Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l. 10
, No
. 1, Febru
a
r
y
2
020, pp
. 22
~
3
4
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v10
i1
.p
p22
-34
22
Jo
urn
a
l
h
o
me
pa
ge
: http://ijece.iaesc
o
re
.c
om/index
.
php/IJ
E
CE
Impact of LCC–HVDC multiter
minal on generator rotor
angle stability
Oluwa
f
emi
E
.
Oni, Andrew G.
Sw
a
n
so
n, Rudiren
Pillay
Ca
rpanen
Discipline
of
El
e
c
tri
cal
,
Ele
c
tron
i
c
and
Com
puter
E
ngineering, Un
iversity
of
Kwa
Zulu-Nat
al,
S
out
h Africa
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Ja
n
2, 2019
Rev
i
sed
Ap
r
24
, 20
19
Accepted
Jun 26, 2019
Multitermin
al H
i
gh Voltag
e
Dir
ect Cu
r
r
ent (HVDC) transmission utilizing
Line Commutated Converter (LCC-HVDC) technolog
y
is on th
e incr
ease
in
inter
c
onnecting
a remote gener
a
ting stat
ion to
an
y
urban cen
t
re via long
distance DC lines.
This Multiterm
inal-HVDC (MTDC) s
y
stem offers
a redu
ced
right
of way
b
e
ne
fi
ts,
reduc
tion
in
tra
n
sm
ission losses, as
well
as
robust power controllab
ility
w
ith en
h
a
nced s
t
ability
marg
in. However,
utili
zing th
e M
T
DC s
y
stem
in
an AC networ
k bring about
a new area of
as
s
o
ciat
ed fault
anal
ys
is
as
well as
the effec
t
on the entir
e AC s
y
s
t
em
during
a
tr
ansient faul
t condition
.
This paper
anal
yses t
h
e
fau
lt current
contribut
ion
of an MTDC sy
s
t
em during transient fau
lt to the r
o
tor angle of a s
y
nchronous
generator. The r
e
sults show a high rotor ang
l
e swing during a tr
ansient f
a
ult
and the eff
ect
i
v
enes
s
of fas
t
power s
y
s
t
e
m
s
t
abilizer
c
onnect
ed to
the gen
e
ra
tor aut
o
m
a
tic vol
tage
r
e
gula
t
or in d
a
m
p
ing the s
y
stem
oscilla
tions.
The MTDC link improved the s
y
stem
performance b
y
provid
i
ng
an al
terna
tiv
e p
a
th of power tr
ans
f
er and qui
c
k
s
y
s
t
em
recov
e
r
y
du
ring
transien
t fau
lt th
us increasing
th
e rat
e
a
t
which
t
h
e s
y
st
em
oscill
ations wer
e
damped out. Th
is shows great improvement co
mpared to when
power was
being
transm
itte
d via
AC l
i
nes.
K
eyw
ords
:
MTDC system
Sho
r
t circu
it R
a
tio
Th
yr
istor
co
nver
t
er
s
Transien
t stab
ility
Vol
t
a
ge
de
pe
n
d
ent
c
u
rre
nt
o
r
d
e
r li
m
iter (VDC
OL)
Copyright ©
202
0 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Oluwafem
i E. Oni,
Discipline
of E
l
ectrical, Electroni
c a
n
d C
o
m
put
er E
n
gi
nee
r
i
n
g
,
Uni
v
ersity of
Kwa
Zul
u
-Natal,
23
8
M
azi
si
Ku
nene
R
d
, Gl
en
wo
o
d
, D
u
r
b
a
n
40
4
1
, So
ut
h
A
f
ri
ca.
Em
a
il: max
i
p
h
e
m
@yah
oo
.com
1.
INTRODUCTION
An
i
n
crease i
n
d
e
m
a
n
d
for electricity h
a
s b
r
o
ugh
t
Sou
t
h
e
rn
African
po
wer u
tilities in
to
p
l
ann
i
ng
to
ex
p
a
nd
their tran
sm
issio
n
corridor
u
tilizin
g
M
u
ltite
rmin
al High
Vo
ltag
e
Di
rect Cu
rren
t
(HVDC)
Transm
issio
n
.
Th
is Mu
ltitermin
al–
H
VDC
(MTDC) is
not
o
n
l
y k
e
y in
t
h
e in
tegration
o
f
ren
e
wab
l
e en
erg
y
suc
h
as
wi
n
d
f
a
rm
s and s
o
l
a
r
par
k
s
,
b
u
t
al
s
o
t
h
e
de
pl
oy
m
e
nt
o
f
di
st
ri
b
u
t
e
d
gene
rat
o
rs i
n
t
o
t
h
e
gri
d
. It
i
s
al
so
i
m
p
o
r
tan
t
for larg
e-scale in
terreg
i
on
al
po
wer tran
sm
is
sio
n
[1
]. Th
is will h
e
lp
brin
g
abo
u
t
a
sm
art,
eco-frie
ndly a
n
d
decent
r
alized powe
r sy
stem
.
Being
a regi
on with relativel
y weak i
n
terc
onnections a
nd high
su
scep
tib
ility t
o
a tran
sien
t fau
lt, th
e
prop
er an
alysis n
e
ed
s to
b
e
m
a
d
e
to
g
i
v
e
p
o
wer syste
m
p
l
an
n
e
rs and
en
g
i
n
eers seekin
g
t
o
u
tilize t
h
is MTDC
syste
m
m
o
re un
derstand
ing
o
f
th
e im
p
act o
n
g
e
n
e
rator
ro
t
o
r ang
l
e
stab
ility. Maj
o
r setb
acks o
f
ex
cessiv
e
u
s
ag
e o
f
HVDC syst
e
m
s are th
e co
n
cern
asso
ciated
with
th
e reliab
ility
an
d in
teracti
o
n with AC
n
e
t
w
o
r
k
s
, in wh
ich
th
e
g
e
n
e
rator i
s
a m
a
j
o
r reci
pien
t [2
, 3
]
. During
a
system
fau
lt,
t
h
e g
e
ne
rat
o
r l
o
ses a
l
a
r
g
e a
m
ount
o
f
po
we
r, a
n
d t
h
i
s
i
m
p
act
t
h
e e
n
t
i
r
e i
n
t
e
rc
on
nect
ed
sy
st
em
as wel
l
as ot
her
connected sync
hr
onous m
achines.
MTDC system can adopt
either
th
yristor con
v
e
rter tech
no
log
y
(LC
C
-HVDC
) or
th
e Insu
lated
B
i
pol
ar
Ju
nct
i
o
n
(
I
GB
T
s
) V
o
l
t
a
ge So
urce
C
o
n
v
ert
e
r
(VS
C
-H
VDC
)
tec
h
n
o
lo
gy
[4
, 5]
.
While
V
S
C
p
r
o
v
ide
s
AC net
w
orks
with robust
n
ess and fu
ll controllability of
AC active and r
eactive powe
r
,
but the ca
pa
city of
th
e av
ailab
l
e so
lid
-state d
e
v
i
ces with
tu
rn
-o
ff cap
ab
ility
are li
m
i
ted
an
d
still req
u
i
res sp
ecially co
n
f
igu
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
El
ec &
C
o
m
p
En
g
ISS
N
:
2
0
8
8
-
87
08
Imp
a
ct o
f
LCC–
HVDC
mu
ltit
ermina
l
o
n
g
e
nera
to
r ro
t
o
r
ang
le stab
ility (Olu
wa
femi E.
On
i)
23
Direct Cu
rre
nt (DC)
b
r
eake
r
s
to isol
ate the c
o
nve
r
ter during a DC line
fa
ult [6
]. Un
lik
e
VSC HVDC, research
st
udi
es
ha
ve s
h
ow
n t
h
at
LC
C
HV
DC
sy
st
em
i
s
l
e
ss susce
p
t
i
bl
e t
o
DC
l
i
n
e
faul
t
wi
t
h
t
h
e
use
of c
o
nve
nt
i
onal
DC lin
e pro
t
ectio
n
and
rug
g
e
d
con
t
ro
ller [7
-9
]. Th
is co
nv
erter tech
no
log
y
h
a
s th
e cap
a
b
i
l
ities o
f
with
stan
d
i
n
g
hi
g
h
p
o
w
e
r a
n
d v
o
l
t
a
ge rat
i
n
gs f
o
r
bul
k p
o
w
er t
r
a
n
sm
i
ssi
o
n
. A
lthou
gh
w
ith
ob
stacles
suc
h
as; reactive power
co
nsu
m
p
tio
n
an
d
cases
o
f
commu
tatio
n
failu
re
d
u
ring
a fa
u
lt, ho
wev
e
r, th
is tech
no
log
y
still
h
a
s th
e larg
est
fo
ot
p
r
i
n
t
wi
t
h
m
a
ny
poi
nt
-t
o
-
p
o
i
n
t
i
n
st
al
l
a
t
i
ons
, and t
h
re
e M
T
DC
l
i
nk arou
n
d
t
h
e gl
obe
. A
n
Exam
pl
e i
s
th
e 19
20
M
W
,
±533
kV Caho
ra Bassa
po
int to
po
in
t in
terco
n
n
ection
link
i
ng
Mo
zam
b
i
q
u
e
and
So
u
t
h
Africa;
while that
of
MTDC are the 8 GW
Nort
h-Ea
st Agra s
y
ste
m
(fo
ur term
in
als in
th
ree co
nv
erter statio
n
s
),
30
0 M
W
, 2
0
0
kV
Sar
d
i
n
i
a
-C
orsi
ca
-
I
t
a
l
y
sy
st
em
, and t
h
e
2,
00
0 M
W
, ±
4
5
0
k
V
Hy
dr
o
Q
u
ébec
–
N
ew
En
gl
an
d
syste
m
[10-13]
.
Research on
LCC HVDC sho
w
s th
at t
h
e stab
ility
lev
e
l d
e
p
e
nd
s predomin
an
tly o
n
t
h
e Effective
Sh
ort
C
i
rc
ui
t
R
a
t
i
o
(ESC
R
)
of t
h
e AC
gri
d
[1
4-
1
6
]
.
The
fi
rst
i
m
pact
i
s
seen i
n
t
h
e f
r
e
que
nt
occ
u
rre
n
ce of
co
mm
u
t
at
io
n
failu
re at th
e in
v
e
rter station
d
u
ring
an
y syste
m
d
i
stu
r
b
a
n
c
es lead
in
g
to
po
wer o
s
cillation
s
of
th
e syn
c
hro
nou
s g
e
n
e
rato
r, wh
ich
can
fu
rt
h
e
r lead
to to
tal syste
m
co
llap
s
e du
e to
th
e in
ab
il
ity o
f
th
e conv
erter
statio
n
to
recover fro
m
the dis
t
urbances
. Power system
s are
oft
e
n s
u
b
j
ect
ed
t
o
di
f
f
e
r
ent
de
grees
an
d sev
e
rities o
f
fau
lts as a
resu
lt
o
f
o
c
cu
rren
ces su
ch
as; ad
v
e
rse
weat
h
e
r con
d
ition
s
lead
ing
to
l
o
ss of
t
r
ansm
i
ssi
on l
i
ne, fl
as
ho
ve
r d
i
schar
g
e, o
r
su
dde
n l
o
ss
of
load, etc. The
r
e is a need
for power system planne
rs
t
o
carry
o
u
t
a
sel
ect
ed set
of cont
i
n
genci
e
s
anal
y
s
i
s
on t
h
e sy
st
em
for pr
o
p
er desi
gn
and sm
oot
h
-
r
u
nni
n
g
o
p
e
ration
of the syste
m
. Th
e en
tire system
i
s
said
to
b
e
tran
sien
tly stab
le
wh
en
it h
a
s t
h
e ab
ility to
m
a
in
tain
sy
nch
r
o
n
i
s
m
when
s
u
b
j
ect
ed
t
o
a t
r
ansi
e
n
t
di
st
ur
bance
[
1
7,
18]
.
The long-esta
b
lishe
d m
e
thod of a
d
dressing tra
n
si
ent sta
b
ility has bee
n
by
using a
n
Aut
o
m
a
tic
Vo
ltag
e
Regu
l
a
to
r
(AVR),
wh
ich
h
e
lp
s in
co
n
t
ro
lling
th
e electro
m
a
g
n
e
tic t
o
rq
u
e
o
f
th
e
syn
c
h
r
o
nou
s
g
e
n
e
rator. Th
e ex
citatio
n syste
m
with
Po
wer System
St
abilizers is als
o
adde
d to
offe
r a
quick res
p
ons
e in
ad
ju
sting
th
e fi
eld
cu
rren
t supp
lied
du
ri
n
g
fau
lt to
m
a
tc
h
th
e g
e
n
e
rat
o
r cap
a
b
ility [1
9, 20
]. Differen
t
FACTS
devi
ces s
u
ch a
s
St
at
i
c
Sy
nchro
n
ous C
o
m
p
ensat
o
r (S
TATCOM), Static Var Co
m
p
en
sato
r (SVC), Thyristo
r
C
ont
r
o
l
l
e
d Se
r
i
es C
o
m
p
ensat
o
r
(TC
S
C
)
, ca
paci
t
o
r
ba
nks
et
c. were
di
sc
usse
d i
n
[
2
1,
22]
as
ot
he
r m
eans
of
en
h
a
n
c
ing
po
wer system
stab
i
lity. Ken
n
é
et al
. i
n
[
2
3]
pr
o
pos
ed
an
ada
p
t
i
ve n
o
n
l
i
n
ear
e
x
ci
t
a
t
i
on c
o
nt
r
o
l
f
o
r
fast respon
se an
d
d
a
m
p
in
g
ou
t o
f
o
s
cillatio
n
s
du
ri
n
g
a tran
sien
t d
i
st
u
r
b
a
n
ce on
th
e synch
r
on
ou
s g
e
n
e
rato
r.
Al
so,
O
n
i
and
M
b
an
g
u
l
a
i
n
[
2
, 8
,
2
4
]
ob
ser
v
ed t
h
at
a p
o
i
n
t
-
t
o
-
poi
nt
HV
DC
schem
e
gi
ves an e
nha
nce
d
cri
t
i
cal
clearin
g
tim
e
wh
en
in
tegrated
in
to
an
AC network, wh
ich
in
tu
rn
im
p
r
oves th
e g
e
n
e
rator ro
t
o
r ang
l
e as well
as th
e en
tire
vo
ltag
e
p
r
ofile.
A
repo
rt
on
M
T
DC state
o
f
th
e art con
t
ro
l
strateg
y
an
d co
nv
erter arch
it
ectu
r
e
was
gi
ve
n i
n
[
25]
.
Ji
an
g a
n
d
Ekst
r
o
m
i
n
[2
6
]
gave
an
analy
s
is of LCC MT
DC system
s in reducing t
h
e i
m
pact
of a
gr
ou
n
d
fa
ul
t
on s
u
b-t
r
a
n
sm
i
ssi
on an
d d
i
st
ri
but
i
o
n net
w
o
r
k
.
T
h
ey
fo
cuse
d o
n
t
h
e c
o
n
v
e
r
t
e
r res
p
o
n
se o
f
t
h
e M
T
DC
l
i
n
k ne
gl
ect
i
n
g t
h
e sy
nc
hr
o
n
o
u
s
ge
nerat
o
r
res
p
o
n
se
of
t
h
e
AC
net
w
o
r
k
.
Vasq
uez
-
A
r
ne
z
et al
.
in
[2
7
]
co
v
e
r
bo
th
the conv
ert
e
r respo
n
s
e as
well as th
e synch
r
on
ou
s
g
e
nerato
r
resp
on
se
in
th
eir an
alysis o
f
dy
nam
i
c
m
odel
l
i
ng o
f
LC
C
–
M
T
DC
sy
st
em
i
n
an
AC
net
w
or
k,
b
u
t
fai
l
e
d
t
o
co
nsi
d
e
r
t
h
e
AC
net
w
o
r
k
st
ren
g
t
h
u
s
ing
Sho
r
t Ci
rcu
it Cap
acity (SSC)
with
reg
a
rd
s t
o
t
h
e
en
tire
n
e
two
r
k stab
ility
m
a
rg
in
, an
d its effect o
n
the interc
onnec
t
ed sync
hronous m
achine.
In
o
r
d
e
r
to
en
h
a
n
ce
t
h
e tran
sien
t
stab
ility
marg
in
of
an
AC n
e
twork,
th
is pap
e
r g
i
v
e
s
t
h
e pe
rf
orm
a
nce eval
uat
i
o
n
of a t
h
r
ee-termin
al HVDC mo
d
e
l im
p
l
e
m
en
ted
on
Sing
le
Mach
in
e Infin
i
te Bu
s
(
S
MI
B)
n
e
twor
k, an
d r
e
su
lts
w
e
r
e
ob
tain
ed
th
ro
ugh
sim
u
latio
n
s
an
alysis
o
n
PSC
AD. Two case st
u
d
i
es were
co
nsid
ered
; the first scen
ari
o
in
vo
lv
ed
usin
g
MTDC
syste
m
in
p
a
rallel with
AC
lin
e to
in
terco
n
n
ect
th
e infin
ite
b
u
s
with th
e sy
n
c
hrono
u
s
g
e
n
e
rato
r,
wh
ile
th
e seco
nd
scen
ario in
vo
lved rep
l
acin
g
t
h
e MTDC lin
k
with
ano
t
h
e
r AC lin
e to
mak
e
a do
ub
le AC tran
sm
issi
o
n
circu
it lin
kin
g
th
e syn
c
hro
nou
s g
e
n
e
rat
o
r
with
th
e in
fi
n
ite b
u
s. Th
e
resu
lts o
f
wh
ich
were an
alysed
to d
e
term
in
e wh
ich
system
h
e
lp
ed
i
n
alleviatin
g
th
e eff
ect
o
f
th
e t
h
r
e
e-
phase shor
t cir
c
u
it f
a
u
lt on
t
h
e sy
n
c
hr
onou
s
g
e
n
e
r
a
tor
.
An
im
p
r
ov
emen
t o
f
in
cor
p
o
r
ating
a vo
ltag
e
co
n
t
r
o
ller
i
n
to
two
of
t
h
e conver
t
er
station
s
,
p
r
ef
er
ab
ly th
e in
v
e
r
t
er
s, w
e
r
e
also
i
m
p
l
e
m
en
ted
.
Th
e Sho
r
t Circu
it Ratio
(SCR
) of th
e
AC n
e
t
w
ork and
th
e co
n
t
ro
l setup
o
f
th
e DC co
nv
erters t
o
avoi
d re
occu
rr
i
ng com
m
ut
at
ion
fai
l
u
re
du
r
i
ng t
h
e m
ode
l
l
i
ng of t
h
e
M
T
DC
l
i
nk
were al
l
t
a
ken i
n
t
o
consideration. The fa
ult curre
nt co
nt
ri
b
u
t
i
on
of eac
h c
o
n
v
e
r
t
e
r wi
t
h
respect to t
h
e interconnected AC
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r
has b
een anal
y
s
ed
. The p
o
w
er s
w
i
ng e
quat
i
on
us
i
ng eq
ual
area
cri
t
e
ri
on
was u
s
ed i
n
anal
y
s
i
ng t
h
e
m
a
xim
u
m
power t
r
a
n
sfe
r
a
nd t
h
e
faul
t
c
l
eari
ng a
ngl
e
t
o
al
l
o
w t
h
e g
e
nerat
o
r
dam
p
er an
d
p
r
o
t
ectio
n circu
it to
work
effectiv
ely in
stabilizin
g
th
e en
tire syste
m
.
Th
e
o
r
g
a
n
i
zatio
n of t
h
e
p
a
p
e
r fo
llows
Sectio
n 2 an
alysin
g th
e sho
r
t ci
rcu
it ratio
and
sh
ort circu
its
l
e
vel
of t
h
e A
C
net
w
o
r
ks
w
h
i
l
e
Sect
i
on 3
gi
ves t
h
e
ge
ne
rat
o
r
AVR
m
odel
l
i
ng an
d co
nt
r
o
l
.
Sect
i
on
4 gi
ves
th
e ro
tor an
g
l
e stab
ility an
aly
s
is o
f
th
e sy
n
c
h
r
on
ou
s m
ach
in
e
u
s
ing
eq
u
a
l
area criterio
n
. Th
e system
m
o
d
e
l
and
sy
st
em
param
e
t
e
rs are p
r
esent
e
d i
n
Sect
i
on
5
whi
l
e
Se
ct
i
on
6
gi
ves t
h
e re
sul
t
s
a
n
d
di
scussi
o
n
. Se
ct
i
on
7
fi
nal
l
y
pre
s
ent
s
t
h
e c
oncl
u
si
o
n
an
d c
ont
ri
b
u
t
i
ons
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
24
2.
E
net
w
o
in
terc
mech
a
SCL
o
AC/
D
side
o
The
h
stren
g
in
cre
a
Wher
e
freq
u
e
th
e c
o
th
e n
e
th
e A
C
th
an
I
angl
e
th
e s
y
th
e i
n
syste
m
chara
c
E
lec & C
o
m
p
E
SC
R ANA
L
The ESC
R
o
rk
.
Th
e
r
a
ti
o
c
onn
ection
.
A
a
n
i
cal in
ertia.
In
(1
) - (
2
o
f a
n
ac s
y
st
e
D
C system
is
o
o
f the
H
VDC
h
arm
oni
c
fi
l
t
e
g
th
b
y
i
n
jecti
n
a
se t
h
e T
h
eve
n
e
Q
f
(in
M
V
e
ncy
,
an
d
Q
a
o
nve
rt
er st
at
i
o
n
Usi
ng t
h
e
etworks at
t
h
C
/DC n
e
two
r
k
Mo
st MT
D
I
max
(m
a
x
im
u
m
γ
(the
m
a
rg
i
y
st
em
condi
t
i
o
n
crease must
b
m
vol
t
a
ge, or
a
c
teristi
c
wh
ic
h
En
g, V
o
l
.
10
,
L
YSIS
R
analysis is
o
o
f
S
C
t
o
t
wea
k
AC
sy
) fr
o
m
Figur
e
e
m.
W
h
en
th
e
o
bt
ai
ne
d [
2
8]
.
links are
co
n
e
rs beha
v
e
l
i
n
g t
o
o
m
u
ch
r
n
i
n
e
qui
val
e
n
t
V
AR) is
the
r
a
(in M
V
AR
)
n
.
active powe
r
h
e in
it
ial
s
t
a
g
k
. AC
syste
m
Tab
l
SCR value
SCR > 3
2 < SCR < 3
SCR < 2
D
C sche
m
e
s
t
m
rated curre
n
i
n of c
o
m
m
u
t
o
n, an inc
r
eas
i
b
e b
e
lo
w th
e
m
a
ny
ot
he
r
net
w
h
will
rep
r
ese
n
,
No
. 1, Feb
r
u
used
i
n
AC
/
t
h
e
D
C
pow
e
ste
m
can be
t
e
1 use
t
h
e T
h
SC
L of
the s
y
Whe
n
the r
e
a
n
si
dere
d, t
h
e
i
ke s
h
u
n
t
c
a
p
r
eactive pow
e
t
i
m
pedance
a
Fi
gu
re 1.
A
C
r
eactive pow
e
)
is th
e rea
c
r
(M
W) ratin
g
g
e of pl
anni
n
st
rengt
h i
n
r
e
l
l
e 1
.
SCR
in
d
i
Ef
f
ect o
n
Str
ong g
r
In
ter
m
e
d
functio
n
a
Weak n
sy
nchr
o
n
t
hat ar
e curre
n
n
t o
f
th
e conv
e
t
ation) that c
a
n
g
ex
tin
ctio
n
m
a
x
i
m
um
po
w
w
or
k dat
a
o
f
F
n
t th
e
m
a
x
i
m
u
u
ar
y 20
20
:
2
2
/DC sy
ste
m
e
r rating (P
d
c
t
erm
e
d as a
s
h
e
v
eni
n
equi
v
a
y
st
em
i
s
di
vi
d
a
ctiv
e p
o
wer
g
ESCR o
f
th
e
p
acitors
at f
u
e
r in
t
o
th
e A
C
a
t th
e fun
d
a
m
e
C/
DC system
e
r contrib
u
ti
o
c
tive power
o
g
of H
VDC li
n
n
g. The w
o
r
s
t
l
ative to DC
p
i
cato
r
fo
r A
C
/
n
AC/DC networ
k
r
id with lit
tle or
n
d
iate gr
id s
t
r
e
ngt
h
a
l OLTC o
r
stati
c
n
etwork that re
q
n
ous con
d
e
nser
o
r
n
tly in
serv
ic
e
erters), say
a
t
a
n be vari
ed
b
angle (
γ
) can
w
er curve an
d
F
i
gure
2, a d
e
u
m power cur
v
2
-
34
in
teractio
n
t
o
c
)
of a c
o
n
v
e
y
ste
m
with
h
a
len
t
im
p
e
d
a
n
d
ed
with
rate
d
g
ene
r
ator and
e
entire AC/
D
u
ndam
ental f
r
C
n
e
twor
k du
r
e
ntal fre
quen
c
in
t
e
r
c
onn
ect
i
o
n fr
om
t
h
e
h
o
f an
y ad
d
iti
n
k, a power
u
t
case of S
C
p
ower t
r
a
n
sm
i
t
/
DC netw
o
r
k
s
k
n
o-
fault occur
r
e
n
h
,
r
e
quir
e
voltag
e
c
VAR
co
m
p
ens
a
q
uires stron
g
V
A
r
ST
A
T
COM
e
are desi
gne
d
t
poi
nt
(
i
n
=1.
0
b
etween 15
o
bri
n
g ab
out
a
d
not above.
T
f
in
ite v
a
lu
e o
f
v
e.
o
d
e
term
in
e
t
h
e
rt
er gi
ves t
h
i
gh s
h
ort
ci
r
c
n
ce t
o
calcula
t
d
DC po
wer
,
t
h
arm
onic filt
e
D
C
line gover
n
r
eque
ncy
t
h
e
r
i
n
g a
di
st
u
r
b
a
c
y o
f
th
e A
C
s
on
h
arm
onic filt
e
o
nal
shunt
c
a
u
tilit
y ca
n
est
i
R has t
o
be
t
ted i
s
i
ndi
cat
e
st
re
ngt
h
c
e
e
control ability l
a
to
r
A
R gener
a
tor
,
l
to operat
e n
o
0
p.u
),
due
t
o
t
h
t
o 18
o
. Unle
s
an
increase in
a
T
hus, f
o
r a g
i
f
SCR will b
r
i
ISS
N
:
2
he st
re
ngt
h
o
h
e SCR o
f
a
c
ui
t
im
pedanc
t
e the short
c
i
t
he
sh
ort
ci
rc
u
e
rs connecte
d
n
ed
by
(3) is
r
eb
y r
e
du
cin
g
a
nc
e [
29]
.
Th
i
s
yst
e
m
.
(
(
(
e
rs at
the fu
n
c
apacitors co
n
i
mat
e
th
e S
C
R
used i
n
im
p
e
d i
n
Tabl
e 1
l
ike
l
ike
o
rm
ally at a
p
t
hei
r
co
nst
a
nt
s
s changes ar
e
active power.
i
ve
n sy
st
em
i
m
i
n
g
about a u
n
2
088
-87
08
o
f t
h
e AC
a
n AC
/
D
C
e a
nd l
o
w
rcu
it lev
e
l
u
it ratio
of
to
th
e
AC
ob
tain
ed
.
g
th
e
g
r
id
i
s
t
e
nds
t
o
(
1)
(
2)
(
3)
n
da
m
e
n
t
a
l
n
nec
t
ed t
o
R
val
u
e of
p
l
e
men
tin
g
[
28]
.
oi
nt
l
o
wer
ex
tin
ctio
n
e
mad
e
to
Ho
wever
,
m
pedance
,
n
iqu
e
P
d
-I
d
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
E
3.
G
(PSS
)
orde
r
typ
e
t
h
Excit
a
th
e r
e
overc
u
is fed
4.
R
with
a
tran
s
m
th
e to
t
Fo
llo
w
p
artic
u
The
s
in
(6)
th
e s
p
E
lec & C
o
m
p
Im
Fi
g
G
ENERAT
O
Sy
nchro
n
o
)
, and the ge
n
to
m
a
in
t
a
in
g
t
hat
i
n
cl
udes
a
a
ti
on Lim
i
t
e
r
e
ference level
u
rre
nt
[2
2,
31
into the
PSS
w
R
OTO
R
AN
G
The Single
M
a
const
a
nt
fi
e
l
m
iss
i
o
n
lin
e.
T
t
al line reacta
n
w
in
g a th
ree
-
ul
ar faul
t
e
d l
i
s
wi
ng equ
a
t
i
o
n
. Int
e
grat
i
ng (
p
eed de
vi
at
i
o
n
Eng
Im
pa
ct
of
LC
C
g
ure 2.
Active
O
R MO
DEL
L
o
us g
e
nerat
o
r
n
erator itself.
G
g
enerator s
t
at
o
a
PSS and an
A
(OEL). The
U
and t
h
e O
EL
, 32
]. Figu
r
e
3
w
h
i
ch
is in
tu
r
Fi
gure 3.
IE
E
G
LE STABI
L
M
a
c
hi
ne In
fi
n
l
d vol
t
a
ge, l
i
n
k
T
he
system
e
n
ce.
P
e
equal
s
-
p
hase t
o
gro
i
ne dr
ops
t
o
z
e
n
in
co
n
s
id
er
a
7
)
gi
ves
(
8
),
t
n
m
u
st
becom
e
I
S
C
–
H
VDC mul
t
p
o
we
r – DC
c
L
IN
G AN
D
C
cont
r
o
l
m
o
d
G
enerating pl
a
o
r vol
t
a
ge.
T
h
A
VR
[30]
.
I
t
a
U
EL prevent
s
h
e
lp
s to
p
r
e
v
3
shows the
P
r
n use
d
i
n
da
m
E S
T
4
A
ex
c
i
t
L
ITY
n
ite Bu
s (SMI
B
k
ed to an infi
n
qui
val
e
nt
eq
u
s
P
ma
x
at
δ
=90
0
u
nd
f
a
u
lt
on
e
ro
an
d
hen
c
e
a
tio
n
to
th
e
i
n
t
hus
f
o
r a
st
ab
e
zero t
o
gi
ve
t
SSN
:
208
8-8
7
t
it
ermina
l o
n
g
c
ur
rent
c
h
a
r
a
c
C
ON
TR
O
L
d
el co
n
s
ists o
f
ants are
equi
p
h
e ex
citatio
n
a
l
s
o equi
pped
s
loss of syn
c
v
en
t th
e g
e
n
e
r
P
SS connecte
d
m
pi
ng out
os
c
i
t
ation syste
m
w
B) sy
ste
m
in
n
ite b
u
s
with
u
at
i
on i
s
gi
ve
n
0
, corresp
on
di
any of
the
t
e
P
m
will b
e
h
i
n
ertia co
n
s
ta
n
l
e
ope
rat
i
on,
t
t
he cri
t
e
ri
on
fo
7
08
g
e
n
erat
or
rot
o
c
teristics wit
h
f
th
e ex
c
ita
ti
o
p
ped wi
t
h
Au
t
s
yste
m
u
s
ed
i
with
an
Un
d
e
c
hro
n
i
s
m
wh
e
r
at
or fr
om
ov
e
d
to the excite
r
i
ll
ati
ons d
u
ri
n
g
w
ith
AVR an
d
Fi
gure 4
[
30]
c
onst
a
nt
fre
q
u
n
in
(4
, 5
)
,
w
ng t
o
m
a
xim
u
t
ransm
i
ssi
on
l
i
gher t
h
at
P
e
l
n
t
H
and t
h
e
c
t
he de
vi
at
i
on
o
fo
r stab
ilit
y in
o
r ang
le
stab
i
re
spect to S
C
o
n syste
m
,
P
o
t
omat
ic Vo
lt
a
i
n
th
is m
o
d
e
l
er
-Ex
c
itatio
n
L
e
n the excitat
i
e
rheating d
u
ri
n
r
. The shaft s
p
g
power syste
m
d
PSS
1A stab
i
,
con
s
ists o
f
a
u
e
n
cy and vo
l
w
here
P
e
is th
e
u
m
power t
r
a
n
l
ines, the
po
w
l
e
a
di
ng t
o
an
i
c
hange i
n
an
g
o
f
roto
r an
gle
(9) [3
0]
.
i
lity (Olu
wa
fe
m
C
R l
e
v
e
l
o
wer Sy
stem
a
ge R
e
gul
at
or
is
th
e bu
s-fe
d
L
im
it
er (UEL
)
i
on vol
t
a
ge
fa
i
ng
lo
ng
-
t
er
m
p
eed from
th
e
e
m
di
st
urbanc
e
i
lise
r
a
sy
nchr
on
ou
s
l
tag
e
m
a
g
n
itu
d
e ter
m
in
al
P
o
n
sf
er duri
n
g st
e
w
er
tr
a
n
s
m
i
t
t
e
i
ncrease roto
r
g
ula
r
speed
ω
δ
m
u
st
be bo
u
m
i E.
On
i)
25
Stabilizer
(AV
R
) in
d
thyristo
r
)
and Over
a
lls
b
e
lo
w
ex
cita
tio
n
e
generat
o
r
e
.
s
generat
o
r
d
e via two
o
we
r,
X
t
is
e
ady sta
t
e.
e
d by
t
h
at
angle (
δ
).
ω
o
i
s
gi
ven
u
nded
,
i.e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
n
t J Elec & C
o
m
p
Eng
,
Vo
l.
1
0
,
N
o
.
1
,
Febru
a
r
y
20
20
:
22 -
34
26
Fi
gu
re
4.
Eq
ui
val
e
nt
SM
IB
n
e
t
w
o
r
k
sin
(4)
(5)
sin
(6)
(7)
(8
)
0
(9
)
0
(1
0)
0
(1
1)
0
(12
)
Consi
d
er a three-phase s
h
ort circu
it fault of zero fa
ult react
ance bei
ng
a
p
plied at line L2 of the SM
IB
net
w
or
k sh
o
w
n i
n
Fi
g
u
re
4,
and t
h
e
faul
t
i
s
cl
eared by
i
s
o
l
at
i
ng t
h
e faul
t
e
d l
i
n
e wi
t
h
a ci
rcui
t
brea
ker
.
Usi
n
g
the equal area
criterion, a powe
r – angle
(Pe-
δ
)
di
ag
ra
m
used i
n
un
derst
a
ndi
ng t
h
e basi
cs rel
a
t
i
ons
hi
p
betwee
n the
ge
nerat
o
r ac
celerating
po
we
r a
n
d its rotor a
n
gle accordi
n
g to
(10), the
net
w
ork conditions
before
(2 lines i
n
o
p
e
ration
)
,
du
rin
g
(th
r
ee
-p
hase
fault o
n
l
i
n
e
L2)
,
an
d
post
-
faul
t
(l
i
n
e L
2
out
of se
rvi
c
e
)
was
ev
alu
a
ted
.
Th
ese resu
lts will
g
i
v
e
t
h
e stab
ility li
mit o
f
th
e
syste
m
b
y
weig
h
i
n
g
th
e m
a
x
i
m
u
m
ro
to
r ang
l
e
of
t
h
e sy
st
em
. From
Fi
gure 5,
d
u
ri
ng a st
abl
e
ope
rat
i
n
g st
at
e, t
h
e sy
st
em
i
s
bo
un
de
d by
a
r
ea A
1
(a
bco
)
,
a faul
t
on the system
will shift the
steady-state condition from
point ‘a’ to po
int
‘b’, causi
ng t
h
e rotor t
o
accelerate
u
n
til op
erating p
o
i
n
t
c is reach
e
d
b
ecau
s
e Pm>Pe, th
e op
er
atin
g
po
in
t wi
ll th
u
s
sh
i
f
t to
p
o
i
n
t
b
after the fau
l
t
has bee
n
cleared at
δ
ct1, ca
using a decelera
ting roto
r angle. The
kinetic energy ga
ine
d
by the rotor
from
area
A1
is th
en
d
i
ssip
ated
to
area
A2
(od
e
f) th
us sh
ifting
fu
rth
e
r th
e o
p
e
ratin
g
p
o
i
n
t
fro
m
‘d
’ to
‘e’, su
ch
th
at
δ
has
reache
d
its maxim
u
m
value
δ
m
,
and if a
r
ea A1 is e
q
ua
l to area A2
,
the rotor be
gi
ns to
decelera
t
e and
the operating
poi
nt follows t
h
e pat
h
of e to d accordi
ng t
o
Pe-
δ
di
a
g
ra
m
.
The am
pl
itude
of t
h
e osci
l
l
a
t
i
ons
redu
ces
with
t
h
e h
e
lp of a d
a
m
p
er ci
rcu
it; oth
e
rwise, it co
ntin
u
e
s t
o
o
s
cillate with
a
con
s
tan
t
am
p
litu
d
e
[33
]
.
Howe
ver,
with a prolonge
d
fault clear
ing ti
me, the cle
a
ring angle will reach
δ
ct2
, th
e ro
to
r an
g
l
e
operating point will reach poi
nt ‘e’ leading to an unexp
ended
kinetic e
n
ergy which results in a
continuous
increase of the rotor speed and angle (
P
e
<P
m
beyond ‘e’).
This will
cause the pre-fault area
A1
(
abc
ˊ
o
ˊ
) to
b
e
greater than
post-fault area
A2
(
o
ˊ
d
ˊ
e
ˊ
) (1
1), th
is ev
en
tu
ally l
ead
s to
lo
ss of
syn
c
h
r
on
is
m
[3
4
,
35
].
GS
X
ˊ
d
E
t
P
e
X
tr
X
l1
X
l2
X
t
=X
tr
+ X
ˊ
d
+ (
X
l1
//
X
l2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
El
ec &
C
o
m
p
En
g
ISS
N
:
2
0
8
8
-
87
08
Imp
a
ct o
f
LCC–
HVDC
mu
ltit
ermina
l
o
n
g
e
nera
to
r ro
t
o
r
ang
le stab
ility (Olu
wa
femi E.
On
i)
27
Fi
gu
re 5.
Pe –
δ
d
i
ag
ram
for
b
o
t
h
stab
le and un
stab
le system
co
n
d
itio
n
A sim
u
l
a
t
i
on resul
t
of t
h
e SM
IB
net
w
ork
duri
n
g t
h
e t
h
re
e-phase faul
t
at
ci
rcui
t
2 for 0.
07s i
s
sho
w
n i
n
Fig
u
r
e 6. Th
is
syste
m
reco
rd
ed
a slo
w
d
a
m
p
in
g
o
f
ro
tor ang
l
e o
s
cilla
tio
n
s
wh
en th
e g
e
n
e
rato
r u
s
es a con
s
tan
t
field
su
pp
ly. AVR with
ou
t PSS g
e
n
e
rato
r con
t
ro
l m
o
d
e
w
itn
essed
a second
swing
in
stab
i
lit
y. Wh
ile AVR with
PSS gene
rator
control setup
gi
ves
a positive fast da
m
p
ing re
sult.
Fi
gu
re
6.
Ge
ne
rat
o
r
r
o
t
o
r a
ngl
e f
o
r
SM
IB
sy
s
t
em
duri
n
g
7
0
m
s faul
t
5.
SYSTE
M
MO
DEL
The Single Machine Infinite Bus (SMIB) sy
ste
m
cons
idered in the
research
w
o
rk
has th
e param
e
ters
of t
h
e SM
IB
sy
st
em
used i
n
[30]
. The t
r
ansm
i
ssi
on sy
stem
has been ext
e
nded t
o
i
n
c
l
ude a paral
l
e
l t
h
ree-
ter
m
in
al th
yris
to
r con
v
e
rter co
n
f
igu
r
atio
n with
a p
a
rallel AC lin
e as shown
in Figu
re
7. In o
t
h
e
r t
o
e
v
a
l
u
a
t
e
th
e
p
e
rform
a
n
ce of th
is MTDC syste
m
o
n
the g
e
n
e
ra
t
o
r
tran
sien
t stab
ility
, a 2
4
k
V
,
22
2
0
M
V
A
sy
nchr
on
ou
s
g
e
n
e
rato
r
was
m
o
d
e
lled
wit
h
altern
ato
r
sup
p
lied
ex
citer with
Ef
max
and
Ef
min
i
ndepen
d
ent
of t
h
e t
e
rm
i
n
al
voltage. The exciter was IEEE type AC4A exciter with
IEEE PSS1A sta
b
ilizer for damping out oscillations
duri
n
g t
h
e sy
stem
di
st
urbance
.
Each conve
rt
er’s cont
r
o
l
l
e
r param
e
t
e
rs rat
e
d, and act
ual
p
o
wer t
r
ans
f
er and DC
line specifica
tions are s
h
own
in Table
2
,
while th
e g
e
n
e
rato
r ratin
g
s
an
d
AC lin
es sp
ecificatio
n
are sho
w
n in
t
h
e Tabl
e 3. The M
T
DC
cont
rol
l
e
r
m
odel
s
used resem
b
l
e
t
h
at
of t
h
e convent
i
onal
poi
nt
-t
o
-
poi
nt
sy
st
em
whi
c
h
has bee
n
di
scussed i
n
[1
2,
25
, 3
6
]
wi
t
h
m
odi
fi
cati
on m
a
de t
o
t
h
e PI
an
d t
h
e V
D
C
O
L c
o
nt
rol
pa
ram
e
t
e
rs t
o
obt
ai
n a desi
red V-I charact
er
i
s
t
i
cs of t
h
e co
nvert
er. Th
e re
ct
i
f
i
e
r
convert
e
r
i
s
on current
cont
rol
m
ode
whi
l
e
t
h
e i
nvert
ers ar
e capabl
e
of
s
w
i
t
c
hi
ng bet
w
e
e
n v
o
l
t
a
ge c
ont
rol
m
ode or c
u
rrent
co
nt
rol
m
ode
based
on
s
y
st
e
m
condi
t
i
on. The
INV_1
sub
s
tati
o
n
with
ex
tin
ct
io
n
an
g
l
e
γ
=
γ
o
cont
rol
s
and de
fi
nes t
h
e vol
t
a
ge l
e
vel
of t
h
e
ent
i
r
e
net
w
or
k whi
l
e
al
l
ot
her subst
a
t
i
ons i
n
are curre
nt
cont
rolled
m
ode. A central
m
a
s
t
er co
ntroller was used for
powe
r-sha
ri
ng
and cur
r
ent
ba
l
a
ncer bet
w
een al
l t
h
e convert
ers, and t
h
e rect
i
f
i
e
r st
at
i
on rat
e
d
m
oderatel
y
t
o
cater for the
power transf
e
r
t
o
bot
h i
n
vert
ers.
a
b
c
d
c
ˊ
d
ˊ
e
e
ˊ
P
δ
(de
g
)
P
m
δ
0
δ
ct
1
δ
ct
2
δ
m
δˊ
uns
t
a
bl
e
P
e
– p
r
e
f
a
u
lt
P
e
– p
o
s
t
f
a
u
l
t
P
e
– d
u
r
i
n
g
fa
u
l
t
o
o
ˊ
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
n
t J Elec & C
o
m
p
Eng
,
Vo
l.
1
0
,
N
o
.
1
,
Febru
a
r
y
20
20
:
22 -
34
28
Fi
gu
re
7.
Paral
l
el
M
T
DC
sy
st
em
em
bedde
d i
n
AC
Net
w
or
k
m
odel
Tabl
e
2. M
T
D
C
co
nve
rt
er
pa
ram
e
t
e
rs
Rect.
I
nv-
1
I
nv-
2
Rated/Actual power
(MW
)
2000/
120
0
1000/
700
1000/
500
Rated/Actual DC c
u
rrent (kA)
4.
0/2.
4
2.
0/1.
4
2.
0/1.
0
SCR
2.
5
3
2.
5
AC voltage (
k
V)
450
450
500
γ
0
(
i
nver
t
er
)
15
15
T
r
ansform
e
r per
6
pulse thy
r
istor
s
Rating (
M
VA)
1200
700
600
Voltage (
k
V)
500/2
5
0
500/2
5
0
500/2
5
0
Leakage re
actance
(pu)
0.
18
0.
18
0.
18
PI
Contr
o
ller
Pr
opor
tional Gain
1.
0989
1.
5363
1.
5363
I
n
tegr
al ti
m
e
constant (
s
)
0.
0109
2
0.
0152
4
0.
0152
4
VDCOL
T
h
r
e
shold input
0.
4-
1.
0
0.
4-
0.
9
0.
4-
0.
9
T
h
r
e
shold output
0.
55-
1.
5
0.
55-
1.
0
0.
55-
1.
0
DC T
r
ans
m
ission line (
T
-
m
odel)
L
i
ne 1
L
i
ne 2
R(
Ω
)
1.
5
2.
5
Reactor (H)
0.5968
0.5968
DC filter (uF
)
15
26
Tabl
e
3.
Ge
ner
a
t
o
r a
n
d t
r
a
n
s
m
i
ssi
on l
i
n
e
pa
ram
e
t
e
rs
Sy
nchr
onous m
a
chine
data
Genr
ator
Data
AVR and PSS
Ra (
pu)
0.
003 pu
I
nput signal
Speed
Xp (
pu)
0.
130 pu
T
R
0.
015
sec
Xd (
pu)
1.
81 pu
Vim
a
x
10 pu
Xd
ˊ
(
pu)
0.
3 pu
Vim
i
n
-
10 pu
Xd
ˊˊ
(
pu)
0.
23 pu
K
A
200
pu
Td
o
ˊ
8.
0 sec
E
f
m
a
x
7.
0 pu
Td
o
ˊˊ
0.
0294 (
s
)
E
f
m
i
n
-
6
.
4
pu
Xq 1.
76
pu
K
ST
A
B
9.
5
Xq
ˊ
0.
65
pu
T
W
1.
41
sec
Xq
o
ˊˊ
0.
25
pu
T
1
0.
154
sec
Tq
o
ˊ
1.
0
(
s
)
T
2
0.
033
sec
Tq
o
ˊˊ
0.
07
(
s
)
V
st
ma
x
0.
2
H 3.
5
(
s
)
V
st
min
-0
.2
AC T
r
ans
m
ission line (
500kV base)
L
i
ne 1
L
i
ne 2
R (
pu/m
)
0.
012
0.
012
X
(
pu/m
)
0.
12
0.
12
B
(
pu/m
)
2.
0
2.
0
AC
Gr
i
d
I
dc
1
I
dc
3
I
dc
2
Ex
t
G
r
i
d
_
2
T
a
p_R
ec
t
.
T
a
p_i
nv
1
T
a
p_i
nv
2
AC
Gr
i
d
Ex
t
G
r
i
d
_
1
Ge
n
Sy
nc
G
e
n
4x
55
5 M
V
A
A
V
A
V
A
V
A
V
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
El
ec &
C
o
m
p
En
g
ISS
N
:
2
0
8
8
-
87
08
Imp
a
ct o
f
LCC–
HVDC
mu
ltit
ermina
l
o
n
g
e
nera
to
r ro
t
o
r
ang
le stab
ility (Olu
wa
femi E.
On
i)
29
6.
SIMULATION RESULTS
To investigate the im
pact of MTDC
syste
m
on power syste
m
rotor an
g
l
e
stab
il
ity, a so
li
d
th
ree-p
h
a
se
sh
o
r
t circu
its fau
lt was ap
p
lied
at th
e
RECT
,
INV_1
, and
INV_2
su
b
s
tatio
ns o
n
e
after th
e
o
t
h
e
r an
d
th
e critica
l
clearing time
T
c
was recorde
d
.
The generat
o
r
powe
r
o
u
t
put
, r
o
t
o
r an
gl
e, gen
e
rat
o
r speed, e
x
ci
t
e
r fi
el
d vol
t
a
ge,
and t
h
e sy
nc
h
r
oni
zi
ng
t
o
rq
u
e
are t
h
e m
a
j
o
r
obser
vat
i
o
n
of t
h
i
s
st
u
d
y
.
These pa
ram
e
t
e
rs, i
n
cl
udi
n
g
P
e
–
δ
d
i
ag
ram
,
were d
e
p
i
cted
o
n
a su
bp
lo
t to
i
llu
str
a
te s
y
ste
m
perf
orm
a
nce before, duri
n
g
,
and
aft
e
r t
h
e faul
t peri
od.
DC
power
, vol
t
a
ge and curre
nt
were al
so ill
ust
r
at
ed on
a
pl
ot
t
o
anal
yse t
h
e convert
er current
cont
ri
b
u
t
i
o
n
d
u
r
ing
and
after th
e fau
lt co
nditio
n
o
f
th
e syste
m
.
Aft
e
r appl
y
i
ng
faul
t
at
sim
u
l
a
ti
on t
i
m
e
t=2
s
, i
t
was found o
u
t
t
h
at
IN
V
_
1
l
i
nki
ng sy
nchro
n
o
u
s
g
e
n
e
rato
r with
INV_2
h
a
s th
e least cri
tica
l
cl
e
a
rin
g
ti
m
e
T
c
=0.0
81s,
whi
l
e
t
h
e generat
o
r b
u
s and t
h
e
INV
_2 b
u
s
has a cl
ear
i
ng t
i
m
e
of 0.11s an
d 0.1
8
s respect
i
v
ely
.
Sol
u
t
i
on t
i
m
e
st
eps of 50
μ
s and cha
n
n
e
l
pl
ot
st
ep of 50
0
μ
s
were u
s
ed
in
co
m
p
u
tin
g
th
e resu
lts.
Fi
gure
8 sh
ows
t
h
e act
i
v
e and
react
i
v
e power
out
p
u
t
fr
om
t
h
e sy
nchro
n
o
u
s
generat
o
r.
Fr
o
m
t
h
i
s
pl
ot
,
a disturbance on the weakest
INV_1
bus res
u
l
t
e
d i
n
a
l
a
rge drop i
n
t
h
e act
i
v
e power ge
nera
t
e
d from
1750
M
W
to 280M
W
,
which result in
the incr
ease o
f
the reactive
powe
r
supplied
to the system
. The oscillations
g
e
n
e
rated
were q
u
i
ck
ly d
a
mp
ed
ou
t with
th
e h
e
lp
o
f
th
e MTDC VDCOL co
n
t
ro
ller wh
ich
act as a fau
lt
m
i
nim
i
zer. This shows the syst
e
m
is transiently stable.
The DC
po
we
r, cu
rrent
a
n
d
vol
t
a
ge are s
h
own
i
n
Fi
gure
9 t
o
Fi
gu
re
1
1
. F
r
om
Fi
gur
e 9, t
h
e
faul
t
caused t
h
e VD
C
O
L cont
rol
l
e
r t
o
reduce t
h
e current
or
der t
o
al
l
o
w
m
i
nimum
power fl
o
w
across t
h
e convert
er.
As al
so seen in Fi
gures 10 a
nd 1
1
, t
h
e current
shoot
abo
v
e 5kA w
h
i
l
e
t
h
e vol
t
a
ge dips do
wn t
o
-2
00
kV
,
howe
v
er,
wi
t
h
VDC
OL set
p
o
i
n
t
,
t
h
e M
T
DC
sy
stem
onl
y recorde
d
a hi
gh cu
rrent
i
n
fl
ow d
u
e t
o
t
h
e current
cont
ri
but
i
o
n
fr
om
t
h
e t
h
ree co
nvert
ers
but
rec
o
rde
d
no
co
m
m
u
t
at
io
n
failu
re at th
e two
in
verters.
Fi
gu
re 8.
Sy
nc
hr
o
n
o
u
s ge
nera
t
o
r p
o
we
r out
p
u
t
Figu
re
9.
DC
p
o
we
r ac
ro
ss th
e three
co
n
v
ert
e
rs
Figure
10. MT
DC c
u
r
r
ent
Fi
gu
re 1
1
. DC
vol
t
a
ge
f
o
r
t
h
e
t
h
ree
c
o
nve
rt
er
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
n
t J Elec & C
o
m
p
Eng
,
Vo
l.
1
0
,
N
o
.
1
,
Febru
a
r
y
20
20
:
22 -
34
30
R
o
t
o
r angl
e dy
nam
i
cs can b
e
seen i
n
Fi
gure 12 f
o
l
l
o
wi
ng a t
h
ree-pha
se short
ci
rcuit
s
faul
t o
n
th
e
INV_1
b
u
s.
A c
h
an
ge o
f
operat
i
n
g
p
o
i
n
t
was
obser
ved,
causi
ng
t
h
e g
e
nerat
o
r
rot
o
r
angl
e
δ
to accelerate
until it reached its
m
a
xi
mu
m
δ
m
a
x=175
o
, t
h
e poi
nt
ab
ove
whi
c
h t
h
e sy
st
em
s beco
m
e
unst
a
bl
e. Thi
s
can be i
n
t
h
e second sce
n
ari
o
w
h
ere d
o
u
b
l
e
AC
t
r
ansm
i
s
si
on l
i
n
es were used i
n
r
e
pl
acem
e
nt
of
t
h
e M
T
DC
sy
st
em
.
The generat
o
r
havi
ng y
i
el
ded i
t
s
excit
a
ti
on cont
r
o
l
,
and
wi
t
hout
sup
p
l
em
ent
a
ry
cont
rol
l
e
r suppo
rt
from
th
e MTDC l
i
n
k
,
cau
sed
th
e
syn
c
h
r
on
ou
s
mach
in
e to
lo
se its s
t
ab
i
lit
y
at th
e firs
t s
w
in
g
.
Th
e g
e
n
e
rato
r
ex
citat
i
o
n
v
o
ltag
e
in
Fig
u
re 13
also
fo
llo
ws
th
e sa
m
e
co
n
d
itio
n
o
f
a stab
le o
p
e
ratin
g stat
e d
u
r
ing
MTDC lin
k
interconnection. It,
however,
becam
e
unstable duri
ng the
second sce
n
ario of
double AC circuits replacem
e
nt.
Th
is cau
sed
th
e syn
c
h
r
o
n
o
u
s
mach
in
e
to
h
a
v
e
y
i
eld
e
d
al
l
its
co
n
t
ro
llin
g
cap
ab
ilit
y l
ead
in
g
to
th
e fie
l
d
v
o
ltag
e
swi
ngs bet
w
ee
n i
t
s
VFmin
an
d
VFmax
val
u
e
of -6.
4
and 7.
0
pu respect
i
v
el
y
.
Thi
s
was not
so when M
T
D
C
li
nk
was in
op
eratio
n
as th
e syste
m
m
a
in
ta
in
ed
its
stab
il
ity wi
th
p
o
s
itiv
e d
a
m
p
in
g
of o
s
cillatio
n
s
.
Fi
gure
12.
Sy
n
c
hro
n
o
u
s ge
ner
a
t
o
r rot
o
r an
gl
e
response (deg)
Fi
gure
13.
Sy
n
c
hro
n
o
u
s ge
ner
a
t
o
r exci
t
e
r fi
eld
vol
t
a
ge (p
u)
The rot
o
r an
g
u
l
a
r speed i
n
Fi
gure 14 d
u
ri
ng M
T
DC
lin
k interconnection recorded a
n
increase in
freq
u
ency
up t
o
38
0.8
r
ad/
s
t
h
ereaft
e
r di
ppi
ng d
o
w
n
t
o
37
3.5 rad/
s. Thes
e swi
ngs were qui
ckl
y
dam
p
ed out
from
t
h
e second and su
bseq
u
e
nt
osci
l
l
at
i
ons of t
h
e rot
o
r an
gl
e. The sam
e
generat
o
r an
gu
l
a
r speed exper
i
ence
t
h
e sam
e
di
st
urbance wi
t
h
t
h
e second scen
ari
o
of
do
ubl
e
AC
t
r
ansm
i
s
si
on l
i
n
es. Thi
s
caused t
h
e ge
nerat
o
r
speed t
o
i
n
cr
ease t
o
382.8
r
ad/
s
whi
c
h f
u
rt
her l
e
d t
o
an une
xpan
d
e
d
ki
net
i
c
energy
whi
c
h res
u
l
t
s
i
n
a continuous increase of the
rotor s
p
eed and angle (
P
e
<P
m
) and t
hus t
o
l
o
ss of sy
nch
r
oni
sm
due t
o
lack o
f
decelerating torque to
reduce
the rotor s
p
eed.
Fi
gure 1
5
an
d Fi
gure 1
6
sh
o
w
t
h
e Pe –
δ
di
agram
for t
w
o case st
udy
of M
T
DC
sy
st
em and d
o
u
b
l
e
AC
tran
s
m
iss
i
o
n
lin
es resp
ectiv
ely. Fro
m
Fig
u
r
e 1
5
,
fo
llo
wing
a fau
lt at t=2
s
, th
e activ
e p
o
w
er was ob
serv
ed
to
d
i
p
t
o
28
0M
W
at
δ
=70
o
.
Whe
n
t
h
e fault was
cleared at t=2.081s, a
s
h
arp inc
r
ease of active
powe
r
was obs
e
rved,
reaching a maxim
u
m
value
P
emax
=2300M
W, an
d
δ
max
=175
o
. Thi
s
pl
ot
al
so sho
w
s
bo
un
ded
pos
t
-faul
t
oscillations, with the system
r
e
turning
to its pre-fa
ult stead
y state conditio
n.
This shows that the pre-faul
t and
post
-fa
ul
t
boun
ded area
A
1
and
A
2
respectively
are of equal or less a
cce
lerating power
(
i
.e. A
1
– A
2
≤
= 0
).
Fi
gure
16
sh
o
w
s t
h
e seco
nd
scenari
o
of
5
0
0
k
V
do
ubl
e
circuits AC transmissi
on lines used, instead of
t
h
e M
T
DC
l
i
nk, i
n
i
n
t
e
rco
nnect
i
ng t
h
e i
n
fi
ni
t
e
busses
t
o
t
h
e sy
nchron
ous
genera
t
o
r. Thi
s
pl
ot
shows
a continuous increase of
the
rotor angle above
δ
ma
x
=175
o
at firs
t swing with the continuous oscillation o
f
the active power (
P
ac
) b
e
tween
±2
00
0
M
W.
Th
is o
s
cillat
i
o
n
ten
d
s
to
red
u
ce in
a
m
p
litu
d
e
b
u
t
at an
ex
ceed
in
g
l
y
large rotor angle degree. This re
sult fro
m
lo
ss of synchronizing eff
ect from
both the AVR and PSS which
cau
ses th
e g
e
nerato
r to
lo
se syn
c
h
r
on
is
m
with
su
b
s
equ
e
n
t
o
s
cilla
tio
n
s
an
d
th
e ad
d
itio
n
a
l i
m
p
e
d
a
n
ce ad
d
e
d
to
the syste
m
w
h
ich resulted in a
m
o
re weakened gr
i
d
st
rengt
h l
eadi
ng t
o
t
h
e cascading of the entire
SM
IB
net
w
or
k
.
Fi
gure 1
7
sho
w
s t
h
e generat
o
r o
u
t
put
vol
t
a
ge com
p
ared
to its reference value. The gen
e
rator used wa
s
set
t
o
a const
a
nt
reference va
l
u
e of 1.
01
pu.
It
can be obse
r
ved t
h
at
fol
l
o
wi
ng t
h
e faul
t
,
t
h
e
m
achi
n
e
out
p
u
t
voltage deviates from
its
reference value but is eventual
l
y
set
t
l
i
ng t
o
a st
eady
st
at
e val
u
e. The sy
nchro
n
i
zi
ng
t
o
rque i
s
show
n i
n
Fi
gure 18.
It
can be observed t
h
at
fol
l
o
wi
ng t
h
e faul
t
,
t
h
e sy
nchroni
zi
n
g
t
o
rque ex
peri
ences
a di
p du
ri
ng
faul
t
,
but
i
t
t
h
en i
n
creases aft
e
r a faul
t
ha
s been cleared and the electri
ca
l torque is eventually
sett
lin
g
to
a n
o
rmal
i
zed reference value.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
El
ec &
C
o
m
p
En
g
ISS
N
:
2
0
8
8
-
87
08
Imp
a
ct o
f
LCC–
HVDC
mu
ltit
ermina
l
o
n
g
e
nera
to
r ro
t
o
r
ang
le stab
ility (Olu
wa
femi E.
On
i)
31
Fig
u
r
e
14
. Synch
r
on
ou
s g
e
n
e
rato
r
sp
eed
(
r
a
d/s)
Fi
gure 15. Gen
e
rat
o
r
Po
wer – angl
e
(Pe-
δ
) di
agram
duri
ng s
t
abl
e
condi
t
i
on
Fig
u
r
e
16
. G
e
ner
a
to
r
pow
er
– an
g
l
e (
P
e-
δ
)
d
i
ag
ram
d
u
ring
un
stab
le con
d
itio
n wh
ile using
2
x50
0kV
AC
circu
its (MTDC lin
k
ou
t of serv
ice)
G
e
n
e
ra
t
o
r S
p
e
e
d
(
r
a
d
/
s)
Active Power
(MW
)
Evaluation Warning : The document was created with Spire.PDF for Python.