TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
9
4
~ 660
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.607
8
6594
Re
cei
v
ed Ap
ril 9, 2014; Re
vised J
une 2
3
, 2014; Acce
pted Jul
y
20,
2014
A Flux Weaken
ing Control Algorithm Based on Notch
Filter
Yu Jiabin*
1
, Wang
Xiao
y
i
1
, Xu Jiping
1
, Qi
n X
i
aofei
2
, Zheng Jun
2
1
Beijin
g T
e
chnolo
g
y
an
d Busi
ness Un
iversit
y
, Beijin
g 10
004
8, Chin
a
2
Institute of Automatio
n
, Chin
e
s
e Academ
y of
Sciences, Bei
j
i
ng 10
01
90, Chi
n
a
*Corres
p
o
n
id
n
g
author, e-ma
i
l
:
y
u
j
i
a
b
in
_1
98
4@h
o
tmail.co
m
A
b
st
r
a
ct
In order to sol
v
e the probl
e
m
t
hat the SVPW
M
over mod
u
lati
on
c
aus
ed
the
fluctuati
o
n
of ste
ady-
state spee
d in
the flux w
e
a
k
eni
ng re
gio
n
of su
rface-
mo
unted per
ma
n
ent
ma
g
net sy
nchro
nous
mo
tor
(PMSM), by ana
ly
z
i
n
g
the
mecha
n
is
m
of the l
ead
in
g
ang
le fl
ux w
eake
n
in
g co
ntrol a
l
gor
ith
m
,
th
e
concl
u
sio
n
is t
hat th
e sixth
h
a
rmonic
of
inv
e
rter
o
u
tput v
o
l
t
age c
aus
ed
b
y
SVPWM ove
r
mod
u
lati
on
w
h
i
c
h
is trans
mitted
to the
d-q r
e
fer
ence c
u
rre
nts throu
gh th
e flux
w
eaken
ing
vol
t
age cl
ose-
loo
p
det
erior
a
tes t
h
e
current an
d sp
eed co
ntrol p
e
r
f
orma
nce.
A no
tch filter is desi
gne
d in the vo
ltage cl
ose-l
o
o
p
to filter the sixth
har
mo
nic c
o
mpon
ent of th
e i
nput v
o
lt
ag
e si
gna
l, mea
n
w
h
il
e the
other s
i
g
nal c
o
mp
one
nt
s are
not affect
ed
.
T
he ex
peri
m
e
n
t resu
lts sho
w
that, after a
ddi
ng
notch
filt
er, the s
i
xth
h
a
rmonic
co
mp
one
nt of th
e i
nput
voltag
e sign
al i
s
significa
ntly reduc
ed an
d the current w
a
veforms are re
ma
rkably i
m
pr
ove
d
, so
that
th
e
fl
u
x
w
eakeni
ng sp
e
ed contro
l perf
o
rmanc
e is effectively e
n
h
a
n
c
ed.
Ke
y
w
ords
:
surface-
m
o
unt
ed per
manent m
a
gn
et synchr
onous motor, SVPWM
over modulation, leading
ang
le flux w
e
a
k
eni
ng co
ntrol,
sixth har
mo
nic,
notch filter
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
High
-spee
d, high-preci
s
io
n
pe
rma
nent
magnet
syn
c
hron
ou
s m
o
to
r(PMSM
)
is o
ne of th
e
core compo
n
ents of high
-level CNC
machi
ne t
ool
, which i
s
widely u
s
ed
in
the field of
aero
s
p
a
ce, automotive, preci
s
ion
in
stru
ments
an
d m
ould man
u
fa
cturin
g [1]. As
CNC ma
chi
ne
tools ma
nufa
c
turin
g
the
work pie
c
e,
it
requires
not o
n
ly
a large
o
u
tput torq
ue
of PMSM
at low
spe
ed to
me
et the fast
starting, a
c
cele
ration
an
d ot
her
req
u
irem
ents, b
u
t also a
go
od
sp
eed
perfo
rman
ce
in flux wea
k
ening
regi
on.
Theref
ore, PMSM
can run
ste
adily with
wi
de sp
eed
rang
e in the case of limited
inverter capa
city.
SVPWM over modulation control i
s
often used to
im
prove the utilization
ratio of
i
n
verter
output
voltage when PMSM
is in flux weakening
regi
on [2, 3]. But it
will cause
the decrease of
the pulse n
u
mbe
r
of
inverter o
u
tput voltage,
thus the times of chop
per
will redu
ce in
a
sinu
soi
dal
cy
cle and the
low ord
e
r
harm
oni
c
co
mpone
nts of
output voltage
will in
crease.
These
ha
rmo
n
ic
co
mpon
e
n
ts
can
ma
ke the
input
signal
of curre
n
t loop
com
posite
a
ce
rt
ain
freque
ncy A
C
sig
nal th
rou
g
h
the flux
we
ake
n
in
g
voltage
clo
s
e-l
oop
, and
co
nseq
uently there
will
be positive
fe
edba
ck of current loop a
nd cu
rre
nt
oscill
ation to cau
s
e the sy
stem insta
b
ili
ty,
meanwhile the speed control capa
city of PMSM in flux weakeni
ng region
will decli
ne seriously.
T
o
impr
o
v
e th
e
s
p
ee
d p
e
rfo
r
ma
nc
e o
f
PMSM
in flux
we
akenin
g
region,
schol
a
r
s have
con
d
u
c
ted m
any control method
s, su
ch as ada
pt
ive flux weake
n
ing co
ntrol [4],
direct torq
ue
control [5], flux wea
k
eni
n
g
cont
rol ba
sed o
n
a re
duced-order
controlle
r [6], flux weake
n
i
ng
control b
a
sed
on im
agin
a
ry instanta
neo
us
po
wer th
e
o
ry [7, 8] a
n
d
so
on.
Unfo
rtunately, these
method
s a
r
e
all compli
cate
d an
d difficult to rea
lize. S
o
me im
prove
d
method
s a
r
e al
so
pre
s
e
n
t
ed
based o
n
the
s
e
control st
rategie
s
. For
example,
the
flux wea
k
enin
g
co
ntrol al
go
rithm u
s
ing th
e
differen
c
e bet
wee
n
d-q
cu
rrents an
d voltage oute
r-l
oo
p output to co
rre
ct the co
m
m
and current
is
prop
osed
in
referen
c
e [9],
a
simplified
flux wea
k
e
n
in
g voltage
co
ntrol alg
o
rith
m is p
r
op
ose
d
in
referen
c
e [10
], and refe
re
nce [1
1] co
n
duct
s
a le
adi
ng an
gle flux
wea
k
e
n
ing
control meth
od.
Ho
wever, th
e
study o
n
ho
w to elimi
nat
e the in
flue
nce on
spe
ed p
e
rform
a
n
c
e i
n
flux wea
k
e
n
ing
region by the low order harm
onic
com
p
onents of SVPWM over m
o
dulation i
s
rel
a
tively less.
In this pape
r,
based
on the
leadin
g
angle
flux w
eake
n
i
ng co
ntrol alg
o
rithm, a notch filter
is de
sig
ned i
n
the voltage
clo
s
e-l
oop to
filter
the sixt
h harmoni
c
compon
ent of
the input volt
age
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Flux We
akening
Control
Algorithm
Based o
n
Not
c
h
Filter (Yu Jia
b
in)
6595
sign
al,
mea
n
w
hile
the oth
e
r sig
nal co
mpone
nts
ar
e not
affecte
d
. The
expe
ri
ment results
sho
w
the effectiven
ess of this m
e
thod.
2. The Mathematical Model of PMSM
In d-q axis, th
e stator volta
ge equ
ation o
f
surfa
c
e-mou
n
ted PMSM is:
d
ds
d
d
r
q
q
q
qs
q
q
r
d
d
r
f
d
d
d
d
i
uR
i
L
L
i
t
i
uR
i
L
L
i
t
(1)
Whe
r
e
i
d
and
i
q
are
the d-q axis
stator cu
rre
nts,
L
d
a
nd
L
q
a
r
e th
e in
ducta
nces of
d-q
axis
stator coil.
F
o
r surfa
c
e
-
m
ounted
PMS
M
,
L
d
=
L
q
.
R
s
is
the pha
se resi
stan
ce
of
stator,
ω
r
is
the
rotor el
ectri
c
a
l
angula
r
velo
city,
ψ
f
is the
magneti
c
linkage of perma
nent magn
et.
Whe
n
PMS
M
is
at hig
h
spe
ed, the
stator
voltage
can
be i
g
n
o
red,
an
d th
e voltage
equatio
n ca
n be reg
a
rded
as:
dr
q
q
qr
d
d
r
f
uL
i
uL
i
(
2
)
As the stator
voltage
22
sd
q
uu
u
, from
equatio
n (2
) we can get:
2
2
sr
q
q
d
d
f
uL
i
L
i
(
3
)
As sho
w
n in
Equation (3
), the excitation
magn
eto-motive force
is pro
d
u
c
ed
by the
perm
ane
nt magnet
an
d
ca
nnot be a
d
ju
sted. When
above the b
a
se
sp
eed,
as the o
u
tpu
t
of
curre
n
t regul
ator exce
edi
ng inverter’
s
DC bu
s vo
lta
ge whi
c
h will
cause the current reg
u
lat
o
r
saturation, th
e flux-wea
ke
ning
co
ntrol i
s
n
e
cessa
r
y. The
spe
ed
ω
r
is
rai
s
ed
with
out brea
king
the
voltage b
a
lan
c
e
by in
crea
sing the
di
re
ct axis dem
agn
etization
current
i
d
an
d
r
edu
c
i
ng
th
e
c
r
os
s
axis cu
rrent
i
q
.
3. The Leadi
ng Angle Flu
x
Wea
kening
Contr
o
l Alg
o
rithm
22
q
d
uu
Figure 1. Block
Diag
ram o
f
Leading An
gl
e Flux Wea
k
eni
ng Control Algorithm
Figure 1 sh
o
w
s the
block diagram of leadin
g
angl
e
flux weake
n
i
ng co
ntrol al
gorithm.
The b
a
si
c
principl
e is tha
t
the
output
of
cu
rrent loo
p
is
rega
rde
d
as the in
put
of voltage
PI
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
94 – 660
1
6596
regul
ator in t
he
cont
rol
ci
rcuit, an
d
the
differen
c
e
bet
wee
n
the
giv
en voltag
e
U
ma
x
an
d
22
dq
uu
is u
s
ed
to ge
nerate
the
le
ading
angl
e
bet
wee
n
stator
cu
rrent
vector a
nd q
-
axis throug
h
the
voltage PI re
gulator.
U
max
is
U
dc
/
,3 ,
and
U
dc
is the
DC
bus voltage
o
f
the inverte
r
.
Wh
en
u
s
is
less than
U
ma
x
, due to the satu
ration
element in P
I
regulato
r
, the PI
regul
ator is in
po
sitive
saturation
an
d the
lea
d
in
g an
gle
=
0
.
A
s
a
r
e
s
u
l
t
,
i
d
=
i
s
sin
= 0 a
nd
PMSM
ru
ns
in con
s
tant
t
o
rqu
e
re
gion.
Whe
n
u
s
is highe
r than
U
max
, the input of PI voltage
reg
u
lato
r
is
negative. Th
e PI regulato
r
begin
s
to withdra
w
from
the
satu
rated
state, and t
he leadi
ng a
ngle
is
neg
ative (
-
/2
≤
< 0). As
a result,
i
d
is also
n
egative an
d
PMSM
run
s
i
n
flux wea
k
e
n
ing
region. At the s
a
me time,
i
d
shoul
d be li
mited less th
an the
maxim
u
m
dema
gnet
izing
cu
rre
nt of
PMSM.
In the leadi
ng angl
e flux weakening cont
rol algorithm, SVPWM over m
odulation
control
is often used to im
prove the
utilization
ra
tio of
inverter DC bus
voltage and the
voltage
output
ability, so that the fluctuation
of current
is
reduced in the dy
namic process
of
spee
d
respon
se. B
a
se
d on th
e prin
ciple
of the
vo
ltage sou
r
ce in
verter, there
are not e
v
en
harm
oni
c
and
three
h
a
rm
o
n
ic
in the
in
verter o
u
tput
voltage. Th
e ha
rmoni
c
prop
ortio
nal
in
voltage
signal
generated by SVPWM ov
er
modulation will
increase with the rising
of
modulati
on
ratio [12, 13]. Whe
n
the six-step mod
e
is
rea
c
he
d, the A-pha
se volta
ge is:
1r
5
7
c
o
s
c
os
5
c
os
7
.
.
.
ar
r
UU
t
U
t
U
t
(
4
)
In Equation (4),
U
1
is the
amplitude of
fundame
n
tal comp
one
nt of
stator voltag
e sign
al,
U
5
and
U
7
are the amplitu
de of fifth
and seventh
ha
rmoni
c
comp
onent
s. As the amplitu
d
e
of
highe
r ha
rmo
n
ic compo
n
e
n
t is
small,
so
the
ha
rm
onic
comp
on
ents contain
e
d
in
the voltage
sign
al is main
ly fifth and se
venth harm
o
n
i
cs.
The stato
r
voltage is tra
n
sformed from
ABC
th
ree
-
ph
ase axi
s
to
d-q two
-
ph
ase
axis.
From E
qua
tion (5
)
～
(7), throug
h
Cla
r
k&Pa
rk tra
n
sfo
r
m
,
the fifth and
sev
enth
harm
oni
c
co
mpone
nts of A
B
C
three
-
ph
a
s
e volta
g
e
are t
r
a
n
sformed
to
sixth
harm
oni
c
co
mpone
nt of d
-
q voltage. A
s
a
result, the cu
rrent
loo
p
output
u
d
a
nd
u
q
co
ntain
sixth
harm
oni
c co
mpone
nt.
5r
5
7
7
,6
55
7
7
,6
55
7
7
co
s
(
5
)
co
s
(
7
)
co
s
(
5
1
2
0
)
c
o
s
(
7
1
2
0
)
c
o
s
(
5
2
40
)
c
os
(7
240
)
r
d
rr
q
rr
Ut
U
t
u
TU
t
U
t
u
Ut
U
t
(5)
In Equation (5),
T
is the transfo
rmatio
n matrix of Clark&Park.
°°
r
°°
c
o
s
c
o
s
-
1
20
c
o
s
-
240
sin
s
i
n
-
1
2
0
sin
-
24
0
rr
rr
r
tt
t
T
tt
t
(6)
From Equ
a
tio
n
(5) a
nd Equ
a
tion (6
), we
can g
e
t:
,6
5r
5
7
7
,6
55
7
7
c
o
s6
c
o
s6
3
2
si
n
6
si
n
6
d
r
q
rr
u
Ut
U
t
u
Ut
U
t
(7)
Acco
rdi
ng to
the leadin
g
a
ngle flux we
a
k
eni
ng contro
l
algorithm m
entione
d in literatu
r
e
[14], the flux wea
k
eni
ng controlle
r
is
desi
gne
d
in
Figure1. In the
over mo
d
u
lation
re
gion
, the
roun
ding of
u
d
and
u
q
which
contai
n
sixth harmonic
com
p
o
nent ca
n b
e
rega
rd
ed
as
the actual vol
t
age vector,
so
u
s
also contain
s
sixth
harmo
nic
co
mpone
nt whi
c
h exist
s
in
u
d
and
u
q
. It is
transmitted to the d-q
ref
e
renc
e currents
i
d
*
and
i
q
*
throu
gh th
e
flux wea
k
eni
ng
voltage cl
ose
-
loop. In th
e
curre
n
t loop,
this sixth h
a
rmonic co
mpo
nent
may ca
use
the
p
o
siti
ve
feedba
ck of
current loo
p
a
nd dete
r
io
rat
e
the curr
ent
control pe
rformance. The
r
efore, a
s
PM
SM
runni
ng
with
l
oad
in
co
nsta
nt po
we
r
regi
on, the
spee
d an
d to
rqu
e
will
o
scillate
and
the
spe
e
d
control performance is
affected, even the system
will be instability.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Flux We
akening
Control
Algorithm
Based o
n
Not
c
h
Filter (Yu Jia
b
in)
6597
The sixth harmonic
com
p
o
nent is
the main harm
oni
c comp
one
nt of
u
d
and
u
q
in the
over
modulatio
n
p
hase. In order to avoi
d t
he
impact
on the
current loop
a
n
d
the spe
e
d
perfo
rman
ce
and a
s
mu
ch as p
o
ssibl
e
retain the
real
voltage si
gnal
in ad
dition to the si
xth
harm
oni
c, a
notch filte
r
i
s
de
sig
ned i
n
the vo
ltag
e clo
s
e
-
loo
p
to filter the
sixth ha
rmo
n
ic
comp
one
nt of input voltage sign
al, meanwhile
the other signal comp
one
nts are
not
affe
cted.
The not
ch filter is de
sig
n
e
d
by all-pa
ss
filter in this paper.
4. Flux Weak
ening Con
t
r
o
l Algorithm
Based o
n
Notch Filter
In the signal
pro
c
e
ssi
ng sy
stem, notch filter is
often ut
ilized to filter out the sign
al
of one
or more pe
rio
d
ic interfe
r
e
n
c
e, and the ot
her fre
que
ncy
compo
nent
s are not affe
ct. Notch filter i
s
actually a ba
nd-stop filter
with
narro
w b
and
width [15,
16]. Block di
agra
m
of notch filter is sho
w
n
in Figure 2.
Figure 2. Block
Diag
ram o
f
Notch Filter
Figure 2 sho
w
s that the
notch filter
i
s
con
s
iste
d of
a
2-o
r
de
r G
r
ay-Ma
r
kel
lat
t
ice
all-
pass filter an
d an add
er. T
he tran
sfer fu
nction
H(z) i
s
:
1(
)
()
2
A
z
Hz
(
8
)
In Equation (8), A(z) is the
transfe
r funct
i
on of 2-o
r
de
r all-pa
ss filter.
12
12
1
12
21
1
(1
)
()
1(
1
)
kk
k
z
z
Az
kk
z
k
z
(
9
)
Block dia
g
ra
m of tra
n
sfe
r
function
A(z)
is
sho
w
n
in F
i
gure
3. In E
q
uation
(9
),
k
1
controls
the band
widt
h
coeffici
ent of notch filter BW whic
h i
s
related to the distan
ce b
e
twee
n the pole
and the
unit
circle. Con
s
ide
r
ing
it
s stabilit
y,
k
1
usually t
a
ke
s
a
co
nst
ant.
k
2
i
s
rela
ted to
ω
0
.
ω
0
is the notch freque
ncy which is the fr
equ
ency filtered
out by notch filter.
Figure 3. Block
Diag
ram o
f
Transfe
r Fu
nction A(z)
As de
signi
n
g
the not
ch filter, the para
m
eters
k
1
and
k
2
sho
u
ld
b
e
desi
gne
d
indep
ende
ntly
in order to facilitate the
separate co
ntrol
of
the notch freque
ncy
ω
0
and the -3dB
attenuation b
and
width [17]
. It is sho
w
n i
n
Equation (1
0).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
94 – 660
1
6598
1
20
1t
a
n
2
1t
a
n
2
co
s
BW
k
BW
k
(
1
0
)
Acco
rdi
ng to Equation (8)
and (9
), H (z) can be exp
r
e
s
sed a
s
:
12
12
12
21
2
1
11
2
()
21
kk
z
z
Hz
kk
k
z
k
z
(
1
1
)
In order to facilitate t
he programming,
we
define
2
1
kR
,
20
co
s
k
, so that the notch
filter can be d
e
sig
ned a
s
Equation (12
)
.
12
2
0
21
2
2
0
12
c
o
s
1
()
2
11
c
o
s
zz
R
Hz
R
Rz
R
z
(
1
2
)
In Equation
(12),
ω
0
i
s
the
notch f
r
eq
ue
ncy,
R
2
is the
adju
s
table
p
a
ram
e
ter of t
he not
ch
freque
ncy. In
order to
sati
sfy the
stabili
ty
c
ondition
o
f
the not
ch
filter, we
sho
u
l
d
ma
ke
|
k
1
|<1,
that is
R
2
<1.
Block diag
ra
m of leadin
g
angle flux
weak
enin
g
con
t
rol ba
sed
on
notch filte
r
i
s
s
h
ow
n
in
F
i
gu
r
e
4
.
22
q
d
uu
Figure 4. Block
Diag
ram o
f
Leading An
gle Flux
Wea
k
eni
ng Control Based o
n
Notch Filter
As sh
own in
Figure 4, a
notch filter i
s
added
b
e
fore the input o
f
PI regulator in flu
x
wea
k
e
n
ing v
o
ltage cl
ose-l
oop to filter t
he sixth ha
rmonic
of inp
u
t voltage
sig
nal
u
s
ca
us
e
d
by
SVPWM over modul
ation,
meanwhile
the other
signal com
ponents
are not
affected. The
notch
filter is desi
gned a
c
cord
ing to Equation
(12
)
. The value of param
eter
k
1
is
obtai
ned
with
experi
e
n
c
e, and it ca
n be adju
s
te
d
accord
ing t
o
the actu
al situation. Parameter
k
2
is
the
notch frequ
e
n
cy which is
the
sixt
h harmonic f
r
eq
ue
ncy. We
ca
n get
0r
6
, and
ω
r
is
th
e
electri
c
an
gul
ar velocity of PMSM.
5. Experiment Re
sult
In ord
e
r to ve
rify the validity of the co
ntro
l method
m
entione
d ab
o
v
e, the digital
PMSM
drive
sy
stem experim
ental
platform was desi
gne
d
ba
sed on the di
gital signal p
r
o
c
e
s
sor (DSP) in
this pa
per.
DSP was
TMS
320LF
281
2 o
f
TI, inverter wa
s PM75
RS
A120 of MIT
S
UBISHI, PMSM
wa
s HSB15
0
0908 of INVT
, the paramet
ers of the PM
SM are shown in Table 1 a
s
follows:
Table 1. Para
meter Ta
ble of the PMSM
Parameter Value
rated voltage
310V
rated cur
r
ent
14A
rated po
wer
7.5kW
rated speed
9000rpm
maximum speed
18000rpm
rated to
rque
8N·m
number of p
o
les
2
rotor ine
r
tia
19.5×10
-
4
kg·
m
2
rated voltage
310V
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Flux We
akening
Control
Algorithm
Based o
n
Not
c
h
Filter (Yu Jia
b
in)
6599
Load
torq
ue
wa
s
T
L
=4
N·m.
Wh
en
the
steady
-state
sp
eed
wa
s 1
600
0
r
pm, the
PMSM
was i
n
to the
deep
flux weake
n
ing re
gi
on
and the inv
e
rter
wa
s al
ways in the
over
modulatio
n
state. Since
th
e
inverter
o
u
tput c
apa
city wa
s limited, t
he
sixth ha
rmonic
com
p
o
nent
in the
a
c
tual
voltage
sign
a
l
u
d
a
nd
u
q
was th
e m
a
in
comp
one
nt
of ha
rmoni
c
co
mpone
nts. T
h
e
experim
ent was do
ne
with the flux wea
k
ening
cont
rol
algorithm
ba
sed o
n
not
ch
filter prop
osed
in this p
ape
r.
The exp
e
rim
ental
re
sults
of the input v
o
ltage
sign
al
u
s
and
output
voltage si
gn
a
l
u
s
*
is sho
w
n i
n
Figure 5 an
d Figure 6. From the
co
m
pari
s
on of th
e two
gra
p
h
s
, it is shown that,
becau
se of
n
o
tch filter
filtering out th
e
sixth harm
onic, the ha
rmonic
com
p
onent of
u
s
*
is
signifi
cantly redu
ce
d
in
Figur
e 6
co
mpared
with
that of
u
s
in Figu
re
5,
and
the vo
ltage
waveform is
improved s
i
gnific
antly.
(a) T
he wavef
o
rm of voltag
e sign
al
u
s
(b) T
he pa
rtia
l enlarg
ed d
r
a
w
ing of
u
s
at 1s~2
s
Figure 5. The
Waveform of
Voltage Sign
al
u
s
before
Notch Filter
(a) T
he wavef
o
rm of voltag
e sign
al
u
s
*
(b) T
he pa
rtia
l enlarg
ed d
r
a
w
ing of
u
s
*
at
1s~2
s
Figure 6. The
Waveform of
Voltage Sign
al
u
s
*
after Not
c
h Filter
The flux wea
k
eni
ng
cont
rol expe
rimen
t
without n
o
tch filter
wa
s
also
don
e to
make a
comp
ari
s
o
n
. Figure 7 a
nd
Figure 8
sho
w
the
wavefo
rms
of d-q cu
rre
nts at
stea
dy
stage with and
without not
ch
filter. In Figure 7, due to t
he si
xth ha
rmonic
com
p
o
nent from the
flux weake
n
i
n
g
voltage clo
s
e
-
loop,
the
r
e a
r
e d-q curren
ts oscillati
on.
After adding
the notch filter, as the
sixth
harm
oni
c
co
mpone
nt is filtered
out
by the n
o
tch
filter, d-q
current
s oscillatio
n
i
s
smalle
r i
n
Fig
u
re
8, so that the curre
n
t wavef
o
rm is imp
r
ov
ed sig
n
ifica
n
tly.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
94 – 660
1
6600
0
4
8
12
16
20
24
1
23
4
5
67
8
Ti
me
(s
)
0
(a) T
he wavef
o
rm of d-axis
curre
n
t
(b) T
he wavef
o
rm of q-axis
curre
n
t
Figure 7. The
Waveform
s
of d-q Cu
rren
ts without
Notch Filter in th
e Flux Wea
k
e
n
ing Region
(a) T
he wavef
o
rm of d-axis
curre
n
t
(b) T
he wavef
o
rm of q-axis
curre
n
t
Figure 8. The
Waveform
s
of d-q and
Cu
rre
nts with
Notch Filter in t
he Flux Wea
k
ening
Regio
n
Figure 9 and
Figure 10 sh
ow the waveform
s of
sp
ee
d at steady st
age with a
nd
without
notch filter in
the flux weakeni
ng voltage
close-lo
op. As sho
w
n in
Figure 9, due
to the influence
of sixth harm
onic
comp
on
ent on the pe
rforma
nce of
curre
n
t
loop, there a
r
e
spe
ed oscillatio
n
at
steady
stag
e
,
and
the
sp
eed
pe
rform
ance in
fl
ux
wea
k
e
n
ing
region
be
com
e
s
wo
rse. Af
ter
addin
g
the n
o
tch filter in
Figure 10, a
s
the
sixt
h h
a
rmo
n
ic of d
-
q current
s is filtered out, th
e
spe
ed o
s
cillat
i
on at ste
ady
stage i
s
small
e
r an
d
the
sp
eed p
e
rfo
r
ma
nce i
n
flux we
ake
n
ing
regi
o
n
is obviously improved.
Figure 9. The
Waveform of
Steady State
Speed with
ou
t Notch Filter
in the Flux
Wea
k
e
n
ing Region
Figure 10. Th
e Wavefo
rm of Steady Sta
t
e
Speed with
Notch Filter in t
he Flux Wea
k
ening
regio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Flux We
akening
Control
Algorithm
Based o
n
Not
c
h
Filter (Yu Jia
b
in)
6601
6. Conclusio
n
To solve the
pro
b
lem
tha
t
the sixth
h
a
rmo
n
ic of i
n
verter outp
u
t
voltage
ca
use
d
by
SVPWM over modulation
whic
h is
trans
mitted to the d-q ref
e
renc
e
c
u
rrents
t
h
rough the flux
wea
k
e
n
ing vo
ltage cl
ose-lo
op dete
r
io
rat
e
the
curr
e
n
t and
spe
ed
co
ntrol p
e
rfo
r
m
ance of
surfa
c
e-
mounted PM
SM, a flux we
ake
n
ing
co
ntrol algo
rithm i
s
p
r
opo
se
d.
A notch filter i
s
de
sig
ned i
n
the
voltage clo
s
e
-
loop to filter
the sixth harmonic
com
p
o
nent of the in
put voltage si
gnal, mea
n
while
the othe
r si
g
nal compo
n
e
n
ts a
r
e n
o
t affected. Ex
periment re
sult
s
sho
w
that, th
e sixth ha
rmo
n
ic
comp
one
nt of the input voltage sig
nal
is signi
fican
t
ly reduce
d
and the fluct
uation of sp
eed
decrea
s
e
s
,
so that
the
ste
ady pe
rform
a
nce
of fl
ux weakenin
g
con
t
rol is effectiv
ely improved
and
the robu
stne
ss of system i
s
remarka
b
ly enhan
ce
d.
Ackn
o
w
l
e
dg
ements
Proje
c
t su
pp
orted by the
gene
ral p
r
o
g
ram
of scie
nce
and te
chnolo
g
y developme
n
t
proje
c
t of Be
ijing mu
nici
p
a
l edu
catio
n
commi
ssion
of Chin
a
(No
.
KM2014
10
0110
02); Beij
ing
universities a
nd coll
ege
s enha
nci
ng scientific
and
t
e
ch
nolo
g
ical innovation ca
pability
proje
c
t
(No. PXM
201
4_01
4213
_00
0033
); Beijin
g high
er
scho
ol intro
d
u
c
tio
n
and
cultivation of hi
gh le
vel
talents proje
c
t (No. CIT&T
C
D201
4040
3
1
).
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ces
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ao-
ji
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e
sig
n
a
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i
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F
eedb
ack L
i
n
eariz
ation
Co
ntrol S
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Internatio
na
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a
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ectronics a
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[2]
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ng, GAO Lin, LIU Xi
nz
he
ng, et al.
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7
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ontro
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w
itc
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ree–
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