Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
1
,
M
a
r 202
1
, p
p.
67
~
79
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
1
.
pp67
-
79
67
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Reduci
ng to
rque pul
satio
ns
i
n PM
a
-
SynRM:
a way fo
r
improvi
ng moto
r perfor
manc
e
Percy
R
.
V
ie
go
1
, Juli
o R
. Gómez
2
, Vla
dimi
r Sousa
3
, José
P. M
ontea
gudo
Yanes
4
, E
nrique
C.
Qui
spe
5
1,2,4
Cent
er
of En
erg
y
and
Env
iro
nme
nt
al
Stud
ie,
Univer
sidad
d
e Cie
nfue
gos,
Cub
a
3
Ene
rgy
Dep
artme
nt
,
Univ
ersid
ad
de
l
a
Costa
,
B
arr
anquilla
,
Co
lo
mbi
a
5
Ene
rgy and
Me
cha
ni
ca
l
Depa
r
t
me
nt
,
Univ
ersid
ad
Autónom
a
d
e
Occ
id
ente,
C
al
i
,
Colom
bi
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
3
1,
20
20
Re
vised
Jan
19
, 2021
Accepte
d
Ja
n
2
9
, 2
0
21
Thi
s
pap
er
aim
s
to
eva
lu
ate
t
he
pe
rform
an
ce
of
synchronou
s
rel
uc
ta
n
ce
mot
ors
assisted
by
a
per
m
ane
n
t
ma
gne
t
(PM
a
-
SynR
M
)
foc
used
on
eff
i
cienc
y
and
torque
pulsa
ti
ons.
PM
a
-
SynR
M
show
s
high
eff
icienc
y
and
p
ower
fa
ct
or
,
com
par
ed
to
ind
uct
ion
mot
o
rs
(I
M),
a
lt
hough
th
e
y
hav
e
a
gre
a
te
r
cost.
The
se
ma
ch
ine
s
d
evelo
p
re
la
t
ive
ly
h
igh
torqu
e
r
ipple,
c
ogging
to
rque
,
a
nd
torqu
e
im
balanc
es.
Con
seque
ntl
y
,
the
elec
tro
ma
gne
ti
c
to
rque
is
red
u
ce
d
,
the
mo
to
r
te
mp
era
tur
e
is
in
cre
ase
d
,
and
m
e
cha
ni
ca
l
vibr
at
io
ns
are
induc
ed
.
The
opt
imal
design
of
th
e
m
ac
hin
e
stru
ct
ur
e
s
such
as
f
low
b
arr
ie
rs,
p
ermane
nt
ma
gne
ts,
and
sta
tor
slo
t
s,
a
mong
o
thers
,
a
ll
ow
r
edu
ci
ng
torque
pu
lsat
ions.
A
com
par
ison
is
m
ade
b
et
we
en
dif
fer
ent
designs
o
f
the
PM
a
-
SynR
M
rep
orte
d
in
the
sc
ie
nt
ific
l
it
er
at
ure
,
and
the
eff
ects
on
eff
i
cienc
y,
torque
pu
l
sati
on,
and
oper
ating
costs
are
evalua
te
d.
A
ca
se
study
o
n
the
mo
tor
dri
ving
th
e
ai
r
condi
ti
on
er
blo
wer
in
a
hot
el
room
was
m
a
de,
to
determ
in
e
th
e
b
est
ec
onom
ic
var
i
a
nt
b
et
wee
n
IM
or
PM
a
-
SynR
M.
A
sensiti
v
e
a
nal
ysis
was
ma
de
to
ev
al
u
ate
sev
era
l
un
ce
rt
ai
nties.
The
adv
ant
ag
es
of
using
one
of
the
PMa
-
SynR
M
ana
lyzed
we
re
de
monstra
t
ed.
Also,
i
t
was
prov
e
d
th
at
the
inve
stme
n
t
is
fe
asibl
e
e
conom
i
c
al
ly
,
al
though
N
PV
and
payb
ac
k
ar
e
not
th
e
best,
du
e to
low
loa
d
f
ac
to
r
in
in
ver
te
r
-
cont
rol
le
d
mot
ors
in ai
r co
ndit
ione
rs
.
Ke
yw
or
d
s
:
Coggin
g
t
orque
Eco
nomic anal
ys
is
Perma
ne
nt ma
gn
et
mo
t
or dri
ves
Synchr
onous
r
el
uctance
mo
t
or
dr
i
ves
Torq
ue rip
ple
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Vladimir
S
ou
s
a San
t
os
Energ
y Dep
a
rt
ment
Un
i
ver
si
dad d
e
la Costa
Ca
ll
e 5
8 N
o.55
-
66,
Barra
nquil
la
, Co
lo
mb
ia
Emai
l:
v
sousa
1@cuc
.edu.c
o
1.
INTROD
U
CTION
Ele
ct
ric
mo
to
r
s
are
amo
ng
the
main
c
onsume
rs
of
el
ect
ri
cal
ener
gy,
re
pr
ese
ntin
g
ar
ound
50
%
of
world
c
ons
umpti
on
an
d
a
r
ound
67%
of
el
e
ct
rici
ty
co
ns
umpti
on
in
the
i
ndus
tria
l
sect
or
[
1
]
,
[
2].
D
ue
to
this,
te
chnolo
gies
s
uch
as
s
olid
-
st
at
e
adju
sta
ble
vo
lt
age
–
fr
e
que
ncy
c
on
t
ro
ll
ers
[
3
]
,
[
4]
an
d
re
gu
la
to
r
y
mech
anism
s
su
c
h
as
minim
um
e
ne
rgy
-
ef
fici
ency
pe
rform
ance
sta
nd
a
r
ds
(MEPS
)
hav
e
been
im
pleme
nted
[
5]
to
re
duce
th
e
consu
mp
ti
on
of
el
ect
rical
e
ne
rgy
i
n
t
he
m
oto
rs
. M
E
PS
ai
m
s
the
g
ra
du
al
ly
co
mme
rcial
iz
e
an
d
use
mo
t
ors
with
high levels
of e
ff
ic
ie
nc
y
s
uc
h as IE
4 (s
up
e
r
-
premi
um) a
nd
I
E5 (u
lt
ra
-
prem
ium) [
5
]
,
[
6].
The
high
de
m
and
to
achie
ve
these
le
vels
of
ef
fici
enc
y
ha
s
dri
ve
n
t
he
de
velo
pm
e
nt
a
nd
desig
n
of
new
te
ch
no
l
ogie
s
in
el
ect
ric
mo
to
rs.
Eme
rgi
ng
te
c
hnologi
es
inclu
de
permane
nt
ma
gn
e
t
sy
nc
hro
nous
mo
to
rs,
sy
nc
hro
nous
r
el
uctance
mo
t
or
s
,
a
nd
a
c
ombinati
on
of
t
hese
te
c
hnologies
s
uch
as
s
yn
c
hro
nous
re
lucta
nce
mo
to
rs
a
ssist
ed
by a pe
rma
nent
magnet (
PM
a
-
SynR
M
)
[6
]
-
[
8].
PM
a
-
S
yn
R
M
s
hows
high
e
ff
i
ci
ency
a
nd
power
f
act
or
c
ompa
red
to
i
nduction
mo
t
or
s
(IM),
al
t
hough
they
hav
e
a
great
er
co
st.
Both
thei
r
desi
gn
a
nd
their
man
uf
act
ur
e
a
re
co
mp
le
x
[
9].
F
ur
t
hermo
re
,
these
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
67
–
79
68
machine
s
de
ve
lop
relat
ivel
y
high
tor
que
pulsa
ti
on
s
[10
]
-
[
12]
.
The
high
tor
que
pulsa
ti
on
s
are
due
to
th
e
com
plex
str
uct
ur
e
of
t
he
P
M
a
-
SynR
M
.
F
igure
1
(
a)
s
hows
t
he
str
uctur
e
of
a
P
Ma
-
SynR
M
with
ou
t
the
permane
nt
ma
gn
et
s
(PM
)
in
place.
In
Fig
ure
1
(
b),
the
det
ai
ls
of
t
he
str
uc
ture
of
a
r
ot
or
la
minati
on
w
it
h
the
PM
i
ns
erte
d
a
r
e g
ive
n [
13].
(
a)
(
b)
Figure
1. Str
uc
tural
detai
ls of
a PMa
-
S
ynRM
,
a)
P
M
a
-
S
ynR
M
with
ou
t t
he PM
i
n place
,
b) Rot
or lami
nat
ion
arr
a
ng
e
ment
w
it
h
de P
M
in
p
l
ace [
13]
The
to
r
qu
e
pulsa
ti
on
s
ha
ve
two
main
c
omp
on
e
nts:
to
rque
rip
ple
an
d
c
ogging
to
rque.
Be
sides,
t
hi
s
machine
prese
nts
imp
ort
ant
mecha
nical
an
d
ma
gnet
ic
imbala
nces
.
A
s
a
res
ult,
the
a
ve
rag
e
el
ect
r
om
a
gn
et
ic
tor
qu
e
is
re
duc
ed
[
14],
t
he
m
otor
te
mp
e
ratu
re
is
increase
d,
and
unwa
nted
mecha
nical
vib
rati
ons
a
re
in
du
ce
d,
causin
g
noise
a
nd p
re
mature
bea
rin
g
a
ging
a
nd
the
r
ed
uctio
n
of
t
he
li
fe
s
pa
n
[
15
]
-
[
19
].
A
dd
it
io
nally,
the
y
ca
n
aff
ect
t
he
stabi
li
ty o
f
m
otor c
on
t
ro
l,
esp
eci
al
ly at hi
gh s
pee
ds
.
Torq
ue
rip
ple
res
ults
from
the
interact
i
on
betwee
n
the
s
patia
l
ha
rm
on
ic
s
of
the
sta
to
r
mag
netomoti
ve
f
or
c
e
a
nd
t
he
ai
r
ga
p
per
me
ance.
T
hey
a
re
hi
gh,
due
to
th
e
to
oth
e
d
str
uc
ture
an
d
the
presence
of
P
M
in
the
P
M
a
-
SynR
M
.
S
o,
i
n
t
his
ty
pe
of
m
oto
r
,
redu
ci
ng
t
orq
ue
pu
l
sat
ion
is
one
of
the
highest
pr
i
or
it
ie
s
in
it
s
dev
el
opment.
T
he
per
c
ent
of
(%
T
rip
ple)
is
the
relat
ion
s
hip
bet
wee
n
t
he
var
ia
ti
on
s
of
t
he
pea
k
-
to
-
pea
k
tor
qu
e
(
∆T
pp) t
o
the a
ve
rag
e
torq
ue
(
T
ave
)
i
n
a
n
el
ect
ric c
yc
le
. I
t i
s
giv
e
n by
(
1
)
.
%
=
∆
100
(1)
In
Fi
gure
2
a
tor
que
wa
ve
is
giv
e
n,
w
he
re:
aver
a
ge
to
rque
is
5.1;
pea
k
-
to
-
pea
k
tor
que
is
0.8
67
Nm,
and the
pe
rcen
t
age
of torq
ue ripp
le
is
17%
[
9].
Figure
2.
To
r
que
wav
e
[9]
Coggin
g
to
rqu
e
occurs
pr
ima
rily
w
he
n
the
s
ides
of
the
sta
t
or
te
et
h
matc
h
the
sides
of
t
he
ro
t
or
te
et
h
and
a
to
rque
c
ompone
nt
is
r
equ
i
red
t
o
br
e
ak
the
at
tract
i
on
that
occ
urs.
Anot
her
c
ommo
n
ca
us
e
of
coggin
g
tor
qu
e
is
due
to sligh
t
as
ym
m
et
ries
in
the
m
agn
et
ic
fiel
d g
ener
at
e
d
by
t
he
wi
nd
i
ngs,
w
hi
ch
ca
us
e
v
ariat
ion
s
in
reluctance
,
de
pendin
g
on
t
he
r
otor
po
sit
io
n
[20].
T
he
c
on
t
rib
ution
of
this
pap
e
r
is
the
e
valuati
on
of
the
performa
nce
of
the
ope
rati
on
of
P
M
a
-
S
yn
R
M
fo
c
us
e
d
on
eff
ic
ie
n
c
y
a
nd
tor
que
pu
lsa
ti
on
s
,
s
pecifica
ll
y
the
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Red
ucin
g
tor
que
pu
ls
atio
ns
i
n
PM
a
-
Sy
nRM
: a way
for
im
provi
ng
m
oto
r
pe
rforma
nce
(
P
ercy R.
Vie
go
)
69
pro
blems
of
t
orq
ue
rip
ple
an
d
co
gg
i
ng
tor
qu
e
are
asse
sed
.
I
n
se
ver
al
w
ork
s
the
op
e
rati
on
of
P
M
a
-
SynR
M
has
been anal
yze
d [15
]
-
[
19]
, how
ever,
none of
them is
an anal
ys
is
with the
a
ppr
oach p
rop
ose
d
i
n
this
stu
dy.
Fir
stl
y,
a
n
ana
lysis
of
opti
m
iz
ed
PMa
-
S
yn
RM
desi
gn
di
mensi
on
s
t
o
r
edu
ce
t
orq
ue
pu
lsa
ti
ons
is
carried
ou
t.
A
co
mp
a
rison
betwee
n
dif
fere
nt
var
ia
nts
of
this
m
otor
i
s
ma
de
t
o
e
va
luate
the
ef
fe
ct
s
on
op
e
rati
onal
ch
aracte
risti
cs
an
d
a
dv
a
ntage
s
a
nd
disa
dvanta
ge
s
in
oth
e
r
fac
tors,
inclu
ding
costs.
A
case
study
on
t
he
m
otor
that
dri
ves
th
e
ai
r
co
nd
it
io
ner
blower
i
n
a
hote
l
room
was
made,
t
o
de
te
r
mine
the
best
var
ia
nt:
employin
g
a
n
IM
or
one
of
three
P
M
a
-
S
ynRM
t
yp
es
ob
ta
ined.
T
he
a
dvanta
ges
of
usi
ng
on
e
of
the
PM
a
-
SynRM
was
d
e
monstrate
d.
2.
RESEA
R
CH MET
HO
D
2.1.
Effect
s
of
r
oto
r desig
n par
am
eters
on t
or
que pul
sation
s
The
most
im
portant
diff
ic
ulty
encou
ntere
d
i
n
the
desi
gn
a
nd
operati
on
of
t
he
PM
a
-
S
ynRM
is
to
rqu
e
rip
ple.
W
he
n
s
tudyin
g
the
bibl
iog
ra
phy
relat
ed
to
the
reduc
ti
on
of
this
phenomen
on,
it
is
evide
nt
that
amo
ng
the
de
sig
n
paramet
ers
t
hat
m
or
e
af
fect
to
rque
rip
ple
is:
th
e
num
ber
of
r
otor
fl
ux
barriers,
sta
tor
slot
s/roto
r
flu
x
ba
rr
ie
r
s,
qu
a
ntit
y
p
os
it
ion
of
P
M
an
d
ins
ulati
on
r
at
ios
(kq
a
nd
kd).
In
[21
]
a
desig
n
proce
dure
is
dev
el
op
e
d
for
a
PM
a
-
S
ynRM
of
a
wa
sh
i
ng
machine
,
base
d
on
a
finite
el
ement
s
of
t
ware.
The
obje
ct
iv
e
is
to
achieve
t
he
be
st
desig
n
t
hat
giv
es
t
he
rated
ave
rag
e
tor
qu
e
induce
d,
with
mi
nimal
to
r
qu
e
ri
pp
le
.
Th
e
rated
mo
to
r
values
a
re
1.1
N
m,
563
rpm,
a
nd
1.62
A
for
the
wa
s
hing
m
ode
a
nd
0.2
Nm,
13
200
r
pm,
a
nd
3.2
A
fo
r
the s
pin
mode.
The
desi
gn
e
d
sta
tor
has
36
s
lots,
with
a
di
stribu
te
d
t
hr
ee
-
phase,
4
-
pole
windin
g,
integ
ral
slots
per
pol
e.
The
co
nduct
or
c
urre
nt
densi
ty
sel
ect
ed
wa
s
4.7
A/
mm2
f
or
t
he
wash
i
ng
m
od
e
(which
de
ma
nd
s
lo
w
powe
r)
,
an
d
7.4
A/
mm
2
f
or
the
s
pinnin
g
m
od
e
(
wh
ic
h
de
man
ds
high
power).
In
Fig
ure
3,
t
he
diagr
a
ms
t
o
determi
ne
the
best
va
riant
in
te
rms
of
the
num
ber
of
flu
x
b
ar
riers
ar
e
show
n;
an
d
in
T
able
1,
t
he
ef
f
ect
that
the
num
ber
of
flu
x
barriers
causes
on
ave
r
age
to
rque
a
nd
tor
qu
e
rip
ple
for
the
was
hing
m
ode
case
c
an
be
ob
s
er
ved.
I
niti
al
ly,
the
sel
ect
ed
val
ues
f
or
kq
an
d
kd
a
re
th
os
e
gi
ven
i
n
[
22]
as
op
ti
mal
(
kq
=
0,6
a
nd
kd
=1
),
wh
ic
h remai
n
const
ant
durin
g
the
an
al
ys
is.
Figure
3. Sc
he
me of t
he varia
nts w
it
h diff
e
re
nt num
be
rs of f
lux
ba
rr
ie
rs
[2
2]
Table
1.
E
ffec
t o
f
the
num
ber
of b
a
rr
ie
r
s
on the a
ver
a
ge
t
orqu
e
and t
orq
ue
r
ip
ple
[
22]
3
6
slo
t stato
r
(
k
q
=
0
.6
, k
d
= 1)
1
barrie
r
2
barrie
rs
3
barrie
rs
4
barrie
rs
Av
e.
to
rqu
e (
N
m
)
0
.76
3
0
.79
5
0
.80
5
0
.82
1
Torq
u
e r
ip
p
le (
%
)
1
5
.07
1
3
.38
1
0
.90
9
.90
Accor
ding
to
Table
1,
the
be
st
var
ia
nt
is
th
at
of
4
ba
rr
ie
rs
.
H
ow
e
ver,
co
ns
ide
rin
g
the
di
mensions
of
the
m
otor
(
with
a
la
mi
nation
pac
ka
ge
of
32
mm
lo
ng
a
nd
11
7
mm
of
e
xter
nal
diamet
er)
,
it
is
nece
s
sary
to
sel
ect
o
nl
y 3 b
arr
ie
rs
, to g
ua
r
antee ad
eq
uate
r
igi
d
it
y
a
nd m
echan
ic
al
resist
ance.
In
t
he
nex
t
ste
p,
t
he
be
st
isol
at
ion
rati
os
are
determi
ne
d.
It
is
obta
ined:
kq
=
0.9
a
nd
kd
=
1,
w
hich
diff
e
r
from
t
hose
ob
ta
ine
d
i
n
[
22].
As
f
or
the
P
M
to
be
inserte
d
in
t
he
flu
x
ba
r
riers
,
the
best
va
ri
ant
is
ob
ta
ine
d
with
t
he
f
ollo
wing
pa
rameters:
P
M
typ
e:
f
er
rite
;
nu
m
ber
of
P
M
a
nd
posit
ion
pe
r
po
le
as
de
picte
d
in
Figure
4
[
21];
PM
vol
um
e:
19.
12
cm
3.
T
he
data
wit
h
t
hes
e
m
od
el
value
s
are
giv
e
n
in
Table
2.
With
these
resu
lt
s,
a
proto
typ
e
was
buil
t.
The
e
xperime
n
ta
l resu
lt
s
wer
e
sati
sfactory.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
67
–
79
70
Figure
4. Be
st
var
ia
nt arran
ge
ment
[21]
Table
2.
Sele
ct
ed
m
odel
p
a
ra
mete
rs
Av
e.
to
rqu
e
(Nm)
Torq
u
e r
ip
p
le
(%)
Cu
rr
en
t
(A)
Ef
fic
ien
cy
(%)
Po
wer
f
acto
r
(p.u
.)
1
.34
5
6
.7
1
.6
69
0
.77
On
e
way
to
re
du
ce
c
ogging
tor
que
is
by
pro
per
l
y
a
rr
a
ng
i
ng
t
he
P
M
in
th
e
flu
x
ba
rr
ie
rs.
I
n
Fig
ur
e
5,
PM
a
rr
a
ngeme
nt
f
or
4
m
od
el
s
of
a
1.8
kW,
4
pole
s,
36
slo
ts
PM
a
-
SynR
M
is
sho
wn
[
23]
.
Table
3
s
hows
t
he
resu
lt
s
of to
rqu
e v
al
ue
s.
T
he o
ptimum
P
M
a
-
S
yn
R
M
ge
om
et
r
y wit
hout the
P
M
s is
sho
wn in
Fig
ur
e
6 [
24].
Table
3.
T
orq
ue
r
es
ults f
or th
e f
our
m
odel
s [23]
Item
s
Bas
ic
Mod
el
Mod
el 1
Mod
el
2
Mod
el
3
Av
e.
to
rqu
e (
N
m
)
1
1
.77
1
1
.35
1
1
.73
1
1
.83
Co
g
g
in
g
torq
u
e (
Nm
)
0
.09
8
0
.06
5
0
.17
5
0
.15
4
Torq
u
e r
ip
p
le (
%
)
2
1
.8
3
0
.8
1
9
.3
1
7
.6
Figure
5. P
M
a
rr
a
ng
e
ment
f
or the
4
m
odel
s [23]
Figure
6. O
ptimum
P
M
a
-
Syn
RM
geomet
r
y wit
hout the
P
M
[24]
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Red
ucin
g
tor
que
pu
ls
atio
ns
i
n
PM
a
-
Sy
nRM
: a way
for
im
provi
ng
m
oto
r
pe
rforma
nce
(
P
ercy R.
Vie
go
)
71
As
ca
n
be
obs
erv
e
d
in
the
ta
ble,
f
or
re
duci
ng
c
ogging
to
r
qu
e
,
Mo
del
1
is
the
best
s
olu
ti
on
bu
t
is
worth
f
or
dec
r
easi
ng
t
orq
ue
r
ipp
le
. On
the
c
on
t
rary,
t
he
be
st
so
luti
on r
el
at
ed
to
t
orqu
e
ri
pp
le
is usi
ng
M
odel
3
[23].
T
her
e
by,
the
desi
gn
e
r
mu
st
a
nalyze
the
sp
eci
fic
si
tu
at
ion
for
de
ci
din
g
w
hat
to
do.
A
s
in
th
e
case
analyze
d
be
fore
i
n
[
21],
th
e
r
otor
best
va
riant
r
el
at
ed
to
flu
x
ba
rr
ie
r
num
be
r
is
f
our;
but
due
t
o
t
he
man
uf
act
ur
i
ng
diff
ic
ulti
es
an
d
the
mec
ha
nical
stren
gth
,
in
t
his
stu
dy
th
ree
-
la
yer
of
flu
x
barriers
a
re
sel
ect
ed.
Wh
e
n
t
he
opti
mal
flu
x
barrier
ge
om
et
ry
w
it
ho
ut
PM
ha
d
bee
n
achie
ve
d,
t
hr
ee
dif
fere
nt
case
s
a
re
s
tud
ie
d
dep
e
ndin
g
on
t
he
inse
rted
P
M
.
In
Fig
ur
e
7,
the
sel
ect
ed
ge
om
et
r
y
for
C
ase
1
ca
n
be
obser
ve
d,
wh
e
re
PM
is
introd
uced in
both
base a
nd si
de
sect
ors,
and
only
i
n
the i
nnerm
os
t flu
x ba
r
rier laye
r.
The
r
e are three
dif
f
eren
t
cases f
or the c
omparis
o
n:
➢
Ca
se 1
(C1):
T
hr
ee
P
M
in
sert
ed
in
the i
nner
mo
st
flu
x bar
rier laye
r.
➢
Ca
se 2
(C2):
T
hr
ee
P
M
in
sert
ed
in
the
first t
wo in
nermost
f
lux
ba
rr
ie
r
laye
rs.
➢
Ca
se 3
(C3):
T
hr
ee
P
M
in
sert
ed
in
all
the t
hree flu
x bar
rier
la
yer
s.
In Table
4, s
ome
p
a
ramete
rs of t
he
t
hr
ee
va
r
ia
nts (
C
1,
C
2,
and C3
)
a
re sp
eci
fied.
Figure
7. Sele
c
te
d
r
otor
geom
et
ry
for
Ca
se
1 [
24]
Table
4.
Some
sp
eci
ficat
io
ns
of the t
hr
ee
m
ot
or
s
for
ai
r
con
diti
on
er
b
l
ow
e
rs [24]
Para
m
eters
PMa
-
Sy
n
RM
C1
C2
C3
Ou
tp
u
t po
wer
(kW
)
0
.9
0
.9
0
.9
Av
erage torq
u
e (
N
m
)
6
.38
6
.38
6
.38
Ef
fic
ien
cy
(
%)
9
1
.81
9
3
.17
9
3
.46
Rated
sp
eed (r
p
m
)
1350
1350
1350
Op
eration
al sp
eed
rang
e
(r
p
m
)
500
-
1750
500
-
1750
500
-
1750
Co
st o
f
m
o
to
rs (
U
SD)
604
639
686
Ca
se
C1
pr
es
ents
t
he
l
ow
e
st
in
vestme
nt
(only
on
e
la
ye
r
with
P
M
inserte
d)
bu
t
ha
s
the
wor
s
t
eff
ic
ie
nc
y;
wh
i
le
C3
sho
ws
t
he
hi
gh
e
st
ef
fici
ency
bu
t
ha
s
t
he
hi
gh
e
st
c
os
t
(
the
th
ree
la
ye
rs
with
P
M
inse
r
te
d)
.
C2 is a
n
inte
rm
ediat
e case.
So, the
va
riant to
be
sel
ect
ed
w
il
l dep
e
nd
on
a
de
ta
il
ed
analysis
.
2.2.
Effect
s
of
st
ator d
e
sign
p
ar
amet
er
s
on
torque rippl
e
Althou
gh
the
r
otor
desig
n
pa
r
amet
ers
discu
s
sed
t
o
determi
ne
t
he
gr
eat
est
re
du
ct
io
n
in
t
orq
ue
rip
ple
in
P
M
a
-
S
yn
R
M
,
the
sta
to
r
de
sign
is
al
so
i
mporta
nt.
I
n
[
25],
a
de
sig
n
i
s
dev
el
op
e
d
usi
ng
a
FE
M
s
oft
war
e
to
ob
ta
in
the
best
sta
tor
par
am
e
te
rs,
from
a
te
st
mo
t
or
of
1.
62
A,
563
rpm,
1.2
N
m,
4
po
le
s
,
24
sl
ots,
3
flu
x
barriers
per
po
le
,
an
d
values
of
kq
=
0.9
a
nd
kd
=
1.0
.
T
he
ro
t
or
struc
tu
re
re
mains
c
on
sta
nt.
T
he
sta
tor
is
identic
al
to
t
ha
t use
d
in
a c
onven
ti
onal
IM.
The
te
st m
achi
ne
str
uctu
re is
sh
ow
n
in
Fi
gur
e 8
[
22].
Table 5
g
i
ves
t
he
a
ver
a
ge of d
evelo
ped to
rqu
e an
d
to
rque
ripp
le
values
for 1
2,
24, a
nd
36
slots.
As
is
evide
nt,
th
e
va
riant
with
36 slots is
bette
r.
Figure
8. Test
mo
to
r
st
ru
ct
ur
e
[
22
]
Table
5.
C
omp
ariso
n of t
he di
ff
e
ren
t
num
ber o
f
slots
in a three
-
phas
e
distrib
ute
d
w
ind
in
g [
22]
Slo
t
n
u
m
b
er
Torq
u
e
(Nm)
Torq
u
e r
ip
p
le
(%)
12
1
.6
2
9
.38
24
1
.52
3
2
.89
36
1
.54
7
.12
2.2.1.
Stat
or w
indi
ng
s
The
m
os
t
fr
e
quent
sta
to
r
wi
nd
i
ng
c
onfig
urat
ion
s
in
these
m
otors
a
re
th
e
distri
bu
te
d
integ
ral
sl
ots
windin
gs
a
nd
the
c
on
ce
ntrate
d
f
racti
onal
slo
ts
on
e
[
19
]
,
[
26]
.
T
he
a
dv
a
nt
ages
of
co
nce
nt
rated
windin
gs
over
the
distrib
uted
ones
a
re
t
he
sig
nifica
nt
re
du
ct
io
n
in
c
oppe
r
volu
me
and
c
oppe
r
l
osse
s
possibil
it
y
of
a
reducti
on
i
n
t
he
m
otor
t
otal
le
ng
t
h
[
27];
a
de
crease
i
n
ma
nufact
ur
in
g
co
st;
highe
r
sl
ot
fill
s
facto
r.
How
ever,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
67
–
79
72
reg
a
rd
i
ng
t
orq
ue
rip
ples,
th
e
us
e
of
the
con
ce
ntrate
d
windin
gs
see
ms
t
o
ha
ve
mixed
res
ults
[
28]
.
So,
gen
e
rall
y, sta
to
r dist
rib
uted wi
nd
i
ngs, ha
ving
integral
or frac
ti
on
al
slots
are
pr
e
ferred
[2
9]
.
In
[25]
t
he
us
e
of
6
slots/
4
pole
s
and
12
sl
ots/4
pole
s
with
con
ce
ntrate
d
w
ind
in
gs,
was
e
valuated
.
I
t
was
obta
ine
d
that,
f
or
6
slots,
the
aver
a
ge
to
rque
wa
s
1.8
Nm
a
nd
t
orqu
e
ripp
le
44%,
w
hile,
for
12
sl
ot
s,
th
e
values
wer
e
0.578
Nm
a
nd
43.
25%,
re
sp
ect
ively.
T
hese
hig
h
value
s
caus
e
that,
in
the
li
te
ratur
e
c
onsu
l
te
d,
it
is
su
ggest
e
d
not
to
us
e
thes
e
slots/
po
le
c
ombinati
ons
f
or
con
ce
ntrate
d
or
distrib
uted
wi
ndin
gs
.
So,
it
is
pro
po
se
d
f
or
a
bette
r
s
olu
ti
on,
to
us
e
a
sta
to
r
of
36
slots
.
Also
,
tw
o
var
ia
nts
are
co
mp
a
re
d:
sing
le
an
d
do
ub
le
la
yer
fo
c
us
e
d
to
re
duce
ha
r
monics.
T
he
s
econd
la
yer
of
the
la
st
wi
nd
i
ng
has
a
fr
act
ion
al
c
oil
pitch
.
Th
e
aver
a
ge
t
orque
, th
e t
orq
ue
ri
pple
, a
nd it
s p
e
r
centage
f
or
eac
h win
ding a
re
giv
e
n
in
Ta
ble
6 [25].
Table
6.
C
omp
ariso
n betwee
n a si
ngle
-
a
nd
double
-
la
yer
dis
tribu
te
d win
dings
for 36 sl
ots
[25]
Layers
Av
e.
to
rqu
e
(Nm)
Torq
u
e r
ip
p
le
(Nm)
Rip
p
le
(%)
Sin
g
le
Do
u
b
le
1
.54
0
.10
9
7
.12
1
.5
0
.08
5
.33
The
double
-
la
ye
r
s
uppresses
the
odd
5t
h,
7t
h,
11
t
h,
13th
ha
rm
on
ic
s.
Howe
ver,
the
sin
gle
-
la
yer
has
a
fun
dame
ntal
com
pone
nt
of
hi
gh
e
r
to
rque
t
ha
n
in
the
doub
le
la
yer
.
All
th
is
analysis
ser
ves
as
an
exa
mp
le
to
sh
ow
th
at
the
typ
e
of
wi
nd
i
ng
has
to
be
care
f
ully
sel
ect
ed
a
nd
t
hat
it
mu
st
be
eval
uated
f
or
eac
h
s
pecifi
c
case
of ap
plica
ti
on
of the
PM
a
-
S
ynRM
.
2.2.2.
Slo
t geo
metric
optimi
zat
i
on
In
[25
],
the
slo
t's
geomet
ric
opt
imi
zat
ion
is
performe
d.
Th
e
slot
sh
a
pe,
t
he
heig
ht
of
it
s
op
e
ning,
the
too
th
bo
tt
om
r
oundin
g,
an
d
the
wedge
hei
gh
t,
pr
act
ic
al
ly
do
no
t
at
al
l
aff
ect
the
re
su
lt
s,
w
hile
th
e
slot
op
e
ning
widt
h
and
t
he
to
oth
width
a
ff
e
ct
th
em
sig
nificantl
y.
T
he
op
ti
miz
at
ion
m
et
hod
use
d
in
t
his
stu
dy
can
be
see
n
i
n
[
25]
. T
he
m
os
t
relevan
t
res
ults o
n t
he
slot
openi
ng a
nd to
oth
wi
dth
a
re
desc
rib
ed belo
w.
Slot
ope
ning
,
t
he
slot
openi
ng
ca
us
es
a
vera
ge
to
r
qu
e
an
d
tor
qu
e
rip
ple
t
o
c
hange
s
ubst
antia
ll
y.
I
n
Figure
9
a)
t
he
slot
openi
n
g
i
s
show
n.
Table
7
[
25]
s
hows
t
hat
the
small
er
the
ope
ning,
t
he
bette
r
t
he
re
su
lt
s,
al
tho
ug
h
it
is
ne
cessar
y
to
a
na
lyze
if
the o
pe
ning
al
lows
or n
ot
the u
se o
f
automatic
w
in
ding
mac
hin
es
,
wh
ic
h
pro
du
ce
an ad
di
ti
on
al
sav
i
ng in
m
otor c
os
t.
To
oth
widt
h
,
i
n
[17]
an
e
xp
e
riment
with
a
36
-
slots
mac
hin
e
is
ca
rr
ie
d
out,
s
howi
ng
th
at
with
cl
os
ed
slots
a
to
rque
r
ipp
le
of
13.
7%
is
pro
duced
,
wh
il
e
for
se
mi
-
cl
os
e
d
sl
ots
it
is
18%
a
nd
f
or
open
slots
22.
4%.
A
cro
ss
-
sect
io
n o
f
a
mo
t
or
with
cl
os
ed
slots is
sh
ow
n
in
Fi
gur
e 9
(
b)
[
18].
(a)
(b)
Figure
9. Stat
or slots
str
ucture o
f
P
M
a
-
S
ynRM,
(
a)
Stat
or
slot o
pe
ning
pa
rameters
,
(
b) C
ro
ss
-
sect
io
n of
a
mo
to
r wit
h
cl
ose
d
sl
ots [1
7],
[18]
Table
7.
A
ver
a
ge
a
nd to
rque
r
ipp
le
dep
e
ndin
g on the
slot
openi
ng [1
8]
Slo
t
o
p
en
in
g
(mm)
Av
e.
Torq
u
e
(Nm)
Torq
u
e r
ip
p
le
(%)
4
1
.31
3
9
.52
3
1
.42
6
8
.63
2
1
.53
0
7
.12
1
1
.60
5
5
.79
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Red
ucin
g
tor
que
pu
ls
atio
ns
i
n
PM
a
-
Sy
nRM
: a way
for
im
provi
ng
m
oto
r
pe
rforma
nce
(
P
ercy R.
Vie
go
)
73
Althou
gh
t
he
a
ver
a
ge
to
rque d
ecrease
s
som
ewh
at
w
it
h
cl
ose
d
slots
,
the
s
peed
al
s
o
inc
re
ases
sli
gh
tl
y,
so
t
he
powe
r
ou
t
pu
t
is
r
arel
y
a
ff
ect
e
d.
Th
e
same
aut
hor
repor
ts
that
t
he
re
a
re
s
om
e
t
echn
i
qu
e
s
t
o
c
lose
the
sta
tor
slots
a
ft
er
t
he
windin
g
pro
cess
us
i
ng
ferroma
gnet
ic
wedges
,
wh
ic
h
re
duces
t
he
ec
onom
ic
imp
act
.
T
he
eff
ect
s
of
vary
ing
the
t
oo
t
h
width
a
re
eval
uated
by
kee
pin
g
t
he
total
slot
area
co
ns
ta
nt
w
hile
keep
i
ng
e
qual
the
dia
mete
r
of
the
sta
tor
.
T
able
8
s
hows
the
var
ia
ti
on
of
ave
rag
e
to
rqu
e
an
d
t
orqu
e
r
ipp
le
with
t
he
too
t
h
width.
Table
8.
T
orq
ue
and to
r
qu
e
r
i
pp
le
va
riat
ion
with to
oth wi
dth
[18]
Too
th
width
(mm)
Av
e.
to
rqu
e
(Nm)
Torq
u
e r
ip
p
le
(N
m)
Torq
u
e r
ip
p
le
(%)
4
.54
0
1
.55
8
0
.08
5
5
.46
0
4
.09
0
1
.60
0
0
.09
0
5
.63
0
3
.63
8
1
.61
0
0
.09
5
5
.90
0
3
.18
5
1
.61
3
0
.09
6
5
.95
0
2.3.
Oth
er
mea
sur
es for red
ucin
g to
r
que
pulsa
tion
s
2.3.1.
Ske
wing
Fo
r
av
oid
i
ng
t
he
co
ggin
g
to
r
qu
e
t
hat
ap
pea
rs
w
he
n
the
sta
tor
a
nd
r
oto
r
to
oth
si
des
are
in
al
ign
me
nt,
the
slots
sk
e
w
may
be
a
ppli
ed.
The
sk
e
w
ca
n
be
ca
rr
ie
d
ou
t
on
the
sta
tor
or
t
he
ro
t
or,
s
o
that
the
i
nters
ect
io
n
occurs
not
in
a
strai
ght
li
ne,
but
in
a
n
incli
ne
d
wa
y,
ma
king
the
c
orrespo
ndin
g
e
ff
e
ct
m
ore
gr
a
dual
.
S
ke
wing
in
the
sta
to
r
i
s
the
m
os
t
c
onve
ntio
nal
an
d
eff
ect
ive
met
hod
of
re
du
ci
ng
co
ggin
g
to
rque.
Be
si
des,
sk
e
w
diminis
h
tor
qu
e
rip
ple.
H
ow
ever,
it
mu
st
a
lso
be
c
onside
red
t
hat
this
m
easur
e
make
s
the
windin
g
sl
igh
tl
y
longer
, its resist
ance incr
ease
s
in
pro
portio
n,
and
t
he
ef
fici
ency
dec
rease li
gh
tl
y [30
]
A
no
ther
di
ff
ic
ulty is that
sk
ewi
ng
does
not
pro
piti
at
e
aut
om
at
ic
windin
g
w
hich
a
dds
cost
in
m
ot
or
ma
nufactu
re.
Howev
e
r,
man
uf
act
ur
e
rs
can
sta
c
k
th
e
la
minati
ons,
insert
slot
li
ner
s
,
place
t
he
coils
an
d
a
f
te
r
that,
th
e
s
ta
ck
of
la
minati
on
s
is
sk
ew
ed
.
Af
te
r
ward,
the
sta
c
k
is
wel
ded
to
hold
it
in
place.
This
proce
ss
is
esse
ntial
ly
i
de
ntica
l
to con
ven
ti
on
a
l man
uf
act
ur
i
ng, e
xce
pt that
weldin
g
is
do
ne
after
t
he
c
oils are i
ns
erte
d,
r
at
her
t
han b
e
f
ore.
2.3.2.
Ske
w
-
n
ot
c
hing
I
n
[
30]
an
oth
e
r
meth
od
is
pro
po
s
ed
to
re
duc
e
the
co
ggin
g
t
orq
ue
a
nd
pr
ac
ti
cal
ly
el
imi
nate
the
tor
que
rip
ple,
us
in
g
s
kew
i
ng
an
d
no
tc
hes
in
t
he
sta
tor
sl
ots.
In
Fi
gure
10,
the
sc
heme
of
a
P
Ma
-
S
yn
R
M
with
these
char
act
e
risti
cs can be see
n [30].
Figure
11
s
hows
how
c
oggi
ng
to
rque
var
i
es
with
dif
fer
e
nt
r
otor
posit
ion
s
in
a
P
MA
-
SynR
M
.
The
peak
val
ues
of
that
tor
que,
wi
th
te
et
h
with
out
no
tc
hes
a
nd
with
s
ke
wing
a
nd
notc
hi
ng
ar
e
1.2
6
N
-
m
a
nd
0.49
N
-
m, res
pecti
ve
ly.
T
his
dem
onstrat
es t
hat cogg
i
ng to
rque is
great
l
y
re
duce
d [30].
Figure
10.
Sche
me
of a
P
M
A
-
SynR
M
with s
kew
-
no
tc
hing in
the
stat
or
slots
[30
]
Figure
11. C
ogging to
r
qu
e
v
a
r
ia
ti
on
w
it
h r
ot
or
po
sit
io
n [30
]
3.
RESU
LT
S
A
ND
DI
SCUS
S
ION
S
3.1.
Ec
onomic
ana
ly
sis: a
c
as
e
st
udy
To
ac
hieve
the
best
so
l
ution
f
or
ob
ta
i
ning
sa
vings
in
the
ai
r
conditi
on
e
r
m
otor
dri
ving
blo
we
rs
in
a
Cub
a
n
beac
h
hote
l
hav
i
ng
222
r
ooms,
a
cas
e
stu
dy
was
im
plemente
d.
A
c
omparis
on
was
stu
died
to
know
t
he
best
va
riant:
e
mp
lo
ying
a
n
I
M
or
one
of
th
e
three
P
M
a
-
S
yn
R
M
t
yp
es
a
nalyze
d
a
bove
(C1,
C2,
or
C
3).
Data
of
the
la
st
thre
e
m
otors
are
gi
ven
in
Ta
ble
4.
All
the
m
ot
or
s
a
re
of
90
0
W,
1350
r
pm
,
eff
ic
ie
nc
y
cl
as
s
I
E4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
67
–
79
74
The
anal
ys
is
w
as
accom
plish
ed
em
ployin
g
the
dif
fer
e
ntial
net
pr
e
sent
va
lue
(
NPV)
disc
ount
meth
od,
wh
ic
h
al
lows
el
imi
na
ti
ng
e
qual
(
or
quasi
e
qual
)
costs,
f
or
exa
mp
le
,
instal
la
ti
on
a
nd
mainte
nan
ce
c
os
ts.
NPV
i
s
cal
culat
ed
as
(
2)
[
31]:
=
−
0
+
∑
(
1
+
)
=
1
(2)
Wh
e
re:
k0
is
t
he
in
vestme
nt
cost,
D
is
the
t
ax
rate,
n
is
t
he
li
fe
s
pan
of
t
he
in
vestme
nt,
i
is
the
yea
r
of eval
uation a
nd Cf
is
the ca
sh
flo
w
cal
cula
te
d
as
(3)
:
=
(
−
−
)
∙
(
1
−
100
)
+
(3)
Wh
e
re:
I
is
t
he
i
ncome,
G
the
outc
om
e
,
t
the
interest
rate,
an
d
De
p
t
he
depreci
at
ion
of
the
te
chnolo
gy cal
culat
ed
as
(
4)
[
32]:
=
0
(4)
Diff
e
re
ntial
N
PV
is
t
he
di
ff
e
ren
ce
betw
een
the
N
PV
obta
ined
f
or
ea
ch
s
ub
sti
tuti
on
opti
on
anal
yzed
(i.e.
P
M
a
-
S
ynRM
(C
1),
(C
2),
an
d
(C3))
c
on
cern
i
ng
t
he
NPV o
f
t
he
I
M
.
T
he
in
vestme
nt p
ay
bac
k
per
i
od
is
the
year
(i)
for
w
hi
ch
NPV
=
0.
The
mai
n
pa
ra
mete
rs,
for
a
ba
se
eco
nomic
analysis,
a
re
s
how
n
in
Ta
ble
9
[
24],
[33
]
-
[
37]
.
K
fa
ct
or
is
a
c
oeffici
ent
ap
plied
t
o
the
e
nerg
y
c
os
t
f
or
c
onside
rin
g
th
e
va
riat
ion
of
f
uel
co
sts
duri
ng
the
li
fe
s
pa
n,
it
has
a
nonli
near
be
ha
vior
[34],
[35].
T
he
inv
e
stment
cost
is
t
he
c
ost
of
the
m
otors,
t
he
economic
i
ncome
is
the
e
nergy
savi
ngs
cal
culat
ed
as
t
he
diff
e
re
nce
be
tween
the
e
nergy
co
nsum
ptio
n
of
t
he
PM
a
-
S
yn
R
M
(
C
1)
,
(C
2)
,
an
d
(C3)
a
bout
I
M
,
a
nd
c
onsid
erin
g
the
pri
ce
of
el
ect
rici
ty
accor
ding
t
o
t
he
M
1A
ta
riff
a
nd
t
he
k
factor
[34
],
[
35]
.
The
outc
ome
s
are
the
ma
intenanc
e
an
d
instal
la
ti
on
cost
s
that
are
el
imi
nate
d
in the calc
ulati
on of t
he diffe
r
entia
l NP
V.
Table
9
. Mai
n para
mete
rs for
the stu
dy
Para
m
eters
IM
PMa
-
Sy
n
RM
(
C1
)
PMa
-
Sy
n
RM
(
C2
)
PMa
-
Sy
n
RM
(
C3
)
Rated
ou
tp
u
t po
we
r
(kW
)
0
.9
0
.9
0
.9
0
.9
Ef
fic
ien
cy
class
IE4
IE4
IE4
IE4
Ef
fic
ien
cy
(
%)
8
6
,5
9
1
.81
9
3
.17
9
3
.46
Rated
sp
eed (r
p
m
)
1350
1350
1350
1350
Op
eration
al sp
eed
rang
e (
rp
m
)
500
-
1
7
5
0
500
-
1
7
5
0
500
-
1
7
5
0
500
-
1
7
5
0
Load
f
acto
r
weig
h
ted
average
0
.45
0
.45
0
.45
0
.45
Op
eration
al ho
u
rs per year
5000
5000
5000
5000
Inv
estment co
st (
U
SD)
555
604
639
686
Moto
r
liv
e sp
an
(
y
ears)
10
10
10
10
Electr
i
c tar
i
ff
M1 A
M1 A
M1 A
M1 A
Initial
K
f
acto
r
3
.9
3
.9
3
.9
3
.9
Tax ra
te
(
%
)
35
35
35
35
Interest
rate (%)
15
15
15
15
The
loa
d
facto
r
wei
gh
te
d
a
ve
rag
e
is
cal
c
ul
at
ed
ap
ply
i
ng
(5)
f
or
the
t
ypic
al
case
of
H
VA
C
us
es
,
ta
kin
g t
he val
ue
s sho
wn in T
a
ble 10
[
38].
=
∑
∙
∑
(5)
W
he
re
LF
W
A
is
the
loa
d
fact
or
weig
hted
a
ve
rag
e
,
PRFR
is
the
per
ce
nt
of
rate
d
flo
w
rat
e,
a
nd
PTS
the p
e
rce
nt ti
meshar
e
.
Table
10. L
oa
d p
rofil
e f
or
t
yp
i
cal
H
V
AC
us
e
s
Percent of
r
ated
fl
o
w r
ate
(%)
Percent ti
m
e sh
a
re
(%)
25
45
50
35
75
15
100
5
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Red
ucin
g
tor
que
pu
ls
atio
ns
i
n
PM
a
-
Sy
nRM
: a way
for
im
provi
ng
m
oto
r
pe
rforma
nce
(
P
ercy R.
Vie
go
)
75
With
the
l
oad
f
act
or
weig
hted
aver
a
ge
a
nd
t
he
eff
ic
ie
nc
y
of
Table
6,
the
el
ect
rical
power
and
e
ne
rgy
consu
mp
ti
on a
re calculat
ed
for ea
ch
case
with
(
6)(
7)(8)
[5]
:
=
∙
(6)
=
(7)
=
∙
(8)
W
he
re
P
out
is
the
operati
onal
mecha
nical
powe
r,
P
r
is
the
rated
ou
t
pu
t
powe
r,
Pi
n
is
th
e
el
ect
rical
powe
r,
E
is
th
e
ene
rgy
c
ons
umpti
on
an
d
t
is
the
ope
rati
onal
ho
ur
s
pe
r
year.
T
he
r
esu
lt
s
ob
ta
ine
d
from
t
he
economic
anal
ys
is ca
n be see
n
in
Ta
ble 11.
Table
11. Mai
n ec
onomi
c res
ul
ts
Moto
r
v
ariants
Diff
e
rential in
v
est
m
en
t
(USD
)
Diff
e
rential N
PV
(USD
)
Pay
b
ack
(years)
PMa
-
Sy
n
RM
(
C1
)
-
IM
49
5
5
.2
4
PMa
-
Sy
n
RM
(
C2
)
-
IM
84
4
9
,3
6
PMa
-
Sy
n
RM
(
C3
)
-
IM
131
2
.02
10
Wh
e
re
the
in
ve
stment
dif
fere
ntial
is
the
diff
e
ren
ce
in
the
cost
of
(PMa
-
SynRM
(C
1),
(C2),
(C3))
about
the
IM.
The
best
res
ults
wer
e
ac
hieve
d
with
t
he
va
ri
ant
PMa
-
S
ynR
M
(C
1)
si
nce
it
has
the
highes
t
NP
V
and
a
paybac
k
of
f
our
ye
ars
.
T
his
is
a
go
od
so
l
ution,
c
on
siderin
g
the
ca
se
of
a
m
otor
f
or
a
n
ai
r
c
ondi
ti
on
er
blower
dr
ive
n
by
a
n
i
nv
e
rter
con
t
ro
l,
wh
ic
h
impli
es
a
n
una
vo
i
dab
le
lo
w
l
oad
factor.
Ac
cordin
g
to
[
37]
,
base
d
on
t
he
ge
ner
al
it
y
of
cases
of
the
HVAC
fi
el
d,
w
he
n
the
eff
ic
ie
nc
y
gai
n
m
ov
i
ng
fro
m
one
eq
uipm
ent
to
ano
t
her
m
or
e
e
ff
ic
ie
nt,
ma
y
not
b
e
e
noug
h
t
o
j
us
ti
fy
the
ad
diti
on
al
i
niti
al
inv
est
me
nt.
Th
at
is
the
case
s
how
n
in
Ta
ble
11.
S
ince
it
is
nece
ssary
to
e
valu
at
e
the
ef
fect
of
some
te
ch
ni
cal
and
ec
onomi
c
uncertai
nt
ie
s,
a
mu
lt
ifact
ori
al
sen
sit
ivit
y
a
naly
sis was
done
, a
s it
is sho
wn bel
ow
.
3.2.
Sen
sitivi
ty an
alysi
s
Un
ce
rtai
nty
i
n
the
eco
nomic
analysis
due
to
var
ia
ti
ons
i
n
e
conomic
i
nd
ic
at
or
s
a
nd
ot
her
facto
rs
has
a
ma
rk
e
d
in
flu
ence
on
the
re
su
lt
s
of
a
propose
d
feasibil
it
y
stu
dy.
For
this
reas
on,
a
s
ensiti
vity
a
nal
ys
is
i
s
performe
d
to
va
li
date
the
p
r
oposa
l
in
the
fa
ce
of
possible
var
ia
ti
ons
in
th
e
mo
st
in
flue
ntial
factor
s.
T
he
study
analyze
d
ho
w
the
N
PV
a
nd
t
he
paybac
k
be
ha
ve
with
var
ia
t
ion
s
in
operati
ng
ec
onomi
c
f
act
or
s.
T
he
bas
e
case
is
the
P
M
a
-
SynRM
(C
1)
with
the
data
fro
m
ta
bles
9
a
nd
10.
For
thi
s
study,
the
dif
fere
ntial
inv
est
m
ent
co
st
,
the
an
nual
ope
rati
on
al
ti
me,
a
nd
the
gro
wth
rate
of
the
f
uel
facto
r
(
facto
r
K)
we
re
var
ie
d
in
e
qu
at
io
ns
(
2),
(
3),
and
(4),
keep
i
ng
t
he
loa
d
fact
or
c
on
sta
nt.
T
he
gro
wth
rate
of
the
f
uel
fac
tor
is
i
nd
ic
at
iv
e
of
va
ri
at
ion
s
in
the
energ
y pr
ic
e.
T
he
init
ia
l K
f
ac
tor
c
onside
red
in the base
cas
e is 3
.9
; i
t
var
i
es an
nual
ly
by
8%
acc
ordin
g
t
o
(9)
:
=
3
.
9
∙
(
1
+
)
(9)
Wh
e
re:
k
is
th
e
annual
gro
wt
h
rate
of
the
f
uel
facto
r
an
d
n
is
the
yea
r
a
nalyze
d.
T
he
r
esult
s
of
t
he
analysis a
re sh
own
i
n
F
i
gures
12 to 1
4 o
btained
in Excel
.
Figures
12
(
a
)
a
nd
12
(
b)
s
how
the
va
riat
ion
of
the
N
PV
a
nd
t
he
paybac
k
on
in
vestme
nt,
resp
ect
ivel
y,
to
th
e
var
ia
ti
on
s
in
t
he
dif
fer
e
ntial
cost
of
in
vestme
nt
f
or
a
grow
t
h
rate
of
the
K
fact
or
eq
ual
to
8%
a
nd
50
00
hours
of
opera
ti
on
.
As
ca
n
be
seen
i
n
Fi
gure
12,
the
NPV
decr
eases
w
it
h
increase
s
in
the
diff
e
re
ntial
co
st,
maki
ng
the
inv
est
ment
le
ss
at
tract
ive.
Fo
r
di
ff
e
ren
ti
a
l
costs
a
bove
55
U
SD,
the
NPV
becomes e
ve
n l
ess than t
he
i
nc
reme
ntal i
nv
e
stment a
nd the
paybac
k peri
od is great
er t
han 4
yea
rs.
Figure
13
(
a)
and
(
b)
pr
ese
nt
the
var
ia
ti
on
of
NPV
an
d
pa
yb
ac
k,
res
pec
ti
vely,
be
f
or
e
var
ia
ti
ons
in
the
K
facto
r
grow
t
h
rate
of
8
%
f
or
a
dif
fer
e
ntial
cost
of
49
USD
a
nd
5,0
00
hours
of
ope
rati
on.
Fig
ure
13
(
a
)
sh
ows
that
inc
r
eases
in
e
nerg
y
pri
ces
(th
r
ough
i
ncr
eas
es
i
n
K)
le
ad
to
inc
r
eases
in
NPV.
Howe
ver,
it
ha
s
li
tt
le
influ
e
nce
on th
e p
a
yb
ac
k (as
s
how
n
in
Fig
ure
13
(
b).
In
Fi
gure
14
(
a
)
a
nd
(
b)
ca
n
be
see
n
va
riat
ion
s
of
NPV
a
nd
pa
ybac
k,
res
pe
ct
ively,
relat
e
d
t
o
an
nual
op
e
rati
onal
ti
me
f
or
va
riat
ion
s
in
the
K
f
act
or
gro
wth
r
at
e
of
8
%
a
nd
a
diff
e
re
ntial
cost
of
49
U
SD
.
The
op
e
rati
onal
ti
me
has
t
he
sa
me
eff
ect
on
NPV
as
the
va
riat
ion
in
the
pri
ce
of
e
nergy
de
picte
d
in
Fig
ure
14
(
a).
Fo
r
operati
ona
l
ti
mes
of
le
ss
t
han
5000
h/
yea
r,
the
pa
ybac
k
reaches
unat
tra
ct
ive
ec
onom
ic
val
ues
as
s
hown
in
Figure
14
(
b).
This
sensiti
vit
y
a
nal
ys
is
dem
on
st
rated
that
in
t
he
case
of
a
ir
c
onditi
on
e
rs
,
th
e
st
udy
m
ust
be
handled
care
f
ul
ly.
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IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
67
–
79
76
(a)
(b)
Figure
12. Vari
at
ion
of NPV
a
nd p
a
yback
vs.
d
if
fer
e
ntial
cost
,
(
a
) NPV,
(
b)
paybac
k
(a)
(b)
Figure
13.
Var
i
at
ion
of NPV
a
nd p
a
yback
vs.
K
facto
r
i
ncr
e
ase rate,
(
a)
NPV,
(
b) p
a
ybac
k
(a)
(b)
Figure
14. Vari
at
ion
of NPV
a
nd p
a
yback
vs.
operati
onal
ti
me
(
a
)
NPV,
(
b) p
a
yback
4.
CONCL
US
I
O
N
An
al
ys
is
of
diff
e
re
nt
desi
gn
el
eme
nts
and
st
ru
ct
ur
al
opti
miza
ti
on
of
P
M
a
-
Syn
RM
al
l
ow
e
d
dem
onstrat
in
g
that
t
he
redu
ct
ion
of
to
r
que
pulsa
ti
ons
c
an
be
achie
ve
d
by
a
dju
sti
ng
the
num
ber,
sh
a
pe,
Evaluation Warning : The document was created with Spire.PDF for Python.