Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
6
,
No
. 2,
J
une
2
0
1
5
,
pp
. 33
7~
34
7
I
S
SN
: 208
8-8
6
9
4
3
37
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
An Improved Double Fuzzy PI
Controller For Shunt Active
Power Filter DC Bus Regulation
Nabil Elhaj*,
Moulay Br
ahi
m
Sedr
a*, T
a
rik Jarou*, Hi
nd
Dje
g
hloud
*
*
* Labor
ator
y
of
High Energ
i
es,
Engineering Sciences, an
d
Re
act
ors
,
Ibn
Tofai
l
U
n
ivers
i
t
y
,
Ken
itr
a, M
o
ro
cco
** Labor
ator
y
of
Electr
i
cal
Engin
eering
,
Cons
tantine 1
University
, Constantine, Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 30, 2015
Rev
i
sed
May 16
, 20
15
Accepted
May 25, 2015
This
paper t
a
rg
ets
to dem
ons
trate th
e im
porta
nce of the
cho
i
ce of th
e
algorithm references detection to
be a
pplied with
a double fuzzy
P
I
correcto
r
(DFPI) for the
control and
the regulation
of
a shunt
active
power filter
(SAPF) DC bus voltag
e
.
In a previ
ous work, the s
y
n
c
hrono
us referen
ce
frame (SRF) algorithm was applied and
g
a
ve
satisfac
t
or
y res
u
lts. In th
e
present p
a
per
,
the SRF is co
m
p
ared to
the
positive
seque
nce of
th
e
fundamental of the sour
ce voltage algorithm
(PSF)
which offered b
e
tter
results reg
a
rding
the
power qu
ali
t
y
of
the
cons
id
ered m
a
in
uti
lit
y f
eed
ing
a
variab
le DC RL load throughout
a diode bridg
e
.
The results were carried ou
t
using computer simulation
performed
under MATLAB/Simulink
environment.
To
make the obtained re
sults more convenient, a
comparison
be
twe
e
n
the c
o
uple
s (SRF,
PI), (PSF,
P
I),
(SRF,
DFPI),
(PSF,
DF
PI) is a
dded
to prove th
e ef
fectiveness of the
couple (PSF, DFPI) in satisf
y
i
ng th
e
compromise between a good regulation of th
e SAPF DC bu
s v
o
ltag
e
and a
good qual
i
t
y
of
f
ilter
i
ng r
e
sulting
in
an
im
proved
qualit
y
of pow
er
.
Keyword:
Harm
oni
cs
S
A
PF
SRF &
PSF
algorithm
s
DFP
I
DC
vol
t
a
ge
c
ont
rol
l
e
r
C
o
m
p
ari
s
ons
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
:
Nab
il elh
a
j,
Lab
o
rat
o
ry
of
Hi
g
h
E
n
er
gi
es,
En
gi
nee
r
i
n
g S
c
i
e
nces a
n
d
R
e
act
ors,
Ibn
Tofail Un
iv
ersity,
Ken
itra, Morocco
.
Em
a
il: Nab
i
l
m
aill@yah
o
o
.fr
1.
INTRODUCTION
Recently, i
m
provi
ng the
quality of
e
n
ergy in electrical distributio
n
powe
r
utilities becomes a subj
ect
o
f
great in
terest. Th
e power
qu
ality o
f
t
h
ese
u
tilities is
m
a
i
n
ly related
t
o
t
h
e
v
o
ltage an
d curren
t
wav
e
fo
rm
s
th
at sho
u
l
d
b
e
sin
u
s
o
i
d
a
l and
in
p
h
a
se each
o
t
h
e
r. Howev
e
r, th
e
p
o
wer qu
ality can
b
e
affected
by th
e
i
n
fl
ue
nce
of
m
a
ny
di
st
ur
ba
nces, t
h
ese
di
st
ur
bance
s
are
fo
u
n
d
u
n
d
er
di
f
f
ere
n
t
f
o
r
m
s (harm
oni
cs, sa
gs,
un
bal
a
nce
,
fl
i
c
kers
an
d swel
l
s
)
[
1
]
-
[
2]
.
To
m
i
n
i
m
i
ze
t
h
e effect of
d
i
stu
r
b
a
n
ces on
po
wer
q
u
a
lity sev
e
ral so
lu
tions are
p
r
op
o
s
ed as effectiv
e
rem
e
d
i
atio
n
n
a
mely ac
tiv
e p
o
w
er filters (APFs) b
a
sed
o
n
v
o
ltag
e
sou
r
ce (VSIs)
or
cu
rren
t source (CSIs)
in
v
e
rters th
at can
b
e
con
n
ected
in
p
a
rallel, series o
r
bo
th
o
f
th
em
b
e
tween
th
e power
u
tilit
y an
d
th
e
d
i
sturb
i
ng
lo
ad
[3
]-[4
]
. Th
e prin
cip
l
e
o
f
th
ese to
po
log
i
es is to
p
r
ovi
de
t
h
e o
p
p
o
si
t
e
di
st
ur
bance t
h
at
cou
n
t
e
rs t
h
e ex
i
s
t
i
ng
d
i
stu
r
b
a
n
ce,
so th
at it can’t attain
th
e
po
wer
u
tility.
To
b
e
effective in
its o
p
e
ratio
n
th
e activ
e
p
o
wer filterin
g
syste
m
n
eed
s to
b
e
well supp
lied
with
a
su
fficien
t
an
d
n
o
n
flu
c
t
u
atin
g DC
v
o
ltag
e
in its DC
b
u
s
termin
als an
d well co
n
t
ro
lled
t
o
p
r
ov
id
e th
e
d
e
sired
out
put
si
g
n
al
s.
To
ac
hi
eve t
h
ese co
n
d
i
t
i
ons
,
t
h
e c
o
nt
r
o
l
ci
r
c
ui
t
i
s
desi
g
n
e
d
on
t
h
e
b
a
si
s
of
t
h
ree m
a
i
n
bl
oc
ks:
the algorithm
that
detects the
refe
renc
e
signa
l
s, the
correct
or
th
at
co
m
p
en
sates th
e
flu
c
tuatio
n
s
of th
e DC bu
s
vol
t
a
ge
an
d t
h
e m
odul
at
or
t
h
at
gene
rat
e
s t
h
e swi
t
c
hi
ng
si
g
n
al
s t
o
be l
a
u
n
c
hed
t
o
t
h
e i
n
v
e
rt
er s
w
i
t
c
hes
gat
e
s.
Th
ese
th
ree b
l
o
c
ks work
togeth
er
t
o
ou
tpu
t
th
e
co
m
p
en
sating signals. T
h
us, they m
u
st be care
f
ully c
o
nceived
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
.
2,
Ju
ne 20
15
:
337
–
3
47
33
8
to
av
o
i
d
failin
g
i
n
o
p
e
ration
o
f
th
e
APF syste
m
. Sev
e
ral
k
i
n
d
s
o
f
th
eses blo
c
k
s
can
b
e
fo
und
i
n
th
e literatu
re
[
5
]-[
6
]
, [7
]-
[8
], [9
]-
[1
0
]
.
In t
h
i
s
pape
r t
w
o al
go
ri
t
h
m
s
of
refe
rence c
u
rre
nt
s det
ect
i
o
n are c
onsi
d
ere
d
t
o
be as
soci
a
t
ed wi
t
h
t
h
e
DFP
I
co
ntr
o
ller intr
od
uce
d
in
[1
1]
. It’s a m
a
tter of the
sy
nc
hr
o
n
o
u
s re
fe
re
ntial fram
e
(SRF) alg
o
rithm
and t
h
e
p
o
s
itiv
e
sequ
en
ce
o
f
v
o
ltag
e
sou
r
ce
fund
amen
tal (PSF)
alg
o
rith
m
.
Th
e o
b
j
ectiv
e is t
o
con
c
l
u
d
e
abo
u
t
t
h
e
m
o
st su
itab
l
e alg
o
rith
m
to
b
e
ap
p
lied
with
t
h
e DFPI co
n
t
ro
l
l
er in
tend
ed
t
o
regu
late th
e DC b
u
s
vo
ltag
e
o
f
a
shunt
APF
syste
m
. The
pulses
ge
nerat
o
r is a
hysteresis
m
o
du
lato
r
and
th
e
v
a
lid
ation
of t
h
e
p
r
esen
ted stu
d
i
es
i
s
base
d
on
si
m
u
l
a
t
i
on
w
o
r
k
s
per
f
o
r
m
e
d u
n
d
e
r M
A
TLAB
/
S
i
m
u
l
i
nk.
Th
is work
is
su
mm
arized
in
fiv
e
section
s
. Sec
t
i
on
2 c
o
ncer
ns t
h
e
des
c
ri
pt
i
o
n o
f
t
h
e
con
s
i
d
er
e
d
t
o
p
o
l
o
gy
an
d cont
rol
t
ech
ni
que
. Sect
i
o
n 3 p
r
esent
s
t
h
e
al
gori
t
h
m
s
SR
F and P
SF.
Sect
i
on
4 reca
l
l
s
t
h
e
p
r
i
n
cip
l
e of th
e in
trodu
ced
DFPI [11
]
. Section
5
is co
ns
ecra
t
ed t
o
t
h
e
veri
f
i
cat
i
on by
com
put
e
r
si
m
u
l
a
t
i
o
n a
n
d
to
th
e co
m
p
arativ
e stud
ies.
2.
DESC
RIPTI
O
N OF
THE
CO
NSI
D
ERE
D
TOP
O
LOG
Y
AN
D CO
N
T
ROL
TEC
H
N
IQ
UE
Fig
u
re 1
shows th
e stud
ied
syste
m
th
at co
n
s
ists of a th
ree p
h
a
se po
wer supp
ly an
d its in
tern
al
im
pedance
(R
s
L
s
), a non
lin
ear lo
ad
(d
iod
e
rectifier) an
d a
sh
un
t
activ
e
p
o
wer filter. Th
e
rectifier load
ed b
y
a
passi
ve
ci
rc
ui
t
(R
L
L
L
).
Th
e SAPF co
m
p
rises a three-ph
ase vo
ltag
e
inv
e
rter an
d an ou
tpu
t
filter
(R
f
L
f
).
Th
is
inve
rter is
fo
r
m
ed by
a t
h
ree
half
-b
rid
g
es
(
T
1
-T
4
, T
2
-T
5
, T
3
-T
6
)
base
d
on
IGB
T
s
wi
t
h
an
t
i
-
paral
l
e
l
di
od
es. T
h
e
i
nve
rt
er l
e
gs a
r
e f
e
d
by
a
D
C
v
o
l
t
a
ge
V
dc
.
To
ge
ne
rat
e
t
h
e
IGB
T
s
pul
s
e
s a
hy
st
eresi
s
cu
rre
nt
c
ont
ro
l
l
e
r i
s
use
d
. The re
fe
rence curre
nts
are achieved first by th
e
SRF algorithm
,
then by
the PSF algorithm
.
The
reg
u
l
a
t
i
o
n
o
f
t
h
e
DC
vol
t
a
ge
of
SA
PF i
s
bas
e
d
on
a
Do
u
b
l
e
Fuzzy
l
ogi
c
PI
co
nt
r
o
l
l
e
r [
1
1]
-[
12]
.
A
resi
st
o
r
R
dc
is ad
d
e
d
to
the syste
m
wh
ich
is co
nn
ected in
p
a
rallel to
th
e cap
acito
r
C
dc
feed
in
g
the SAPF throug
h
the
regu
latin
g
l
o
op
. Th
e ro
le o
f
th
is resisto
r
i
s
to
min
i
m
i
ze
V
dc
ri
p
p
l
e
s b
y
cont
r
o
l
l
i
ng t
h
e co
nst
a
nt
t
i
m
e
as
expl
ai
ne
d i
n
(1
).
R
C
(
1
)
Whe
r
e C
dc
i
s
di
m
e
nsi
oned
i
n
[1
1]
a
n
d
t
a
kes as
val
u
e
few
al
t
e
rna
n
ce
s o
f
t
h
e f
u
nda
m
e
nt
al
fre
que
n
c
y
[1
3]
.
The othe
r passi
ve
elem
ents
and V
dc
are
al
so
di
m
e
nsi
oned
i
n
[
11]
.
Fi
gu
re
1.
Sc
he
m
a
t
i
c
di
agram
of
t
h
e st
udi
e
d
s
y
st
em
3.
SRF &
PSF ALGORIT
HMS
FOR REFE
RENCE DETECTION
a.
SRF Algorithm
The p
r
i
n
ci
pl
e of t
h
i
s
al
g
o
ri
t
h
m
i
s
t
o
force t
h
e so
urce c
u
r
r
e
nt
t
o
hav
e
t
h
e
sam
e
angul
ar
fre
que
ncy
as
th
at o
f
th
e sour
ce vo
ltag
e
(
i
.e. sour
ce
voltage and c
u
rrent
wave
s are
in s
y
nch
r
o
n
i
s
m
each
ot
he
r),
i
n
t
h
i
s
way
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
An
Imp
r
o
v
ed
Doub
le Fu
zzy
PI C
o
n
t
ro
ller fo
r
S
hun
t Active Po
wer Filter DC Bu
s Regu
la
tio
n
(Nab
il El
h
a
j
)
33
9
the p
o
we
r fa
ctor is
fo
rced t
o
rem
a
in
n
ear the u
n
ity. Th
e ex
traction
of th
e refe
rence c
u
rrents is
based
on t
h
e
Park
tran
sformatio
n
app
lied
to
th
e lo
ad thre
e-phase curre
nts so that the
angl
e i
s
pr
oc
ure
d
fr
om
source t
h
ree-
pha
se vol
t
a
ges
ang
u
l
a
r fr
eq
u
e
ncy
t
h
r
o
u
g
h
a t
h
ree-
pha
se PLL. The
n
f
r
om
t
h
e obt
ai
ne
d d
i
phase l
o
a
d
cu
rre
nt
s,
fu
n
d
am
ent
a
l
part
i
s
rem
oved
usi
n
g a 2
nd
order lo
w-p
a
ss filter tu
n
e
d
o
n
t
h
e fun
d
a
m
e
n
t
al frequ
en
cy an
d
wh
ich
rem
a
i
n
s are t
h
e desi
re
d di
ph
ase refe
rence
cur
r
ent
s
as e
x
press
e
d i
n
(
2
).
Fi
nal
l
y
by
us
i
ng t
h
e i
nve
rs
e Par
k
trans
f
orm
a
tion, the three
-
phas
e
refe
rence c
u
rrents a
r
e car
ried out.
All these
steps ar
e s
u
mmarized in the
set of
eq
u
a
tion
s
(2
)-(4
) and
illu
strat
e
d
in th
e
syno
ptic sch
e
m
e
o
f
Fig
u
re
2
[14
]
.
∗
.
∗
(
2
)
Whe
r
e [P]
-1
is
th
e inv
e
rse of
th
e Park
t
r
an
sfo
r
m
a
tio
n
[P]
[1
5
]
,
∗
are
t
h
e
di
pha
se re
fere
nc
e cu
rre
nt
s gi
ve
n
b
y
(3
).
∗
(
3
)
Wi
t
h
:
.
(4)
An
d
are ou
tputs o
f
th
e
second
o
r
d
e
r low-p
a
ss filter tun
e
d
o
n
th
e
fu
nd
amen
tal frequ
en
cy.
Fig
u
r
e
2
.
Synop
tic sch
e
m
e
o
f
th
e SRF algo
r
ith
m
(
n
eg
lecting th
e zer
o
sequ
en
ce)
b.
PSF Algorith
m
Th
e obj
ectiv
e o
f
th
is algo
rithm is a
l
so
to
keep
th
e power facto
r
arou
nd th
e u
n
ity b
u
t
th
is ti
m
e
b
y
fo
rci
n
g t
h
e s
o
urce c
u
r
r
e
n
t
t
o
have t
h
e sam
e
arg
u
m
e
nt
as that of t
h
e posi
tive se
quence
of the s
o
urce
voltage
fu
n
d
am
ent
a
l
com
pone
nt
. Th
us t
h
e fi
r
s
t
st
ep o
f
t
h
e al
g
o
ri
t
h
m
i
s
t
o
ext
r
act
fun
d
am
ent
a
l
com
pone
nt
s fr
om
t
h
e
so
urce
v
o
ltag
e
s u
s
ing
a seco
nd
ord
e
r
b
a
nd
-pass filter. Th
en, th
e ob
tain
ed
in
stan
tan
e
ou
s si
g
n
a
ls are converted
in
to
co
m
p
lex
sig
n
a
ls
with h
e
l
p
o
f
Fo
urier blo
c
k
.
Afterward
,
po
sitiv
e se
qu
en
ce
o
f
th
ese co
m
p
lex
si
g
n
als is
extorted through the F
o
rtesc
u
e
tran
sform
a
tion. From
this pos
itive seque
nce com
pone
nt,
the
m
odule will
serve
t
oget
h
e
r
wi
t
h
l
o
ad act
i
v
e p
o
w
er t
o
com
put
e t
h
e
m
odul
e o
f
t
h
e fu
n
d
am
ent
a
l
com
ponen
t
of t
h
e sou
r
ce
curre
nt
as ex
pressed
in (5
), wh
ereas t
h
e arg
u
m
en
t will b
e
th
e an
g
l
e o
f
th
is cu
rren
t. Th
en
, fro
m
th
e to
tal lo
ad
cu
rren
t,
t
h
e new cu
rr
e
n
t
i
s
rem
oved;
as a resul
t
a
pu
re ha
rm
onic refere
nce current is produc
ed. The algorithm is
illu
strated
in Fi
g
u
re
3
[16
]
.
.
(
5
)
The
dem
onst
r
a
t
i
on
of
t
h
i
s
e
q
u
a
t
i
on i
s
gi
ve
n i
n
[1
6]
. T
h
e
ref
e
rence
cu
rre
nt
s
are t
h
en
ex
pr
e
ssed
by
(
6
):
∗
∗
∗
.
sin
sin
2
3
⁄
sin
2
3
⁄
(6)
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I
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:
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S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
337
–
3
47
34
0
Fig
u
r
e
3
.
Synop
tic sch
e
m
e
o
f
th
e PSF algor
ith
m
4.
THE DFPI
CONTROLLER
a.
Principle of V
dc
regulation
Fuzzy logic controller is used for c
o
m
p
licate
d
sy
st
em
s and al
l
o
ws t
r
an
sl
at
i
ng
kn
o
w
l
e
d
g
e and
hum
an
reason
ing to
sim
p
le ru
les th
at a co
m
p
u
t
er can
u
s
e, wh
ile
artificial in
te
l
l
i
gence
a
n
d
P
I
C
ont
r
o
l
a
r
e
us
ed t
o
achieve t
h
is objective. T
h
e
diagram
o
f
Figure 4 shows th
e con
t
ro
l al
g
o
rith
m
o
f
th
e capacito
r vo
ltag
e
o
f
t
h
e
SAP
F
DC
, t
h
i
s
cont
rol
i
s
ba
s
e
d o
n
a
do
u
b
l
e
fuzzy
P
I
con
t
ro
ller. Th
e DC
b
u
s
vo
ltag
e
cap
acito
r is co
mp
ared
with
th
e referen
ce to ob
tain th
e erro
r
‘e
’ gi
v
e
n by
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n:
e
t
V
∗
t
V
t
(
7
)
The
re
fere
nce voltage V
dc
*
corres
p
onds to the charge of the
capacitor C
dc
, th
ese qu
an
tities are d
i
m
e
n
s
io
n
e
d
i
n
[1
1]
. T
h
e
deri
v
a
t
i
v
e o
f
t
h
e
er
r
o
r
i
s
gi
ven
by
(
8
)
.
∆e
t
e
t
e
t1
(
8
)
Fi
gu
re 4.
The
pr
o
pose
d
DF
PI
C
o
nt
rol
l
e
r
f
o
r
V
dc
regu
latio
n
b.
Struc
t
ur
al construc
tion
of
the fuz
z
y
contr
o
ller
The st
ruct
ural
di
ag
ram
of a
fu
zzy
cont
rol
l
e
r
i
s
sh
o
w
n
i
n
Fi
g.
5.
It
c
onsi
s
t
s
o
f
f
o
u
r
di
st
i
n
ct
bl
ock
s
[1
7]
:
Fi
gu
re
5.
The
s
t
ruct
u
r
al
di
a
g
ra
m
of t
h
e f
u
zzy
cont
rol
l
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
An
Imp
r
o
v
ed
Doub
le Fu
zzy
PI C
o
n
t
ro
ller fo
r
S
hun
t Active Po
wer Filter DC Bu
s Regu
la
tio
n
(Nab
il El
h
a
j
)
34
1
1.
Base of ru
les
It con
s
ists on
th
e estab
lish
m
en
t of th
e fu
zzy
ru
les
b
a
se
d o
n
t
h
e di
rect
i
o
n
o
f
va
ri
at
i
on
of t
h
e er
ro
r ‘e
’, a
n
d t
h
e
algebraic sign
of the e
r
ror ‘e
’
and its de
rivati
ve
‘
Δ
e’.
2.
Fuzzification i
n
terface
In this ste
p
the
me
m
b
ership
functio
ns
of t
h
e i
n
put/output fo
r each
fuzzy pa
rtition of the
universe
of
discourse
are defi
ne
d (Fi
g
u
r
e 6)
.
3.
Infere
nce m
echanism
It is th
e
pro
cess of
d
e
sign
ing
fu
zzy
ru
les like: If e is ...
&
e is ..
. S
o
...
the
com
m
and is.
4.
Defuzzification inte
rface
In t
h
i
s
st
e
p
rea
l
val
u
e a
ssi
g
n
e
d
t
o
t
h
e
va
ri
ab
l
e
s of
f
u
zzy
o
u
t
p
ut
(se
v
e
r
al
m
e
t
hods
are a
v
ai
l
a
bl
e a
n
d
m
o
st
of
t
h
em
use t
h
e c
e
nt
r
o
i
d
or
t
h
e
b
i
sect
or m
e
t
hod
s).
(a)
(b
)
(c)
Fi
gu
re
6.
M
e
m
b
ers
h
i
p
f
u
nct
i
o
n
use
d
i
n
f
u
zzi
fi
cat
i
on
fo
r a
)
i
n
p
u
t
vari
a
b
l
e
e
,
b
)
i
n
p
u
t
vari
a
b
l
e
e,
an
d c) ou
tpu
t
var
i
ab
le
V
dc
As sh
o
w
n i
n
F
i
gu
re 6 t
h
e f
u
z
z
i
f
i
cat
i
on co
ns
i
s
t
s
i
n
usi
ng t
r
i
a
ng
ul
ar m
e
m
b
ershi
p
f
unct
i
o
n
s
fo
r ‘e’ a
n
d
its d
e
riv
a
tiv
e ‘
e’. T
h
e infe
re
nce m
echanism describes 49 fuzzy
ru
les summarized
in
Tab
l
e 1
,
Th
e ling
u
i
stic
v
a
lu
es are
d
e
fi
n
e
d
as fo
llows: {Po
s
itiv
e Big
(PB), Po
sitiv
e Med
i
u
m
(PM), Positiv
e Small (PS), Zero
(ZO),
Negat
i
v
e
Sm
all
(NS
)
,
Ne
gat
i
v
e M
e
di
um
(N
M
)
,
Negat
i
v
e
B
i
g (
N
B
)
}.
Fo
r de
f
u
zzi
fi
cat
i
o
n, t
h
e bi
sect
or
m
e
t
hod
is app
lied
.
Tabl
e 1. Fuzzy
r
u
l
e
s
t
a
bl
e
Δ
e/e
NB
NM
NS
Z
PS
PB
NB NB
NB
NB
NB
NM
NS
NM
NB
NB
NB
NM
NS
Z
NS NB
NB NS
NS
Z
PS
Z NB
NM
Z
Z
PS
PM
PS NM
NS
PS
PS
PM
PB
PM
NS
Z
PM
PM
PB
PB
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
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S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
337
–
3
47
34
2
c.
Dimensioning
of the
PI c
o
ntroller
Th
e
h
a
rm
o
n
i
c
cu
rren
ts in
fl
u
e
n
ce
o
n
th
e
stabilit
y o
f
t
h
e capacito
r
v
o
ltag
e
an
d causes a co
rrug
ation
o
f
th
is latter. To
red
u
ce th
e
ripp
les o
f
DC
v
o
ltag
e
, a PI
c
ont
r
o
l
l
e
r i
s
used. T
h
e dim
e
nsi
oni
n
g
o
f
coef
fi
ci
en
t
s
K
p
and K
i
of t
h
e
PI ca
n
be
achi
e
ved starting
from
the followi
ng
dia
g
ram
(Figure
8) which leads t
o
t
h
e transfe
r
function of
t
h
e corrected system
in
the
open loop e
x
pres
sed
by (9).
Fi
gu
re
7.
C
o
e
f
f
i
ci
ent
s
Di
m
e
nsi
oni
n
g
o
f
P
I
c
o
nt
r
o
l
l
e
r
.
(9)
Where
,
and
(
1
0)
Whe
r
e i
F
an
d
V
F
are
act
i
v
e c
o
m
pone
nt
s
of t
h
e S
A
P
F
out
pu
t
cur
r
ent
a
n
d
v
o
l
t
a
ge.
The
passi
ng
ba
nd
o
f
t
h
e
v
o
l
t
a
ge l
o
o
p
i
s
i
n
fer
i
or t
o
th
at
o
f
th
e cu
rren
t l
o
op, con
s
eq
uen
tly
th
e po
le
of
TF
i
(p
)
will not in
terv
en
e i
n
th
e
v
o
ltag
e
lo
op
stab
ility, so
o
n
e
can co
n
s
i
d
er th
at
1
[1
8]
.
By
neg
l
ecting
the switching
lo
sses in the
a
c
tive filter a
n
d in the output
filt
er, the ener
gy
is the same in
both
DC and
AC si
des. Th
us:
.
∗
.
.
.
(
1
1)
Whe
r
e,
3
.
.
√
.
.
(
1
2)
Therefore
,
.
√
.
.
∗
.
.
(
1
3)
Wi
t
h
,
√
.
.
∗
.
(
1
4)
Now
by intr
oducing the PI
controller,
the
tr
ansfer func
tion for
th
e open
loop becom
e
s:
.
.
.
.
(
1
5)
Where,
and
(
1
6)
In the peri
odi
c
al state,
is expressed
as
:
.
(
1
7
)
So t
h
at,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
An
Imp
r
o
v
ed
Doub
le Fu
zzy
PI C
o
n
t
ro
ller fo
r
S
hun
t Active Po
wer Filter DC Bu
s Regu
la
tio
n
(Nab
il El
h
a
j
)
34
3
and
(
1
8)
Accor
d
i
n
g t
o
B
o
de
di
agr
a
m
of
,
and
can be
deduc
ed fr
om th
e c
u
ttin
g
freque
ncy
2.
.
fo
r which
the ga
in
o
f
1
is null a
n
d its
pha
s
e
equals
ata
n
ω
ω
⁄
.
Fin
a
lly,
and
√
(
1
9)
Gen
e
rally, th
e
cu
ttin
g
frequ
ency is set at 20
Hz
[18
]
.
5.
VERIF
I
C
A
TI
ON B
Y
CO
MPUTER SIMULATION
In
t
h
i
s
sect
i
o
n
sim
u
l
a
t
i
on w
o
r
k
s a
b
out
t
h
e
pr
evi
o
us st
udy
a
r
e p
r
o
v
i
d
e
d
.
Th
ey
were
car
ri
ed
out
usi
n
g
MATLAB/Simu
lin
k so
ftware
an
d con
s
i
d
ering
th
e p
a
ram
e
te
rs repo
rted
in
Tab
l
e
2
.
Tabl
e 2. Si
m
u
lat
i
on
Pa
ram
e
t
e
rs
Para
m
e
ter Value
AC supply
voltage a
nd fr
equency
380V-
50Hz
Supply
im
pedance
R
s
= 0.
07
Ω
, L
s
= 0.
25
m
H
Rectifier load
R
L
= 10
Ω
,
L
L
=
5
0
m
H
Output filter i
m
pe
dance
R
F
= 10
m
Ω
, L
F
= 0.
95 m
H
Upstrea
m
filte
r i
m
pedance
R
c
= 0.
387
Ω
, L
c
= 0.
3
m
H
DC link capacitor
DC Résistance
C
dc
= 3.
1
m
F
R
dc
= 64.
5
Ω
DC link r
e
fer
e
nce
voltage
∗
= 550 V
PI
angle,
coefficients and satur
a
tion
60°
,
K
p
= 0.
1,
K
i
= 7.
28,
±5V
The
si
m
u
l
a
t
i
ons
m
odel
s
co
n
cern fo
r pai
r
s of (al
g
ori
t
h
m
of refe
renc
es,
V
co
n
t
ro
ller) con
s
id
ering
(SRF,
PI
),
(SR
F
, D
F
P
I),
(P
SF
, PI
) a
n
d
(P
SF,
DFP
I
)
.
T
h
e
ob
tained r
e
sults a
r
e p
r
ese
n
ted i
n
the fi
gu
res
8 t
o
13
,
note t
h
at only results
of
phas
e
a
ar
e
pr
e
s
en
te
d
s
i
n
c
e th
er
e
is
s
i
mila
r
i
t
y
wi
th t
h
e
ot
he
r
ph
a
s
es shi
f
t
e
d
by
120
°
fr
om
a
.
Fig
u
re 8
p
r
esen
ts th
e sou
r
ce
cu
rren
t b
e
fo
re
p
e
rf
orm
i
n
g
th
e filterin
g
op
eratio
n
.
A
n
o
n
s
i
n
u
s
o
i
d
a
l wav
e
can be
seen i
n
Fi
gu
re
8.a. T
h
e ha
rm
oni
c spect
r
u
m
of t
h
i
s
wav
e
gi
ves
a TH
D% o
f
2
5
.
4
8
%
w
h
i
c
h i
s
not
con
f
orm
t
o
t
h
e st
anda
rd
s IEE
E
5
19 a
n
d IEC
61
0
0
0
-
3-
2. B
e
sid
e
s, th
e curren
t is no
t in
ph
ase
with
th
e so
urce
v
o
ltag
e
wh
ich
mean
s th
at th
e
PF is
n
o
t
clo
s
e
to
th
e
un
ity.
Fi
gu
re 8.
R
e
sul
t
s
bef
o
re
st
art
i
ng
t
h
e o
p
erat
i
o
n of
t
h
e SA
PF (a).
W
a
ve
fo
rm
s
o
f
V
and
i
(b
) H
a
rm
onic
spectrum
of
i
0.
8
0.
85
0.
9
0.
95
1
-5
0
0
50
is
a
(
A
)
0
5
10
15
20
25
30
0
10
20
30
40
50
60
H
a
r
m
oni
c
or
de
r
H
a
r
m
o
n
i
c
m
a
gni
t
ude
0.
8
0.
85
0.
9
0.
95
1
-
500
0
500
Ti
m
e
(
s
)
Am
p
(
A
,
V)
is
a
(a
)
(b
)
T
H
D
i
s
%
=
2
5
.
48%
D
u
r
a
t
i
on =
1
s
Vs
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
337
–
3
47
34
4
Fig
u
re 9
shows th
e resu
lts after p
u
tting th
e SA
PF und
er op
eratio
n
b
u
t
witho
u
t
in
serting
th
e
cont
rol
l
e
r
of
V
. Th
e
upp
er p
l
o
t
of
Figure 9
.
a illu
strates
V
wit
h
its
re
fre
nce
V
∗
, it is
ob
v
i
ou
s t
h
at
V
is
inferi
or
to
V
∗
(
t
he d
e
v
i
atio
n is
ar
oun
d 6%)
.
Ho
w
e
v
e
r
the two
o
t
h
e
r
p
l
o
t
s of
Fi
g
u
r
e
9.b d
e
m
o
n
s
tr
ate a
good
q
u
a
lity of filtering
in
bo
th
cu
rren
t and
so
urce vo
ltag
e
as
w
e
ll as a
g
ood co
m
p
en
sation o
f
th
e
po
w
e
r
factor
since no delay
is noticed bet
w
een the two
signals. T
h
e
T
HD%
of t
h
e sou
r
ce cu
rre
nt
i
s
4.
79% as
de
pi
ct
ed i
n
Fi
gu
re
9.c
w
h
i
c
h a
g
rees
wi
t
h
t
h
e st
an
dar
d
s
r
e
st
ri
ct
i
ons.
Fi
gu
re
9.
R
e
sul
t
s bef
o
re i
n
se
rt
i
ng t
h
e
V
cont
roll
er (ca
s
e
of
PSF algorithm
)
.
(a)
V
and
V
∗
(b
)
i
and
i
with
V
(c
)
Harm
onic spectrum
of
i
Fig
u
re
10
sh
ows th
e ob
tain
ed
resu
lts after i
n
ser
t
i
n
g t
h
e P
I
cont
rol
l
e
r a
n
d
usi
n
g t
h
e SR
F
as al
g
o
ri
t
h
m
fo
r
detecting
t
h
e
refe
re
nces
of
the
S
A
PF
c
u
r
r
ents
. T
h
e
fi
rst c
u
r
v
e
(Fi
g
u
r
e
10
.a)
m
e
ntions
that
V
fo
llows
p
e
rfectly its re
feren
ce after a
tran
sien
t state o
f
m
o
re
th
an
0.3
s
. C
o
n
c
ern
i
ng
th
e filtering
q
u
a
lity an
d
th
e p
o
wer
fact
or
c
o
m
p
en
sat
i
on. Fi
g
u
re 10
.b desc
ri
bes si
nus
oi
dal
wav
e
fo
rm
s
for bot
h
cu
rre
nt
an
d vol
t
a
ge
i
n
t
h
e sou
r
ce
,
m
o
reover t
h
ey are
in
phase
whic
h m
eans a
satisfactor
y valu
e o
f
th
e PF.
Figur
e 10
.c g
i
v
e
s
th
e
TH
D
%
of
i
wh
ich
is also
co
nfo
r
m
to
no
rm
s (2
.79
%
).
Fig
u
re
10
. Resu
lts after in
sertin
g
t
h
e PI con
t
ro
ller asso
ciated
to th
e
SRF al
g
o
rith
m
(a)
V
and
V
∗
(b
)
i
and
i
with
V
(c) Harm
onic spectrum
of
i
0
0.
2
0.
4
0.
6
0.
8
1
-
100
0
100
is
a
(
A
)
0
0.
2
0.
4
0.
6
0.
8
1
-5
0
0
0
50
0
Am
p (
A
, V)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
500
550
600
Am
p (
V
)
vd
c
*
vd
c
0
10
20
30
0
20
40
60
80
H
a
r
m
oni
c
or
de
r
H
a
r
m
on
ic
m
a
gn
it
ud
e
Ti
m
e
(
s
)
(a
)
T
H
D
i
s
%
=
4.
79 %
D
u
r
a
t
i
o
n
=
1
s
Vs
a
is
a
(c
)
Ti
m
e
(
s
)
(b
)
0
10
20
30
0
20
40
60
80
H
a
r
m
oni
c
or
de
r
Ha
r
m
on
i
c
m
a
gnitude
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
500
550
600
Am
p (
V
)
vd
c
*
vd
c
0
0.
2
0.
4
0.
6
0.
8
1
-
100
0
100
isa
(
A
)
0
0.
2
0.
4
0.
6
0.
8
1
-
500
0
500
Tim
e
(
s
)
Am
p
(
A
,
V)
(c)
Ti
m
e
(
s
)
(a
)
(b
)
is
a
T
H
D
i
s
%
=
2.
79 %
D
u
r
a
t
i
o
n
=
1
s
Vs
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
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8-8
6
9
4
An
Imp
r
o
v
ed
Doub
le Fu
zzy
PI C
o
n
t
ro
ller fo
r
S
hun
t Active Po
wer Filter DC Bu
s Regu
la
tio
n
(Nab
il El
h
a
j
)
34
5
Fi
gu
re 1
1
pr
o
v
i
d
es t
h
e res
u
l
t
s of t
h
e DFP
I
associ
at
ed t
o
t
h
e SR
F al
gori
t
hm
. As show
n i
n
Fi
gu
re
11.a, less
trans
i
ent state occ
u
rs (less
tha
n
0.1s), the
n
V
reac
hes
V
∗
an
d e
vol
v
e
s wi
t
h
i
t
.
The
im
pact
of t
h
e
DFP
I
i
n
red
u
c
i
ng t
h
e t
r
ans
i
ent
st
at
e dura
t
i
on i
s
ve
ry
cl
ear. Fi
g
u
re
1
1
.
b
dem
onst
r
a
t
es t
h
e sy
nch
r
oni
sm
bet
w
ee
n s
o
u
r
c
e
vol
t
a
ge a
n
d
cur
r
ent
whe
r
ea
s Fi
gu
re
11
.c i
ndi
cat
es a
n
ac
cept
a
bl
e T
H
D
%
of i
sa
. Whic
h
m
ean
th
at th
e im
p
r
ov
em
en
t in
trodu
ced in
V
regulatio
n
h
a
sn
’t
in
fl
u
e
n
c
ed
th
e p
o
wer factor an
d
th
e filterin
g
q
u
a
lity.
Fig
u
re
11
. Resu
lts after in
sertin
g
t
h
e
DFPI
c
ont
roller a
ssoci
ated to t
h
e
SRF algorithm
(a)
V
and
V
∗
(b
)
i
and
i
with
V
(c) Harm
onic spectrum
of
i
Now,
resu
lts
co
n
c
ern
i
ng
the co
up
les (PSF alg
o
rith
m
,
PI con
t
ro
ller), (PSF algo
rith
m
,
DFPI
cont
roller) will be dresse
d.
The obj
ec
tive is to carry out
better results
than those of th
e precede
n
t couple
s
(SRF alg
o
rith
m
,
PI cont
rolle
r) an
d (
S
RF algo
rithm
,
D
FPI
cont
r
o
l
l
e
r)
. Fi
g.
12 s
h
ows t
h
e
resul
t
s
o
f
t
h
e
cou
p
l
e
(PSF algo
rithm
,
PI co
n
t
ro
ller). On
e can
see b
e
tter
resu
lt in
V
regu
latio
n
co
m
p
arin
g to
t
h
at sh
own
in Fi
g
u
re
11
.a, t
h
e t
r
a
n
si
ent
st
at
e i
n
Fi
gu
re
12
.a
desc
ri
bes a
n
e
x
cee
di
n
g
val
u
e
o
f
25
V,
w
h
i
l
e
Fi
gu
re
11
.a i
n
di
cat
ed a
lack
o
f
5
0
V
in
th
e
tran
sien
t state.
Altho
ugh
th
e o
b
t
ained
THD% o
f
i
(3.89%) is
greater t
h
an that
of Figure
11
.c
(3
.0
7%
),
but
i
t
rem
a
i
n
s con
f
orm
t
o
n
o
r
m
s (< 5 %)
.
Fig
u
re
12
. Resu
lts after in
sertin
g
t
h
e PI
con
t
ro
ller asso
ciated
to th
e
PSF alg
o
rith
m
(a)
V
and
V
∗
(b
)
i
and
i
with
V
(c) Harm
onic spectrum
of
i
0
10
20
30
0
20
40
60
80
H
a
r
m
oni
c
or
de
r
Ha
r
m
onic
m
a
gnit
u
d
e
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
500
550
600
Am
p (
V
)
vd
c
*
vd
c
0
0.
2
0.
4
0.
6
0.
8
1
-1
0
0
0
10
0
isa
(
A
)
0
0.
2
0.
4
0.
6
0.
8
1
-
500
0
500
Ti
m
e
(
s
)
A
m
p
(A
,
V
)
(c)
Ti
m
e
(
s
)
(a
)
(b
)
Vs
a
is
a
T
H
D
i
s
%
=
3.
07
%
D
u
r
a
t
i
o
n
=
1
s
0
10
20
30
0
20
40
60
80
H
a
r
m
o
n
i
c
or
de
r
Ha
r
m
o
n
i
c
m
a
gn
it
ud
e
0
0.2
0.4
0.6
0.8
1
-1
0
0
0
10
0
is
a
(
A
)
0
0.2
0.4
0.
6
0.
8
1
-5
0
0
0
50
0
Am
p
(
A
, V)
0
0.1
0.
2
0.3
0.
4
0.5
0.
6
0.7
0.8
0.
9
1
50
0
55
0
60
0
Am
p (
V
)
vd
c
*
vd
c
(c
)
is
a
Vs
a
Tim
e
(
s
)
(a
)
(b
)
Tim
e
(
s
)
TH
D
i
s
%
=
3
.
8
9
%
D
u
r
a
t
i
o
n
=
1
s
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
.
2,
Ju
ne 20
15
:
337
–
3
47
34
6
Fi
nal
l
y
Fi
gu
re
13
gi
ves t
h
e re
sul
t
s
o
f
t
h
e l
a
st
co
upl
e
(P
SF al
go
ri
t
h
m
,
DFP
I
cont
rol
l
e
r
)
.
Fig
u
re
13
. Resu
lts after in
sertin
g
t
h
e
DFPI
c
ont
roller a
ssoci
ated to t
h
e
PSF algorithm
(a)
V
and
V
∗
(b
)
i
and i
sa
with V
sa
(c) Ha
rm
onic
spectr
u
m
of
i
Ob
vi
o
u
sl
y
t
h
e reg
u
l
a
t
i
on of
V
is th
e b
e
st fo
r
th
is latest co
up
le. In
fact as
d
e
p
i
cted
i
n
Fi
g
u
re 13
.a
V
desc
ribes
less
exceedi
n
g
value (<
25V) in t
h
e transien
t stat
e com
p
aring t
o
Figure
12.a.
Furt
herem
o
re t
h
e
THD
%
of Fi
g
u
re 1
3
.c
(3
.6
2
%
) i
s
l
e
ss t
h
an t
h
at
of Fi
g
u
r
e 12
.c. C
o
nse
que
nt
l
y
, one c
a
n co
ncl
u
de t
h
at
t
h
e
co
up
le (PSF alg
o
rith
m
,
DFPI con
t
ro
ller) is th
e
b
e
st in
regu
latin
g
V
, correcting the
powe
r fact
or
and
im
pro
v
i
n
g
i
wa
vef
o
rm
.
6.
CO
NCL
USI
O
N
In th
e obj
ective of im
p
r
ov
ing th
e
resu
lts carried
ou
t in a
form
er work, t
h
e presen
t article h
a
s
fo
cu
sed
o
n
ch
ang
i
ng
th
e algo
rith
m
o
f
d
e
tection
of th
e
refe
r
e
nce cu
rr
en
ts of
a SA
PF to
obtain
b
e
tter
r
e
sp
on
se
si
m
u
ltan
e
o
u
s
ly
in
regu
lating
t
h
e DC v
o
ltage
V
o
f
th
e
SAPF, m
a
in
tain
in
g
th
e
p
o
wer
factor at a satisfact
o
r
y
lev
e
l and
im
p
r
o
v
i
n
g
th
e filterin
g
qu
ality (obtain
i
n
g
a co
nform
THD%
of t
h
e sou
r
ce curren
t). In
t
h
e
p
r
ev
iou
s
work, th
e SRF algo
rith
m
was
u
s
ed,
it was
associated
to
t
h
e DFPI
V
con
t
ro
ller.
In th
is
stu
d
y
, th
e SR
F is
com
p
ared to the PSF al
gorithm
s
i
nce it is based
on t
h
e
pr
i
n
ciple of forci
n
g the
fund
am
ental source c
u
rrent to
h
a
v
e
the sam
e
an
g
l
e as th
at
o
f
th
e po
sitive seq
u
e
n
ce of th
e fun
d
a
m
e
n
t
al so
u
r
ce
v
o
l
t
a
g
e
. Th
u
s
, th
e
m
a
in
feature
of the
PSF is to ens
u
re a
unity power
factor
in
the source side. After
prese
n
ting the c
o
ns
idere
d
al
go
ri
t
h
m
s
and c
ont
r
o
l
l
e
rs
,
a veri
fi
cat
i
on
t
h
r
o
u
g
h
si
m
u
lat
i
ons
were
p
e
rf
orm
e
d u
n
d
e
r
M
A
T
L
AB
/
S
i
m
uli
n
k
envi
ronm
ent which c
once
r
ned four c
o
uples
of algor
ithm
/
controller (SRF/
P
I, SR
F/DF
PI,
PSF/PI, PS
F/DFP
I).
The
results i
n
dicated that the
best
couple sat
i
sfying t
h
e targets (less
tr
ans
i
ent state and less excee
ding
value
of
V
,
a
un
iqu
e
P
F
and
a co
nfo
r
m T
H
D
%
of
i
) i
s
t
h
e c
o
upl
e (P
SF/
D
F
P
I).
Th
e c
o
nt
i
nuat
i
on
o
f
t
h
e
st
u
d
y
conce
r
ns t
h
e
a
ppl
i
cat
i
o
n
of a
DFP
I
c
o
n
t
ro
ller for regu
latin
g th
e SAPF cu
rren
t
.
REFERE
NC
ES
[1]
A.
Pavas,
H.
Torres,
D.
Urrutia,
G.
Ca
jam
a
rc
a, L
.
E
.
Gall
eg
o and L.
Bu
itrago, "A Novel Approach to th
e
S
i
m
u
lation of P
o
wer Quali
t
y
Di
sturbances
in E
l
ectr
i
c P
o
wer S
y
stem
s," IEEE/P
E
S
Transm
ission & Distribu
tio
n
Conference and Exposition:
L
a
ti
n
Am
erica,
2006
. TDC
'
0
6
,
C
a
racas, 15-18
Aug. 2
006.
[2]
Roger C. Dugan, Mark F. McGranagha
n S
u
r
y
a S
a
ntos
o, H.
W
a
y
ne B
eat
y,
"
Ele
c
tri
cal P
o
wer
S
y
s
t
em
s
Qualit
y,
Second Ed
ition
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"
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