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1566
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h
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v
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ir
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c
t
c
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rre
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p
r
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r
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g
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o
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t
t
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wo
rld
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n
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m
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n
stra
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th
e
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tere
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t
h
is
e
lec
tri
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it
y
tran
sm
issio
n
tec
h
n
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l
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.
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h
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it
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o
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v
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d
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VSC
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VD
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c
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rima
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o
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tw
o
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tr
a
n
sm
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ies
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t
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p
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u
r
c
o
n
tri
b
u
ti
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t
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g
h
a
d
a
p
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iv
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tr
o
l
b
a
se
d
o
n
t
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b
a
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ste
p
p
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a
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ro
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c
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ll
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re
g
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t
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F
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ti
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s b
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M
ATLAB
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k
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o
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m
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t.
K
ey
w
o
r
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s
:
Ad
ap
tiv
e
co
n
tr
o
l
HVDC
-
VS
C
tr
an
s
m
is
s
io
n
L
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ap
u
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v
t
h
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P
ar
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u
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ce
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tain
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T
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s
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o
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n
a
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
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SA
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se
.
C
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r
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s
p
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A
uth
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r
:
Mo
h
am
ed
Am
in
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Kaz
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Dep
ar
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t o
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Stru
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in
g
,
I
n
tellig
en
t Sy
s
tem
s
&
E
lectr
ical
E
n
er
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NSAM
Has
s
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2
Un
iv
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s
ity
1
1
5
Nil Str
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t,
Sid
i O
th
m
an
e
C
asab
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ca
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Mo
r
o
cc
o
E
m
ail:
m
ed
am
in
ek
az
i@
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m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
E
lectr
ical
en
er
g
y
is
n
o
wad
ay
s
p
r
o
d
u
ce
d
,
tr
a
n
s
m
itted
,
an
d
d
is
tr
ib
u
ted
in
alter
n
atin
g
cu
r
r
en
t
v
ia
h
ig
h
-
v
o
ltag
e
alter
n
atin
g
cu
r
r
en
t (
A
C
)
tr
an
s
m
is
s
io
n
n
etwo
r
k
s
[
1
]
,
[
2
]
.
T
h
is
tech
n
o
lo
g
y
is
s
u
p
p
o
r
ted
b
y
s
p
ec
ialis
ts
in
th
e
f
ield
o
f
p
o
wer
elec
tr
o
n
ics b
ec
au
s
e
o
f
th
e
s
im
p
licity
o
f
p
r
o
d
u
ctio
n
an
d
th
e
p
o
s
s
ib
ilit
y
o
f
ch
an
g
in
g
th
e
lev
e
l
o
f
v
o
ltag
es
with
t
h
e
h
elp
o
f
tr
an
s
f
o
r
m
er
s
.
Ho
wev
e
r
,
t
h
e
tr
an
s
m
is
s
io
n
o
f
elec
t
r
ical
e
n
er
g
y
in
alter
n
atin
g
cu
r
r
en
t
f
ac
es
s
er
io
u
s
p
r
o
b
lem
s
th
at
ar
e
in
cr
ea
s
in
g
ly
d
if
f
icu
lt
to
s
o
lv
e
[
3
]
,
esp
ec
ially
wh
en
th
e
n
ee
d
f
o
r
elec
tr
icity
is
lar
g
e
en
o
u
g
h
a
n
d
o
v
er
lo
n
g
d
is
tan
ce
s
,
as
well
as
th
e
p
r
o
b
lem
o
f
co
m
p
e
n
s
atio
n
o
f
r
ea
ctiv
e
p
o
wer
th
at
m
u
s
t
b
e
m
ad
e
as
clo
s
e
as
p
o
s
s
ib
le
to
its
co
n
s
u
m
p
tio
n
in
o
r
d
er
to
lim
it
lo
s
s
es
an
d
v
o
l
tag
e
d
r
o
p
s
,
an
d
th
e
p
r
o
b
lem
o
f
asy
n
c
h
r
o
n
o
u
s
lin
k
s
o
r
in
ter
co
n
n
ec
tio
n
s
[
4
]
.
T
h
e
co
n
tr
o
l
o
f
HVDC
s
y
s
tem
s
is
a
v
ast
f
ield
o
p
e
n
to
an
y
r
esear
ch
co
n
t
r
ib
u
tio
n
.
Ma
n
y
r
esear
ch
e
s
h
av
e
b
ee
n
c
o
n
d
u
cted
in
o
r
d
er
to
im
p
lem
en
t
ad
v
an
ce
d
an
d
r
o
b
u
s
t
tech
n
iq
u
es
to
s
tab
ilize
an
d
g
u
ar
an
tee
b
etter
p
er
f
o
r
m
an
ce
s
[
5
]
,
eith
e
r
b
y
cl
ass
ical
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI
)
co
n
tr
o
ls
[
6
]
o
r
b
y
n
o
n
-
lin
ea
r
co
n
tr
o
ls
[
7]
-
[9
]
.
R
ec
en
t
wo
r
k
h
as
f
o
cu
s
ed
o
n
to
p
ics
r
el
ated
to
HVDC
s
y
s
tem
s
f
o
r
ex
am
p
le
th
e
in
teg
r
a
tio
n
o
f
r
e
n
ewa
b
le
en
er
g
ies
in
HVDC
n
etwo
r
k
s
[
1
0
]
,
th
e
s
tu
d
y
an
d
s
y
n
ch
r
o
n
iz
atio
n
o
f
c
o
n
v
er
te
r
s
tatio
n
s
[
1
1
]
,
th
e
tech
n
o
lo
g
y
o
f
ca
b
les u
s
ed
f
o
r
HVDC [
1
2
]
,
[
1
3
]
,
th
e
r
ip
p
le
o
f
ca
p
ac
ito
r
v
o
ltag
es [
1
4
]
.
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
a
n
d
d
esig
n
o
f a
n
a
d
a
p
tive
co
n
tr
o
l fo
r
V
S
C
-
HV
DC
s
ystem
… (
Mo
h
a
med
A
min
e
K
a
z
i
)
1567
Ad
ap
tiv
e
co
n
tr
o
l,
alth
o
u
g
h
o
ld
,
h
as
b
ee
n
o
f
g
r
ea
t
in
ter
es
t
an
d
h
as
co
n
tr
ib
u
te
d
to
s
o
l
v
in
g
m
a
n
y
s
tab
ilizatio
n
an
d
r
o
b
u
s
tn
ess
p
r
o
b
lem
s
f
o
r
HVDC
tr
an
s
p
o
r
t
s
y
s
tem
s
[
15
]
,
wo
r
k
h
as
also
d
ea
lt
with
ad
ap
tiv
e
co
n
tr
o
l b
ased
o
n
a
r
ef
e
r
en
ce
m
o
d
el
r
ef
er
e
n
ce
ad
ap
tiv
e
co
n
t
r
o
l
(
MRAC
)
[
16]
-
[
1
8
]
wh
ich
h
as d
em
o
n
s
tr
ated
th
e
ef
f
ec
tiv
en
ess
o
f
th
is
ty
p
e
o
f
c
o
n
tr
o
l
esp
ec
ially
wh
e
n
o
n
e
wis
h
es
to
im
p
r
o
v
e
th
e
d
y
n
am
ic
r
esp
o
n
s
e
an
d
tak
e
in
to
ac
co
u
n
t
th
e
p
a
r
am
etr
ic
v
ar
iatio
n
s
o
f
th
e
s
y
s
tem
.
I
n
th
i
s
wo
r
k
,
we
r
ea
lized
an
ad
ap
ti
v
e
co
n
tr
o
l
b
ased
o
n
th
e
b
ac
k
s
tep
p
in
g
ap
p
r
o
ac
h
o
f
th
is
VS
C
-
HVD
C
s
y
s
tem
w
h
ich
allo
ws
r
eg
u
latin
g
th
e
d
i
r
ec
t
cu
r
r
en
t
(
DC
)
v
o
ltag
e
also
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
u
n
d
er
f
a
u
lts
co
n
d
itio
n
s
[
1
9
]
-
[
2
1
]
.
T
h
e
f
ir
s
t
p
ar
t
will
b
e
d
ed
icate
d
to
th
e
m
ath
em
atica
l
m
o
d
elin
g
o
f
th
e
VSC
-
HVDC
tr
an
s
m
is
s
io
n
s
y
s
tem
th
en
th
e
co
n
tr
o
l
l
aws
elab
o
r
ated
f
o
r
th
e
two
s
tatio
n
s
an
d
f
in
ally
a
s
im
u
latio
n
to
test
th
e
v
alid
ity
o
f
th
e
co
n
tr
o
l.
Fig
u
r
e
1
s
h
o
w
s
o
u
r
VSC
-
HVDC
s
y
s
tem
co
m
p
o
s
ed
o
f
2
VSC
co
n
v
er
ter
s
co
n
n
ec
ted
to
th
e
A
C
n
etwo
r
k
th
r
o
u
g
h
an
im
p
ed
a
n
ce
lin
e.
On
t
h
e
DC
s
id
e,
th
e
two
co
n
v
er
ter
s
tatio
n
s
ar
e
in
ter
co
n
n
ec
te
d
b
y
DC
tr
an
s
m
is
s
io
n
ca
b
les.
Fig
u
r
e
1
.
VSC
-
HVDC sy
s
tem
2.
M
O
DE
L
I
NG
O
F
VSC
-
H
VD
C
SYST
E
M
C
o
n
v
er
ter
s
ar
e
th
e
m
ain
ac
to
r
s
in
an
HVD
C
tr
an
s
m
i
s
s
io
n
s
i
n
ce
th
ey
en
s
u
r
e
th
e
tr
an
s
f
o
r
m
atio
n
o
f
th
e
AC
p
o
wer
in
to
DC
p
o
wer
,
a
s
well
as
th
e
r
ev
er
s
e
o
p
e
r
atio
n
.
T
h
e
b
asic
s
tr
u
ctu
r
e
o
f
t
h
e
VSC
co
n
v
er
ter
is
d
ep
icted
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
Stru
ctu
r
e
o
f
VSC
co
n
v
er
ter
Ap
p
ly
in
g
Kir
c
h
h
o
f
f
’
s
v
o
ltag
e
an
d
cu
r
r
en
t la
ws we
f
in
d
:
L.
di
j
dt
+R
.
i
j
=
u
gj
-
u
mj
(
1
)
T
h
e
s
y
s
tem
(
1
)
ca
n
b
e
wr
itten
as:
u
m
a
b
c
=
-
R.
i
a
b
c
-
L.
di
a
b
c
dt
+
u
g
a
b
c
(
2
)
In
(
2
)
is
th
en
wr
itten
in
t
h
e
Par
k
tr
an
s
f
o
r
m
:
u
m
d
q
0
=
-
R.
i
d
q
0
-
L
.P
(
θ
)
.
di
a
b
c
dt
+
u
g
d
q
0
(
3
)
T
h
e
tr
a
n
s
f
o
r
m
ati
o
n
l
o
s
s
es
b
ei
n
g
n
eg
lec
te
d
o
n
t
h
e
co
n
v
e
r
t
er
s
id
e
,
t
h
e
ac
t
iv
e
p
o
w
er
t
r
an
s
m
i
tte
d
o
n
t
h
e
AC
s
i
d
e
will
b
e
th
e
s
am
e
o
n
th
e
DC
s
i
d
e,
s
o
w
e
f
i
n
d
:
P
g
d
q
=
P
DC
(
4
)
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
:
156
6
–
157
5
1568
T
h
e
ac
t
iv
e
a
n
d
r
ea
cti
v
e
p
o
we
r
s
d
eli
v
e
r
ed
b
y
t
h
e
s
o
u
r
ce
a
r
e
d
ef
i
n
ed
r
es
p
e
cti
v
el
y
b
y
(
5
)
,
(
6
)
:
P
g
d
q
=
3
2
.
(
u
gd
.
i
d
+
u
gq
.
i
q
)
=
3
2
.
(
u
gq
.
i
q
)
(
5
)
Q
g
d
q
=
3
2
.
(
u
gq
.
i
d
-
u
gd
.
i
q
)
=
3
2
.
(
u
gq
.
i
d
)
(
6
)
I
f
w
e
ap
p
l
y
t
h
e
Ki
r
c
h
h
o
f
f
c
u
r
r
en
t
l
aw
,
i
t
co
m
es
:
i
m
=
i
c
+
i
L
(
7)
3
2
.
u
gq
.
i
q
=
V
dc
.(
i
c
+
i
L
)
(
8
)
W
h
e
r
e:
i
c
=
3
2
.
u
q
.
i
q
V
dc
-
i
L
(
9
)
Kn
o
wi
n
g
th
at
i
c
=C
.
d
V
dc
dt
(
1
0
)
T
h
u
s
,
t
h
e
(
1
1
)
r
ep
r
ese
n
t
r
ep
r
es
en
t
a
f
i
r
s
t
m
o
d
el
e
x
p
r
ess
e
d
i
n
t
h
e
s
ta
te
s
p
ac
e
as:
{
dV
dc
dt
=
3.u
gq
.
i
q
2.
C
.V
dc
-
i
L
c
di
q
dt
=
-
ω
.
i
d
-
R
L
.
i
q
+
u
q
di
d
dt
=
ω
.
i
q
-
R
L
.
i
d
+
u
d
(
1
1
)
[
x
1
x
2
x
3
]
T
=
[
V
dc
i
q
i
d
]
T
W
h
er
e
u
q
=
(
u
gq
-
u
mq
)
L
;
u
d
=
(
u
gd
-
u
md
)
L
-
i
d
an
d
i
q
ar
e
th
e
cu
r
r
en
t in
Par
k
t
r
an
s
f
o
r
m
.
-
u
gd
,
u
gq
an
d
u
md
,
u
mq
ar
e
th
e
d
q
c
o
m
p
o
n
en
ts
o
f
th
e
AC
v
o
ltag
e,
a
n
d
VSC
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
r
esp
ec
tiv
ely
.
W
e
s
et
q
-
ax
is
to
b
e
in
p
h
ase
o
f
th
e
s
o
u
r
ce
v
o
ltag
e
u
g
(
u
gd
=0
).
3.
NO
NL
I
N
E
AR
CO
N
T
RO
L
O
F
VSC
-
H
VDC
3
.
1
.
I
ntr
o
du
ct
io
n
T
h
e
co
n
tr
o
l
o
f
HVDC
s
y
s
tem
s
[
2
2
]
-
[
2
4
]
r
e
q
u
ir
es
th
e
d
e
v
el
o
p
m
en
t
o
f
ad
v
a
n
ce
d
an
d
r
o
b
u
s
t
co
n
tr
o
ls
[
2
5
]
ca
p
ab
le
o
f
m
ai
n
tain
in
g
a
n
d
g
u
ar
an
teein
g
h
ig
h
p
e
r
f
o
r
m
an
ce
in
th
e
f
ac
e
o
f
an
y
d
is
tu
r
b
an
ce
o
r
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
,
b
ea
r
in
g
in
m
in
d
th
at
an
HVDC
tr
an
s
p
o
r
t
s
y
s
tem
is
c
o
n
s
id
er
ed
to
b
e
h
ig
h
l
y
n
o
n
-
lin
ea
r
an
d
r
ec
o
g
n
iz
ed
b
y
its
m
u
ltip
l
e
co
m
p
lex
ities
.
Ad
ap
tiv
e
c
o
n
t
r
o
l
is
a
co
n
tr
o
l
f
o
r
n
o
n
-
lin
ea
r
s
y
s
tem
s
[
2
6
]
,
[
2
7
]
u
s
in
g
a
s
et
o
f
co
n
ce
p
ts
an
d
tech
n
iq
u
es
f
o
r
th
e
au
to
m
atic,
r
ea
l
-
tim
e
ad
ju
s
tm
en
t
o
f
co
n
tr
o
ller
s
to
ac
h
iev
e
o
r
m
ain
tain
a
ce
r
tain
lev
el
o
f
d
es
ir
ed
p
er
f
o
r
m
an
ce
wh
e
n
s
y
s
tem
p
ar
am
eter
s
ar
e
u
n
k
n
o
wn
o
r
v
ar
y
in
g
,
th
er
ef
o
r
e
in
th
is
p
ap
er
ch
an
g
es in
s
y
s
tem
p
ar
am
eter
s
will b
e
tak
en
in
to
ac
co
u
n
t a
n
d
will b
e
f
o
r
m
u
lated
in
th
e
co
n
tr
o
l la
ws.
T
h
e
ad
ap
tiv
e
c
o
n
tr
o
l
will
b
e
estab
lis
h
ed
is
b
ein
g
as
s
tatio
n
1
is
ch
o
s
en
as
a
r
ec
tifie
r
to
r
eg
u
late
th
e
DC
b
u
s
v
o
ltag
e
an
d
r
ea
ctiv
e
p
o
wer
Q1
,
s
tatio
n
2
as
an
in
v
er
ter
to
r
eg
u
late
th
e
ac
tiv
e
p
o
w
er
P2
an
d
r
ea
ctiv
e
p
o
wer
Q2
.
3
.
2
.
Co
ntr
o
l desig
n f
o
r
t
he
r
ec
t
if
ier
s
t
a
t
io
n
T
h
e
m
ath
em
atica
l m
o
d
el
ad
o
p
ted
f
r
o
m
(
1
1
)
is
d
ef
in
e
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
a
n
d
d
esig
n
o
f a
n
a
d
a
p
tive
co
n
tr
o
l fo
r
V
S
C
-
HV
DC
s
ystem
… (
Mo
h
a
med
A
min
e
K
a
z
i
)
1569
{
x
1
̇
=a.
x
2
x
1
+D
x
2
̇
=
-
b.
x
2
-
ω
.
x
3
+
u
q1
+
θ
q1
x
3
̇
=
ω
.
x
2
-
b.
x
3
+
u
d1
+
θ
d1
(
1
2
)
W
h
er
e:
a=
3
.
u
gq
2
.
C
b=
R
L
D=
-
i
L
c
θq
1
an
d
θd
1
allo
w
to
r
ef
lect
t
h
e
im
p
ed
a
n
ce
v
ar
iatio
n
o
f
th
e
AC
lin
e,
th
ese
v
alu
es
m
u
s
t
b
e
co
n
s
tan
t
an
d
b
o
u
n
d
e
d
.
T
h
e
r
ec
tifie
r
s
t
atio
n
is
co
n
s
id
er
ed
o
f
th
ir
d
o
r
d
er
an
d
ca
n
b
e
co
n
tr
o
lled
b
y
two
co
n
tr
o
l
in
p
u
ts
.
First,
th
e
tr
ac
k
in
g
er
r
o
r
is
d
ef
i
n
ed
b
y
:
Z
1
=
x
1r
e
f
-
x
1
(
1
3
)
An
d
Z
2
=γ
-
x
2
(
1
4
)
γ
is
a
v
ir
tu
al
co
n
tr
o
l la
w
to
s
tab
ilize
Z
1
T
h
e
tim
e
d
er
iv
ativ
e
o
f
Z
1
an
d
Z
2
ar
e
g
iv
en
:
Z
1
̇
=
x
1re
f
̇
-
a.
x
2
x
1
–
D
(
1
5
)
W
e
u
s
e
th
e
f
o
llo
win
g
L
y
a
p
u
n
o
v
ca
n
d
id
ate
f
u
n
ctio
n
:
V
0
=
1
2
.C
.
Z
1
2
(
1
6
)
T
h
e
ter
m
1
2
.
C
.
Z
1
2
r
ep
r
esen
ts
a
ca
p
ac
it
o
r
en
er
g
y
f
l
u
ctu
atio
n
.
T
h
e
tim
e
d
er
iv
ativ
e
o
f
V
0
is
g
iv
en
:
V
̇
0
=C
.Z
1.
(
x
1re
f
̇
-
a.
γ
x
1
-
D)
+a
.C
.
Z
1.
Z
2
x
1
(
1
7
)
T
h
en
if
Z
2
=0
,
we
o
b
tain
:
V
̇
0
=
-
K
1
.C
.
Z
1
2
(
1
8
)
Wi
th
:
γ=
x
1
a
.(
x
1re
f
̇
-
D
+
K
1
.
Z
1
)
(
1
9
)
T
h
e
er
r
o
r
Z
3
is
d
ef
in
ed
as:
Z
3
=
x
3re
f
-
x
3
(
2
0
)
W
e
d
er
iv
e
th
e
two
ter
m
s
Z
2
,
Z
3
:
Z
̇
2
=
γ
̇
+b
.
x
2
+
ω
.
x
3
-
u
q1
-
θ
q1
(
2
1
)
Z
̇
3
=
x
̇
3re
f
-
ω
.
x
2
+b
.
x
3
-
u
d1
-
θ
d1
(
2
2
)
W
h
er
e
:
γ
̇
=
x
1
a
̇
.
(
x
1re
f
̇
-
D
+
K
1
.
Z
1
)
+
x
1
a
.(
x
1re
f
̈
-
D
̇
+
K
1
.
Z
1
̇
)
(
2
3
)
T
h
e
ly
ap
u
n
o
v
f
u
n
ctio
n
d
escr
ib
ed
b
elo
w
is
ch
o
s
en
to
en
s
u
r
e
t
h
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
t
h
e
s
y
s
tem
:
V
1
=
V
0
+
1
2
.L
(
Z
2
2
+
Z
3
2
)
+
1
2.
m
1
.
(
θ
q1
̂
-
θ
q1
)
2
+
1
2.
m
2
.
(
θ
d1
̂
-
θ
d1
)
2
(
2
4
)
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
:
156
6
–
157
5
1570
W
h
er
e:
-
θ
q1
̂
an
d
θ
d1
̂
ar
e
th
e
esti
m
ates o
f
θ
q1
an
d
θ
d1
.
-
m
1
an
d
m
2
ar
e
th
e
ad
a
p
tatio
n
g
ai
n
s
.
-
1
2
.L
(
Z
2
2
+
Z
3
2
)
r
ep
r
esen
ts
a
ca
p
ac
ito
r
e
n
er
g
y
f
lu
ctu
atio
n
o
f
th
e
AC
r
ea
cto
r
.
T
h
er
ef
o
r
e,
we
g
et
th
e
tim
e
d
er
iv
ativ
e
o
f
V
1
:
V
̇
1
=
-
K
1
.C
.
Z
1
2
+L
.Z
2
(
a
.C
.
Z
1.
L.
x
1
+
γ
̇
+b
.
x
2
+
ω
.
x
3
-
u
q1
-
θ
q1
̂
)
+
L
.Z
3
(
x
3re
f
-
̇
ω
.
x
2
+b
.
x
3
-
u
d1
-
θ
d1
̂
)
+
(
θ
q1
̂
-
θ
q1
)
.
(
θ
q1
̂
m
1
̇
+L
.Z
2
)
+
(
θ
d1
̂
-
θ
d1
)
(
θ
q1
̂
m
2
̇
+L
.Z
3
)
(
2
5
)
I
n
(
2
6
)
an
d
(
2
7
)
allo
w
ca
n
ce
l
in
g
an
d
elim
in
ate
th
e
ter
m
s
(
θ
q1
̂
-
θ
q1
)
an
d
(
θ
d1
̂
-
θ
d1
)
:
θ
q1
̂
̇
=
-
m
1
.L
.Z
2
(
2
6
)
θ
d1
̂
̇
=
-
m
2
.L
.Z
3
(
2
7
)
So
,
we
ca
n
d
ed
u
ce
th
e
two
co
n
tr
o
l in
p
u
ts
f
o
r
th
e
co
n
v
er
ter
(
s
tatio
n
1
)
:
u
q1
=a
.C
.
Z
1.
L.
x
1
+
γ
̇
+b
.
x
2
+ω
.
x
3
-
θ
q1
̂
+
K
2
.
Z
2
(
2
8
)
u
d1
=
x
3re
f
̇
-
ω
.
x
2
+b
.
x
3
-
θ
d1
̂
+
K
3
.
Z
3
(
2
9
)
T
h
en
we
o
b
tain
:
V
̇
1
=
-
K
1
.C
.
Z
1
2
-
K
2
.L
.
Z
2
2
-
K
3
.L
.
Z
3
2
≤
0
(
3
0
)
W
h
er
e
K
1
>0
,
K
2
>0
an
d
K
3
>0
.
Fig
u
r
e
3
s
h
o
ws co
n
tr
o
l b
lo
c
d
i
ag
r
am
f
o
r
r
ec
tifie
r
s
tatio
n
.
Fig
u
r
e
3
.
C
o
n
tr
o
l b
lo
c
d
iag
r
a
m
f
o
r
r
ec
tifie
r
s
tatio
n
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
a
n
d
d
esig
n
o
f a
n
a
d
a
p
tive
co
n
tr
o
l fo
r
V
S
C
-
HV
DC
s
ystem
… (
Mo
h
a
med
A
min
e
K
a
z
i
)
1571
3
.
3
.
Co
ntr
o
l desig
n f
o
r
t
he
i
nv
er
t
er
s
t
a
t
io
n
T
h
is
co
n
tr
o
l
aim
s
to
r
eg
u
late
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
.
T
h
e
s
tate
-
s
p
ac
e
o
f
th
e
s
tatio
n
o
p
er
atin
g
on
p
o
we
r
co
n
tr
o
l m
o
d
e
i
s
wr
itten
is
b
ein
g
as:
{
x
3
̇
=
-
b.
x
4
-
ω
.
x
5
+
u
q2
+
θ
q2
x
4
̇
=
ω
.
x
4
-
b.
x
5
+
u
d2
+
θ
d2
(
3
1
)
Θq
2
an
d
θd
2
allo
w
to
r
ef
lect
th
e
im
p
ed
an
ce
v
ar
iatio
n
o
f
t
h
e
AC
lin
e,
th
ese
v
alu
es
m
u
s
t
b
e
co
n
s
tan
t
an
d
b
o
u
n
d
ed
.
T
h
e
in
v
er
te
r
s
tatio
n
is
co
n
s
id
er
e
d
s
ec
o
n
d
-
o
r
d
er
a
n
d
ca
n
b
e
co
n
tr
o
lled
b
y
two
c
o
n
tr
o
l
in
p
u
ts
.
First,
th
e
tr
ac
k
in
g
e
r
r
o
r
is
d
ef
in
ed
b
y
:
Z
4
=
x
4re
f
-
x
4
(
3
2
)
Z
5
=
x
5re
f
-
x
5
(
3
3
)
I
f
we
co
n
s
id
er
t
h
e
tim
e
d
er
i
v
ativ
e
Z
4
an
d
Z
5
:
Z
̇
4
=
x
̇
4re
f
-
ω
.
x
5
+b
.
x
4
-
u
q2
-
θ
q2
(
3
4
)
Z
̇
5
=
x
̇
5re
f
-
ω
.
x
4
+b
.
x
5
-
u
d2
-
θ
d2
(
3
5
)
T
o
in
v
esti
g
ate
th
e
s
tab
ilit
y
o
f
t
h
e
er
r
o
r
s
,
a
L
y
ap
u
n
o
v
f
u
n
ctio
n
V
2
is
ch
o
s
en
as:
V
2
=
1
2
.L
(
Z
4
2
+
Z
5
2
)
+
1
2.
m
4
.
(
θ
q2
̂
-
θ
q2
)
2
+
1
2.
m
5
.
(
θ
d2
̂
-
θ
d2
)
2
(
3
6
)
W
h
er
e:
-
θ
q2
̂
an
d
θ
d2
̂
ar
e
th
e
esti
m
ates o
f
θ
q2
an
d
θ
d2
.
-
m
4
an
d
m
5
ar
e
th
e
ad
ap
tatio
n
g
ain
s
.
-
1
2
.L
(
Z
4
2
+
Z
5
2
)
r
ep
r
esen
t a
ca
p
ac
ito
r
en
e
r
g
y
f
lu
ctu
atio
n
o
f
th
e
AC
r
ea
cto
r
.
T
h
e
d
er
iv
ativ
e
o
f
V
2
alo
n
g
t
h
e
tr
ajec
to
r
ies o
f
th
e
er
r
o
r
s
is
g
iv
e
n
b
y
:
V
̇
2
=L
.Z
4
(
x
4
re
f
+
̇
ω
.
x
5
+b
.
x
4
-
u
q2
-
θ
q2
̂
)
+L
.Z
5
(
x
5
re
f
-
̇
ω
.
x
4
+b
.
x
5
-
u
d2
-
θ
d2
̂
)
+
(
θ
q2
̂
-
θ
q2
)
.
(
θ
q2
̂
m
4
̇
+L
.Z
4
)
+
(
θ
d2
̂
-
θ
d2
)
(
θ
q2
̂
m
5
̇
+L
.Z
5
)
(
3
7
)
I
n
(
3
8
)
an
d
(
3
9
)
allo
w
ca
n
ce
l
in
g
an
d
elim
in
ate
th
e
ter
m
s
(
θ
q2
̂
-
θ
q2
)
an
d
(
θ
d2
̂
-
θ
d2
)
:
θ
q2
̂
̇
=
-
m
4
.L
.Z
4
(
3
8
)
θ
d2
̂
̇
=
-
m
5
.L
.Z
5
(
3
9
)
S
o
f
in
ally
,
we
f
in
d
th
e
two
c
o
n
tr
o
l in
p
u
ts
o
n
th
e
i
n
v
er
ter
s
id
e
(
s
tatio
n
2
)
u
q2
=
x
4re
f
̇
+b
.
x
4
+
ω
.
x
5
-
θ
q2
̂
+
K
4
.
Z
4
(
4
0
)
u
d2
=
x
5re
f
-
̇
ω
.
x
4
+b
.
x
5
-
θ
d2
̂
+
K
5
.
Z
5
(
4
1
)
W
h
er
e
K
4
>0
an
d
K
5
>0
T
h
u
s
,
we
ar
r
iv
e
at
th
e
s
tab
ilizatio
n
eq
u
atio
n
V
̇
2
=
-
K
4
.L
.
Z
4
2
-
K
5
.L
.
Z
5
2
≤
0
(
4
2
)
T
h
e
B
ar
b
alat
an
d
L
aSalle
-
Yo
s
h
izaw
a
th
eo
r
em
s
[2
7
]
c
o
n
f
ir
m
th
e
co
n
v
er
g
en
ce
o
f
tr
ac
k
in
g
er
r
o
r
s
to
ze
r
o
∑
Z
i
→0
5
i=1
.
Fig
u
r
e
4
s
h
o
ws co
n
tr
o
l
b
lo
c
d
iag
r
a
m
f
o
r
r
ec
tifie
r
s
tatio
n
.
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
:
156
6
–
157
5
1572
Fig
u
r
e
4
.
C
o
n
tr
o
l b
lo
c
d
iag
r
a
m
f
o
r
i
n
v
er
ter
s
tatio
n
4.
SI
M
UL
A
T
I
O
N
A
NAL
YSI
S
AND
RE
SUL
T
S
I
n
o
r
d
e
r
to
test
th
e
ef
f
icien
c
y
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
a
n
d
th
e
s
y
s
tem
b
eh
av
io
r
u
n
d
e
r
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
,
a
s
im
u
latio
n
is
ca
r
r
ied
o
u
t
u
n
d
er
th
e
MA
T
L
AB
/S
im
u
lin
k
en
v
ir
o
n
m
en
t.
Fig
u
r
e
5
s
h
o
ws
th
e
s
tu
d
ied
s
y
s
tem
.
T
ab
le
1
p
r
esen
ts
th
e
s
im
u
latio
n
p
ar
a
m
et
er
s
o
f
th
e
s
tu
d
ied
s
y
s
tem
:
Fig
u
r
e
5
.
VSC
-
HVDC tr
an
s
m
i
s
s
io
n
s
y
s
tem
T
ab
le
1
.
Simu
latio
n
p
ar
am
eter
s
P
a
r
a
me
t
e
r
s
o
f
t
h
e
st
u
d
y
sy
s
t
e
m
V
a
l
u
e
Ea
c
h
A
C
S
y
s
t
e
m
n
o
m
i
n
a
l
v
o
l
t
a
g
e
3
2
0
K
V
Ea
c
h
D
C
n
o
m
i
n
a
l
v
o
l
t
a
g
e
2
5
0
K
V
B
a
se
p
o
w
e
r
1
0
0
0
M
V
A
R
e
si
st
o
r
R
1
a
n
d
R
2
9
0
0
mΩ
I
n
d
u
c
t
a
n
c
e
L
1
a
n
d
L2
1
6
.
5
mH
D
C
Li
n
k
c
a
p
a
c
i
t
o
r
C
8
0
µ
F
N
o
mi
n
a
l
f
r
e
q
u
e
n
c
y
5
0
H
z
Le
n
g
t
h
o
f
t
r
a
n
smiss
i
o
n
l
i
n
e
1
0
0
K
m
D
C
c
a
b
l
e
r
e
si
s
t
a
n
c
e
1
3
,
9
mΩ
/
k
m
D
C
c
a
b
l
e
i
n
d
u
c
t
a
n
c
e
0
,
1
5
9
mH
/
k
m
D
C
c
a
b
l
e
c
a
p
a
c
i
t
a
n
c
e
0
,
2
3
1
µ
F
/
k
m
I
n
o
r
d
er
to
ca
r
r
y
o
u
t
a
s
im
u
latio
n
s
tu
d
y
an
d
test
th
e
v
ali
d
ity
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l,
we
h
av
e
p
r
o
p
o
s
ed
th
e
f
o
llo
win
g
ac
tio
n
p
o
in
ts
,
C
ase
1
:
t
<
2
s
n
o
r
m
al
o
p
er
atin
g
c
o
n
d
itio
n
.
t
=
2
s
a
li
n
e
b
r
e
a
k
o
c
c
u
r
s
at
p
h
a
s
e
2
a
n
d
c
a
u
s
es
a
n
i
m
b
al
a
n
c
e
o
n
t
h
e
AC
n
e
tw
o
r
k
o
f
s
t
a
ti
o
n
1
,
F
i
g
u
r
e
6
s
h
o
ws
t
h
is
b
e
h
a
v
i
o
r
.
F
i
g
u
r
e
7
s
h
o
ws
t
h
e
r
e
s
p
o
n
s
e
o
f
t
h
e
D
C
b
u
s
f
o
r
b
o
t
h
s
t
a
t
i
o
n
s
,
it
c
a
n
b
e
s
e
e
n
t
h
a
t
t
h
e
s
y
s
t
e
m
f
o
l
l
o
w
s
t
h
e
s
et
p
o
in
t
d
e
s
p
i
t
e
t
h
e
p
h
a
s
e
b
r
e
a
k
p
r
o
d
u
c
e
d
a
t
t
=
2
s
a
n
d
c
o
n
v
e
r
g
e
s
q
u
i
c
k
l
y
t
o
t
h
e
r
e
f
e
r
e
n
c
e
v
a
l
u
e
.
Fig
u
r
e
6.
Sin
g
le
-
p
h
ase
f
au
lt a
t
s
tatio
n
1
Fig
u
r
e
7.
DC
-
lin
k
v
o
ltag
e
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
a
n
d
d
esig
n
o
f a
n
a
d
a
p
tive
co
n
tr
o
l fo
r
V
S
C
-
HV
DC
s
ystem
… (
Mo
h
a
med
A
min
e
K
a
z
i
)
1573
C
ase
2
:
A
co
m
m
o
n
p
r
o
b
lem
in
elec
tr
ical
p
o
wer
s
y
s
tem
s
is
v
o
ltag
e
d
ip
s
,
wh
ich
a
r
e
d
e
f
in
ed
as
a
s
u
d
d
en
d
r
o
p
o
f
1
0
%
o
r
m
o
r
e
o
f
th
e
n
o
m
in
al
v
o
ltag
e,
af
f
e
ctin
g
o
n
e
o
r
m
o
r
e
p
h
ases
,
last
in
g
b
etwe
en
eig
h
t
m
illi
s
ec
o
n
d
s
,
an
d
o
n
e
m
i
n
u
te.
Gen
er
ally
,
v
o
ltag
e
d
ip
s
ar
e
c
o
n
s
id
er
ed
as
d
is
tu
r
b
an
ce
s
,
a
n
d
th
er
ef
o
r
e,
t
o
test
th
e
r
o
b
u
s
tn
ess
o
f
o
u
r
s
y
s
tem
,
we
h
av
e
ca
u
s
ed
th
is
p
h
en
o
m
en
o
n
d
u
r
in
g
t
h
e
p
er
io
d
b
etwe
en
1
.
5
s
an
d
2
s
as
s
h
o
wn
in
F
ig
u
r
e
8
.
Fig
u
r
e
9
an
d
Fig
u
r
e
1
0
s
h
o
w
th
e
b
e
h
a
v
io
r
o
f
th
e
DC
b
u
s
f
o
r
t
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wo
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s
in
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d
ip
p
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it
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th
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e
is
a
s
tab
ilizatio
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o
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t
h
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to
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d
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th
e
r
ef
e
r
en
ce
v
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e
= 2
5
0
KV
.
Fig
u
r
e
8.
Gr
id
v
o
ltag
e
in
s
tatio
n
1
Fig
u
r
e
9
.
DC
v
o
ltag
e
s
tatio
n
1
Fig
u
r
e
10.
DC
v
o
ltag
e
s
tatio
n
2
Fig
u
r
e
1
1
an
d
Fig
u
r
e
1
2
s
h
o
w
th
e
ev
o
lu
tio
n
o
f
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
wer
s
o
f
e
ac
h
s
tatio
n
k
n
o
win
g
th
at
th
e
im
p
o
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ed
r
ef
er
en
ce
in
p
u
ts
ar
e
Q
1r
e
f
=0
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3
p
u
a
n
d
P
2
=
-
0
.
5
p
u
.
I
t
is
clea
r
f
r
o
m
th
e
s
im
u
latio
n
r
esu
lts
p
r
esen
ted
th
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
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ca
n
s
tab
ilize
th
e
s
y
s
tem
b
y
atten
u
atin
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f
lu
ctu
atio
n
s
in
th
e
DC
b
u
s
v
o
ltag
es,
d
am
p
en
th
e
o
s
cillatio
n
s
o
f
th
e
co
n
tr
o
lled
v
ar
iab
les,
an
d
e
n
s
u
r
e
t
h
e
r
eg
u
latio
n
o
f
ac
tiv
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an
d
r
ea
ctiv
e
p
o
wer
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T
h
e
f
au
lts
in
jecte
d
in
th
e
HVDC
s
y
s
tem
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wh
ich
ar
e
r
esp
ec
tiv
ely
th
e
p
h
ase
b
r
ea
k
an
d
t
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v
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d
ip
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allo
wed
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e
r
o
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u
s
tn
ess
o
f
th
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ad
ap
tiv
e
c
o
n
tr
o
l.
Fig
u
r
e
11.
Activ
e
p
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s
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2
Fig
u
r
e
12.
R
ea
ctiv
e
p
o
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Sta
tio
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1
T
h
e
p
r
o
p
o
s
ed
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n
tr
o
l
o
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f
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r
s
a
s
m
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o
l
c
o
m
p
a
r
e
d
with
th
e
r
esu
lts
o
f
th
e
s
lid
in
g
m
o
d
e
co
n
tr
o
l
[
2
8
]
,
[
2
9
]
,
esp
ec
ially
th
e
o
s
cillatio
n
o
r
ch
atter
in
g
p
r
o
b
lem
s
in
h
e
r
en
t
to
th
is
ty
p
e
o
f
d
is
co
n
tin
u
o
u
s
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
:
156
6
–
157
5
1574
co
n
tr
o
l
th
at
ap
p
ea
r
s
q
u
ick
ly
.
No
te
th
at
ch
atter
in
g
ca
n
ex
cit
e
n
eg
lecte
d
h
ig
h
-
f
r
e
q
u
en
c
y
d
y
n
am
ics
s
o
m
etim
es
lead
in
g
to
in
s
tab
ilit
y
.
T
h
e
in
teg
r
atio
n
o
f
th
e
p
a
r
am
eter
s
θ
q
a
n
d
θ
d
allo
ws to
q
u
ick
ly
ca
tch
u
p
with
th
e
s
etp
o
in
t
d
u
r
in
g
lin
e
b
r
ea
k
f
ailu
r
es c
o
m
p
ar
ed
to
a
n
o
r
m
al
b
ac
k
s
tep
p
i
n
g
co
n
tr
o
l [
3
0
-
32
].
Af
ter
m
u
ltip
le
test
s
o
f
d
if
f
er
e
n
t
v
alu
es
f
o
r
ad
ap
tatio
n
g
ain
s
,
it
was
f
o
u
n
d
th
at
tak
in
g
v
er
y
s
m
all
o
r
m
u
ch
h
ig
h
e
r
v
alu
es
th
an
th
o
s
e
tak
en
in
T
ab
le
2
in
s
tan
tly
ca
u
s
es
d
iv
er
g
en
ce
an
d
in
s
tab
ilit
y
in
th
e
s
y
s
tem
th
er
ef
o
r
e
th
e
v
alu
es
o
f
d
esig
n
ad
ap
tatio
n
g
ain
s
o
f
th
e
elab
o
r
ated
ad
ap
tiv
e
co
n
tr
o
l
h
av
e
a
m
ajo
r
im
p
ac
t
o
n
th
e
f
in
al
co
n
tr
o
l,
s
o
th
e
ch
o
ice
o
f
th
ese
p
ar
am
eter
s
is
v
er
y
im
p
o
r
tan
t,
d
esp
ite
th
e
d
if
f
icu
lt
y
o
f
o
b
tain
in
g
o
p
tim
al
v
alu
es.
T
h
is
p
a
p
er
d
o
es
n
o
t
p
r
o
v
id
e
th
e
m
ea
n
s
t
o
s
elec
t
th
es
e
p
ar
am
eter
s
p
r
o
p
er
ly
.
T
ab
le
2
s
h
o
ws
th
e
v
alu
es
ch
o
s
en
f
o
r
ea
ch
s
tatio
n
.
T
ab
le
2
.
C
o
n
tr
o
ller
p
ar
am
eter
s
S
t
a
t
i
o
n
1
S
t
a
t
i
o
n
2
B
a
c
k
s
t
e
p
p
i
n
g
c
o
n
t
r
o
l
l
e
r
p
a
r
a
m
e
t
e
r
s &
a
d
a
p
t
a
t
i
o
n
g
a
i
n
s
K
1
=
10
3
K
2
=
1
1
6
0
0
K
3
=
1
7
1
0
m
1
=
1
5
0
m
2
=
2
1
0
K
4
=
3
0
0
K
5
=
254
m
4
=
2
0
0
m
5
=
1
5
0
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
d
ea
ls
with
th
e
s
u
b
j
ec
t
o
f
th
e
co
n
tr
o
l
o
f
a
VSC
-
HVDC
s
y
s
tem
,
we
p
r
o
p
o
s
ed
th
e
co
n
tr
o
l
o
f
two
co
n
v
e
r
ter
s
tatio
n
s
co
n
n
ec
ted
to
ea
c
h
o
th
e
r
v
ia
a
DC
n
et
wo
r
k
.
W
e
p
r
o
p
o
s
ed
an
ad
ap
ti
v
e
co
n
tr
o
l
b
ased
o
n
th
e
b
ac
k
s
tep
p
in
g
m
et
h
o
d
wh
ich
allo
ws
tak
in
g
in
to
ac
co
u
n
t
th
e
v
ar
iatio
n
s
o
f
th
e
s
y
s
tem
p
ar
am
eter
s
an
d
im
p
r
o
v
es
its
d
y
n
am
ic
b
eh
a
v
i
o
r
.
T
h
r
o
u
g
h
th
e
s
im
u
latio
n
r
e
s
u
lts
o
b
tain
ed
,
we
n
o
te
th
at
t
h
e
co
n
tr
o
l
s
tr
ateg
y
ad
o
p
ted
lead
s
to
a
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
o
f
th
e
s
y
s
tem
p
e
r
f
o
r
m
a
n
ce
co
m
p
ar
ed
to
a
class
ical
PI
co
n
tr
o
l
a
n
d
also
to
a
b
etter
co
n
t
r
o
l
o
f
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
o
f
th
e
s
tatio
n
s
d
esp
ite
th
e
p
r
esen
ce
o
f
d
is
tu
r
b
an
ce
s
,
ev
en
o
f
s
o
m
e
d
ef
ec
ts
th
at
m
ay
ap
p
ea
r
d
u
e
to
th
e
co
m
p
le
x
ity
o
f
th
e
p
o
wer
tr
an
s
m
is
s
io
n
s
y
s
tem
an
d
th
e
u
n
m
ea
s
u
r
ab
le
r
an
d
o
m
d
is
tu
r
b
an
ce
s
th
at
m
ay
a
r
is
e
at
an
y
tim
e,
an
d
n
o
t
f
o
r
g
ettin
g
th
e
d
if
f
icu
lty
o
f
f
in
d
in
g
o
p
tim
al
v
alu
es
f
o
r
ad
ap
tatio
n
g
a
in
s
.
As
a
p
er
s
p
ec
tiv
e
o
u
r
atten
tio
n
will
b
e
d
ir
ec
ted
to
th
e
s
tu
d
y
o
f
MT
DC
m
u
lti
-
ter
m
in
al
HVDC
tr
an
s
p
o
r
t
s
y
s
tem
s
with
in
teg
r
atio
n
o
f
r
en
ewa
b
le
en
e
r
g
ies
an
d
also
,
t
o
s
tu
d
y
t
h
e
MM
C
m
o
d
u
lar
m
u
lti
-
lev
el
co
n
v
er
ter
s
wh
ich
ar
e
wid
ely
u
s
ed
i
n
ele
ctr
ic
en
er
g
y
tr
an
s
p
o
r
t a
p
p
licati
o
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
A
.
Ab
u
z
a
y
e
d
,
“
An
o
v
e
rv
iew
o
f
HV
DC
a
p
p
li
c
a
ti
o
n
s:
a
stu
d
y
o
n
m
e
d
iu
m
v
o
lt
a
g
e
d
istri
b
u
t
io
n
n
e
t
wo
rk
s
,”
t
h
e
sis
fo
r
:
Ba
c
h
e
lo
r
o
f
S
c
ien
c
e
in
E
n
e
rg
y
E
n
g
in
e
e
rin
g
,
De
c
e
m
b
e
r
2
0
1
7
,
d
o
i:
1
0
.
1
3
1
4
0
/RG
.
2
.
2
.
1
3
7
9
0
.
9
5
0
4
8
.
[2
]
J.
Do
rn
,
H.
G
a
m
b
a
c
h
,
a
n
d
D.
Re
tzm
a
n
n
,
“
HV
DC
tran
sm
i
ss
i
o
n
tec
h
n
o
lo
g
y
f
o
r
su
sta
in
a
b
le
p
o
we
r
su
p
p
ly
,
”
In
ter
n
a
t
io
n
a
l
M
u
lt
i
-
Co
n
fer
e
n
c
e
o
n
S
y
ste
ms
,
S
i
g
n
a
ls & De
v
ice
s
,
2
0
1
2
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/
S
S
D.
2
0
1
2
.
6
1
9
8
1
0
9
.
[
3
]
C.
R.
Ba
y
li
ss
,
C.
Ba
y
l
iss,
a
n
d
B.
Ha
rd
y
,
“
Tran
sm
issio
n
a
n
d
d
istr
ib
u
ti
o
n
e
lec
tri
c
a
l
e
n
g
i
n
e
e
rin
g
,”
El
se
v
ier
,
2
0
12
.
[4
]
K.
M
e
a
h
,
a
n
d
S
.
Ula
,
“
Co
m
p
a
ra
ti
v
e
e
v
a
lu
a
ti
o
n
o
f
HV
DC
a
n
d
H
VA
C
tran
sm
issio
n
sy
ste
m
s,
”
2
0
0
7
IEE
E
Po
we
r
En
g
i
n
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
2
0
0
7
,
p
p
.
1
-
5
,
d
o
i
:
1
0
.
1
1
0
9
/
P
ES
.
2
0
0
7
.
3
8
5
9
9
3
.
[5
]
S
.
Ru
i
h
u
a
,
Z
.
Ch
a
o
,
L
.
Ru
o
m
e
i
,
a
n
d
Z
Xia
o
x
in
,
“
VSCs
b
a
se
d
H
VD
C
a
n
d
it
s
c
o
n
tr
o
l
stra
teg
y
,
”
2
0
0
5
I
EE
E/
P
ES
T
ra
n
sm
issio
n
&
Distri
b
u
t
io
n
Co
n
fer
e
n
c
e
&
Exp
o
sit
io
n
:
Asia
a
n
d
Pa
c
if
ic
,
2
0
0
5
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/
TDC.
2
0
0
5
.
1
5
4
6
8
0
0
.
[6
]
F.
Ya
n
g
,
Z
.
Xu
,
a
n
d
J
.
Zh
a
n
g
,
“
An
a
p
p
r
o
a
c
h
to
se
lec
t
P
I
p
a
ra
m
e
ters
o
f
HV
DC
c
o
n
tro
ll
e
rs,
”
2
0
0
6
IEE
E
P
o
we
r
En
g
i
n
e
e
rin
g
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
2
0
0
6
,
p
.
5
,
d
o
i
:
1
0
.
1
1
0
9
/
P
ES
.
2
0
0
6
.
1
7
0
9
2
6
1
.
[7
]
X.
Y.
Li
,
“
A
n
o
n
l
in
e
a
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3
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1
9
IEE
E
M
il
a
n
P
o
we
rTec
h
,
2
0
1
9
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
1
0
9
/P
TC
.
2
0
1
9
.
8
8
1
0
7
9
4
.
[2
4
]
N
.
F
.
I
b
ra
h
im
a
n
d
S
.
S
.
De
ss
o
u
k
y
,
“
VSC
-
HV
DC
c
o
n
tro
l
sy
ste
m
,
”
De
sig
n
a
n
d
Imp
lem
e
n
ta
ti
o
n
o
f
Vo
lt
a
g
e
S
o
u
rc
e
Co
n
v
e
rte
rs
in
HVDC S
y
ste
ms
,
S
p
rin
g
e
r,
Ch
a
m
,
2
0
2
1
,
p
p
.
15
-
30
,
d
o
i:
1
0
.
1
0
0
7
/
9
7
8
-
3
-
0
3
0
-
5
1
6
6
1
-
1_3
.
[2
5
]
M
.
Ay
a
ri,
M
.
M
.
Be
lh
a
o
u
a
n
e
,
X.
G
u
il
lau
d
,
a
n
d
N.
B.
Bra
ie
k
,
“
No
n
li
n
e
a
r
c
o
n
tr
o
l
d
e
sig
n
o
f
VSC
-
M
TDC
sy
ste
m
s
b
a
se
d
o
n
Ba
c
k
ste
p
p
i
n
g
a
p
p
ro
a
c
h
,
”
2
0
1
5
1
2
t
h
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
In
fo
rm
a
ti
c
s
i
n
Co
n
tro
l
,
Au
to
m
a
ti
o
n
a
n
d
Ro
b
o
ti
c
s (ICINCO)
,
2
0
1
5
,
p
p
.
5
9
6
-
6
0
2
.
[2
6
]
B.
P
a
l
a
n
d
B.
Ch
a
u
d
h
u
ri
,
“
Li
n
e
a
r
Co
n
tr
o
l
i
n
p
o
we
r
sy
ste
m
s
,
”
Ro
b
u
st
C
o
n
tr
o
l
i
n
Po
we
r
S
y
ste
ms
,
2
0
0
5
,
p
p
.
1
3
-
3
8
,
d
o
i:
1
0
.
1
0
0
7
/
0
-
3
8
7
-
2
5
9
5
0
-
3
_
3
.
[2
7
]
T
.
I.
F
o
ss
e
n
,
“
Ha
n
d
b
o
o
k
o
f
ma
rin
e
c
ra
ft
h
y
d
ro
d
y
n
a
mic
s
a
n
d
m
o
ti
o
n
c
o
n
tr
o
l
,
Ap
p
e
n
d
ix
A:
No
n
li
n
e
a
r
S
tab
il
it
y
Th
e
o
ry
,
Jo
h
n
Wi
ley
&
S
o
n
s,
2
0
1
1
.
[2
8
]
B.
P
ra
sa
n
n
a
Lak
sh
m
i,
K.
Ra
m
e
sh
,
a
n
d
R.
Kira
n
m
a
y
i,
“
HV
DC t
ra
n
sm
issio
n
sy
ste
m
o
f
slid
i
n
g
m
o
d
e
c
o
n
tr
o
ll
e
r
Vis
-
a
-
Vis
P
i
c
o
n
tro
ll
e
r,
”
in
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
f
o
r
Res
e
a
rc
h
i
n
A
p
p
l
ied
S
c
ien
c
e
&
En
g
in
e
e
rin
g
T
e
c
h
n
o
l
o
g
y
(IJ
RA
S
E
T
)
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
2
9
4
1
-
2
9
5
3
,
Ja
n
u
a
ry
2
0
1
8
,
d
o
i:
1
0
.
2
2
2
1
4
/
ij
ra
se
t.
2
0
1
8
.
1
4
0
4
.
[2
9
]
B
.
S
a
b
e
r,
B
.
Ab
se
l
k
a
d
e
r,
B
.
M
a
n
so
u
r,
a
n
d
B
.
S
a
i
d
,
“
sli
d
in
g
m
o
d
e
c
o
n
tro
l
o
f
t
h
re
e
lev
e
ls
b
a
c
k
-
to
-
b
a
c
k
VSC
-
HV
DC
sy
ste
m
u
sin
g
sp
a
c
e
v
e
c
to
r
m
o
d
u
l
a
ti
o
n
,
”
i
n
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(IJ
PE
DS
)
,
v
o
l.
4
,
n
o
.
2
,
p
p
.
2
6
5
-
2
7
3
,
Ju
n
e
2
0
1
4
.
[3
0
]
S
.
B
o
u
a
fia,
A.
Be
n
a
issa
,
M
.
Bo
u
z
id
i
,
a
n
d
S
.
Ba
rk
a
t,
“
Ba
c
k
ste
p
p
i
n
g
c
o
n
tr
o
l
o
f
t
h
re
e
-
lev
e
ls
VSC
b
a
se
d
b
a
c
k
-
to
-
b
a
c
k
HV
DC
sy
ste
m
,
”
3
rd
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
S
y
ste
ms
a
n
d
C
o
n
tr
o
l
,
2
0
1
3
,
p
p
.
9
0
0
-
9
0
5
,
d
o
i
:
10.
1
1
0
9
/IC
o
S
C.
2
0
1
3
.
6
7
5
0
9
6
4
.
[3
1
]
P
.
H
.
Div
sh
a
li
,
G
.
B.
G
h
a
re
h
p
e
ti
a
n
,
a
n
d
S
.
H
.
Ho
ss
e
in
ian
,
“
VSC
-
HV
DC
c
o
n
tro
ll
e
r
p
a
ra
m
e
ter
tu
n
i
n
g
b
a
se
o
n
o
p
ti
m
iza
ti
o
n
,
”
i
n
Ira
n
ia
n
C
o
n
fer
e
n
c
e
o
n
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
,
Ja
n
u
a
ry
2
0
1
1
.
[3
2
]
R.
M
a
jd
o
u
l,
E
.
Ab
d
e
lmo
u
n
im,
M
.
Ab
o
u
lfata
h
,
a
n
d
A.
Ab
o
u
l
o
ifa,
“
Th
e
P
e
rfo
rm
a
n
c
e
c
o
m
p
a
ra
ti
v
e
o
f
b
a
c
k
ste
p
p
i
n
g
,
slid
in
g
m
o
d
e
a
n
d
P
ID
c
o
n
tr
o
ll
e
r
s
d
e
sig
n
e
d
f
o
r
a
sin
g
le
-
p
h
a
se
in
v
e
rter
UPS
,
”
2
0
1
4
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
M
u
lt
ime
d
ia
C
o
mp
u
ti
n
g
a
n
d
S
y
ste
ms
(ICM
CS
)
,
2
0
1
4
,
p
p
.
1
5
8
4
-
1
5
8
9
,
d
o
i:
1
0
.
1
1
0
9
/ICM
C
S
.
2
0
1
4
.
6
9
1
1
3
1
0
.
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