Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 16
8
~
17
7
I
S
SN
: 208
8-8
6
9
4
1
68
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
A New Multilevel Active Powe
r F
ilter Usi
n
g Swit
ches
Meticulously Controlled
Z
a
hz
ouh Z
o
ubir*,
Kh
ochm
ane L
a
kh
dar
*
, H
a
dd
ouc
h
e
Ali**
* Department of
Mechanical Eng
i
n
eering
,
Faculty
of Technolog
y
,
20 Aout 1955
University
, Skikda, Alger
i
a
** Departement
of Electromechan
ical Eng
i
neerin
g, Facu
lty
of
Technolog
y
,
Badji
Mokhtar Univer
sity
, Annab
a
, Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 29, 2014
Rev
i
sed
Jan 28, 201
5
Accepted
Feb 10, 2015
Shunt active po
wer fil
t
er
based
on m
u
ltil
ev
el
in
verter
is used
to
com
p
ensate
the power factor
and to delete th
e ha
rmonics. Th
is one pe
rm
its to
reduce
the
inverse voltag
e
s
applied to
the f
i
lter sw
itch
e
s and
their switching f
r
equencies
.
Nevertheless,
th
e high number
of used
s
w
it
c
h
es
requir
e
s
a
com
p
lica
t
ed
controll
er and
in
creas
es
th
e s
w
it
ching los
s
e
s
;
where th
e ne
ces
s
i
t
y
of finding
another r
e
solut
i
o
n
s
y
stem
. In
this
work a new top
o
log
y
of m
u
ltil
e
v
el inv
e
rte
r
is proposed as a
shunt activ
e power filter using two IG
BT transistors in series
of opposite sense meticulously controlled b
y
a
par
a
ll
el con
t
r
o
l algorithm
,
with the con
cep
t
of reduced num
ber of s
i
x s
w
itch
e
s
which are
abl
e
to cr
eat
e
five levels of the output voltag
e
.
This s
y
s
t
em
s
ubs
tute th
e c
l
as
s
i
ca
l s
y
s
t
em
of
eight switch
e
s.
The harmonic
currents id
en
tification is carried
out using the
instantan
e
ous active and r
eactive power
method. The simulation is performed
using Matlab
/
Simulink. Th
e
obtain
e
d
res
u
lt
s
s
how that t
h
e fil
t
erin
g
perform
ances
ar
e
wel
l
enhanc
ed.
Keyword:
Activ
e filter
Fuzzy c
ont
roll
er
Harm
oni
cs
Mu
ltilev
e
l in
v
e
rter
PDP
W
M
c
ont
r
o
l
Copyright ©
201
5 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
:
Zahz
ou
h Z
o
ubi
r,
Depa
rtem
ent de Gé
nie Mecanique
, Fac
u
lté de Technologie,
Uni
v
ersi
t
é
20
Ao
ut
19
5
5
-s
ki
kda
,
B
.
P. 26
,
R
out
e d’El
hadai
e
k,
S
k
i
k
da 21
0
0
0
,
Al
ge
ri
a.
Em
a
il: zzahzouh@yahoo.fr
1.
INTRODUCTION
The us
e of
cont
rol
l
e
d sy
s
t
em
s, especi
al
l
y
t
h
e powe
r
st
at
i
c
conve
rt
ers bas
e
d
o
n
el
ect
ro
ni
c
com
pone
nt
s, l
e
ads t
o
a se
ri
o
u
s
p
r
o
b
l
e
m
of di
s
t
ur
bed
cu
rre
nt
s
i
n
t
e
rm
s of
el
ect
ri
cal
net
w
or
k
s
o
f
di
st
ri
b
u
t
i
o
n.
Th
ese
d
i
stu
r
b
e
d
curren
t
s engen
d
e
r d
a
m
a
g
e
s in
th
e po
wer
q
u
a
lity. Tho
s
e
ex
p
l
ain
t
h
e in
crease of th
e
harm
oni
c rat
e
and
t
h
e
u
nbal
a
nce
of
b
o
t
h
c
u
rre
nt
s an
d
v
o
l
t
a
ges, a
n
d al
s
o
an i
m
port
a
nt
c
ons
um
m
a
ti
on
of t
h
e
reactive powe
r. These ha
rm
onics disturba
nc
es have catas
t
r
op
hi
c co
nse
q
u
e
nces o
n
t
h
e perform
a
nces of all
the
receivers connected to electri
cal netw
orks and the supply
sour
ce. So, it is necessary
to find
a well
adapted
sol
u
t
i
o
n pe
rm
it
t
i
ng t
o
decrea
se t
h
ese di
st
ur
bance
s
at
t
h
e lowest
l
e
vel
.
A
shu
n
t
sy
st
em
of t
h
e di
st
ur
bi
ng l
o
a
d
m
u
st be con
n
e
c
t
e
d i
n
or
der t
o
m
a
ke bot
h t
h
e cur
r
e
n
t
and
t
h
e vol
t
a
ge u
nde
r si
n
u
soi
d
a
l
wavef
o
rm
and t
h
e
powe
r fact
or closer to
unity.
The idea
of the
active powe
r
filter
prese
n
ts a
well ada
p
ted solution to
t
h
ese problem
s
faced in active
po
we
r l
i
n
es
[
1
]
.
It
ha
s
kn
o
w
n a
fast
de
vel
o
pm
ent
si
nce t
h
e arri
val
of
ne
w el
ect
r
oni
c c
o
m
pone
nt
s (
s
wi
t
c
hes)
su
ch
as GTO t
h
yristors, IGC
T
an
d
IGBT tran
sistors [2
].
Activ
e filters can
b
e
stru
ctured
in
p
a
rallel
[3
], in
ser
i
es
[4
],
[
5
] or
h
y
b
r
id
[
6
],
[7]
in
th
e n
e
two
r
k
.
In
vert
e
r
s wi
t
h
t
w
o
or t
h
ree l
e
vel
s
,
have a
re
duce
d
num
ber
of s
w
i
t
c
hes
.
T
h
ey
are al
s
o
us
ed as s
h
u
n
t
active powe
r fi
lters to suppre
ss the ha
rm
onic currents a
n
d
to com
p
ensate
the powe
r fact
or. Howe
ve
r, a
high
swi
t
c
hi
n
g
fre
q
u
ency
i
s
re
qui
r
e
d t
o
achi
e
ve a
p
u
rel
y
si
n
u
s
o
i
d
al
wa
ve
fo
rm
of t
h
e s
u
ppl
y
c
u
r
r
ent
[8]
,
[
9
]
.
As
a
resul
t
,
t
h
e del
a
y
creat
ed du
r
i
ng swi
t
c
he
s t
u
r
n
-
o
n/
o
ff cr
eates p
o
w
er lo
sses, li
m
i
tin
g
th
e robu
stn
e
ss o
f
th
e
D
C
/A
C conver
s
ion
.
Fu
r
t
h
e
r
m
o
r
e, h
i
gh
in
v
e
r
s
e vo
ltage ap
p
lied
to th
e sw
itch
e
s can
d
e
m
o
lish
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Multilevel Active Pow
e
r Filter Using Switc
hes
Meticulously Controlled (Zahzouh Zoubir)
16
9
semico
n
d
u
c
tor ch
aracteristics. Co
nsequ
e
n
tly, a n
e
g
a
tiv
e i
m
p
act o
n
th
e en
erg
y
quality ap
p
ears o
n
th
e
w
a
v
e
fo
r
m
o
f
bo
th
supp
ly vo
ltag
e
an
d cur
r
e
nt.
Mu
ltilev
e
l in
v
e
rters stru
ctures p
e
rm
it
to
redu
ce th
e prob
lem
s
b
y
p
r
odu
cin
g
a
h
a
tch
e
d
ou
tpu
t
vo
ltag
e
com
posed
o
f
m
a
ny
l
e
vel
s
[
10]
-
[
12]
. T
h
e
use
of
t
h
i
s
s
o
r
t
of t
o
p
o
l
o
gy
hel
p
s t
o
l
i
m
it
t
h
e st
ress
i
n
i
nve
rs
e
vol
t
a
ge s
u
pp
o
r
t
e
d by
swi
t
c
h
e
s vi
a di
vi
di
n
g
t
h
e c
ont
i
n
ue
vol
t
a
ge
b
u
s
DC
. Eac
h
swi
t
ch, i
n
l
o
c
k
e
d
st
at
e,
su
ppo
rts a
p
a
rt o
f
t
h
e fu
ll contin
u
e
v
o
ltag
e
DC. Th
e m
u
lti
p
licatio
n
o
f
lev
e
ls p
e
rm
its to
redu
ce the amp
litu
de
of each pa
rt increasing
or dec
r
easin
g the
out
put
voltage.
Th
ese so
rts of
m
u
ltilev
e
l
in
v
e
rters m
u
st o
p
erate with
exact co
n
t
ro
l alg
o
r
ith
m
s
to
tu
rn
on
/off the
po
we
r swi
t
c
he
s i
n
o
p
t
i
m
a
l
t
i
m
e
. The al
g
o
ri
t
h
m
per
m
i
t
s
also t
o
s
u
pp
ress
som
e
hi
gher
or
der
harm
oni
cs, an
d
con
s
eq
ue
nt
l
y
, t
o
im
pro
v
e t
h
e
out
p
u
t
cu
rre
nt
and v
o
l
t
a
ge f
r
eq
ue
ncy
spect
rum
s
[13]
, [
1
4
]
. Nevert
hel
e
ss
, t
h
e
num
ber
o
f
se
m
i
cond
uct
o
rs
can
be
hi
g
h
e
r
;
i
t
req
u
i
r
e
s
a
very
c
o
m
p
l
e
x
cont
rol
l
e
r
t
h
at
en
ge
nde
rs s
w
i
t
c
hi
n
g
losses
of each
switch. This ca
n
have
a
negati
ve im
pact on the
robustness
of the m
u
ltilevel inve
rter.
Seve
ral
t
echni
que
s are
use
d
t
o
det
ect
di
st
u
r
ba
nces i
n
t
h
e
el
ect
ri
cal
net
w
o
r
k
s
. F
r
e
que
ncy
det
ect
i
o
n
techniques a
r
e carried
out by the Discrete Fourier T
r
a
n
sf
or
m
(DFT)
whi
c
h can
be us
e
d
to analyze the voltage
o
r
cur
r
e
n
t
no
n-
sinu
so
i
d
al sign
als.
Fast Fo
ur
ier Trans
f
o
r
m
(FFT
) an
d Dis
c
rete Recursiv
e (TFDR
)
[1
5]
, [1
6]
rep
r
ese
n
t
wel
l
effi
ci
ent
com
put
at
i
onal
m
e
t
h
ods
. H
o
weve
r,
t
h
e di
rect
ap
p
l
i
cat
i
on of t
h
e
s
e
m
e
t
hods
req
u
i
r
es
a
sig
n
i
fican
t
com
p
u
t
atio
n
ti
me wh
ich
d
e
lays th
e filte
r
co
n
t
ro
l respo
n
se. Nev
e
rth
e
less, th
ere are o
t
h
e
r
tech
n
i
qu
es, su
ch
as No
tch
filter [17
]
. Th
e
Artificial Neu
r
on
Netwo
r
k
(ANN) techn
i
qu
e has b
een
d
e
v
e
l
o
p
e
d
t
o
t
h
e o
p
t
i
m
al
i
d
ent
i
f
i
cat
i
on
of
t
h
e ha
rm
oni
c si
gnal
s
[
1
8]
, [
1
9]
an
d t
h
e i
n
st
ant
a
ne
ou
s p
o
w
er m
e
t
hod [
2
0
]
,[2
1
]
wh
ich
is t
h
e con
s
tan
tly u
s
ed
on
e.
Cu
rren
t stud
ies are fo
cu
sed
o
n
th
e
d
e
termin
atio
n
of
a ro
bu
st con
t
ro
l strateg
y
for d
i
fferen
t
filter
t
o
p
o
l
o
gi
es, s
u
c
h
as sl
i
d
i
n
g m
ode t
e
c
hni
que
[2
2]
. P
u
l
s
e
W
i
dt
h M
o
d
u
l
a
t
i
o
n (P
WM
) c
o
nt
rol
t
ech
ni
q
u
e a
ppl
i
e
d
for m
u
lt
i–
lev
e
l an
d
th
e Fu
zzy co
n
t
ro
ller [2
3], [2
4
]
are ab
le
to create the logic sign
als which are se
nt to the
electronic c
o
m
p
one
n
ts. Hyste
r
esis [25]
or three-dim
e
nsional space vector
m
odulation [26] can also
be
use
d
to
cont
rol t
h
e inverters.
In
t
h
i
s
pape
r,
a
ne
w t
o
p
o
l
o
gy
of
fi
ve
-l
evel
i
n
vert
er
u
s
i
n
g t
w
o
IGB
T
t
r
an
si
st
ors i
n
se
ri
es
o
f
op
p
o
si
t
e
sen
s
e m
e
ticu
l
o
u
s
ly con
t
ro
lled
b
y
a
p
a
rallel co
n
t
ro
l al
g
o
rith
m
,
is proposed
as a shu
n
t
activ
e
p
o
w
e
r filter
(SA
P
F
)
. Thi
s
t
o
p
o
l
o
gy
has a
sm
al
l
nu
m
b
er of
po
wer s
w
i
t
c
hes (si
x
IGB
T
t
r
ansi
st
o
r
s + zero Di
o
d
es f
o
r n
e
ut
ral
poi
nt
cl
am
ped)
abl
e
t
o
genera
t
e
fi
ve l
e
vel
s
of out
put
v
o
l
t
a
g
e
. C
l
assi
cal syst
em
s of t
h
e NPC
i
nvert
er
re
qui
re
ei
ght
po
we
r s
w
i
t
c
hes (ei
g
ht
I
G
B
T
t
r
a
n
si
st
o
r
s + zer
o
Di
o
d
e
s
f
o
r
ne
ut
ral
po
i
n
t
cl
am
ped).
I
t
can
im
p
r
ov
e th
e f
ilter
i
ng
per
f
o
r
m
a
n
ces an
d
an
sw
er b
e
tt
er
to
th
e ind
u
s
t
r
ial r
e
qu
ir
em
e
n
ts [2
7
]-[3
0
]
.
It can
also
m
i
n
i
mize th
e p
o
wer l
o
sses in
t
h
e inv
e
rter b
y
a redu
ced
nu
mb
er
o
f
switch
i
n
g
pu
lses. Th
i
s
filter
p
e
rm
its to
m
a
i
n
tain
th
e switch
ch
aracteristics b
y
redu
ci
n
g
t
h
e i
n
ve
rse
vol
t
a
ge a
ppl
i
e
d t
o
sem
i
cond
uct
o
r
s
.
The ide
n
tification
of t
h
ese
harm
onic curre
n
ts is
m
a
d
e
with
th
e in
stan
tan
e
ou
s activ
e
an
d
reactiv
e
powe
r m
e
thod. These techniques m
a
ke
th
e su
pp
ly cu
rren
t un
d
e
r th
e sinu
soid
al wav
e
form
with
a po
wer facto
r
clo
s
er t
o
un
ity. Th
e con
t
ro
l o
f
t
h
e filter switch
e
s
is m
a
d
e
b
y
a
PDPWM (p
h
a
se d
i
sp
ositio
n
Pu
lse
W
i
d
t
h
Mo
du
latio
n) op
erating
with
fo
ur triangu
lar
carriers
of low switch
i
ng
fr
e
q
uency
e
qual
t
o
50
0
0
Hz i
n
t
h
e fi
rst
ti
m
e
an
d
equ
a
l
to
15
000
Hz in
th
e
seco
nd
Ti
m
e
in
order
to
eli
m
in
ate th
e rip
p
l
es app
e
aring
o
n
th
e cu
rren
t
wave
f
o
rm
(hi
g
h f
r
e
que
ncy
di
st
ort
i
o
ns)
.
We
are al
so
, i
n
t
e
re
st
ed t
o
re
gul
at
e t
h
e i
n
ject
e
d
cur
r
ent
by
usi
n
g
t
h
e
fuzzy
-c
o
n
t
r
ol
l
e
r t
ech
ni
q
u
e.
T
h
e n
u
m
e
ri
cal
sim
u
l
a
t
i
on i
s
de
vel
o
ped
a
n
d
pe
rf
orm
e
d by
usi
n
g
M
a
t
l
a
b/
Si
m
u
l
i
n
k
.
Th
e
o
b
t
ained
resu
lts show
th
at th
e pr
opo
sed
5
L
-SAPF
with
two
switch
e
s i
n
series of
o
ppo
site sen
s
e
im
p
r
ov
es
th
e filtering
p
e
rfo
r
m
a
n
ces. Th
is im
p
r
o
v
e
m
e
n
t
in
t
h
e first o
r
i
n
th
e secon
d
ti
m
e
(5
000&15
000
H
z
) sh
ow
s
a
redu
ction
of the to
tal h
a
rm
o
n
ic d
i
sto
r
tion
s
o
f
t
h
e cu
r
r
ents
(T
HD<
5%
) c
o
n
f
orm
to
th
e
p
e
rm
issib
l
e li
mits in
accorda
n
ce to
IEEE
norm
s [31]. T
h
e
propos
ed system
m
a
de the s
u
pply c
u
rrent
under
a
sinus
oidal
wa
veform
and i
n
p
h
ase
wi
t
h
t
h
e su
ppl
y
vol
t
a
ge. F
u
r
t
herm
ore, t
h
e t
h
ree p
h
ase v
o
l
t
a
ges ha
ve t
h
e sam
e
am
pli
t
udes
,
si
nus
oi
dal
wa
v
e
fo
rm
s
and p
h
a
ses
bal
a
nce.
2.
SYSTE
M
P
R
OCESSE
D
DESCRIPTIO
N
Fig
u
re 1
shows th
e n
e
w top
o
lo
g
y
o
f
th
e m
u
ltilev
e
l
in
v
e
rter co
nn
ected
to
th
e th
ree-p
h
a
se electrical
network. It is c
o
m
posed of thr
ee identical structures
whic
h
ope
rate
inde
pe
nde
ntly at each phase.
In a single pha
se each structur
e is com
posed of two capac
ities
C
1
and
C
2
and si
x bi
pol
a
r
swi
t
c
he
s
Sw
1
,
Sw
2
,
Sw
3, Sw
4, Sw
5
an
d
Sw
6
(Figu
r
e 2
)
. Th
e two
first are m
e
tic
u
l
ously control
l
ed, connecte
d
in anti-
seri
es bet
w
ee
n
t
h
e poi
nt
s
O
(center of the
C
1
and
C
2
) and
n
(n
eu
tral). They g
e
n
e
rate th
e v
o
ltag
e
lev
e
ls
V
dc
/2
,
0, -V
dc
/2
and e
n
sure t
h
e
bidi
rectional for t
h
e curre
nt a
n
d
t
h
e
voltage ac
ross t
h
e
ground and t
h
e m
i
ddle of t
h
e
DC
bus
. To g
e
nerat
e
t
h
e 5 l
e
vel
s
of t
h
e o
u
t
p
ut
vol
t
a
ge
-V
dc
, -V
dc
/2
, 0
,
+V
dc
/2
, +V
dc
,
we have ch
os
en t
o
dispose two capacitors (
C
1
, C
2
), that ensure a continuous supply of
the DC bus, each
one has an a
m
plitude
equal
t
o
V
dc
/2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
16
8
–
17
7
17
0
Fi
gu
re
1.
Ne
w
5L-
S
A
PF l
i
n
ke
d at
t
h
e
el
ect
ri
cal
net
w
or
k
Fi
gu
re
2.
M
o
di
fi
ed m
odel
f
o
r
a si
n
g
l
e
p
h
ase
The st
at
es of
ope
ni
n
g
an
d cl
osi
n
g f
o
r al
l
SAPF s
w
i
t
c
hes
of t
h
i
s
ne
w t
o
pol
ogy
are s
u
m
m
a
ri
zed i
n
Tabl
e 1.
Tab
l
e 1
.
Sw
itch
i
ng
tab
l
e fo
r
pr
opo
sed
system
Sw1
Sw2
Sw3
Sw4
Sw5=Sw
6
van
1 0
0 1
0
V
dc
1 0
0 0
1
V
dc
/2
1 0
1 0
0
0
0 1
0 0
1
-V
dc
/2
0 1
1 0
0
-V
dc
3.
INST
ANT
AN
EOUS
A
C
TI
VE A
N
D
RE
ACTI
V
E P
O
WER I
D
ENT
I
FIC
A
TIO
N
METHO
D
The t
h
ree
phas
e voltages a
n
d
curr
en
ts v
a
l
u
es in
stan
tan
e
ou
s
in
α
-
β
s
p
ace ca
n
be e
x
presse
d
by:
∝
√
√
√
1
0
√
√
(1)
∝
√
√
√
1
0
√
√
(2)
The i
n
stanta
ne
ous
active a
n
d
reactive
powe
rs in t
h
is s
p
ace
are calculated
by:
∝
∝
∝
̅
(3)
From
t
h
e e
x
p
r
e
ssi
on
(
3
)
,
we
h
a
ve:
∝
∝
∝
̅
(4)
To e
x
tract t
h
e refere
nce c
u
rre
n
ts e
x
pression
in
fun
c
tio
n of i
n
stan
tan
e
ou
s
po
wer i
n
th
e
α
-
β
sp
ace, th
is is giv
e
n
by
:
∝
∝
∝
̅
0
∝
∝
0
∝
∝
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Multilevel Active Pow
e
r Filter Using Switc
hes
Meticulously Controlled (Zahzouh Zoubir)
17
1
To
c
o
m
p
ensat
e
t
h
e react
i
v
e po
wer
an
d harm
oni
c
cu
rre
nt
s ge
nerat
e
d by
t
h
e no
nl
i
n
ea
r
l
o
a
d
sim
u
l
t
a
neousl
y
,
t
h
e
refe
rence
cu
rre
nts m
u
st includ
e
,
as
fo
llowings:
∝
∝
∝
0
∝
∝
∝
∝
(6)
The
refe
rence
currents
in t
h
e
a-b-c s
p
ace a
r
e
give
n
by:
10
√
√
∝
(7)
Th
e m
o
d
e
l
o
f
th
e instan
tan
e
ou
s
p
o
wers m
e
t
h
od
h
a
s b
e
en
i
m
p
l
e
m
en
ted
in Matlab
/ Sim
u
lin
k
to ex
t
r
act th
e
refe
rence
cu
rre
nt
s
of t
h
e E
q
ua
t
i
on
(7
) s
h
ow
n
i
n
Fi
g
u
r
e
3.
Fig
u
re
3
.
Al
g
o
rith
m
fo
r ex
tractio
n
o
f
referen
ce cu
rren
ts in
Matlab
/
si
m
u
lin
k
4.
CO
NTR
O
L S
T
RATEG
Y
The injecte
d
harm
onic curre
n
t by the SAPF
is obtai
n
e
d
t
h
ro
ugh
th
e con
t
ro
l of IGBT switch
e
s. Th
is
i
s
achi
e
ve
d by
t
h
e p
h
ase
di
sp
osi
t
i
on
p
u
l
s
e w
i
dt
h m
odul
at
i
o
n (
P
DP
WM
)
,
t
h
i
s
t
ech
ni
q
u
e i
s
m
a
i
n
l
y
based
on t
h
e
com
p
arison be
tween t
h
e
refe
rence c
u
rrent
signal
(
I
ref
) a
n
d the
four ide
n
tical triangular
ca
rriers
(
U
p1
, U
p2
, U
p3
,
U
p4
) as
s
h
o
w
n
i
n
Fi
g
u
r
e
4.
Th
i
s
o
n
e se
n
d
s
6
l
ogi
cal
si
g
n
al
s
sim
u
l
t
a
neousl
y
, 0
o
r
1
f
o
r
eac
h
one;
t
r
an
sm
ited t
o
th
e switch
e
s
(
Sw1
,
Sw
2
,
Sw
3
,
Sw
4
,
Sw
5
,
and
S
w
6
).
The two ca
rrie
r
s
U
p1
an
d
U
p2
allo
w
g
e
neratin
g th
e lev
e
ls
V
dc
and
V
dc
/2
resp
ectiv
ely. B
y
sy
mmetry,
th
e lev
e
ls
–V
dc
/2
and
-V
dc
are
created by the carriers
U
p3
and
U
p4
resp
ectiv
ely. Th
e level
V
dc
=0
is ob
tain
ed
whe
n
t
h
e
refe
rence si
gnal is
located
betwee
n the
carriers
U
p2
and
U
p3.
0.
002
0.
004
0
.
006
0.
008
0.
01
0.
012
0.
014
0
.
016
0.
018
0.
02
-2
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
Fig
u
re
4
.
Ph
ase Disp
o
s
ition
PWM
with
four id
en
tical Trian
g
u
l
ar Carriers
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
16
8
–
17
7
17
2
Th
e sim
u
latio
n
m
o
d
e
l ex
p
l
ain
s
in d
e
tail th
e co
n
t
ro
l
of t
h
e switch
e
s
(Fig
ure
5
)
, th
e new
p
a
rallel
alg
o
rith
m
mak
e
s si
m
u
ltan
e
ously th
e co
m
p
arison
b
e
t
w
een
I
ref
wi
t
h
4 car
r
i
ers, a
nd t
h
i
s
m
e
t
hod ca
n
q
u
i
c
kl
y
gene
rat
e
t
h
e
si
gnal
s
sent
t
o
t
h
e swi
t
c
hes
o
f
t
h
e
pr
o
pose
d
m
odel
at
t
h
e
ri
g
h
t
t
i
m
e
.
5
lev
e
ls of the SAPF
o
u
t
pu
t v
o
ltag
e
(
V
an
) resp
ect
5
co
nd
itio
ns p
e
rfo
r
m
e
d
si
m
u
lta
n
e
ou
sly (in
p
a
rallel) as fo
llo
ws:
a.
If Iref
≥
U
p1
, S
w
1=
1, Sw
2=
0,
Sw
3=
0, Sw
4=
1, Sw
5=
0, Sw
6
=
0
&
v
an
=v
dc
.
b.
If U
p1
> I
r
ef
≥
U
p2
, Sw
1=
1,
Sw
2=
0,
Sw
3=
0,
S
w
4=
0,
Sw
5=
1,
Sw
6=
1
&
v
an
=v
dc
/2
.
c.
If U
p2
> I
r
ef
≥
U
p3
, Sw
1=
1,
Sw
2=
0,
Sw
3=
1,
S
w
4=
0,
Sw
5=
0,
Sw
6=
0
&
v
an
=0
.
d.
If U
p3
> I
r
ef
≥
U
p4
, Sw
1=
0,
Sw
2=
1,
Sw
3=
0,
S
w
4=
0,
Sw
5=
1,
Sw
6=
1
&
v
an
=-v
dc
/2
.
e.
If U
p4
>
I
ref
,
Sw
1=
0,
Sw
2=
1,
S
w
3=
1,
Sw
4=
0,
Sw
5=
0,
Sw
6=
0
&
v
an
=v
dc
.
5.
F
U
ZZY
-
CONTROLLER APPLICATION
To i
n
ject
an
o
p
t
im
al
harm
oni
c
cu
rre
nt
by
t
h
e
p
r
o
p
o
sed
m
o
d
e
l
,
t
h
e
fuz
z
y
l
o
gi
c c
ont
r
o
l
l
e
r
was c
h
osen
to
regu
late the switch
e
s con
t
ro
l sig
n
a
ls t
h
rou
g
h
th
e
p
a
rallel co
n
t
ro
l alg
o
rith
m
.
In
th
is work
, a
m
o
d
e
l
established in
Matlab/Sim
u
link is s
h
own i
n
Figure
6.
T
h
e
operation
he
re
consists to re
place the
class
i
cal PI
regu
lato
r b
y
a
fu
zzy co
n
t
ro
ller. Th
is techn
i
qu
e allows
c
o
rrecting the
error bet
w
een the
refere
nce c
u
rre
n
t (
I
ref
)
and the i
n
jecte
d
one
(
I
inj
).
Th
e err
o
r a
n
d
i
t
s
deri
vat
i
v
e a
r
e
defi
ned
by
t
h
re
e su
b-set
s
:
n
e
gativ
e
N
, zero
ZE
and
p
o
s
itiv
e
P
,
k
nowing
th
at th
e
me
m
b
ersh
ip
fun
c
tio
ns are
Gau
ssian
typ
e
. Th
e ou
tpu
t
signal
C
de
depe
nds
on t
h
e
i
n
p
u
t
st
at
es de
fi
ne
d by
fi
ve
s
u
b
-
set
s
, l
a
rge
negat
i
v
e
LN
, neg
a
tiv
e
N
, zero
ZE, po
sitiv
e
P
and
larg
e
po
sitiv
e
LP
. In t
h
is case, the m
e
mbers
h
ip
fu
n
c
ti
o
n
s
are triang
u
l
ar typ
e
. Fu
zzy con
t
ro
ller shou
ld
fo
llow the
fuzzification st
eps that
use t
h
e "minim
u
m
"
ope
rato
r, a
n
d the in
fere
nce
m
ech
anism
that contains
five
rules
.
Fin
a
lly b
y
th
e
h
e
lp
of th
e d
e
fu
zzificatio
n of th
e
fu
zzy
ou
tpu
t
, th
e
b
a
rycentric m
e
th
o
d
is
ap
p
lied. Fu
zzy
ru
les
are base
d o
n
t
h
e err
o
r va
ri
a
t
i
on sense (
e
),
t
h
e al
gebrai
c
si
gn, as wel
l
as i
t
s
deri
vat
i
ve "
de/
d
t
". So, the
cont
roller
C
de,
will b
e
g
i
v
e
n
acco
rd
ing
t
o
th
e fo
llo
wi
n
g
state con
d
ition
s
:
1.
If
e
is
ZE
th
en
C
de
is
ZE
2.
If
e
is
P
, th
en
C
de
is
LP
3.
If
e
is
N
, t
h
en
C
de
is
LN
4.
If
e
is
ZE
and "
de/
d
t
" is
P
, the
n
C
de
is
N
5.
If
e
is
ZE
and "
de/
d
t
" is
N
, then
C
de
is
P
After ha
ving the
correcte
d
signal
(
C
de
) at th
e b
l
o
c
ou
t
p
u
t
o
f
t
h
e fuzzy co
n
t
ro
ller, it will b
e
in
tersected
with
th
e
four trian
g
u
l
ar carriers to
g
e
n
e
rate lo
g
i
c sign
als sen
t
to
th
e
IGBT switch
e
s
o
f
t
h
e
pr
o
pose
d
m
ode
l
.
5
Sw
5
4
Sw
4
3
Sw
3
2
Sw
2
1
Sw
1
Up
4
Up
3
Up
2
Up
1
Su
m
o
f
El
e
m
e
n
t
s
<
>=
Re
la
tio
n
a
l
Oper
ator6
<
Re
la
tio
n
a
l
Oper
ator5
>=
Re
la
tio
n
a
l
Oper
ator4
<
Re
la
tio
n
a
l
Oper
ator3
>=
Re
la
tio
n
a
l
Oper
ator2
>=
Re
la
tio
n
a
l
Oper
ator11
<
Re
la
tio
n
a
l
Oper
ator1
P
r
oduct
4
P
r
oduct3
P
r
oduct2
P
r
oduct1
P
r
oduct
AND
Lo
gi
cal
Ope
r
ator
2
AND
Lo
gi
cal
Ope
r
ator
1
AND
Lo
gi
cal
Op
erator
(1
0
1
0
0)
F6
(1
0
0
1
0)
F5
(0
1
1
0
0)
F4
(0
1
0
0
1)
F2
(1
0
0
0
1)
F1
1
I
ref
6
Sw
6
Fi
gu
re 5.
Lo
gi
cal
si
gnal
s
o
f
p
a
ral
l
e
l
cont
rol
alg
o
rith
m
Fi
gu
re
6.
Sc
he
m
e
bl
oc
of
f
u
z
z
y
cont
rol
l
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Multilevel Active Pow
e
r Filter Using Switc
hes
Meticulously Controlled (Zahzouh Zoubir)
17
3
6.
S
I
ZI
N
G
O
F
TH
E
DC
BU
S
C
A
P
AC
I
T
ORS
An app
r
o
a
ch
has b
e
en
p
r
op
osed
i
n
th
e literatu
re
[32
]
, t
o
size cap
acito
rs
th
at feed
th
e activ
e filter.
Th
e transien
t variatio
n
s
in
th
e in
stan
tan
e
o
u
s
p
o
wer ab
so
rb
ed
b
y
th
e lo
ad
en
g
e
nd
er fl
u
c
tuatio
n
s
in
vo
ltag
e
V
dc
acros
s the
capacitors.
The
a
m
plitude of t
h
ese fluct
u
ati
o
n
s
can
be
co
nt
r
o
l
l
e
d
by
a
ju
d
i
ci
ous c
h
oi
ce
of t
h
e
equi
val
e
nt
ca
p
aci
t
y
val
u
e
C
whi
c
h i
s
ex
press
e
d
by
1
2
.
.
.
⁄
.
I
FA
is th
e m
a
x
i
m
u
m
a
m
plitude of t
h
e injected current.
Δ
V
dc
is the flu
c
t
u
atio
n eq
u
a
l t
o
5
%
o
f
Vd
c.
f
s
is th
e
switch
i
ng
freq
u
en
cy of
the carriers
(
ω
s
= 2.
π
.
f
s
). In t
h
is case,
I
FA
=
40 A
w
ith
I
FA
(presen
t
ed in
th
e
resu
lts)
,
V
dc
= 10
00
V
,
Δ
V
dc
= 5
%
.
V
dc
,
f
s
= 15 kHz,
C
will
eq
u
a
l
to
32.
42
; th
en
:
C
1
= C
2
=
2
.
C =
64.84
,Because
C
1
an
d
C
2
are
connected
in
series.
7.
DC VOLTAGE REGULAT
I
ON
OF T
H
E
ACTIVE FIL
TER
Reg
u
l
ating
th
e DC bu
s
vo
ltag
e
of th
e propo
sed
system
ca
n
b
e
im
p
r
o
v
e
d b
y
adju
stin
g th
e sm
all rate
of act
i
v
e p
o
w
e
r
i
n
ca
paci
t
o
rs.
Th
us, i
t
c
o
m
p
ensat
e
s t
h
e
l
o
s
s
es by
c
o
n
d
u
ct
i
on a
n
d s
w
i
t
c
h
i
ng
[3
3]
,
[3
4]
.
The
regu
latio
n loo
p
o
f
th
e
vo
ltag
e
is d
e
si
g
n
a
ted
t
o
b
e
sm
a
ller th
an
th
e curren
t
lo
op
. Th
e
reg
u
latio
n
circu
it of th
e
DC vo
ltag
e
mu
st b
e
fast an
d th
at an
swer on
ly for th
e steady state conditions
. Tra
n
si
en
t
v
a
riatio
ns in
th
e DC
v
o
ltag
e
are not p
e
rm
itted
an
d
are tak
e
n
into
con
s
ider
atio
n wh
en
selectin
g
th
e app
r
op
riate
v
a
lu
e
of the
capaci
t
o
r
.
F
r
o
m
t
h
e st
eady
st
at
e, t
h
e f
u
nda
m
e
nt
al
com
ponent
i
s
n
o
t
i
n
cl
ude
d i
n
t
h
e
re
f
e
rence
cu
rre
nt
.
Fo
r t
h
at
,
a regu
lato
r
o
f
a lo
w-p
a
ss
first o
r
d
e
r filter is requ
ired
to
main
tain
DC vo
l
t
ag
e (
V
dc
) closer to
th
e
DC vo
ltag
e
refe
rence
(
V
dc
-r
ef
), th
e tran
sfer
fun
c
tion
can
be written
as
fo
l
l
o
w
ing
:
.
(8)
Wi
t
h
:
K
c
,
τ
c
gain
an
d ti
m
e
co
nstan
t
of th
e low
p
a
ss
filter
Th
e regu
lation
lo
op
o
f
th
e
DC
vo
ltag
e
is exp
r
essed
b
y
th
e follo
wing
tran
sfer fun
c
tio
n
:
.
.
.
.
.
(9)
8.
MODEL AND SIMULA
TION PARAME
TERS
Fo
r t
h
is sim
u
la
tio
n
,
a three phase d
i
od
e bridge rectifie
r with RL lo
ad
is u
s
ed
as th
e
n
o
n
linear lo
ad
i
n
th
is work
. Table 2
su
mm
ariz
es th
e sim
u
lat
i
o
n
p
a
ram
e
ters. Th
e stud
y is d
o
n
e
o
n
l
y in
t
h
e ph
ase
a
, kn
owi
n
g
that the two ot
her phases
(
b
an
d
c)
are d
e
lay
e
d
resp
ectively b
y
1
2
0
°
and
24
0°
relativ
ely to
th
e ph
ase
a
.
Tabl
e 2.
Sim
u
lation Pa
ram
e
ters
Variable
Values
Sour
ce voltage ,
in
ductance line,
fr
equency
V
s
=220 V
,
L
s
=3 .10
-4
H , F=50 Hz
Non-
linear
load (
G
r
aëtz br
idge 6
diodes + r
e
sistance + inductance)
R=4
Ω
,
L=0.
001H
Capacitors voltage of
m
u
ltilevel
inverter
C
1
= C
2
= 64,
84 .
1
0
-6
F
Refer
e
nce Continu
ous supply
DC bus
V
dc-r
e
f
/2= 500 V
Inductance at output of the active filter
L
f
=1
,2
. 1
0
-3
H
9.
RESULTS
A
N
D
DI
SC
US
S
I
ON
9.
1.
Before Filtering
F
i
g
u
r
e
7
sh
ow
s th
e
su
pp
ly vo
lta
g
e
with th
e so
urce cu
rren
t an
d its h
a
rm
oni
c cur
r
e
n
t
s
s
p
ec
t
r
um
befo
re
filterin
g
.
Fig
u
re
7
.
Su
pply cu
rren
t
an
d
v
o
ltag
e
wav
e
form
s
an
d
its
h
a
rm
o
n
i
c cu
rren
t
s sp
ectru
m
b
e
fore filtering
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
16
8
–
17
7
17
4
Th
e sup
p
l
y cu
rren
t
ob
tain
ed
b
e
fo
re filterin
g
is co
m
p
letely d
i
sto
r
ted
an
d its current Harm
o
n
i
c
Di
st
ort
i
o
n (
THD
) is
23
.45
%.
Th
is
v
a
lu
e is h
i
g
h
e
r t
h
an th
e i
n
tern
atio
n
a
l
stan
d
a
rd
(
THD
<
5
%).
9.
2.
After Filtering
Th
e sim
u
latio
n was m
a
d
e
for
two
d
i
fferen
t freq
u
e
n
c
ies
o
f
the triang
u
l
ar carriers
9.
2.
1.
Results
f
o
r
f
s
=1
00
.f
SAP
F
usi
n
g
two
Transistors in
series
Cla
m
p
e
d
in
to Fiv
e
-lev
el In
v
e
rter is si
m
u
la
ted
in
M
A
TLAB
/
S
I
M
U
LI
NK a
n
d
t
h
e o
u
t
p
ut
v
o
l
t
a
ge wa
ve
fo
rm
obt
ai
ne
d
bet
w
een t
h
e
ne
ut
ral
‘‘
n’
’
an
d t
h
e
pha
se
‘‘
a’
’
is show
n
in
Figur
e
8
.
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
12
-500
0
500
Ti
m
e
(
s
)
.
Fi
gu
re
8.
O
u
t
p
ut
v
o
l
t
a
ge
wa
v
e
fo
rm
Van
Fi
gu
re
9.
Active filter cu
rren
t
with
low
switch
i
ng
fre
que
ncy
Th
e filter inj
e
cted
cu
rren
t; th
e su
pp
ly cu
rren
t sin
u
so
i
d
al wav
e
fo
rm
an
d
its
THD
e
qual
t
o
4.
4
1
% are
sho
w
n i
n
Fi
gu
r
e
9 a
n
d Fi
gu
re
10
.
Figure 10.
Supp
ly curren
t
and its h
a
rm
o
n
i
c sp
ectru
m
after filterin
g
with
low switch
i
ng
freq
u
e
n
c
y
(5KHz)
9.
2.
2.
Results
f
o
r
fs
=30
0
.
f
After sim
u
lati
o
n
, with
th
is
hig
h
carrier freq
u
e
n
c
y (1
5
KHz), th
e filter in
j
ected
current; sin
u
s
o
i
d
a
l
wave
f
o
rm
of t
h
e su
p
p
l
y
cur
r
e
nt
an
d i
t
s
THD
eq
ual
t
o
2.
1
9
% are s
h
ow
n
i
n
Fi
g
u
re
11
and
Fi
g
u
re
12
.
These
Fig
u
res show th
at th
e filtering
p
e
rfo
rm
an
ces o
f
th
e pr
opo
sed
syste
m
are i
m
p
r
o
v
e
d
with
a p
o
wer fact
o
r
clo
s
er
to
un
ity (
F
i
g
ure 13
).
Fig
u
re 11
. Activ
e filter
current
with
h
i
gh
swi
t
ch
in
g
frequ
e
ncy
0
0.
0
2
0.
04
0.
0
6
0.
08
0.
1
0.
12
-5
0
0
50
Ti
m
e
(
s
)
Ii
n
j
(
A
)
0
0.
0
2
0.
0
4
0.
06
0.
08
0.
1
0.
12
0.
14
0.
16
0.
18
0.
2
-1
0
0
-5
0
0
50
10
0
Ti
m
e
(
s
)
Vs
(
V
)
0
50
100
150
200
250
300
0
1
2
3
H
a
r
m
oni
c
o
r
de
r
F
undam
ent
al
(
5
0
H
z
)
=
105.
2 ,
T
H
D
=
4.
41%
M
a
g
(
%
o
f
F
u
n
d
am
e
n
t
a
l
)
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
0.
1
0.
1
2
-5
0
0
50
Ti
m
e
(
s
)
Iin
j
(A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A New Multilevel Active Pow
e
r Filter Using Switc
hes
Meticulously Controlled (Zahzouh Zoubir)
17
5
Fig
u
re
12
.
Supp
ly curren
t
and its h
a
rm
o
n
i
c sp
ectru
m
after filterin
g
with
h
i
g
h
switch
i
ng
freq
u
e
n
c
y
(15KHz)
At th
e stead
y
state, Fig
u
re
1
4
illu
strates th
e
su
pp
ly curren
t
s wh
ich
h
a
v
e
sin
u
s
o
i
d
a
l
wav
e
form
s with
bal
a
nce
d
ph
ase
s
a,
b a
n
d c.
F
u
rt
herm
ore,
t
h
e
wave
f
o
rm
s h
a
ve th
e sam
e
a
m
p
litu
d
e
s with th
e sam
e
freq
u
e
n
c
ies.
Ti
m
e
(
s
)
Vs(
V
)
200
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
12
‐
200
‐
10
0
0
100
ph
a
s
e
c
ph
a
s
e
b
Ph
as
e
a
Figu
re 1
3
. Po
w
e
r
fact
or
Fig
u
r
e
14
. 3
-
ph
ase w
a
v
e
fo
r
m
s
of
th
e
su
pp
ly cu
rr
en
ts
after filterin
g
Du
ri
n
g
t
h
e ap
pl
i
cat
i
on
of
t
h
e m
odul
at
or
P
D
P
W
M
,
t
h
e
s
w
i
t
c
hi
n
g
fre
qu
ency
i
s
i
m
posed
by
t
h
e
triangular
carriers.
Indee
d
, the sum
of t
h
e s
w
itching
fre
quencies of
t
h
e four
s
w
itch
e
s SW
1,
SW
2,
SW
3
,
SW
4
is equ
a
l to th
e
carrier frequ
e
ncy 1
5
k
H
z. Fi
gu
re 15
an
d
Figu
re 16
illu
st
rate clearly th
e co
m
p
le
m
e
n
t
ariti
es of
th
e switch
e
s: Sw2
=
1
-
Sw1
and Sw4
=
1
-
Sw3
;
th
ese two
con
d
i
tio
n
s
p
r
o
t
ect the filterin
g
syste
m
ag
ain
s
t th
e
sh
ort
circu
it.
Fig
u
r
e
15
.
Sw
i
t
ch
pu
lses
of
the Sw1
a
n
d
Sw
2
Fig
u
r
e
16
.
Sw
i
t
ch
pu
lses
of
the Sw3
a
n
d
Sw
4
10
.
Co
nclusion
I
n
t
h
is
w
o
rk
,
a n
e
w
topo
logy o
f
f
i
v
e
-
l
ev
el
in
v
e
r
t
er
w
ith
tw
o
I
G
B
T
tr
an
sistor
s link
e
d in
ser
i
es
of
o
ppo
site sen
s
e, m
e
ticu
l
o
u
s
ly con
t
ro
lled
b
y
a
p
a
rallel con
t
ro
l algo
rithm
l
i
m
its th
e harm
o
n
i
c curren
t
s an
d
ens
u
res t
h
e robust
n
ess
of t
h
e conve
r
ter in the elect
ri
cal
di
st
ri
b
u
t
i
on
net
w
or
k. T
h
e
sy
st
em
m
odel
was
i
m
p
l
e
m
en
ted
in
Matlab
/
Sim
u
lin
k
and
th
e si
m
u
la
tio
n
s
are
c
a
rried
o
u
t. Th
e
results ar
e sati
sfactory and conform
to the pe
rm
issible lim
its
in accord
a
n
ce to IE
EE norm
s. The harm
onic cu
rre
nts ide
n
tification wa
s conducte
d
by
t
h
e i
n
st
ant
a
neo
u
s act
i
v
e a
nd
react
i
v
e
po
wer m
e
t
hod as
a fi
rst
st
ep. T
h
e sy
st
em
i
s
cont
rol
l
e
d
by
P
D
P
W
M
ope
rat
i
n
g wi
t
h
fo
ur t
r
i
a
ng
ul
a
r
carri
e
r
s o
f
s
w
i
t
c
hi
n
g
f
r
eq
u
e
ncy
eq
ual
t
o
50
0
0
Hz
. O
n
t
h
e ot
her
han
d
we are
in
terested
on
t
h
e
regu
latio
n
o
f
th
e i
n
j
ected curren
t
b
y
u
s
i
n
g th
e
fu
zzy-co
n
t
ro
ller m
e
th
o
d
. Th
e
resu
lts sho
w
th
at th
e proposed
filter en
h
a
n
ces th
e
filterin
g
p
e
rform
a
n
ces. It also
i
m
p
r
o
v
e
s th
e en
erg
y
qu
ality w
ith
a
reduction
of s
w
itching
pulses. T
h
e i
n
creas
e of t
h
e s
w
itch
i
ng
f
r
e
qu
en
cy u
p
to
1
500
0 H
z
eli
m
in
ates so
m
e
ripples appeari
ng
on t
h
e supply current wa
veform
. A si
gn
ifican
t redu
ctio
n
in
th
e to
tal h
a
rm
o
n
i
c d
i
sto
r
tion
0
0.
02
0.
04
0.
06
0.
08
0.
1
-10
0
-5
0
0
50
10
0
Ti
m
e
(
s
)
Vs
(
V
)
0
50
100
150
20
0
25
0
30
0
0
0.
5
1
H
a
r
m
oni
c
or
d
e
r
F
u
n
d
a
m
e
n
t
al
(
50H
z
)
=
105.
2 ,
T
H
D
=
2.
19
%
M
a
g (
%
of
Fu
nda
m
e
n
t
a
l
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 6
,
No
. 1
,
Mar
c
h
2
015
:
16
8
–
17
7
17
6
rate (
THD
)
i
s
o
b
ser
v
e
d
a
n
d cal
cul
a
t
e
d t
h
r
o
ug
h
FFT
anal
y
s
i
s
t
ool
i
n
M
A
T
L
AB
/
S
IM
UL
I
N
K
.
G
ood
com
p
ensation
of the
reactive
power i
n
the
electrical di
strib
u
tion
n
e
two
r
k
is ob
tain
ed
with
a po
wer
facto
r
closer t
o
unity.
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BIOGRAP
HI
ES OF
AUTH
ORS
Z
o
ubir Z
A
H
Z
OUH
was born in Drean, Algeria in 1973. H
e
received
the
engin
e
er diploma
and
the Magister d
e
gree from the University
of An
n
a
ba in electromechan
ical engin
e
ering in 1998
and 2001 respectively
.
He is actually
working to
wa
rd the Doctor
ate th
esis. His ar
ea of research
includ
es
power ele
c
troni
cs
, ha
r
m
onics in power s
y
stems, pow
er quality
and active h
a
rmonics
filte
ring. Sinc
e Decem
ber 2001, he is a lectur
er tea
c
her a
t
th
e Departm
e
nt o
f
Mechanic
al
Engineering (Option Electromechan
ical) and
P
r
oces
s
Engineering
,
at th
e F
acult
y of
T
e
c
h
n
o
l
o
gy
, Un
iv
e
r
si
ty
o
f
Sk
i
k
da
,
Al
ge
r
i
a
.
Lakhdar KHOCHMANE
w
as born in Skikda, Algeria, 1958. He
received his en
gineer degr
ee
and Magister degree from the University
of A
nnaba, Alg
e
ria in 1
984 and 1990 respectiv
ely
,
and
received his Doctorate from Annaba University
,
Algeria 2006.
He is currently
a professor at
departm
e
nt of F
acul
t
y
o
f
Te
chn
o
log
y
, M
ech
ani
cal
Engine
ering
(Option Ele
c
tro
m
echanic
al)
at
Skikda Universit
y
. His are
a
s of interest in
cl
ude
powe
r sy
ste
m
s op
timi
zation, power quality
and
power s
y
stems protection
and r
e
n
e
wable en
ergies
.
Ali HADDOUCHE
w
as born
in Oued Zen
a
ti, Algeria,
in 195
9. He receiv
e
d
his Phd degree
from mines inst
itute Univ
ersity
,
Moscow, USSR in
1988. Curr
ently
,
he is a p
r
ofessor at the
ele
c
trom
ech
anic
al depa
rtm
e
nt o
f
Annaba Unive
r
s
i
t
y
, Alger
i
a. H
i
s
m
a
in res
earch
interes
t
s
ar
e
focused on
power quality
and po
wer s
y
st
em
s
prot
ect
ion and
ren
e
wable
energ
i
es
.
Evaluation Warning : The document was created with Spire.PDF for Python.