
tr
ib
u
tio
n
n
etwo
r
k
lo
s
s
es
[
3
9
]
.
F
o
r
o
p
tim
al
r
ea
ctiv
e
p
o
wer
a
n
d
co
o
r
d
in
atio
n
b
etwe
en
FAC
T
S
d
ev
ices
s
u
ch
as
SV
C
an
d
T
C
SC
with
o
th
er
s
o
u
r
ce
s
,
s
im
p
le
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
SP
SO)
,
ev
o
l
u
tio
n
ar
y
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
E
SP
O)
,
an
d
ad
ap
tiv
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
APSO)
alg
o
r
ith
m
s
wer
e
u
s
ed
[
40]
–
[
5
1
]
.
Po
wer
f
lo
w
m
o
d
elin
g
o
f
th
e
AC
-
DC
h
y
b
r
id
HVDC
m
u
lti
-
t
er
m
in
al
s
y
s
tem
was
p
r
esen
ted
in
[
5
2
]
,
[
5
3
]
,
wh
ic
h
ac
h
iev
e
d
a
v
er
y
g
o
o
d
p
o
wer
f
lo
w
an
d
co
n
v
er
g
e
n
ce
s
o
lu
tio
n
.
I
n
[
5
4
]
,
a
n
ew
p
o
wer
f
l
o
w
m
eth
o
d
in
clu
d
in
g
FAC
T
S
an
d
HVDC
d
ev
ices
wa
s
in
v
esti
g
ated
in
wh
ich
th
e
b
ass
eq
u
atio
n
s
in
clu
d
ed
a
P
-
Q
b
u
s
(
in
th
is
b
u
s
th
e
r
ea
l
p
o
wer
(
P)
an
d
r
ea
ctiv
e
p
o
wer
(
Q)
ar
e
s
p
ec
if
ied
)
i
n
th
e
al
ter
n
atin
g
cu
r
r
e
n
t
(
AC
)
s
y
s
tem
to
r
em
o
v
e
co
m
p
o
n
en
ts
f
r
o
m
th
e
AC
s
y
s
te
m
an
d
in
cr
ea
s
e
t
h
e
co
n
v
er
g
en
ce
s
p
ee
d
.
I
n
n
o
n
e
o
f
th
e
p
r
ev
i
o
u
s
wo
r
k
s
th
e
s
im
u
ltan
eo
u
s
u
s
e
o
f
FAC
T
S
d
ev
ices
h
as
b
ee
n
in
v
esti
g
ated
u
s
in
g
c
o
m
p
r
eh
e
n
s
iv
e
m
o
d
elin
g
.
I
n
t
h
is
ar
ticle,
th
e
s
im
u
ltan
eo
u
s
co
m
b
in
atio
n
o
f
two
d
ev
ices
an
d
b
etwe
en
two
b
u
s
es
h
as
b
ee
n
u
s
ed
,
b
u
t
in
p
r
ev
io
u
s
wo
r
k
s
,
eith
er
t
h
ese
d
ev
ic
es
h
av
e
b
ee
n
u
s
ed
in
d
iv
id
u
ally
o
r
n
o
t
s
im
u
ltan
eo
u
s
ly
b
etwe
en
two
b
u
s
es
to
in
v
esti
g
ate
its
ef
f
ec
ts
.
W
e
s
o
u
g
h
t
to
in
v
esti
g
ate
th
e
m
o
d
elin
g
o
f
SVC
an
d
HVDC
d
ev
ices
an
d
to
o
b
tain
co
m
p
r
e
h
en
s
iv
e
m
o
d
e
lin
g
o
f
th
e
s
im
u
l
tan
eo
u
s
ap
p
licatio
n
o
f
all
th
e
two
d
ev
ices
b
y
th
e
New
to
n
-
R
ap
h
s
o
n
p
o
wer
f
lo
w
m
eth
o
d
an
d
d
ete
r
m
in
e
th
e
ef
f
ec
ts
o
f
s
er
ies
an
d
p
ar
allel
co
m
p
en
s
atio
n
s
o
n
th
e
n
etwo
r
k
.
Simu
latio
n
s
wer
e
im
p
lem
en
ted
with
th
e
h
elp
o
f
MA
T
L
AB
s
o
f
twar
e
o
n
a
5
-
b
u
s
test
s
y
s
tem
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
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
694
Mo
d
elin
g
o
f sta
tic
va
r
co
mp
e
n
s
a
to
r
-
h
ig
h
vo
l
ta
g
e
d
ir
ec
t c
u
r
r
en
t to
…
(
A
b
d
o
lma
jid
J
a
va
d
ia
n
)
1661
2
.
1
.
M
o
delin
g
o
f
F
ACTS
dev
ices
T
h
e
g
en
er
al
m
o
d
el
o
f
F
AC
T
S
d
ev
ices
wh
en
u
s
ed
in
s
er
ies
o
n
th
e
n
etwo
r
k
as
Fig
u
r
e
1
is
f
o
r
m
u
lated
in
th
e
m
an
n
er
[
2
8
]
.
=
+
=
(
−
∗
)
(
1
)
=
+
=
(
−
∗
)
(
2
)
=
+
(
3
)
T
h
e
m
o
d
el
o
f
th
e
p
ar
allel
ap
p
licatio
n
o
f
F
AC
T
S d
ev
ices is
as Fig
u
r
e
2
[
2
8
]
.
=
+
=
(
−
∗
)
(
4
)
=
−
(
[
]
+
[
]
)
(
5
)
=
−
(
[
]
−
[
]
)
(
6
)
I
n
th
ese
eq
u
atio
n
s
,
S,
P
,
Q
an
d
I
ar
e
th
e
a
p
p
ar
en
t
p
o
wer
,
ac
ti
v
e
an
d
r
e
ac
tiv
e
p
o
wer
s
,
a
n
d
li
n
e
cu
r
r
en
t,
r
esp
ec
tiv
ely
.
Po
wer
co
n
tr
o
l
b
y
F
AC
T
S d
ev
ices a
cc
o
r
d
in
g
to
th
e
p
o
wer
as
s
h
o
wn
in
(
7
)
[
3
4
]
.
=
(
−
)
=
=
=
>
(
−
)
,
,
=
>
=
=
=
=
>
(
7
)
2
.
2
.
SVC
mo
delin
g
I
n
th
is
p
ap
e
r
,
SVC
is
m
o
d
eled
as
an
id
ea
l
r
ea
cti
v
e
p
o
wer
s
o
u
r
ce
in
jecte
d
in
t
o
b
u
s
A
.
S
tatic
VAR
co
m
p
en
s
ato
r
ca
n
c
o
n
tin
u
o
u
s
ly
g
en
er
ate
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
b
y
o
p
e
r
atin
g
in
in
d
u
ctiv
e
an
d
ca
p
ac
itiv
e
m
o
d
es.
Static
VA
R
co
m
p
en
s
ato
r
m
o
d
el
a
n
d
s
tr
u
ctu
r
e
ar
e
s
p
ec
if
ied
in
Fig
u
r
e
3
[
5
5
]
.
T
h
e
r
o
le
o
f
SVC
is
to
k
ee
p
th
e
v
o
ltag
e
in
th
e
b
u
s
co
n
s
tan
t,
w
h
ich
is
d
o
n
e
b
y
in
jectin
g
p
o
wer
i
n
t
o
th
e
b
u
s
[
3
0
]
.
I
n
m
o
d
elin
g
,
we
co
n
s
id
er
e
d
SVC
as a
p
ar
allel
v
ar
iab
le
s
u
s
ce
p
ta
n
ce
as Fig
u
r
e
3
[
9
]
,
[
3
0
]
,
[
5
5
]
.
=
(
8
)
T
h
e
p
o
wer
ab
s
o
r
b
e
d
o
r
in
jecte
d
in
to
th
e
b
ass
is
as (
9
)
[
3
0
]
[
5
5
]
.
=
=
−
2
(
9
)
Fig
u
r
e
1
.
Mo
d
el
o
f
a
FAC
T
S s
er
ies
b
r
an
ch
[
2
8
]
Fig
u
r
e
2
.
Mo
d
el
o
f
a
FAC
T
S
p
ar
allel
b
r
an
c
h
[
2
8
]
Fig
u
r
e
3
.
Mo
d
el
o
f
p
ar
allel
v
ar
iab
le
s
u
s
ce
p
tan
ce
f
o
r
SVC
2
.
3
.
H
VDC
s
y
s
t
em
m
o
delin
g
A
HVDC
s
y
s
tem
co
n
s
is
t
s
o
f
two
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
t
er
s
co
n
n
ec
ted
to
b
u
s
b
ar
s
A
an
d
B
b
y
tr
an
s
f
o
r
m
er
s
.
T
h
e
e
q
u
iv
alen
t
cir
cu
it
o
f
th
e
HVDC
s
y
s
tem
i
n
clu
d
es
a
co
m
b
in
atio
n
o
f
th
e
v
o
ltag
e
s
o
u
r
ce
an
d
tr
an
s
f
o
r
m
er
im
p
e
d
an
ce
s
er
ies.
Dep
en
d
in
g
o
n
th
eir
ap
p
licatio
n
,
b
o
th
co
n
v
er
ter
s
ar
e
co
n
n
ec
ted
b
ac
k
to
b
a
ck
o
r
b
y
a
DC
ca
b
le
[
2
1
]
,
[
2
4
]
.
T
h
e
HVDC
s
y
s
tem
is
co
n
v
en
ien
tly
m
o
d
eled
with
two
v
o
ltag
e
s
o
u
r
ce
s
alo
n
g
with
an
eq
u
atio
n
t
h
at
s
tates
th
e
ac
tiv
e
p
o
wer
co
n
d
itio
n
.
W
ith
t
h
e
in
tr
o
d
u
ctio
n
o
f
HVDC,
th
e
r
a
n
g
e
o
f
tr
an
s
m
is
s
io
n
p
o
wer
i
n
cr
ea
s
ed
(
f
r
o
m
b
elo
w
1
0
0
0
W
to
3
to
4
GW
)
[
5
6
]
.
Hig
h
-
v
o
ltag
e
alter
n
ativ
e
c
u
r
r
en
t
(
HV
AC
)
d
esig
n
U
T
U
S
U
R
S
RT
S
ST
U
P
U
P
S
PT
B
s
vc
B
U
S
a
I
s
vc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
16
59
–
167
2
1662
an
d
co
n
s
tr
u
ctio
n
a
r
e
n
o
t
ec
o
n
o
m
ical
f
o
r
lo
n
g
d
is
tan
ce
s
,
b
u
t
u
s
in
g
HVDC
im
p
r
o
v
es
th
e
co
s
t
an
d
tr
an
s
m
is
s
io
n
o
f
h
ig
h
v
o
ltag
es
[
5
7
]
.
I
n
th
e
s
y
s
tem
HVDC
an
d
F
AC
T
S
d
ev
ices,
d
u
e
to
less
in
s
u
latio
n
an
d
r
esis
tan
ce
DC
le
s
s
th
an
AC
,
f
ewe
r
lo
s
s
es
[
5
8
]
,
th
e
n
ee
d
f
o
r
two
co
n
d
u
cto
r
s
in
th
e
s
y
s
tem
an
d
as
a
r
esu
lt
o
f
th
e
v
o
lu
m
e
an
d
s
p
ac
e
o
f
th
e
less
to
in
s
tall,
r
e
d
u
ce
o
f
th
e
t
h
ick
n
ess
an
d
cr
o
s
s
-
s
ec
tio
n
o
f
th
e
ca
b
le
in
a
ce
r
tain
p
o
wer
,
u
s
e
o
f
th
e
g
r
o
u
n
d
as
a
r
etu
r
n
wir
e,
it
h
as
lo
wer
co
s
ts
th
an
HV
A
C
,
w
h
ich
in
Fig
u
r
e
4
,
we
s
ee
th
e
d
if
f
er
en
ce
in
co
s
ts
b
ased
o
n
r
e
f
er
en
ce
s
[
5
9
]
,
[
6
0
]
.
Mo
r
e
o
v
er
,
th
e
HVDC
is
ab
l
e
to
im
p
r
o
v
e
s
tab
ilit
y
o
f
in
ter
-
co
n
n
ec
ted
HVAC
b
y
m
o
d
u
latin
g
p
o
wer
i
n
r
esp
o
n
s
e
to
s
m
all/lar
g
e
d
is
tu
r
b
a
n
ce
s
[
6
1
]
.
T
h
e
DC
te
r
m
i
n
als
will
a
lwa
y
s
b
e
m
o
r
e
ex
p
e
n
s
i
v
e
t
h
a
n
AC
t
er
m
i
n
a
ls
s
im
p
l
y
b
e
ca
u
s
e
t
h
e
y
h
a
v
e
t
o
h
a
v
e
t
h
e
c
o
m
p
o
n
e
n
ts
to
t
r
a
n
s
f
o
r
m
DC
v
o
lta
g
e
as
well
as
co
n
v
e
r
t
t
h
e
DC
t
o
A
C
.
B
u
t
t
h
e
DC
v
o
lta
g
e
c
o
n
v
e
r
s
i
o
n
a
n
d
c
ir
cu
it
b
r
e
ak
er
s
h
a
v
e
b
ee
n
d
r
o
p
p
i
n
g
i
n
p
r
ic
e,
t
h
e
b
r
e
ak
-
e
v
en
p
r
i
ce
c
o
n
ti
n
u
es
t
o
d
r
o
p
.
T
h
e
HVDC
m
o
d
el
in
p
o
wer
f
lo
w
s
tu
d
ies
is
as
F
ig
u
r
e
5
[
2
3
]
,
[
2
4
]
,
[
6
2
]
.
T
o
t
a
l
A
C
C
o
s
t
T
o
t
a
l
D
C
C
o
s
t
D
C
L
i
n
e
C
o
s
t
A
C
L
i
n
e
C
o
s
t
A
C
T
e
r
m
i
n
a
l
C
o
s
t
D
C
T
e
r
m
i
n
a
l
C
o
s
t
I
n
v
e
s
tm
e
n
t
C
o
s
ts
D
i
s
tan
c
e
C
r
i
t
i
c
a
l
D
i
s
t
a
n
c
e
Fig
u
r
e
4
.
C
o
m
p
a
r
e
th
e
c
o
s
ts
o
f
HVDC a
n
d
HVAC sy
s
tem
s
[
6
0
]
B
U
S
a
B
U
S
b
I
1
I
2
E
1
E
2
Y
1
Y
2
Ia
Ib
Ea
Eb
Fig
u
r
e
5
.
Mo
d
el
o
f
HVDC f
o
r
p
o
wer
f
lo
w
[
9
]
1
=
1
(
1
+
1
)
(
1
0
)
2
=
2
(
2
+
2
)
(
1
1
)
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
694
Mo
d
elin
g
o
f sta
tic
va
r
co
mp
e
n
s
a
to
r
-
h
ig
h
vo
l
ta
g
e
d
ir
ec
t c
u
r
r
en
t to
…
(
A
b
d
o
lma
jid
J
a
va
d
ia
n
)
1663
[
]
=
[
1
−
1
0
0
0
0
2
−
2
]
.
[
1
2
]
(
1
2
)
=
{
1
1
∗
}
(
1
3
)
=
{
1
1
∗
}
(
1
4
)
Fo
r
b
o
th
HVDC c
o
m
p
o
n
en
ts
c
o
n
n
ec
ted
b
y
a
DC
ca
b
le
[
9
]
,
[
2
3
]
.
{
1
1
∗
+
2
2
∗
+
}
=
0
(
1
5
)
An
d
if
R
d
c
=
0
(
T
h
at
R
d
c
r
esis
to
r
co
n
n
ec
tio
n
lin
e
in
HVDC)
th
en
:
[
9
]
,
[
2
3
]
.
{
1
1
∗
+
2
2
∗
}
=
0
(
1
6
)
2
.
4
.
Co
m
prehens
iv
e
SVC
-
H
VDC
m
o
delin
g
f
o
r
po
wer
f
lo
w
Du
e
to
th
e
lim
itatio
n
s
o
f
tr
an
s
m
is
s
io
n
lin
es
an
d
th
e
ad
v
an
tag
es
o
f
u
s
in
g
F
AC
T
S
d
ev
ices
as
p
ar
allel
an
d
s
er
ies
co
m
p
en
s
ato
r
s
in
t
h
e
n
etwo
r
k
,
also
,
f
o
r
c
o
n
n
ec
t
in
g
th
e
p
o
wer
g
r
id
a
n
d
ta
k
in
g
in
to
ac
co
u
n
t
th
e
ad
v
an
tag
es
o
f
HVDC
lin
es,
estab
lis
h
in
g
HVDC
co
n
n
ec
tio
n
s
as
a
co
m
p
lem
en
t
to
AC
s
y
s
tem
s
is
ess
en
tial.
I
n
th
is
p
ap
er
,
a
co
m
p
r
eh
en
s
iv
e
m
o
d
el
f
o
r
m
o
d
elin
g
SVC
an
d
HVDC
d
ev
ices
was
u
s
ed
as
Fig
u
r
e
6
.
T
h
en
,
th
e
New
to
n
-
R
ap
h
s
o
n
p
o
wer
f
lo
w
o
n
th
e
f
in
al
m
o
d
el
was
ap
p
lied
.
Acc
o
r
d
i
n
g
t
o
th
e
Fig
u
r
e
6
,
an
SVC
is
u
s
ed
as
a
p
ar
allel
co
m
p
en
s
ato
r
an
d
an
H
VDC as a
lin
k
.
B
U
S
a
B
U
S
b
I
1
I
2
E
1
E
2
Y
1
Y
2
Ia
B
s
v
c
I
s
v
c
Ea
Eb
S
V
C
H
V
D
C
Ib
Fig
u
r
e
6
.
Mo
d
el
o
f
SVC
-
T
C
S
C
-
HVDC f
o
r
p
o
wer
f
lo
w
B
y
wr
itin
g
th
e
r
elatio
n
s
o
f
cu
r
r
en
ts
p
ass
in
g
t
h
r
o
u
g
h
b
u
s
es
an
d
lin
es
a
n
d
th
e
r
elatio
n
o
f
p
o
wer
a
n
d
s
ep
ar
atio
n
o
f
t
h
eir
r
ea
l a
n
d
im
ag
in
ar
y
p
ar
ts
,
=
+
=
∗
(
1
7
)
=
(
+
)
(
1
8
)
=
(
+
)
(
1
9
)
=
(
+
)
(
2
0
)
1
=
1
(
1
+
1
)
(
2
1
)
2
=
2
(
2
+
2
)
(
2
2
)
=
+
(
2
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
16
59
–
167
2
1664
0
=
(
2
4
)
1
=
1
+
1
(
2
5
)
2
=
2
+
2
(
2
6
)
3
=
0
+
1
=
1
+
3
(
2
7
)
3
=
+
1
(
2
8
)
wh
er
e:
=
1
2
−
1
1
c
os
(
−
1
)
−
1
1
s
in
(
−
1
)
(
2
9
)
=
−
3
2
−
1
1
s
in
(
−
1
)
+
1
1
c
os
(
−
1
)
(
3
0
)
=
−
2
2
+
2
2
c
os
(
−
2
)
+
2
2
s
in
(
−
2
)
(
3
1
)
=
2
2
+
2
2
s
in
(
−
2
)
−
2
2
c
os
(
−
2
)
(
3
2
)
=
−
2
(
3
3
)
1
=
−
1
1
2
+
1
1
c
os
(
−
1
)
−
1
1
s
in
(
−
1
)
(
3
4
)
1
=
1
1
2
−
1
1
s
in
(
−
1
)
−
1
1
c
os
(
−
1
)
(
3
5
)
2
=
−
2
2
2
+
2
2
c
os
(
−
2
)
−
2
2
s
in
(
−
2
)
(
3
6
)
2
=
2
2
2
−
2
2
s
in
(
−
2
)
−
2
2
c
os
(
−
2
)
(
3
7
)
wh
er
e
V
a
,
V
b
,
V
1
,
V
2
,
ϴ
a
,
ϴ
b
,
δ
1
,
an
d
δ
2
ar
e
th
e
v
o
lta
g
e
an
d
an
g
les
o
f
th
e
b
u
s
a
,
b
,
a
n
d
HVDC
lin
k
,
r
esp
ec
tiv
ely
.
B
1
,
B
2
an
d
B
S
V
C
ar
e
s
u
s
ce
p
tan
ce
f
o
r
th
e
r
ec
tifie
r
,
in
v
er
ter
an
d
SVC
,
r
esp
ec
ti
v
ely
.
G
1
an
d
G
2
ar
e
th
e
s
id
e
co
n
d
u
ctan
ce
o
f
th
e
r
e
ctif
ier
an
d
in
v
er
ter
,
r
esp
ec
tiv
ely
.
P
1
, P
2
,
P
a
, P
b
ar
e
t
h
e
ac
tiv
e
p
o
wer
s
o
f
r
ec
tifie
r
an
d
in
v
er
ter
,
b
u
s
es
a,
an
d
b
,
r
e
s
p
ec
tiv
ely
.
Fin
ally
,
Q
a
,
Q
b
,
Q
S
VC
,
Q
1
,
an
d
Q
2
ar
e
th
e
r
ea
ctiv
e
p
o
wer
s
f
o
r
a,
a
n
d
b
b
u
s
es,
th
e
SVC
r
ea
ctiv
e
p
o
w
er
an
d
th
e
r
ec
tifie
r
an
d
in
v
e
r
te
r
s
id
es o
f
th
e
m
o
d
el,
r
esp
ec
tiv
ely
.
I
n
(
2
9
)
to
(
3
7
)
we
s
ee
th
at
t
h
e
h
y
b
r
id
m
o
d
el
is
ef
f
ec
tiv
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
r
elate
d
to
b
u
s
es
an
d
lin
es.
Fo
r
ex
am
p
le,
in
(
3
0
)
B
3
is
u
s
ed
wh
ich
is
a
co
m
b
in
atio
n
o
f
SVC
an
d
HV
DC
.
T
h
ese
s
h
o
w
a
co
m
p
r
eh
e
n
s
iv
e
h
y
b
r
i
d
m
o
d
el
th
at
ca
n
b
e
g
en
er
alize
d
to
lar
g
er
n
etwo
r
k
s
,
a
n
d
th
is
m
o
d
el
ca
n
also
b
e
u
s
ed
i
n
lo
ad
f
lo
w
an
d
s
tab
ilit
y
an
aly
s
is
,
etc.
T
o
s
o
lv
e
th
e
New
to
n
-
R
ap
h
s
o
n
p
o
wer
f
lo
w
(
3
8
)
-
(
4
4
)
.
T
h
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
is
s
cien
tific
ally
ef
f
icien
t
d
u
e
to
q
u
ad
r
ati
c
co
n
v
er
g
en
ce
an
d
h
ig
h
co
n
v
er
g
en
ce
v
elo
city
,
wh
ich
is
o
b
tain
ed
b
y
ex
te
n
d
in
g
th
e
T
ay
lo
r
s
er
ies
[
6
3
]
–
[
6
7
]
.
[
(
)
]
=
[
]
.
[
]
(
3
8
)
T
h
e
m
atr
ix
[
J
]
is
t
h
e
J
ac
o
b
in
m
atr
ix
o
b
tain
ed
b
y
th
e
p
ar
tia
l
d
er
iv
ativ
es
o
f
ea
ch
f
u
n
ctio
n
a
s
s
h
o
wn
in
(
2
9
)
-
(
3
7
)
r
elativ
e
to
t
h
e
v
ar
iab
les:
=
[
∆
∆
∆
∆
1
∆
1
1
∆
2
]
,
(
)
=
[
∆
∆
∆
∆
1
∆
1
∆
]
,
=
[
[
1
]
[
2
]
[
3
]
[
4
]
]
(
3
9
)
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
694
Mo
d
elin
g
o
f sta
tic
va
r
co
mp
e
n
s
a
to
r
-
h
ig
h
vo
l
ta
g
e
d
ir
ec
t c
u
r
r
en
t to
…
(
A
b
d
o
lma
jid
J
a
va
d
ia
n
)
1665
1
=
[
0
0
0
]
(
4
0
)
2
=
[
1
1
1
0
1
0
1
1
0
0
0
]
(
4
1
)
3
=
[
1
1
0
1
1
0
0
]
(
4
2
)
4
=
[
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
]
(
4
3
)
W
h
er
e
in
th
e
ab
o
v
e
r
elatio
n
s
,
1
,
2
,
3
,
4
ar
e
th
e
J
ac
o
b
in
m
atr
ix
an
d
its
co
m
p
o
n
e
n
ts
an
d
f
(
x
)
ar
e
th
e
f
u
n
ctio
n
o
f
s
tate
v
ar
iab
les
an
d
x
a
r
e
s
tate
v
ar
iab
les in
lo
a
d
f
lo
w
eq
u
atio
n
s
an
d
we
h
av
e:
=
1
−
2
(
4
4
)
Sin
ce
th
e
ac
tiv
e
p
o
wer
is
s
et
a
t
th
e
en
d
o
f
t
h
e
r
ec
tifie
r
in
th
e
HVDC
lin
e
an
d
th
e
v
o
ltag
e
r
a
n
g
e
at
b
u
s
b
is
k
ep
t c
o
n
s
tan
t,
t
h
e
eq
u
atio
n
s
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
we
r
o
f
th
e
in
v
er
ter
ar
e
ad
d
itio
n
al
[
9
]
.
3.
R
E
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
W
e
ap
p
lied
th
e
m
o
d
el
o
b
tain
e
d
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
o
n
a
5
-
b
u
s
test
s
y
s
tem
ac
co
r
d
in
g
to
Fig
u
r
e
7
,
wh
er
e
all
th
e
in
f
o
r
m
atio
n
ab
o
u
t
th
e
b
u
s
es
an
d
lin
es
a
n
d
t
h
e
wh
o
le
n
etwo
r
k
was
e
x
tr
ac
ted
f
r
o
m
r
ef
er
e
n
ce
[
3
8
]
.
T
h
e
in
f
o
r
m
atio
n
r
e
q
u
ir
ed
f
o
r
t
h
e
test
s
y
s
tem
is
p
r
o
v
id
ed
in
Ap
p
en
d
ix
.
First,
p
o
wer
f
l
o
w
was
with
o
u
t
ad
d
i
n
g
F
AC
T
S
d
ev
ices,
an
d
th
en
i
n
t
h
is
n
etwo
r
k
,
we
ad
d
e
d
th
e
SV
C
an
d
HVDC
d
ev
ices
in
d
iv
id
u
ally
to
th
e
n
etwo
r
k
an
d
o
b
s
er
v
ed
th
e
r
esu
lts
.
Fin
ally
,
b
ased
o
n
th
e
SVC
-
HVDC
m
o
d
el
o
b
tain
ed
i
n
th
e
p
r
e
v
io
u
s
s
ec
tio
n
o
f
th
is
p
ap
er
,
all
th
e
b
o
th
d
e
v
ices
wer
e
ad
d
ed
to
th
e
s
y
s
tem
an
d
th
e
r
esu
lts
wer
e
r
ec
o
r
d
e
d
.
I
n
th
is
p
ap
er
,
th
e
f
o
c
u
s
was
o
n
lo
ad
f
lo
w
in
b
u
s
es
o
n
wh
ich
th
e
d
ev
ices
h
av
e
a
d
ir
e
ct
ef
f
ec
t,
s
u
ch
as
b
u
s
es
3
an
d
4
(
L
ak
e
an
d
Ma
in
)
,
alth
o
u
g
h
th
ey
af
f
ec
t th
e
wh
o
le
n
etwo
r
k
.
Fig
u
r
e
7
.
Sy
s
tem
test
5
b
u
s
es with
SVC
-
HVD
C
L
a
k
e
N
o
r
t
h
S
o
u
t
h
E
l
m
Ma
i
n
D
D
D
D
S
V
C
R
E
C
IN
V
HV
D
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
16
59
–
167
2
1666
I
n
Fig
u
r
e
8
,
wh
ich
s
h
o
ws v
o
lt
ag
e
ch
an
g
es in
th
e
p
r
esen
ce
o
f
v
ar
io
u
s
FAC
T
S d
ev
ices,
th
e
v
o
ltag
e
s
tate
f
o
r
s
tab
ilizatio
n
at
1
p
.
u
.
is
p
r
esen
t
ed
.
Usi
n
g
SVC
,
was b
etter
th
an
th
e
m
o
d
e
with
o
u
t FAC
T
S d
ev
ices a
n
d
th
e
m
o
d
e
o
f
u
s
in
g
HVDC,
an
d
i
n
b
u
s
es 3
an
d
4
,
it wa
s
1
p
.
u
.
clo
s
er
.
B
u
t th
e
b
est s
tate
an
d
v
o
lt
ag
e
s
tab
ilizatio
n
o
cc
u
r
r
e
d
in
th
e
ca
s
e
th
at
t
h
e
SVC
-
HVD
C
co
m
b
in
atio
n
was
u
s
ed
.
Als
o
,
co
m
p
a
r
ed
to
t
h
e
d
i
f
f
er
en
t r
e
f
er
en
ce
s
in
Fig
u
r
e
9
,
th
e
SVC
-
HVDC
m
o
d
el
h
as
th
e
b
est s
tate
o
f
r
ec
o
v
er
y
a
n
d
v
o
ltag
e
s
tab
ilizatio
n
.
T
h
e
b
est s
tate
f
o
r
v
o
ltag
e
im
p
r
o
v
em
e
n
t w
as th
e
m
o
d
e
o
f
u
s
in
g
SVC
in
r
ef
er
e
n
ce
[
9
]
.
Fig
u
r
e
8
.
V
o
ltag
e
o
f
m
o
d
els
Fig
u
r
e
9
.
V
o
ltag
e
in
d
if
f
er
en
t
m
o
d
el
o
f
r
ef
er
e
n
ce
s
I
n
all
d
iag
r
am
s
an
d
f
ig
u
r
es,
P
G1
,
PG2
,
P3
-
4
an
d
P4
-
3
ar
e
t
h
e
ac
tiv
e
p
o
wer
s
p
r
o
d
u
ce
d
b
y
th
e
No
r
th
an
d
So
u
th
g
e
n
er
ato
r
s
,
an
d
th
e
ac
tiv
e
p
o
wer
s
ar
e
b
etwe
en
b
u
s
es
3
an
d
4
,
r
esp
ec
tiv
ely
.
I
n
ad
d
itio
n
,
QG1
,
QG2
,
Q3
-
4
an
d
Q4
-
3
ar
e
th
e
r
ea
ctiv
e
p
o
wer
s
g
en
er
ated
b
y
th
e
No
r
th
an
d
So
u
th
g
en
e
r
ato
r
s
,
an
d
th
e
r
ea
ctiv
e
p
o
wer
s
ar
e
b
etwe
en
b
u
s
es
3
an
d
4
,
r
esp
ec
tiv
ely
.
B
y
a
p
p
ly
in
g
New
to
n
-
R
ap
h
s
o
n
lo
ad
f
lo
w
in
th
e
f
in
al
m
o
d
el
an
d
d
if
f
er
en
t
m
o
d
els
in
Fig
u
r
e
1
0
an
d
Fig
u
r
e
1
1
(
b
y
k
ee
p
in
g
th
e
o
u
tp
u
t
o
f
th
e
So
u
th
g
e
n
er
ato
r
co
n
s
tan
t
at
4
0
MW),
an
in
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
b
etwe
en
th
e
b
u
s
es
u
s
ed
b
y
th
e
d
ev
ices
is
n
o
ted
,
w
h
ich
is
th
e
b
est
way
to
u
s
e
SV
C
-
HVD
C
.
I
t
is
th
e
m
o
s
t
ef
f
icien
t
m
o
d
el
in
co
m
p
en
s
atin
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
I
n
th
e
f
in
al
h
y
b
r
id
m
o
d
el,
t
h
e
g
e
n
er
a
to
r
s
ar
e
f
o
r
ce
d
to
p
r
o
d
u
ce
m
o
r
e
p
o
wer
,
wh
ich
is
m
o
r
e
c
o
s
tly
f
o
r
th
e
s
y
s
tem
an
d
is
am
o
n
g
th
e
d
is
ad
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Po
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f
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tu
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ies
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at
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to
lar
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m
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u
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ed
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s
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is
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s
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io
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s
tu
d
ies
an
d
o
th
er
p
o
wer
s
y
s
tem
s
tu
d
ies.
Fu
tu
r
e
s
tu
d
ies
ar
e
n
ee
d
ed
to
ex
am
in
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th
e
o
p
tim
al
lo
ad
f
lo
w
o
f
th
is
m
o
d
el
an
d
o
p
tim
al
p
lace
m
en
t o
f
th
es
e
d
ev
ices in
th
e
n
etwo
r
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.