In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
2
8
1
~1
2
9
6
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1281-1296
1
2
81
Jou
rn
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l
h
o
me
pa
ge
:
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tp:
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score
.
com
/
j
o
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s
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n
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e
x
.
p
hp/IJ
PED
S
R
o
bust s
tability pow
er in the tr
a
nsmission line w
i
th the use of
a
UPFC
system and neural contr
ol
lers based
adaptive control
Bo
ua
n
a
ne A
bdelk
rim,
Ya
h
ia
o
u
i
Merzo
u
g
L.G.
E Laboratory, Depart
e
ment o
f
Electri
cal E
ngin
e
e
r
i
n
g
,
D
r. M
o
u
l
ay
Tah
er
U
niv
e
rs
it
y
of
S
AIDA
,
A
l
g
e
ria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Dec
1
3
,
2
018
Re
vise
d F
e
b 15,
201
9
A
c
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pte
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A
pr 3,
201
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s
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ur
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t © 2
019 In
stit
u
t
e
of Advanced
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c
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All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Boua
na
ne
A
bd
elkr
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borat
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ngi
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r
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ay Ta
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nivers
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fr
1.
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d
t
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g
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popu
l
a
ti
o
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are
the
first
f
a
c
t
o
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s
for
which
the
con
s
um
pt
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f
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od
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p
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nt
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s
of
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t
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f
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ons
ume
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s
w
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n
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ore
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ma
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w
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mor
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rgy
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b
e
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q
ua
li
ty
,
enter
p
rises
of
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r
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o
f
electrical
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r
g
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ust
t
h
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t
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degr
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env
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nm
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t [1
]
.
The
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A
nd t
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nti
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s
ca
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w
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p to
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coils
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Ca
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ma
i
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na
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Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
281
–
1
2
96
1
282
m
a
na
gem
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n
t
o
f
t
h
e
r
e
a
g
e
n
t
[
2
,
3]
.
H
o
w
e
ve
r
,
p
r
oble
m
s
of
w
e
a
r
a
s
we
ll
a
s
the
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r
sl
ow
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c
tio
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t
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t
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refo
re
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ifficult
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a
co
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t
i
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uo
us
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on
tr
o
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of
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l
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w
of
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r
.
A
n
o
t
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tec
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n
i
q
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dj
us
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t
a
n
d
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o
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o
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o
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t
e
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sio
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s
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tr
ansits
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t
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t
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onic
s
h
a
s
m
ade
it
s
e
v
i
d
e
n
c
e
.
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s
o
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ti
o
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t
h
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e
pr
o
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s
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m
pr
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v
e
the
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o
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l
of
t
he
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l
e
c
t
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l
s
y
s
t
e
m
s
alre
ad
y
i
n
p
lace
.
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is
n
ece
ssa
r
y
t
o
e
q
u
ip
t
he
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s
y
s
t
e
ms
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f
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e
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ain
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m
t
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ett
e
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ad
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qu
ir
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a
pid
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n
t
o
f
t
he
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o
nic
pow
er
h
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h
a
d
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on
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de
rab
l
e
e
ffe
ct
i
n
the
i
m
p
r
ov
e
m
e
n
t
of
t
h
e
c
on
dit
i
ons
f
o
r
t
he
f
un
ct
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nin
g
o
f
t
h
e
e
l
e
c
t
r
i
c
a
l
n
et
wo
rk
s i
n
th
e
p
erfo
rma
n
ce
o
f
th
e
co
nt
rol
of
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he
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e
t
t
i
n
g
s
b
y
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n
t
r
od
uct
i
on
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f
c
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n
t
r
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l
de
v
i
ces
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n
t
h
e
b
a
s
is
o
f
c
o
mpone
n
t
s
of
E
l
e
ctr
o
n
i
c
P
o
w
e
r
ve
r
y
a
dva
nce
d
(
G
T
O
,
I
G
B
T)
kno
w
n
u
n
d
er
t
he
a
cr
on
ym
f
a
c
ts:
"
f
le
x
i
b
l
e
a
l
t
er
na
t
i
n
g
c
ur
r
e
nt
t
r
a
nsm
i
ss
i
on
sys
t
em
s”
.
The
co
n
t
r
i
bu
ti
on
of
t
h
i
s
te
ch
no
l
o
g
y
"
F
A
C
T
S
"
[
4-
6]
for
t
h
e
com
p
an
ies
of
t
he
e
l
e
ctr
i
ci
t
y
i
s
to
o
pe
n
ne
w
pr
o
s
pec
t
s
for
c
o
n
t
r
o
l
l
i
n
g
t
h
e
f
l
ow
o
f
p
o
w
e
r
i
n
netw
or
ks
a
nd
t
o
inc
r
ea
se
t
he
c
a
p
ac
i
t
y
used
e
x
i
s
t
ing
l
i
ne
s
s
i
m
i
l
a
r
t
o
e
x
t
e
n
s
i
o
n
s
i
n
t
h
e
l
a
t
t
e
r
.
T
h
e
U
P
F
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c
o
n
s
i
s
t
s
o
f
t
w
o
v
olt
a
g
e
-sou
rce
i
n
v
e
rt
ers
wi
th
f
u
lly
s
wi
tch
a
bl
e
e
l
e
m
e
n
ts
(
G
T
O
,
I
G
B
T)
t
ha
t
ar
e
conne
cte
d
t
hr
ou
g
h
a
c
om
m
on
co
nt
i
n
u
o
us
l
i
nk
(
D
C-
li
nk)
F
igur
e
1.
O
ne,
M
ount
e
d
i
n
shu
n
t
,
c
al
l
e
d
S
T
ATC
O
M
(S
t
a
tic
c
o
m
p
e
nsa
t
o
r),
i
n
j
ect
s
a
n
a
lm
ost
sin
u
s
o
i
d
a
l
c
urre
n
t
o
f
ad
j
u
s
t
ab
l
e
m
a
gni
t
ude.
Th
e
sec
o
n
d
,
m
ount
e
d
i
n
ser
i
es,
ca
l
l
e
d
S
S
S
C
(S
t
a
ti
c
S
e
r
ies
sync
hr
o
n
ous
c
om
pensa
t
or
)
,
i
nj
ec
t
s
i
n
se
r
i
es
a
n
a
l
m
o
st
a
l
t
e
r
na
t
i
ve
v
ol
ta
ge
w
i
t
h
a
n
a
djus
ta
ble
a
m
p
l
i
t
u
de
a
n
d
p
ha
se
a
ng
le
i
n
t
h
e
tr
ansp
or
t
line
.
E
a
c
h
in
ver
t
e
r
c
a
n
s
wa
p
t
h
e
ne
cess
a
ry
r
ea
cti
v
e
p
o
w
e
r
loca
l
l
y,
a
n
d
p
r
o
duc
e
t
h
e
ac
t
i
ve
p
owe
r
a
s
a
re
sult
o
f
t
h
e
seria
l
in
jec
t
io
n
of
a
v
o
l
t
a
ge.
T
h
e
b
a
sic
fu
nc
ti
o
n
o
f
t
h
e
sh
un
t
in
v
e
rte
r
(In
v
e
rter
1
)
is
t
o
supp
ly
o
r
ab
s
o
rb
t
h
e
a
ctiv
e
pow
e
r
r
eq
uest
e
d
by
t
h
e
se
r
i
a
l
i
n
v
e
r
ter
(
I
nve
r
t
e
r
2
)
t
h
r
o
u
g
h
t
he
c
om
m
on D
C
c
onne
c
t
io
n.
I
t
ca
n a
l
so
p
r
o
d
u
ce
or
a
b
sor
b
r
e
acti
v
e
pow
er
a
s
r
e
qui
r
e
d
and
pr
o
v
i
d
e
vol
ta
ge
s
u
ppor
t
a
t
the
netw
or
k
co
nne
c
t
i
o
n
poin
t
[
7,
8
]
.
Fig
u
r
e 1
.
Basic circu
it co
n
f
i
guratio
n
of
a U
PFC
2.
MO
DELI
N
G
O
F
A U
PFC
S
YSTEM
The
e
q
u
i
va
le
nt
c
i
r
cui
t
o
f
a
UP
F
C
s
ystem
is
s
how
n
i
n
F
ig
u
r
e
2.
w
her
e
t
he
s
e
r
ies
and
sh
u
n
t
i
n
ve
r
t
er
s
a
r
e r
e
pr
esented
by
v
o
lta
ge
s
o
u
r
ce
s
vc
a
nd v
p
r
espec
tive
l
y.
T
he
tr
ansm
i
s
si
o
n
l
ine
is m
ode
l
e
d [9-
13]
as a se
r
i
es
co
mb
in
ati
o
n
of
r
es
i
s
t
a
n
c
e
r
an
d
i
ndu
ct
a
n
ce
L
.
T
h
e
p
a
ra
me
t
e
rs
r
p
a
nd
L
p
r
e
pr
ese
n
t
the
sh
un
t
tr
an
sf
or
me
r
re
si
s
t
a
n
ce
a
nd
l
e
ak
ag
e
ind
u
c
t
a
n
c
e
r
es
p
ecti
v
ely
.
T
h
e
non
l
in
ea
ri
ty
’s
c
au
s
e
d
by
t
he
s
wi
t
c
hin
g
of
t
h
e
se
mico
nd
uc
tor
de
vice
s,
t
r
a
nsf
o
r
m
er
s
a
t
ur
at
i
on
an
d
c
o
n
t
r
o
ll
e
r
t
i
me
d
el
a
y
s
a
r
e
n
e
gl
ecte
d
i
n
t
h
e
eq
uiv
a
l
e
nt
ci
r
c
uit
a
n
d
it
i
s
assum
e
d
that
t
he
t
rans
m
i
ss
ion
sys
t
em
i
s
sym
m
e
trica
l
.
T
h
e
sim
p
l
i
fi
e
d
c
ircu
it
of
t
he
U
PFC
c
o
n
t
r
o
l
an
d
c
o
mpe
n
sa
tio
n
system
i
s
show
n
i
n
F
i
gur
e
2.
Fi
g
u
r
e 2
.
E
q
u
iv
a
l
ent
ci
rc
ui
t
of
UP
F
C
sy
st
em
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
R
obus
t st
a
b
i
lit
y
power
i
n
t
h
e tr
ansm
i
ss
io
n l
i
ne w
i
t
h
t
h
e use
of a
U
PFC
… (Bou
an
a
n
e
Ab
delk
rim
)
1
283
Th
e
mod
e
li
n
g
o
f
th
i
s
c
i
r
cu
it
i
s
b
a
s
ed
o
n
h
ypo
th
e
s
es
s
imp
l
i
f
y
i
ng
.
Th
e
dy
na
mic
e
q
uat
i
o
n
s
o
f
th
e
U
P
F
C
a
re
d
iv
ide
d
i
nt
o
thre
e
sys
t
em
s
of
e
q
u
a
tio
ns.
B
y
p
e
rform
in
g
d
-
q
t
ra
nsf
o
rm
atio
n,
t
h
e
c
urrent
t
h
r
o
u
gh
t
h
e
transm
i
s
s
i
on l
i
n
e c
a
n
be de
s
crib
e
d
b
y the
fo
l
l
ow
i
ng e
q
ua
tio
ns.
(
1
)
S
i
milarl
y,
the shu
n
t
in
v
er
t
e
r c
a
n
be de
s
cri
b
e
d
b
y
:
(
2
)
By
t
h
e
u
se
o
f
p
o
w
e
r
b
al
an
ce
i
f
o
n
e
n
eg
l
e
c
t
s
t
h
e
lo
ss
es
o
f
t
h
e
i
n
v
erte
r
i
t
i
s
p
o
ss
ible
t
o
expr
ess
th
e
con
t
in
uou
s
vol
tage
b
y
:
(
3
)
The
DC-l
in
k ca
paci
t
o
r
C
must be
selec
t
ed t
o
be
lar
ge e
no
ugh
to m
i
n
im
ize
vo
ltage
tra
nsie
nt
s
3.
CONT
ROLLER D
E
S
IG
N
Th
e
con
t
r
o
l
sys
t
em
o
f
t
h
e
UPFC
c
o
n
s
i
s
t
s
o
f
th
e
shun
t
i
n
v
e
rt
er
w
i
t
h
the
c
o
n
t
r
o
l
c
i
rc
u
i
t
[14-
17]
a
s
w
e
ll
a
s
t
he
s
e
r
ies
i
n
verte
r
.
First,
w
e
j
u
st
i
f
y
t
h
e
p
o
ss
ib
i
lit
y
of
s
ep
a
r
a
t
i
o
n
of
t
h
e
t
wo
c
on
t
r
o
l
c
i
r
cu
it
s
and
si
m
i
larly
w
e
a
r
e
i
n
t
e
r
este
d in
the
a
dj
ustm
ent
of
t
he inve
r
t
er f
or the
a
dd
iti
o
n
al
v
o
l
tage
an
d
mor
e
p
a
r
t
i
c
u
la
rly t
o
the se
t
t
i
ng o
f
t
h
e
a
cti
v
e a
n
d re
acti
v
e
p
o
wer
transm
i
t
ted.
The
n
w
e
w
ill
deve
l
op
t
h
e
d
i
ffe
r
ent
se
t
t
i
n
gs
c
on
side
red
in
t
his
st
ud
y
a
nd
w
e
w
il
l
s
how
t
he
t
ra
nsie
n
t
beha
v
i
or of t
h
e
c
o
n
t
r
o
l circ
u
i
t
s
u
s
i
n
g
a
s
imul
ati
o
n
o
f
t
he reg
u
l
a
to
rs
c
on
si
d
e
re
d
i
n
t
h
e
a
djust
m
e
n
t
of
t
h
e
c
l
o
sed
lo
op
U
P
F
C
s
ystem
i
n
o
rde
r
t
o
impr
o
v
e
the
pe
rfor
ma
nces
i
n
the
ca
se
o
f
acti
v
e
or
r
e
acti
v
e
p
o
wer
c
h
ange.
,
(cha
n
g
e
o
n
e
o
f
t
he thre
e
p
ara
m
e
t
e
r
s of
t
he l
i
n
e)
.
3.1.
PI d
ecoupling
cont
rol (PI-
D)
The
o
b
j
e
c
t
i
ve
o
f
usi
ng
t
h
e
P
I
-D
i
s
to
p
ro
v
i
d
e
i
n
d
e
p
en
de
nt
c
on
tr
o
l
o
f
a
c
t
i
ve
P
a
nd
r
eac
t
i
ve
Q
pow
e
r
f
l
o
w
i
n
t
h
e
s
y
s
t
e
m
f
o
r
f
i
x
e
d
v
a
l
u
e
s
o
f
V
s
a
n
d
V
r.
Th
is
c
an
b
e
ac
h
i
e
v
e
d
b
y
p
r
o
p
erly
c
on
tro
l
l
i
n
g
t
he
s
e
r
ies
in
j
e
c
t
e
d
v
o
l
t
a
ge
o
f
the
UP
FC.
The
vo
lta
ge,
curr
ent
an
d
p
o
wer
fl
o
w
a
re
r
e
l
a
t
e
d
t
h
r
ou
gh
t
h
e
f
ol
l
o
w
i
ng
equa
t
i
o
n
s
:
(
4
)
(5
)
With
a
nd
The
pri
n
c
i
p
l
e
of
t
h
i
s
c
o
n
t
ro
l
strate
gy
is
t
o
con
v
er
t
t
h
e
m
e
a
s
ur
ed
t
hre
e
p
hase
c
urre
nt
s
a
n
d
v
o
lta
ge
s
i
n
t
o
d
-q
v
a
l
u
e
s a
n
d
t
h
e
n
to
ca
lc
u
l
at
e
t
h
e cu
rren
t
re
f
e
r
en
c
e
s
a
n
d m
e
a
s
ured
v
o
l
tage
s
as
f
ol
low
:
∗
∗
∗
∆
(
6
)
∗
∗
∗
∆
(
7
)
With
∆
(
8
)
A
c
cordi
n
g
to
t
he
s
ystem
of
e
q
u
at
i
o
n
s
(
1)
o
r
(2),
one
c
an
h
ave
t
h
e
s
y
s
t
e
m
con
t
a
i
ns
a
c
oupl
ing
betw
ee
n
t
h
e
r
e
ac
tive
a
n
d
a
c
t
i
v
e
c
u
rre
nt
I
d
Iq.
The
i
n
te
rac
tio
n
be
t
w
e
e
n
c
urre
nt
c
a
u
se
d
by
t
h
e
c
o
upl
i
n
g
term
(ω
) F
i
gure
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
281
–
1
2
96
1
284
F
i
gur
e
3.
Co
ntr
o
l
de
si
g
n
w
it
h
P
I
c
or
r
e
ctor
To
b
e
a
b
le
t
o
lea
d
t
o
a
rel
i
ab
le
c
omm
a
nd
o
f
t
he
s
ys
te
m
,
it
is
i
nd
is
pen
s
ab
le
t
o
pr
oce
e
d
t
o
a
de
co
u
p
l
i
ng
of
t
he
t
w
o
c
om
p
one
n
t
s.
T
he
d
e
c
ou
p
lin
g
o
f
t
w
o
l
o
o
p
s
i
s
o
b
t
a
i
n
ed
b
y
su
b
t
ra
ct
ing
t
h
e
ter
m
(
)
t
h
r
o
u
g
h
a
r
e
a
c
t
i
o
n
a
g
a
i
n
s
t
.
I
t
i
s
t
h
e
n
c
o
n
d
u
c
t
e
d
t
o
a
r
u
l
e
w
h
i
c
h
pr
o
v
i
d
es
a
c
om
m
a
nd
w
i
th
d
e
c
o
up
l
i
n
g
(
PI
-
D
)
of
t
he
c
ur
r
e
nts
I
d
an
d
I
q
w
i
t
h
a
m
odel
w
h
i
c
h
c
a
n
be
r
e
w
r
itt
e
n
i
n
the
f
o
ll
ow
in
g
for
m
:
1
1
(
9
)
The des
i
gn of
t
he co
n
tr
ol
s
ys
te
m
m
u
st be
g
in
w
ith the
s
e
l
ec
tio
n
of
v
ari
a
bl
es
t
o
a
d
ju
st
a
nd
t
h
e
n
th
a
t
o
f
the
co
n
t
ro
l
va
riab
les
a
n
d
t
h
ei
r
assoc
i
at
i
o
n
wit
h
v
ar
i
a
ble
s
s
et.
T
her
e
a
r
e
v
ar
ious
a
d
j
ust
m
ent
te
c
h
n
i
qu
e
s
w
e
l
l
su
ite
d
t
o
t
he
P
I
contr
o
l
l
er
.
The
str
u
c
t
ur
e
of
t
he
P
I
con
t
r
o
l
l
er
i
s
r
e
pr
ese
n
t
e
d
b
y
t
he
f
ir
s
t
b
l
o
c
k
d
ia
gr
am
o
f
Figu
re 4
.
F
i
gur
e
4.
Adjustm
e
n
t
struc
tur
e
of
the P
I
t
ype
In
c
o
n
t
r
ol
,
we
o
bt
a
i
n
t
h
e
f
o
l
l
o
w
i
ng
c
ont
rol
l
er,
d
e
p
e
nd
ing
on
t
h
e
d
a
m
p
ing
c
o
e
f
fi
ci
en
t
ξ
and
th
e
f
r
e
que
n
c
y
:
(
10)
Ther
e
ar
e
tw
o
w
e
ll-
k
now
n
em
pi
r
i
c
a
l
a
p
p
r
o
ac
hes
pr
op
ose
d
by
Zie
g
l
er
a
nd
T
i
t
f
o
r
dete
rm
ining
th
e
op
t
i
ma
l
par
a
m
e
ter
s
o
f
t
h
e
P
I
c
o
n
tr
o
l
ler
Tabl
e
1.
Tab
l
e
1.
O
pt
im
al
p
a
r
am
ete
r
s
of
t
he
P
I
contr
o
l
l
e
r
.
T
yp
e
of
K
p
T
i
K
P
I
0
.
45K
cr
0.
83
P
cr
0
The
m
e
th
o
d
Z
i
e
gler
-
N
ich
o
l
s
[
18]
u
se
d
in
t
he
p
r
e
se
nt
a
r
t
ic
le
i
s
base
d
on
a
tr
ia
l
c
ond
uc
t
e
d
in
c
l
o
se
d
lo
o
p
w
i
t
h
a
s
i
m
p
le
a
na
log
y
p
r
o
por
ti
ona
l
c
o
n
t
r
o
l
l
er
.
The
gai
n
K
p
o
f
t
h
e
r
e
gula
t
or
i
s
gr
adua
l
l
y
inc
r
ea
sed
u
n
til
the
s
t
a
b
il
it
y
l
i
m
it,
w
hich
i
s
c
h
ara
c
ter
i
z
e
d
by
a
ste
a
d
y
osci
l
l
a
ti
o
n
.
B
a
s
e
d
o
n
th
e
re
su
l
t
s
ob
t
a
in
e
d
,
th
e
pa
r
a
m
e
ter
s
o
f
the
P
I
c
ontr
o
lle
r
give
n
by
Ta
bl
e
2.
2
2
N
i
N
p
k
a
k
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
R
obus
t st
a
b
i
lit
y
power
i
n
t
h
e tr
ansm
i
ss
io
n l
i
ne w
i
t
h
t
h
e use
of a
U
PFC
… (Bou
an
a
n
e
Ab
delk
rim
)
1
285
Tab
l
e
2.
P
a
r
ameter
s
of
t
he
PI c
o
n
t
r
o
l
l
er
in o
u
r
syste
m
Pa
ra
m
t
K
i
ω
K
p
ξ
Val
e
as
2
0
.
000
3
1
4
.
15
6
0
.
4
5
0
.2
00
a.
Perform
a
nce
evalua
t
ion
S
i
mulat
i
o
n
ar
e
pe
rfor
me
d
a
P
e
nti
u
m
P
C
u
n
d
e
r
M
A
TLA
B
/
S
i
mul
i
n
k
so
f
twar
e
pr
ogram
.
The
transm
i
s
s
i
on
l
i
n
e
a
n
d
the
U
P
F
C
(
t
w
o
i
n
ve
r
t
ers)
s
yst
e
m
are
imple
me
n
t
e
d
w
it
h
si
m
u
l
i
nk
b
loc
k
s.
F
or
eac
h
o
f
t
h
e
c
o
n
t
r
o
l
s
y
s
t
e
m
s
,
a
s
i
m
u
l
a
t
i
o
n
m
o
d
e
l
i
s
c
r
e
a
t
e
d
w
h
i
c
h
i
n
c
l
u
d
es
t
he
r
eq
uire
d
P
W
M.
T
he
p
ara
m
e
t
e
r
s
of
t
he
si
m
u
lat
i
on
m
o
del
are
se
le
cte
d
t
o
be
e
q
u
a
l
t
o
t
h
e
par
a
m
e
ters
o
f
a
la
b
o
ra
to
ry
U
P
F
C
m
ode
l
[19],
[2
0]
w
hic
h
a
re
liste
d
in
T
ab
le
3
.
Ta
b
l
e
3.
The
p
ar
am
eters
of th
e
l
abora
t
ory
U
P
F
C
m
odel
P
a
r
a
m
e
t
e
r
n
a
m
e
S
ym
bol
V
al
ue
U
nit
Ne
tw
or
k
volta
ge
V
r
220
V
V
o
l
t
ag
e
o
f
t
h
e
r
ec
ei
v
e
r
Vs
2
2
0
V
D
C
volta
ge
V
dc
280
V
N
e
twork
fr
e
que
ncy
f
50
H
Z
Th
e
cap
aci
t
y
o
f
t
h
e
co
mm
o
n
c
i
r
c
uit DC
C
2
m
F
I
n
du
c
t
an
ce 1
L
1
1
.
125
m
H
Re
sist
a
n
ce
1
R
1
100
Ω
I
n
du
c
t
an
ce 2
L
2
1
.
125
m
H
Re
sist
a
n
ce
2
R
2
100
Ω
b.
Simula
tion
resu
l
t
s (
s
ystem U
P
F
C
with
PI dec
o
upl
i
ng
cont
ro
l)
The
resul
t
o
f
t
h
e
simula
ti
o
n
is show
n in
F
i
gur
e
5.
F
i
gure
5.
Currents
waveform
s
I
sa
,
I
sb
a
nd
I
sc
(A
)
.
The
t
e
s
t
r
ob
us
tne
ss
i
s
o
bserv
e
d
tha
t
t
he
0
.
4
s
a
n
d
0
.
6
s
m
ome
n
t
s
cau
se
a
n
al
most
zero
v
a
ri
ati
o
n
con
s
i
d
ere
d
a
s
a
d
i
st
urba
nc
e
of
a
c
t
ive
an
d
re
acti
v
e
power
F
ig
ure
6
due
t
o
t
h
e
in
t
e
rac
t
ion
be
tw
e
e
n
th
e
tw
o
pow
er
s.
The
contr
o
l sy
stem
ha
s
a
f
ast-dy
na
mi
ca
l
respo
n
se
a
n
d
th
e
sam
e
i
n
D
C
vo
l
t
a
ge
F
i
gure
7.
0.
35
0.
4
0.
4
5
0.
5
0.
55
0.
6
0.
65
-2
-1.
5
-1
-0.
5
0
0.
5
1
1.
5
2
C
u
rr
e
n
t
s
I
s
a,I
s
b
an
d
I
s
c
(
A
)
t(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
3
, Se
p
2
019 : 1281 –
1
2
96
1
286
(a)
(b
)
(c)
F
i
gure
6.
P
o
w
e
rs re
s
po
nse
s
o
u
r
s
ystem
w
ith P
I-D
:
(a).
a
t+
3
0
%
of
X
L, (b). at
X
L
a
nd (c
).
a
t -
30% of X
L
F
i
gure
7.
D
C
vol
ta
ge
B
y
i
n
t
r
o
duc
i
n
g
pert
urba
t
i
o
n
F
i
g
ure
8
dura
t
i
o
n
of
25
ms
a
n
d
a
m
p
l
i
t
u
d
e
1
.
5
t
o
t
e
s
t
a
g
a
i
n
s
t
a
b
i
l
i
t
y
o
f
our sys
tem
.
A
s c
a
n be
see
n, the
contr
o
l
l
er
(
P
I
-D
) re
jecte
d
t
he
e
x
t
e
rna
l
p
ert
u
rba
t
i
o
n qu
i
t
e r
a
pi
dly.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Ro
bus
t
sta
b
i
l
ity
po
wer
in
t
h
e
tr
a
n
sm
iss
i
on l
i
ne
w
i
t
h
the
use
of
a
U
PFC …
(
B
ou
an
a
n
e Ab
delk
rim
)
1
287
F
i
gur
e
8.
System
r
espon
se in
the
pre
s
ence
o
f
exter
n
a
l
d
is
tur
b
a
n
ce
3.
2.
Neura
l
a
da
p
t
iv
e co
nt
ro
l
Cur
r
ent
l
y
the
adap
t
i
ve
c
ontrol
i
s
o
f
a
gr
eat
i
m
p
o
r
t
a
nce
in
t
he
f
i
e
l
d
of
c
on
tr
o
l
.
T
h
is
c
om
ma
nd
i
s
dom
i
n
a
n
t
in
s
y
s
tem
s
t
ha
t
pre
s
e
n
t
uncer
ta
in
ti
es,
st
r
u
c
t
ura
l
d
is
t
ur
ba
nce
s
a
n
d
c
h
a
nges
in
t
he
e
n
v
ir
onm
en
t.
T
h
e
ma
i
n
o
bj
e
c
t
o
f
t
h
e
a
dapt
i
v
e
co
nt
rol
i
s
t
h
e
s
yn
th
e
s
i
s
o
f
th
e
ac
t
o
f
a
d
a
p
ta
t
i
on,
f
or
t
he
a
u
t
om
ati
c
a
d
j
us
tm
ent
in
r
eal
tim
e
o
f
t
h
e
r
e
gul
a
t
or
s
of
t
he
c
on
tr
o
l
l
oops
i
n
or
der
to
a
c
hie
v
e
or
m
a
i
n
t
a
i
n
c
e
r
t
ai
n
l
e
ve
l
of
p
e
r
f
o
r
m
anc
e
w
h
e
n
t
h
e
p
a
r
a
m
e
t
e
r
s
o
f
t
h
e
p
r
o
c
e
s
s
t
o
o
r
d
e
r
a
r
e
d
i
f
f
i
c
u
l
t
t
o
d
e
term
ine
or
v
a
r
y
wi
t
h
tim
e.
T
he
i
n
t
er
est
of
t
h
e
a
d
ap
t
i
ve
c
o
n
t
r
ol
a
p
p
ea
r
s
m
ai
n
l
y
at
t
h
e
l
e
v
el
o
f
d
i
s
t
ur
ba
nc
e
pa
r
am
e
t
r
i
c
,
t
ha
t
is
t
o
sa
y
a
r
e
ac
t
i
n
g
on
t
h
e
c
h
ar
a
c
ter
i
s
t
ics
of
t
he
p
r
o
c
e
ss
to
o
r
d
er
,
di
s
t
ur
ba
n
c
e,
a
ct
o
n
t
h
e
var
i
a
b
le
s
to
r
egula
t
e
or
t
o
or
de
r
.
T
he
i
nte
r
e
s
t
o
f
t
h
e
ad
apt
i
v
e
co
nt
rol
app
e
ars
mai
n
ly
a
t
t
h
e
l
e
v
e
l
o
f
d
i
s
t
u
rb
an
c
e
p
ar
am
etric,
t
ha
t
i
s
t
o
say
ar
e
ac
tin
g
o
n
t
h
e
c
h
ar
a
c
ter
i
s
t
ics
of
t
he
p
r
o
cess
to
o
r
d
er
,
d
i
s
t
ur
bance
,
a
c
t
on
t
h
e
va
riab
les
t
o
r
egu
l
ate
or
t
o
or
der.
F
i
n
a
l
l
y
,
t
h
e
co
mb
in
ati
o
n
of
t
h
e
a
d
a
pt
iv
e
c
o
nt
rol
wit
h
o
t
h
er
t
yp
e
s
o
f
con
v
e
nt
i
ona
l
c
o
m
m
a
nds
o
f
the
a
u
tom
a
t
i
c
ha
s
bor
n
e
f
r
u
i
t
a
nd
ha
s
been
t
he
s
o
u
r
c
e
of
m
an
y
j
o
b
s
.
The
a
d
a
p
t
i
v
e
l
a
w
s
i
mp
la
nt
ed
i
n
the
i
d
eal
c
a
s
e
cou
l
d
le
ad
t
o
in
sta
b
ili
ty i
n t
h
e
ca
se
of exte
rnal d
is
t
u
rban
ce
s bou
n
d
e
d
.
I
n
t
h
i
s
ar
t
i
cle
w
e
p
r
e
se
nt
t
he
A
djustm
en
t
m
e
tho
d
p
r
o
p
o
se
d
f
o
r
t
h
e
U
P
F
C
,
f
a
v
o
r
i
n
g
t
h
e
c
l
a
s
s
i
c
a
l
a
ppr
oac
h
b
a
s
e
d
o
n
ne
ur
o
n
s
n
e
tw
or
ks.
N
e
ur
a
l
N
etw
o
r
k
i
s
tr
aine
d
b
y
ada
p
t
i
ve
[
2,
1
9-
25]
t
he
n
e
t
w
o
r
k
‘
l
e
a
r
ns’
how
t
o
do
ta
sks,
p
er
for
m
f
u
n
c
t
i
o
n
s
b
ase
d
on
t
h
e
da
ta
g
ive
n
f
or
t
r
ai
n
i
n
g
.
The
k
now
le
dge
l
ear
ne
d
d
u
r
i
ng
tr
a
i
ni
n
g
i
s
s
t
o
r
ed
i
n
t
h
e
s
y
nap
t
ic
w
e
i
g
h
ts
.
The
sta
ndar
d
N
eur
a
l
N
e
t
w
o
r
k
s
t
r
u
c
t
u
r
e
s
(
f
e
e
d
f
o
r
w
a
r
d
a
n
d
r
ecur
r
ent)
ar
e
b
o
t
h u
s
e
d
t
o
m
ode
l the
U
P
F
C
system
.
The m
ain tas
k of th
i
s
pa
per
is t
o
de
sig
n
a
n
e
u
r
a
l ne
tw
or
k
c
o
n
t
r
o
ller
whic
h
kee
p
s
the
UPF
C
s
ys
t
e
m
sta
b
il
i
z
e
d
.
Elma
n
'
s
netw
or
k
sa
id
h
i
d
den la
yer
n
e
t
w
or
k
is
a
r
ec
ur
r
e
n
t
ne
t
w
or
k
F
i
g
u
r
e
9
,
th
us
b
et
ter
sui
t
e
d
f
or
m
odel
i
ng
d
yna
mi
c
sys
t
e
m
s
.
His
cho
i
ce
in
t
h
e
n
eura
l
c
o
n
t
r
o
l
b
y
s
ta
t
e
f
eed
ba
c
k
,
i
s
j
u
st
if
ied
b
y
i
ts r
o
l
e,
th
i
s
ne
tw
or
k
ca
n
be
i
n
t
e
r
p
r
et
ed
a
s
a
st
a
t
e sp
ac
e
mod
e
l
no
nl
i
n
ea
r.
L
ea
rni
n
g
by
ba
ck
p
r
opa
ga
ti
on
al
g
o
r
i
thm
sta
ndar
d
i
s
the
la
w
used
f
or
i
de
nti
f
icati
o
n
of
th
e
U
PFC.
F
i
gur
e
9.
S
t
r
u
c
t
ur
e
of
t
he
E
lm
a
n
n
etw
o
r
k
3
.
2
.
1
.
N
e
ura
l
a
da
p
t
iv
e
co
nt
ro
l b
y
sta
te sp
a
ce U
PFC
S
y
s
tem
w
i
th
E
RNN (
NAC
S
S
S-ERNN)
The
in
t
e
grat
io
n
o
f
t
he
se
t
w
o
a
p
p
roac
h
e
s
(
n
eura
l
a
d
a
p
t
i
ve
c
o
n
t
r
o
l
)
[
2
6
,
27]
.
i
n
a
s
in
gle
hy
br
i
d
str
u
c
t
ur
e
,
t
ha
t
ea
ch
b
e
n
e
f
it
fr
om
t
he
o
t
h
er
,
bu
t
t
o
c
ha
nge
t
he
dyna
mic
b
e
hav
i
or
o
f
t
h
e
U
P
F
C
s
ystem
w
a
s
a
dde
d
a
g
a
i
n
s
t
a
r
e
a
c
tion
ca
l
c
ul
a
t
e
d
f
r
o
m
the
state
vec
t
or
(
st
at
e
spac
e)
F
igu
r
e
10.
Inp
u
t
la
ye
r-
H
i
dde
n
l
a
ye
r
-
O
u
tput
l
a
y
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
281
–
1
2
96
1
288
Fi
g
u
re
1
0
.
Dia
g
ram
of a UPFC co
ntro
l b
y
s
ta
te feed
ba
c
k
The
st
a
t
e
f
eed
b
a
ck
c
on
t
r
o
l
i
s
t
o
c
on
si
der
the
pr
ocess
mode
l
i
n
t
h
e f
o
rm
o
f an e
qua
t
i
o
n
o
f
sta
t
e
:
X
∗
t
A
x
t
B
U
t
(
11)
A
nd
o
b
ser
v
a
tio
n
equa
t
i
o
n
:
Y
t
C
x
t
D
U
t
(
12)
Whe
r
e
u
(
t
)
i
s
t
he
c
on
tr
o
l
v
e
c
t
or
,
x
(
t
)
t
h
e
s
t
ate
ve
c
t
or
,
an
d
y
(t
)
t
h
e
out
put
v
ect
o
r
o
f
di
me
n
s
i
o
n
fo
r
a
di
scr
e
te
s
ys
tem
to
t
he
s
am
p
lin
g
pr
oce
s
s
par
a
me
ter
s
T
e
a
t tim
es of T
e
sample
k
are
f
o
r
malized
as
f
o
llo
w
s
:
X
t
1
A
X
t
B
U
t
(
13)
Y
t
C
x
t
D
U
t
(
14)
T
h
e
sy
st
em
i
s
o
f
o
rd
e
r
1
,
so
i
t
re
q
u
i
r
es
a
s
in
gl
e
st
at
e
v
a
ri
ab
l
e
x
.
t
hi
s
st
at
e
v
a
ri
abl
e
r
epres
e
n
t
s
th
e
ou
t
p
u
t
o
f
an
i
n
t
egr
a
t
o
r
a
s
s
how
n
in
F
ig
ur
e
11.
x
(
t
)
=
y
(
t
)
x
*
(
t
)
=
y
*
(
t
)
F
i
gur
e
1
1
.
Bl
o
c
k
dia
g
r
a
m
of
t
he
s
ta
te
r
epr
e
senta
t
io
n
o
f
t
he
U
P
F
C
The
t
r
ans
f
e
r
f
unc
t
i
on
G
s
Y
s
U
s
⁄
o
f
o
u
r
p
ro
cess UP
FC
c
an
b
e wr
i
tten
as:
G
s
⁄
(
15)
We
d
ed
uc
e
t
h
e
equa
ti
on
s
of
s
t
a
te
r
epr
e
senta
t
i
on
o
f
t
he
U
P
F
C
:
∗
(
16)
W
ith
:
U
t
e
t
k
x
t
Let:
X
t
1
x
t
e
t
(
17)
(
18)
The
dy
nam
i
cs
o
f
the
pr
oces
s
cor
r
ec
t
e
d
b
y
sta
t
e
s
p
ac
e
is
p
re
sen
t
ed
b
ase
d
o
n
t
h
e
c
h
a
r
ac
t
e
ri
stic
e
qua
t
i
o
n
o
f the
m
a
trix [A
d
-
B
d
K
]
,
w
h
e
re K
i
s
th
e matrix
s
ta
t
e
sp
a
ce-cont
r
o
l
l
e
d
p
ro
ces
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Ro
bus
t
sta
b
i
l
ity
po
wer
in
t
h
e
tr
a
n
sm
iss
i
on l
i
ne
w
i
t
h
the
use
of
a
U
PFC …
(
B
ou
an
a
n
e Ab
delk
rim
)
1
289
Ou
r
s
y
stem
i
s
d
e
scrib
e
d
in
matrix
fo
rm
i
n
the
s
t
at
e sp
ace:
W
h
ere:
∗
(
19)
,
1
0
0
1
,
10
01
,
00
00
,
,
a.
U
PFC sy
s
tem
ident
i
f
i
ca
tio
n
u
sing
ernn(N
E
WEL
M
)
The
id
en
t
i
fica
tio
n
m
a
ke
s
it
p
o
ss
ible
t
o
obta
i
n
a
m
a
t
h
em
ati
cal
m
od
e
l
t
h
a
t
r
e
p
r
es
en
t
s
a
s
fai
t
hf
ull
y
a
s
pos
si
b
l
e
the
d
yna
mic
beha
v
i
or
o
f
t
h
e
pr
oc
ess
[
2
8]
.
A
p
r
ocess
i
d
en
t
i
f
i
e
d
w
i
ll
t
h
en
b
e
cha
r
ac
t
e
r
i
zed
b
y
t
h
e
str
u
c
t
ur
e
of
t
he
m
ode
l,
o
f
its
o
r
d
e
r
a
nd
b
y
t
h
e
va
lue
s
o
f
the
S
etting
s
.
I
t
is
t
h
e
refo
re,
a
c
o
ro
ll
ary
of
t
h
e
p
r
o
cess
sim
u
la
ti
on
f
o
r
w
h
ic
h
one
u
ses
a
m
odel
a
nd
a
set
of
c
oe
ff
ic
ie
nt
s
i
n
or
der
t
o
p
r
e
dic
t
t
he
r
espo
nse
o
f
t
he
s
y
s
tem
.
T
h
e
f
i
g
u
r
e
s
h
o
w
s
t
h
e
n
e
t
w
o
r
k
E
l
m
a
n
c
o
n
s
i
s
t
i
n
g
o
f
t
h
r
e
e
l
a
y
e
r
s
:
a
l
a
yer
of
e
n
t
r
y
,
hi
d
d
e
n
l
a
y
er
a
nd
a
laye
r
of
o
ut
put
.
The
l
a
yer
s
o
f
en
tr
y
a
nd
e
x
it
i
nt
e
r
fe
r
e
w
i
t
h
t
h
e
out
sid
e
e
nvi
ron
m
e
n
t
,
w
hi
ch
i
s
n
o
t
t
h
e
c
a
s
e
fo
r
the i
n
t
e
rm
edia
t
e
l
ayer
c
a
lle
d
h
i
d
d
e
n
l
ayer
.
In
t
h
i
s
d
i
agr
a
m
,
t
h
e
e
n
tr
y
o
f
t
he netw
o
r
k
is the com
m
a
nd
U
(
t
)
an
d
its o
u
tp
ut
i
s
Y
(
t
)
.
T
h
e
v
ecto
r
o
f
state
X
(
t
)
fr
o
m
th
e h
i
dd
en
layer
is
i
nje
c
te
d
int
o
t
he
i
n
p
u
t
layer
F
i
gur
e
12.
F
i
gur
e
1
2
.
S
t
r
u
ctur
e
of
t
he
N
EWEL
M
The
s
t
a
t
e
ve
ct
or
X
(
t)
from
t
h
e
h
i
dd
en
l
aye
r
i
s
in
jec
t
e
d
i
n
t
o
t
he
i
np
ut
l
a
y
e
r
.
We
d
e
duc
e
t
h
e
fo
llow
i
n
g
e
qua
tio
ns
:
X
t
W
X
t1
W
U
t
1
(
20)
Y
t
W
Xt
(
21)
W
h
e
r
e
,
W
h
,
W
r
e
t
W
o
a
r
e
t
h
e
w
e
i
g
h
t
m
a
t
r
i
c
e
s
.
E
q
u
a
t
i
o
n
s
a
r
e
s
t
a
n
da
rd
d
escr
i
p
t
i
ons
o
f
t
h
e
sta
t
e
spac
e
o
f
d
y
n
a
m
ica
l
s
ystem
s
.
The
or
der
o
f
t
he
s
ys
t
e
m
de
p
e
nd
s
o
n
the
n
u
m
be
r
of
s
ta
tes
e
qua
ls
t
he
num
ber
of
h
i
dd
e
n
l
ay
e
r
s.
W
h
e
n
an
i
np
ut-o
ut
put
d
at
a
i
s
p
rese
nt
e
d
t
o
the
n
e
tw
or
k
a
t
i
t
e
r
a
t
i
on k
s
quar
e
d
er
r
o
r
a
t
t
he ou
t
pu
t
of
t
he
n
e
t
w
o
r
k
i
s
de
f
i
ned
as
:
(
22)
Fo
r t
h
e
wh
o
l
e trai
ni
ng
d
a
t
a u
(t
), y
d
(
t)
d
e
t
= 1,
2
…
N
,
t
he
s
um
me
d
squar
e
d
e
r
r
o
r
s
i
s:
∑
(
23)
The
weig
h
t
s
are
m
odifie
d
a
t ea
ch
t
im
e
ste
p
for
W
0
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
281
–
1
2
96
1
290
.
(
24)
For
W
h
e
t Wr,
.
.
.
.
(
25)
.
.
.
.
(
26)
The
l
a
tt
e
r
w
e
obta
i
n:
1
(
27)
Eq
uat
i
on
s
how
s
t
h
a
t
t
her
e
i
s
a
dy
nam
i
c
t
r
ac
e
of
t
he
g
r
a
d
i
e
n
t
.
T
h
i
s
is
s
imilar
t
o
b
ac
k
pr
opa
ga
t
i
o
n
thr
o
u
g
h
tim
e. Beca
use the
g
e
ner
a
l
e
x
pressi
o
n
for
weig
h
t m
o
d
i
fic
a
t
io
n
i
n
t
he
g
r
a
die
n
t
des
c
e
n
t
me
t
hod
is:
(
28)
The
d
yna
mic
back
p
r
opa
ga
ti
on
a
lg
or
i
t
h
m
u
se
d
t
o
i
de
n
t
i
f
y
a
sta
t
e
s
p
a
c
e
m
o
d
e
l
o
f
t
h
e
U
P
F
C
f
o
r
N
E
WEL
M
(
Elm
a
n
netw
or
k)
can
b
e
summ
ariz
ed
a
s
fo
l
l
ow
s
:
(
29)
.
(
30)
.
(
31)
I
f
t
he
d
e
p
en
de
nce
of
X
(
t
-
1)
o
n
W
i
i
s
i
g
n
o
r
e
d
,
t
h
e
ab
ov
e
a
l
go
ri
th
m
d
e
grad
e
s
i
s
t
h
e
sta
n
d
a
rd
b
ac
k
pr
opa
ga
t
i
o
n
a
l
gor
it
hm:
1
(
32)
F
i
gur
e
1
3
.
UP
F
C
s
y
s
te
m
p
r
e
s
e
n
ta
t
i
o
n
w
i
th
s
ta
te
s
p
a
c
e
a
n
d
(
E
RN
N
-
N
E
WE
L
M
)
b.
Estima
tio
n
o
f the
p
a
ra
meter
s
The
in
pu
t
u
s
ed
o
f
t
h
e
Ec
hel
o
n
t
ype,
is
e
nv
i
s
age
d
f
or
i
de
ntif
ic
a
tio
n
sys
t
e
m
s
[13]
.
I
t
i
s
ob
v
i
o
u
s
th
a
t
the
e
n
t
r
y
is
b
et
t
e
r
tha
n
o
n
t
h
e
ot
her
(
r
ail,
S
inuso
i
d……)
f
r
o
m
t
he
p
o
i
n
t
o
f
vie
w
o
f
t
h
e
i
d
e
n
t
i
f
ica
tio
n.
I
n
or
de
r
to al
l
ow
a
n id
e
n
t
i
fica
t
i
o
n
b
y
e
n
tr
ies t
o
e
xc
i
t
e
th
e
ma
ximum
of
th
e
mo
des
of
t
h
e
s
y
s
t
e
m
wit
hou
t
too
di
sr
u
p
t
i
t
s
nor
m
a
l
o
p
er
at
i
o
n,
i
f
it
w
a
nts
to
p
u
l
l
a
l
o
t
of
i
n
f
or
m
a
tio
n,
i
n
par
tic
u
l
ar
t
he
e
xci
t
e
i
n
t
he
e
ntir
e
fr
eq
ue
nc
y
ban
d
in
tere
sti
ng,
o
n
e
u
ses
i
n
g
e
n
e
r
al
a
v
ar
iat
i
o
n
i
n
the
ni
che
m
a
r
k
e
t
o
f
p
se
ud
or
an
do
m
bina
r
y
s
eq
uen
c
e
(
P
RB
S
)
S
uper
i
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.