Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
3, No. 4, Decem
ber
2013, pp. 374~
383
I
S
SN
: 208
8-8
6
9
4
3
74
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
Shunt Active Power Filter Syst
em Design for Inter-harmonic
Z
h
ang Ch
ao
1
, Z
h
ang Yi
-
J
un
2
, Ren
Z
i
-Hui
1
, Ma
X
i
ao-
Ping
1
1
School of In
for
m
ation and
Electrical Eng
i
neerin
g, CUMT
2
Longkou Miner
a
l Group Co
.
Ltd, 265700
Long
kou, Chin
a
e-m
a
il:
di
y
007_z
@163.com
,
lun
w
enzzz@163
.co
m
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 12, 2013
Rev
i
sed
Sep
22
, 20
13
Accepte
d Oct 8, 2013
Given the comp
lex situations of
the gr
id with i
n
ter-harm
onics
, three-
leve
l
m
odel of shunt activ
e power f
ilter (SAPF) was built. For the harm
onics
accur
a
t
e
det
e
c
t
i
on, the CPT pr
i
n
cipl
e was used to det
ect
the f
undam
e
nta
l
component of the grid.
The
inter-harm
onics, p
a
rameter
fluctuation of APF
and the deadb
a
n
d
effect wer
e
co
nsider
ed as the
non-periodic disturbance to
the
controller
.
To eliminate th
e non-
per
i
odic
disturbance imp
act on th
e
controller and to
improve the control
s
y
stem per
f
ormance, equ
i
v
a
len
t
input-
disturbance (EI
D
) was used based on th
e tr
adi
tional
rep
e
ti
tive
contro
lle
r
.
W
ith Matlab an
d three-l
e
ve
l tes
t
platform
, th
e
SAPF control system
was
built.
The perfo
rm
ance of dete
ction and com
p
ensation for har
m
onic and
inter-h
armonic
was verified b
y
the simulation
an
d exper
i
ment.
Keyword:
conservative powe
r
t
h
eory
equi
val
e
nt
i
n
p
u
t
-
di
st
ur
ba
nce
i
n
t
e
r-
harm
oni
c
rep
e
titiv
e co
n
t
ro
l
Copyright ©
201
3 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
:
Z
h
an
g Ch
ao
Sch
ool
o
f
I
n
fo
r
m
at
i
on an
d El
e
c
t
r
i
cal
En
gi
nee
r
i
n
g
Ch
in
a
Un
iv
ersity o
f
Min
i
n
g
an
d Tech
no
log
y
(CUMT)
丁
11
Xu
ey
u
a
n Rd
, Haid
ian
,
B
e
ij
in
g,
C
h
in
a
Em
a
il:
diy
007_
z@163.com
1.
INTRODUCTION
Int
e
r
-
h
arm
oni
c
m
eans t
h
at
harm
oni
c com
ponent
s w
h
i
c
h fr
eque
ncy
i
s
not
equal
t
o
t
h
e f
u
n
d
am
ent
a
l
and m
u
ltiple fundam
ental freque
ncy [1].
W
i
t
h
the a
ppl
i
cation of
HVDC equipm
en
t, electric arc furnaces,
con
v
e
r
t
e
rs a
n
d
ot
her
p
o
we
r
el
ect
roni
c e
qui
pm
ent
s
, i
n
t
e
r-
harm
oni
cs we
r
e
pr
od
uce
d
[
2
,
3]
. Int
e
r-
har
m
oni
cs
have sim
ilar hazards
with ha
rm
onics. More
seriously, th
e
y
also can cause voltage
flicker a
nd im
pact torque
[4
]. As freq
u
e
n
c
ies
of
in
ter-h
a
rm
o
n
i
cs h
a
ve
always
b
e
en ch
an
g
e
d
with d
i
fferen
t op
eratin
g
co
nd
ition
s
of
harm
oni
c s
o
u
r
ce eq
ui
pm
ent
s
, i
n
t
e
r-
ha
rm
oni
cs i
s
di
ffi
cult t
o
be acc
urately detected and e
l
iminated.
SAP
F
has
bee
n
wi
del
y
use
d
t
o
resol
v
e ha
r
m
oni
c pol
l
u
t
i
o
n i
ssues
. Fo
r t
h
e desi
gn
of S
A
PF
, di
f
f
ere
n
t
gri
d
e
nvi
r
o
nm
ent
s
a
nd l
o
a
d
req
u
i
r
em
ent
s
sho
u
l
d
be
co
ns
i
d
ere
d
.
SAP
F
sho
u
l
d
be
abl
e
t
o
r
u
n at
di
ff
eren
t
com
p
l
e
x gri
d
envi
ro
nm
ent
s
, and
d
o
n
o
t
m
a
ke i
n
t
e
r
f
ere
n
ce
to
th
e grid
.
At p
r
esen
t,
the
research
focuse
s of
i
n
t
e
r-
harm
oni
c
are
o
n
t
h
e
det
ect
i
on m
e
t
hod
.
The
ha
rm
oni
c su
pp
ressi
on
m
e
t
h
o
d
, i
s
m
a
i
n
ly
use
d
wi
t
h
pa
ssi
ve
filters. Th
e
way th
at u
s
i
n
g SAPF to
elim
in
ate in
ter-
h
a
rm
o
n
i
c con
t
en
t was less stud
ied.
And
ex
isting
harm
o
n
i
c
det
ect
i
o
n
an
d
cont
rol
m
e
t
h
o
d
s
of
S
A
PF
a
r
e
not
e
ffect
i
v
e f
o
r i
n
t
e
r
-
ha
r
m
oni
cs envi
ro
nm
ent
[5]
.
So
,
i
t
i
s
si
gni
fi
ca
nt
t
o
do t
h
e resea
r
c
h
f
o
r t
h
e i
n
t
e
r
-
ha
rm
oni
cs an
d ha
rm
oni
cs d
e
t
ect
i
on an
d com
p
ensat
i
on
m
e
t
hods
base
d on
S
A
P
F
.
C
u
r
r
ent
l
y
,
det
ect
i
on m
e
t
hods
of
ha
rm
oni
cs a
n
d
i
n
t
e
r
-
harm
oni
cs
can
be
di
vi
de
d i
n
t
o
t
w
o
cat
ego
r
i
e
s:
fre
que
ncy
-
d
o
m
ai
n and t
i
m
e-d
o
m
a
i
n
. Har
m
oni
c curre
nt
can
be o
b
t
a
i
n
ed
by
f
r
e
que
ncy
-
dom
ai
n d
e
t
ect
i
on
m
e
t
hods
[
6
-
9
]
.
B
u
t
t
h
ese m
e
t
h
o
d
s a
r
e c
h
a
r
act
eri
zed
by
l
a
rge
am
ount
of
cal
cul
a
t
i
o
n,
an
d
p
o
o
r
rea
l
-t
im
e
per
f
o
r
m
a
nce. The exi
s
t
i
n
g t
i
m
e-dom
ai
n de
t
ect
i
on m
e
t
hod
s are base
d o
n
no
n-si
n
u
soi
d
a
l
po
wer t
h
e
o
ry
, an
d
they are applicable fo
r SAPF. These m
e
thods are sim
p
le in
structur
e, a
n
d they are wi
dely used. T
h
ere a
r
e two
t
y
pes of com
m
onl
y
use
d
t
i
m
e
-d
om
ai
n det
ecti
on m
e
t
hods w
h
i
c
h ba
sed
on t
h
e p
o
we
r t
h
e
o
r
y
, t
h
e i
n
st
ant
a
n
e
ou
s
po
we
r the
o
ry
and
the
Fry
z
e
po
we
r the
o
ry
.
The
ha
rm
onic
current
can not be acc
urat
ely detected by
method
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
hun
t Active Po
wer Filter System Design
fo
r In
ter-h
a
r
mo
n
i
c (Zha
ng
C
h
ao)
37
5
with
trad
itio
n
a
l in
stan
tan
e
ou
s reactiv
e
po
wer th
eo
ry
(p-q
t
h
eory)
when three
-
phase
vol
t
age is
unbalance and
wave
f
o
rm
i
s
di
st
ort
e
d
[
1
0
]
.
H
a
rm
oni
c and
r
eact
i
v
e cu
rre
nt
det
ect
i
on
p
r
o
b
l
e
m
s
can be
sol
v
e
d
by
u
n
i
v
ersal
in
stan
tan
e
ou
s
p
o
wer th
eo
ry
an
d
its im
p
r
ov
ed algo
r
ithm whe
n
t
h
e three-phase
voltage is unbalance and
wave
f
o
rm
i
s
di
st
ort
e
d [
1
1
,
12]
. FB
D m
e
tho
d
wa
s p
r
o
p
o
se
d by
Fry
z
e
,
an
d im
pro
v
e
d
by
B
u
c
h
h
o
l
z
and
Dpe
n
br
oc
k. B
y
separat
i
ng t
h
e curre
nt
wi
t
h
conce
p
t
o
f
eq
u
i
val
e
nt
co
nd
uc
t
a
nce, t
h
e p
h
y
s
i
cal
m
eani
ng of t
h
e
current c
o
m
ponent
was disc
ussed.
And c
o
m
p
are
d
to th
e traditional insta
n
tane
ous
powe
r de
finition, without
coo
r
di
nat
e
t
r
ansf
orm
a
t
i
on, F
B
D
m
e
t
hod w
a
s charact
eri
z
e
d
by
a rel
a
t
i
v
el
y
sim
p
l
e
al
gori
t
h
m
[13,
14
]
.
The
i
n
st
ant
a
ne
o
u
s
po
we
r was
de
fi
ne
d by
C
P
T
(co
n
ser
v
at
i
v
e
po
wer t
h
eo
ry
) i
n
t
h
e t
h
ree pha
se u
nbal
a
n
ce and
di
st
ort
i
o
n sy
st
em
[15]
. C
o
m
p
are
d
t
o
t
h
e
p
-
q
po
wer t
h
eo
ry
and FB
D p
o
we
r t
h
e
o
ry
, t
h
e u
n
b
a
l
a
nce
d
and
distortion c
u
rrent is
m
o
re accurately express
e
d by CPT th
e
o
ry [16, 17]. Bu
t it needs furt
her st
udy for t
h
e grid
with
in
ter-h
a
rm
o
n
i
cs situ
atio
n
.
Th
e
p
e
riod
ic referen
ce si
g
n
a
l o
r
th
e p
e
riod
ic in
terferen
ce sign
al
will b
e
con
t
ro
lled
b
y
rep
e
titive
co
n
t
ro
l m
e
th
od
.
An
d
wh
en
i
t
co
m
b
in
ed
wi
th
PI co
n
t
ro
l,
o
r
pred
ictiv
e co
n
t
ro
l, th
e PWM con
v
e
rter can
g
e
t
b
e
tter con
t
ro
l p
e
rform
a
n
ce fo
r cu
rren
t. B
u
t
rep
e
titiv
e contro
l p
e
rfo
r
m
a
n
ce for no
n-p
e
rio
d
i
c sign
al, or no
n-
peri
odi
c i
n
t
e
r
f
e
rence si
g
n
al
i
s
po
or. T
h
ere
f
ore
,
i
t
i
s
im
port
a
nt
t
o
im
prov
e t
h
e cont
r
o
l
sy
st
em
for bet
t
er no
n
-
p
e
ri
o
d
i
c con
t
rol p
e
rfo
r
m
a
n
ce. Th
ere are two ways to
i
m
p
r
ov
e th
e p
e
rforman
ce,
HORC (h
igh
-
o
r
d
e
r repetitiv
e
co
n
t
ro
ller) [18] an
d
ad
ap
tiv
e
rep
e
titiv
e co
n
t
ro
ller [19
]
.
Th
ou
gh
t
h
e co
n
t
rol p
e
rform
a
n
ce can
b
e
im
p
r
oved
b
y
these m
e
thods, the com
p
lexity of th
e syste
m
will be increased, a
n
d it w
ill be difficult to achieve s
y
ste
m
stab
ility. If we co
n
s
ider th
e
n
on-p
e
riod
ic sig
n
a
ls as in
terferen
ce, th
e d
i
stu
r
b
a
n
ce
o
b
serv
er can
b
e
u
s
ed
to
i
m
p
r
ov
e th
e
no
n-p
e
riod
ic con
t
ro
l p
e
rfo
r
m
a
n
ce of
rep
e
titiv
e con
t
ro
ller.
EID
(eq
u
i
v
a
len
t
in
pu
t
d
i
stu
r
b
a
n
c
e)
obs
er
ver [
2
0]
i
s
di
ffere
nt
wi
t
h
t
h
e usu
a
l
d
i
st
urba
nce o
b
s
e
rve
r
, w
h
i
c
h i
s
not
base
d o
n
t
h
e i
nve
rse
sy
st
e
m
t
h
eo
ry
,
but
bas
e
d
on
a
n
act
i
v
e di
st
u
r
bance
r
e
ject
i
o
n m
e
t
hod.
Thi
s
m
e
t
hod
i
s
si
m
p
l
e
t
o
i
m
pl
em
ent
and
can
b
e
use
d
f
o
r re
peat
edl
y
co
nt
r
o
l
l
e
r
t
o
i
m
prove
t
h
e
no
n
-
pe
ri
o
d
i
c
di
st
ur
bance
re
jec
t
i
on
per
f
o
r
m
a
nce.
In
th
is p
a
p
e
r, th
e m
o
d
e
l o
f
th
ree-lev
e
l SAPF
was bu
ilt. SAPF
d
i
rectiv
e h
a
rm
o
n
i
c cu
rren
t
d
e
tection
m
e
thod under the
inter-harm
onic
e
nvi
ronm
ent base
d on the de
finition
of
CPT powe
r
theory was studied.
Bo
th
th
e
rep
e
t
itiv
e co
n
t
ro
l an
d
PI con
t
ro
l
was used
for
th
e grid
cu
rren
t h
a
rm
o
n
i
cs an
d
i
n
ter-h
a
rmo
n
i
cs
com
p
ensat
i
o
n
.
B
y
i
n
t
r
od
uci
ng E
I
D co
nt
r
o
l
l
e
r im
pro
v
es
t
h
e SAPF co
nt
r
o
l
perf
o
r
m
a
nce fo
r n
o
n
-
p
e
ri
o
d
i
c
sig
n
a
l in
terferen
ce.
An
alysis o
f
t
h
e d
e
si
g
n
ed
system
stab
ilit
y an
d
sen
s
itiv
ity o
f
th
e issu
e.
Giv
e
s a suitab
l
e
i
n
t
e
r-
harm
oni
c
s
en
vi
ro
nm
ent
SAP
F
sy
st
em
desi
g
n
m
e
t
h
o
dol
ogy
.
Si
m
u
lat
i
on a
nd e
x
pe
ri
m
e
nt
show t
h
at
t
h
e
designe
d
system can accurately detect
harmonic, inter-ha
rm
onic
content, effective
on th
e gri
d
to c
o
m
p
ensat
e
harm
oni
cs a
n
d
i
n
t
e
r-
harm
oni
c
s
.
2.
MAT
H
EMAT
IC MODEL OF
THREE-L
E
VEL
SAPF ON VI
RTUAL
FLUX
O
R
I
E
NTED
The m
a
i
n
ci
rcui
t
t
opol
ogy
o
f
SAPF i
s
a di
ode
-cl
a
m
p
ed t
h
ree
-
l
e
vel
i
n
v
e
rt
er. T
h
ree ki
n
d
s o
f
swi
t
c
h
st
at
e can
be
o
b
t
ai
ned
by
fo
ur
swi
t
c
hes
o
f
eac
h
pha
se l
e
g
f
r
o
m
t
h
ree-l
e
vel
c
o
n
v
e
r
t
e
r,
w
h
i
c
h i
s
sh
o
w
n
i
n
Fi
gu
re
1
(a). Accord
i
n
g to
t
h
e co
ncep
t of t
h
e fl
ux in
m
o
to
r sp
eed
co
n
t
ro
l, b
y
sp
atial coord
i
n
a
te tran
sfo
r
m
a
tio
n
,
vect
o
r
di
agr
a
m
o
f
t
h
e
vi
rt
ual
-
f
l
ux
o
r
i
e
nt
ed
sy
st
em
can be
d
r
awn
as s
h
ow
n i
n
Fi
gu
re
1
(b
).
(
a
)
Th
e top
o
l
og
y of
t
h
r
e
e-
level co
nv
er
ter
.
φ
i
β
e
β
β
Ψ
β
q
I
E
I
L
I
R
s
V
i
q
i
d
i
α
e
α
Ψ
α
d
α
Ψ
ω
(b
) Vect
o
r
di
ag
ram
of
t
h
e vi
rt
ual
-fl
ux
o
r
i
e
nt
ed
syste
m
.
Fi
gu
re 1.
T
h
re
e-l
e
vel
S
A
P
F
o
n
vi
rt
ual
fl
u
x
o
r
i
e
nt
ed
.
According to
Kirc
hhoff la
w
and the
structure s
h
own in Fi
gure
1, st
ate-s
p
ace e
x
pressi
on
of SAPF in
dq
re
fere
nce
fr
am
e i
s
gi
ve
n
di
rect
l
y
by
:
Be
AX
X
Z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
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S
Vo
l.
3
,
No
.
4
,
D
ecem
b
er
2
013
:
37
4 – 383
37
6
Whe
r
e,
]
[
2
1
C
C
L
L
diag
Z
,
T
2
1
]
[
C
C
q
d
V
V
i
i
X
,
]
0
0
1
1
[
diag
B
,
T
]
0
0
2
3
0
[
m
V
e
0
0
0
0
2
2
1
1
2
1
2
1
q
d
q
d
q
q
d
d
S
S
S
S
S
S
R
L
S
S
L
R
A
3.
THE INTER-HARMONIC
D
ETECTION METHOD B
A
SED ON
CPT THEORY
3.
1.
T
h
e CPT
framew
ork
CPT
th
eo
ry, wh
ich
h
a
s b
e
en
p
u
t
forward
in
recen
t
years, is
po
wer
defin
itio
n m
e
th
o
d
und
er t
h
e
n
o
n
lin
ear tim
e
-
do
m
a
in
co
nd
i
tio
n
.
Fo
r a con
tin
uou
s
v
a
riab
le
x
(
t),
o
v
e
r
p
e
ri
o
d
T, th
e
o
r
i
g
in
al
fun
c
tio
n and
deri
vat
i
v
e fu
nc
t
i
on
ca
n be def
i
ned
a
s
f
o
l
l
o
ws
:
d
)
(
)
(
0
t
x
t
x
;
)
(
d
d
)
(
t
x
t
t
x
The
DC
c
o
m
pone
nt
i
s
defi
ne
d as:
T
t
t
x
T
x
0
d
)
(
1
C
o
n
s
id
e
r
in
g
ω
=2
π
/
T
, hom
o-
v
a
ri
abl
e
of x ca
n be defi
ned
as
:
)
(
x
x
x
;
x
x
1
No
te th
at
x
and
x
are di
m
e
nsi
o
n
a
l
l
y
hom
ogene
ous t
o
x
,
an
d t
h
ey
are eq
ual
i
n
t
h
e am
pl
i
t
ude of t
h
e
resu
ltan
t
si
g
n
a
ls, so
we called
x
,
x
and
x
t
h
e hom
o-
vari
abl
e
s. Acc
o
r
d
i
n
g t
o
t
h
e
defi
ni
t
i
on o
f
C
P
T t
h
e
o
ry
,
fo
r th
ree-
p
h
ase
sy
stem
,
act
i
v
e p
o
we
r
P
i
s
de
fi
ne
d as:
t
t
i
t
u
T
P
T
d
)
(
)
(
1
0
i
u,
Reactive powe
r Q is
defi
ned
as:
t
t
i
t
u
T
Q
T
d
)
(
)
(
1
0
i
,
u
Activ
e cu
rren
t
ia is d
e
fi
n
e
d as:
u
G
u
u
P
i
a
a
2
(
1
)
Reactive curre
nt ir is
de
fine
d
as:
u
B
u
u
Q
i
r
r
2
(
2
)
Voi
d
c
u
r
r
ent
i
v
i
s
de
fi
ne
d as:
r
a
v
-i
=i-i
i
3.
2. Th
e inter
-
harm
onic
dete
ction
method
based
on
CPT
the
o
r
y
In
ord
e
r to
u
s
e th
e CPT t
h
eory to
d
e
tect SAPF
three-phase
harm
onic c
u
rrent, ass
u
m
i
ng three
-
phase
sin
u
s
o
i
d
a
l and
b
a
lan
ce
syste
m
, with th
e i
n
itial p
h
a
se of su
p
p
ly v
o
ltag
e
wh
ich
eq
u
a
ls t
o
0
,
p
e
r
un
it vo
ltage can
be e
x
p
r
esse
d a
s
:
)
3
2
sin(
)
3
2
sin(
)
sin(
t
e
t
e
t
e
c
b
a
Whe
r
e,
e
a
,
e
b
and
e
c
a
r
e t
h
r
ee p
h
ase
per
uni
t
s
u
ppl
y
v
o
l
t
a
ge, a
n
d
ω
i
s
t
h
e a
n
gul
a
r
f
r
e
que
ncy
.
Accord
ing
to
CPT d
e
fin
ition, ho
m
o
-v
ar
iabl
e of ea ca
n
be
expresse
d as:
)
cos(
)
cos(
t
e
t
e
a
a
The t
h
ree
-
phas
e load curre
nt i
s
gi
ven by:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
hun
t Active Po
wer Filter System Design
fo
r In
ter-h
a
r
mo
n
i
c (Zha
ng
C
h
ao)
37
7
1
0
0
1
0
0
1
0
0
)
sin(
)
3
2
sin(
)
3
2
sin(
[
)
sin(
)
3
2
sin(
)
3
2
sin(
[
)
sin(
)
sin(
)
sin(
[
h
h
h
h
h
h
h
c
h
h
h
h
h
h
h
b
h
h
h
h
h
h
h
a
t
h
I
t
h
I
t
h
I
i
t
h
I
t
h
I
t
h
I
i
t
h
I
t
h
I
t
h
I
i
Wh
ere, ia, ib
an
d
ic are the thr
ee-pha
se load
current.
I is the a
m
pl
i
t
ude of
t
h
e harm
oni
c c
u
r
r
ent
.
θ
is
th
e in
itial p
h
a
se an
g
l
e
o
f
t
h
e
h
a
rm
o
n
i
c curren
t
. Su
bscrip
t
h is th
e h
a
rm
o
n
i
c n
u
m
b
e
r.
Wh
en
h
=
1
,
it indicates
t
h
e fu
n
d
am
ental
co
m
pon
ent
;
whe
n
h i
s
i
n
t
e
ger
,
i
t
m
eans
m
u
lt
i
p
l
e
fun
d
a
m
ent
a
l
freq
u
en
cy
co
m
pone
nt
s
;
whe
n
h is non-i
n
tege
r, it indicates the ha
rm
onic com
pone
nts. S
u
persc
r
ipt +, - a
nd
0 represe
n
t positive
,
ne
gative and
zero
seq
u
e
n
ce
com
pone
nt
.
Accord
ing
to
CPT d
e
fin
ition, tak
i
ng
i
n
to the vo
ltag
e
a
n
d c
u
r
r
ent
e
x
pres
si
ons
, i
t
ca
n
be c
a
l
c
ul
at
ed as:
)]}
)
1
cos((
)
)
1
cos((
[
)
2
cos(
cos
{
2
3
2
1
1
1
1
h
h
h
h
h
t
h
I
t
h
I
t
I
I
P
(3
)
If
AC co
m
p
o
n
en
t of equ
a
tio
n (1
)
was
filtered
o
f
f, lin
ear act
iv
e power can
b
e
o
b
t
ain
e
d
as:
1
1
cos
2
3
I
P
(
4
)
Not
e
t
h
at
eq
uat
i
on
(
4
) c
o
rres
p
on
ds
wi
t
h
t
h
e
f
u
n
d
am
ent
a
l
cu
rre
nt
act
i
v
e c
o
m
ponent
.
Accord
ing
to
CPT th
eo
ry, hom
o
-
v
a
riab
les
of th
ree-phase
s
u
pply
voltage
can be defi
ned as:
)
3
2
cos(
)
3
2
cos(
)
cos(
t
e
t
e
t
e
c
b
a
According to t
h
e rea
c
tive
power
de
finition
of C
P
T the
o
ry, instanta
ne
ous reactive
powe
r Q can be
obt
ai
ne
d a
s
:
)]}
)
1
sin((
)
)
1
sin((
[
)
2
sin(
sin
{
2
3
2
1
1
1
1
h
h
h
h
h
t
h
I
t
h
I
t
I
I
Q
(5
)
If
AC co
m
p
o
n
en
t of equ
a
tio
n (3
)
was
filtered
o
f
f,
lin
ear reactiv
e
po
wer
can
b
e
o
b
t
ained as:
1
1
sin
2
3
I
Q
(6)
Tak
i
ng
th
e equatio
n
(4) and
eq
u
a
tion
(6) in
t
o
equ
a
tion
(1)
an
d
equ
a
tion
(2
), th
e
fund
amen
tal po
sitiv
e
sequ
en
ce co
m
p
on
en
t can
b
e
g
o
t
b
y
t
h
e ad
d
i
tio
n
o
f
th
e two fin
a
l
equ
a
tions. Besid
e
s th
e
fund
am
en
tal p
o
s
itiv
e
seq
u
ence c
o
m
p
o
n
e
n
t
,
t
h
e
re
st
com
pone
nt
s
i
s
t
h
e S
A
PF
harm
oni
c d
e
t
ect
i
on si
g
n
al
.
B
a
sed
on C
P
T
p
o
we
r
defi
ni
t
i
on,
S
A
PF
harm
oni
c
d
e
t
ect
i
on sy
st
e
m
i
s
sho
w
n i
n
Fi
gu
re
2.
Fi
gu
re.
2
Har
m
oni
c det
ect
i
on sy
st
em
based
o
n
C
P
T
.
Consi
d
eri
ng ip-iq detecting m
e
t
hod ba
sed
on instantane
ous reactive
power the
o
ry as
a com
p
arison,
t
h
e gri
d
i
n
t
e
r
-
h
arm
oni
c det
e
ct
i
on ef
fect
of
t
h
e sy
st
em
,
whi
c
h was s
h
ow
n i
n
Fi
gu
re
2, can
be ve
r
i
fi
ed by
sim
u
l
a
t
i
on. The fu
n
d
am
ent
a
l
freq
u
ency
of t
e
st
i
ng w
a
ve was 5
0
H
z.
The harm
oni
c com
ponent
s
whi
c
h
fre
que
nci
e
s
w
e
re
80
Hz a
n
d
2
5
0
H
z,
we
re
ad
ded
at
Ti
m
e
=0.0
8s.
Th
e si
m
u
l
a
ti
on
r
e
sul
t
s
we
re s
h
ow
n i
n
Fi
gu
re 3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
3
,
No
.
4
,
D
ecem
b
er
2
013
:
37
4 – 383
37
8
The
wave
f
o
rm
i
a
an
d t
h
e
f
u
ndam
e
nt
al
det
ect
i
on
wave
f
o
r
m
s whi
c
h det
e
ct
ed by
i
p
-i
q
m
e
t
hod a
n
d
C
P
T m
e
t
hod,
were
sh
o
w
n i
n
t
h
e
Fi
g
u
re
3 (a
).
N
o
t
e
t
h
at
, bef
o
re a
d
d
i
ng t
h
e h
a
rm
oni
c com
p
o
n
en
t
,
t
h
e
fu
n
d
am
ent
a
l
d
e
t
ect
i
on wave
f
o
rm
got
by
C
P
T
m
e
t
hod can
coi
n
ci
de
wi
t
h
i
a
. B
u
t
for t
h
e
wave
f
o
rm
got
by
i
p
-i
q
m
e
t
hod,
t
h
e
r
e i
s
a cert
a
i
n
p
h
a
s
e o
ffset
,
w
h
i
c
h i
s
ca
used
by
t
h
e co
or
di
n
a
t
e
t
r
ans
f
o
r
m
a
ti
on
of
t
h
e i
n
st
ant
a
neo
u
s
po
we
r t
h
e
o
ry
.
Su
bt
ract
ed t
h
e fu
n
d
am
ent
a
l det
ect
i
on
wa
vef
o
rm
and i
a
, t
h
e
harm
oni
c com
pone
nt
can b
e
obt
ai
ne
d,
whi
c
h was s
h
o
w
n i
n
Fi
g
u
re
3 (b
).
It
can be sh
o
w
n as t
h
at
, si
n
ce t
h
ere i
s
pha
se of
fset
phe
n
o
m
enon
,
t
h
e am
pl
i
t
ude
of
ha
rm
oni
c co
m
ponent
det
ect
ed
by
i
p
-i
q m
e
tho
d
was
fi
nal
l
y
am
pl
i
f
i
e
d.
(a)
Fundam
ental detection wa
veform
.
(b
) Harm
onic detection
wa
ve
fo
rm
.
Fi
gu
re.
3
C
o
m
p
ari
s
on
o
f
c
u
r
r
e
nt
wa
ve
fo
rm
s.
4.
COMPENSATION
SYSTEM B
A
SED ON
EID AND REPETITIVE CONTROLLER
4.
1. Desi
gn of
con
t
rol
s
y
s
t
e
m
Accord
ing
to th
e three-lev
e
l
SAPF m
o
d
e
l,
b
a
se
d
o
n
t
h
e
EID and
repetitiv
e con
t
ro
l meth
od
,
SAPF
cur
r
ent
c
o
m
p
ensat
i
o
n c
ont
r
o
l
sy
st
em
was
de
si
gne
d,
as s
h
o
w
n
i
n
Fi
g
u
re
4
(a).
The SAPF com
p
ensation signal, which is the ha
rm
oni
c cur
r
ent
com
p
o
n
e
nt
s besi
de
s t
h
e fu
ndam
e
nt
al
current
com
p
onent, m
a
inly contains m
u
ltiple fund
am
ental fre
que
n
cy com
ponents.
When t
h
e c
onte
n
t of the
g
r
i
d
in
ter-h
a
rm
o
n
i
cs are o
b
v
i
ou
s, it
m
ean
s th
e co
m
p
en
satio
n
sig
n
a
l is
m
i
x
e
d
with
n
on-in
teg
e
r mu
ltip
le
fund
am
en
tal freq
u
e
n
c
y si
g
n
a
l
.
Th
ese
n
on-p
e
riod
ic sign
als can
n
o
t
b
e
con
t
ro
lled
b
y
rep
e
titiv
e con
t
ro
ller.
(a)
SAPF cu
rren
t co
m
p
en
sation
co
n
t
ro
l system
.
(b) C
o
m
p
lex
rep
e
titiv
e con
t
ro
l syste
m
.
d
ˆ
d
~
x
ˆ
(c)
EI
D c
ont
rol
sy
stem
Figure
4. T
h
e
current c
o
m
p
ensation system
of S
A
PF
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
hun
t Active Po
wer Filter System Design
fo
r In
ter-h
a
r
mo
n
i
c (Zha
ng
C
h
ao)
37
9
Co
m
p
lex
rep
e
titiv
e co
n
t
ro
l
syste
m
co
n
s
ists of im
p
r
ov
ed rep
e
titiv
e con
t
ro
ller an
d PI co
n
t
ro
ller,
wh
ich
are conn
ected
i
n
p
a
ral
l
el. Th
e periodic sig
n
a
l can
be co
n
t
ro
lled by rep
e
titiv
e con
t
ro
ller, so
th
e SAPF
com
p
ensation accuracy will
be
im
proved. And non-pe
riodic
signal
ca
n
be c
ont
rolled by PI c
ont
roller, which
can
also adju
st th
e d
e
lay time b
y
rep
e
titiv
e co
n
t
ro
ller,
so
th
e d
y
n
a
m
i
c p
e
rfo
rm
an
ce o
f
SAPF
will b
e
im
pro
v
ed
. T
h
e
cont
rol
sy
st
em
i
s
sh
ow
n i
n
Fi
g
u
re
4
(
b
)
.
W
i
t
h
th
e ag
ing
o
f
APF
d
e
v
i
ces, d
e
v
i
ces param
e
ters will
b
e
v
o
l
atile. Fu
rt
h
e
rm
o
r
e, wi
th
d
ead
b
a
nd
p
l
u
s
effect, t
h
e lo
ad
fl
u
c
tu
ati
o
n
and
o
t
h
e
r
facto
r
s, t
h
e p
e
ri
o
d
i
c an
d
no
n-p
e
ri
o
d
i
c
d
i
stu
r
b
a
n
c
es will app
ear i
n
th
e actu
a
l op
eratio
n
of SAPF. For th
e
repetitiv
e co
n
t
ro
lle
r, th
e p
e
riod
ic in
terferen
ce can
b
e
elim
in
ate
d
. B
u
t
th
e effect of no
n-p
e
riod
ic
d
i
stu
r
b
a
n
c
e con
t
ro
l
will d
e
te
rio
r
ate.
Th
is
p
a
p
e
r i
n
tro
d
u
ces th
e equ
i
v
a
lent in
pu
t
d
i
stu
r
b
a
n
ce meth
od
for
non-
p
e
r
i
od
ic signal in
ter
f
e
r
e
n
c
e sup
p
r
e
ssion
,
so
th
e ro
bu
st
ness of
SA
PF
cu
rr
en
t
com
p
ensation
cont
roller
and t
h
e SAPF c
o
m
p
ensation
effect can be
im
proved.
4
.
2
.
Sta
b
ility ana
l
y
s
is of co
ntro
l sy
stem
Sy
st
em
st
abi
l
i
t
y
desi
gn i
s
t
h
e
m
o
st
basi
c requi
rem
e
nt
for cont
rol
sy
st
em
. Onl
y
base
d o
n
t
h
e st
abl
e
cont
rol
sy
st
em
, t
h
e f
u
rt
her
sy
s
t
em
desi
gn
, c
o
nsi
d
e
r
i
n
g t
h
e
r
e
st
of
t
h
e sy
st
e
m
perform
ance
req
u
i
r
em
ent
s
,
coul
d
be c
ont
i
n
ue
d.
As it is sh
own in
Fig
u
re 4
(a), th
e co
n
t
ro
l
syste
m
can
b
e
seen
as two
su
bsystem
s
wh
ich
are t
h
e
co
m
p
lex
rep
e
ti
tiv
e PI co
n
t
ro
l
syste
m
an
d
th
e EID con
t
ro
l syste
m
in
series. Th
e stab
ility
o
f
t
h
e con
t
ro
l syste
m
,
co
u
l
d
b
e
con
s
i
d
ered
as two
su
b
s
ystem
s
b
o
t
h
are stab
le.
As con
t
ro
l p
a
ra
m
e
ters o
f
th
e co
m
p
o
s
ite rep
e
titiv
e
cont
rol
sy
st
em
an
d t
h
e E
I
D
co
nt
r
o
l
sy
st
e
m
are wi
t
h
o
u
t
o
v
erl
a
p,
t
h
e
t
w
o
su
bsy
s
t
e
m
s
can be
de
si
gne
d
in
d
i
v
i
d
u
a
lly. Fo
r the co
m
p
o
s
ite rep
e
titiv
e co
n
t
ro
l system
,
wh
ich
is shown
i
n
Figu
re
4
(b
), con
s
id
erin
g
the
tran
sfer fu
n
c
tion
o
f
th
e PI
contro
ller G
PI
(z), t
h
e ch
aracteristic equ
a
tio
n is
g
i
v
e
n b
y
:
)
(
)
(
1
)
(
)
(
)
(
)
(
)
(
1
z
P
z
G
z
P
z
S
z
k
z
Q
z
z
P
z
G
PI
k
r
N
PI
Th
ere are two
p
a
rts in
th
e characteristic eq
uatio
n
of
co
m
p
lex
rep
e
titiv
e co
n
t
ro
l system
.
It is easy to
see that the
characte
r
istic equation is 1+G
PI
(z)
P
(z
),
whe
n
t
h
e sy
s
t
em
i
s
cont
r
o
l
l
e
d by
PI
c
ont
rol
l
e
r
in
d
i
v
i
d
u
a
lly. Th
e latter p
a
rt is th
e ch
aracteristic eq
u
a
tio
n
wh
en
th
e rep
e
t
itiv
e co
n
t
ro
ller ad
d
to
th
e sy
ste
m
.
Th
erefo
r
e, t
h
e
stab
ility o
f
com
p
lex
rep
e
titiv
e co
n
t
ro
l system
req
u
i
red
,
b
a
sed
on
the stable sep
a
rate PI
co
n
t
ro
l
syste
m
, th
e com
p
lex
co
n
t
ro
l
syste
m
is also
stab
le after th
e
ad
d
ition
o
f
repetitiv
e co
n
t
ro
ller.
In
ord
e
r to an
alyze th
e stab
ility o
f
th
e con
t
ro
l syst
em
, b
y
settin
g
inp
u
t
si
gn
al and
i
n
terferen
ce
sign
al
o
f
t
h
e system sho
w
n
i
n
Figu
re
4
(a) to
zero, tak
i
n
g
t
h
e in
pu
t an
d
ou
tpu
t
of low-pass filter F(z) in
the
i
n
t
e
rfe
rence
es
t
i
m
a
t
o
r as t
h
e
sy
st
em
i
nput
an
d o
u
t
p
ut
, t
h
e E
I
D c
o
nt
r
o
l
sy
st
em
show
n i
n
Fi
g
u
re
4
(c) i
s
eq
u
i
v
a
len
t
t
o
t
h
e system
sh
own in
Figu
re 5. Th
e co
m
p
on
en
t in
t
h
e
d
o
tted- lin
e
G(z) is
g
i
v
e
n b
y
:
B
LC
A
zI
A
sI
B
B
LC
A
zI
LC
B
z
G
1
1
)
(
)
(
)
(
1
)
(
d
~
d
ˆ
Fi
gu
re
5.
T
h
e
equi
val
e
nt
c
o
nt
rol
sy
st
em
of E
I
D.
As i
t
i
s
show
n
i
n
Fi
gure
5, E
I
D sy
st
em
i
s
di
vi
ded i
n
t
o
t
h
r
ee part
s, t
h
e st
at
e obser
ve
r, t
h
e l
o
w
-
p
a
ss
filter an
d
th
e state feed
b
a
ck
sectio
n
.
As stat
e feed
back
sectio
n
will n
o
t
affect o
t
h
e
r system stab
ili
ty, i
t
c
a
n
b
e
designe
d
as i
n
depe
ndent
pa
rt accordi
ng t
o
t
h
e LMI or
opt
im
al control m
e
thod.
Acc
o
rdi
n
g to t
h
e sm
all gain
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l.
3
,
No
.
4
,
D
ecem
b
er
2
013
:
37
4 – 383
38
0
theory,
unde
r t
h
e
prem
ise that state
ob
serv
er
an
d low-p
a
ss fi
lter are
stab
le,
it is n
e
ed
to m
e
et th
at th
e H
∞
no
rm
o
f
system
tran
sfer
fu
n
c
tion
is l
e
ss th
an
1
for t
h
e en
tire system
stab
il
ity, which
m
ean
s:
1
)
(
)
(
z
G
z
F
(
7
)
4.
3. Sensi
t
i
v
i
t
y an
al
ysi
s
o
f
c
o
nt
rol
s
y
s
t
em
Sen
s
itiv
ity is an
im
p
o
r
tan
t
ind
i
cato
r
o
f
syst
e
m
p
e
rf
o
r
m
a
n
ce. For th
e co
n
t
ro
l system
sh
o
w
n
i
n
Figu
re
4
(a),
sen
s
itiv
it
y is d
e
fin
e
d
as
th
e tran
sfer fun
c
tio
n fro
m
th
e ex
tern
al d
i
st
u
r
b
a
n
ce d to
t
h
e ou
tpu
t
y o
f
plan
t. It
can al
so be
d
e
fi
ne
d as t
h
e fu
nct
i
o
n
from
the external input signal r to
the error signal e.
Therefore, the
sen
s
itiv
ity reflects th
e track
ing
p
e
rfo
r
m
a
n
ce o
f
th
e inpu
t sig
n
a
l an
d
th
e
d
i
stu
r
b
a
n
ce su
ppressio
n
p
e
rforman
ce.
Th
e sen
s
itiv
ity fu
n
c
tion
S
of
t
h
e c
ont
rol
sy
st
em
sho
w
n i
n
F
i
gu
re
4 (a
),
i
s
g
i
ven
by
:
)
(
)
(
)
(
1
)
(
)
(
)
(
)
(
)
(
)
(
z
P
z
G
z
H
z
P
z
D
z
Y
z
R
z
P
z
E
S
R
In
ad
d
ition
to
co
nsid
er t
h
e math
em
at
ical
mo
d
e
l
an
d
p
e
rform
an
ce in
d
i
cato
r
s, th
e d
e
sign o
f
co
n
t
ro
l
system
should also be subject to certain constrai
nt
s. Sensitivity function is the im
portant perform
ance
i
ndi
cat
o
r
of
t
h
e co
nt
r
o
l
sy
st
em
. B
u
t
i
t
can
not
be
any
val
u
e.
It
s
h
o
u
l
d
t
o
be
bo
u
n
d
b
y
t
h
e B
o
de i
n
t
e
gral
th
eorem
.
Accord
i
n
g
t
o
Bod
e
in
teg
r
al th
eo
rem
,
th
e sen
s
itivity in
teg
r
al is a co
n
s
tan
t
. If th
e con
t
ro
l syste
m
i
s
stab
le, th
e in
teg
r
al
will b
e
zero
,
wh
ich
m
ean
s:
0
d
)
j
(
ln
0
S
(8)
Wh
en
S<1, t
h
e lo
g
a
rith
m
i
c sen
s
itiv
ity is n
e
gativ
e; wh
en S> 1
,
th
e log
a
rithmic sen
s
itiv
ity
is po
sitiv
e.
Th
erefo
r
e, acco
r
d
i
ng
to
eq
u
a
t
i
o
n
(8), it is req
u
i
red
th
at
th
e
sen
s
itiv
ity in
teg
r
al will b
e
zero
,
th
e area wh
en
the
lo
g
a
rith
m
i
c se
n
s
itiv
ity is p
o
s
itiv
e eq
u
a
ls to
th
e area
o
f
n
e
gativ
e lo
g
a
rith
mic sen
s
itiv
ity. Alth
oug
h
t
h
e smaller
sen
s
itiv
ity can
b
e
go
t, it will b
e
b
e
tter p
e
rfo
r
m
a
n
ce o
f
th
e con
t
ro
l sy
ste
m
. Acco
rd
i
n
g
t
o
Bod
e
integ
r
al
th
eorem
,
if th
e
sen
s
itiv
ity is red
u
c
ed
i
n
a cert
ain
frequ
e
n
c
y
b
a
nd
, it will b
e
rose in th
e
o
t
her
b
a
nd
s. Sen
s
itiv
ity
will b
e
redu
ced
in
t
h
e
p
e
ri
od
ic sign
al b
a
nd
b
y
rep
e
titiv
e con
t
ro
l, bu
t it will b
e
in
creased
in non
-p
eriod
i
c
b
a
nd
s, resu
lting
in p
e
rform
a
n
ce d
e
teri
o
r
ation
o
f
non
-p
eri
o
d
i
c sign
al co
n
t
ro
l.
Fo
r rep
e
titiv
e co
n
t
ro
l system
, sen
s
itiv
ity fun
c
tio
n
S
r
i
s
gi
ve
n
by
:
)
(
)
(
1
)
(
)
(
)
(
z
P
z
G
z
P
z
D
z
Y
S
RE
r
(
9
)
Whe
r
e,
)
(
)
(
z
Q
z
z
S
z
k
G
N
k
r
RE
Fo
r rep
e
titiv
e an
d PI co
n
t
ro
l syste
m
, sen
s
itiv
ity fu
n
c
tion
S
p
i
s
gi
ve
n by
:
)
(
)
(
)
(
1
)
(
z
P
z
G
z
G
z
P
S
PI
RE
p
(
1
0)
Whe
r
e,
1
)
(
1
z
K
z
K
z
G
I
P
PI
Fo
r th
e con
t
ro
l syste
m
sh
own
in
Figure
4
(c), sen
s
itiv
ity fu
nctio
n
S
e
i
s
gi
ve
n by
:
)
(
)
(
)
(
)
(
1
)
(
z
P
z
H
z
G
z
G
z
P
S
PI
RE
e
(11)
Whe
r
e,
]
)
(
1
1
)
(
)
(
[
)
(
1
)
(
)
(
2
1
z
G
z
G
z
G
z
F
z
F
L
B
z
H
R
)
(
)
(
)
(
z
G
z
G
z
G
PI
RE
R
,
B
LC
A
zI
C
z
G
1
1
)]
(
[
)
(
,
L
A
zI
C
z
G
1
2
]
[
)
(
Fro
m
eq
u
a
tion (9
) t
o
equ
a
tion
(1
1), it can
b
e
seen
t
h
at, after th
e add
ition
of PI co
n
t
ro
l
l
er an
d
EID
co
n
t
ro
ller,
b
y
ad
ju
sting
th
e tran
sfer fun
c
tion
v
a
lu
e
o
f
th
e PI an
d
EID
co
n
t
ro
ller, th
e syste
m
sen
s
itiv
ity
fu
nct
i
o
n val
u
e can be decrea
s
e
d.
Accord
ing
to
eq
u
a
tion
s
fro
m
eq
u
a
tion
(9) to eq
u
a
tion
(11
)
, it is sh
o
w
n
in Fig
u
re 6
t
h
at sen
s
itiv
ity
function com
p
arison am
ong the repetitive cont
rol syst
em
, the repetitive and PI c
ont
rol system
, and the
co
n
t
ro
l system ad
d
i
ng
with
EID co
n
t
ro
ller. It can
b
e
seen
th
at th
e sen
s
itiv
ity
fu
n
c
tion v
a
lu
e of rep
e
titiv
e
co
n
t
ro
ller is low at th
e fun
d
a
men
t
al frequ
ency 5
0
H
z an
d
its
m
u
ltip
le frequ
en
cies.
Wh
ile at th
e n
o
n
-perio
d
i
c
p
o
s
ition
b
e
tween
t
h
e
fund
amen
tal
m
u
ltip
le frequ
en
cies, sen
s
itiv
ity fu
n
c
tion v
a
l
u
e is at a h
i
g
h
p
o
i
n
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
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8-8
6
9
4
S
hun
t Active Po
wer Filter System Design
fo
r In
ter-h
a
r
mo
n
i
c (Zha
ng
C
h
ao)
38
1
Th
erefo
r
e, t
h
e rep
e
titiv
e contro
ller has a go
od
track
i
ng
or inh
i
b
itio
n
p
e
rfo
r
m
a
n
ce for
th
e fu
nd
am
en
tal an
d
m
u
lt
i
p
l
e
frequ
enci
es si
gnal
.
An
d f
o
r i
n
t
e
r
-
h
arm
oni
cs an
d
no
n-
peri
odi
c
di
st
ur
ba
nce t
o
SAPF, t
h
e c
ont
rol
per
f
o
r
m
a
nce i
s
det
e
ri
orat
e
d
.
Fro
m
Fig
u
re 6 it can
b
e
seen, add
i
ng
wit
h
PI a
n
d
EID con
t
ro
ller, th
e sen
s
itiv
ity fun
c
tio
n
v
a
lu
e is
decrease
d
ove
ral
l
l
o
w f
r
eq
u
e
nci
e
s ba
n
d
. I
t
m
eans t
h
at
sy
st
em
cont
rol
per
f
o
r
m
a
nce get
s
bet
t
e
r f
o
r
t
h
e
fundam
ental a
nd m
u
ltiple freque
ncies signal and the
non
-peri
odic inte
rfe
rence si
gna
l
,
in accord wi
th the
cont
rol
l
a
w e
m
bodi
ed i
n
eq
uat
i
o
n
(
7
)
.
M
e
anw
h
i
l
e
, acc
or
di
n
g
t
o
t
h
e B
ode
i
n
t
e
g
r
al
t
h
eorem
and
as
i
t
ha
s
sho
w
n i
n
Fi
g
u
r
e
6, i
n
t
r
od
uct
i
o
n of E
I
D c
ont
r
o
l
l
e
r m
a
ke a cont
rol
pe
rf
orm
a
nce det
e
ri
orat
i
on d
u
r
i
n
g som
e
hi
gh
freq
u
e
n
c
ies. Th
e m
a
in
fun
c
tio
n of
SAPF is
to
co
m
p
en
sate
th
e grid ch
aracteristic h
a
rm
o
n
ic co
n
t
en
t
with low
freq
u
e
n
c
ies.
Alth
oug
h th
e in
trodu
ctio
n
o
f
EID con
t
ro
ller m
a
k
e
s th
e deterioratio
n
of system co
n
t
ro
l
p
e
rform
a
n
ce fo
r so
m
e
h
i
g
h
-
freq
u
e
n
c
y signal, b
u
t
it will n
o
t
im
p
act p
r
actical ap
p
licatio
n
p
e
rfo
r
m
a
n
ce of
SAP
F
.
Fre
que
nce
(H
z)
Magn
itud
e
(d
eg)
Fig
u
re.6
Th
e sen
s
itiv
ity co
mp
ariso
n
of con
t
ro
l system
.
5.
SIM
U
LATI
O
N
AN
D
E
X
PE
RIME
NTAL
VERIF
I
C
A
TI
ON
In
o
r
de
r t
o
ver
i
fy
t
h
e
desi
g
n
e
d
S
A
P
F
c
ont
r
o
l
per
f
o
r
m
a
nce, base
d
o
n
t
h
e
M
a
t
l
a
b so
ft
war
e
an
d t
h
ree-
l
e
vel
expe
ri
m
e
nt
pl
at
fo
rm
, sim
u
l
a
t
i
on an
d
expe
ri
m
e
nt
al
m
odel
of SA
P
F
co
nt
rol
sy
st
em
was est
a
bl
i
s
hed
,
w
h
ich
w
a
s show
n in
Figu
r
e
7.
a
e
a
e
Figu
re.
7
Th
re
e-level S
A
P
F
c
ont
rol sy
stem
structu
r
e.
Three
-
phase
g
r
i
d
c
u
rre
nt
,
v
o
l
t
a
ge a
n
d t
h
e
i
r h
o
m
o
l
o
go
us v
a
riab
les
were d
e
tected b
y
th
ree-lev
e
l
SAP
F
.
Wi
t
h
ou
t
coo
r
di
nat
e
t
r
ansf
o
r
m
a
ti
on,
harm
oni
c c
u
r
r
e
n
t
det
ect
e
d
by
t
h
e C
P
T m
e
t
hod
was
t
a
ke
n i
n
t
o
t
h
e
cont
rol
l
e
r.
Aft
e
r t
h
e i
n
t
e
rfe
r
e
nce su
p
p
ressi
on
by
EID c
o
nt
r
o
l
l
e
r, t
h
e s
w
i
t
c
h co
nt
r
o
l
si
gnal
was
got
by
t
h
e
th
ree-lev
e
l SVPW
M m
o
du
latio
n
,
wh
ich was u
s
ed
t
o
m
a
k
e
th
e t
h
ree-lev
e
l SAPF g
e
nerate co
m
p
en
sation
current,
whic
h
can offset ha
rm
onic co
m
ponent of
gri
d
current.
Harm
onic
source in Figure 7 was t
h
ree
-
pha
se
u
n
c
on
tro
lled
rectifier with resi
stiv
e lo
ad
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l.
3
,
No
.
4
,
D
ecem
b
er
2
013
:
37
4 – 383
38
2
Si
m
u
latio
n
syste
m
b
u
ilt b
y
Matlab
was
sh
own
in
Figu
re
7
.
Grid
cu
rren
t
wav
e
form
b
e
fo
re the
com
p
ensat
i
on
was g
o
t
i
n
Fi
g
u
re
8 (a)
.
A
f
t
e
r t
h
e com
p
ens
a
t
i
on by
S
A
PF
, t
h
e gri
d
cu
rre
nt
wave
f
o
rm
was g
o
t
in
Figu
re 8
(b
). Mak
e
t
h
e simu
latio
n
for th
e
two
system
s with
and
withou
t th
e EID con
t
ro
ller. Sub
t
racted
th
e
com
p
ensation current from
th
e
detected
ha
rm
onic curre
nt comm
and to
obtain the
error c
u
rrent
signa
l
as it
was s
h
o
w
n i
n
Fi
gu
re 8
(c)
.
A
s
i
t
can be see
n
, t
h
e e
r
r
o
r
bet
w
een c
o
m
p
ens
a
t
i
on cu
rre
nt
a
nd
refe
re
nce c
u
r
r
ent
h
a
s been
sm
all
e
r b
y
ad
d
ition
o
f
EID con
t
ro
ller. It ind
i
cates th
at b
y
add
i
ng EID con
t
ro
ller, th
e b
e
tter track
i
ng
perform
a
nce can
be
got
for t
h
e control system
.
(a) C
u
r
r
e
n
t wa
vef
o
rm
bef
o
re
com
p
ensation
Cu
rr
ent(
A
)
(b
) C
u
r
r
ent
wa
vef
o
rm
after c
o
m
p
ensation
(c)
Er
ro
r
betwe
e
n c
o
m
p
ensation
cu
rre
nt a
n
d
refe
rence
cu
rre
nt
Fi
gu
re
8.
C
o
m
p
ari
s
on
o
f
SAP
F
ha
rm
oni
c co
m
p
ensat
i
on.
6.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r, th
e m
o
d
e
l o
f
th
ree-lev
e
l SAPF
was bu
ilt. SAPF
d
i
rectiv
e h
a
rm
o
n
i
c cu
rren
t
d
e
tection
m
e
thod under the
inter-harm
onic
e
nvi
ronm
ent base
d on the de
finition
of
CPT powe
r
theory was studied.
Bo
th
th
e
rep
e
t
itiv
e co
n
t
ro
l an
d
PI con
t
ro
l
was used
for
th
e grid
cu
rren
t h
a
rm
o
n
i
cs an
d
i
n
ter-h
a
rmo
n
i
cs
com
p
ensat
i
o
n
.
B
y
i
n
t
r
od
uci
ng E
I
D co
nt
r
o
l
l
e
r im
pro
v
es
t
h
e SAPF co
nt
r
o
l
perf
o
r
m
a
nce fo
r n
o
n
-
p
e
ri
o
d
i
c
sig
n
a
l in
terferen
ce.
An
alysis o
f
t
h
e d
e
si
g
n
ed
system
stab
ilit
y an
d
sen
s
itiv
ity o
f
th
e issu
e.
Giv
e
s a suitab
l
e
i
n
t
e
r-
harm
oni
c
s
en
vi
ro
nm
ent
SAP
F
sy
st
em
desi
g
n
m
e
t
h
o
dol
ogy
.
Si
m
u
lat
i
on a
nd e
x
pe
ri
m
e
nt
show t
h
at
t
h
e
designe
d
system can accurately detect
harmonic, inter-ha
rm
onic
content, effective
on th
e gri
d
to c
o
m
p
ensat
e
harm
oni
cs a
n
d
i
n
t
e
r-
harm
oni
c
s
.
AC
KN
OWLE
DG
MENT
Th
e au
thors
wou
l
d lik
e t
o
th
ank
C
h
in
a Nation
a
l
Natu
ral
Scien
ce
Fou
n
d
a
tion
(51
077
124
) and
Gra
d
uat
e
St
u
d
e
nt
R
e
searc
h
a
n
d
I
n
no
vat
i
o
n
Pro
g
r
am
of Ji
a
ngs
u
Pr
o
v
i
n
ce
(C
XZZ
1
3_
0
9
3
1
)
REFERE
NC
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