Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
4
,
No
. 2,
J
une
2
0
1
4
,
pp
. 21
2~
22
2
I
S
SN
: 208
8-8
6
9
4
2
12
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Design and Simulation of Dyna
mic
V
o
ltage Restor
er
Based on
Fuzzy Contr
o
ller
Optimized by
ANFIS
Bra
h
im Ferdi*
,
Sa
mira
Dib*
, Bra
h
im Berbao
ui**
,
**
*,
Rac
h
i
d
Dehi
ni
*
* Technolog
y
D
e
partment, B
ech
ar University
, B.P 417 Bech
ar (0
8000), Algeria
** Unité de rech
erche en
En
ergie Renouve
lables en
milieu
sah
a
rien, URERMS,
Centre de Développement des
Energies R
e
nouvelables, CDER
, 0
1000,
Adrar
,
Algeria,
*** Labor
atoire
de dév
e
lopp
ement
durab
le et inf
o
rmatique
LDDI
, Université Adrar, Alg
e
ria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 27, 2014
Rev
i
sed
Feb
28
2
014
Accepted
Mar 16, 2014
The fuzzy
logic
controller (FLC)
appears to b
e
th
e unique solu
tio
n when the
process is too complex for analy
s
is b
y
conv
entional techniqu
es
or when the
avai
labl
e infor
m
ation data ar
e
interpre
ted qua
lita
tive
l
y, in
exa
c
tl
y or with
uncertainty
. In literature, the proposed
FLC in ge
neral consists of two inputs
(error and der
i
v
a
tiv
e of error) and one output. The number of
membership
functions
is
ch
os
en in m
o
s
t
cas
es
to
be five or seven regar
d
less of the
approach used
f
o
r the design
. I
n
this paper
,
we propose Adap
tive Neuro-
Fuzzy
Inf
e
ren
c
e Sy
stem (ANFI
S
) appr
oach to optimize th
e two inputs one
output FLC with seven member
ship f
unctions
to one inpu
t one output FLC
with thre
e m
e
m
b
ership funct
i
on
s without com
p
rom
i
sing accura
c
y
. The stu
d
y
is appli
e
d to
con
t
rol a
D
y
n
a
m
i
c
Voltage
Restorer (DVR) in
voltage sag/swell
m
itigation
.
Th
e
results of sim
u
la
ti
on using MAT
L
AB/SIMULINK show that
the pe
rform
ance
of the op
tim
al F
L
C gene
rat
e
d b
y
ANF
IS
is
com
p
arabl
e
with
the init
ial
giv
e
n FLC.
Keyword:
FLC
M
e
m
b
ershi
p
F
unct
i
o
ns
AN
FIS
DVR
Vo
ltag
e
Sag
/
Swell
Copyright ©
201
4 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
:
Brah
im
Ferd
i,
Tech
nol
ogy
D
e
part
m
e
nt
, B
echar
U
n
i
v
e
r
si
t
y
,
B.P 417
Bech
ar
(08
000
),
A
l
ger
i
a.
Em
ail: ferdi_brahim
@yahoo.c
o
m
1.
INTRODUCTION
In
recen
t
years, an in
creased
n
u
m
b
e
r
o
f
sen
s
itiv
e lo
ad
s
h
a
v
e
b
e
en
i
n
teg
r
ated
in electrical po
wer
syste
m
s. Co
n
s
eq
u
e
n
tly, th
e
d
e
m
a
n
d
fo
r
hig
h
p
o
wer
quality an
d
vo
ltag
e
stab
ility h
a
s
b
een
i
n
creased
sig
n
i
fican
tly [1
]. Power qu
ality
p
r
ob
lem
s
lik
e v
o
lta
g
e
sag
and
v
o
ltage swell are
maj
o
r con
cern
o
f
th
e
industrial a
n
d
commercial electrical co
n
s
u
m
ers d
u
e t
o
e
n
orm
ous l
o
ss i
n
t
e
rm
s of t
i
m
e
and
m
oney
.
Fa
ul
t
s
at
eith
er th
e tran
smissio
n
o
r
d
i
st
ribu
tio
n
lev
e
l
may cau
se v
o
lta
g
e
sag
or swell in
th
e en
tire
syste
m
o
r
a lar
g
e p
a
rt
o
f
it. A
l
so
, under h
e
av
y lo
ad
co
nd
itio
ns, a sign
ifican
t vo
ltage d
r
o
p
m
a
y o
ccu
r in
th
e system
.
V
o
ltag
e
sags can
occu
r at
any
i
n
st
ant
of t
i
m
e
,
wi
t
h
am
pl
it
ude
s ran
g
i
n
g fr
om
10 –
90% a
nd
a dur
at
i
on l
a
st
i
ng f
o
r hal
f
a cy
cl
e t
o
one
m
i
nut
e [2]
.
F
u
rt
her,
t
h
ey
coul
d
be ei
t
h
e
r
bal
a
nced
o
r
u
nbal
a
nced
,
de
p
e
ndi
ng
o
n
t
h
e t
y
pe o
f
fa
ul
t
an
d t
h
ey
coul
d have
u
n
p
r
e
d
i
c
t
a
bl
e m
a
gni
t
ude
s, d
e
pen
d
i
n
g o
n
fact
or
s
s
u
ch
as
di
st
ance
f
r
o
m
t
h
e
faul
t
and
t
h
e
t
r
ans
f
o
r
m
e
r connect
i
o
ns
. V
o
l
t
a
ge swel
l
,
o
n
t
h
e ot
her
han
d
, i
s
defi
ne
d as a sud
d
en i
n
creasi
ng
of s
u
p
p
l
y
vol
t
a
ge
up
11
0
%
t
o
18
0% i
n
R
M
S vol
t
a
ge a
t
t
h
e net
w
or
k f
u
n
d
am
ent
a
l
freque
ncy
wi
t
h
d
u
rat
i
o
n fr
om
hal
f
a
cycle to 1
minute [2]. Voltage swells are not as im
por
tant as voltage sa
gs
because they are less common in
distribution system
s. Voltage
sag a
nd s
w
ell
can ca
use se
nsitive equi
pm
ent (s
uch
as found i
n
sem
i
conduct
o
r
o
r
ch
em
ica
l
p
l
an
ts) to
fail, or sh
u
t
d
o
wn
, as well as cr
eate a large curre
nt unbalance
t
h
a
t
coul
d
bl
o
w
f
u
ses
o
r
trip
b
r
eak
e
rs. Th
ese
effects
can
b
e
v
e
ry
expen
s
iv
e
fo
r th
e
cu
sto
m
er, rangin
g
fro
m
m
i
n
o
r
q
u
a
lity v
a
riatio
n
s
to
production
downtim
e and e
q
uipm
ent dam
a
ge [3]. T
h
e
r
e a
r
e m
a
ny diffe
rent m
e
thods t
o
m
itigate voltage sa
gs
and
sw
el
l
s
, b
u
t
t
h
e
use
of
a
D
V
R
i
s
c
o
n
s
i
d
er
ed t
o
be
t
h
e m
o
st
c
o
st
ef
fi
ci
ent
m
e
t
hod
[4]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
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9
4
Desi
g
n
a
n
d
Si
mul
a
t
i
o
n
of
Dy
na
mi
c V
o
l
t
a
ge
Rest
orer
Base
d on F
u
zzy
Controller
Op
timized
… (Brah
i
m Ferd
i)
21
3
DVR is a series cu
sto
m
p
o
w
er d
e
v
i
ce in
tended
to
pr
o
t
ect sen
s
itiv
e lo
ads fro
m
th
e effects o
f
vo
ltag
e
di
st
ur
ba
nces s
u
ch as v
o
l
t
a
ge
sags an
d swe
l
l
s
at t
h
e poi
n
t
of com
m
on
cou
p
l
i
n
g (PC
C
). D
V
R
essent
i
a
l
l
y
co
nsists o
f
a series-co
n
n
ected
in
j
ecti
o
n
tran
sfo
r
m
e
r,
a v
o
ltag
e
so
urce inv
e
rter, in
verter o
u
t
pu
t filter an
d
an
ener
gy
st
ora
g
e
devi
ce co
n
n
e
c
t
e
d t
o
t
h
e dc
-
l
i
nk. T
h
e basi
c ope
rat
i
on
of
DVR
i
s
t
o
i
n
ject
a vol
t
a
ge of t
h
e
req
u
i
r
e
d
m
a
gn
i
t
ude,
p
h
ase
a
ngl
e
an
d
fre
q
u
e
ncy
i
n
seri
es
wi
t
h
di
st
ri
but
i
on
fee
d
er
t
o
m
a
i
n
t
a
i
n
t
h
e
d
e
si
red
am
pl
i
t
ude a
n
d
wave
f
o
rm
for
l
o
ad
v
o
l
t
a
ge
ev
en
whe
n
t
h
e
vo
l
t
a
ge i
s
u
n
b
al
anced
o
r
di
st
o
r
t
e
d.
Th
e m
o
st co
m
m
o
n
cho
i
ce for th
e con
t
ro
l
of th
e DVR is th
e so
called
PI co
n
t
ro
ller since it h
a
s a
sim
p
le structure and it can
offer relatively a satisfact
ory
p
e
rf
orm
a
nce o
v
e
r a wi
d
e
ra
ng
e of
ope
rat
i
o
n.
The
main
p
r
ob
lem
o
f
t
h
is sim
p
le co
n
t
ro
ller is the correct c
hoi
c
e
o
f
t
h
e
PI
gai
n
s a
n
d
t
h
e
fact
t
h
at
by
usi
n
g
fi
xe
d
g
a
in
s, th
e contro
ller m
a
y n
o
t
p
r
ov
id
e t
h
e
requ
ired
co
ntrol perform
ance, when t
h
er
e are
va
riations in
the
syste
m
p
a
r
a
m
e
ter
s
and op
er
at
in
g
cond
itio
n
s
. To so
lv
e t
h
ese pr
ob
lem
s
f
u
zzy lo
g
i
c con
t
ro
l app
e
ar
s t
o
be th
e
m
o
st p
r
o
m
isin
g
d
u
e
to its rob
u
s
t
n
ess.
Also
, a m
a
th
e
m
at
ic
al m
o
d
e
l is not requ
ired
t
o
describ
e
th
e syste
m
in
fu
zzy log
i
c based
d
e
sign
.
Bu
t, th
e m
a
in
p
r
o
b
l
em
with
th
e co
nv
en
tio
n
a
l fu
zzy co
n
t
ro
llers is t
h
at th
e
p
a
ram
e
ters asso
ciated
with
t
h
e m
e
m
b
ersh
ip
fun
c
tio
ns and
th
e
ru
les d
e
p
e
nd
b
r
o
a
d
l
y o
n
th
e in
t
u
ition
o
f
t
h
e
ex
p
e
rts.
If it is requ
ired
to
ch
an
g
e
t
h
e
p
a
ram
e
ters, it is to
b
e
d
o
n
e
b
y
trial an
d
error on
ly.
Th
ere is
no
sci
e
n
tific
o
p
tim
izat
io
n
meth
o
d
o
l
og
y i
n
bu
ilt in
t
h
e
gen
e
ral
fu
zzy in
feren
c
e system
[5
]. To
ov
erco
m
e
th
is prob
lem
o
f
opt
i
m
i
zati
on,
r
e
searche
r
s
ha
v
e
use
d
m
a
ny
di
ffe
re
nt
m
e
t
hods
ove
r t
h
e
p
a
st
deca
des,
t
h
ese m
e
t
hods i
n
cl
u
d
e
genet
i
c
al
g
o
r
i
t
h
m
s
[6]
-
[
9
]
,
P
a
rt
i
c
l
e
swarm
[1
0]
, [
1
1]
, Im
m
une Al
g
o
ri
t
h
m
[12]
, ne
ural
net
w
or
ks
[
13]
, [
14]
,
evol
ut
i
ona
ry
p
r
o
g
ram
m
i
ng [1
5]
, ge
om
et
ri
c
m
e
t
hods
[1
6]
,
fuzzy
e
qui
val
e
nce rel
a
t
i
o
ns [
17]
,
he
uri
s
t
i
c
m
e
t
h
o
d
s
[18
]
,
g
r
ad
ien
t
d
e
scen
t [1
9
]
,
[7
], Kalm
an
filtering
[20
]
, H
∞
filterin
g
[2
1
]
,
th
e sim
p
lex
meth
od
[22
]
, [23], least
squ
a
res
[
24]
,
b
ackp
r
opa
gat
i
o
n
[2
5]
, a
n
d
ot
h
e
r
num
eri
cal
t
echni
que
s [
2
6]
.
In t
h
i
s
pape
r
we p
r
ese
n
t
an
unc
o
n
st
rai
n
e
d
opt
i
m
i
zati
on b
a
sed o
n
Ada
p
t
i
ve Ne
ur
o-
Fuz
z
y
Infe
renc
e
Sy
st
em
(ANF
I
S
) t
o
ge
ne
rat
e
an o
p
t
i
m
a
l
fuzzy
cont
r
o
l
l
e
r fr
om
a gi
ven un
-
opt
i
m
i
zed fuzzy
co
nt
rol
l
e
r. The
gi
ve
n f
u
zzy
c
ont
rol
l
e
r c
o
n
s
i
s
t
s
of t
w
o i
n
p
u
t
s
an
d o
n
e
ou
tpu
t
with
seven
m
e
m
b
ersh
ip
fu
nctio
n
s
, bu
t th
e
g
e
n
e
rated op
timal fu
zzy con
t
ro
ller con
s
ists o
f
on
e i
n
pu
t and
on
e
ou
tpu
t
with only th
ree m
e
mb
ersh
i
p
fu
nct
i
o
ns. T
h
e
gene
rat
e
d
o
p
t
i
m
al
fuzzy
cont
rol
l
e
r i
s
use
d
t
o
co
nt
r
o
l
D
V
R
i
n
sag/
swel
l
c
o
m
p
ensat
i
on a
nd t
h
e
resu
lts are co
mp
ared
with
t
h
at g
i
v
e
n
b
y
th
e i
n
itial u
n
-op
timized
fu
zzy co
n
t
ro
ller.
2.
D
YNA
M
I
C
VOLTA
GE R
E
STOR
ER
(DVR
)
A
Dy
nam
i
c Voltage Rest
ore
r
(
DVR
) is a
se
ries
con
n
ected
solid state devi
ce th
at in
j
ects v
o
ltag
e
in
t
o
th
e syste
m
in
o
r
d
e
r t
o
regu
late th
e lo
ad
si
de v
o
ltag
e
. Th
e DVR
was fi
rst in
stalled
in
19
96
[27
]
, [28
]
. It is
no
rm
al
ly
i
n
st
al
l
e
d i
n
a di
st
r
i
but
i
o
n sy
st
em
bet
w
ee
n
the
supply and the critical
load feede
r
. Its
prim
ary
fu
nct
i
o
n i
s
t
o
rapi
dl
y
bo
ost
u
p
t
h
e l
o
ad
-si
d
e
vol
t
a
ge i
n
t
h
e
event
o
f
a di
st
ur
ba
nce i
n
or
d
e
r t
o
avoi
d any
po
wer
di
sr
upt
i
o
n t
o
t
h
at
l
o
ad
[2
9]
.
There a
r
e va
ri
ous ci
rcui
t
t
o
p
o
l
o
gi
es an
d co
nt
r
o
l
schem
e
s
t
h
at
can be
us
ed t
o
i
m
p
l
e
m
en
t a DVR
[30
]
,
[31]. In
add
itio
n
t
o
its m
a
in
tas
k
wh
ich
is vo
l
t
ag
e sags and
swells co
m
p
ensatio
n
,
DVR
can
al
so adde
d ot
he
r fe
at
ures suc
h
as:
l
i
n
e vol
t
a
ge
harm
onics com
p
ensation, re
du
ctio
n of
t
r
an
sien
ts i
n
vol
t
a
ge
a
n
d
fa
ul
t
cu
rre
nt
l
i
m
i
t
a
t
i
ons
[3
2]
.
The
ge
ne
ra
l
co
nfigu
r
ation
o
f
th
e
DVR co
n
s
ists of a
vo
ltag
e
in
j
ection
tran
sfo
r
m
e
r, an ou
tpu
t
filte
r, an
en
erg
y
st
o
r
ag
e
d
e
v
i
ce,
Vo
ltag
e
Sou
r
ce
In
v
e
rter (VSI), an
d a
Co
n
t
ro
l
syste
m
as sh
ow
n in
Figu
r
e
1.
Fi
gu
re
1.
D
V
R
ge
neral
c
o
nfi
g
urat
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
21
2
–
22
2
21
4
2.
1. Oper
ati
n
g
Pri
n
ci
pl
e
The basi
c f
u
n
c
t
i
on o
f
t
h
e D
V
R
i
s
t
o
i
n
jec
t
a dy
nam
i
cal
ly
cont
r
o
l
l
e
d v
o
l
t
a
ge Vi
nj
ge
nerat
e
d by
a
forced comm
utated conve
rter in se
ri
es to the bu
s
v
o
ltag
e
b
y
m
ean
s o
f
a vo
ltag
e
inj
ecti
o
n tran
sfo
r
m
e
r. Th
e
m
o
mentary am
plitudes
of
the three inje
cted phase
voltag
e
s are con
t
ro
lled
su
ch
as to elim
inate any
d
e
trim
en
tal effects o
f
a bu
s fau
lt to
th
e lo
ad v
o
ltag
e
V
L
. T
h
is m
eans that
any diff
eren
tial v
o
ltag
e
s cau
s
ed
by
d
i
stu
r
b
a
n
ces in th
e ac feed
er
will b
e
co
m
p
en
sated
b
y
an
eq
u
i
v
a
len
t
v
o
ltag
e
. Th
e
DVR
works ind
e
pend
en
tly
of t
h
e t
y
pe of
faul
t
or a
n
y
event
t
h
at
ha
pp
ens i
n
the syste
m
. For m
o
st
practical cases, a
m
o
re econom
i
ca
l
design ca
n
be
achieve
d
by only com
p
ensating the
pos
itive
and ne
gative s
e
que
nce c
o
m
pone
nts
of t
h
e
voltage
d
i
stu
r
b
a
n
ce seen
at th
e in
p
u
t o
f
th
e DVR (b
ecau
s
e th
e zero
seq
u
e
n
ce
p
a
rt of a d
i
sturb
a
n
ce will n
o
t p
a
ss
t
h
r
o
u
g
h
t
h
e
st
ep
do
w
n
t
r
a
n
s
f
o
r
m
e
r whi
c
h
ha
s i
n
fi
ni
t
e
i
m
pedance
f
o
r
t
h
i
s
c
o
m
pone
nt
).
The
DVR
has
t
w
o m
odes
of
ope
rat
i
o
n w
h
i
c
h are:
st
a
n
d
b
y
m
ode and
bo
o
s
t
m
ode. I
n
st
and
b
y
m
ode
(
V
i
n
j
=
0
)
, th
e
v
o
ltag
e
inj
ectio
n tr
an
sfo
r
m
e
r
’
s
l
o
w vo
ltage w
i
nd
ing
is
sh
or
ted thr
ough
th
e conv
er
ter
.
N
o
swi
t
c
hi
n
g
o
f
s
e
m
i
cond
uct
o
rs
occu
rs i
n
t
h
i
s
m
ode o
f
o
p
e
rat
i
o
n
,
beca
u
s
e t
h
e i
ndi
vi
d
u
al
i
nve
rt
er l
e
gs are
trig
g
e
red su
ch
as to
estab
lish
a sho
r
t-ci
rcu
it
p
a
th
fo
r th
e t
r
an
sform
e
r co
nn
ectio
n. Th
e
DVR will b
e
m
o
st of
th
e ti
m
e
in
th
i
s
m
o
d
e
. In
boo
st m
o
d
e
(V
inj
>
0)
, th
e
DV
R is inj
ectin
g a
co
m
p
en
satio
n
v
o
ltag
e
thr
ough
th
e
vol
t
a
ge
i
n
ject
i
o
n
t
r
a
n
sf
orm
e
r d
u
e t
o
a
det
ect
i
on
o
f
a s
u
ppl
y
v
o
l
t
a
ge
di
st
u
r
bance
.
2.2. Voltage
Reference Calculati
o
n Method
There are l
o
t
s
of m
e
t
hods f
o
r
DVR
vol
t
a
ge cor
r
ect
i
on
gen
e
rat
i
ng re
fere
n
ce vol
t
a
ge t
h
at
DVR
m
u
st
in
j
ect it in
to
th
e bu
s vo
ltag
e
[33
]
-[3
9
]
. The strateg
y
o
f
vo
ltag
e
referen
c
e calcu
latio
n
used
in
th
is work
is
sho
w
n i
n
Fi
gu
r
e
2.
Fi
gu
re
2.
SIM
U
LI
N
K
m
odel
of
SR
F m
e
t
hod
f
o
r
v
o
l
t
a
ge
ref
e
rence
cal
cul
a
t
i
o
n
Fi
gu
re
2 s
h
ow
s t
h
e
basi
c c
o
nt
r
o
l
schem
e
and
pa
ram
e
t
e
rs t
h
at
are
m
easure
d
fo
r c
ont
r
o
l
p
u
r
p
o
ses.
Wh
en
t
h
e supp
ly v
o
ltag
e
is
at its n
o
r
m
a
l l
e
v
e
l th
e
DVR
is co
n
t
ro
lled
t
o
redu
ce th
e l
o
sses i
n
th
e
DVR to
a
minim
u
m
.
W
h
en voltage sags/swells are de
tected, the DV
R should react
as fast as pos
sible and injec
t
an ac
vol
t
a
ge
i
n
t
o
t
h
e g
r
i
d
.
It
ca
n
b
e
im
pl
em
ent
e
d usi
n
g
t
h
e
sy
nc
hr
o
n
o
u
s
refe
re
nce
fram
e
(SR
F
) t
e
c
hni
que
b
a
sed
o
n
t
h
e i
n
st
ant
a
ne
ous
val
u
e
s
o
f
t
h
e su
ppl
y
v
o
l
t
a
ge. T
h
e co
nt
r
o
l
al
go
ri
t
h
m
pro
duce
s
a t
h
ree p
h
ase r
e
fere
nce
v
o
ltag
e
to th
e PW
M
inv
e
rter th
at t
r
ies to m
a
in
tain
th
e
lo
ad
vo
ltag
e
at its referen
c
e v
a
lu
e. Th
e
vo
ltage
sag/
swel
l
i
s
de
t
ect
ed by
m
easuri
ng t
h
e e
r
r
o
r
bet
w
ee
n t
h
e d
-
v
o
l
t
a
ge o
f
t
h
e
sup
p
l
y
and t
h
e d-re
fe
rence
val
u
e.
The d
-re
fere
nc
e com
pone
nt
i
s
set
t
o
a rat
e
d vol
t
a
ge
. The
M
A
TLAB
/
Si
m
u
l
i
nk e
n
vi
ro
n
m
ent
i
s
a usefu
l
t
ool
t
o
im
plem
ent this
m
e
thod (SR
F
) because it has
m
a
ny tool
boxes that can
be
used easily. T
h
e SRF m
e
thod can
be u
s
ed t
o
co
m
p
ensat
e
al
l
ty
pe o
f
v
o
l
t
a
ge
di
st
ur
ba
nces,
vol
t
a
ge
sag/
s
w
el
l
,
vol
t
a
ge
u
n
b
al
ance a
n
d ha
rm
oni
c
vol
t
a
ge
, b
u
t
i
n
t
h
i
s
wo
rk
we
have st
udi
e
d
onl
y
v
o
l
t
a
ge s
a
g/
swel
l
.
T
h
e di
ffe
re
nce bet
w
een t
h
e refe
r
e
nce
v
o
ltag
e
an
d
the in
j
ected
vo
ltag
e
is ap
p
lied
to th
e VSI to
prod
u
ce th
e lo
ad
rated
v
o
ltag
e
, with
th
e h
e
lp
of p
u
l
se
wi
dt
h
m
odul
at
i
o
n
(P
WM
)
t
h
r
o
u
g
h
t
h
e
P
I
(
o
r
f
u
zzy
) c
ont
rol
l
er.
3.
UN-OPTIMIZ
ED FUZZ
Y CONTROLLER
We suppose that we ha
ve a
l
ready a fuzzy contro
ller
o
f
two
inpu
ts and
on
e ou
tpu
t
with
sev
e
n
me
m
b
ersh
ip
fun
c
tio
ns th
at g
i
v
e
s satisfactory resu
lts in
cont
r
o
l
l
i
ng t
h
e D
V
R
.
The i
nputs are the error
and the
deri
vat
i
v
e
of
t
h
e e
r
r
o
r
,
den
o
t
e
d as
ε
and
∆ε
r
e
sp
ectiv
ely. Fig
u
r
e
3
shows
th
e Mem
b
ers
h
ip
function c
u
rves
of
t
h
e i
n
put
s
an
d t
h
e
out
put
,
Ta
bl
e 1
gi
ve
s t
h
e
r
u
l
e
base.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Desi
g
n
a
n
d
Si
mul
a
t
i
o
n
of
Dy
na
mi
c V
o
l
t
a
ge
Rest
orer
Base
d on F
u
zzy
Controller
Op
timized
… (Brah
i
m Ferd
i)
21
5
Fig
u
re
3
.
Memb
ersh
ip fun
c
tion
cu
rv
es
of th
e in
pu
ts
ε
and
∆ε
and
th
e ou
tput
Tabl
e
1. T
h
e
r
u
l
e
ba
se
ε
/
∆ε
mf
1
mf
2
mf
3
mf
4
mf
5
mf
6
mf
7
mf
1
mf
1
mf
1
mf
1
mf
1
mf
2
mf
3
mf
4
mf
2
mf
1
mf
1
mf
1
mf
2
mf
3
mf
4
mf
5
mf
3
mf
1
mf
1
mf
2
mf
3
mf
4
mf
5
mf
6
mf
4
mf
1
mf
2
mf
3
mf
4
mf
5
mf
6
mf
7
mf
5
mf
2
mf
3
mf
4
mf
5
mf
6
mf
7
mf
7
mf
6
mf
3
mf
4
mf
5
mf
6
mf
7
mf
7
mf
7
mf
7
mf
4
mf
5
mf
6
mf
7
mf
7
mf
7
mf
7
Th
e M
A
TLA
B
/SI
M
U
L
I
N
K
i
m
p
l
e
m
en
tatio
n
of
th
e fu
zzy co
n
t
r
o
ller
fo
r
one ph
ase is
show
n in
Figu
r
e
4
Fi
gu
re
4.
SIM
U
LI
N
K
m
odel
of
t
h
e
fuzzy
l
o
gi
c co
nt
r
o
l
l
e
r
(
F
LC
)
4.
ANF
IS P
R
I
N
CIPLES
Thi
s
sect
i
on i
n
t
r
od
uces t
h
e
basi
cs o
f
A
N
F
IS
net
w
or
k a
r
chi
t
ect
u
r
e an
d i
t
s
hy
bri
d
l
earni
ng
rul
e
.
In
sp
ired
b
y
th
e id
ea of
b
a
sing th
e fu
zzy log
i
c in
feren
ce
procedure
on a fe
ed forw
ar
d
n
e
t
w
or
k stru
ctur
e, Jang
[4
0]
p
r
o
p
o
sed
an A
d
a
p
t
i
v
e N
e
t
w
o
r
k
-
ba
sed
Fuzzy
I
n
fe
re
n
ce Sy
st
em
(ANFI
S
)
or
sem
a
nt
i
cal
l
y
equi
va
l
e
nt
l
y
,
the Adaptive
Neural Fuzzy
Infe
rence
System
, whose arc
h
itecture is sh
ow
n
i
n
Figu
r
e
5. H
e
r
e
po
r
t
ed
t
h
at th
e
AN
FIS ar
chi
t
e
ct
ure can be e
m
pl
oy
ed t
o
m
o
del
no
nl
i
n
ea
r f
unct
i
o
ns
, i
d
ent
i
fy
nonl
i
n
ear c
o
m
pone
nt
s on
-
l
i
n
e i
n
a control system
, and pre
d
ict a cha
o
tic tim
e
series.
It is a h
y
b
r
i
d
n
e
uro
-
fu
zzy tech
n
i
q
u
e
t
h
at bring
s
learn
i
ng
cap
ab
ilities o
f
n
e
ural n
e
t
w
ork
s
to
fu
zzy
infere
nce system
s.
The learni
ng algorithm
tune
s the m
e
m
b
ershi
p
f
unct
i
o
n
s
of a Su
ge
no
-t
y
p
e Fuzzy
I
n
fe
rence
Syste
m
u
s
in
g th
e train
i
n
g
in
pu
t-o
u
t
p
u
t
d
a
ta. Th
e
ANFIS is,
from
th
e to
po
log
y
po
in
t
o
f
v
i
ew, an
im
pl
em
ent
a
t
i
o
n o
f
a re
prese
n
t
a
t
i
v
e fuzzy
i
n
f
e
rence sy
st
em
usi
n
g a bac
k
p
r
opa
gat
i
o
n (B
P
)
neu
r
al
net
w
or
k-l
i
k
e
structure. It c
o
nsists of
five l
a
ye
rs [41], [42]. The
role
of
each layer
is
briefly presente
d as
follows: l
e
t
Oi
l
den
o
t
e
t
h
e o
u
t
put
of n
ode
i
in
l
a
y
e
r
l,
and
x
i
is th
e
i
th
i
nput
of t
h
e A
N
F
I
S,
i = 1,
2,
...
,p
. In
layer 1, th
ere is a
no
de f
unct
i
o
n
M
associated
with e
v
ery
node:
(1)
-1
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0.
2
0.
4
0.
6
0.
8
1
0
0.
2
0.
4
0.
6
0.
8
1
D
e
g
r
ee
of
m
e
m
b
er
s
h
i
p
mf
1
m
f
2
mf
3
m
f
4
mf
5
m
f
6
mf
7
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
21
2
–
22
2
21
6
The r
o
l
e
of t
h
e
no
de fu
nct
i
o
n
s
M
1
,
M
2
...
Mq
h
e
re is eq
u
a
l to
th
at o
f
th
e me
m
b
ersh
i
p
functio
n
s
μ
(
x
)
u
s
ed
in
th
e regu
lar fu
zzy syste
m
s, an
d
q
is the num
b
er of
nodes for each i
nput.
Gaussian sha
p
e functi
ons a
r
e
th
e typ
i
cal choices. Th
e adju
stab
le p
a
ram
e
te
rs th
at
d
e
term
i
n
e th
e po
sitio
ns and
sh
apes
o
f
th
ese
n
o
d
e
functio
n
s
are refe
rre
d to as the prem
is
e param
e
ters. The output
of ev
er
y nod
e in
layer
2
is th
e pr
odu
ct o
f
all th
e
incom
i
ng signa
l
s:
(2)
Each
n
ode
o
u
t
put
re
prese
n
t
s
t
h
e fi
ri
n
g
st
re
n
g
t
h
o
f
t
h
e
rea
s
oni
ng
r
u
l
e
.
I
n
l
a
y
e
r 3
,
eac
h
of
t
h
ese
fi
ri
n
g
streng
th
s of the ru
les is co
m
p
ared
with
t
h
e su
m
o
f
all
the
firin
g
st
ren
g
th
s. T
h
ere
f
o
r
e,
the
no
rm
alized firin
g
streng
th
s are co
m
p
u
t
ed
in th
i
s
layer as:
∑
(
3
)
Layer
4
im
p
l
e
m
en
ts th
e Sug
e
no-typ
e
inferen
c
e system
,
i.e., a lin
ear co
m
b
in
atio
n
o
f
th
e i
n
pu
t
vari
a
b
l
e
s of A
N
FI
S,
x
1
, x
2
, ...
x
p
pl
us a const
a
nt
t
e
r
m
,
c
1
, c
2
,
...,c
p
, f
o
rm
t
h
e out
p
u
t
of eac
h
IF
−
THE
N
rul
e
. The
out
put
o
f
t
h
e
n
ode
i
s
a
wei
g
ht
ed s
u
m
of t
h
e
s
e i
n
t
e
rm
edi
a
t
e
out
put
s:
∑
(
4
)
Whe
r
e pa
ram
e
ters
P
1
, P
2
, ...
,P
p
and
c
1
,c
2
, ...,c
p
, i
n
t
h
i
s
l
a
y
e
r are
re
fer
r
e
d t
o
as t
h
e c
ons
eq
ue
nt
p
a
r
a
m
e
ter
s
. The no
de in layer 5 pr
odu
ces t
h
e su
m
o
f
its
inputs
,
i.e.,
defuzzificati
on pr
o
cess
o
f
f
u
zzy
s
y
st
e
m
(u
si
n
g
wei
g
h
t
ed
av
erag
e m
e
th
o
d
) is
ob
tain
ed:
∑
(
5
)
Th
e f
l
ow
ch
ar
t o
f
AN
FI
S p
r
oced
ur
e
is show
n
in
Figu
r
e
6
.
AN
FIS d
i
stin
gu
ish
e
s
itself
f
r
o
m
n
o
r
m
a
l
fuzzy logic sy
ste
m
s by the
adaptive
pa
ra
meters, i.e
.,
b
o
t
h
t
h
e
prem
ise an
d c
ons
eq
uent
par
a
m
e
t
e
rs are
adjusta
b
le. The
m
o
st rem
a
r
k
able feature
of the
ANFI
S is its h
y
b
r
id
learn
i
ng
algo
ri
th
m
.
Th
e ad
ap
tation
pr
ocess
of
t
h
e
param
e
t
e
rs of
t
h
e A
N
F
I
S i
s
di
vi
ded i
n
t
o
t
w
o st
e
p
s.
F
o
r t
h
e fi
r
s
t
st
ep o
f
t
h
e
co
n
s
eq
uent
p
a
ram
e
ters train
i
ng
, th
e
Least Squ
a
res m
e
t
h
od (LS) is
us
ed, beca
use
the output
o
f
the ANFIS is a
lin
ear
com
b
ination of the consequent param
e
ters. The prem
is
e param
e
ters
are fixe
d at this step. Afte
r the
con
s
eq
ue
nt
pa
r
a
m
e
t
e
rs have
b
een a
d
j
u
st
e
d
, t
h
e a
p
p
r
o
x
i
m
at
ion
er
ro
r i
s
bac
k
-
p
r
o
pagat
e
d t
h
r
o
ug
h e
v
ery
l
a
y
e
r t
o
update t
h
e
pre
m
ise param
e
te
rs as
the
second step. T
h
is p
a
rt of
th
e
adap
tatio
n
pr
o
ced
ur
e is b
a
sed
o
n
th
e
gra
d
i
e
nt
desce
n
t
p
r
i
n
ci
pl
e,
w
h
i
c
h
i
s
t
h
e
sa
m
e
as i
n
t
h
e t
r
ai
ni
ng
of t
h
e
B
P
ne
ural
net
w
o
r
k
.
T
h
e
co
n
s
eq
uenc
e
param
e
ters identified by the LS
m
e
thod are
optim
al in
the sense of least squares
under t
h
e condition that the
prem
ise param
e
ters are
fix
e
d
[4
3]
.
Fi
gu
re 5.
St
r
u
c
t
ure of
A
N
F
I
S
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Desi
g
n
a
n
d
Si
mul
a
t
i
o
n
of
Dy
na
mi
c V
o
l
t
a
ge
Rest
orer
Base
d on F
u
zzy
Controller
Op
timized
… (Brah
i
m Ferd
i)
21
7
Fi
gu
re 6.
A
N
F
I
S pr
oce
d
u
r
e
Th
e MATLAB/SI
MU
LI
NK i
m
p
l
e
m
en
tati
o
n
of
th
e
Sugen
o
fu
zzy contr
o
ller
for
on
e p
h
a
se in
ou
r
case i
s
sh
ow
n
i
n
Fi
g
u
re
7.
From
t
h
i
s
fi
g
u
re
we ca
n o
b
ser
v
e t
h
at
t
h
e gene
rat
e
d
o
p
t
i
m
a
l
Suge
no
fuzz
y
co
n
t
r
o
ller
do
es no
t n
e
ed
scalin
g f
act
o
r
s (
t
un
i
n
g g
a
i
n
s).
Fi
gu
re
7.
SIM
U
LI
N
K
m
odel
of
t
h
e
Su
ge
no
f
u
zzy
l
o
gi
c c
ont
rol
l
e
r
(S
FLC
)
5.
SIM
U
LATI
O
N
RESULTS
AN
D DIS
C
US
SION
To
gene
rat
e
t
h
e opt
i
m
al
fuzzy
cont
r
o
l
l
e
r
re
prese
n
t
e
d
by
a
Su
gen
o
fuzzy
i
n
fe
rence
sy
st
em
(SFIS
)
we
have
use
d
AN
FIS E
d
i
t
o
r G
U
I
f
r
om
M
A
TLAB
/
SIM
U
LI
N
K
F
u
zzy
Lo
gi
c
To
ol
b
o
x
,
we
h
a
ve be
ga
n by
l
o
adi
n
g
a Trai
ni
ng
dat
a
set
t
h
at
co
n
t
ai
ns t
h
e
desi
r
e
d i
n
p
u
t
/
out
pu
t
dat
a
o
f
t
h
e
gi
ve
n
fuzzy
c
ont
rol
l
e
r
fr
om
t
h
e
si
m
u
latio
n
of
DVR. Th
is d
a
t
a
set is an
array with
th
e i
n
put d
a
ta arrang
ed as th
e
first co
lu
m
n
v
ecto
r
s, an
d th
e
out
put
dat
a
i
n
t
h
e l
a
st
c
o
l
u
m
n
.
A
N
F
I
S st
ru
ct
ure
wi
t
h
S
u
g
e
no
m
odel
co
n
t
ai
ni
ng
3
r
u
l
e
s
has
bee
n
co
ns
i
d
ere
d
.
Hy
bri
d
l
ear
ni
n
g
al
g
o
ri
t
h
m
m
e
t
hod
was
u
s
ed t
o
a
d
just
t
h
e pa
ram
e
t
e
r
of m
e
m
b
ersh
i
p
f
unct
i
o
n.
A
l
l
t
h
e
v
a
r
i
ab
les’
f
u
zzy su
bsets fo
r th
e inpu
t
ε
are
d
e
fi
n
e
d as (M
1
,
M
2
, M
3
) wi
th
triangu
lar me
m
b
ersh
i
p
functio
n.
Th
e m
e
m
b
ersh
ip
fun
c
tio
ns and
in
itial u
n
i
v
e
rses o
f
th
e inp
u
t g
e
n
e
rated
b
y
ANFIS train
i
n
g
are illu
strat
e
d
in
Fi
gu
re
8. T
h
e
out
put
vari
a
b
l
e
Y gi
ven
by
A
N
FI
S t
r
ai
ni
ng i
s
a vect
o
r
o
f
c
onst
a
nt
s.
Y= [
y
1
, y
2
, y
3
] where, y
1
= -
1
222
, y
2
= 82.57,
y
3
=
13
87
. Th
e co
n
t
ro
l
ru
les are t
h
e
fo
llowing
:
Fig
u
re
8
.
Memb
ersh
ip fun
c
tion
cu
rv
es
of th
e in
pu
t
ε
-4
-3
-2
-1
0
1
2
3
4
0
0.
5
1
ER
R
O
R
D
e
gr
ee of
m
e
m
ber
s
h
i
p
M1
M2
M3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
21
2
–
22
2
21
8
a)
If (in
p
u
t
ε
is M
1
) th
en
(ou
t
pu
t is y
1
)
b)
If (in
p
u
t
ε
is M
2
) th
en
(ou
t
pu
t is y
2
)
c)
If (in
p
u
t
ε
is M
3
) th
en
(ou
t
pu
t is y
3
)
A DVR is co
n
n
ected
to
th
e syste
m
th
roug
h
a series tran
sform
e
r wit
h
a cap
ab
ility to
in
sert a
max
i
m
u
m
v
o
ltag
e
of
9
0
%
of th
e ph
ase to
g
r
ou
nd
system v
o
ltag
e
. In
the fo
llowing
si
m
u
la
tio
n
s
, th
e
m
a
in
characte
r
istics of t
h
e
DVR a
r
e set as: voltage source
fu
l
l
-
b
r
i
d
ge I
G
B
T
ba
sed i
n
ve
rt
er c
o
nt
r
o
l
l
e
d wi
t
h
P
W
M
si
gnal
ge
nerat
o
r wi
t
h
com
m
u
t
a
t
i
on f
r
eq
ue
ncy
of
12
k
H
z,
capaci
t
o
r ene
r
gy
st
o
r
age
ba
nk
8.
8m
F, coupl
i
n
g
tran
sform
e
r ratio
1
:
1
,
no
m
i
n
a
l
d
c
link
vo
ltage 85
0V, LC
o
u
tp
u
t
filter v
a
l
u
es C=80
µF i
n
series with a
d
a
m
p
in
g
resistance R
d
= 0.1
Ω
, L =
1m
H
,
so
ur
ce
voltag
e
220
Vr
m
s
and
sou
r
ce fr
eq
u
e
n
c
y
o
f
50Hz. Th
e l
o
ad is
8
0kV
A
wi
t
h
0.
92
p.
f.
, l
a
ggi
ng
. T
h
e
gi
ven
f
u
zzy
c
ont
rol
l
e
r t
uni
ng
i
s
m
a
de such
t
o
ha
ve
hi
g
h
t
r
a
n
si
ent
s
p
ee
d a
n
d
t
o
h
a
v
e
v
e
ry low
track
ing
erro
r fo
r th
e
fund
am
e
n
tal (5
0Hz).
A
case of Three-phase 50% balance
d
volta
ge
sa
g
is
sim
u
lated
and
th
e
resu
lt is sho
w
n in
Figu
re 9.
Voltage sa
g is
initiated at 200m
s and it is kept until
300m
s, with total voltage sag
duration of 100m
s
. As a
resu
lt of th
e co
n
t
ro
l
o
f
DVR
b
y
th
e op
tim
a
l
fu
zzy con
t
ro
ller; th
e lo
ad
vo
ltag
e
is k
e
p
t
at 1
.
00p
.u
throu
gho
u
t
th
e sim
u
latio
n
in
clud
ing
th
e v
o
ltag
e
sag
period
.
We
can n
o
tice th
at
during
norm
a
l o
p
eration
,
t
h
e
DVR is
doi
ng
n
o
t
h
i
n
g
but
once
vol
t
a
ge sag i
s
det
ect
ed, i
t
qui
c
k
l
y
i
n
ject
s
necessa
r
y
vol
t
a
ge com
p
o
n
e
n
t
s
t
o
sm
oot
h t
h
e
l
o
ad
v
o
l
t
a
ge.
E
x
cept
t
h
e sl
i
g
h
t
am
el
i
o
rat
i
on
i
n
dy
nam
i
c perfo
rm
ance of
t
h
e gi
ve
n c
o
nt
r
o
l
l
e
r, w
e
ca
n say
t
h
at
t
h
e t
w
o c
ont
rol
l
ers ha
ve t
h
e sa
m
e
perf
o
r
m
a
nce.
(a)
(b
)
Fi
gu
re 9.
Si
m
u
l
a
t
i
on
res
u
l
t
of DVR
res
p
o
n
se
t
o
a bal
a
nce
d
v
o
l
t
a
ge
sa
g;
(
a
)
Th
e g
i
v
e
n fu
zzy con
t
ro
ller,
(b
) T
h
e
optimal fuzzy c
o
ntroller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Desi
g
n
a
n
d
Si
mul
a
t
i
o
n
of
Dy
na
mi
c V
o
l
t
a
ge
Rest
orer
Base
d on F
u
zzy
Controller
Op
timized
… (Brah
i
m Ferd
i)
21
9
(a)
(b
)
Fig
u
re 10
. Simu
latio
n
resu
lt
of
DVR re
sp
on
se to
a
b
a
lan
ced vo
ltag
e
swell;
(a)
The
gi
ven
f
u
zzy
co
nt
r
o
l
l
e
r
,
(b) T
h
e
optimal fuzzy c
o
ntroller
Fo
r th
e case of b
a
lan
c
ed
vo
ltag
e
swell co
mp
ensatio
n
represen
ted
b
y
Figu
re 10
, th
e lo
ad
vo
ltag
e
is
kept at t
h
e
nominal value
with the
help
of the
DVR.
Si
milar to the c
a
se of
voltage
sag, the
DVR
reacts
qui
c
k
l
y
t
o
i
n
j
ect
t
h
e appr
op
ri
at
e vol
t
a
ge c
o
m
pone
nt
(ne
g
at
i
v
e v
o
l
t
a
ge
m
a
gni
t
ude
) t
o
cor
r
ect
t
h
e sup
p
l
y
vol
t
a
ge
.he
r
e,
a
l
so e
x
cept
t
h
e
sl
i
ght
am
el
i
o
rat
i
on i
n
dy
nam
i
c pe
rf
orm
a
nce
of
t
h
e
gi
ven
co
nt
r
o
l
l
e
r;
we
ca
n sa
y
th
at th
e two con
t
ro
llers
h
a
v
e
th
e sam
e
p
e
rforman
ce.
At th
e en
d
Three-ph
ase
un
b
a
l
a
n
ced vo
ltag
e
s co
nd
itio
n
is inv
e
stig
ated
(4
0% swell,
2
0
%
sag
an
d
60
%
sag)
. Acc
o
r
d
i
n
g t
o
Fi
g
u
re 1
1
,
t
h
e DVR
i
s
abl
e
t
o
pr
o
duc
e t
h
e req
u
i
r
ed
vol
t
a
ge com
pone
nt
s f
o
r di
ff
ere
n
t
pha
ses ra
pi
dl
y
and
hel
p
t
o
m
a
i
n
t
a
i
n
a bal
a
nc
ed an
d co
nst
a
n
t
l
o
ad vol
t
a
ge at
1.0
0
p
u
.
In t
h
i
s
case no di
f
f
e
r
enc
e
bet
w
ee
n t
h
e t
w
o c
o
nt
r
o
l
l
e
rs
i
s
appa
rent
s
o
, we ca
n say
t
h
at
t
h
e t
w
o co
nt
r
o
l
l
e
rs ha
ve
t
h
e sam
e
perfo
rm
ance.
As a resu
lt, the p
e
rform
a
n
ce o
f
DVR
un
d
e
r th
e two
co
n
t
ro
llers in
m
itig
atin
g
vo
ltag
e
sag
s
/swell and
v
o
ltage
un
bal
a
nce i
s
al
m
o
st
t
h
e sam
e
. In ad
di
t
i
on t
h
e pr
op
ose
d
f
u
z
z
y
cont
r
o
l
l
e
r (
g
ene
r
at
ed
by
AN
FIS
)
has
o
n
l
y
one
i
n
p
u
t
wi
t
h
m
i
n
i
m
u
m
num
ber
of m
e
m
b
ershi
p
fu
nct
i
o
ns a
n
d
do
n
o
t
need
ga
i
n
s w
h
i
c
h m
a
ke i
t
s
im
pl
em
ent
a
t
i
on
practically very easy with a
minim
u
m
cost.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
21
2
–
22
2
22
0
(a)
Fig
u
re 11
. Simu
latio
n
resu
lt
of
DVR
res
p
o
n
s
e
t
o
un
bal
a
n
c
e
d
vol
t
a
ge
s;
(a)
The
gi
ven
f
u
zzy
co
nt
r
o
l
l
e
r
,
(b) T
h
e
optimal fuzzy c
o
ntroller
6.
CO
NCL
USI
O
N
Thi
s
pa
per
pre
s
ent
s
a sim
p
l
e
unc
on
st
rai
n
e
d
opt
i
m
i
zat
i
on m
e
t
hod ba
sed
on
AN
FIS t
o
opt
i
m
i
ze
t
h
e
i
n
p
u
t
s
an
d t
h
e
num
ber o
f
m
e
m
b
ershi
p
f
u
n
c
t
i
ons o
f
a gi
v
e
n f
u
zzy
cont
r
o
l
l
e
r. T
h
e m
e
tho
d
wa
s ap
pl
i
e
d t
o
a
fu
zzy co
n
t
ro
ller of two
inpu
ts an
d on
e
o
u
t
pu
t with
sev
e
n
me
m
b
ersh
ip
fun
c
tio
ns in
con
t
ro
lling
a
DVR
. Th
e
pr
o
pose
d
c
o
nt
r
o
l
l
e
r i
s
ge
ne
ra
t
e
d by
AN
FIS
t
r
ai
ni
n
g
acc
or
di
n
g
t
o
a
gi
ve
n i
n
p
u
t
o
u
t
p
ut
dat
a
t
a
ke
n
fr
o
m
t
h
e
DVR sim
u
lati
o
n
. Th
e sim
u
latio
n
resu
lts hav
e
shown
al
m
o
st a sa
me
p
e
rform
a
n
ce with
a slig
h
t
n
e
g
lig
i
b
le
diffe
re
nce in dynamic respence of the
t
w
o c
ont
t
r
ol
l
e
rs. C
o
m
p
ared t
o
t
h
e gi
ve
n fu
zzy
cont
r
o
l
l
e
r, t
h
e p
r
op
ose
d
o
n
e
is t
h
e simp
lest; it co
n
s
ists o
n
l
y of on
e
in
pu
t and
ou
tpu
t
with
three
me
m
b
ersh
ip
fun
c
tio
ns (3
ru
les o
n
l
y)
an
d
t
h
e m
o
st c
o
st efficien
t con
t
ro
ller. In
additio
n
th
is con
t
ro
ller h
a
s
no
g
a
in
s to
adju
st and
so
l
v
e th
e
p
r
ob
lem
o
f
trad
ition
a
l fu
zzy con
t
ro
ller g
a
ins tun
i
ng
.
ACKNOWLE
DGE
M
ENTS
The a
u
t
h
ors
g
r
at
eful
l
y
ack
no
wl
ed
ge a
nd
wi
sh t
o
ex
pre
ss t
h
ei
r
pr
of
o
u
n
d
t
h
an
ks t
o
,
Pr.
R
a
hl
i
M
o
st
efa
an
d Pr
. Mazar
i
Ben
youn
es
f
o
r th
eir
h
e
lp and
en
cour
ag
em
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Desi
g
n
a
n
d
Si
mul
a
t
i
o
n
of
Dy
na
mi
c V
o
l
t
a
ge
Rest
orer
Base
d on F
u
zzy
Controller
Op
timized
… (Brah
i
m Ferd
i)
22
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