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
. 19
6~
20
4
I
S
SN
: 208
8-8
6
9
4
1
96
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
Power Factor Correction in
Two Leg Inverter Fed BLDC Drive
Using Cuk Dc-Dc Converter
A.
Purn
a
Ch
a
ndra
R
a
o*
,
Y.
P. O
bulesh
*
*
,
Ch
. S
a
i Ba
bu
**
*
*
Prasad V. Potl
uri Siddhar
t
ha In
stitute of
Te
chno
log
y
, Vi
jay
a
w
a
d
a
, Andhr
a Prad
esh, India
** KL Univ
ersity
, Guntur
, Andh
ra Pradesh
,
India
***
Jawaharlal Nehru
Tec
hnolo
g
ical University
Kakinada,
Kak
i
n
a
da, Andhra Pradesh, India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 26, 2015
Rev
i
sed
Ap
r
29
, 20
15
Accepted
May 12, 2015
Earlier for v
a
riable speed
applicati
on conven
t
ional motors were used, b
u
t
these motors have poor characteristics.
Th
ese dr
awbacks were o
v
ercome b
y
brushless Dc motor drive. Now day
s
in
most of the applications such as
industrial, domestic, aerosp
ace,
defense, medical a
nd traction etc, brushless
DC
motor (BLDCM) is popular f
o
r its hi
gh efficiency
, high torqu
e
to weight
ratio
, sm
all
size
, and
high
rel
i
a
b
ilit
y,
ease
of
c
ontrol
and low
m
a
intenan
c
e
etc
.
BLDC m
o
tor is
a electron
i
c
com
m
u
tator driven drive i.
e. it u
s
es
a three-
phase voltage so
urce inv
e
rter for
its ope
ra
tion
,
e
l
e
c
troni
c dev
i
ces
m
eans
ther
e
is a problem of poor power quality
,
more torque ripple and speed
fluctu
ations. Th
is paper
deals with th
e CUK con
v
erter
two
leg
i
nverter
fed
BLDCM drive in closed loop
o
p
erati
on.
The pr
oposed control
strateg
y
on
CUK converter
two leg inv
e
rter
fed BLDCM drive with split D
C
source is
modeled and
implemented
using
MA
TLAB/Simulink. The propo
sed method
im
proves
the ef
fici
enc
y
of the
drive s
y
s
t
em
with P
o
wer factor
correc
tion
featur
e in
wide
range of
the s
p
eed
c
ontrol, less torque
ripp
le and
smooth
s
p
eed con
t
rol
.
Keyword:
BLDC m
o
to
r
CUK c
o
nv
erter
PFC
Power qu
ality
Torque ripple
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
:
A
.
P
u
r
n
a Ch
and
r
a Ra
o
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Prasad
V. Po
tl
u
r
i Sidd
h
a
rth
a
In
stitu
te o
f
Tech
no
log
y
,
V
i
j
a
yaw
a
d
a
, An
dhr
a Pr
ad
esh, In
d
i
a
Em
a
il: alap
ati.
p
u
rn
a@yahoo
.co
m
1.
INTRODUCTION
Co
nv
en
tio
n
a
l
m
o
to
r lik
e in
du
ctio
n
m
o
to
r an
d
DC m
o
to
rs are m
o
st p
o
p
u
l
ar electric driv
es in
20
th
cent
u
ry
. R
ece
nt
l
y
devel
opm
ent
i
n
po
wer
el
ect
roni
cs t
e
c
h
n
o
l
o
gy
an
d c
ont
rol
t
ech
n
o
l
ogy
, i
t
a
ppl
i
c
a
t
i
on t
o
electrical drive syste
m
has increase
d
. T
h
e
m
a
i
n
adva
nt
ages o
f
i
n
d
u
ct
i
on m
o
t
o
r a
r
e sim
p
l
e
const
r
u
c
t
i
on,
si
m
p
le
m
a
in
ten
a
n
ce,
n
o
slip
ri
n
g
s
and
m
o
d
e
rate reliab
ility
.
Th
e drawb
a
ck
s are sm
al
l air g
a
p
crack
i
ng
of
ro
t
o
r
bars
d
u
e t
o
hot
sp
ot
s a
n
d
l
o
w
e
r
efficiency a
n
d power factor.
The use of per
m
anent
m
a
gnet
s
i
n
co
nst
r
uct
i
on o
f
el
ectric machine has
following
b
e
n
e
fits th
ere is
no
ex
citatio
n
lo
sses, h
i
gh
to
rque to
weigh
t
ratio
, b
e
tte
r dy
n
a
m
i
c perfo
rm
ance, si
m
p
l
e
const
r
uct
i
o
n a
n
d l
e
ss
maintenance t
h
ere
f
ore
permanent m
a
gnet
m
o
tors has
be
com
e
s an attractive opti
o
n.
The
devel
opm
ent in
powe
r electronics technology
and cont
r
o
l
t
echn
o
l
o
gy
a
nd
d
r
oo
pi
n
g
of
cost
i
n
p
o
w
er el
ect
r
oni
cs
de
vi
ces
m
a
ke
pos
si
bl
e o
f
o
p
e
rat
i
ng t
h
e m
o
t
o
r o
v
e
r
a wi
d
e
speed
ra
nge
and m
a
i
n
t
a
i
n
i
n
g g
o
od e
ffi
ci
e
n
cy
. A
3% i
n
c
r
ease i
n
m
o
tor efficienc
y
can sa
ve
2%
of ene
r
gy
use
d
[1]
In
PM
B
L
DC
m
o
t
o
r onl
y
t
w
o p
h
ase
wi
ndi
ng
co
n
duct
t
h
e cur
r
e
n
t
an
d
t
h
i
s
cu
rre
nt
i
n
t
h
e s
h
ape
o
f
squ
a
re o
r
t
r
a
p
e
z
oi
dal
w
h
i
c
h
p
r
o
d
u
ce a rot
a
t
i
ng m
a
gnet
i
c
fi
el
d due t
o
t
h
i
s
l
o
ss are re
d
u
ce
d. A
n
ot
he
r ad
v
a
nt
age
o
f
bru
s
h
l
ess m
o
tor is th
at
p
o
wer l
o
ss
o
c
cu
r in
stato
r
on
ly, b
ecau
s
e
o
f
t
h
is h
eat tran
sfer con
d
ition
is
go
od
.
Consi
d
era
b
le im
provem
e
nt in the
dynam
i
c
s
is achieve
d
because the air
gap
flux de
nsit
y high, rotor has low
in
ertia, thu
s
the v
o
l
u
m
e o
f
the
m
o
to
r is redu
ced
b
y
m
o
re th
an
4
0
% [2
].
Now
d
a
ys du
e to
th
e sim
p
lic
ity in
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
:
196
–
2
04
19
7
t
h
ei
r c
ont
rol
,
P
e
rm
anent
-
m
a
gnet
b
r
ushl
ess
d
c
m
o
t
o
rs are
m
o
re
wi
del
y
use
d
i
n
hi
gh
-
p
er
fo
rm
ance appl
i
c
a
t
i
ons
and
,
t
h
e
p
r
od
u
c
t
i
on
of
ri
p
p
l
e
-
free t
o
r
q
ue i
s
o
f
pri
m
ary
conc
ern
i
n
t
h
ese a
p
pl
i
cat
i
ons.
BLDC m
o
tor
is a electronic
comm
utator dri
v
en
d
r
i
v
e
i
.
e. i
t
uses
a t
h
ree-
pha
se
vol
t
a
ge s
o
urce
in
v
e
rter fo
r its o
p
e
ration
,
electron
ic d
e
v
i
ces
m
ean
s th
ere
is a p
r
o
b
l
em
o
f
po
or
p
o
wer
q
u
a
lity, m
o
re to
rqu
e
ripp
le and
sp
eed
flu
c
t
u
ation
s
.
Fo
r
driv
ing
th
e BLDC m
o
to
r we u
s
e
sing
le p
h
a
se ac supp
ly wh
ich
is co
nv
ert
t
o
DC
wi
t
h
di
ode
bri
d
ge rect
i
f
i
e
r an
d i
t
out
p
u
t
i
s
gi
ven t
o
capacito
r i.e. DC lin
k
cap
acito
r.
Du
e to
th
is
DC lin
k
capaci
t
o
r
cha
r
gi
n
g
a
n
d
di
sc
h
a
rgi
ng;
o
n
AC
su
p
p
l
y
si
de c
u
r
r
ent
i
s
i
n
p
u
l
sat
i
ng f
o
rm
, thi
s
ca
use t
h
e
po
we
r
q
u
a
lity prob
lem
.
Du
e to
m
a
n
y
adv
a
n
t
ag
es
o
v
e
r co
nv
en
tion
a
l driv
es its po
pu
larity and
i
t
s u
s
ag
e is in
creased
an
d on
u
tility s
i
d
e
it cau
se m
o
re sev
e
re
PQ prob
lem
.
Research
Work is go
i
n
g on
to d
e
v
e
l
o
p an
electrical d
r
i
v
e
syste
m
with
in
h
e
ren
t
power factor co
rrect
io
n
con
v
e
rt
er
(PFC). PFC
will fo
rce th
e
driv
e system
to
draw
si
nus
oi
dal
c
u
r
r
e
nt
fr
om
AC
sup
p
l
y
m
a
i
n
s and m
a
i
n
t
a
i
n
n
e
arly u
n
ity po
wer factor.
A PFC converte
r means a
n
extra c
o
st and
com
p
lexity which is
not acceptable. T
h
e
r
e a
r
e so m
a
ny PF
C converte
r topol
ogies a
r
e available
in
wh
ich DC
-DC co
nv
erter t
o
po
log
y
is m
o
re po
pu
lar du
e t
o
low co
st and less co
m
p
lex
ity. Bu
ck
,
bo
o
s
t, bu
ck
boost, SE
PIC are the exam
ples for
DC-DC co
nv
erters topo
log
y
. In
air-co
nd
itio
n
e
rs app
licatio
n
s
, a BLDCM
with boost PF
C conve
rter [3] and PMSM with im
prove
d
power quality converter [4]
have
been re
porte
d
for
p
o
wer qu
ality i
m
p
r
ov
em
en
t, resu
lts in im
p
r
o
v
e
m
e
n
t
in
p
e
rfo
r
m
a
n
ce su
ch
as im
p
r
ov
ed efficien
cy, red
u
c
tion
of
ha
rm
oni
cs o
n
AC
s
u
p
p
l
y
si
de,
n
o
i
s
e re
d
u
c
t
i
on et
c .
Th
is p
a
p
e
r
d
e
als with
th
e applicatio
n
o
f
cu
k co
nv
erter as PFC to
feed
two leg
in
v
e
rter fed
BLDCM
with
sp
lit DC
su
pp
ly, resu
lts in
i
m
p
r
ov
emen
t in
p
e
rf
orman
ce su
ch
as i
m
p
r
ov
ed
efficien
cy, red
u
c
tio
n
of
harm
oni
cs o
n
AC
su
ppl
y
si
d
e
, noi
se
red
u
ct
i
on,
nearl
y
u
n
i
t
y
powe
r
fact
o
r
at
ac sup
p
l
y
si
de, l
e
ss t
o
r
q
ue
ri
ppl
e
and
sm
oot
h s
p
ed c
ont
rol
.
Fig
u
re
1
.
Sch
e
matic Diag
ram of Propo
sed
C
U
K PFC
t
w
o leg
inv
e
rter
fed
BLDCM with
sp
lit DC sup
p
l
y
2.
OPER
ATIO
N O
F
CU
K P
F
C TW
O LE
G IN
VE
RTER FE
D BLD
C
M
DRI
VE
Fig
u
re 1
shows th
e sch
e
m
a
t
i
c
d
i
ag
ram
o
f
p
r
opo
sed
CUK PFC two
inv
e
rter fed
BLDC
M with
sp
lit
DC
su
ppl
y
f
o
r
spee
d co
nt
r
o
l
as wel
l
as PFC
i
n
vi
de ra
nge
of
i
n
p
u
t
AC
v
o
l
t
a
ge. It
c
onsi
s
t
of t
w
o sc
hem
e
s one
is Power
factor correction
con
t
ro
l sch
e
m
e
wh
ich
u
s
es
a cu
rren
t m
u
ltip
li
er appro
a
ch
con
cep
t
with
a cu
rrent
cont
rol
l
o
o
p
i
n
si
de an
d sec
o
n
d
o
n
e i
s
t
h
e s
p
eed co
nt
r
o
l
l
o
o
p
f
o
r c
o
nt
i
n
u
o
u
s-c
o
nd
uct
i
o
n-
m
ode ope
rat
i
o
n o
f
t
h
e
co
nv
erter.
First referen
c
e DC
lin
k
vo
ltag
e
is co
m
p
ared
wi
t
h
t
h
e
act
ual
D
C
l
i
nk
v
o
l
t
a
ge
whi
c
h
gene
rat
e
s t
h
e
DC
l
i
nk v
o
l
t
a
ge er
ro
r si
g
n
al
(V
dc_e
rr
o
r),
whi
c
h i
s
pr
oc
essed t
h
ro
u
gh
a PI co
nt
r
o
l
l
e
r
t
o
gene
rat
e
cont
rol
sig
n
a
l (Ic). This co
n
t
ro
l signal
m
u
ltip
lied
with
a
u
n
it tem
p
la
te o
f
inp
u
t ac v
o
ltag
e
t
o
g
e
t referen
ce
DC lin
k
cur
r
ent (I
dc
_re
f). This refe
re
nce
DC
li
nk
c
u
r
r
ent (I
dc
_r
ef) is co
m
p
ared
with
dc lin
k cu
rren
t
(IDC)
wh
ich
is
sense
d
aft
e
r di
ode bri
dge rect
i
f
i
e
r.
The resul
t
ant
DC
cu
rrent error (IDC
_
e
rr) is a
m
p
lified
an
d
co
m
p
ared with
a saw t
oot
h car
ri
er wa
ve o
f
fi
xed f
r
e
que
ncy
(Fs) t
o
gene
rat
e
t
h
e pul
se wi
d
t
h
m
odul
at
i
o
n (P
W
M
) p
u
l
s
e f
o
r t
h
e
C
uk c
o
n
v
e
r
t
o
r
.
It
s dut
y
rat
i
o
(D
) at
a swi
t
c
hi
n
g
f
r
eq
ue
nc
y
(Fs) c
ont
r
o
l
s
t
h
e dc l
i
nk
v
o
l
t
a
ge at
t
h
e d
e
si
red
val
u
e.
F
o
r
spe
e
d c
ont
rol
refe
rence
spee
d i
s
com
p
ared
wi
t
h
act
ual
sp
eed
o
f
t
h
e m
o
t
o
r
w
h
i
c
h gi
ves s
p
ee
d er
r
o
r
(Ne
r
r
)
w
h
i
c
h i
s
pr
ocesse
d t
h
ro
u
gh P
I
c
ont
r
o
l
l
e
r,
whi
c
h gi
ve re
fere
nce c
u
r
r
ent
si
gnal
(
Ire
f), t
h
i
s
re
fe
rence
cu
rren
t sign
al is
m
u
ltip
ly
wit
h
h
a
ll sen
s
o
r
cu
rren
t po
sition in
form
at
io
n
,
wh
ich
g
e
n
e
rat
e
th
e referen
c
e stato
r
cur
r
ent sig
n
al (Ia
_re
f
)
.
This refe
ren
ce stator current signa
l
(Ia_ref) proc
essed
with
h
y
steresis co
n
t
ro
ller t
o
gene
rat
e
t
h
e
fi
r
i
ng
p
u
l
s
e f
o
r
v
o
l
t
a
ge s
o
urce i
nve
rt
er.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Power F
a
ctor
Correction in
Two Le
g Invert
e
r Fed BLDC
Drive
Using C
u
k
Dc-Dc C
o
nverter (A. P
u
rna C.R
.
)
19
8
3.
D
E
SIGN
OF PFC
CU
K CONV
ER
TER
Fi
gu
re 2
sh
o
w
s t
h
e schem
a
t
i
c of C
UK c
o
n
v
ert
e
r
use
d
f
o
r
PFC
an
d spee
d co
nt
r
o
l
f
o
r
p
r
o
p
o
sed C
U
K
PFC two
inv
e
rter fed
BLDC
M d
r
iv
e. Th
is
co
nv
erter is obtain
e
d
b
y
u
s
ing
th
e
du
ality p
r
in
cip
l
e
o
f
bu
ck
boo
st
co
nv
erter. CUK conv
erter
g
i
v
e
s n
e
g
a
tiv
e
po
larity regu
lated
ou
tpu
t
vo
ltag
e
w.r.t. t
h
e
co
mm
o
n
ter
m
i
n
al o
f
in
pu
t DC v
o
l
t
a
g
e
.
Th
e cap
acito
r C
1
act
s as ener
gy
st
ori
ng a
nd e
n
er
gy
t
r
ansfe
rri
ng e
l
em
ent
from
inp
u
t
t
o
out
put
.
Fi
gu
re
2.
Sc
he
m
a
t
i
c
of C
U
K
con
v
e
r
t
e
r
T
h
e
av
e
r
ag
e ind
u
c
to
r vo
lta
g
e
V
L1
and V
L2
is zero at steady s
t
ate, there
f
ore
V
C1
=V
dc
+V
o
(1
)
V
C1
is larg
e th
an
b
o
t
h
V
dc
and
V
O
.
Whe
n
t
h
e s
w
itch
(S
W) is
o
f
f, i
n
d
u
cto
r
c
u
r
r
ents
I
L1
and I
L2
f
l
ow
s t
h
ro
ugh
d
i
od
e, t
h
e cir
c
u
it is as
sho
w
n i
n
Fi
gu
r
e
3. C
a
paci
t
o
r
C
1
char
ged t
h
r
o
u
g
h
t
h
e
di
o
d
e
by
ener
gy
f
r
o
m
bot
h t
h
e i
n
p
u
t
an
d L
1
. Curr
ent I
L1
decrease
s
, bec
a
use V
C1
is
g
r
eater th
an
V
dc
.
Ener
gy st
ore
d
i
n
L
2
fee
d
s t
h
e
out
put
,
t
h
e
r
ef
o
r
e I
L2
als
o
decreases.
Fi
gu
re
3.
C
U
K
C
o
nve
rt
er
wa
vef
o
rm
whe
n
s
w
i
t
c
h
(S
W) is
o
f
f
Fi
gu
re
4.
C
U
K
C
o
nve
rt
er
wa
vef
o
rm
whe
n
s
w
i
t
c
h
(S
W) is
o
n
Whe
n
the
swit
ch (S
W)
is o
n
,
V
C1
re
verse bias
the diode
,
the
induct
o
r currents I
L1
and I
L2
fl
ows
th
ro
ugh
switch (SW), th
e circu
it as sh
own
in Figu
re
4
.
Sin
c
e V
C1
is
g
r
eater th
an
V
O
, ca
pacitor C
1
di
sch
a
rge
d
th
ro
ugh
th
e switch
(SW), and tran
sferri
n
g
t
h
e ener
gy
t
o
t
h
e out
put
a
nd L
2
. Therefore C
u
rrent I
L1
in
cr
ea
s
e
s
.
The i
n
put fe
ed
energy to L
1
ca
usi
n
g
I
L1
to i
n
c
r
ease.
The i
n
ductor
currents
IL
1a
nd
IL2 are
ass
u
m
e
d
to
b
e
co
n
tinuo
us an
d we assu
m
e
th
e cap
acito
r
vol
t
a
ge
VC
1
t
o
be
c
o
nst
a
nt
,
t
h
en eq
uat
i
n
g
t
h
e
i
n
t
e
gral
o
f
t
h
e vol
t
a
ge
ac
r
o
ss L1
an
d L2
ove
r o
n
e
t
i
m
e
peri
od
t
o
zer
o
gi
ves
At L
1,
V
dc
DT
s
+(V
dc
-V
C1
)(
1-
D
)
T
s
=0
therefore
V
V
(2
)
At L
2,
(V
C1
-V
o
)D
T
s
+ (
-
V
o
)(
1-D
)
T
s
=
0
therefore
V
V
(
3
)
The
dc l
i
n
k
v
o
l
t
a
ge o
f
t
h
e P
F
C
co
nve
rt
er i
s
gi
ve
n as
,
v
(4
)
Wh
e
r
e
V
the a
v
e
r
age
output
of t
h
e
DBR for a
given ac
in
p
u
t v
o
ltage
,
V
√
∏
(5
)
The
Cu
k co
nv
er
ter
u
s
es a
b
o
o
s
t i
n
d
u
ct
o
r
and a
c
a
p
a
c
ito
r
f
o
r
ene
r
g
y
tra
n
s
f
er
. Their
valu
e
s
a
r
e
gi
ve
n a
s
,
L
∆
(
6
)
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
:
196
–
2
04
19
9
C
∆
(
7
)
Whe
r
e
∆
I
L1
is
a specified i
n
ductor c
u
rre
n
t ripple,
∆
V
C1
is a specified voltage ri
pple in t
h
e
in
term
ed
iate c
a
p
acito
r
(C
1
), and I
dc
is th
e cu
rren
t drawn
by th
e BLDCM fro
m
th
e d
c
lin
k. A ri
p
p
l
e fi
lter i
s
designe
d
for ripple
-
free volta
ge at the dc link
of the Cu
k conve
r
ter. T
h
e
inducta
nce
(L
2) of the rippl
e
filter
restricts the in
duct
o
r
peak
-to
-
pea
k
rip
p
le c
u
r
r
ent (
∆
I
L2
)
wi
t
h
i
n
a speci
fi
ed val
u
e f
o
r
t
h
e gi
ve
n sw
i
t
c
hi
ng
fre
que
ncy
(Fs
)
, whe
r
eas t
h
e
capacitance
(C
o) is calcula
tor for th
e allowed ri
p
p
l
e i
n
th
e dc link
v
o
ltag
e
(
∆
V
Cd
). Th
e
v
a
lu
es
o
f
t
h
e
ripple filter ind
u
c
t
o
r and
cap
acitor are g
i
v
e
n as,
L
.
.
∆
(8
)
ɷ
∆
(9
)
The adva
ntage
of CUK converter ci
rcu
it is th
at b
o
t
h
th
e i
n
pu
t curren
t
an
d
th
e cu
rren
t
feed
i
n
g
th
e
out
put
a
r
e reas
ona
bl
e ri
ppl
e f
r
ee, t
h
e
r
ef
ore i
t
i
s
possi
bl
e t
o
sim
u
l
t
a
neousl
y
el
im
i
n
at
e t
h
e ri
ppl
e i
n
b
o
t
h
t
h
e
in
du
ctor cu
rren
ts co
m
p
letely
, lead
i
n
g to
l
o
wer ex
te
rnal
fi
l
t
e
ri
ng
re
qui
re
m
e
nt
s an
d t
h
e
di
sa
dva
nt
age
i
s
t
h
e
requ
irem
en
t o
f
a cap
acit
o
r C
1
with
la
rg
e ri
p
p
le cu
rren
t
carryin
g
cap
a
b
ility.
4.
MO
DELING
OF P
R
OP
OS
ED PF
C
CO
NVERTER BASED PMBLDCM DRIVE
The PFC
c
u
k
t
w
o l
e
g i
nve
rt
er fe
d B
L
DC
M
dri
v
e
wi
t
h
t
w
o
DC
so
urc
e
are t
h
e m
a
i
n
part
s
of t
h
e
pr
o
pose
d
dri
v
e
sy
st
em
, whi
c
h
are m
odel
e
d
b
y
m
a
t
h
em
at
i
c
al
equat
i
o
ns
an
d a c
o
m
b
i
n
at
i
on
of t
h
ese e
q
u
a
t
i
ons
represen
ts th
e co
m
p
lete
m
o
d
e
l of th
e
p
r
op
o
s
ed
d
r
i
v
e s
y
ste
m
. The PFC conve
r
ters
consist
of
DBR, cuk
co
nv
erter an
d
rip
p
l
e filter.
Voltag
e
co
n
t
ro
ller, referen
ce curren
t
g
e
n
e
rator,
PW
M co
n
t
ro
ll
er, sp
eed
con
t
ro
ller,
a refe
rence
cu
rre
nt ge
nerat
o
r
,
a P
W
M
cu
rr
ent co
nt
ro
ller
an
d
a PMBLDC m
o
to
r are u
s
ed
fo
r co
m
p
lete
rep
r
ese
n
t
a
t
i
on
of
cu
k
fed
B
L
DC
M
d
r
i
v
e
sy
st
em
.
PFC Con
v
erte
r
Th
e PFC conver
t
er
b
l
o
c
k
con
s
ists of
vo
ltag
e
con
t
ro
ller
,
PW
M co
n
t
ro
ll
er
and
a
r
e
f
e
ren
ce cu
rr
en
t
gene
rat
o
r.
Vol
t
age Contr
o
ller
Th
e
p
r
op
ortional in
teg
r
al
(PI)
co
n
t
ro
ller is u
s
ed
to con
t
ro
l the DC link
vo
ltag
e
.
DC voltage
error Vdc
_
e(k) at
kth is calculat
e
d as
V
_
k
V
∗
k
V
k
V
∗
k
is referen
ce
DC lin
k
vo
ltag
e
an
d
V
k
is sen
s
ed
DC link
v
o
ltage at k
t
h in
stan
t
Th
is DC
v
o
ltag
e
error is processed
throug
h th
e Pro
p
o
r
ti
on
al
i
n
t
e
gral
v
o
l
t
a
ge co
nt
r
o
l
l
e
r t
o
get
desi
re
d cont
ro
l
si
gnal
Ire
f_
dc
(
k
)
at
kt
h i
n
st
a
n
t
i
s
gi
ve
n as
,
Ire
f_
dc(
k
)
= I(
k-
1)
+ Kp
vc
[V
e(k
)
– Ve(
k
-
1
)]
+
Ki
vcVe
(
k
)
(1
0)
W
h
er
e
Kp
v
c
an
d K
i
cv
ar
e
th
e pr
opo
r
tion
a
l an
d
in
tegral g
a
in
s o
f
th
e vo
ltag
e
co
n
t
ro
ller
Refere
nce Current Gener
a
tor
The
refe
rence i
n
ductor c
u
rre
n
t,
I
∗
,
of
th
e Cuk
co
nv
er
te
r
is
g
i
ve
n
a
s
,
I
∗
I
k
u
(
1
1
)
Wh
ere
uv
i is the un
it tem
p
late
of th
e inp
u
t
AC m
a
in
s vo
ltage calcu
lated
as,
u
;
V
|
V
|
; Vi=
Vin
s
i
n
ω
t
(
1
2
)
whe
r
e
ω
is
frequ
en
cy i
n
rad
/
s
at in
pu
t AC
m
a
in
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Power F
a
ctor
Correction in
Two Le
g Invert
e
r Fed BLDC
Drive
Using C
u
k
Dc-Dc C
o
nverter (A. P
u
rna C.R
.
)
20
0
PWM Control
l
er
T
h
e r
e
f
e
r
e
n
c
e
Cu
k co
nv
e
r
ter
c
u
rr
e
n
t is
co
mp
a
r
ed w
ith its
se
n
s
ed
cu
rr
en
t to
g
e
n
e
r
a
te th
e
c
u
rr
e
n
t e
r
r
o
r
∆i
I
∗
I
. Th
is curren
t
erro
r is
am
p
lifie
d
b
y
g
a
i
n
Pd
c
and
com
p
are
d
with
ca
rrier wa
veform
Qd(t). The
swi
t
c
hi
n
g
si
g
n
a
l
s
fo
r t
h
e I
G
B
T
of t
h
e PFC
c
o
n
v
e
r
t
e
r are
ge
nerat
e
d by
c
o
m
p
ari
ng t
h
i
s
a
m
pli
f
i
e
d cu
rre
nt
err
o
r
with sa
w-t
oot
h
carrie
r
wave
fo
rm
of 2
k
H
z.
If Pdc
∆
idc > Q
d
(t) the
n
Scu
k
= 1
(1
3)
If Pdc
∆
id
c
≤
Q
d
(t)
the
n
Scu
k
=
0
(1
4)
wh
ere Scuk
is
th
e switch
i
n
g
fu
n
c
tion
o
f
t
h
e
switch
u
s
ed in
Cu
k
con
v
e
rter
represen
tin
g, “o
n
”
po
sitio
n
with
Scuk
=
1
an
d its “off” po
sitio
n with Scu
k
=
0
.
PM
BLDCM
D
r
iv
e
Th
e m
o
d
e
llin
g o
f
a sp
eed
contro
ller is qu
ite i
m
p
o
r
tan
t
as the p
e
rform
a
n
ce o
f
th
e system
d
e
p
e
nd
s on
th
is con
t
ro
ller. If at k
t
h
in
stan
t of tim
e,
ω
∗
k
is refere
nce s
p
ee
d,
ω
r(k
)
is
ro
to
r sp
eed
th
en
the sp
eed
er
ro
r
ω
e(k) ca
n
be c
a
lculated as,
ω
k
ω
∗
k
ω
k
(
1
5
)
Thi
s
s
p
ee
d er
r
o
r
i
s
p
r
ocesse
d
t
h
r
o
ug
h a
spee
d c
ont
rol
l
e
r t
o
get
de
si
red
co
n
t
rol
si
g
n
al
.
Speed Contr
o
l
l
er
The
o
u
t
p
ut
o
f
t
h
e P
I
c
o
nt
rol
l
e
r at
kt
h i
n
st
ant
T (
k
)
i
s
gi
ven
a
s
,
T (k
) = T
(k
-1
) + Kp
s[
ω
e(k)
–
ω
e(k-1)] + Kis
ω
e
(
k
)
(
1
6
)
W
h
er
e
Kp
s
and
K
i
s
a
r
e th
e
pr
opo
r
tion
a
l an
d
in
tegral g
a
i
n
s
o
f
th
e sp
eed
con
t
ro
ller.
Refere
nce Wi
nding Currents
The am
pl
i
t
ude
of
st
at
or
wi
ndi
ng
cu
rre
nt
i
s
as
,
I
∗
_
(
1
7
)
Whe
r
e
K
b_em
f
i
s
t
h
e
bac
k
e
m
f const
a
nt
of
t
h
e B
L
DC
M
.
The
refe
re
nce
pha
se c
u
r
r
ent
s
of
t
h
e
m
o
t
o
r
w
i
ndi
n
g
are
de
n
o
t
e
d
by
f
o
r
p
h
a
ses
i
∗
,i
∗
fo
r
p
h
a
ses a,
b
respect
i
v
el
y
.
F
o
r
d
u
rat
i
o
n
of
0-
6
0
º t
h
e
re
fer
e
nce c
u
r
r
ent
s
c
a
n b
e
gi
ven
as
i
∗
1
,
a
n
d
i
∗
1
,
Si
m
ilarly, th
e
refe
rence
wi
nd
i
ng c
u
rre
nt
s
d
u
ri
ng
ot
her
6
0
º
d
u
r
at
i
o
n
are
gene
rat
e
d
i
n
re
ct
ang
u
l
a
r
1
2
0
º
bl
oc
k
f
o
rm
i
n
p
h
ase
with
trap
ezo
i
d
al v
o
ltag
e
o
f
resp
ec
tive
pha
s
es. T
h
ese re
ference c
u
rre
nts are com
p
are
d
with
sense
d
pha
se
cur
r
ents
to
ge
n
e
rate the c
u
rre
nt er
ro
rs
∆i
i
∗
i
,
∆i
i
∗
i
,
fo
r t
h
ree
p
h
ases
o
f
the m
o
tor.
5.
R
E
SU
LTS AN
D ANA
LY
SIS
Sim
u
l
a
t
i
on m
odel
wa
s
devel
ope
d
usi
n
g
M
A
TL
AB
/
SIM
U
LI
N
K
s
o
ft
w
a
re t
o
t
e
st
an
d
val
i
d
at
e t
h
e
p
e
rform
a
n
ce of PFC cuk
two
leg
i
n
v
e
rter
fed
BLDC
M
d
r
i
v
e using
split DC su
pp
ly. Fig
u
re
5
Shows th
e
Sim
u
link bl
oc
k dia
g
ram
of PFC cu
k two leg inve
rter fed PMBLDC
dri
v
e usi
ng s
p
lit DC supply. The
p
e
rform
a
n
ce o
f
th
e PFC cuk two
leg
inv
e
rt
er fed
BLDC
M d
r
iv
e
u
s
ing sp
lit DC su
pply is an
alyzed
o
n
th
e
basis of
vari
ous factor s
u
ch a
s
m
echanical param
e
ters
, electrical param
e
te
rs of the
BLDC
m
o
tor a
nd t
h
e front
end C
UK c
onverter i.e
.
the
speed, stator
current
a
nd e
l
ect
rom
a
gnet
i
c
t
o
rq
ue,
DC
l
i
nk
v
o
l
t
a
ge, t
h
e cuk
in
du
ctor cu
rren
t, the
v
o
ltag
e
acro
ss
t
h
e bu
lk
cap
acito
r, wh
ich
sh
ow
s
sa
tisfactory
perform
ance of t
h
e CUK
co
nv
erter fed
BLDCM d
r
i
v
e. Param
e
ters s
u
ch
as th
e
p
o
wer fact
o
r
, th
e To
tal Harm
o
n
i
c Disto
r
tion, su
pp
ly
cu
rren
t and
su
pp
ly v
o
ltag
e
d
e
term
in
e th
e p
e
rform
a
n
ce o
f
th
e driv
e in
ter
m
s o
f
p
o
wer qu
ality. Th
e
per
f
o
r
m
a
nce of t
h
e dri
v
e i
s
sim
u
l
a
t
e
d for c
onst
a
nt
rat
e
d t
o
r
q
ue (2 Nm
) at
rat
e
d speed
of 1
0
00 r
p
m
,
wi
t
h
an
i
n
p
u
t
AC
v
o
l
t
a
ge
of
2
2
0
V
,
50
Hz s
u
ppl
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l. 6,
No
.
2,
Ju
ne 20
15
:
196
–
2
04
20
1
Fi
gu
re
5.
Si
m
u
l
i
nk m
odel
of
PFC
cu
k
t
w
o l
e
g i
n
ve
rt
er
fed
PM
B
L
DC
dri
v
e usi
n
g
t
w
o
D
C
su
ppl
y
a. Perform
a
nc
e
of CUK Converter
Fe
d
P
M
BLD
CM
Dr
ive D
u
ring
S
t
artin
g
The pe
rform
a
nce of the C
U
K converte
r fe
d BLDCM dr
i
v
e is ev
alu
a
ted
at startin
g
,
wh
ile th
e
m
o
to
r
i
s
feed f
r
om
220
V,
50
Hz AC
su
ppl
y
at
r
a
t
e
d t
o
r
que
of
2 Nm
wi
t
h
a refere
nce spee
d
of 5
0
0
r
p
m
.
Figu
re
6
per
f
o
r
m
a
nce of B
L
DC
M
dri
v
e d
u
ri
ng st
art
i
ng i
n
t
e
rm
s of i
n
p
u
t
AC
v
o
l
t
a
ge, Ac so
ur
ce curre
nt
, D
C
l
i
nk
vol
t
a
ge
, s
p
ee
d
o
f
t
h
e
d
r
i
v
e
,
t
o
r
q
ue
devel
o
p
e
d
by
m
o
t
o
r a
n
d
p
h
ase
a st
a
t
or c
u
r
r
e
n
t
.
M
o
t
o
r rea
c
he
d t
o
a
set
spee
d of
5
0
0
r
p
m
wi
t
h
a l
o
ad t
o
r
q
ue of
2
N
m
at
t
=
0.0
15 sec
.
at
t
h
e t
i
m
e
of st
art
i
ng m
o
t
o
r i
s
t
a
ki
ng a c
u
r
r
e
nt
o
f
3am
p
peaks,
Ac v
o
l
t
a
ge wa
vef
o
rm
and so
urce c
u
r
r
ent
ar
e i
n
phase m
e
ans nea
r
l
y
uni
t
y
curre
nt
and
vol
t
a
g
e
are in ph
ase m
a
in
tain
s
u
n
ity
po
we
r fact
or
f
r
o
m
st
art
i
ng.
(a).
AC
so
u
r
ce
vol
t
a
ge
an
d
so
urce
cu
rre
nt
r
e
spo
n
se
(b
). Spee
d res
p
ons
e du
rin
g
sta
r
ting
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
-
500
-
400
-
300
-
200
-
100
0
10
0
20
0
30
0
40
0
50
0
Ti
me
i
n
s
e
c
AC
Sour
c
e
V
o
lt
a
g
e
AC
Sour
c
e
C
u
rre
nt
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
0
20
0
40
0
60
0
80
0
10
00
12
00
Ti
me
i
n
s
e
c
S
p
e
e
d
(r
p
m
)
Re
f
S
p
e
e
d
M
o
t
o
r Sp
eed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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S
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:
208
8-8
6
9
4
Power F
a
ctor
Correction in
Two Le
g Invert
e
r Fed BLDC
Drive
Using C
u
k
Dc-Dc C
o
nverter (A. P
u
rna C.R
.
)
20
2
(c).
T
o
r
que
res
p
o
n
se
d
u
ri
ng
st
arting
(d
).
Stator
cu
rr
ent res
p
on
se
d
u
ri
ng
startin
g
Fi
gu
re
6.
Per
f
o
rm
ance of B
L
DC
M
d
r
i
v
e
d
u
r
i
n
g st
art
i
n
g
b. Per
f
or
mance of the dri
v
e
when spee
d i
n
crease
fr
om
500 r
p
m
to 1000 rpm
(a).
AC
so
u
r
ce
vol
t
a
ge
an
d
so
urce
cu
rre
nt
r
e
spo
n
se
(b
). Spee
d res
p
ons
e
(c).
T
o
r
que
res
p
o
n
se
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
-2
-1
0
1
2
3
Ti
me
i
n
s
e
c
T
o
rq
u
e
(N
m
)
0
0.
02
0.
0
4
0.
0
6
0.
08
0.
1
-3
-2
-1
0
1
2
Ti
me
i
n
s
e
c
S
ta
to
r c
u
rre
n
t (
A
)
0.
1
0.
1
2
0.
1
4
0.
16
0.
18
0.
2
-
500
-
400
-
300
-
200
-
100
0
10
0
20
0
30
0
40
0
50
0
Ti
me
i
n
s
e
c
AC
Sour
c
e
V
o
lt
a
g
e
AC
Sour
c
e
C
u
rre
nt
0.
1
0.
1
5
0.
2
0.
2
5
0
20
0
40
0
60
0
80
0
10
00
12
00
Ti
me
i
n
s
e
c
S
p
e
e
d
(rp
m
)
R
e
f
Sp
eed
M
o
t
o
r S
peed
0.
1
0.
1
2
0.
1
4
0.
16
0.
18
0.
2
1
1.
5
2
2.
5
3
Ti
me
i
n
s
e
c
T
o
rq
u
e
(N
m
)
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
:
196
–
2
04
20
3
(d
).
Stator
cu
rr
ent res
p
on
se
Fi
gu
re
7.
Per
f
o
rm
ance of B
L
DC
M
d
r
i
v
e
w
h
en s
p
ee
d i
n
c
r
e
a
se f
r
om
50
0r
p
m
t
o
1
0
0
0
r
p
m
Fi
g
u
re 7 s
h
o
w
s t
h
e perf
orm
a
nce be
havi
or o
f
PFC
cuk fe
d
B
L
DC
M
dri
v
e
wi
t
h
t
w
o dc s
u
p
p
l
y
du
ri
n
g
spee
d variation from
500 rpm
to 1000 rpm
at rated torque
of 2
Nm
. The
dri
v
e reache
s
to a se
t speed of 1000
rp
m
in
0.1 sec. in th
is case also
Ac
v
o
ltag
e
wav
e
fo
rm
and s
o
urce
curre
nt are
in phase
m
eans nearly
unity
po
we
r fact
or
.
c. Perform
a
nc
e of the
Drive
when Spee
d
Decrease from 1000
rpm to
500 rpm
(a).
AC
so
u
r
ce
vol
t
a
ge
an
d
so
urce
cu
rre
nt
r
e
spo
n
se
(b
). Spee
d res
p
ons
e
(c).
T
o
r
que
res
p
o
n
se
(d
).
Stator
cu
rr
ent res
p
on
se
Fig
u
r
e
8
.
Perfor
m
an
ce o
f
BLD
C
M dr
iv
e when
sp
eed
d
ecr
eases fr
o
m
1
000r
p
m
to
500
rpm
0.
1
0.
1
2
0.
1
4
0.
16
0.
18
0.
2
-2
-1
0
1
2
Ti
me
i
n
s
e
c
S
ta
to
r c
u
rre
n
t (
A
)
0.
25
0.
3
0.
3
5
0.
4
-500
-400
-300
-200
-100
0
100
200
300
400
500
Ti
me
i
n
s
e
c
AC
So
urc
e
V
o
lt
age
AC
So
urc
e
C
u
rren
t
0.
2
5
0.
3
0.
3
5
0.
4
0
20
0
40
0
60
0
80
0
100
0
120
0
Ti
me
i
n
s
e
c
S
p
e
e
d
(rp
m
)
R
e
f
Spee
d
M
o
t
o
r Sp
eed
0.
25
0.
3
0.
35
0.
4
-4
-2
0
2
4
Ti
me
i
n
s
e
c
T
o
rq
u
e
(N
m
)
0.
25
0.
3
0.
35
0.
4
-2
-1
0
1
2
Ti
me
i
n
s
e
c
S
ta
to
r c
u
rre
n
t (
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Power F
a
ctor
Correction in
Two Le
g Invert
e
r Fed BLDC
Drive
Using C
u
k
Dc-Dc C
o
nverter (A. P
u
rna C.R
.
)
20
4
Fi
gu
re 8 s
h
ow
s t
h
e per
f
o
rm
ance be
ha
vi
o
r
o
f
PFC
cu
k t
w
o
l
e
g i
nve
rt
er fe
d B
L
DC
M
d
r
i
v
e wi
t
h
t
w
o
dc s
u
p
p
l
y
d
u
r
i
n
g
spe
e
d
va
ri
at
i
on
fr
om
100
0
rpm
t
o
5
0
0
rp
m
at
rat
e
d t
o
rq
ue
of
2
Nm
. The
dri
v
e reac
h
e
s t
o
a
set speed
of 500
rpm
in 0.05 sec.
i
n
this
case also Ac
voltage
wa
vefo
rm
and s
o
urc
e
current a
r
e in phas
e
means nea
r
ly unity powe
r fact
or .
d. Per
f
or
man
ce under
S
t
eady
State
Con
d
i
tion
AC
s
o
u
r
ce c
u
r
r
e
nt
an
d
harm
oni
c spect
ra
of
PFC
cu
k t
w
o l
e
g i
n
vert
e
r
fe
d
B
L
DC
M
d
r
i
v
e
wi
t
h
t
w
o
d
c
su
pp
ly during
stead
y-state con
d
ition
at rated to
rq
u
e
, sp
ee
d
at 5
0
0
r
p
m
an
d
1
000
rp
m
is fo
un
d.
A THD
of
7
%
is
obs
er
ved
at
a
spee
d o
f
50
0
rpm
and
w
h
en
t
h
e s
p
eed
i
s
10
0
0
r
p
m
THD
i
s
3.
5%.
M
o
r
e
ove
r, a
n
i
m
pr
ove
d
p
e
rform
a
n
ce of th
e PMBLDCM d
r
iv
e is
ob
serv
ed
in
te
r
m
s of red
u
ce
d
ri
p
p
l
e
s i
n
t
o
r
que
, c
u
r
r
ent
a
nd
spee
d
during stea
dy s
t
ate conditions
.
6.
CO
NCL
USI
O
N
Bru
s
h
l
ess DC
m
o
to
r (BLDC
M
) is p
o
p
u
l
ar for its h
i
gh
efficien
cy, h
i
gh
to
rqu
e
to
wei
g
ht ratio
, sm
a
ll
size, an
d
h
i
gh
reliab
ility, ease
o
f
con
t
ro
l an
d lo
w m
a
in
ten
a
n
ce etc an
d
replacin
g
th
e conv
en
tion
a
l m
o
to
r in
so
man
y
ap
p
licatio
n
s
.
In th
is
p
a
p
e
r a PFC cuk
b
a
sed
tw
o
leg
i
n
v
e
rter
PMBLDCM driv
e wi
th
sp
lit DC so
urce is
anal
y
zed
a
n
d
val
i
d
at
ed f
o
r
a
ppl
i
cat
i
o
ns. A sm
oot
h
spee
d cont
rol
i
s
o
b
se
rve
d
whi
l
e
c
o
nt
r
o
l
l
i
ng
t
h
e
d
c
l
i
n
k
v
o
ltag
e
. Th
e
perfo
r
m
a
n
ce of th
e
d
r
i
v
e is
go
od
and
satisfacto
r
y in th
e
wid
e
ran
g
e
of in
pu
t ac
vo
ltag
e
an
d
m
a
i
n
t
a
i
n
i
ng
g
o
o
d
p
o
w
er
fact
o
r
wi
t
h
l
e
ss t
o
r
que
ri
ppl
e,
sm
oot
h s
p
ee
d c
o
n
t
rol
of
t
h
e
PM
B
L
DC
M
d
r
i
v
e
.
T
h
e
THD
of ac main
s curren
t
is o
b
s
erv
e
d
wel
l
b
e
lo
w
7
%
i
n
m
o
st o
f
th
e cases and
satisfies th
e in
tern
atio
n
a
l
standa
rds.
REFERE
NC
ES
[1]
Mc Naught C
IEE Rev
i
ew 3
,
pp
89-91, 1993
[2]
Cremer R. Current status of rar
e
ear
th p
e
rmanent
magnet. Int conf
on Maglev and
liner dr
ives, Ger
m
an
y
,
1998
, pp
.
391-398
[3]
Singh, B. Singh
, B.P. and
Kum
a
r, M. (2003).
PFC conve
rter
f
e
d PMBLDC m
o
tor driv
e for
air cond
itionin
g
.
Institution
of
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