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
)
Vo
l
.
1
1
, No
.
1
, M
a
r
c
h
2
02
0
,
pp
.
9
7
~
106
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
9
7
-1
06
97
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Improv
emen
t of d
irect torque c
ontrol appl
ied to doubly fed
induction m
otor under variable speed
H
a
l
a
A
la
mi
A
r
o
us
s
i
1
, ElMostafa Z
iani
2
,
Ma
n
a
l
e
B
o
u
de
rb
a
l
a
3
,
Badr
e
Bossou
f
i
4
1,
2
Lab
o
rat
o
ry
o
f
E
l
ectri
cal an
d
Mai
nt
e
n
ance E
n
g
i
n
eeri
n
g
(LGEM
)
, M
o
ha
m
e
d
P
r
emi
e
r Un
iv
ers
ity, M
o
ro
cco
3,
4
LISTA
Laborator
y
,
Si
d
i
M
ohammed Ben
Abdell
ah
U
nivers
ity,
M
orocco
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
2
8
,
2
018
Re
vise
d Ju
l 3
1
,
201
9
Ac
ce
p
t
ed
No
v
2
1
,
2
019
Th
is
w
o
r
k
is
d
e
d
icat
ed
t
o
th
e
stud
y
o
f
a
n
i
m
p
r
o
v
ed
d
irect
t
orq
u
e
co
nt
ro
l
o
f
th
e
d
o
u
b
ly
f
ed
i
nd
ucti
on
m
oto
r
(
DF
IM
).
T
h
e
c
ontro
l
m
e
th
od
ado
p
t
s
d
i
rect
to
rqu
e
c
o
n
tro
l
'
DTC'
b
ecaus
e
o
f
its
v
arious
a
dv
ant
a
ges
l
i
ke
t
he
ease
of
im
plem
en
t
a
ti
on
wh
ich
allo
ws
a
goo
d
p
e
rf
orm
a
nce
at
t
rans
ien
t
a
n
d
s
teady
st
ate
w
ith
ou
t
P
I
r
egu
l
ato
r
s
and
rot
a
tin
g
co
ordi
n
a
t
e
t
rans
f
o
rm
at
io
ns.
To
d
o
th
is
,
t
h
e m
o
deli
n
g
of
th
e m
o
t
o
r is
p
erf
o
rm
ed.
S
ubseq
uent
ly
, an
ex
p
l
anat
io
n of
th
e
s
a
id
c
o
m
m
a
nd
i
s
s
p
r
ead
o
u
t
a
s
wel
l
a
s
th
e
p
r
in
ciple
of
a
dj
u
s
ting
the
f
l
ux
and
th
e
electro
m
a
gn
etic
t
orq
u
e
acco
rdin
g
t
o
t
he
d
esi
r
ed
s
p
e
e
d
.
T
h
en
,
th
e
est
i
m
a
tion
m
e
t
h
o
d
o
f
t
h
es
e
two
con
t
ro
l
v
a
riab
les
will
b
e
p
r
esen
t
e
d
as
w
ell
as
th
e
ad
op
ted
s
w
itchi
n
g
t
a
bl
e
of
t
h
e
h
yst
e
resi
s
cont
roller
m
o
del
us
e
d
b
as
ed
o
n
the
mode
l
of
t
he
m
ul
tilevel
i
n
vert
ers.
F
inal
l
y
,
the r
o
bust
ness
of
t
he
d
evel
oped
syst
e
m
w
ill
b
e
a
n
alyzed
w
it
h
va
l
i
dation
in
M
at
l
a
b
/
S
i
mulink
en
v
i
ronme
n
t
to
illus
t
rate
t
he per
for
m
ance of
t
his
control.
K
eyw
ord
s
:
DF
I
M
hys
t
e
res
i
s c
ont
rol
l
er
s
DTC
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
H
a
la
A
lam
i
A
rous
si,
Lab
o
ra
tor
y
of
Elec
tric
a
l
and
Ma
in
t
e
nance
E
n
g
i
neer
ing
(LG
E
M),
Eco
l
e
S
upé
rie
u
r de
Te
c
hno
lo
gie
, Mo
h
a
m
e
d
Pr
e
m
i
er
U
ni
ve
rs
ity,
BP
473
Com
p
le
xe
u
n
i
ve
rsita
ire
A
l
Q
ods, O
ujda
6
0
0
0
0
O
uj
da,
Moroc
co
Em
ail
: h.a
l
am
ia
rroussi
@
u
mp.
ac.
ma,
alam
i.a
r
ous
si.
h
a
l
a
@
g
m
ail.com
1.
I
N
TR
OD
U
C
TI
O
N
O
v
e
r
t
he
l
a
s
t
dec
a
de
s,
t
he
t
e
c
h
n
i
que
o
f
va
r
i
ab
le
s
p
eed
e
l
e
ctric
d
ri
ves
h
a
s
been
d
e
v
e
l
ope
d
r
a
p
i
d
l
y
tha
n
ks
t
o
a
dva
nce
s
i
n
p
o
w
e
r
ele
c
tr
on
ics
a
n
d
the
te
c
h
n
i
c
a
l
a
dva
n
tage
s
tha
t
a
n
as
ync
hro
n
ous
m
ac
h
i
ne
o
ffers
over
a
D
C
m
a
c
hi
ne,
such
a
s t
h
e
rob
u
st
ness
of
t
he
m
ac
hine
and
i
t
s low
co
st of
p
u
rcha
se
a
nd m
a
in
t
e
na
n
c
e
.
Also,
one
o
f
t
h
e
la
t
e
st
d
e
v
el
o
p
ed
s
trate
g
ie
s
i
s
d
irec
t
torq
ue
r
egula
t
io
n.
T
h
i
s
tec
h
n
i
q
u
e
w
a
s
init
ia
te
d
dur
in
g
t
h
e
198
0s
b
y
Ta
ka
has
h
i
an
d
D
e
pe
nb
r
o
ck
a
s
c
o
m
p
e
t
i
tive
w
i
t
h
c
o
n
v
e
n
t
i
o
n
a
l
c
o
n
t
r
ols,
b
ase
d
o
n
pu
lse
w
i
d
t
h
mod
u
l
a
t
i
on (P
WM)
po
w
e
r
supply,
dec
ou
p
l
i
n
g of t
he
f
lu
x an
d
by t
h
e or
i
e
n
t
at
ion
o
f
the
m
agne
tic
f
lux.
T
h
e
s
e
d
i
r
e
c
t
c
o
n
t
r
o
l
m
e
t
h
o
d
s
b
e
l
o
n
g
t
o
t
h
e
c
a
t
e
g
o
r
y
o
f
a
m
p
l
i
t
u
d
e
co
ntr
o
l
a
nd
w
e
r
e
o
rig
i
na
ll
y
d
e
s
i
g
n
e
d
f
o
r
a
t
w
o
-
l
e
v
e
l
i
n
v
e
r
t
e
r
[
1
]
.
T
h
e
d
i
r
e
c
t
c
o
n
t
r
o
l
o
f
t
h
e
to
rqu
e
(
DTC)
c
on
si
st
s
of
c
o
n
t
r
oll
i
ng
d
i
r
e
c
t
l
y
the c
l
osin
g or
ope
n
i
n
g
of t
h
e in
verter
s
w
i
tc
h
e
s from
t
h
e
pre
c
a
l
cu
la
te
d va
l
u
es of t
h
e
sta
t
or
f
l
u
x a
n
d the
c
o
u
p
le
.
The
cha
nge
s
o
f
s
ta
t
e
s o
f
t
he
s
w
itc
hes
are
re
l
a
ted t
o
t
he
ev
o
l
u
t
ion
o
f
t
he
ele
c
t
roma
g
n
et
ic st
a
tes
of t
he
en
g
i
ne.
The
m
a
in
goa
l
of
t
h
i
s
w
o
rk
i
s
to
p
r
e
se
n
t
a
n
adva
nc
ed
m
e
t
ho
d
o
f
d
i
rec
t
t
orq
u
e
co
ntro
l
app
l
i
e
d
t
o
D
F
I
M
s
how
n
sc
hem
a
t
i
cal
l
y
i
n
the
fo
ll
ow
i
ng
fi
gur
e
b
y
u
s
i
ng
m
ul
t
i
l
e
ve
l
i
nver
t
er
s
tha
t
o
ffe
r
hu
ge
a
d
v
a
n
ta
ges
over
inverter
s
with
2
-level
s
[2].
Th
us,
th
e
d
i
str
i
b
u
t
i
o
n
o
f
t
he
v
o
l
tage
i
n
t
h
e
mult
i-le
ve
l
i
nver
t
e
r
s
is
o
b
t
a
i
ne
d
in
a
n
a
t
ur
al
w
ay
i
n
st
e
a
dy-s
t
ate
, w
hic
h
m
akes
i
t
poss
i
b
l
e t
o
sw
i
t
c
h
eac
h sem
i
co
nd
uc
tor
inde
pe
nde
n
t
l
y
o
f
th
e
ot
her
s
.
Th
is
m
ake
s
t
he
c
on
ve
rter
m
ore
rob
u
st
a
n
d
m
ore
perfor
m
a
n
ce
dur
in
g
sw
it
c
h
in
g.
A
lso,
t
h
e
s
w
itc
he
d
v
o
l
t
a
ge
i
s
a
t
t
h
e
r
edu
c
ed
a
mp
l
i
t
u
d
e
an
d
t
h
e
swit
ch
ing
is
t
h
e
re
fo
re
e
a
s
ie
r
to
m
ana
g
e.
O
n
t
h
e
m
a
c
h
in
e
si
de
: t
h
e
num
ber
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
97
– 10
6
98
vo
lta
ge
g
e
n
er
a
t
ed
b
y
a
m
u
lt
il
eve
l
i
n
v
erte
r
i
s
h
ig
her
tha
n
t
h
a
t
of
t
he
i
nver
t
er
w
it
h
2-vo
lta
ge
l
e
v
e
l
s,
w
h
i
c
h
w
i
l
l
all
o
w
to
im
p
r
o
ve
t
he
q
ua
li
t
y
of
its w
a
v
ef
orm and w
ill ma
n
i
fes
t
itse
l
f by
r
educ
in
g i
t
s ha
r
m
onic
d
i
st
ort
i
on. T
his
w
ill
als
o
r
esu
l
t
i
n
t
he
d
e
c
re
a
s
e
of
i
ron
l
o
ss
es,
the
i
n
cr
ease
i
n
t
h
e
li
fe
o
f
ins
u
lat
o
rs
o
r
t
h
e
re
duc
t
i
on
o
f
t
he
elec
tr
oma
gne
t
i
c
ra
diat
i
o
n
fro
m
the
w
ind
i
n
g
s
o
f the
ma
ch
in
e.
I
n
t
h
i
s
pe
rs
pe
c
t
i
v
e,
a
c
om
ple
t
e
stu
dy
o
f
t
he
a
rc
hi
t
e
c
t
ur
e
is
p
r
o
pose
d
i
n
orde
r
to
e
la
b
o
rate
t
he
impro
v
e
d
d
i
r
ect
c
on
t
r
ol
o
f
the
t
o
r
que
l
aw
[
3-
5].
T
h
e
n
,
t
h
e
w
h
o
l
e
sys
t
em
i
s
val
i
da
te
d
un
der
the
Ma
t
l
a
b
/
S
i
m
u
l
i
n
k
e
nv
ir
onme
n
t
t
o
e
ns
u
r
e
the
effi
c
i
e
n
c
y
of t
h
e
co
ntro
l
.
F
i
gure
1.
S
yno
ps
is of
the
D
T
C of t
he
D
F
I
M
2.
DOUB
LY
F
ED
I
NDUCTI
O
N
MOT
O
R MODELING
:
I
n
t
he
lite
rat
u
r
e
,
w
e
f
in
d
tha
t
t
he
D
FI
M
m
o
del
i
n
t
he
r
e
f
e
r
enc
e
i
s
summarized
i
n
three
types
of
equa
t
i
o
n
s
:
e
lec
t
r
i
ca
l,
m
a
gneti
c
and e
l
e
c
t
rom
a
gne
t
i
c[
6, 7]
.
2.1.
E
l
e
c
tr
ic
al eq
u
at
ion
s
:
In
t
h
e
f
r
a
me
,
the sta
t
or
a
nd r
o
tor
vo
l
t
a
g
es a
re
e
xpre
s
se
d b
y
t
he
fo
l
l
o
w
i
ng
equa
ti
on
s:
⎩
⎪
⎪
⎨
⎪
⎪
⎧
(1)
2.2.
Flux
e
q
u
a
t
io
ns:
The
sta
t
or
a
n
d
rot
or
f
lu
xes a
r
e
give
n b
y
:
⎩
⎨
⎧
(2)
W
h
ere:
a
nd
:
R
e
si
st
anc
e
s
o
f
a
p
h
a
s
e
of t
h
e sta
t
or
/ro
t
or.
a
nd
:
C
ycl
i
c
ind
u
c
t
a
n
ce
s
o
f
a
stat
o
r/ro
tor
p
h
a
s
e.
:
M
a
x
i
m
um
mut
ua
l in
d
u
c
t
anc
e
be
t
w
e
e
n
a sta
t
or
/rot
or
phase.
a
n
d
:
Angul
a
r speed of
th
e
ro
t
o
r/
s
t
ato
r
.
2.3.
E
l
e
c
tr
om
agn
e
t
ic t
orq
u
e
:
The
e
q
u
a
t
i
on o
f
t
he
e
l
e
c
t
rom
a
gne
t
i
c tor
que a
s
a
f
unc
t
i
on o
f
t
he
s
ta
t
o
r
flu
x
a
nd
sta
t
or
c
urre
nt
i
s
g
i
ve
n
by t
h
e
ex
pre
s
si
on be
low
:
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
Im
prov
em
en
t
of
dire
ct t
o
r
q
u
e
c
o
n
t
r
o
l ap
p
lie
d
to do
u
b
ly
fe
d i
n
d
u
c
t
i
o
n m
o
t
o
r
… (H
a
l
a
Alam
i
Arouss
i
)
99
)
(3)
3.
DIRECT
T
ORQUE
CONT
R
O
L:
3.1.
Prin
cip
l
e
of
t
he
con
trol:
D
i
re
ct tor
qu
e
c
o
n
t
r
o
l
o
f
an as
ync
hro
n
ous
m
ac
hine
i
s
ba
se
d
on t
h
e
d
i
re
ct
d
e
t
erm
i
na
tio
n o
f
t
he
c
ontro
l
seq
u
enc
e
a
p
p
l
i
e
d
t
o
t
h
e
swi
t
c
h
es
o
f
the
s
t
at
i
c
power
c
o
n
v
e
r
ter
i
n
o
r
d
e
r
t
o
i
m
p
o
s
e
t
h
e
d
e
s
i
r
e
d
l
e
v
e
l
s
o
f
t
o
r
q
u
e
and
flu
x
[
8]
.
The
o
b
je
c
tive
of
a
D
TC
i
s
t
o
m
a
i
nt
a
i
n
the
e
l
ectro
m
a
g
n
e
tic
t
or
que
a
n
d
t
he
m
odu
l
e
o
f
t
h
e
sta
t
or
fl
u
x
i
nside
the
hys
tere
si
s
ba
nds
b
y
c
hoos
i
ng
the
ou
t
p
u
t
v
o
l
t
a
ge
o
f
the
in
ver
t
e
r
.
Whe
n
t
he
t
orq
u
e
o
r
t
he
modu
le
o
f
t
h
e
sta
t
or
f
l
u
x
re
ac
hes
the
u
p
p
er
o
r
l
o
w
e
r
l
i
m
i
t
of
t
he
hys
t
e
res
i
s,
a
n
a
p
propr
i
a
te
v
o
ltage
v
ec
t
o
r
is
app
l
ied
to
b
ri
n
g
t
he
q
ua
nt
i
t
y
conc
er
ne
d
i
n
s
i
de
i
t
s
h
ys
tere
sis
b
an
d
.
T
o
choo
se
t
he
volt
a
g
e
v
e
c
t
o
r,
i
t
i
s
e
ssent
i
a
l
to k
n
o
w
the
rul
e
s for the
ev
ol
ut
ion
o
f
t
he
t
or
que
a
n
d
t
he
s
t
a
to
r flu
x
m
odu
l
e
[
9-10].
I
n
t
he
c
om
pl
e
x
p
la
ne
c
o
n
s
i
sti
ng
of
t
he
a
x
e
s
(
),
t
h
e
c
om
ple
x
v
olta
ge
v
ec
t
o
r
r
e
pre
s
e
n
t
i
n
g
the
st
at
e
of
a
t
hre
e
-pha
se
v
o
l
ta
ge
i
n
v
e
r
ter
c
a
n
have
o
nl
y
ei
g
h
t
dis
t
i
n
c
t
p
o
si
t
i
o
n
s
be
c
a
use
e
ach
o
f
t
h
e
t
h
re
e
ar
ms
o
f
t
h
e
in
verter
ca
n
o
n
l
y ha
ve
tw
o
p
o
ssi
bl
e
s
t
ates.
The
vec
t
or
vo
l
t
a
ge
is
t
he
n de
f
i
n
e
d by t
h
e
fol
l
o
w
i
n
g
r
elat
io
n [11]
:
(4)
Where
:
V
a
,
V
b
and V
c
a
r
e
t
h
e
o
ut
p
u
t
vo
lt
ag
e
s
o
f
t
h
e
inv
e
r
t
e
r
.
The
ex
pre
s
si
on
of stat
or flux
i
n
the r
efe
r
enc
e
fram
e linke
d t
o
t
h
e
st
at
o
r
o
f
th
e ma
ch
i
n
e i
s
o
bt
ai
n
e
d
by
the
fo
l
l
ow
i
n
g
eq
ua
ti
o
n
:
(5)
3.2.
Hyster
es
i
s
C
ont
r
oll
e
r:
The
ma
in
o
b
j
e
c
ti
v
e
o
f
t
h
e
dire
ct
t
or
que
c
ontr
o
l
is
t
o
ma
int
a
in
th
e
i
n
st
an
t
st
at
o
r
f
lu
x
and
elec
tr
oma
gne
t
i
c
torq
ue
i
n
a
s
p
eci
fic
ba
nd.
T
h
e
D
TC
i
s
b
a
se
d
o
n
tw
o
h
y
s
t
ere
s
i
s
c
om
p
a
ra
tors
w
hic
h
u
se
a
s
in
put
t
h
e
e
rror
sig
n
a
l
s
be
tw
e
e
n
t
h
e
ref
e
rence
values
a
nd
e
sti
m
a
tes
o
f
t
he
s
ta
t
o
r
fl
ux
and
e
l
e
c
t
rom
a
gne
t
i
c
tor
que.
The
s
e
tw
o
c
o
n
t
r
o
l
l
e
r
s
a
r
e
r
e
sponsi
b
le
f
or
d
e
c
i
di
n
g
h
ow
m
u
ch
a
n
ew
s
w
itc
h
a
n
d
/
or
o
u
t
pu
t
v
o
l
t
a
g
e
v
e
ct
o
r
o
f
t
h
e inv
e
rt
er i
s ap
pl
i
e
d
.
I
f
t
h
e
e
r
r
o
r
s
(
e
o
r
eT
)
is
i
nc
rea
s
ing
a
n
d
rea
c
he
s
a
hig
h
er
l
e
v
el,
the
h
y
ster
esis
c
o
n
t
ro
l
l
e
r
s
w
itc
he
s
its
out
pu
t o
n
'
1
'
.
3.3.
Ve
ctor
S
e
l
ect
i
o
n
:
F
r
om
t
he
v
e
c
t
o
r
s
of
t
he
v
o
l
ta
g
e
s
sche
ma
tiz
e
d
i
n
F
i
g
u
re
2
w
e
can
d
is
tin
g
u
i
s
h
fo
ur
g
r
oups
o
f
vec
t
or
s:
1)
T
he
g
ro
up
o
f
ve
ct
ors
"zer
o
te
ns
io
n"
:
T
h
e
y
a
re
o
bta
i
ned
by
th
ree
differe
nt
c
o
m
bi
na
ti
o
n
s
of
t
he
s
ta
t
e
s
o
f
t
he
three
arm
s
o
f
t
h
e
inverter
[
12-1
5]:
(
1
,1,1)
,
(-1,-
1,
-1)
a
nd
(0,
0,0)
n
a
m
ed
r
e
s
pecti
v
ely
V
7
,
V
14
a
nd
V
0
.
2) T
h
e
gr
o
u
p
o
f the
vec
t
or
s
"half
te
ns
i
o
n"
t
ha
t w
e
c
a
n
dec
ompos
e
i
n
to
2
o
ther
s
u
bgr
ou
ps:
The fi
r
s
t
con
s
i
s
ts of
the
vec
t
o
r
s: V
1
, V
2
,
V
3
,
V
4
, V
5
and
V
6
.
Th
e
se
c
o
nd
g
ro
up
s
th
e
v
ect
ors:
V
8
,
V
9
,
V
10
,
V
11
,
V
12
a
nd
V
13
.
Th
e
s
e
v
ect
o
r
s
con
s
t
i
t
u
t
e
t
h
e
int
e
rn
al
hexa
g
on "ha
l
f t
e
ns
io
n.
3
)
T
h
e
g
r
o
u
p
o
f
"
f
u
l
l
v
o
l
t
a
g
e
"
v
e
c
t
o
r
s
:
T
h
i
s
g
r
o
u
p
c
o
n
t
a
i
n
s
t
h
e
v
olta
g
e
s
vec
t
or
s
nam
e
d:
V
15
,
V
16
,
V
17
,
V
18
,
V
19
a
nd
V
20
. These vec
t
o
r
s
cons
t
itute
th
e ex
t
e
rn
a
l
h
e
x
a
gon
o
f "fu
l
l
vo
lt
ag
e".
4) The
gr
o
u
p
o
f "in
t
er
me
di
a
t
e
v
o
l
t
a
g
es"
:
t
he
v
ec
tor
s
o
f
the
vo
l
t
a
ge
s of t
hi
s gro
u
p
a
r
e ca
ll
ed V
21
,
V
22
,
V
23
,
V
24
,
V
25
a
nd
V
26
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
97
–
10
6
10
0
F
i
gure
2
.
V
ector of
t
e
nsion
s
i
n
the f
r
ame
(
)
3.
4.
S
w
i
tc
h
i
ng
t
a
b
l
e
:
The
swi
t
c
h
ing
tab
l
e
sele
c
t
s
th
e
ap
pro
p
r
i
a
t
e
v
o
lta
ge
v
e
c
t
or
o
f
t
h
e
i
n
v
e
r
t
e
r
i
n
o
r
d
e
r
t
o
o
r
i
e
n
t
t
h
e
s
t
a
t
o
r
f
l
u
x
a
n
d
e
lec
t
r
o
ma
gne
t
i
c
tor
que
i
n
the
i
r
d
e
sir
e
d
va
lues,
als
o
b
a
s
ed
o
n
t
h
e
p
o
si
ti
on
o
f
t
he
s
our
c
e
v
o
l
t
a
ge
ve
ct
or
a
nd
the
er
r
o
r
s
o
f
the
st
a
t
or
f
l
u
x
an
d
e
l
ec
tr
om
ag
ne
tic
t
o
r
q
u
e
[
1
6
,
17]
.
I
n
t
h
i
s
w
o
r
k
,
w
e
a
dop
t
e
d
a
m
odi
f
i
ed
s
w
i
tc
hi
n
g
t
ab
le
c
om
par
e
t
o
e
n
s
u
r
e
o
p
tim
al
m
in
i
m
iza
t
i
o
n
i
n
erro
r
.
4.
APPLICATIO
NS
A
N
D
RE
S
U
L
TS:
The
f
o
l
l
o
w
i
ng
fi
g
u
r
e
d
e
s
c
r
ibe
s
t
he
m
ode
l
u
s
ed
f
or
t
he
c
o
n
t
r
o
l
o
f
t
h
e
d
o
u
b
l
y-
fe
d
i
n
duc
t
i
o
n
m
ot
or
i
n
Ma
tla
b
/
S
i
m
u
l
i
nk
en
v
i
r
o
nme
n
t
[1
8-
2
1
]
:
F
i
gur
e
3.
D
i
r
e
c
t
t
or
q
u
e
c
o
n
t
r
o
l
(
D
TC)
bl
oc
k
d
i
agr
a
m
4.
1.
Se
tpo
i
nt
t
ra
ck
i
n
g
test:
The
s
y
ste
m
i
s
ana
l
y
z
ed
d
ur
i
n
g
st
e
a
d
y-sta
t
e
an
d
t
r
ans
i
e
n
t
s
c
on
d
i
t
i
on
s
at
v
a
r
ia
b
l
e
s
p
eed
(
su
b-
syn
c
hr
o
nou
s,
s
ync
hr
o
n
ous
a
n
d
s
u
p
er
-
s
ync
hr
on
o
u
s)
.
The
r
e
sults
o
f
t
h
e
s
imu
l
at
io
n
a
r
e
su
mmari
z
ed
i
n
Fi
g
u
r
e
6
[
2
2,
23]
:
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
I
m
provem
en
t o
f
di
rect
tor
q
u
e
con
t
r
o
l
ap
p
l
ie
d
to do
u
b
ly f
e
d i
n
d
u
c
tio
n
m
o
t
o
r
… (
H
ala A
l
am
i
Aro
u
ss
i)
10
1
(a)
(b
)
(c
)
(d
)
(e)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
97
–
10
6
10
2
(f)
(g
)
F
i
gur
e
6.
(
a)
C
ur
ves
o
f
:
t
h
e
r
o
tat
i
ona
l
spee
d,
(
b)
t
he
e
lec
t
r
o
m
a
gnet
i
c
t
o
r
q
u
e
,
(
c
)
the
stat
or
a
nd
r
o
tor
flu
x
e
s,
(
d
)
the
vo
lt
a
g
e
s
o
f
the
sta
t
or
,
(
e
)
the
c
u
r
r
e
nt
s
of
t
he
s
ta
t
o
r
,
(f)
t
he
vol
tag
e
s
of
t
he
r
ot
or
,
(
g
) the
curr
ents
of
the r
o
tor
.
4.
2.
R
o
bustness
T
e
st:
T
h
e
p
a
r
a
m
e
t
e
r
s
o
f
t
h
e
D
F
I
M
a
r
e
e
x
p
o
s
e
d
t
o
v
a
r
i
a
t
i
o
n
s
c
a
u
s
e
d
b
y
var
i
ous
c
ha
ng
e
s
s
uc
h
as
tem
p
er
at
ure
i
n
cre
a
se,
skin
e
ffe
c
t,
e
tc.
I
n
t
h
i
s
ca
se,
the
pro
p
o
sed
di
rec
t
t
orq
u
e
c
o
n
t
r
ol
m
u
s
t
gu
ara
n
t
e
e
g
ood
r
e
sults
r
ega
r
dle
ss
of
t
he
p
a
r
ameter
v
a
r
iat
i
ons
[
2
4
,
25]
:
So
,
t
h
e
robu
st
n
e
ss
o
f
th
e
co
mma
n
d
u
s
ed
(
DT
C
)
h
as
b
e
e
n
t
e
st
ed
a
c
c
o
rd
in
g
t
o
t
he
f
o
llow
i
n
g
co
nd
i
tio
ns
:
R
e
si
st
a
n
ce
R
m
ulti
pl
ie
d b
y
2
In
du
c
t
an
ce
s
L
an
d
L
m
ulti
p
lied
b
y
0.
5
.
F
i
g
u
r
e
7
sho
ws t
h
e
s
i
m
ul
a
t
i
o
n’
s
res
u
lt
s ob
t
a
in
e
d
:
(a)
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
I
m
provem
en
t o
f
di
rect
tor
q
u
e
con
t
r
o
l
ap
p
l
ie
d
to do
u
b
ly f
e
d i
n
d
u
c
tio
n
m
o
t
o
r
… (
H
ala A
l
am
i
Aro
u
ss
i)
10
3
(
b
)
(
c
)
(d
)
(e)
(f)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
97
–
10
6
10
4
(g
)
F
i
gur
e
7.
(
a)
C
ur
ves
of
:
r
o
ta
t
i
ona
l
spe
e
d
,
(
b
)
t
h
e
e
l
e
c
t
r
o
m
a
gne
tic
to
r
q
u
e
,
(c) th
e
st
ato
r
an
d
ro
to
r
f
l
ux
es,
(d
)
t
h
e
vo
ltage
s
of
t
he
s
ta
tor
,
(
e)
t
he
c
ur
r
e
nts
o
f
t
he
s
ta
tor
,
(
f)
t
h
e
v
oltag
e
s
of
th
e
r
oto
r
,
(g
)
th
e cu
rr
en
ts
o
f
th
e ro
tor.
Com
p
ar
i
n
g
t
h
e
r
e
sul
t
s
o
f
t
he
s
imula
t
i
ons
i
l
l
u
s
tr
a
t
e
d
in
F
i
g
u
r
e
6
a
n
d F
i
g
u
r
e
7
,
w
e
c
a
n
e
nsu
r
e,
eve
n b
y
ch
anging
th
e
in
iti
al valu
e
s
of D
F
I
M,
t
h
a
t:
T
h
e ro
t
a
ti
on
al
sp
eed
fol
lo
ws it
s
re
f
ere
n
ce
.
The
s
t
at
or
f
lu
x
has
a
c
i
r
c
ul
a
r
t
r
a
jec
t
or
y
si
nc
e
it
is
s
upp
l
i
ed
by
a
si
n
u
so
i
d
a
l
v
o
lta
ge
f
r
o
m
th
e
gr
id.
Thoug
h,
t
he
r
e
i
s
a
r
i
pp
le
s
uper
i
m
p
ose
d
o
n
the
c
i
r
c
ular
t
r
aj
ec
to
ry
o
f
th
e
ro
to
r
f
l
u
x
du
e
to
t
he
h
ys
ter
e
si
s
ba
n
d
c
hose
n
i
n
the
d
i
r
ect
t
or
q
u
e
c
o
ntr
o
l.
The
e
l
e
c
t
r
o
m
a
gne
t
i
c
t
o
r
q
ue
f
oll
o
w
s
its
r
efe
r
enc
e
w
i
t
h
fe
w
e
r
osc
illa
t
i
o
n
s
a
n
d
d
i
s
t
u
rba
n
c
e
s
due
t
o
t
h
e
hy
ste
r
esis
c
ontr
o
l
l
e
r
a
nd
t
h
e
c
h
a
n
g
e
o
f
the
i
n
i
t
ia
l
p
a
rameters o
f
th
e mach
in
e.
T
h
e
s
t
a
t
o
r
a
n
d
r
o
t
o
r
c
u
r
r
e
n
t
s
i
n
t
h
e
f
r
a
m
e
(
a
,
b
,
c
)
h
a
v
e
a
s
i
n
us
o
i
da
l
sha
p
e
de
sp
ite
t
he
f
act
tha
t
t
he
b
e
h
a
v
ior
of
t
he
e
le
ctr
o
m
a
gne
tic
t
or
q
u
e
chan
ge
s.
F
r
om
t
hese
r
esul
ts,
w
e
can
c
onc
lude
t
ha
t
t
h
e
d
i
r
e
c
t
t
or
q
u
e
c
on
t
ro
l
ha
s
a
low
respo
n
se
t
im
e
in
t
he
tr
a
n
sie
n
t
r
e
gim
e
,
a
n
d
fe
w
e
r
d
i
stur
ba
nce
osc
i
ll
a
t
i
o
ns
i
n
the
c
u
r
ves
o
f
t
he
v
ar
ious
c
ur
ves
t
h
at
q
u
i
ck
l
y
r
egai
n
th
eir
referen
c
e v
a
lu
es.
5.
CONCLUSION:
Th
is
w
or
k
p
u
t
f
or
w
a
r
d
a
n
enha
ncem
e
n
t
o
f
t
he
c
la
ssica
l
d
ir
ec
t
to
r
que
c
on
tr
o
l
u
s
i
ng
a
mult
i-
le
vel
in
ver
t
e
r
i
n
or
d
e
r
t
o
h
a
v
e
a
l
a
r
g
e
sw
i
t
c
h
in
g
t
a
bl
e
.
T
he
u
se
o
f
s
uc
h
a
k
i
n
d
o
f
t
ab
le
a
ll
ow
s
us
t
o
incr
e
a
s
e
a
nd
de
cr
e
a
se
t
he
m
od
u
l
e
o
f
t
he
f
l
uxe
s
an
d
the
e
l
e
c
tr
om
agne
t
i
c
tor
q
u
e
a
s
w
e
l
l
.
T
h
e
r
e
s
u
l
t
s
(
s
e
t
p
o
i
n
t
t
r
a
c
k
i
n
g
a
n
d
r
obust
n
ess
tes
t
)
in
s
tea
d
y
an
d
tr
ansie
n
t
r
e
gim
e
s
show
a
c
o
m
pl
e
t
e
c
o
r
r
elat
io
n.
T
he
y
b
o
th
p
r
ove
t
he
r
o
b
u
s
t
ness
a
nd
ef
fic
i
e
n
c
y
o
f
the
m
e
th
od
de
ve
l
ope
d.
I
n
g
ene
r
a
l
,
the
si
m
u
lat
i
on
r
e
s
u
lts
o
b
t
a
i
ne
d
d
u
r
i
ng
the
a
p
pl
i
cat
ion
of
t
h
e
c
o
n
t
r
ol
und
e
r
v
a
r
i
a
bl
e
s
p
eed
show
e
x
c
el
le
n
t
d
yna
mic
pe
r
f
or
m
a
nc
e
an
d
tr
ac
kin
g
a
b
i
l
i
t
y
of
t
he
f
l
ux
es
a
nd
the
e
l
e
c
t
r
o
ma
g
n
et
ic
t
or
q
u
e
ge
ner
a
t
e
d
a
t
t
h
e
c
or
r
e
spo
n
d
i
n
g
r
e
fer
e
nce
val
u
es
w
i
t
h
t
he
p
r
e
se
r
v
a
ti
on
o
f
si
nu
soi
d
a
l
s
h
a
pe
s
f
o
r
bot
h
c
u
r
r
en
t
s
a
nd
v
o
l
t
a
ges
(
s
t
a
tor
and
r
o
t
o
r
)
.
APPENDIX
:
Tab
l
e
2.
P
a
r
ameter
s
of
t
he
d
o
u
b
l
y
fe
d
i
n
duc
t
i
o
n
m
ot
or
D
F
IM
P
AR
AM
ETER
S
No
m
i
n
a
l P
o
w
e
r
Pn
=
1
.5
K
W
St
a
t
or
V
o
l
t
a
g
e
V
s =
220/380V
Sta
t
or
F
r
e
que
n
c
y
f
s
=
50 Hz
S
t
a
t
o
r
R
esist
a
n
c
e
Rs
=
1
.1
8
Ω
S
t
a
t
or
I
nduc
t
a
nce
L
s
=
0
.
4
H
R
o
t
o
r
Re
sist
a
n
ce
R
r =
1.
66
Ω
R
o
tor
I
n
d
u
c
t
a
n
c
e
L
r
=
0.
18
H
Mutua
l
I
nduc
t
a
n
c
e
M =
0.
17
H
No.
o
f
Pa
ir
o
f
Poles
P =
2
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
Im
prov
em
en
t
of
dire
ct t
o
r
q
u
e
c
o
n
t
r
o
l ap
p
lie
d
to do
u
b
ly
fe
d i
n
d
u
c
t
i
o
n m
o
t
o
r
… (H
a
l
a
Alam
i
Arouss
i
)
10
5
REFE
RENCES
[1]
W
a
n
g
,
F.;
Zhan
g
,
Z
.;
M
e
i
,
X
.
;
Ro
d
r
ígu
ez,
J
.;
K
en
nel,
R
.
“Adv
anc
ed
C
on
tro
l
S
t
r
ateg
ies
of
I
n
d
u
c
ti
o
n
M
achi
n
e:
F
ield
Ori
e
nted
C
ontrol,
D
i
r
ect
To
r
qu
e Con
t
ro
l
an
d
M
odel
P
r
e
d
ic
t
i
v
e
C
o
ntro
l.”
E
n
er
g
i
es
2
018
,
11
,
120
.
[2]
H.
Alami
Aro
u
s
s
i,
EL.
M
.
Z
iani,
B.
Boss
oufi “
C
ont
ributi
o
n
to
th
e
e
n
h
anc
e
m
e
n
t
o
f
du
al D
TC A
pplica
t
io
n:
Do
ubly
fed
induct
ion
moto
r”
I
nter
na
ti
on
a
l
Co
nf
erence O
n
Ad
van
ced T
echn
o
lo
gi
es
For S
i
g
n
a
l
&
Ima
g
e Pr
ocessin
g
ATSI
P'2017
,
M
a
y
22
-
24,
2
017,
F
ez,
M
o
r
occo
.
[3]
La
c
h
ta
r
Sa
la
h,
G
ho
gg
a
l
A
de
l,
K
o
u
ssa
K
h
a
le
d
,
B
ou
ra
io
u
Ah
me
d,
A
tt
oui
Iss
a
m
"
B
roken
rotor
bar
f
a
ul
t
d
i
agnostic
f
o
r
DT
C
F
e
d
in
d
u
ct
io
n
m
o
t
o
r
u
s
ing
st
ator
i
nsta
nt
aneo
us
c
o
m
p
l
e
x
apparen
t
p
o
w
er
e
nv
elo
p
e
signat
u
re
a
nal
y
s
i
s"
IJPE
DS Inter
natio
nal Jo
ur
na
l
of
Power Electron
i
cs
and
Dr
ive S
y
stem
(
I
JPEDS)
,
pp
1
1
8
7
-1
1
9
6
Vo
l.
1
0
N
o
.
3,
S
e
pt
emb
e
r
20
19
.
[4]
Drao
ui
A
b
d
el
gha
n
i
,
Allao
u
a
Boum
ed
ièn
e
“
Di
re
ct
T
orq
u
e
Cont
rol
o
f
T
w
o
I
nd
ucti
on
M
otors
Using
t
h
e
N
in
e-Sw
it
ch
Inverter”
"
I
J
P
E
DS
Int
e
r
n
a
t
i
o
n
a
l
Jo
ur
na
l of
Power
El
ec
t
r
o
n
i
c
s an
d D
r
ive S
y
st
e
m
(
I
J
P
ED
S
)
,
pp
1
5
5
2
-1
56
4
Vo
l.9
No
.4, Decem
ber 2
0
1
8
.
[5]
H.ALA
M
I
AR
OU
SSI
,
E
l.M.ZIAN
I,
M
.BOUDERBALA,
B.BOSSOU
FI
“
Enhancem
ent
Of
T
h
e
D
irect
P
ower
Control
Appli
e
d
to
D
FIG-
WEC
S”
In
ter
natio
nal
Jou
r
n
a
l
of El
ectrical
a
nd Co
mput
er
En
gin
eeri
n
g
(
I
JECE),
V
ol.1
0
No.1
, p
p.3
5
–
4
6
, F
ebru
ary 2
0
2
0
.
[6]
D.
R
oy
e,
“
M
odéli
sa
t
i
on,
c
ont
rô
l
e
v
ect
ori
e
l
et
D
TC
”
,
H
E
R
M
ES
S
c
ie
n
c
e
Eu
ro
pe
L
t
d,
20
00
,
sou
s
la
di
re
c
tion
d
e
Car
l
os Ca
nud
as
de
Wit
, pp
.
8
1
-1
32
vo
l
.1
.
[7]
Ab
ad G
,
L
opez
J,
Ro
d
ri
gu
e
z
M
,
M
a
rroy
o
L
,
Iwan
sk
i G.
“
D
oubly F
e
d
I
nd
ucti
on
M
achi
n
e:
M
odelin
g an
d Co
nt
rol
f
o
r
Wi
nd En
ergy
Generat
i
o
n
,
”
1
st
ed.
,
H
obo
ken
,
N
ew J
ersey,
USA
:
Wil
ey‐IEEE P
res
s
; 20
11
,
IS
BN:
978‐0
‐
47
0‐76
86
5‐
5.
[8]
A.
N
abae,
I
.
Ta
k
a
hash
i,
a
nd
H.
A
kagi
,
“
A
n
ew
n
eut
r
al
p
o
i
n
t
c
lam
ped
PWM
i
nvert
er,
”
IE
EE T
r
ansaction
on
I
n
d
u
s
t
r
y
A
p
p
l
i
c
at
i
o
ns
;
V
o
l.
IA-17,
N
o
.
5
,
p
p.
5
1
8
–523,
S
ep
t
e
mb
er- Oct
o
b
e
r
19
81
.
[9]
I.
T
ak
ahash
i
a
nd
T
.
No
gu
ch
i
,
“
A
new
q
u
i
c
k-resp
on
se
a
nd
h
ig
h-ef
f
ici
e
ncy
co
nt
rol
s
t
rat
e
g
y
o
f
an
i
n
d
uct
i
o
n
m
o
t
or,
”
IEEE
Trans. Ind
.
Appl
.
,
Vol.
IA-22
,
N
o
.
5
,
O
ctob
er
p
p
.
8
20-8
2
7
,
1986
.
[10]
S
e
ok
H
o
J
e
on,
S
tud
e
nt
,
K
w
a
n
g
K
yo
O
h
,
a
n
d
J
in
Y
ou
ng
C
ho
i
,
“
Flu
x
O
b
s
e
r
v
e
r
w
i
t
h
O
n
l
i
n
e
T
u
n
i
n
g
o
f
S
t
a
t
o
r
a
n
d
Rot
o
r Resis
t
ances
f
or In
d
u
c
ti
on
M
oto
r
s
,
”
IEEE
Tr
ans
actio
ns On
Ind
u
s
t
ri
a
l
Electr
o
n
i
cs
,
V
ol.
49
,
No
.
3
,
J
une
200
2
.
[11]
Y
.
D
je
r
i
r
i
,
A
.
M
e
r
o
u
f
e
l
,
B
.
B
e
l
a
b
b
e
s
a
n
d
A
.
M
a
s
s
o
u
m
,
“T
h
r
e
e
-
l
e
v
el
N
PC
v
o
ltag
e
s
ource
conv
erter
b
a
sed
di
rect
po
wer
cont
rol
o
f
t
he
d
ou
bl
y
f
e
d
ind
u
ct
io
n
generat
o
r
at
l
ow
c
o
n
s
ta
n
t
s
w
itc
hing
f
r
e
qu
e
n
c
y
;”
Re
vu
e d
e
s
Ener
gi
es
Ren
o
u
v
el
ab
les
,
Ce
n
t
r
e
de Dévelo
p
p
e
ment
des
Ener
gies
Reno
uvel
abl
es- CDER
,
Algé
rie
,
V
ol
.16
,
N
o
.
1,
p
p.9
1
-
1
0
3,
20
13
.
[12]
Rachi
d
,
D;
O
t
h
m
a
n,
H
.;
F
ao
uzi,
B
.,“
A
C
o
m
p
l
e
t
ely
V
e
c
t
ored
D
i
r
ec
t
Torque
C
ont
r
ol
S
chem
e
f
o
r
Induct
ion
Motor”
,
Sys
t
ems
,
M
a
n
and Cyb
e
rnet
ics
,
IE
EE
In
ter
nati
onal
Con
f
eren
ce
, v
o
l
.
5
, Issue ,
6-9
oct., 2
00
2
[13]
B.Bos
s
ou
fi,
M.
Kari
m
,
S
.
I
onita,
A
.
Lagriou
i
,
“T
he
O
ptimal
D
irect
T
o
r
q
u
e
C
o
n
t
r
o
l
o
f
a
P
M
S
M
d
r
i
v
e
:
F
P
G
A
-
B
a
s
e
d
Impl
e
m
entation
with
M
atla
b
&
S
i
m
u
lin
k
S
i
m
u
lat
i
on
”
Jour
nal of
T
h
eor
e
ti
ca
l a
n
d
A
p
p
l
ied
Inform
a
t
io
n
T
echno
lo
gy
JAT
I
T
,
V
o
l
.
2
8,
N
o.
2,
p
p6
3-7
2
,
30t
h
Jun
e
2
0
1
1
.
[14]
B
u
ja
,
G
.
;
C
a
s
a
d
e
i
,
D
.;
S
e
r
r
a
,
G.
,
“D
ir
e
c
t
to
r
q
u
e
c
o
n
t
r
o
l
o
f
i
n
d
u
c
t
i
o
n
m
oto
r
d
rives”
,
P
ro
ceedi
ngs
o
f
The
IEE
E
Int
e
rnati
o
n
a
l
S
y
m
p
o
s
iu
m,
I
s
s
ue,
7-1
1
J
ul
1
9
9
7
P
a
ge(S
):T
u2
- T
u
8
Vol.1
[15]
Ni
k
Ru
m
z
i
Nik
Id
ris,
a
n
d
A
b
d
u
l
H
a
l
im
M
oham
e
d
Y
a
tim,
“
Direct
T
or
qu
e
Cont
rol
of
I
n
d
u
c
tion
M
achi
n
es
w
it
h
Con
s
tan
t
S
w
i
t
c
hi
ng
Freq
uen
c
y
a
n
d
Redu
ced
T
orqu
e
Rip
p
l
e
”
,
IEE
E
T
r
ansactio
ns on
Ind
u
st
ri
a
l
El
ectr
o
n
i
cs
,
Vo
l.
5
1
, No
. 4
,
Au
gu
st 20
0
4
.
[16]
P
u
ra,
P
,
I
wan
s
ki, G.
Direct
t
o
r
qu
e
con
t
ro
l
o
f
a
d
ou
bl
y
f
e
d
in
du
ction gen
e
rat
o
r work
in
g
w
i
t
h
u
nb
ala
n
ce
d
p
o
wer
grid
.
Int
Trans
El
ectr Energ
Syst
.
2
0
1
9
;
29:e2
815
.
[17]
Iwan
ski
G,
P
ura
P
,
L
u
s
zczyk
T
.
“
P
r
op
erti
es
a
n
d
c
o
n
tro
l
o
f
vari
a
ble
s
p
eed
d
o
u
b
l
y
fed
in
du
cti
on
generat
o
r.
”
20
15
te
nth In
t. Co
n
f
.
Ec
ol.
Ve
h
.
Re
ne
w.
Ene
r
gie
s
,
pp.
1
–8,
2
0
1
5
.
[18]
Xi
on
g
P
,
S
u
n
D
.
“
B
acks
t
ep
pi
ng‐b
a
sed
DP
C
s
t
rat
e
gy
of
a
w
in
d
turb
i
n
e‐d
r
iv
e
n
D
F
I
G
un
der
n
o
rm
al
a
nd
h
arm
o
n
i
c
gri
d
v
o
l
tage.
”
I
n
IEEE Trans
.
Power Elect
rons
.
Vo
l.
3
1
,
No.
6
,
pp.
4
21
6‐42
25
,
2
01
6
.
[19]
S
o
n
g
Y
,
N
i
an
H
.
“M
o
d
u
l
arized
c
on
trol
s
t
r
ategy
and
perf
orm
a
n
ce
a
n
a
ly
si
s
of
D
FIG
s
y
s
t
em
u
n
d
er
u
n
b
al
anced
a
n
d
harm
o
n
ic
g
rid
volt
a
ge”.
I
E
EE
Tr
ans
Power E
l
ectron
.
V
o
l.
30,
N
o
.
9
,
pp.
4
8
3
1
‐
48
4
2
,
20
15.
[20]
Y.
E
rram
i,
A
.
Ob
bad
i
,
S
.
S
ahn
oun
,
M.
B
arara,
M
.
Ou
ass
a
id
,
an
d
M
.
Maaro
u
fi
,
“Co
n
t
r
ol
o
f
H
i
g
h
-P
ow
er
W
in
d
En
ergy
Conv
ersion
S
ystem
F
e
d
b
y
M
u
l
ti-l
evel
C
o
n
vert
e
r
s
,
”
E
n
ergy Pr
oced
ia
,
vol.
11
9,
pp.
2
1
4
–
227,
2
01
7.
[21]
A.
Z
em
m
it,
S
.
M
e
ss
alt
i
,
an
d
A
.
H
arrag
,
“
A
new
im
prov
ed
D
T
C
o
f
d
ou
b
l
y
f
e
d
i
n
d
u
cti
o
n
m
ach
in
e
u
s
in
g
G
A
-bas
e
d
PI controller,
”
A
i
n
Sh
am
s
Eng
.
J
.
, p
p.
0–
8
,
20
1
6
.
[22]
C.
B
alas
un
dar,
S
.
S
u
dhars
han
a
n,
a
n
d
R
.
E
l
akk
i
yaven
d
an,
“
D
esi
g
n
of
a
n
O
p
t
i
m
a
l
Tip
S
peed
R
at
io
C
on
trol
M
P
P
T
Al
gor
ithm
f
o
r
S
t
andalone W
EC
S
,
”
Int
.
J.
Res.
A
p
pl.
Sci.
Eng.
Technol.
,
v
o
l
.
3,
no
.
V, 20
1
5
.
[23]
P
e
ñ
a
R
,
C
á
r
d
e
n
a
s
R
,
A
s
h
e
r
G
.
“
O
v
e
r
v
i
e
w
o
f
c
o
n
t
r
o
l
s
y
s
t
e
m
s
f
o
r
t
h
e
o
perat
i
on
o
f
DF
IGs
in
w
in
d
energ
y
app
l
i
c
at
io
n
s
.”
IE
CON 2013
‐
39
th
A
nnu
al
Con
f
eren
ce
o
f
t
h
e IEE
E
Ind
u
s
t
ri
al
El
e
c
t
r
o
n
i
c
s So
ciety
,
Vie
n
n
a
,
20
13
,
p
p
.
88‐95.
[24]
Y.
L
i
et
a
l
.
,
“An
Im
proved
D
TC
C
ont
r
o
ller
f
o
r
D
F
IG-Base
d
W
ind
G
enerat
ion
S
y
s
t
em
,”
i
n
20
16
IEE
E
8
t
h
Int
e
rna
t
i
o
n
a
l
Power Electr
onics
an
d M
o
tio
n Co
n
t
ro
l
Confer
ence
,
pp.
6
–
9
,
201
6.
[25]
M
.
R
.
A
gha
K
ash
k
o
o
l
i
,
S.
M
.
Madani
,
an
d
R.
S
a
d
eghi
,
“
I
m
p
ro
ve
d
D
i
r
e
c
t
T
o
r
q
u
e
C
o
n
t
r
o
l
o
f
D
F
I
G
w
i
t
h
r
e
d
u
c
e
d
torq
ue
a
nd
f
lu
x
ripp
le
s
a
t
c
o
n
sta
n
t
sw
itc
h
i
n
g
fre
qu
e
n
c
y
,”
i
n
7
t
h
Po
wer El
ec
t
r
o
n
i
c
s, D
r
ive Sys
t
em
s
a
n
d
T
echn
o
lo
gi
es Conf
erence,
PE
DS
T
C
2
0
1
6
,
no
.
P
e
ds
tc,
pp.
5
8
–
6
3
,
201
6.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
97
–
10
6
10
6
BIOGRAPHI
E
S
OF
AUT
HORS
Hal
a
A
LA
M
I
A
RO
USS
I
r
ecei
ve
d
h
e
r
M
.
S
deg
r
ee
i
n
Indu
st
rial
A
ut
om
a
te
d
Sys
t
e
m
s
En
gine
e
r
in
g
f
r
o
m
S
i
d
i
M
o
ham
m
ed
B
en
A
bdell
ah
U
nivers
it
y,
F
ez,
M
o
r
occo
.
S
h
e
i
s
currently
p
ursuing
he
r
P
h
.
D
i
n
El
ectri
cal
E
n
g
in
eerin
g
–
Renew
a
ble
En
ergy
a
t
M
o
ha
m
e
d
P
r
emier
Universi
t
y
,
Oujda
,
M
o
ro
c
c
o
. S
h
e
is
a m
e
m
b
er of
th
e l
a
borat
ory
o
f
e
l
ectri
cal en
g
in
e
erin
g
an
d
m
a
i
n
t
e
nance
(L
GEM
)
.
Her
resear
ch
i
n
t
eres
ts
i
n
c
lu
de
m
odel
i
n
g
,
contro
l
of
w
in
d
energ
y
c
on
versi
o
n
s
y
stem
s
app
l
i
e
d
to
a
do
ub
ly
f
ed i
nd
ucti
on m
achi
n
e
u
s
ing
DSP
A
CE
.
Elm
o
st
a
f
a
ZIA
N
I
recei
ved
h
i
s
P
h
D
in
E
l
e
ct
rical
E
ngin
eering
f
r
om
A
bd
e
l
m
a
l
e
k
Es
saad
i
Universit
y
,
T
a
n
g
ier,
M
orocc
o
.
Cu
rrently,
he
i
s
the
director
o
f
the
Ap
pl
i
e
d
En
gine
e
r
ing
Dep
a
rtm
e
nt
o
f
the
E
c
ol
e
S
u
périeu
r
d
e
T
ec
h
n
o
l
o
g
i
e
-O
uj
da
a
nd
a
m
e
mber
o
f
the
the
laboratory
o
f
elect
ri
cal en
g
i
n
e
e
ri
ng
and
m
a
int
e
nan
ce.
He
i
s
aut
hor
o
f
several
art
i
cl
es
d
eal
in
g
w
i
th
t
h
e
a
p
p
l
i
cati
o
n
o
f
in
telli
gen
t
i
nst
r
u
m
ent
a
ti
on
t
o
t
he
mo
ni
tor
i
ng
o
f
c
o
mp
le
x
sys
t
e
m
s,
i
nd
ustri
a
l
system
s
an
d
the
co
n
t
r
i
butio
n
to
t
h
e
c
ont
rol
an
d
op
timizati
on o
f
e
l
ectri
cal co
n
v
e
rs
ion
sy
ste
m
s "
w
i
n
d
a
n
d
ph
otov
o
ltaic".
Hi
s res
earch i
nte
r
es
ts
in
c
lu
de e
l
ectrical
eng
in
eerin
g, p
ow
er e
l
ect
ron
i
cs
a
n
d
a
utomati
o
n
.
BOUDERBALA
M
anal
e
i
s
a
P
h.D.
S
t
udent
i
n
E
l
ect
rical
E
ngi
n
eeri
ng
f
r
o
m
t
h
e
F
acu
lt
y
of
S
c
ien
c
es
D
har
El
M
ah
raz,
S
i
d
i
M
o
ham
m
e
d
Ben
Ab
dell
ah
U
niv
e
rsit
y
,
F
ez
-
M
o
rocco.
S
h
e
is
m
e
mb
er
o
f
L
I
STA
Lab
o
rato
ry.
Sh
e
had
her
m
a
s
t
er'
s
d
egree
in
E
n
g
i
neerin
g
of
I
nd
ustri
a
l
Au
tomat
e
d
Sy
stem
s
at
t
he
F
ac
u
lty
o
f
S
c
ien
ces
D
har
el
M
ahr
ez
F
e
z
.
Her
r
e
s
earch
i
nt
erest
s
in
clud
e Renew
a
bl
e En
ergy, st
a
ti
c con
v
ert
e
rs
, el
e
ctrical
m
o
t
or
d
riv
e
s,
a
nd
po
w
er e
l
ectron
i
cs.
Badre
BOS
S
OUF
I
w
a
s
bo
rn
i
n
F
ez
city
,
M
o
roc
c
o
,
o
n
M
a
y
2
1
,
19
85
.
He
r
ecei
ved
t
h
e
P
h
.D
.
deg
r
ee
i
n
E
lectri
cal
E
n
g
i
n
eeri
ng
f
r
om
U
nivers
ity
S
i
di
M
o
h
amm
e
d
Ben
A
b
d
e
ll
a
h
,
F
aculty
o
f
S
c
ien
c
es
,
M
o
ro
cco
a
nd
P
h
D
.
degree
f
r
om
U
n
i
versity
o
f
Pit
e
st
i,
F
acul
t
y
o
f
E
l
ectron
i
cs
a
n
d
Computer,
Romani
e
and
Montef
i
o
re
I
nstitute
o
f
el
ectrical
e
ngine
eri
n
g
,
L
uik,
B
elgi
um,
i
n
2
0
1
3
.
He
i
s
a
P
r
o
f
ess
o
r
o
f
E
lect
rical
E
ng
in
eeri
n
g
,
a
t
t
h
e
LIS
T
A
Lab
o
r
at
ory
F
acu
lt
y
o
f
S
ci
ences
D
har
El
M
ah
ra
z,
S
i
d
i
M
o
hamm
ed
B
en
A
b
d
ell
a
h
Un
iv
ersit
y
,
F
ez
-
M
o
rocco
.
H
i
s
res
e
a
r
ch
i
nt
erest
s
in
clud
e
stati
c
c
o
nvert
ers,
e
lect
ri
cal
m
o
t
o
r
d
ri
v
e
s
,
p
o
w
er
e
l
ect
ro
nics
,
Sm
art
Gri
d
,
Ren
e
wab
l
e
En
ergy
and
Art
i
fici
al
I
n
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