Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
5
,
No
. 2, Oct
o
ber
2
0
1
4
,
pp
. 18
5~
19
4
I
S
SN
: 208
8-8
6
9
4
1
85
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
Closed Loop Non Linear Contro
l of Shunt Hybrid Power Filter
for Harmonics Mitigation in
Industrial Distribution System
A.
Ariv
ara
s
u,
R.Bal
a
su
bra
m
anium
Departm
e
nt o
f
E
l
ec
tric
al
a
nd
Electronics Engin
e
ering, SA
S
T
RA Univers
i
t
y
,
Th
an
javur
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 30, 2014
Rev
i
sed
Ju
l 14
, 20
14
Accepte
d Aug 8, 2014
In recent
y
e
ars, the am
ount of
non-line
a
r loads
has increased c
onsiderab
l
y
since ther
e wer
e
improvements in pow
er elec
t
r
onic equipm
en
t (s
uch as
adjus
t
abl
e
s
p
ee
d drives
or co
nverter
ac-d
c
,
ac-a
c
, d
c
-a
c an
d dc-dc)
i
n
industrial sector
s which cause
deter
i
or
ation of
the quality
of the
electric
power supply
th
rough distortion
of suppl
y
voltage and supply
current. Th
is
has led
to
improvement of man
y
str
i
ngent needs regard
ing g
e
neration o
f
harm
onic curren
t
, which ar
e fo
und in IEEE51
9
and IEC6100
0 standards.
This pap
e
r prop
oses a non-linear functi
on based
closed
loop
con
t
rol str
a
teg
y
(without lo
ad current ex
traction
)
for
three-phas
e
Shunt Activ
e
Power Line
Conditioner
and
LC passive filter to
com
p
ens
a
t
e
harm
onics
, po
wer facto
r
improvement an
d enhance the d
y
namic
performance of Shunt H
y
brid Power
Filter (SHPF). B
y
using a PI
controll
er th
e DC bus voltage o
f
the Shunt
Active Power Fi
lter
is m
a
intain
e
d
cons
tant. Resu
lts obtain
e
d fro
m simulation
s
hows
the perform
ance of expec
t
ed h
y
br
id filt
er i
n
trans
i
ent and s
t
ead
y s
t
a
t
e
operation . Th
is indicates th
at th
e contro
ller is able to compensate even under
s
e
vere load
curr
ent im
balan
ces
.
Keyword:
d
-
q
tran
sform
a
tio
n
Harm
oni
cs m
i
ti
gat
i
o
n
Non
-
lin
ear fun
c
tio
n
Reactive powe
r c
o
m
p
ensation
Shu
n
t
Hybrid Power Filter
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
:
A.
Ariv
aras
u,
Depa
rtem
ent of Electrical a
n
d
El
ect
ro
ni
cs E
n
gi
nee
r
i
n
g,
SASTR
A
Un
iversity,
Thi
r
um
al
ai
samut
h
i
r
am
, Val
l
a
m
,
Tanjav
ur
62
10
2,
Tam
i
l
Nadu
,
In
di
a.
Em
a
il: ariv
arasu
.
ap
a@g
m
ail.c
o
m
1.
INTRODUCTION
Th
e in
creased lev
e
l of
n
onlin
ear lo
ad
s
du
e to
usa
g
e
of m
o
re elect
ronic equipm
ent leads t
o
d
e
terioration
of power
q
u
a
lit
y in
th
e powe
r
system
. W
h
e
n
eve
r
the
nonl
i
n
ear
l
o
a
d
dra
w
s harm
oni
c
c
u
r
r
ent
fr
om
a suppl
y
t
h
ere
occu
rs a
di
st
ort
i
o
n i
n
t
h
e su
ppl
y
v
o
l
t
a
ge wa
ve
fo
rm
at
t
h
e com
m
on cou
p
l
i
n
g (
P
C
C
)
p
o
i
n
t
because of the source im
pedance
.
T
h
e
distorted volta
ge and curre
nt
m
a
y cause e
n
d-user e
q
uipment to
m
a
l
f
unct
i
o
n an
d o
v
e
r
heat
i
n
g
of c
o
nd
uct
o
rs.
Due t
o
t
h
i
s
, t
h
e com
pone
nt
con
n
ect
ed at
t
h
e PC
C
get
s
af
f
ect
ed
by re
duction in efficiency and life pe
riod.
Usu
a
lly, to
redu
ce and
avo
i
d
cu
rren
t h
a
rm
o
n
i
cs, a p
a
ssi
v
e
LC p
o
w
er filter is u
s
ed
wh
en
con
n
ected
p
a
rallel to
th
e lo
ad. Th
ese types o
f
p
a
ssiv
e
po
wer filter h
a
ve so
m
e
d
r
awb
a
ck
s,
d
u
e
to
wh
i
c
h
it can
no
t p
r
o
v
i
d
e
a com
p
lete solution. These have the
di
sadvantages
of large size, resona
nce,
an
d fi
xe
d c
o
m
p
ensat
i
o
n
.
I
n
rece
nt
days, base
d on powe
r electronic m
e
thods the harm
oni
c suppression fa
cilities
have
been im
prove
d
. These
facilities are known a
s
active powe
r filt
er which ca
n suppress
va
rious
orde
r ha
rm
onic com
pone
nts
si
m
u
ltan
e
o
u
s
ly
fo
r lo
ad
s
wh
ich
are
n
o
n
lin
ear in n
a
t
u
re.
Dep
e
nd
ing
on th
e co
m
p
en
satio
n
typ
e
s, t
h
e activ
e
powe
r filter is categorized i
n
to
r
eactive
powe
r,
harm
oni
c, bala
ncing of three
-
pha
se
syste
m
s and
m
u
l
tipl
e
com
p
ensations
.
Th
is st
u
d
y
of activ
e
p
o
wer filter an
d its op
erati
ng
prin
cip
l
e were
introd
u
c
ed
b
y
H.Sasak
i
and
T.m
ach
id
a in
19
70
[1
]. Th
e cu
rren
t sou
r
ce co
nv
erter
typ
e
b
a
sed
activ
e po
wer filters
were
im
p
l
e
m
en
te
d
with
GTO th
y
r
isto
rs fo
r fi
rst ti
me in
th
e wo
rl
d in
1
9
8
2
[2
], Nowad
a
ys th
e IGBTs are been
u
s
ed
for th
e real
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
85 –
19
4
18
6
im
provem
ent in active powe
r
filter technology.
Am
ong
th
e subjects
related to th
e active filter’s
design
techniques
and applications, t
h
e tech
nique used for
e
x
tracting
the harm
oni
c load curre
nts
and determ
ining the
filter referen
c
e curren
t
h
a
s a m
a
j
o
r ro
le. Th
e accu
r
acy
an
d respo
n
se sp
eed of t
h
e SAPF are tak
e
n in
to
consideration
[3],
[4]. T
h
e t
echni
que
s of refere
nce c
u
rre
n
t ge
neration
are categorize
d
as
below: 1) tim
e
-
dom
ai
n and
2
)
fre
que
ncy
d
o
m
a
i
n
m
e
t
hod
s [
5
]
,
[6]
.
Ti
m
e
-do
m
ai
n
m
e
t
hods
suc
h
as
p
–
q
t
r
a
n
sf
orm
a
t
i
on an
d
d
–
q
tran
sform
a
t
i
o
n
etc.
d
e
p
e
nd
on
t
h
e m
easu
r
emen
ts and
conv
ersi
o
n
o
f
th
ree-ph
ase qu
an
tities. Fast
respo
n
s
e is
t
h
e
m
a
jor a
d
v
a
nt
age o
f
t
h
e
t
i
m
e
-dom
ai
n cont
r
o
l
t
echn
i
ques i
n
c
o
m
p
ari
s
on
w
ith the fre
quency
-dom
ain
t
echni
q
u
es
de
pen
d
i
n
g
o
n
t
h
e fast
F
o
u
r
i
e
r
t
r
ans
f
o
r
m
a
t
i
o
n.
On
t
h
e
ot
h
e
r ha
n
d
,
fre
qu
ency
-
dom
ai
n cont
ro
l
techniques det
ect the indivi
dual an
d m
u
ltiple ha
rm
onic loa
d
c
u
rrent
with
m
o
re accuracy. The
loop for c
ont
rol
of
op
erat
i
o
n o
f
t
h
e co
nt
r
o
l
l
e
r
can be cat
e
g
or
i
zed as o
p
e
n
l
o
o
p
c
ont
rol
a
n
d cl
ose
d
l
o
o
p
cont
rol
.
T
h
e c
ont
rol
alg
o
rith
m
fo
r clo
s
ed loo
p
contro
l system
is l
e
ss co
m
p
licated
th
en
i
n
o
p
en
lo
op
m
e
th
o
d
an
d requ
ires m
i
n
i
m
a
l
num
ber
of
cu
rr
ent
se
nso
r
s.
Many cont
rol techni
que
s ha
ve been shown in the
literature
, suc
h
as insta
n
tane
ous active & reactive
po
we
r t
h
e
o
ry
[
7
]
,
sy
nc
hr
o
n
o
u
s
refe
renc
e f
r
a
m
e [8]
,
Fu
zzy
cont
rol
[
9
]
,
P
I
cont
rol
[
1
0]
, S
l
i
d
i
ng m
ode c
o
nt
r
o
l
[1
1]
,Ne
u
ral
Ne
t
w
o
r
k
ap
pr
oac
h
[1
2]
, a
n
d
O
p
en l
o
o
p
No
nl
i
n
ear c
ont
r
o
l
[1
3
]
.
In
th
is
p
a
p
e
r, a th
ree-ph
ase sh
un
t h
y
b
r
i
d
pow
er filter is
m
o
d
e
led
in
th
e th
ree-ph
ase “abc”
coo
r
di
nat
e
s, a
nd t
h
e
n
, t
o
av
oi
d t
i
m
e depe
nde
nce, t
h
e m
odel
i
s
t
r
ans
f
o
r
m
e
d t
o
t
h
e ro
t
a
t
i
ng "dq"
ref
e
rence
fram
e
. On
t
h
e
ot
he
r
han
d
,
A
pr
o
p
o
r
t
i
onal
–
i
n
t
e
g
r
al
(P
I)
c
o
nt
r
o
l
l
e
r i
s
use
d
t
o
c
o
nt
rol
t
h
e
SAP
F
dc
bu
s
v
o
l
t
a
ge.
The dy
nam
i
c
per
f
o
r
m
a
nces of t
h
e S
A
P
F
u
s
i
ng t
h
e
No
n-l
i
near f
u
n
c
t
i
on
base
d cl
osed l
o
o
p
co
nt
r
o
l
ap
pr
oac
h
with
shu
n
t
LC
p
a
ssiv
e
filter are
o
b
t
ain
e
d
b
y
si
m
u
latio
n
u
s
i
n
g
Sim
u
lin
k
.
2.
R
E
SEARC
H M
ETHOD
Fig
u
re 1
.
Con
f
i
g
uration
o
f
Shu
n
t
Hybrid
Power
Filter
2.
1.
Estima
tion
o
f
Harm
onics
Power
q
u
a
lity measu
r
em
en
ts
are do
n
e
u
s
ing a p
o
we
r
q
u
a
li
ty an
alyzer. Th
e power
q
u
a
li
ty an
alyzer
u
s
ed
in
th
is wo
rk
is
Y
OKOG
AW
A CW
240
.
I
t
is cap
ab
le o
f
d
e
tecting
th
e pr
esen
ce
of
vo
ltag
e
and
cu
rr
en
t
harm
onics a
n
d
measuring their c
h
aracter
istic
s (order, am
plitude
and
phase).
Loa
d
s
un
der
st
udy
i
n
cl
u
d
e
n
onl
i
n
ea
r l
o
ads
i
n
t
h
e E
&
D
bui
l
d
i
n
g
o
f
De
l
phi
-T
VS
, M
a
nn
u
r
. L
o
a
d
s
include
power
electronics
equipm
ent su
c
h
as a
d
j
u
s
t
a
b
le
sp
ee
d
d
r
iv
e
s
an
d
D
C
dr
iv
es
.
The
r
e
ad
ing
s
ar
e
ta
k
e
n
at
t
h
e
i
n
p
u
t
di
st
ri
but
i
o
n pa
nel
.
T
h
e
c
u
r
r
e
n
t
THD
i
s
fo
u
n
d
t
o
be 18
.3
%
a
n
d
vol
t
a
ge
T
H
D
t
o
be 2.
2
5
1
%
.
W
i
t
h
o
n
l
yp
assiv
e
filter b
e
ing
im
p
l
e
m
en
ted
in
th
e
b
u
ild
i
n
g, th
e cu
rren
t THD is foun
d
t
o
b
e
8
.
2
%
an
d
vo
ltage THD
to
b
e
1.71
%.
2.
2.
Hy
brid Po
wer Filter Co
nfiguratio
n
Th
e
h
y
b
r
i
d
filter con
f
i
g
uration
is two
f
o
l
d
,
with
a non
-linear con
t
ro
l of
activ
e filter and
RC p
a
ssi
ve
filter. An active powe
r filter, APF
,
com
p
ris
e
s a th
ree phas
e
pulse widt
h m
odulation
(P
WM) volta
ge source
i
nve
rt
er. T
h
e i
nve
rt
er
has o
n
e
50
0µF ca
pac
i
t
o
r i
n
t
h
e DC
side and is shunt connecte
d
with the electrical grid.
Seri
es p
a
ssi
ve
el
em
ent
whi
c
h
con
s
i
s
t
of
t
h
r
ee 3m
H i
n
d
u
ct
ors a
n
d
0.
01
Ω
resisto
r
.
Th
e p
a
ssiv
e
filters are an
i
m
p
o
r
tan
t
p
a
rt
o
f
th
e
Active Filter d
e
sign
. It m
u
st b
e
d
i
m
e
n
s
io
n
e
d
ap
pro
p
riately
so
th
at th
e switch
i
ng
fre
que
ncy
d
o
e
s
not
af
fect
t
h
e sou
r
ce curre
nts THDafter t
h
e com
p
ensatio
n
.
D
u
ri
ng
de
si
gni
ng car
e m
u
st
be
tak
e
n
to
p
r
ev
en
t th
e in
terferen
ce of th
e p
a
ssiv
e filters with th
e co
n
t
ro
l of
th
e Activ
e Filter. In
th
is p
a
p
e
r an
Activ
e Filter i
s
p
r
esen
ted
where ind
u
c
t
o
r an
d
resistor
h
a
s
b
een u
s
ed
as
series p
a
ssiv
e
filter, bu
t th
e
p
a
ssive
filter con
f
i
g
uratio
n
can
b
e
a LCor RLC, or ev
en m
o
re co
m
p
lex
top
o
l
og
ies. Each
on
e of th
ese topolo
g
i
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Clo
s
ed
Loop
N
o
n Lin
e
a
r
Con
t
ro
l
o
f
Shu
n
t
Hyb
r
id Po
wer Filter fo
r
Harmo
n
ics Mitig
a
tion
i
n
… (A.Ariva
rasu
)
18
7
has
d
ra
wbac
ks
and a
dva
ntage
s
, whic
h
m
u
st be weighted
according wit
h
the type of loads that wi
ll be
co
m
p
en
sated
,
th
e IGBT switch
i
ng
freq
u
e
n
c
y, th
e co
n
t
ro
l o
f
t
h
e Activ
e Filter
and
th
e fin
a
l
co
stTh
e sh
un
t
p
a
ssiv
e
filter param
e
ters are selected
in
su
ch a m
a
n
n
e
r th
at
it is cap
ab
le of eli
m
in
atin
g
5
th
harm
oni
cs a
n
d 7
th
harm
oni
cs
whi
c
h a
r
e m
o
re p
r
om
i
n
ent
.
2.
3.
Modeling
of S
hunt Ac
tive
P
o
wer Filter
2.
3.
1.
Modeling in T
h
ree Phase
‘abc’ Fr
ame
Th
e m
o
d
e
l o
f
activ
e filter is
first d
e
v
e
l
o
p
e
d
in
th
ree-ph
ase ‘ab
c
’ fram
e
. Kirchho
ff’s
v
o
ltag
e
and
current laws are applied at
th
e su
pp
ly ter
m
i
n
al, and
it y
i
el
d
s
th
e fo
ll
o
w
i
n
g
th
ree d
i
fferen
tial eq
u
a
tio
ns in
th
e
st
at
i
onary
‘abc
’ f
r
am
e [13]
.
1
11
1
2
22
2
3
33
3
s
ss
s
s
ss
s
s
ss
s
di
EL
R
I
V
dt
di
EL
R
I
V
dt
di
EL
R
I
V
dt
(
1
)
Whe
r
e
V
1
,
V
2
, and
V
3
i
n
di
cat
e t
h
e l
i
n
e-t
o
-
g
r
o
un
d v
o
l
t
a
ges at
t
h
e poi
nt
of c
o
m
m
on coupl
i
ng
(PC
C
)
,
E
1
, E
2
and
E
3
in
d
i
cate t
h
e
lin
e-to
-groun
d
v
o
ltag
e
at th
e su
pp
ly term
in
al.
Also,
1
11
2
22
3
33
f
fF
M
M
f
f
FM
M
f
f
FM
M
di
VL
V
V
dt
di
VL
V
V
dt
di
VL
V
V
dt
Th
e vo
ltag
e
dro
p
acro
ss th
e in
du
ctor is sm
a
ll as co
m
p
ared to
th
e Sh
un
t Activ
e Filter vo
ltag
e
, wh
ich
gi
ves
us
t
h
e
rel
a
t
i
on,
1
1
2
2
3
3
f
f
FM
M
f
f
FM
M
f
f
FM
M
di
LV
V
dt
di
LV
V
dt
di
LV
V
dt
11
22
33
F
MM
F
MM
F
MM
VV
V
VV
V
VV
V
B
y
sum
m
i
ng the t
h
ree e
q
uat
i
ons i
n
(
1
)
,
an
d
wi
t
h
an ass
u
m
p
ti
on t
h
at
t
h
e vol
t
a
ges
o
f
AC
su
ppl
y
ar
e
bal
a
nce
d
, a
n
d
by
ne
gl
ect
i
ng t
h
e zer
o
-
seq
u
e
n
ce cur
r
e
n
t
s
i
n
t
h
e t
h
ree wi
re s
y
st
em
s, (i
.e.,)
usi
n
g t
h
e
f
o
l
l
o
wi
n
g
assum
p
tions:
12
3
1
2
3
12
3
1
2
3
0;
0
0;
0
ss
s
f
f
f
EE
E
V
V
V
II
I
I
I
I
On
e can ob
tain:
3
1
1
3
F
Mf
M
f
VV
(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.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
85 –
19
4
18
8
Th
e switch
i
ng
fun
c
tion
k
sw
of t
h
e
k
th
leg
(fo
r
k
= 1
,
2
,
3
)
of
t
h
e c
o
n
v
e
r
t
e
r ca
n
b
e
de
fi
ne
d as:
1,
'
0,
'
kk
k
kk
i
f
S
i
sO
n
a
n
d
S
i
sO
f
f
sw
if
S
i
s
O
ff
a
n
d
S
i
s
O
n
(3
)
There
f
ore,
kM
k
d
c
Vs
w
V
.T
h
e
dy
nam
i
c equat
i
on o
f
p
h
ase
-
k
filter’s m
o
d
e
l is d
e
n
o
t
ed
b
y
th
e eq
u
a
ti
o
n
giv
e
n
bel
o
w:
3
1
1
()
3
sk
ks
s
s
k
k
f
d
c
f
di
EL
R
I
s
w
s
w
V
dt
(4
)
In add
itio
n,
we m
a
y d
e
fin
e
a
fu
n
c
tion
nk
ss
switchin
g
state fun
c
ti
o
n
wh
ich is
d
e
n
o
t
ed
as fo
llows:
3
1
1
()
3
nk
k
f
n
f
ss
sw
sw
(5
)
Equ
a
tio
n (5
) den
o
t
es th
at th
e v
a
lu
e of
nk
ss
is
dep
e
nd
en
t on
t
h
e switch
i
n
g
fun
c
tio
n
k
sw
o
f
all three leg
s
of
th
e sh
un
t active po
wer
filter.
Th
is sho
w
s that th
e thr
ee phases
in
teracts with
each
o
t
h
e
r. Furth
e
r, d
e
pen
d
i
n
g
o
n
(5
) an
d from
th
e eigh
t allo
wab
l
e switch
i
n
g
states
o
f
the
activ
e filter
(n
=1… 7
)
,
th
e co
nv
ersion
o
f
[
nk
sw
]
to
[
nk
ss
] is g
i
v
e
n
by th
e fo
llowing:
1
1
22
3
3
21
1
12
1
11
2
n
n
n
ss
s
w
s
ss
w
s
w
ss
(6
)
Note t
h
at [
nk
ss
]
h
as
n
o
ze
ro
-se
que
nce c
o
m
pone
nt
12
3
(.
,
0
)
nn
n
ie
ss
ss
ss
On
t
h
e ot
he
r h
a
nd
, Anal
y
s
i
s
of
t
h
e dc
c
o
m
pone
nt
of
t
h
e
sy
st
em
gi
ves:
3
1
11
dc
dc
k
s
k
m
dV
is
w
i
dt
C
C
(7
)
It can be
shown that,
33
11
ks
k
n
ks
k
km
s
wi
s
s
i
(8
)
An
d i
t
ca
n
be
v
e
ri
fi
ed t
h
at
:
3
1
1
dc
nk
s
k
m
dV
s
si
dt
C
(
9)
An
d, usin
g
12
3
0
ss
s
ii
i
and [
nk
ss
]
in the func
tions leads to t
h
e dif
f
ere
n
tial equatio
n
on th
e dc side as
sho
w
n belo
w:
12
1
1
2
1
11
(2
)
(
2
)
dc
nn
s
n
n
s
dV
s
ss
s
i
s
s
s
s
i
dt
C
C
(1
0)
From
this resul
t
, active filter i
n
the
‘abc’ referential obtains
it com
p
lete
m
o
del by
usi
n
g (4) for phases ‘1’ and
‘2
’, a
n
d
(1
0):
Evaluation Warning : The document was created with Spire.PDF for Python.
I
JPEDS
I
S
SN:
208
8-8
69
4
Closed
Loop N
o
n Linear Control
of
Shunt
Hybrid Power Filter for
Harm
onics Mitigation i
n
… (A.Arivarasu)
18
9
1
11
1
2
22
2
12
1
1
2
1
(2
)
(
2
)
s
ss
s
n
d
c
s
ss
s
n
d
c
dc
nn
s
n
n
s
di
LR
I
s
s
V
E
dt
di
LR
I
s
s
V
E
dt
dV
C
s
s
s
s
i
ss
ss
i
dt
(1
1)
The interaction betwee
n the
three phases indicates
the disadva
ntage
of the ‘abc
’ m
odel. There
f
o
r
e
,
for achieving control, this
m
odel
can
be converted to ‘dq’ refere
nce fram
e. T
h
e
positive-sequence
com
pone
nts a
r
e m
a
de consta
nt be
cause
o
f
tim
e
-vary
ing
trans
f
orm
ation, an
d t
h
ere
is
no
interactio
n
effect
between the phases at the
swit
chin
g state
dec
i
sion le
vel.
2.
3.
2.
The Model Tr
ans
f
orm
e
d into
the
‘dq’
Reference Fr
ame
Using
Park’s transform
a
t
i
on, t
h
e
three-phase quantities
are
converted t
o
a
‘dq’
reference fram
e. The
general transform
a
t
i
on m
a
trix is:
12
3
co
s
c
o
s
(
2
3
)
co
s(
4
3
)
si
n
s
i
n
(
2
3
)
si
n
(
4
3
)
dq
PT
(1
2)
Whe
r
e
θ
=
ω
t
repre
sents the actual phase a
ngl
e of the l
i
ne volta
ge
space vect
or a
n
d
12
3
1
1
2
3
12
3
()
(
)
dq
T
dq
dq
PT
PT
P
T
coordinate m
a
trix transform
a
tion.
The sy
nch
r
on
o
u
s
‘d
q’
f
r
am
e obtained
f
rom
the tra
n
s
f
o
r
m
e
d m
odel is de
n
o
t
ed as:
d
s
s
d
nd
dc
s
q
d
q
s
s
q
nq
dc
s
q
q
dc
nd
d
n
d
q
di
L
RI
s
s
V
L
i
E
dt
di
L
Ri
s
s
V
L
i
E
dt
dV
Cs
s
i
s
s
i
dt
(1
3)
The
res
u
ltant
m
odel from
th
e sy
nc
hr
on
o
u
s
ort
ho
g
onal
rota
ting
fram
e
is d
e
note
d
as
f
o
llo
ws:
0
0
sn
d
ss
dd
d
nq
s
qq
q
ss
dc
dc
nd
nq
Rs
s
LL
ii
E
ss
R
d
ii
E
dt
L
L
VV
ss
ss
(1
4)
The m
odel given in (1
4
)
has no
nlinea
r natu
re b
eca
use of t
h
e m
u
ltiplication term
s prese
nt betwee
n
the state
varia
b
les {i
d
, i
q
, V
dc
} and t
h
e i
n
puts {ss
nd
, ss
nq
}.
Ho
we
ver
,
this
m
odel is inde
p
e
nde
nt
of
tim
e f
o
r
a
give
n s
w
itchin
g
peri
od
.
Her
e
, these
th
ree
va
riables s
h
o
u
ld
ha
ve a
n
i
nde
pe
nde
nt c
o
ntr
o
l. T
h
ere
f
or
e, the
currents i
d
and
i
q
sho
u
ld
be m
a
de to
f
o
llo
w a
refe
re
nce c
u
r
r
e
nt {i
d
, i
q
}
of
v
a
ry
ing
nat
ure
.
F
or
m
a
intaining t
h
e
perform
a
nce of the active
f
ilter in a com
p
ensatory m
a
nner, the
DC
voltage level
V
dc
is adjusted to a set
point
whe
n
t
h
ere
are
dy
nam
i
c variations
.
2.
3.
3.
Current Controller
In
the c
u
r
r
e
n
t loo
p
,
o
n
e
has
th
e f
o
llowi
ng
ex
pressi
o
n
s f
o
r s
w
itchin
g
fu
nctions
ss
nd
an
d s
s
nq
as:
1
1
d
nd
s
s
d
s
q
d
dc
q
nq
s
s
q
s
d
q
dc
di
s
sL
R
i
L
i
E
Vd
t
di
s
sL
R
i
L
i
E
Vd
t
(1
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
85 –
19
4
19
0
Let,
d
d
qq
di
u
dt
di
u
dt
u
d
and u
q
ca
n be use
d
t
o
c
o
n
t
rol
t
h
e cu
rre
n
t
s i
d
and i
q
. An
in
tegrator is ad
d
e
d
fo
r atten
u
a
ting
to
track
the
st
eady
-
st
at
e er
ro
r w
h
i
c
h i
s
u
s
ed as a t
r
ac
ki
ng c
o
nt
rol
l
e
r
.
It
i
s
desi
g
n
ed
by
usi
n
g t
h
e
f
o
l
l
o
wi
ng e
x
pr
essi
ons
[1
3]
:
*
~~
*
~~
dd
dp
d
i
d
qq
qp
q
i
q
di
d
i
uk
i
k
i
d
t
dt
dt
di
di
uk
i
k
i
d
t
dt
dt
Whe
r
e
~~
**
dd
d
q
q
q
ii
i
a
n
d
i
i
i
are
curre
nt errors and
**
{,
}
dq
ii
are the refe
rences
of
{,
}
dq
ii
co
rr
esp
ond
ing
l
y. Th
e pr
opo
r
t
i
o
n
a
l
(k
pc
) a
n
d i
n
teg
r
al (
k
ic
)
gai
n
s a
r
e
obt
ai
ne
d
as f
o
l
l
o
ws:
2
2
2
p
cn
ic
n
k
k
Whe
r
e
is
the da
m
p
ing factor, and
n
is th
e cu
rren
t
loo
p
n
a
t
u
ral an
gu
lar frequen
c
y.
2.
3.
4.
D
C
Vo
lta
g
e Reg
u
lat
i
on
To
m
a
in
tain
co
n
s
i
d
erab
le lev
e
l of
V
dc
ac
ross the
SAPF
dc capacitor,
t
h
e losses t
h
rough the active
p
o
wer filter’s
resistiv
e–
ind
u
ctiv
e bran
ch
es can
b
e
m
a
n
a
g
e
d b
y
wo
rk
ing
o
n
th
e source curren
t.
Id
eally, it
m
u
st
wo
rk
o
n
t
h
e ac
t
i
v
e com
pone
n
t
of c
u
r
r
e
n
t
i
d
.
For
t
h
i
s
pu
r
pos
e, an
o
u
t
e
r c
o
n
t
rol
l
o
op
i
s
de
s
i
gne
d
by
usi
n
g
a PI
regu
lato
r:
**
()
(
)
dc
p
d
c
d
c
i
dc
dc
Ik
V
V
k
V
V
d
t
(1
6)
The cl
osed-loop tra
n
s
f
er
funct
i
on
of
th
e ou
ter lo
op
is g
i
v
e
n as fo
llo
ws:
2
2
2
pv
v
d
c
iv
v
d
c
kC
kC
.
Whe
r
e
is
the da
m
p
ing factor, and
v
is th
e
o
u
t
er loop
n
a
tu
ral
an
gu
lar frequ
e
ncy.
Fig
u
re
2
.
Con
t
ro
l strateg
y
of sh
un
t activ
e power filter
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPE
DS
ISS
N
:
2
0
88
-
8
6
9
4
Closed
Loop N
o
n Linear Control
of
Shunt
Hybrid Power Filter for
Harm
onics Mitigation i
n
… (A.Arivarasu)
19
1
2.
4.
Modeling
of s
hunt p
a
ssive
p
o
wer filter
The
passi
ve
power
filter is t
uned t
o
elim
in
ate 5
th
an
d
7
th
ha
rm
onics.Th
e
pa
ram
e
ters are selecte
d
base
d on
the fo
llowin
g
e
x
p
r
es
sion
.
/
lc
hX
X
Whe
r
e h
is
t
h
e harm
onics nu
m
b
er,
X
l
and X
c
are reacta
n
ce
of passi
ve ele
m
ent.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
The
pr
o
p
o
s
ed
cont
rol st
rateg
y
has
bee
n
si
m
u
lated u
n
d
er
M
A
TL
AB
-Si
m
ulink e
nvi
ro
nm
ent and its
per
f
o
r
m
a
nce is verified
. The
no
nlinea
r
load
consists of two thr
ee-
pha
se re
ctifier, so th
at the effective
n
e
ss of
the control schem
e
to com
p
ensate
for unbalanced load was test
ed. T
h
e rectifiers a
r
e feedi
ng
R
–
L
-ty
p
e
circuits.F
or
va
riation i
n
loa
d
s; the T
H
D
is
obtaine
d
by
a
n
aly
z
ing the
so
urce
cu
rre
nt
w
a
vef
orm
s deter
m
ined
fr
om
the results of sim
u
lation
. The m
a
in ob
jective of the
sim
u
lation is
m
a
de to analy
ze differe
nt aspects
such
as: reactive powe
r c
o
m
p
ensation and
harm
onic load c
u
rr
ents c
o
m
p
ensatio
n; fo
r
v
a
riations in l
o
ad the
cor
r
es
po
n
d
in
g
dy
nam
i
c resp
o
n
se
of
the
S
H
P
F
.S
om
e results are
p
r
esente
d
to dem
onst
r
ate the
per
f
orm
ance o
f
no
n
-
linear
fu
n
c
tion-
base
d c
o
ntr
o
l schem
e
. The sim
u
lation
results a
r
e sh
ow
n in
Fig
ure
3-
6.
The
par
a
m
e
ters
taken i
n
th
ese s
i
m
u
lations are
sho
w
n
belo
w i
n
Ta
ble
1.
Table 1. Shunt Hybri
d
Filter Param
e
ters
PARAMETERS
VALUE
L
i
ne voltage and fr
equency
V
s
=230V(
r
m
s
)
,
f
s
=50Hz
Active filter para
meters
R=0.01
Ω
,L=0
.1
mH
C
dc
=750
uF,
V
dc
=700V
Non Linear
Load
R
1
=10
Ω
,L
1
=10
m
H
R
2
=10
Ω
,L
2
=10
m
H
Regulator
K
pc
=7K
ic
=800
K
p
v
=4.5K
iv
=30
Series el
e
m
ents
R=0.01
Ω
,L=3
m
H
Passive ele
m
ents
L
5
=13
m
H C
5
=30uF
L
7
=6
.5
m
H
C
7
= 30
uF
Figu
re
3 s
h
o
w
s the sy
stem
perf
orm
ance wit
h
o
u
t
hy
bri
d filt
er. T
h
e T
H
D l
e
vel o
f
voltage
an
d cu
rr
ent
bef
ore c
o
m
p
en
sation are s
h
o
w
n i
n
Fig
ure
4
.
The c
u
r
r
ent T
HD le
vels are
obs
er
ved t
o
be
18
.2%
.v
oltag
e
THD
were
2.
2
5
%.T
h
e c
u
r
r
ent T
H
D levels a
r
e o
b
ser
v
e
d
to
be
8.
71
%,
voltage
TH
D we
re
1.
71
% with
o
n
ly
passi
v
e
filter being installed. The
waveform
and THD le
vel are shown in Figure 5 a
nd
6 respectively. The current
THD le
vel after com
p
ensation
red
u
ce
d to 1.
32
% an
d v
o
ltage TH
D lev
e
l to 0.4%
wh
ich can be see
n
wi
t
h
waveform
and
THD level i
n
Figure
7 an
d 8. The
dynam
i
c
perform
a
nce of filte
r
is seen in
Figure 7. It can be
obs
er
ved
that t
h
ere
is sm
ooth
cha
n
geo
v
er
f
r
o
m
one l
o
ad
v
a
lue to
an
othe
r
val
u
e,T
h
e
DC
b
u
s
v
o
ltage
o
f
SA
PF
settles to its st
eady-state value within two cycle of sine
wave. From
these results,
it can be concl
uded that
SHP
F
of
fers
a very
g
o
o
d
dy
n
a
m
i
c
perf
orm
ance fo
r
a step
p
e
d
loa
d
c
u
rre
nt
.
Figu
re
3.
V
o
ltage a
n
d
cu
rre
nt
wave
f
orm
bef
o
re c
o
m
p
ensatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
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088
-86
94
I
J
PEDS
Vo
l.
5
,
No
.
2
,
Octob
e
r 201
4 :
1
85 –
19
4
19
2
Figu
re
4.
C
u
rre
nt an
d
V
o
ltage
THD
b
e
f
ore
co
m
p
enstion
Figure
5. Voltage and current
waveform
with passi
ve
filter
Figure 6.
Current
and Voltage THD
wit
h
passive
filter
Figu
re
7.
V
o
ltage a
n
d
cu
rre
nt
wave
f
orm
after com
p
ensatio
n
0
2
4
6
8
10
5
10
15
20
25
30
Ord
e
r of
Ha
rm
oni
c
M
a
gni
t
ude
bas
e
d
on "
B
as
e P
eak
"
-
P
a
r
a
m
e
t
e
r
P
e
ak
M
a
gn
i
t
u
de S
pec
t
r
u
m
c
a
l
l
ed by
S
i
m
u
l
i
n
k
T
o
t
a
l
RM
S
=
2
1
.
9
347
21.
9794
21.
9387
D
C
=
0.
0681
0.
0039
0.
07
2
F
und.
R
M
S
=
2
1
.
4
2
2
2
1
.
4
6
89
21.
425
Har
m
.
R
M
S
=
4
.
713
9
4
.
709
9
4
.
719
4
A
C
RM
S
=
21.
9346
21.
9794
21
.
938
6
0
2
4
6
8
10
50
100
150
200
250
300
350
O
r
der
of
Har
m
oni
c
M
agni
t
ude
bas
ed
on "
B
as
e P
eak
"
-
P
a
r
a
m
e
t
e
r
Peak
M
agn
i
t
u
d
e Spec
t
r
u
m
ca
l
l
e
d
b
y
Si
m
u
l
i
n
k
T
o
ta
l
R
M
S
= 2
4
8
.2
2
4
8
.
5
2
4
8
D
C
=
0
.
7
0
.
4
1
.
1
F
und.
R
M
S
=
248.
1
248.
5
24
7.
9
H
a
r
m
.
R
M
S
=
5
.
4
4
.
8
5
.
4
A
C
RM
S
=
248.
2
248.
5
24
8
0
1
2
3
4
5
6
7
8
9
10
0
50
10
0
15
0
20
0
25
0
30
0
35
0
O
r
d
e
r o
f
H
a
rm
o
n
i
c
M
agni
t
ude bas
ed
o
n
"
B
as
e P
eak
"
-
P
a
r
a
m
e
t
e
r
P
eak M
agn
i
t
u
de
Spect
r
u
m
cal
l
ed by
S
i
m
u
l
i
n
k
T
o
t
a
l
RM
S
=
2
5
4
.
16
91
254
.
1
063
2
53.
66
3
D
C
=
0
.
4
0
7
2
0
.
4
9
5
9
0
.
9
0
3
1
F
u
nd
.
RM
S
=
254
.
1
549
25
4.
0
8
9
7
2
53.
647
1
Har
m
.
RM
S
=
2
.
65
12
2.
8
5
3
5
2
.
68
83
A
C
RM
S
=
25
4.
1
6
8
7
2
54.
10
58
2
5
3
.
66
14
0
2
4
6
8
10
10
20
30
40
50
60
O
r
der
of
H
a
rm
oni
c
M
a
gni
t
ude
bas
ed
on "B
as
e P
eak
" -
P
a
r
a
m
e
t
e
r
Peak
M
a
g
n
it
u
de
S
p
e
c
t
r
u
m
ca
l
l
ed
by
S
i
m
u
l
i
n
k
T
o
t
a
l
R
M
S
=
41.
214
41
.
1229
41.
165
7
D
C
=
0
.
0359
0.
141
4
0.
10
55
F
u
nd.
R
M
S
=
41.
1144
41
.
0208
41.
06
27
H
a
r
m
.
R
M
S
=
2.
8624
2.
893
2.
9092
A
C
R
M
S
=
41.
2139
41
.
1226
41.
165
6
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPE
DS
ISS
N
:
2
0
88
-
8
6
9
4
Closed
Loop N
o
n Linear Control
of
Shunt
Hybrid Power Filter for
Harm
onics Mitigation i
n
… (A.Arivarasu)
19
3
Figu
re
8.
C
u
rre
nt T
H
D
be
fo
re
and
after
com
p
ensatio
n
4.
CO
NCL
USI
O
N
The
Shunt Hybrid Power Filter
ba
sed on non-linear f
unction control has been
proposed and
sim
u
lated un
d
e
r M
A
TL
AB
envi
ro
nm
ent to eval
uate the
dy
nam
i
c perform
ance fo
r v
a
ry
ing
voltag
e
-so
u
r
ce
ty
pe of
no
nline
a
r load c
o
nditions
. Fr
om
sim
u
lated res
u
lts
, it has also bee
n
sho
w
n that the
contr
o
l strateg
y
has
a fast dy
nam
i
c resp
o
n
se
du
ri
ng la
rge l
o
a
d
v
a
riations a
n
d is
capa
b
le o
f
m
a
intaining the THD
of
the
voltage at
PCC and the
s
u
pply curre
nts
well below t
h
e
m
a
rk of 5%
specified
in
the IEEE-519 standard.
ACKNOWLE
DGE
M
ENTS
The authors thank Del
phi
-TVS,M
annur t
o
carry
out t
h
e
proj
ect work
on power quality.
REFERE
NC
ES
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sa
ki,
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c
h
ida
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w
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ani, H Kan
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a
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Al-Haddad, F
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n
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ontrol t
echn
i
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a
nc
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y
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ce
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e power f
ilter.
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lectri
c Power Ap
plications.
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.
0
2
4
6
8
10
50
10
0
15
0
20
0
25
0
30
0
35
0
O
r
d
e
r
of
Ha
r
m
oni
c
M
a
gni
t
ud
e b
a
s
ed
on
"
B
as
e
P
e
ak
"
-
P
a
r
a
m
e
t
e
r
P
e
ak
M
a
gn
i
t
u
d
e S
p
ect
r
u
m
cal
l
ed by
Si
m
u
l
i
n
k
T
o
ta
l
R
M
S
=
2
4
7
.9
2
4
7
.
4
2
5
2
.
5
D
C
=
4
.
4
2
.
1
6
.
5
H
a
r
m
. R
M
S
=
2
4
.6
2
6
.
1
2
4
.9
A
C
R
M
S
=
2
4
7
.
9
2
4
7
.
4
2
5
2
.5
Fu
n
d
.
R
M
S
=
2
4
6
.6
2
4
6
.
1
2
5
1
.
2
0
2
4
6
8
10
5
10
15
20
25
30
O
r
d
e
r
of H
a
r
m
on
i
c
M
a
gn
i
t
u
d
e b
a
s
ed o
n
"
B
as
e P
e
a
k
"
-
P
a
r
a
m
e
ter
P
e
ak
M
a
g
n
i
t
u
d
e S
p
ec
t
r
u
m
c
a
l
l
ed
b
y
S
i
mu
l
i
n
k
T
o
t
a
l
R
M
S
=
23.
5
6
0
1
23.
3
681
23.
0
225
D
C
= 0
.
1
3
2
2
0
.
1
0
7
3
0
.
0
2
4
9
F
u
n
d
. R
M
S
= 2
3
.
4
1
4
6
2
3
.
2
1
2
4
2
2
.8
8
5
H
a
r
m
.
R
M
S
=
2.
6
109
2
.
69
05 2.
5
127
A
C
R
M
S
= 2
3
.
5
5
9
7
2
3
.
3
6
7
8
2
3
.
0
2
2
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
5
,
No
.
2
,
Octob
e
r 201
4 :
1
85 –
19
4
19
4
BIOGRAP
HI
ES OF
AUTH
ORS
A.Arivarasu was born in Vellore, Tamil Nadu
,
India in 1991
.He is currently pursuing hi
s
M
.
Tech
(Int
e
gr
ated)
P
o
wer s
y
s
t
em
s
in S
A
S
T
RA Univers
i
t
y
,
Than
javur,
Ind
i
a.His
r
e
s
ear
ch
inter
e
sts inc
l
ude
Power quali
t
y
i
m
p
r
ovements, Generati
on Optimization.
K.Muthukumaris currently
w
ith
the dep
a
rtment of
Electr
ical an
d Electronics an
d Engineering
,
S
A
S
T
RA Univers
i
t
y
, Than
javur
, India, as
As
s
i
s
t
ant P
r
ofes
s
o
rHe receiv
e
d M
.
Tech degr
ee in
power s
y
stems from Annamalai
University
; Thanja
vur, India in
2004.He is purs
u
ing his PhD in
ele
c
tri
cal
engin
e
ering in S
A
S
T
R
A
Univers
i
t
y
. H
i
s
res
ear
ch int
e
r
e
s
t
s
includ
e los
s
m
i
nim
i
zation
techn
i
ques in
po
wer distribu
tion
s
y
stems
R.Balasubramanian was born in Th
ennamanadu
,
Tamilnadu
,
India, in 1977
. He receiv
e
d the B
.
E
degree in
electrical and electron
ics engineering
from the University
of Madras,
India, in 1999
and the M
.
Te
c
h
degree in co
ntrol s
y
s
t
em
s
a
nd Instrumentation from SAST
RA University
,
Thanjavur, India in 2006
.
He is currently
with the depar
tment of Elect
r
i
c
a
l and El
ect
roni
cs
a
nd Engineer
ing, SASTR
A
Univers
i
t
y
, Th
an
javur, Indi
a,
as
As
s
i
s
t
ant P
r
ofess
o
r. His
res
earch
interes
t
s
inc
l
ude
P
o
wer qualit
y
improvements, control s
y
s
t
em
s
a
nd P
o
wer el
ec
tro
n
ics
.
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