Int
e
rna
t
i
o
na
l
J
o
u
r
na
l
of
Pow
e
r
El
ec
tro
n
i
c
s a
nd D
r
i
v
e
Sys
t
e
m
(
I
J
P
EDS
)
V
o
l.
11
, No
. 2, Ju
n
e
20
20
, pp
. 89
5
~
90
6
IS
SN
:
208
8-8
6
9
4
,
D
O
I
:
10.115
9
1
/ijp
e
d
s.v
11.
i2
.p
p
8
9
5
-9
0
6
8
95
J
o
urna
l h
o
m
e
p
a
g
e
:
h
t
tp
:
//i
jpe
d
s.ia
esc
o
re
.co
m
Enhancement of cascaded
multi-lev
e
l VSC
STA
T
CO
M
performance us
i
n
g ANN in
the pres
ence of faults
Mo
hamad M
A
l
melia
n
1
, Iz
z
e
ld
in
I Moh
d
2
,
Ab
u
Z
a
har
i
n
A
h
m
a
d
3
,
M
o
ha
m
e
d
A
O
m
ra
n
4
,
Mo
ha
me
d Sal
e
m
5
,
Awa
ng
Ju
so
h
6
, Tol
e
Su
ti
kn
o
7
1
,
2,
3,
4
F
aculty
of E
l
ec
tric
al and
El
ectron
i
cs
En
gin
e
e
r
in
g, Un
iv
ers
i
ti M
a
lays
ia
P
a
h
a
n
g
(UM
P
),
M
a
la
y
s
ia
5
S
c
ho
ol of
Elect
rica
l and
Ele
c
tro
n
ic
En
gin
e
er
i
ng, Universi
t
i
Sain
s Ma
l
a
y
s
ia
, Ma
lay
s
i
a
6
S
c
h
ool o
f
El
ectric
a
l Eng
i
ne
erin
g,
Un
iv
ersi
ti Tek
nolog
i Ma
lays
ia
,
M
a
lays
ia
7
De
pa
rt
me
nt
of
E
l
ec
t
r
ic
a
l
En
gine
e
r
in
g, Fac
u
lt
y
of Ind
u
stri
al
T
e
c
hno
lo
gy
,
Un
ive
r
sita
s Ah
m
a
d
Da
h
l
a
n
, In
do
ne
si
a
Ar
ti
cl
e Info
ABS
T
R
A
CT
Art
i
cl
e hi
sto
r
y
:
R
e
c
e
i
v
ed
N
ov 8, 2
0
1
9
Re
v
i
se
d
J
a
n
7,
2
020
A
c
c
e
p
t
e
d
Feb
1
5
, 2
020
A sy
stem can b
e
d
i
s
t
u
r
bed in ter
m
s o
f
s
t
ab
ility
when
conn
ec
ted
to a nu
m
b
er
of lo
a
d
s
at th
e
d
i
stribu
tion
en
ds
o
r
w
h
en
s
u
b
j
ected
to
fau
l
ts
. To
rev
e
rs
e
such
sys
t
ems
to
a
s
t
ab
le st
ate, F
A
CTS
d
e
v
i
ce
s
s
u
ch
as
s
t
atic
sy
nch
r
ono
us
c
o
mpen
sa
tor (S
TA
TCOM
) are
u
s
ed. In
th
is
pa
p
e
r, a
cas
caded
mul
t
i-level
voltag
e
sou
r
ce
c
onv
erter
(VS
C
) S
T
ATCO
M
w
a
s d
e
signed
and
i
m
plem
ented
with
a
no
ve
l
sp
ace
v
e
cto
r
pu
lse
width
mo
du
lation
(S
VP
W
M
)
sch
e
m
e
.
Art
i
fi
cia
l
ne
ura
l
n
e
twor
k (ANN) c
o
ntro
lle
r wa
s
use
d
i
n
st
ea
d
of i
n
ste
a
d
o
f
Pro
p
o
r
tion
al-In
t
e
gral
(P
I) con
t
ro
ller
in
the
p
r
op
o
s
ed s
c
hem
e
to
i
m
p
r
ov
e
th
e
res
p
o
n
s
e
t
i
me
(
R
T)
an
d
p
e
rfor
m
an
ce
of
S
T
A
T
COM
in
t
e
rms
o
f
p
o
w
e
r
fa
cto
r
(P
F
)
and vo
lta
ge amp
l
itud
e
d
u
r
in
g pe
rio
d
s
o
f
vo
ltag
e
s
a
g.
D
u
ring
th
e
imple
m
ent
a
tio
n
,
tw
o faul
t
sou
r
c
e
s (s
in
gle
-
lin
e
-
t
o
-
grou
nd
(S
LG
)
and
line-
to
-
line (
L
L)
fau
lts) were u
s
ed
to
cr
eate v
o
l
t
age
s
a
g. S
T
ATCO
M
was s
u
b
j
ected
to
p
e
rfo
rman
ce
ev
alua
tio
n
in
th
e p
r
esenc
e
of
th
es
e d
i
st
urb
a
nces
vi
a
M
A
T
L
AB sim
u
la
t
i
o
n
in
IE
EE 3
-
bu
s sy
st
e
m
.
Th
e o
u
t
c
ome
of t
h
e
si
m
u
la
tio
n
stu
d
ies sho
w
ed
t
h
e
A
NN con
t
ro
ll
e
r
to
p
e
rfo
rm
bet
t
er th
a
n
P
I
as it
was able to
ra
p
id
l
y
recover
vol
t
a
g
e v
a
lue
(
<1
c
y
cl
e
)
wi
th
unit
y
PF.
Ke
yw
o
r
d
s
:
AN
N c
ont
r
o
l
l
e
r
Ca
sc
ad
e
d
H
-
b
r
i
d
g
e
t
h
re
e-lev
e
l
VS
C
S
T
ATC
O
M
PI
con
t
r
o
ll
er
SV
PW
M tech
niq
u
e
V
o
lta
g
e
sag
Thi
s
i
s
an open
access
ar
t
i
cl
e under the
CC BY-SA
licens
e
.
C
o
rres
p
o
n
di
n
g
Au
t
h
or:
Mohamad M Almelian,
Fa
cu
l
t
y
of Ele
c
t
r
i
c
a
l
an
d Ele
c
t
r
on
i
c
s Eng
i
n
e
eri
n
g
,
Un
iv
e
r
s
iti M
a
lay
s
ia
P
a
h
a
n
g
(UM
P
),
2
660
0
Pek
a
n,
Pa
h
a
n
g
,
M
a
l
a
ysi
a
.
Ema
il: A
l
ma
lya
n
84@
gma
i
l
.
c
o
m
1.
IN
TRODUC
TI
ON
A
s
a
n
on lin
e
a
r sy
ste
m
, t
h
e
po
w
e
r
sy
ste
m
co
n
s
ist
s
of d
i
ffer
e
n
t
typ
e
s
o
f
m
a
c
h
in
es t
h
a
t
r
e
pre
s
en
t th
e
lo
a
d
s [1
-3]
.
The
v
o
l
t
a
g
e
stab
ili
ty
of a
po
w
e
r
sy
st
em i
s
a
f
f
e
c
t
e
d
wh
en
ev
e
r
th
e
sy
st
em i
s
d
o
min
a
te
d by
f
a
u
lts
an
d
wh
e
n
su
ch
inst
ab
il
ity
is pr
o
l
o
n
g
e
d
,
t
h
er
e
c
o
u
l
d
b
e
da
ma
g
e
s to t
h
e ma
ch
i
n
e
s
c
o
nn
ec
te
d
to
th
e syste
m
.
Th
er
efo
r
e
,
t
h
e
sy
ste
m
n
e
ed
s
to
b
e
re
st
ore
d
t
o
its i
n
itia
l sta
t
e
wi
th
in
a
s
hort
t
i
me
. W
ith
th
e
rap
i
d
in
cr
ease
in
po
we
r el
ect
ro
n
i
cs depl
oy
me
n
t
,
t
h
e
r
e i
s
a
ne
ed f
o
r
p
o
w
er
ne
tw
or
ks
i
m
pr
ove
ment
usi
n
g
F
A
CTS
c
o
ntr
o
ll
e
r
s
.
S
T
ATC
O
M
is
a
m
on
g
t
h
e
F
A
CTS
de
vi
ce
s
use
d
i
n
d
i
st
r
i
buti
o
n
net
w
o
r
ks
f
o
r
p
o
w
er
fac
t
or
a
n
d
vol
ta
ge
re
gu
la
ti
o
n
[4
].
A
STA
T
C
O
M
is t
o
b
e
co
st
-effe
ct
iv
e
a
n
d
cap
a
b
le
o
f
r
e
ac
tin
g
ra
p
i
d
l
y to lo
ad ch
an
g
e
s as it
h
a
s
VS
C
a
s
o
n
e of
it
s
ma
jor
c
o
mp
one
n
t
s.
Owi
ng
to
t
h
e
possi
bi
li
t
y
of
m
u
l
t
i
-
l
e
v
e
l
VS
C
,
i
t
has
be
en
wide
l
y
us
ed
a
s
an
a
l
t
e
rn
a
tiv
e to t
r
an
sfor
me
rs [5
-7
]. The 3 co
mmon top
o
l
og
ie
s ap
pro
v
e
d fo
r
mu
l
ti-
le
v
e
l VSC
-
b
a
se
d
S
T
ATC
O
M
a
r
e
ca
sc
a
d
e
d
to
p
o
l
o
gy
,
f
l
yi
ng
c
a
p
ac
it
or
t
o
p
o
l
o
gy
, a
nddi
ode
c
l
amped
t
o
p
o
lo
gy
a
n
d
am
o
n
g
t
h
e
s
e
to
po
log
i
es
, mo
re a
tte
n
tion
h
a
s b
een
g
i
v
e
n
to ca
sc
a
d
e
d
H-b
r
idg
e
inve
rt
er b
e
cau
se
it
is e
a
s
y to
c
o
n
t
r
o
l,
ha
s
mo
dul
a
r
i
t
y
,
a
nd
re
qu
i
r
e
s
l
e
ss n
u
m
b
e
r
of
com
p
o
n
e
n
t
[
4
,
8]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN:
2088
-86
94
In
t
J
Po
w
Ele
c
&Dr
i
S
y
st, Vo
l. 11
, No
. 2
,
June
20
20
: 895
–
90
6
89
6
A ST
ATC
O
M
ha
s
i
t
s
c
ont
r
o
l
al
gori
t
h
m
as t
h
e
m
o
st vi
ta
l
c
o
m
p
o
n
e
n
t
as i
t
i
s
invol
ved i
n
d
y
n
ami
c
re
a
c
t
i
v
e
po
w
e
r
c
o
n
t
ro
l. Th
e b
e
st
co
mp
en
satio
n
e
f
f
e
ct
c
a
n
b
e
ob
t
a
i
n
ed by
pr
op
e
r
c
o
n
t
r
o
l
o
f
the
S
T
ATC
O
M
[9-
11]
.
C
onv
en
tio
n
a
lly,
a S
T
ATC
O
M
is c
o
n
t
ro
lle
d
by
a
PI
con
t
ro
l
l
e
r
;
se
v
e
ra
l
w
o
r
k
s exi
s
t o
n
th
e
con
t
r
o
l
of
S
T
STC
O
M
usi
n
g
P
I
co
nt
r
o
l
l
e
r
s.
I
n
[
1
2,
1
3
]
,
p
r
obl
em
s
of
p
o
we
r
q
u
al
i
t
y
suc
h
as
vol
t
a
ge
sa
g
a
n
d
TH
D
wer
e
a
d
d
r
esse
d
usi
n
g
SP
WM
a
n
d
PI
c
ont
r
o
l
l
e
r
-
b
ased
S
T
ATCO
M
mo
d
e
l
.
I
n
a
not
her
wo
rk
,
a
n
A
C
a
n
d
DC
si
de
mat
h
ema
t
i
c
a
l
mo
de
l
of
a t
h
re
e-p
h
ase
AC
-
D
C
VSC
was
de
ri
ved
an
d
d
q
-
axi
s
cu
rre
n
t
a
n
d
DC
v
o
l
t
a
g
e
co
nt
rol
we
re
c
a
r
r
i
e
d
o
u
t
wi
th
a
P
I
c
o
nt
r
o
l
l
e
r
[1
4
]
.
A
PI
c
ontr
o
ll
er
de
sig
n
fo
r
a
S
T
ATC
O
M
was
gi
ve
n
b
y
[1
5,
16
]
f
o
r
i
m
pr
o
v
eme
n
t
of
P
F
a
nd
v
o
lt
a
g
e fl
u
c
t
u
at
io
n.
I
n
t
h
ese st
u
d
ie
s,
the
pa
ramet
e
r
s
o
f
P
I
c
o
ntr
o
ll
er
w
e
re
t
une
d
usi
n
g
t
h
e mat
h
emat
i
cal
mo
de
l,
mea
n
in
g t
h
at
t
h
e
st
r
u
ct
ure
o
f
PI
i
s
f
i
x
e
d
.
T
h
us,
t
h
e best
possi
ble
pe
r
f
o
r
ma
nce
f
r
o
m
a
S
T
ATC
O
M
m
i
ght
not
be
o
b
t
a
i
n
ed
f
r
o
m
de
si
g
n
e
d
c
ont
rol
l
e
rs
f
o
r
di
f
f
e
r
e
n
t
ope
rat
i
n
g
p
o
i
n
t
s
[
1
7
,
1
8
]
.
Thi
s
r
a
i
s
es
a
n
e
ed f
o
r t
h
e
de
vel
o
pme
n
t o
f
new c
o
nt
r
o
l
l
e
r
s
w
i
t
h
m
o
re
i
m
p
r
o
v
e
d
pe
rf
o
r
ma
nce
.
I
n
t
h
e
re
cent
ye
ars
,
A
NN t
e
chni
que
s ha
v
e
bee
n
si
gni
fi
cant
l
y
use
f
ul
in p
o
w
er
el
ect
ro
ni
cs f
o
r
t
h
e
mai
n
t
e
na
nc
e
of t
h
e
sta
b
ili
ty
o
f
c
o
n
v
e
r
t
er
sy
ste
m
s
ov
er
a
wid
e
ra
ng
e
o
f
op
er
at
io
n.
ANN
-ba
s
e
d
co
n
t
r
o
ll
ers a
l
so
p
r
ov
id
e f
a
s
t
dy
na
mi
c
res
p
o
n
se a
n
d the
i
r
c
ont
rol
r
e
q
u
i
r
e
s
no
mat
h
e
m
at
i
c
a
l
mo
de
l o
f
t
h
e
syste
m
.
Se
ve
ra
l st
u
d
i
e
s ha
ve
p
r
o
pos
e
d
t
h
e
a
ppl
ic
a
t
ion
of
A
N
N-
base
d c
ont
rol
of
ST
ATC
O
M
i
n
p
o
we
r
sy
ste
m
d
i
str
i
but
io
n
[
1
7
-
20
].
M
o
st of
th
e
lite
r
a
t
u
res
h
a
v
e
use
d
si
n
u
so
i
d
a
l
P
W
M
(
SPWM
)
t
e
c
h
n
i
qu
e
to
c
o
n
t
r
o
l
V
S
C sw
i
t
ch
es.
SPWM
i
s
se
en
a
s
a ma
t
u
r
e
d
tec
h
n
i
q
u
e th
a
t
y
i
e
l
d
s
l
o
w
PF c
o
mpa
r
ed
to
th
e SV
PW
M
te
ch
n
i
qu
e. A
l
t
h
oug
h
th
ese
st
u
d
ies
wer
e
r
e
l
a
ted
t
o
th
e
v
o
lta
g
e
r
e
gu
la
tion
dur
ing
f
a
u
lt o
r
i
n
c
r
e
a
sing l
o
ad
s,
no si
mul
a
t
i
o
n
st
udi
es wa
s
prese
n
t
e
d t
o
de
monst
r
a
t
e
the
pe
r
f
o
r
ma
nce
and R
T
of
c
a
s
ca
de
d 3
-
l
e
vel
VSC
S
T
ATC
O
M
i
n
con
s
i
d
er
at
io
n
o
f
P
F
am
pl
it
ude
an
d
vo
l
t
a
ge
m
a
gni
t
ude
d
u
ri
n
g
pe
ri
ods
o
f
v
o
l
t
a
ge
sag
.
Th
is
s
t
ud
y aims at
th
e d
e
sign an
d simu
lation
of
ANN-b
a
sed
cascad
e
d thr
e
e-
lev
e
l
V
S
C
S
T
ATCOM
by
em
plo
y
i
n
g t
h
e
S
V
P
W
M t
e
chni
que
ba
sed
on
m
o
d
u
la
ti
o
n
inde
x
c
ont
rol
s
t
ra
te
gy
f
o
r
mi
ti
ga
ti
ng
t
h
e
ef
fe
c
t
s of
sa
g
pr
o
b
le
m i
n
di
st
ri
b
u
t
i
on
ne
tw
or
ks.
T
h
i
s
co
mb
i
n
a
t
i
o
n
was a
i
med
a
t
a
c
hi
evi
n
g
ra
pi
d
PF
a
n
d
v
o
l
t
a
g
e
re
gu
la
ti
o
n
.
2.
ST
AT
IC SY
NC
HR
ON
OU
S
C
O
M
P
ENS
A
TOR
(S
TA
TCOM)
2
.
1
.
Con
f
i
g
u
ra
t
i
o
n
a
n
d
funda
men
t
a
l
concep
t
A
s
a
shun
t
-
c
onn
e
c
t
e
d
co
mp
ensa
to
r
d
e
v
i
c
e
,
STATCO
M is co
nn
e
c
t
ed
in
p
a
ra
ll
el
(t
h
r
ou
gh
in
te
r
f
a
c
in
g
i
n
d
u
ct
o
r
Lf
) at
t
h
e b
u
s
3 o
r
p
o
i
n
t
o
f
c
o
mmo
n co
u
p
l
i
ng
(P
C
C
)
. A
t
t
h
e
f
u
nda
ment
al
f
r
e
q
uenc
y,
it
pr
od
u
c
es 3-
pha
se
bal
a
nce
d
v
o
l
t
a
ge
se
ts
w
i
t
h
c
o
ntr
o
ll
abl
e
p
h
a
s
e
a
ngl
e
a
n
d
ma
g
n
it
ud
e
[
1
3
]
.
Fi
gu
re
1
d
e
pic
t
s t
h
e
pr
o
p
o
se
d
ST
A
T
C
O
M
sys
t
em
,
co
n
s
isti
ng
of
th
e
i
n
terfa
cin
g
in
du
ct
or
r
e
pr
e
s
en
t
e
d
as L
f
ilt
er
,
c
a
sc
a
d
ed
3
-
lev
e
l
V
S
C
(
I
G
B
T
devi
ce
s)
wit
h
Vdc
on eac
h
u
n
it
,
a
n
d
c
ont
r
o
l
str
a
t
e
gy
(
S
VP
W
M
te
ch
ni
q
u
e
an
d
c
o
nt
r
o
l
c
i
r
c
ui
t)
.
The
mai
n
pa
r
t
of t
h
e
ST
AT
C
O
M
de
vi
c
e
i
s
t
h
e
VSC
t
h
a
t
t
r
a
n
sf
or
ms
the
dc
i
n
p
u
t
i
n
t
o
a
3-
p
h
ase
out
put
vol
t
a
ge
. T
h
e re
ac
ti
ve po
we
r creat
e
d
due
to
t
h
e vol
t
a
ge d
i
ffere
n
ce
a
c
ros
s
t
h
e Lfi
s
exc
h
an
ge
d be
t
w
e
e
n
t
h
e
S
T
ATC
O
M
a
n
d the
v
o
l
t
a
ge
at
b
u
s 3.
F
i
g
u
r
e
1.
S
T
A
T
C
O
M
c
o
n
f
ig
ur
at
io
n
c
o
nnec
t
e
d
t
o
I
E
E
E
3-
b
us
syst
em
The S
T
A
T
CO
M pr
o
p
o
s
ed
i
n
t
h
i
s
st
ud
y wa
s
i
m
pl
eme
n
t
e
d
on
a 6.
6 k
V
di
str
i
but
i
o
n
ne
t
w
or
k wi
th
t
h
e
a
i
m of ac
hie
v
i
ng
v
o
l
t
a
g
e re
gul
a
t
i
on
wi
th st
eady
P
F
whe
n
t
h
ere
is v
o
lt
a
g
e fl
uct
u
at
i
o
n
(
i
nc
rea
s
e
o
r
dec
r
ease
i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Enh
a
n
c
eme
n
t o
f
cas
c
ad
ed
mu
lti-
le
v
e
l
VS
C S
T
ATC
O
M p
e
rfo
r
ma
nc
e u
s
ing
ANN
…
(
M
oh
ama
d
M
Al
m
e
l
i
a
n
)
8
97
vol
ta
ge
)
a
t
the
b
u
s
3
.
This
wa
s re
al
iz
ed
v
i
a a
c
o
n
t
i
n
u
o
u
s
va
ri
at
i
o
n
of t
h
e STSTC
O
M-ge
nera
te
d re
act
i
v
e
po
we
r
i
n
b
o
t
h
ca
paci
t
i
ve
a
n
d
i
nduc
t
i
v
e
o
p
e
r
a
t
ion
mo
des.
The
exc
h
a
nge
of
po
wer
bet
w
e
e
n S
T
ATC
O
M an
d
th
e
sy
st
em i
s
go
v
e
rn
e
d
by
(1
) a
n
d
(
2
).
In
(
1
), t
h
e v
a
l
u
e
of
P
is n
o
r
m
a
l
ly
p
o
s
i
t
iv
e
as
i
t
on
ly
a
cco
un
ts
fo
r
the
lo
s
s
es
by
mak
i
n
g
a min
i
ma
l ste
a
d
y
-
s
t
a
te
shif
t (a
s
α
=1
).
Th
i
s
s
h
i
f
t
all
o
w
s
a
c
tiv
e
e
x
chan
g
e
o
f
po
w
e
r
to
th
e
S
T
ATCOM
to
s
u
sta
i
n
l
o
sse
s-
re
la
te
d
v
o
lta
g
e
d
e
cr
e
a
ses ac
ross th
e c
a
p
a
c
i
tor
s
[2
1]
.
∗
(1)
(2)
Whe
r
e
,
V1:
V
o
lt
a
g
e
o
f
b
u
s 3,
V
2
:
VS
C
o
u
t
p
ut
vol
t
a
ge
,
XLf:
i
n
te
rfa
c
i
n
g
r
eac
t
a
nce
,
and
α
:
a
ngl
e
bet
w
ee
n V1
an
d V
2
.
2.2 C
a
sc
ade
d
mul
t
i
l
eve
l
VS
C
Mul
t
i
l
e
ve
l
V
S
C
is a
dva
nt
a
g
e
ous
as i
t
al
low
s
t
h
e
use
o
f
l
o
w
-
ra
te
d sw
it
ch
e
s
to
ge
ne
ra
te
hig
h
vol
ta
ge
[2
2],
t
h
e
r
eb
y e
l
imi
n
at
ing t
h
e
need
for ste
p
-up
t
r
a
n
s
f
orme
rs an
d co
nse
q
u
e
nt
l
y
re
d
u
ci
n
g
t
h
e wei
ght
, i
n
ve
rt
er
c
o
st,
an
d
siz
e
[
2
3
]
.
Th
eo
re
tic
a
lly
,
t
h
e n
u
mb
er
o
f
le
v
e
l
s
for
mu
lt
i-
lev
e
l VSC
is
in
f
i
n
ite
,
b
u
t
in
pr
a
c
t
i
ce
,
it
i
s
subje
c
t
to
t
h
e
com
p
l
e
xi
ty
of
t
h
e c
i
rcui
t. T
o
be
c
onsi
d
e
r
e
d
mul
t
i
-
l
e
ve
l, t
h
e
mi
ni
mu
m n
u
mbe
r
o
f
l
e
vel
s
fo
r
mult
i
l
e
v
el
V
S
C must
be 3,
i
.
e
.
+V
, 0,
a
n
d
-V.
S
e
ve
ral
st
udi
es
ha
ve
p
r
o
p
o
se
d di
ffe
r
e
n
t
mu
l
t
i
l
e
v
el
S
T
AT
CO
M
t
o
p
o
lo
gi
es
but
the
c
o
mmo
nl
y
use
d
are di
o
d
e
cl
a
m
pe
d,
H-
bri
dge
c
a
sca
d
ed
, a
n
d
ca
pa
ci
t
o
r
c
l
a
m
pe
d
i
nve
rt
e
r
s
a
n
d
ea
ch
of
t
h
es
e t
o
p
o
l
ogi
es
is
associ
at
ed
wi
th
ce
rt
ai
n a
d
va
nt
a
g
es a
n
d
c
h
a
l
le
nge
s.
Fo
r
i
n
st
a
n
c
e
, c
a
s
cade
d
mul
t
i
l
e
vel
VSC
i
s
c
ont
roll
ed
by
t
h
e
nu
mbe
r
o
f
dc
i
n
p
u
ts t
h
a
t
is
l
a
t
e
r gene
rat
e
d
a
t
t
h
e o
u
t
p
ut to
fo
rm
a st
ai
rca
s
e-li
ke
wa
ve
form. I
n
cre
a
ses
i
n
t
h
e
l
e
vel
s
of uti
l
i
zed
dc
l
e
ve
ls i
n
cre
a
ses
t
h
e
o
u
t
put
p
o
w
er a
s
mo
re st
e
p
s
wi
ll
be
re
qui
red
t
o
s
y
nt
hesi
ze
t
h
e o
u
t
put
wave
form
s.
If
Nm de
note
s
t
h
e n
u
mbe
r
o
f
H
-
b
r
i
d
ge
unit
s
, t
h
e le
vel
of
t
h
e
pha
se
-t
o-
grou
n
d
out
put
v
o
l
t
a
g
e wi
ll
be
descri
be
d by 2
N
m +
1
, whe
r
ea
s 4N
m
+
1
w
i
l
l
be
t
h
e l
e
vel
of
t
h
e p
h
ase-t
o
-
p
h
a
se out
p
u
t
v
o
l
t
a
ge[
2
3].
Fi
gu
re
2
p
r
e
s
e
n
t
s
3-
p
h
a
s
e
c
a
s
c
a
de
d
3-l
e
ve
l
ca
scade
d
VSC
STATC
O
M w
h
ic
h c
o
nsi
s
t
s
o
f
one
H
-
bri
d
ge
u
n
it
s
i
n
eac
h
p
h
a
s
e (N
o. o
f
H-
bri
dge
= (N
o.
of l
e
ve
l
-1)/
2)
for
y
i
e
l
di
ng
5 l
e
vel
pha
se-t
o-
phase
out
put
v
o
l
t
age
.
The
L-fil
t
e
r i
s
u
s
e
d
t
o
pro
v
ide
c
u
rre
n
t
ha
rmo
n
i
c
a
t
t
e
nua
ti
o
n
s
o
lut
i
o
n
i
n
a
si
mpl
e
wa
y a
n
d
he
nc
e, c
onsi
d
ered
a
fi
rst
-
orde
r
fil
t
e
r.
T
o
desi
gn
i
t
,
(3
) w
a
s use
d
.
∆
(3)
Wh
er
e
=
th
e
sw
it
ch
in
g
fre
que
n
c
y,
∆
= the
maxi
mu
m ra
te
d l
o
ad c
u
rrent
pe
ak
rip
p
l
e
w
h
ich
is 5
t
o
20
%
o
f
th
e
r
a
ted
c
u
rr
en
t
su
pp
ly
of
t
h
e
gr
id
n
e
t
w
or
k.
F
i
gu
re
2. Casc
aded
H
-
b
r
i
dg
e
th
re
e-
lev
e
l
VSC
2
.
3
SV
PWM
t
e
ch
nique
signa
l
Ma
ny
a
p
p
r
oa
c
h
es ha
ve be
e
n
pro
pose
d
f
o
r d
r
i
v
i
n
g
a
VSC
t
o
p
o
lo
g
y
usi
n
g
S
V
P
W
M.
T
h
e
tradi
t
i
onal
SV
P
W
M
i
m
pl
ement
a
t
i
o
n
ge
neral
l
y
i
n
v
o
lv
e
s
swi
t
c
h
in
g t
i
m
e cal
cul
a
t
i
on,
volt
a
ge
s
p
a
c
e
v
e
ct
o
r
est
i
mat
i
on,
se
c
t
o
r
id
en
ti
fi
c
a
ti
o
n
,
a
n
d
op
t
i
ma
l sw
itc
h
i
ng
ti
me e
s
tim
a
t
i
o
n
fo
r
ea
ch
se
c
t
o
r
. Re
g
a
rd
in
g
th
e id
e
n
ti
fi
ca
tio
n
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN:
2088
-86
94
In
t
J
Po
w
Ele
c
&Dr
i
S
y
st, Vo
l. 11
, No
. 2
,
June
20
20
: 895
–
90
6
89
8
se
ct
ors
,
i
t
ca
n
be
a
c
h
i
e
ve
d
done
vi
a
t
h
e
c
a
l
c
ul
at
i
on
o
f
t
h
e
se
ct
or
a
ngl
e
via
co
or
dina
te
t
r
ans
f
or
ma
ti
on
by
de
pl
oyi
ng
Cl
ar
ke’s t
r
ans
f
or
ma
ti
on.
A
lo
o
k
u
p
t
a
bl
e i
s
ne
e
d
ed t
o
det
e
r
m
i
n
e t
h
e s
w
i
t
c
hi
ng se
q
u
e
n
ce
f
o
r t
h
e
i
nve
r
t
e
r
l
e
gs.
I
n
t
h
i
s
pa
per
,
t
h
e a
d
o
p
t
e
d
a
p
p
r
oac
h
is
t
o
devi
ce a
sim
p
l
e
wa
y o
f
SV
P
W
M
i
m
pl
eme
n
t
a
t
i
on
an
d
t
h
e em
pl
o
y
ed
te
chni
que
i
s
w
h
ol
l
y
r
e
l
i
a
n
t o
n
the
inst
ant
a
ne
ous am
pl
it
ud
e o
f
t
h
e
re
fe
r
e
nce
pha
se
vol
t
a
ge
of
a
l
l
t
h
e
p
h
ases.
Th
ese
re
fe
rence
vol
ta
ge
s a
r
e
e
x
p
r
e
s
se
d i
n
s
p
ac
e ve
ct
o
r
s[2
4
]
. B
y
c
o
m
p
a
r
ing
t
h
e
s
e s
p
ac
e
vect
o
r
s
w
ith
P
W
M
si
gn
al
(t
ri
angu
l
a
r c
a
r
r
i
er)
,
t
h
e
app
r
op
ri
at
e pu
l
s
es o
f
SVPWM
w
ill
b
e
g
e
n
e
r
a
t
e
d
fo
r
ea
ch
i
n
v
e
rt
er
l
e
g
i
n
ea
ch
pha
se.
T
h
e
S
V
P
W
M t
e
c
hni
q
u
e
i
s
r
e
pre
s
e
n
t
e
d
i
n
t
h
e
bl
ock
di
a
g
r
a
m s
h
o
w
n
in
F
i
gu
re
3.
F
i
gur
e
3.
S
V
P
W
M t
e
c
h
niq
u
e
ci
rc
uit
dia
g
ra
m
The a
ddi
ti
o
n
of a
c
o
mm
on mo
de vol
t
a
ge
V
offs
e
t
to
V
ref
g
e
n
e
r
a
te
s t
h
e ma
x
i
mu
m ob
ta
in
a
b
le
p
eak
am
p
litu
de of t
h
e
p
h
a
se
vo
l
t
ag
e in lin
e
a
r
mo
du
la
tio
n
th
a
t
re
f
l
e
c
te
d
t
h
e
ou
tpu
t
of
sp
ac
e
v
e
ct
or ci
rcu
i
t
.
(4)
is
use
d
t
o
de
r
i
ve
t
h
e ma
g
n
it
u
d
e
of
V
offs
e
t
[
25]
:
/2
(4
)
Whe
r
e,
V
max
an
d
V
min
a
r
e
t
h
e ma
xim
u
m
a
n
d
mi
ni
mum
mag
n
i
t
ude
o
f
t
h
e 3c
o
n
si
de
r
e
d r
e
fe
renc
e
pha
se
v
o
l
t
a
ges
,
re
spe
c
t
i
v
el
y
.
The
i
n
t
r
od
uct
i
on
of
V
offset
c
a
uses t
h
e
ce
nte
r
i
n
g
o
f
ac
ti
v
e
inve
rt
er s
w
it
c
h
i
n
g
v
e
c
t
or
s in
a
sam
p
ling
i
n
terv
a
l; t
h
is make
s SPWM t
e
c
h
n
i
q
u
e
com
p
ar
a
b
le
to SVP
W
M
[26
]
. In
(4
),
th
e
tr
ian
g
u
l
ar
c
a
r
r
i
e
r
i
s
f
i
r
s
t c
r
o
s
sed
by
th
e r
e
fe
r
e
n
c
e
ph
ase
w
i
t
h
t
h
e
le
a
s
t m
a
gn
i
t
ud
e (c
al
led
th
e
min
i
mu
m-
p
h
a
s
e
) to
cau
se
th
e f
i
r
s
t in
ver
t
e
r
sw
itc
h
i
ng
sta
t
e
tr
a
n
si
tio
n,
wh
il
e t
h
e
r
e
f
e
r
e
n
ce ph
ase w
ith
th
e
h
i
g
h
e
st
ma
gn
itu
d
e
(
c
a
l
l
e
d
th
e
max
i
mu
m-
ph
as
e
)
mad
e
th
e l
a
st
c
r
ossi
n
g
t
o
e
lic
it t
h
e l
a
st
sw
itc
hin
g
tr
an
siti
on
[
2
7
]
.
Th
us,
i
t
i
s
po
s
s
i
b
l
e
tha
t
t
h
e a
c
t
i
v
e ve
ct
o
r
s s
w
i
t
c
hi
n
g
pe
r
i
ods
can
be
det
e
rmi
n
e
d
f
r
om t
h
e
am
pli
t
udes
of
t
h
e
sa
mpl
e
d r
e
fe
re
nc
e
pha
se
v
o
l
t
a
ges
(ma
x
i
m
u
m
-
phase
a
n
d
mi
ni
mum-
p
h
a
s
e
)
[
2
8].
T
h
e
S
V
P
W
M
t
e
ch
ni
que
i
s
a
si
mple
a
p
p
r
oa
ch t
h
at
det
e
rmi
n
e
s
t
h
e
t
i
m
e
i
n
st
ant
s
of t
h
e
3 re
fere
nce
p
h
a
ses crossi
n
g
t
h
e tria
ng
ula
r
c
a
rri
e
rs
b
a
s
e
d
o
n
l
y
o
n
th
e
amp
litud
e
s o
f
th
e
in
sta
n
tan
e
ou
s r
e
fe
r
e
n
ce
ph
a
s
es
.
So
r
t
i
n
g th
e
s
e t
i
me
i
n
sta
n
ts wi
ll
reve
al
th
e
V
o
ffset
int
r
od
uc
e
d
t
o
t
h
e
re
fer
e
nce
pha
se
vol
t
a
ges t
h
a
t
el
i
c
i
t
e
d the
s
p
ac
e
ve
ct
or
ge
ner
a
t
i
o
n f
o
r
t
h
e
o
v
e
r
a
l
l
li
nea
r
mo
dul
at
io
n
r
a
n
g
e
suc
h
t
h
at
t
h
er
e
wi
l
l
be
ce
n
t
e
r
i
ng
of
t
h
e
m
i
ddl
e i
n
v
e
r
t
e
r
s
w
i
t
c
hi
n
g
v
e
ct
o
r
s
d
u
ri
ng
sam
p
li
ng
a
s
obt
ai
na
bl
e
i
n
t
h
e
t
r
a
d
i
t
i
ona
l
SP
WM
sc
he
me
[2
9]
.
T
h
e
f
o
l
l
owi
n
g
st
e
p
s
are
i
n
vol
ve
d
i
n
S
V
P
W
M
i
m
ple
m
e
n
ta
t
i
on
fo
r
VSC
sc
he
me u
s
i
n
g t
h
e
a
m
pl
it
ude
s
of t
h
e
i
n
st
ant
a
ne
o
u
s
re
fe
r
e
nce
phas
e
:
a)
C
a
l
c
ul
at
i
on of
t
h
e
e
q
uiva
l
e
nt
t
i
me
of
the
sa
mpl
e
d
am
pli
t
u
des of
V
an
, V
bn
, and
V
cn
for
t
h
e
cu
rre
n
t
sa
mpl
i
n
g
i
n
te
rval
, whe
r
e T
S
r
e
pr
ese
n
t
s
t
h
e s
a
mpli
n
g
pe
ri
od
.
(5
)
(6
)
(7
)
b)
Fin
d
To
ff
set as
fo
llo
w
s:
0.
5
(8
)
Wh
er
e T
max
and
T
min
are
the
maximum and minimum
of T
as
,T
bs
,
a
nd
T
cs
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Enh
a
n
c
eme
n
t o
f
cas
c
ad
ed
mu
lti-
le
v
e
l
VS
C S
T
ATC
O
M p
e
rfo
r
ma
nc
e u
s
ing
ANN
…
(
M
oh
ama
d
M
Al
m
e
l
i
a
n
)
8
99
c)
Ca
l
c
ul
at
ing
Ta
(ga
t
e), T
b
(ga
t
e
)
, a
n
d
Tc
(ga
t
e
)
si
g
n
al
s;
t
h
ese
signa
ls
a
r
e
mat
c
he
d
wi
t
h
hi
gh
fre
q
uenc
y
t
r
i
a
ng
ul
ar
wa
v
e
i
n
P
W
M ge
n
e
rat
o
r to
ge
ne
rat
e
the
g
a
ti
ng
s
i
gnal
s
for VS
C
.
(9)
(10
)
(11
)
F
r
o
m
(5) t
o
(1
1) s
h
o
w
e
d
t
h
e
succe
ssful
c
e
nt
eri
n
g
of t
h
e
S
V
P
W
M
mi
ddl
e i
n
vert
er
swi
t
c
hi
n
g
vect
o
r
s
by
ad
di
n
g
an
offse
t
t
i
m
e
si
g
n
a
l
t
o
t
h
e i
n
v
e
rt
er
gat
i
ng si
gnal
s
de
ri
ve
d
from t
h
e
a
m
pl
i
t
ude
of t
h
e
sa
mpl
e
d
r
e
f
e
r
e
n
c
e
ph
a
s
e
vo
lt
ag
e
s
. W
i
t
h
th
e u
s
e
of
the
p
a
ce
v
e
ct
or
cir
c
u
i
t,
th
e ob
ta
in
e
d
swi
t
ch
ing
p
a
t
t
er
n
is d
e
p
i
cte
d
i
n
F
i
g
u
r
e
4
;
th
e SV
PW
M c
i
rc
u
i
t
i
s
app
lic
a
b
le
i
n
a
ny mu
ltil
ev
e
l
V
S
C
s
e
tt
ing an
d i
n
t
h
e
ov
er-
m
od
u
l
a
tion re
g
i
on
.
Unl
i
ke
the
t
r
a
d
i
t
i
onal
S
V
P
W
M sc
he
me
s
,
t
h
e
gene
rat
i
o
n
of t
h
e
gat
i
ng si
g
n
al
re
qui
re
d
n
o
se
ct
or an
gl
e;
t
h
e sc
he
me a
l
so
d
o
e
s
n
o
t
re
qui
re t
h
e
l
o
o
k
-
up
t
a
bl
es fo
r i
n
vert
er s
w
i
t
c
h
i
n
g
vec
t
o
r
s
sel
ect
i
on,
the
r
eb
y
mini
miz
i
n
g
t
h
e
re
qui
re
d
c
o
mp
ut
at
i
o
n
t
i
m
e
t
o
est
i
ma
te
t
h
e
s
w
i
t
c
hi
ng t
i
me
s for
t
h
e
i
n
vert
e
r
le
g
s
.
This
s
upp
o
r
ts
t
h
e real
-ti
m
e
i
m
pl
eme
n
t
a
t
i
on
ca
pa
bi
li
t
y
o
f
t
h
e a
l
go
rit
h
m.
Fi
gu
re
4. S
w
it
chi
n
g pa
tt
e
r
n
o
f
SV
P
W
M
(o
utp
u
t
of
s
p
ac
e
vec
t
or ci
rc
ui
t
)
2.4. Co
n
t
r
o
l
c
i
rcu
it
str
a
te
g
y
S
T
ATC
O
M
c
o
nt
rol
i
s
mai
n
ly
in
vol
ved
in
ge
nerat
i
o
n
of
s
y
nch
r
on
o
u
s o
u
t
put
v
o
lt
a
g
e
a
s
it
reg
u
l
a
t
e
s
t
h
e VSC
p
o
we
r swi
t
c
h
es t
o
el
i
c
i
t
reac
t
i
ve
po
we
r e
x
cha
n
ge
bet
w
ee
n
t
h
e s
y
ste
m
a
n
d
t
h
e d
e
vi
ce
. T
h
ere are
t
w
o
w
a
y
s
to
co
n
t
r
o
l
th
e
ou
tpu
t
volta
g
e
o
f
STA
T
CO
M
;
ind
i
r
e
ctly
,
it c
a
n
b
e
c
o
n
t
ro
l
l
ed
by
k
eep
in
g
th
e
modul
at
io
n
i
nde
x (M
I) c
o
nst
a
nt
whi
l
e
t
h
e DC
ca
pac
i
t
o
r v
o
l
t
a
ge
is
va
ri
ed.
A
di
rec
t
way
o
f
the
c
o
n
t
rol
i
s
b
y
al
t
e
ri
ng t
h
e
MI
va
l
u
e
whi
l
e
fi
xi
ng
the
v
o
l
t
a
g
e
of
t
h
e
DC
ca
paci
t
o
r [1
1].
∗
(12
)
√
√
√
(13
)
R
e
ga
rdi
ng
di
rec
t
c
ont
rol, t
h
e M
I
val
u
e i
s
a
d
just
e
d
t
o
v
a
ry t
h
e
out
put
v
o
l
t
a
ge, i.e
.
va
ryin
g t
h
e
swi
t
c
h
in
g a
n
gl
es o
f
ea
c
h
H
-
B
r
i
d
ge
uni
t
o
f
t
h
e ca
scad
e
d
V
S
C
w
h
i
l
e kee
p
in
g t
h
e
vol
ta
ges
of the
DC
ca
pa
ci
t
o
r
con
s
t
a
nt
.
M
I
i
s
dir
ect
l
y
rel
a
t
e
d t
o
t
h
e
fu
nd
ament
a
l
out
put
v
o
l
t
age a
m
pl
i
t
ude
as
give
n i
n
(
1
2)
a
n
d
(1
3); s
o
,
t
h
e
a
d
j
u
st
me
nt
of t
h
e
M
I
val
u
e transl
at
es
t
o
t
h
e
di
rec
t
a
d
j
u
st
ment
of
t
h
e
o
u
tput
v
o
l
t
age
.
F
i
gure 5
d
e
pi
c
t
s the
sche
ma
ti
c il
l
u
strat
i
o
n
o
f
t
h
e di
re
ct
c
o
nt
rol
st
rat
e
g
y
. The
refe
re
nce
volt
a
ge
an
d
t
h
e
a
c
t
u
al
syst
e
m
v
o
l
t
a
ge are no
rma
l
l
y
c
o
mp
a
r
ed
,
a
n
d
a P
I-AN
N
c
ont
rol
l
e
r
is use
d
t
o
pr
oc
esses the
di
ffe
renc
e
(e
rro
r
)
bet
w
ee
n t
h
e
t
w
o
vol
t
a
ges.
Wit
h
t
h
i
s
p
r
o
c
e
s
s,
t
h
e
a
p
p
r
opri
a
t
e
MI
va
lue
re
qui
re
d
t
o
c
h
an
ge
t
h
e
out
put
vol
ta
ge
o
f
S
T
ATC
O
M
is
ge
nera
te
d; t
h
i
s
i
m
pl
i
e
s a
c
h
an
ge
in t
h
e
fl
ow
pat
t
ern
o
f
the
rea
c
t
i
ve
po
w
e
r an
d
mai
n
te
na
nce
o
f
t
h
e
AC
syst
e
m
vol
t
a
g
e
a
t
a
no
mi
na
l l
e
ve
l.
The
c
a
pac
i
t
o
r
vol
t
a
ge
i
s
mai
n
t
a
i
n
ed
by
pro
v
i
d
in
g
mini
mal
a
c
t
i
ve
po
we
r
fl
ow
by
ph
a
s
e
shi
f
t
i
ng t
h
e v
o
lt
a
g
e
o
f
S
T
ATC
O
M o
v
e
r a sma
l
l
an
gl
e (
α
)
w
ith
r
e
spec
t
to
t
h
e vol
t
a
ge
of
t
h
e AC
s
y
st
em
(c
al
le
d
t
h
e
l
o
ad a
n
gl
e).
An
o
t
her PI-ANN
c
ont
roll
er
ca
lc
u
l
a
t
es
t
h
i
s
loa
d
angl
e
base
d o
n
t
h
e
diffe
r
e
n
ce
bet
w
ee
n
t
h
e a
c
t
u
al
(V
dc
) a
nd r
e
fe
re
nc
e (
V
dc_r
e
f
) capa
c
i
t
o
r v
o
l
t
age
s
. T
h
e
α
a
nd t
h
e
out
put
o
f
P
L
L
(
θ
)
a
r
e
fe
d
t
o
t
h
e
bl
oc
k
of
t
h
e
p
h
ase
s
h
ifte
r t
o
ge
nerat
e
the
uni
t
ma
gni
t
u
d
e
c
o
ntr
o
l si
g
n
a
l
whi
c
h
i
s
sync
h
r
o
n
o
u
s
an
d
loc
k
e
d
t
o
t
h
e
vol
t
a
ge
of
b
u
s-3
(PC
C
).
Thi
s
c
o
ntr
o
l
si
g
n
al
i
s
fe
d t
o
S
V
P
W
M
bloc
k,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN:
2088
-86
94
In
t
J
Po
w
Ele
c
&Dr
i
S
y
st, Vo
l. 11
, No
. 2
,
June
20
20
: 895
–
90
6
90
0
t
oget
h
e
r
wit
h
MI
,
t
o
ge
ne
rat
e
the
f
i
ri
ng
p
u
l
ses t
o
tr
ig
ge
r
the
se
mi-
c
on
d
u
ct
o
r
s
w
i
t
c
hes
[
3
0]
.
In
t
h
is
st
ud
y,
t
h
e s
ync
hr
o
n
i
z
a
t
i
on of
t
h
e
ST
ATC
O
M o
u
t
p
u
t
vol
ta
ge
w
i
t
h
s
y
st
em o
u
t
p
ut
v
o
l
t
a
g
e
was d
o
n
e
usi
ng PL
L.
Fi
gu
re
5.
Di
rec
t
cont
rol
sc
he
me
o
f
3-l
e
ve
l
VS
C S
T
ATC
O
M
2.
4.
1.
PI
c
o
nt
r
o
ll
e
r
A
c
ont
r
o
ll
e
r
i
s
r
e
qui
re
d
to c
o
nt
r
o
l
o
r
t
o
ope
ra
te
c
a
sca
d
ed
3-l
e
v
e
l
S
T
AT
COM
d
u
r
i
n
g
t
h
e
pe
ri
od o
f
vol
t
a
ge
sa
g.
The
PC
C
vol
t
a
ge
i
s
se
nse
d
an
d f
o
rwa
r
de
d t
h
ro
u
g
h
a s
e
que
nce
a
n
al
y
z
e
r
.
Re
ac
ti
ve
po
w
e
r
c
o
mpe
n
sa
t
i
on
c
ont
r
o
l
l
o
op
(c
ont
rol
u
n
i
t
of
MI
) a
n
d ac
ti
ve
po
w
e
r a
b
sor
p
t
i
on c
ont
r
o
l
l
o
o
p
ha
ve a
sepa
r
a
t
e
P
I
co
n
t
ro
l
l
e
r
(c
ontr
o
l un
it of
α
). A
s
a fe
ed
b
ack
c
o
n
t
ro
ll
er
,
t
h
e
PI
con
t
ro
l
l
er
wo
rk
s by
sum
m
ing
th
e
erro
r
an
d
i
n
t
e
gra
l
of
th
os
e val
u
e
s
as r
e
v
e
a
l
e
d
i
n
F
i
gur
e
6 [
3
1
]
.
Fi
gu
re
6.
St
r
u
c
t
ur
e of
P
I
c
ontr
o
ll
e
r
The
di
ff
e
r
e
n
ce
be
tw
ee
n t
h
e
r
e
fe
re
nc
e a
n
d a
c
t
u
al
vol
t
a
ge s
e
rve a
s
t
h
e
in
p
u
t
of t
h
e
P
I
c
o
ntr
o
ll
e
r
. F
o
r
th
e
M
I
c
o
n
t
ro
l
un
it,
th
e r
e
fe
ren
c
e v
o
l
tag
e
is
1
p
.
u
,
w
h
e
r
e
in
sid
e
t
h
is
c
o
n
t
r
o
l un
it,
t
h
e
pro
por
tio
n
a
l g
a
i
n
is 1
w
h
e
r
e
a
s
th
e in
te
gr
al
g
a
in
is
35
.I
n t
h
e
c
o
n
t
ro
l
un
it o
f
α
,
t
h
e
propo
r
tio
n
a
l
and
i
n
t
e
g
r
al
g
a
i
n
s ar
e
0.025
.
The
o
u
t
p
ut
o
f
t
h
e
PI
c
ont
r
o
l
l
e
r
is
con
v
er
t
e
d i
n
to
3-
p
h
as
e
volt
a
g
e
a
n
d
pr
opa
ga
te
d t
o
t
h
e
SVP
W
M
pul
se
g
e
n
e
r
a
t
o
r to gen
e
r
a
t
e
t
h
e
p
u
l
se
th
a
t
w
ill
b
e
fo
rw
ard
e
d
to the
c
a
s
ca
d
e
d
V
S
C to
tri
g
g
e
r th
e
I
G
B
T
sw
itc
h
e
s.
2.
4.
2.
AN
N c
o
n
t
rol
l
e
r
I
n
th
is st
u
d
y
,
a
mu
ltil
ay
e
r
BP
-t
yp
e
AN
N c
o
n
t
ro
lle
r w
a
s
u
s
e
d
t
o
im
pro
v
e
th
e
p
e
rf
or
man
c
e
o
f
S
T
ATC
O
M
.
T
h
e
A
N
N
wa
s t
r
ai
ne
d usi
ng t
h
e
MA
TLAB
t
o
ol
b
ox;
Le
ve
nb
e
r
g
Mar
qua
r
d
t
(L
M) B
P
al
g
o
r
i
t
hm
w
a
s u
t
i
liz
ed
as th
e
t
r
a
i
n
i
n
g
a
l
go
r
i
t
h
m i
n
th
e
ANN
con
t
ro
l
l
e
r
. Gr
a
d
i
e
n
t
D
e
sc
en
t
(G
D) is a
f
i
r
s
t-
or
d
e
r
opt
i
m
i
z
a
t
io
n f
r
a
me
w
o
r
k
fo
r
fi
ndi
ng
the
l
o
ca
l
mini
m
u
m o
f
a
n
y
gi
ven
f
u
nct
i
o
n
.
It
i
s
a
r
o
b
u
s
t
me
th
od
es
pe
ci
a
l
l
y
w
h
e
n
it
in
iti
at
es
far fr
om th
e fi
n
a
l
min
i
mum
;
me
an
wh
ile
,
it is p
r
on
e t
o
p
oor
con
v
e
rg
en
c
e
. LM
BP is
a
se
c
o
nd-
or
d
e
r
o
p
ti
mi
zat
i
on f
r
ame
w
or
k t
h
at
li
es
bet
w
ee
n G
D
a
nd
G
a
uss-
N
e
wt
o
n
(
G
N
)
f
r
a
m
e
w
or
ks.
L
M
a
l
g
o
r
i
t
h
m c
a
n
fi
nd
so
l
u
tion
s
e
v
en
in
it
ia
tin
g fa
r fro
m t
h
e
fin
a
l
so
lu
t
i
on
. LM
alg
o
ri
th
m
is
a b
e
t
t
e
r
o
p
t
i
o
n
co
mp
are
d
t
o
G
N
a
n
d
G
D
me
thod
s [3
2]
as
it
co
nv
e
r
g
e
s ra
p
i
d
l
y
,
req
u
i
r
e
s l
o
w memor
y
,
an
d
ca
n
l
e
a
r
n
[
33]
.
The st
r
u
ct
u
r
e
of
the
A
NN
cont
rol
l
e
r
use
d
i
n
t
h
i
s
st
u
d
y
has
3 la
ye
r
s
as de
p
i
c
t
e
d
i
n
F
i
g
u
re
7.
The
l
a
ye
rs c
o
n
s
i
s
t
of
1
in
p
u
t
l
a
ye
r
,
1
hid
d
e
n
l
a
yer
(
c
o
m
pr
is
e
d
o
f
10
ne
ur
o
n
s)
,
an
d
1
out
p
u
t
l
a
yer
.
T
h
e
d
a
ta
f
o
r
t
r
a
i
ni
n
g
t
h
e
A
N
N
are
s
o
u
r
ce
d
fr
om
a
c
onv
e
n
ti
ona
l
PI
c
o
nt
r
o
l
l
e
r
.
The
A
N
N
c
o
ntr
o
l
l
e
r
has
t
h
e
e
r
r
o
r
a
n
d t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Enh
a
n
c
eme
n
t o
f
cas
c
ad
ed
mu
lti-
le
v
e
l
VS
C S
T
ATC
O
M p
e
rfo
r
ma
nc
e u
s
ing
ANN
…
(
M
oh
ama
d
M
Al
m
e
l
i
a
n
)
9
01
cha
nge
i
n
e
rro
r si
gnal
s
from
t
h
e
MI
c
ont
rol
uni
t
a
n
d
α
co
n
t
ro
l un
it a
s
its inpu
t
.
The A
N
N
c
o
n
t
ro
lle
r
i
s
e
x
p
e
c
t
ed
to
min
i
miz
e
th
is
e
r
r
o
r.
Th
e p
e
rfor
m
an
c
e
m
e
tri
c
of
t
h
e
ANN
c
o
n
t
r
o
ll
er is
the
M
e
a
n
squ
a
r
e
e
rror
whi
c
h re
fl
ec
t
s
the
e
r
ro
r
bet
w
ee
n i
n
pu
t
v
a
l
u
es an
d
the
t
a
r
g
e
t
val
u
es.
1
0
0
0
ep
oc
hs are
r
e
qui
red
fo
r t
h
e
AN
N
tr
a
i
n
i
ng
in
t
h
e
M
I
co
n
t
ro
l un
it;
th
e
b
e
st
a
c
h
i
e
v
e
d
v
a
li
d
a
t
i
on
p
e
rf
orm
a
n
c
e
(
0
.0
0
000
014
)
i
s
a
c
h
iev
e
d
at
epo
c
h 6.
The
t
o
ta
l
nu
mbe
r
o
f
ep
oc
hs
in t
h
e
α
c
o
ntr
o
l
uni
te
i
s
10
0
0
w
h
i
l
e
t
h
e
be
st
achi
e
ve
d
va
li
dat
i
on pe
rformanc
e
(0
.00
0
0
0
1
4
4
) i
s
ac
hie
v
ed
at
e
p
o
c
h 5.
The
t
r
ai
ni
n
g
of
t
h
e
AN
N
was d
o
n
e
offli
n
e a
n
d
was
desig
n
e
d
fo
r
t
h
e
cont
rol
o
f
t
h
e
casc
a
de
d
VSC
ST
A
T
CO
M
.
Havi
ng
c
o
m
p
l
e
t
e
d t
h
e
offl
i
n
e
t
r
ai
ni
ng
, t
h
e
next
ste
p
i
s
t
o
repl
ac
e
t
h
e
P
I
c
ont
rol
l
e
r w
i
t
h
t
h
e
ge
n
e
rat
e
d
A
N
N
co
ntr
o
ll
e
r
.
F
i
gu
re
7.
S
t
r
u
c
t
ure
of ne
u
r
al
ne
t
w
o
r
k
3.
SY
ST
E
M
SP
E
C
IFI
CAT
IO
NS
The
pe
rfo
r
ma
nc
e o
f
the
S
T
ATC
O
M
m
o
d
e
l
wa
s
i
nvest
i
g
at
ed in
M
A
T
L
AB usi
ng
t
h
e para
me
t
e
r
sho
w
n i
n
Ta
ble
1.
Tabl
e
1. P
o
wer
S
y
st
e
m
Pa
ram
e
t
e
rs
P
a
r
a
me
te
r
Va
lue
3-
p
has
e
Sour
ce
(1and2) P
a
r
a
me
te
rs
R
a
te
d voltage
6.
6 kV
(L-
L
)
F
r
e
quenc
y
50
H
z
I
m
peda
nce 0.
89+
j
5.
18
Ω
I
m
pe
dance
of
T
r
ansm
ission L
i
ne
Z
1
,
2
0.
05+
j
0.
2
Ω
Z
1
,
3
0.
02+
j0.
1
Ω
Z
2
,
3
0.
036+
j0.
12
Ω
I
n
duc
tive
/
Ca
pac
itive
Loa
d
s
A
c
tive pow
er
1 M
W
I
nduct
i
ve/C
apa
c
iti
ve r
e
a
c
tive
pow
e
r
1 M
V
A
R
S
T
A
T
C
O
M
devic
e
Dc Vo
lta
g
e
6
kV
I
nduct
o
r
of
Filt
er
10.
7 m
H
S
w
i
t
ching F
r
e
quenc
y
2 kH
z
4.
SIM
U
LAT
I
O
N
RE
SUL
T
S
Fo
r te
st
in
g th
e
v
i
ab
i
lit
y
of
t
h
e C
a
sc
a
d
e
d
3
-
l
e
v
e
l
VSC
STATC
O
M
w
ith
its
tw
o c
o
n
t
ro
ll
er
s (P
I/ANN
)
i
n
mi
t
i
ga
ti
n
g
vol
ta
ge
sa
g
w
h
i
c
h
occ
u
rre
d a
t
bus
-3, t
h
e
fol
l
ow
i
n
g
a
p
pr
oac
h
wa
s a
d
o
p
te
d
.
Eac
h
case
is
cl
assi
fi
ed i
n
t
o
t
h
re
e
st
at
es
whi
c
h a
r
e
vol
t
a
ge ma
g
n
i
t
u
d
e
an
d P
F
am
pl
it
ude
d
u
ri
ng
pe
ri
ods
of
vol
t
a
ge
sa
g.
For
al
l
t
h
e ca
se
s, the
t
r
a
n
si
t
i
on
t
i
me ra
nge
d fr
om
0.8 t
o
1.3
s
e
c.
4.1. Case
A
:
comp
e
n
sa
tio
n
of v
o
lt
age
s
a
g
gene
r
a
te
d by
SL
G fau
l
t
4.1.
1
V
o
l
t
a
g
e
ma
gni
t
u
d
e
d
u
ri
n
g
S
L
G fa
ul
t
A
n
SL
G
fa
ult
was a
p
pl
ie
d
a
t
bus 3
.
T
h
e
fi
rst
si
mul
a
t
i
o
n wa
s
pe
rformed
wi
tho
u
t
u
s
i
n
g
S
T
ATC
O
M
;
it
ca
n be
obse
r
ve
d t
h
a
t
th
e
v
o
l
t
a
g
e sa
g
of
b
u
s
3
was
0
.
8
2
4
pu
(1
4.
2%
o
f
the
re
fe
re
nce
v
o
l
t
a
g
e (
0
.96
6
pu
))
as
d
i
s
p
lay
e
d
in
F
i
g
u
r
e
8
.
A
s
c
a
n
b
e
seen
, th
e
vol
ta
g
e
at
bu
s 3 w
a
s no
t 1
pu
w
i
t
h
in
0
to
0
.
8 se
c
an
d from
1
.
3
to 2
sec d
u
e t
o
t
h
e
i
n
d
u
ct
i
v
e l
o
a
d
on
t
h
e
syst
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN:
2088
-86
94
In
t
J
Po
w
Ele
c
&Dr
i
S
y
st, Vo
l. 11
, No
. 2
,
June
20
20
: 895
–
90
6
90
2
Fi
gu
re
8.
V
o
l
t
a
ge
of
bus
-
3
wi
t
h
o
u
t
S
T
ATC
O
M du
ri
n
g
S
L
G f
a
ul
t
per
i
o
d
The
se
c
o
nd
si
mul
a
ti
on
wa
s
ca
rri
e
d
out
u
s
i
n
g t
h
re
e
-
l
e
ve
l
V
S
C
S
T
A
T
CO
M
wi
t
h
PI
c
ont
rol
l
e
r
c
o
n
n
ect
ed t
o
t
h
e IE
EE
3-
bus syst
em.
D
u
r
i
n
g
S
L
G fa
ult
,
the
ST
ATC
O
M
gene
rat
e
d t
h
e
r
eac
t
i
ve
p
o
w
e
r
t
o
t
h
e
sy
ste
m
;
th
en
, th
e
v
o
l
ta
g
e
sag w
a
s
m
itig
a
t
e
d
,
a
n
d
t
h
e
PI
to
o
k
0.
065
se
c
to
ma
i
n
t
a
in
v
o
l
t
a
g
e
a
t
th
e
bu
s-
3
t
o
0.
94
7 pu
(
p
er
cent
a
ge
of
i
m
pr
o
v
eme
n
t
1
2
.
3
%)
a
s
s
h
o
w
n in
Fi
g
u
re
9(
a
)
.
F
i
gu
r
e
9(
b
)
ex
pl
ai
ne
d th
e
l
a
st
si
mula
ti
on t
h
at
wa
s
per
f
o
r
me
d wi
t
h
S
T
ATC
O
M
base
d
on
AN
N c
ont
rol
l
e
r.
I
n
t
h
i
s
si
mul
a
t
i
on,
A
N
N
ne
e
d
ed
0.
02
se
c t
o
i
n
c
r
ease
t
h
e
v
o
l
t
a
g
e t
o
0
.
9
8
1
pu
(pe
r
ce
nta
g
e
of
impr
o
v
e
m
e
n
t 1
5
.
7
%
)
beca
use
the
A
N
N
c
ont
r
o
l
l
e
r
redu
ce
d
th
e
erro
rs
to
t
h
e
m
i
n
i
m
u
m
v
a
l
u
e.
(
a
)
(
b
)
F
i
gu
re
9.
V
o
lt
age
of
b
u
s
-
3
w
i
t
h
S
T
ATC
O
M du
ri
n
g
S
L
G
f
a
ul
t
pe
r
i
o
d
base
d
on
:
(a)
P
I
,
(b
) A
N
N
c
ont
rol
l
e
rs
4.
1.
2
P
o
w
e
r
f
a
ct
or am
pl
i
t
u
d
e
du
ri
n
g
SL
G f
a
u
l
t
Be
fo
re
S
L
G f
a
ul
t per
i
od
an
d wi
t
h
o
u
t ST
A
T
COM
,
i
t
ca
n
s
e
e
t
h
at
the
P
F
at
b
u
s-
3 w
a
s 0.
7
1
bec
a
use
o
f
th
e
ef
fe
c
t
o
f
t
h
e
i
ndu
ct
iv
e l
o
a
d
;
th
is
i
n
c
r
ea
sed
fr
om 0
.
71
to u
n
i
t
y
PF d
u
r
in
g fa
u
lt a
s
in
F
i
g
u
r
e
10
d
u
e
to
th
e
lo
a
d
wh
ic
h recei
v
e
s
la
rg
e a
c
t
i
v
e
po
w
e
r
f
r
o
m
th
e supp
l
y
side
.
Wh
en th
e 3-le
v
e
l VSC
STA
T
C
O
M-b
a
sed
P
I
is
ON
, t
h
e
PF
a
m
pl
i
t
ude
re
c
o
r
d
e
d
0
.
9
9
7
du
r
i
ng
SLG
fa
ul
t
a
s
desc
r
i
be
d
i
n
F
i
g
u
re
1
1
(a
).
T
h
e
P
I
c
ont
rol
l
e
r
re
qu
ir
ed
0
.
0
9
2
s
ec
to
a
c
h
i
e
v
e
th
a
t
v
a
lu
e
wh
i
l
e
th
e S
T
A
T
C
O
M-b
a
sed ANN
too
k
0.
019
se
c
t
o
ma
in
ta
in
th
e
PF
a
t
uni
ty
as
c
l
a
r
i
f
i
e
d i
n
Fi
gu
re
11
(
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
En
ha
nc
e
m
ent
of ca
sca
d
e
d
m
u
l
t
i
-
l
e
vel
VSC
STAT
C
O
M
per
f
orm
a
n
ce
usin
g ANN
…
(M
o
h
a
m
ad
M
Al
me
l
i
an)
9
03
Fi
gu
re
1
0
.
PF
of
B
u
s
-
3
wi
t
h
o
u
t ST
ATC
O
M
du
r
i
n
g
SLG
fa
ul
t
pe
ri
o
d
(a)
(b
)
F
i
gu
r
e
1
1
.
P
F
of
B
u
s
-
3
wit
h
STATC
O
M du
ri
n
g
S
L
G
fa
ul
t
per
i
od
base
d
o
n
: (a
)
P
I
,
(
b
)
A
N
N
co
nt
r
o
l
l
e
rs
4.
2.
C
a
se
B
:
Com
p
e
n
s
a
ti
o
n
o
f
vol
t
age
sa
g ge
ne
r
a
te
d b
y
L
L
fa
u
l
t
4.
2.
1.
Vol
t
a
g
e
ma
gni
t
u
d
e
d
u
r
i
n
g
L
L
f
a
u
l
t
As
s
h
ow
n
i
n
F
i
gur
e 12
,
t
h
e
c
o
n
n
ec
ti
o
n
of
L
L
f
a
ul
t wi
th
th
e
B
u
s-
3
p
r
ov
o
k
ed
a r
e
ma
rka
b
le
v
o
l
t
a
g
e
sa
g
at
B
u
s-
3
(
p
hase B
)
,
ma
ki
n
g
it
to
rea
c
h
0.
78
p
u
w
h
ic
h
i
s
18
.
6
% of
t
h
e n
o
mi
nal
va
l
u
e
(
0
.
9
6
6
p
u
)
.
Fi
gu
re
1
2
.
V
o
l
t
a
ge
of
B
u
s
-
3
w
i
t
hout
S
T
ATC
O
M d
u
r
i
n
g
LL
fa
ul
t
per
i
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN:
2088
-86
94
In
t
J
Po
w
Ele
c
&Dr
i
S
y
st, Vo
l. 11
, No
. 2
,
June
20
20
: 895
–
90
6
90
4
Wh
en
the
P
I
c
o
n
t
r
o
lle
r w
a
s
i
n
s
t
al
le
d
w
i
t
h
STATCO
M,
th
e
PI
sp
e
n
t 0
.
06
7 se
c
to
mak
e
the
v
o
ltag
e
a
t
t
h
e
b
u
s-3
a
r
o
u
n
d
0.
9
4
1
pu
(
i
mp
r
ove
me
nt
16
.1
%)
a
s
pr
ese
n
t
e
d
i
n
Fi
gu
re
1
3
(a
).
C
o
mpa
r
ed
wi
t
h
P
I
,
t
h
e
A
N
N
co
nt
r
o
l
l
e
r
r
e
t
u
r
n
e
d
the
v
o
l
t
a
ge o
f
bus-
3
t
o
a
ne
ar
-
n
o
r
mal
st
at
e (0
.
973
p
u
, i
m
pr
o
v
e
me
nt o
f
19
.3
%)
wi
t
h
i
n
0
.
0
2
sec a
s
sh
own
in F
i
g
u
re 13
(b
).
(a)
(b
)
F
i
g
u
r
e
13.
V
o
l
t
a
ge
of
b
u
s-
3
w
i
t
h
S
T
ATCO
M d
u
ri
ng
LL
faul
t
pe
ri
o
d
base
d
on:
(a
)
P
I
,
(b
)
AN
N c
o
nt
r
o
l
l
e
rs
4
.
2
.
2
.
Pow
e
r fa
ct
o
r
am
pl
it
ud
e
du
ri
ng
LL
f
a
ult
Th
e
P
F
of
bu
s
-
3
wa
s
boo
ste
d
f
r
o
m
0.
71 to
0.
7
9
b
y
LL f
a
u
lt wh
en
th
e STATCO
M wa
s
d
i
sc
on
n
e
c
t
ed
as
d
e
p
i
c
t
e
d
i
n
F
i
g
u
r
e
14
.Th
e
i
n
te
rv
en
ti
on
of
t
h
e
S
T
ATCOM c
o
n
t
ro
lle
d by
PI an
d
A
N
N a
l
go
r
ithm
s
re
t
u
rn
ed
t
h
e PF
d
u
ri
ng
fa
ult
to
t
h
e
ac
ce
pt
abl
e
val
u
es
(0.
9
7
8
an
d
u
n
it
y,
res
p
ec
ti
vel
y
)
wi
th
ad
va
nta
g
es
in
t
e
rm
o
f
R
T
for
A
N
N
(
0
.019
sec)
co
mp
ar
ed
t
o
PI
(0
.3
9
sec
)
as
d
e
p
i
ct
ed
i
n
Fi
g
u
r
e
s
15
(a)
and
1
5
(b
)
.
F
i
gur
e
1
4
.
P
F
of
Bus
-
3
wi
th
o
u
t
S
T
ATC
O
Mdu
r
in
g L
L
f
a
ul
t peri
od
(
a
)
(
b
)
Fi
gu
re
1
5
.
PF
of
Bus
-
3
wi
th
STA
T
C
O
M du
r
i
n
g
LL
f
a
ul
t p
e
ri
o
d
b
a
s
e
d
o
n
:
(a)
P
I
,
(b
)
AN
N c
ont
r
o
l
l
e
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.