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I
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en
cie
s
i
n
t
h
e
a
lter
n
ati
n
g
cu
r
r
en
t
(
A
C
)
p
o
w
er
n
et
wo
r
k
h
a
v
e
ca
u
s
ed
t
h
e
tr
ip
p
in
g
o
f
p
o
w
er
lin
es,
is
o
latio
n
o
f
g
en
er
ati
n
g
s
tatio
n
s
an
d
r
ec
o
n
f
i
g
u
r
atio
n
o
f
t
h
e
en
tire
n
et
w
o
r
k
,
lead
in
g
t
o
in
s
tab
ilit
y
i
n
t
h
e
n
et
w
o
r
k
[
4
]
.
T
h
ese
co
n
ti
n
g
e
n
c
ies r
ed
u
ce
t
h
e
n
et
w
o
r
k
s
tr
e
n
g
t
h
an
d
h
av
e
ca
u
s
ed
ad
v
er
s
e
i
n
t
er
ac
tio
n
s
o
f
HVD
C
s
y
s
te
m
s
o
n
a
co
n
n
e
cted
g
r
id
[
5
]
,
[
6
]
.
T
o
elim
i
n
ate
t
h
ese
e
f
f
ec
ts
,
g
u
id
elin
e
s
an
d
m
e
th
o
d
s
f
o
r
v
o
ltag
e
s
tab
ilit
y
ass
es
s
m
en
t
o
f
an
HVD
C
-
co
n
n
ec
te
d
AC
n
et
w
o
r
k
ar
e
in
tr
o
d
u
ce
d
.
Po
w
er
s
y
s
te
m
s
ar
e
d
esig
n
ed
to
tr
an
s
m
i
t
elec
tr
icit
y
ef
f
icie
n
tl
y
,
b
u
t
m
a
n
y
tr
a
n
s
m
i
s
s
io
n
n
et
w
o
r
k
s
s
u
f
f
e
r
f
r
o
m
p
o
o
r
in
f
r
astru
c
tu
r
e,
lead
in
g
to
s
ig
n
i
f
ica
n
t
ch
alle
n
g
e
s
f
o
r
en
g
i
n
ee
r
s
,
cu
s
t
o
m
er
s
,
an
d
u
tili
t
y
co
m
p
a
n
ies.
T
h
e
p
o
w
er
s
y
s
te
m
n
et
w
o
r
k
t
y
p
ica
ll
y
co
n
s
i
s
ts
o
f
g
en
er
atio
n
,
tr
an
s
m
i
s
s
io
n
a
n
d
d
is
tr
ib
u
tio
n
s
ec
t
io
n
s
.
An
in
ter
co
n
n
ec
ted
tr
an
s
m
i
s
s
io
n
n
et
wo
r
k
is
ess
en
tial
f
o
r
d
eliv
er
in
g
elec
tr
icit
y
o
v
er
l
o
n
g
d
is
tan
ce
s
to
m
ee
t
en
er
g
y
d
e
m
a
n
d
[
7
]
,
[
8
]
.
Ho
w
e
v
er
,
tr
ad
itio
n
al
AC
tr
an
s
m
is
s
io
n
n
e
t
w
o
r
k
s
f
ac
e
s
ev
er
al
li
m
itatio
n
s
w
h
e
n
tr
an
s
m
itt
in
g
h
u
g
e
a
m
o
u
n
ts
o
f
p
o
w
er
o
v
er
a
lo
n
g
d
is
tan
ce
;
it
ca
u
s
es
v
o
ltag
e
d
r
o
p
an
d
p
o
w
er
lo
s
s
alo
n
g
th
e
lin
es.
T
o
ad
d
r
ess
th
ese
is
s
u
e
s
,
d
y
n
a
m
ic
s
tab
ilit
y
a
s
s
es
s
m
en
t
s
ar
e
cr
u
cial,
esp
ec
iall
y
as
th
e
p
r
o
b
lem
h
a
s
lef
t
m
an
y
e
n
er
g
y
co
n
s
u
m
er
s
w
it
h
o
u
t
g
r
id
co
n
n
ec
tio
n
[
9
]
.
Vo
ltag
e
s
tab
ilit
y
r
e
f
er
s
to
th
e
ab
ili
t
y
o
f
a
p
o
w
er
s
y
s
tem
v
o
ltag
e
p
r
o
f
ile
to
r
et
u
r
n
to
th
e
o
p
er
atin
g
l
i
m
it
af
ter
a
f
au
l
t
o
cc
u
r
s
.
T
h
e
s
tab
ilit
y
h
er
e
is
i
n
r
ef
er
en
ce
to
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile,
w
h
ic
h
m
u
s
t
o
p
er
ate
w
it
h
i
n
±5%
(
f
r
o
m
0
.
9
5
p
.
u
.
to
1
.
0
5
p
.
u
.
)
.
2.
RE
VI
E
W
O
F
RE
L
A
T
E
D
L
I
T
E
R
AT
U
RE
T
h
er
e
h
as
b
ee
n
a
lo
t
o
f
in
te
r
ests
in
e
n
h
an
ci
n
g
tr
an
s
m
i
s
s
i
o
n
s
y
s
te
m
f
o
r
s
u
s
tai
n
ab
le
an
d
r
eliab
le
elec
tr
icit
y
s
u
p
p
l
y
.
T
h
er
ef
o
r
e,
d
if
f
er
e
n
t
m
et
h
o
d
s
h
av
e
b
ee
n
s
u
g
g
e
s
ted
b
y
r
esear
ch
er
s
to
e
n
h
a
n
ce
t
h
e
v
o
lta
g
e
p
r
o
f
ile
o
f
a
m
u
lti
g
e
n
er
ato
r
p
o
w
er
s
y
s
te
m
l
ik
e
t
h
e
Nig
er
ia
4
0
b
u
s
3
3
0
k
V
tr
an
s
m
i
s
s
io
n
n
et
w
o
r
k
b
u
t
o
n
l
y
a
f
e
w
h
a
v
e
ap
p
lied
an
au
to
m
a
tic
tu
n
in
g
tec
h
n
iq
u
e
in
t
h
is
ap
p
r
o
ac
h
.
A
n
ek
e
a
n
d
An
za
k
u
[
1
0
]
ap
p
lied
th
e
m
o
d
al/e
ig
e
n
v
alu
e
a
n
al
y
s
i
s
tec
h
n
iq
u
e
to
i
m
p
r
o
v
e
t
h
e
v
o
ltag
e
s
tab
ilit
y
o
f
t
h
e
3
3
0
k
V,
4
8
-
b
u
s
p
o
w
er
s
y
s
te
m
n
et
w
o
r
k
in
Ni
g
er
ia.
T
h
ey
s
i
m
u
lated
th
e
n
e
t
w
o
r
k
u
n
d
er
b
o
th
s
tatic
an
d
d
y
n
a
m
ic
lo
ad
s
,
c
o
n
d
u
ctin
g
m
o
d
al/e
ig
e
n
v
alu
e
a
n
al
y
s
i
s
u
n
d
er
v
ar
y
in
g
lo
ad
co
n
d
itio
n
s
.
T
h
e
r
esu
lts
s
h
o
w
ed
th
at
i
n
cr
e
ased
lo
ad
s
at
th
r
ee
id
en
ti
f
ied
v
u
l
n
er
ab
le
b
u
s
es
led
to
r
ed
u
ce
d
s
y
s
te
m
s
tab
ilit
y
.
T
h
e
s
tu
d
y
d
e
m
o
n
s
tr
ated
th
at
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
ato
r
s
co
u
ld
s
i
g
n
i
f
ica
n
tl
y
i
m
p
r
o
v
e
th
e
v
o
lta
g
e
p
r
o
f
ile
o
f
a
n
et
w
o
r
k
.
Ho
w
e
v
er
,
th
e
au
t
h
o
r
s
d
id
n
o
t
co
n
s
id
er
th
e
n
ee
d
f
o
r
a
r
eg
u
l
ated
HVDC
s
y
s
te
m
o
r
t
h
e
u
s
e
o
f
a
n
i
n
telli
g
e
n
t
ap
p
r
o
ac
h
,
s
u
ch
as
p
r
o
p
o
r
tio
n
al
in
te
g
r
al
co
n
tr
o
ller
f
o
r
en
h
an
ci
n
g
v
o
lta
g
e
s
tab
ilit
y
.
F
u
r
th
er
m
o
r
e,
Van
C
u
s
te
m
[
1
1
]
h
i
g
h
l
ig
h
ted
t
w
o
i
m
p
o
r
tan
t
asp
ec
ts
o
f
v
o
ltag
e
i
n
s
tab
ilit
y
w
it
h
i
n
p
o
w
er
s
y
s
te
m
s
,
t
h
eir
w
o
r
k
d
e
m
o
n
s
tr
ated
th
at
v
o
lta
g
e
s
tab
ilit
y
ca
n
b
e
s
ig
n
i
f
ica
n
tl
y
co
m
p
r
o
m
is
ed
b
y
th
e
tr
ip
p
in
g
o
f
k
e
y
g
en
er
at
io
n
o
r
tr
an
s
m
is
s
io
n
eq
u
ip
m
e
n
t,
w
h
ic
h
d
is
r
u
p
ts
t
h
e
b
alan
ce
o
f
p
o
w
er
s
u
p
p
l
y
a
n
d
d
em
a
n
d
.
A
lo
w
v
o
lta
g
e
p
r
o
f
il
e
w
it
h
i
n
an
y
p
o
w
er
s
y
s
te
m
is
a
p
r
im
ar
y
p
r
ec
u
r
s
o
r
to
s
u
ch
b
lack
o
u
ts
,
t
y
p
ica
ll
y
ca
u
s
ed
b
y
v
o
lta
g
e
co
llap
s
e
as
s
t
ated
in
[
1
2
]
,
[
1
3
]
.
W
h
en
a
tr
an
s
m
i
s
s
io
n
li
n
e
tr
ip
s
,
th
e
r
e
m
ai
n
in
g
lin
e
s
m
u
s
t
ca
r
r
y
t
h
e
ad
d
itio
n
al
lo
ad
,
w
h
ich
i
n
cr
ea
s
es
th
e
co
n
s
u
m
p
tio
n
o
f
r
ea
ctiv
e
p
o
w
er
.
T
h
is
h
eig
h
te
n
ed
d
e
m
a
n
d
f
o
r
r
ea
ctiv
e
p
o
w
er
lead
s
to
a
f
u
r
t
h
er
d
ec
lin
e
i
n
v
o
lta
g
e
lev
el
s
,
ex
ac
er
b
atin
g
t
h
e
r
is
k
o
f
a
co
m
p
lete
v
o
ltag
e
co
llap
s
e
[
1
4
]
.
Sev
er
al
f
ac
to
r
s
co
n
tr
ib
u
te
to
th
e
lik
elih
o
o
d
o
f
a
b
lack
o
u
t,
in
clu
d
i
n
g
w
ea
k
g
r
id
s
,
ad
v
er
s
e
cli
m
atic
co
n
d
itio
n
s
,
s
u
d
d
en
ch
a
n
g
es
i
n
lo
a
d
,
s
y
s
te
m
s
t
h
at
ar
e
h
ea
v
il
y
l
o
ad
ed
b
ey
o
n
d
t
h
eir
ca
p
ac
it
y
,
an
d
h
u
m
a
n
er
r
o
r
s
[
1
5
]
–
[
1
7
]
.
E
ac
h
o
f
th
ese
ele
m
en
ts
ca
n
i
n
itiate
a
ca
s
ca
d
e
o
f
f
ailu
r
es,
u
lti
m
atel
y
lead
in
g
to
a
ca
tast
r
o
p
h
ic
lo
s
s
o
f
p
o
w
er
ac
r
o
s
s
th
e
n
et
w
o
r
k
.
T
h
ese
f
ail
u
r
es
r
ein
f
o
r
ce
d
th
e
n
ee
d
f
o
r
th
e
i
m
p
l
e
m
en
ta
tio
n
o
f
a
HVDC
s
y
s
te
m
f
o
r
v
o
lta
g
e
s
tab
ilit
y
en
h
a
n
ce
m
en
t
in
a
m
u
lt
i
-
g
e
n
er
ato
r
p
o
w
er
n
et
w
o
r
k
li
k
e
t
h
e
N
ig
er
ia
3
3
0
k
V
4
0
b
u
s
tr
an
s
m
i
s
s
io
n
n
et
w
o
r
k
s
.
T
h
e
HVDC
tr
an
s
m
is
s
io
n
s
y
s
te
m
h
as
b
ee
n
ex
te
n
s
i
v
el
y
s
tu
d
ied
f
o
r
its
ca
p
a
b
ilit
y
to
tr
an
s
m
i
t
lar
g
e
q
u
an
titi
es
o
f
elec
tr
icit
y
o
v
er
lo
n
g
d
is
ta
n
ce
s
w
h
ile
m
in
i
m
iz
in
g
p
o
w
er
lo
s
s
es.
A
k
e
y
s
tu
d
y
[
1
8
]
ex
p
lo
r
es
th
e
ef
f
ec
ti
v
e
n
es
s
o
f
HVDC
s
y
s
te
m
s
i
n
r
ed
u
ci
n
g
tr
an
s
m
is
s
io
n
lo
s
s
es,
h
i
g
h
lig
h
ti
n
g
t
h
eir
ad
v
a
n
ta
g
es
o
v
er
tr
ad
itio
n
al
AC
tr
an
s
m
is
s
io
n
s
y
s
te
m
s
,
p
ar
ticu
lar
l
y
i
n
lo
n
g
-
d
i
s
tan
ce
ap
p
l
icatio
n
s
.
An
o
th
er
s
t
u
d
y
[
1
9
]
g
o
es
f
u
r
t
h
er
b
y
ca
lcu
lati
n
g
an
d
s
i
m
u
lati
n
g
p
o
w
er
lo
s
s
e
s
in
H
VDC
tr
a
n
s
m
i
s
s
io
n
li
n
e
s
u
s
in
g
t
w
o
d
is
ti
n
ct
m
o
d
els,
p
r
o
v
id
in
g
v
alu
ab
le
in
s
i
g
h
t
s
i
n
to
t
h
e
e
f
f
ic
ien
c
y
o
f
HV
D
C
s
y
s
te
m
s
u
n
d
e
r
d
if
f
er
e
n
t
o
p
er
atin
g
co
n
d
it
io
n
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Si
m
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[
2
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in
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w
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b
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p
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a
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m
.
A
d
d
itio
n
all
y
,
a
n
o
th
er
s
t
u
d
y
[
2
1
]
d
em
o
n
s
tr
ated
th
e
p
o
s
itiv
e
i
m
p
ac
t
o
f
in
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atin
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li
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k
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ip
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m
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ar
ticu
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ter
m
s
o
f
en
h
a
n
cin
g
t
h
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v
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ltag
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p
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ile.
T
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s
t
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y
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ls
o
co
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s
id
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v
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N:
2088
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8708
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n
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co
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itio
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s
.
F
u
r
th
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r
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ch
[
2
2
]
p
r
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ted
a
m
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th
o
d
in
v
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ev
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io
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Si
m
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a
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d
y
[
2
3
]
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im
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lated
th
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i
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teg
r
atio
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HVD
C
n
et
w
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a
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in
[
2
4
]
,
d
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o
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tr
at
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ig
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i
f
ica
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tec
h
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p
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ig
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v
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d
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ed
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cin
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a
n
s
m
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io
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lo
s
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in
p
r
ac
tical
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t
ilit
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tr
a
n
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m
is
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et
w
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n
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er
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m
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tan
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ateg
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ci
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te
m
p
er
f
o
r
m
a
n
ce
[
2
5
]
,
[
2
6
]
.
T
h
is
p
ap
er
f
o
cu
s
e
s
o
n
u
s
i
n
g
an
a
u
to
m
ated
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u
n
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g
p
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p
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te
g
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ased
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C
s
y
s
te
m
to
i
m
p
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v
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th
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v
o
lta
g
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s
tab
ilit
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o
f
a
tr
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s
m
is
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et
w
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k
w
h
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n
s
u
b
j
ec
ted
to
a
b
alan
ce
d
th
r
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e
-
p
h
a
s
e
f
au
lt.
Ma
n
y
r
esear
ch
p
ap
er
s
r
ev
ie
w
ed
h
a
v
e
n
o
t
co
n
s
id
er
ed
th
i
s
tech
n
o
lo
g
y
f
o
r
v
o
lta
g
e
s
tab
ilit
y
i
m
p
r
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v
e
m
en
t.
T
h
e
b
alan
ce
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th
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p
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f
a
u
lt
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th
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d
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tu
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b
an
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t
th
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s
th
e
tr
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s
m
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s
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w
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tab
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v
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s
tead
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tate
o
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atio
n
o
f
g
en
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ato
r
s
a
n
d
s
u
s
tai
n
ab
le
p
o
w
er
s
u
p
p
l
y
.
T
h
e
r
e
m
ain
in
g
s
ec
tio
n
s
o
f
th
i
s
p
ap
er
ar
e
o
r
g
an
ized
as
f
o
llo
w
s
:
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n
3
p
r
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ts
th
e
m
ate
r
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an
d
m
et
h
o
d
s
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m
p
lo
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f
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th
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al
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s
is
co
n
d
u
cted
in
th
i
s
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esear
ch
.
Sectio
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4
d
is
cu
s
s
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th
e
r
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lts
o
b
tain
ed
th
r
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g
h
th
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ap
p
licatio
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o
f
th
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p
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m
et
h
o
d
,
h
ig
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t
s
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t
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w
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Fi
n
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y
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es t
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3.
M
AT
E
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S AN
D
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p
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(
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is
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p
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t
s
,
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ev
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d
n
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w
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s
id
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MA
T
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A
B
/Si
m
u
lin
k
.
I
n
th
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p
ap
er
,
it
is
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to
m
o
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a
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in
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a
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f
a
4
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s
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3
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k
V
Nig
er
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w
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k
as
s
h
o
w
n
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n
Fi
g
u
r
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1
.
T
h
e
n
etw
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k
d
ata
in
cl
u
d
in
g
b
u
s
,
g
e
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ato
r
,
lin
e
a
n
d
lo
ad
d
ata
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o
b
tain
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f
r
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m
th
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ter
o
f
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N
ig
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tr
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s
m
is
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co
m
p
a
n
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.
T
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e
d
ata
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is
t
h
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m
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t
r
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en
t
n
et
w
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k
d
ata
f
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s
a
k
e
o
f
cr
ed
ib
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a
n
d
ac
cu
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ac
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w
h
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h
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u
s
ed
to
co
n
d
u
ct
p
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f
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d
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,
eig
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v
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ies
o
f
t
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et
w
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to
id
en
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f
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cr
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b
u
s
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d
w
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k
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s
m
is
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n
li
n
es
d
u
r
in
g
f
a
u
lt
co
n
d
itio
n
s
.
An
iter
ativ
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tech
n
iq
u
e
ca
lled
th
e
New
to
n
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ap
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p
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p
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eq
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.
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eq
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ar
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n
o
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li
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at
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w
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.
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h
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alan
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p
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ase
f
au
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ap
p
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Fig
u
r
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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I
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4
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A
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3
.
1
.
T
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I
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t
w
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k
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m
ath
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m
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tatio
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f
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f
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m
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f
l
o
w
tec
h
n
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u
es.
T
h
e
in
j
ec
ted
cu
r
r
en
t a
t b
u
s
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g
i
v
e
n
as
i
I
w
h
ile
th
e
v
o
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g
e
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eter
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i
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ed
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s
i
n
g
(
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.
=
|
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(
1
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T
h
e
cu
r
r
en
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t b
u
s
k
i
s
g
iv
e
n
a
s
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,
=
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(
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h
er
e
is
th
e
m
u
t
u
al
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u
s
ad
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ittan
ce
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atr
i
x
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h
er
e
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co
m
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lex
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u
s
i
n
t
h
e
n
e
t
w
o
r
k
d
en
o
t
ed
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y
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h
er
ef
o
r
e,
th
e
ap
p
ar
en
t p
o
w
er
o
f
t
h
e
n
et
w
o
r
k
b
ec
o
m
e
s
,
=
+
(
3
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T
h
e
k
V
an
d
j
V
ar
e
th
e
v
o
lta
g
es a
t t
h
e
b
u
s
es.
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h
e
r
ea
l a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
n
et
w
o
r
k
i
s
g
i
v
e
n
as (
4
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.
+
=
∗
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(
4
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T
h
e
n
o
d
e
cu
r
r
en
t
=
+
∗
(
5
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T
h
e
∗
an
d
∗
r
ep
r
esen
ts
t
h
e
c
u
r
r
en
t
a
n
d
v
o
lta
g
e
co
n
j
u
g
ate
s
o
f
an
d
r
esp
ec
tiv
el
y
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Hen
ce
,
th
e
n
o
d
e
v
o
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g
e
is
g
i
v
e
n
as (
6
)
.
=
1
[
+
∗
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−
∑
≠
1
(
6
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A
l
s
o
,
th
e
r
ea
l
an
d
p
o
w
er
at
an
y
b
u
s
is
d
en
o
ted
in
(
7
)
an
d
(
8
)
.
T
h
is
is
th
e
p
o
w
er
f
lo
w
t
h
r
o
u
g
h
t
h
e
tr
an
s
m
is
s
io
n
li
n
e
s
f
r
o
m
b
u
s
to
.
=
[
∗
[
+
∑
(
−
)
=
1
]
]
(
7
)
=
[
∗
[
+
∑
(
−
)
=
1
]
]
(
8
)
3
.
2
.
T
he
H
VDC
s
y
s
t
e
m
m
o
d
elling
f
o
r
a
m
ulti
-
g
ener
a
t
o
r
net
w
o
rk
T
h
e
HVDC
m
o
d
el
s
h
o
w
n
i
n
Fig
u
r
e
2
o
p
e
r
ates
in
a
b
id
ir
ec
tio
n
al
m
a
n
n
er
.
I
t
co
n
s
is
ts
o
f
t
w
o
v
o
lta
g
e
co
n
v
er
ter
s
ec
tio
n
s
:
th
e
r
ec
ti
f
ie
r
an
d
th
e
in
v
er
ter
.
I
n
r
ec
ti
f
ica
tio
n
m
o
d
e,
th
e
co
n
v
er
ter
f
u
n
c
tio
n
s
s
i
m
ilar
l
y
to
a
co
n
v
e
n
tio
n
al
AC
s
y
s
te
m
,
ac
ti
n
g
as
a
n
o
n
li
n
ea
r
lo
ad
.
I
n
in
v
er
s
io
n
m
o
d
e,
it
ai
m
s
to
en
s
u
r
e
s
y
s
te
m
s
tab
il
it
y
b
y
s
y
n
ch
r
o
n
izin
g
th
e
v
o
lta
g
e
m
ag
n
it
u
d
e,
p
h
a
s
e
a
n
g
le,
a
n
d
f
r
eq
u
en
c
y
w
i
th
t
h
e
n
e
t
w
o
r
k
,
as
il
lu
s
tr
ated
in
Fig
u
r
e
2
(
a)
.
T
h
is
s
y
n
ch
r
o
n
izat
io
n
is
p
ar
ticu
lar
l
y
v
ita
l
f
o
r
en
h
an
ci
n
g
th
e
v
o
lta
g
e
p
r
o
f
ile
in
w
ea
k
o
r
lo
w
-
i
n
er
tia
AC
n
et
w
o
r
k
s
,
w
h
er
e
v
o
lta
g
e
s
tab
ilit
y
m
a
y
b
e
co
m
p
r
o
m
i
s
ed
b
y
f
r
eq
u
e
n
c
y
f
l
u
ct
u
atio
n
s
.
B
y
m
o
d
u
la
tin
g
p
o
w
er
ex
c
h
a
n
g
e
t
h
r
o
u
g
h
t
h
e
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
(
VS
C
)
in
r
esp
o
n
s
e
t
o
r
ea
l
-
ti
m
e
f
r
eq
u
en
c
y
d
ev
ia
tio
n
s
,
t
h
e
co
n
v
er
ter
m
ai
n
tai
n
s
s
tab
le
v
o
ltag
e
lev
els,
m
iti
g
ati
n
g
t
h
e
r
is
k
o
f
v
o
lta
g
e
s
ag
s
o
r
s
w
ells
th
at
co
u
ld
d
estab
ilize
th
e
s
y
s
te
m
.
T
h
i
s
f
r
eq
u
en
c
y
-
r
esp
o
n
s
e
co
n
tr
o
l
s
tr
ate
g
y
is
ap
p
licab
le
in
b
o
th
r
ec
tif
icatio
n
an
d
i
n
v
er
s
io
n
m
o
d
es
an
d
p
la
y
s
a
k
e
y
r
o
le
in
i
m
p
r
o
v
in
g
t
h
e
v
o
lta
g
e
p
r
o
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ile
i
n
b
o
th
co
n
v
e
n
tio
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an
d
VS
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-
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ased
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DC
s
y
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te
m
s
.
I
n
VS
C
HVD
C
s
y
s
te
m
s
,
th
is
co
n
tr
o
l
ap
p
r
o
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h
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te
n
d
s
th
e
ca
p
ab
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eg
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late
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d
p
r
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id
e
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r
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en
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p
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en
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"
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d
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A
C
n
et
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r
k
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th
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e
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co
n
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s
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le
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ter
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al
g
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h
is
d
y
n
a
m
ic
ad
j
u
s
t
m
e
n
t
e
n
h
a
n
ce
s
v
o
lt
ag
e
s
tab
ilit
y
,
en
s
u
r
es
r
eliab
le
p
o
w
er
d
eliv
er
y
,
an
d
s
u
p
p
o
r
ts
th
e
in
teg
r
atio
n
o
f
v
ar
iab
le
r
en
e
w
ab
le
e
n
er
g
y
s
o
u
r
ce
s
in
to
t
h
e
g
r
id
.
T
h
e
eq
u
iv
alen
t
cir
c
u
it
o
f
t
h
e
HVDC
tr
a
n
s
m
is
s
io
n
s
y
s
te
m
m
o
d
el
is
s
h
o
w
n
in
Fig
u
r
e
2
(
b
)
,
w
h
ic
h
is
u
s
ed
to
p
er
f
o
r
m
t
h
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i
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o
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w
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co
n
v
er
ter
s
tatio
n
s
a
s
d
escr
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ed
b
elo
w
.
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
-
8708
E
n
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3597
(
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(
b
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Fig
u
r
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2
.
T
h
e
s
y
s
te
m
atic
m
o
d
el
o
f
HVDC
s
y
s
te
m
,
(
a)
t
w
o
le
v
el
co
n
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ter
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tio
n
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n
d
(
b
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eq
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t
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it
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h
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t
w
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tatio
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tatio
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te
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at
b
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s
m
r
ep
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t
t
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ec
tif
ier
an
d
i
n
v
er
te
r
s
tatio
n
s
w
it
h
a
d
etailed
v
o
ltag
e
r
ep
r
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tatio
n
at
ea
c
h
b
u
s
.
T
h
e
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
i
n
j
ec
ted
at
th
e
r
ec
tif
ier
s
tatio
n
(
b
u
s
k
)
ar
e:
=
1
(
2
+
2
−
(
1
+
1
)
)
+
1
(
1
+
1
)
(
9
)
=
1
(
1
+
1
)
+
1
(
−
(
2
+
2
)
+
1
+
1
)
(
1
0
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Si
m
i
lar
l
y
,
t
h
e
ac
tiv
e
a
n
d
r
ea
cti
v
e
p
o
w
er
f
lo
w
i
n
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t
h
e
in
v
er
te
r
s
tatio
n
(
b
u
s
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ar
e:
=
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2
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2
+
2
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+
2
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2
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2
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(
1
1
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2
2
+
2
)
+
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(
−
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2
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2
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+
2
+
2
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(
1
2
)
T
h
er
ef
o
r
e,
th
e
to
tal
p
o
w
er
i
n
to
th
e
HVD
C
s
y
s
te
m
is
a
s
(
1
3
)
:
=
+
+
(
1
3
)
W
h
er
e
is
th
e
ac
ti
v
e
p
o
w
er
i
n
th
e
HVD
C
,
is
t
h
e
ac
tiv
e
p
o
wer
in
th
e
r
ec
ti
f
ier
an
d
is
th
e
ac
tiv
e
p
o
w
er
in
i
n
v
er
ter
s
tat
io
n
s
,
r
es
p
ec
tiv
el
y
w
h
ile
t
h
e
is
th
e
d
ir
ec
t c
u
r
r
en
t (
DC
)
li
n
k
ac
tiv
e
p
o
w
er
.
3
.
3
.
T
he
t
o
po
lo
g
y
o
f
pro
po
rt
io
na
l int
eg
ra
l c
o
ntr
o
ller
o
pe
ra
t
io
n in H
VDC
s
y
s
t
e
m
T
h
e
P
I
co
n
tr
o
ller
m
o
d
el
co
n
s
is
t
s
a
p
r
o
p
o
r
tio
n
al
an
d
i
n
te
g
r
al
g
ain
s
,
e
x
o
g
e
n
o
u
s
s
i
g
n
al
an
d
f
ir
in
g
an
g
le.
T
h
e
in
v
er
ter
v
o
lta
g
e
a
n
d
cu
r
r
en
t
o
f
th
e
HVD
C
co
n
tr
o
ller
in
tr
o
d
u
ce
h
i
g
h
-
f
r
eq
u
e
n
c
y
d
y
n
a
m
ics
t
h
a
t
s
ig
n
i
f
ica
n
tl
y
i
m
p
ac
t
b
o
th
p
ea
k
an
d
li
g
h
t
lo
ad
co
n
d
itio
n
s
,
as
w
e
ll
as
d
u
r
i
n
g
lar
g
e
s
i
g
n
al
d
is
tu
r
b
an
ce
s
o
n
th
e
n
et
w
o
r
k
.
T
h
e
s
y
s
te
m
i
n
F
ig
u
r
e
3
co
m
p
ar
es
t
h
e
r
ef
er
e
n
ce
cu
r
r
en
t
w
i
th
t
h
e
m
ea
s
u
r
e
d
DC
cu
r
r
en
t
to
d
eter
m
in
e
t
h
e
ap
p
r
o
p
r
iate
co
n
tr
o
l
ac
tio
n
.
T
h
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
s
e
cu
r
r
e
n
ts
s
er
v
e
s
as
t
h
e
b
asis
f
o
r
ad
j
u
s
tin
g
th
e
o
p
er
atio
n
o
f
t
h
e
co
n
v
er
ter
.
T
h
is
ad
j
u
s
t
m
e
n
t
is
i
m
p
le
m
e
n
ted
th
r
o
u
g
h
th
e
m
o
d
u
latio
n
o
f
t
h
e
th
y
r
i
s
to
r
f
ir
i
n
g
a
n
g
le.
A
p
o
w
e
r
r
ef
er
en
ce
in
p
u
t
(
)
an
d
th
e
m
e
asu
r
ed
p
o
w
er
f
r
o
m
t
h
e
s
y
s
te
m
ar
e
co
m
p
ar
ed
.
T
h
e
d
if
f
er
en
ce
r
ep
r
esen
ts
h
o
w
m
u
c
h
t
h
e
ac
tu
al
p
o
w
er
d
ev
iates
f
r
o
m
t
h
e
d
esire
d
s
et
p
o
in
t.
T
h
e
p
r
o
p
o
r
tio
n
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
A
u
g
u
s
t
20
25
:
3
5
9
3
-
3602
3598
g
ain
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p
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e
m
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ased
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ased
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ased
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u
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5
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ase
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ased
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ased
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ased
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ase
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ase,
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h
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ate
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