Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 4
,
A
ugu
st
2015
, pp
. 81
0
~
82
0
I
S
SN
: 208
8-8
7
0
8
8
10
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
/
IJECE
Design of Slotted and Slotless
AFPM Synchronous Generators
and thei
r P
e
rformance Comparis
on An
alysis b
y
u
s
ing FE
A
Meth
od
S
a
in
t Sa
in
t Soe,
Ya
n Au
ng
O
o
Department o
f
Electrical Power
Engineer
ing, Mandalay
Technolo
g
ical University
Mandalay
,
M
y
anmar
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Mar 11, 2015
Rev
i
sed
May 10
, 20
15
Accepted
May 24, 2015
Axial-flux p
e
rmanent magn
et
machines
ar
e p
opular
and wid
e
ly
used fo
r
m
a
n
y
appl
ica
tio
ns due to their
attr
act
ive fe
atur
es such as light weight, low
noise, high
tor
que, robust
an
d higher
efficiency
du
e to
lack of field
exci
tat
i
on.
The
m
a
in es
s
e
nce of
this
pa
per
is to
perform slotted
and slotless
axial-flux perm
anent magnet
s
y
nchr
onous generator d
e
sign
based on
theore
tic
al s
i
z
i
n
g
equations
and
then fini
te e
l
em
e
n
t anal
ys
is
is
rei
n
forcem
ent
in order to get a
m
o
re reliable a
nd accura
c
y
m
a
chine des
i
gn
. A
com
p
arativ
e
stud
y
of machin
e design and per
f
orman
ces over the same rating b
u
t differen
t
configurations i.e., slo
tted
and s
l
otless
ar
e also
discussed. And then, f
i
nite-
element method
(FEM) softwa
re was made for the slo
tted stator
and slotless
stator (AFPMSG) in order
to
compar
e th
eir
magnetic flux
density
and
efficiency
. The AFPMSG
topolog
y
consider
ed
in this p
a
per
is a three-phase
double-rotor
sin
g
le-stator topo
lo
g
y
with
16 po
le-
p
airs, 2kW r
a
ted
power and
188 rpm rated sp
eed.
Keyword:
Ax
ial-flux
p
e
rman
en
t
m
a
g
n
e
t
D
oub
le-
r
o
t
or
Fin
ite-elem
e
n
t
meth
o
d
Slotless stator
Slo
tted
stator
Syn
c
hro
nou
s gen
e
r
a
t
o
r
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
:
Sain
t
Sain
t So
e,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Po
w
e
r E
ngi
neeri
n
g, Mandalay Te
chno
log
i
cal Univ
ersity
Man
d
a
lay, My
an
m
a
r
.
Em
a
il: sein
tsso
e@g
m
ail.co
m
1.
INTRODUCTION
Havi
ng
t
h
e
hi
gh
t
o
rq
ue at
l
o
w
s
p
eeds
,
t
h
e axi
a
l
-
fl
u
x
perm
anent
-
m
a
gnet
sy
nc
hr
o
n
ous
m
achi
n
e
AFPMSM is
very suitable for wheel m
o
tors, direct
dri
v
e
wind ene
r
gy applications and s
o
on.
As t
h
e pole
num
ber i
s
cho
s
en su
ffi
ci
ent
l
y
hi
g
h
, a hi
g
h
t
o
r
que
den
s
i
t
y
com
b
i
n
ed wi
t
h
a go
o
d
pe
rf
orm
a
nce at
l
o
w spe
e
ds i
s
obt
ai
ne
d.
T
h
e
effi
ci
ent
e
xpl
o
i
t
a
t
i
on o
f
the
machine, e
v
en at very l
o
w
s
p
eed
s,
perm
i
t
s
di
rect
c
o
u
p
l
i
n
g
of t
h
e
mach
in
e to the low sp
eed
ap
p
lication
with
ou
t
u
s
ing
a
gearbox. C
o
m
p
ared with
a c
o
nve
nt
i
o
nal
,
ge
arb
o
x
-
cou
p
l
e
d
wi
n
d
t
u
r
b
i
n
e ge
nera
t
o
r, a di
rect
c
o
u
p
l
e
d
gene
rat
o
r system eliminates
m
ech
anical reduction gea
r
,
redu
ces size
of th
e
o
v
e
rall syste
m
, lo
wer in
stallatio
n
a
nd m
a
intenance
costs.
T
h
e
use
of
di
rect
d
r
i
v
e wi
n
d
en
erg
y
g
e
n
e
rat
o
r will resu
lt less
m
a
in
ten
a
n
c
e an
d
in
creased
in
reliab
ility
sig
n
i
fican
tly. As th
e m
a
g
n
e
tic field
i
s
generat
e
d by
t
h
e perm
anent
m
a
gnet
s
, no fi
el
d exci
t
a
t
i
on cur
r
ent
i
s
nece
ssary
and t
h
e c
o
r
r
es
po
n
d
i
n
g cop
p
e
r
lo
s
s
e
s
ar
e
ab
s
e
n
t
.
A
s
a c
o
n
s
equ
e
n
c
e,
A
FPM
machines
have
a good efficiency.
AFPMS m
ach
in
es ex
ist in d
i
fferen
t top
o
l
og
ies and
g
e
om
et
r
i
es suc
h
as
si
n
g
l
e
-si
d
e
d
o
r
do
ubl
e
-
si
de
d
,
wi
t
h
or
wi
t
h
o
u
t
arm
a
t
u
re sl
ot
s,
wi
t
h
or
w
i
t
hout
a
r
m
a
t
u
re core
,
wi
t
h
i
n
t
e
r
n
al
o
r
e
x
t
e
rnal
PM
r
o
t
o
r
s
, eac
h
havi
ng t
h
ei
r adva
nt
age
s
an
d
di
sadva
nt
a
g
es
[1]
.
The A
F
PM
SM
di
scus
sed i
n
t
h
i
s
pa
per i
s
a si
ngl
e-st
at
or
do
u
b
l
e
-r
ot
o
r
t
y
pe
wi
t
h
sl
ot
t
e
d
st
at
or a
n
d
sl
ot
l
e
ss st
at
or
.
In
th
e case of d
oub
le-sid
ed
co
nfigu
r
ation
s
, eith
er ex
tern
al d
u
a
l-ro
t
o
r wit
h
slo
tted
stato
r
o
r
ex
tern
al
d
u
a
l
r
o
t
o
r w
i
t
h
slo
tless stat
o
r
ar
r
a
ng
em
en
t can
b
e
adopted
. Th
e two
co
nstr
u
c
tiv
e typ
e
s
o
f
w
i
nd-
tu
rb
in
e
gene
rat
o
r co
ns
i
d
ere
d
i
n
t
h
i
s
wo
rk a
r
e perm
anent
-
m
a
gne
t
sy
nch
r
o
n
ous
ge
nerat
o
rs
, b
u
t
one has a sl
ot
t
e
d st
at
or
ax
ial-flux
(AFPMSG) to
po
log
y
, th
e o
t
h
e
r
on
e is o
f
slo
tles
s
(air-c
ore
d
) stator axial-
flu
x
(AF
P
M
S
G) ty
pe. I
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
81
0
–
82
0
8
11
th
e fo
llowing
sectio
n
s
, each
of th
e two
PMSG top
o
l
o
g
i
es is
in
v
e
stig
ated
usin
g
fin
ite-elemen
t
field
an
alysis to
com
p
aratively show t
h
eir m
a
gnetic
flux
density.
2.
AX
IA
L
FLUX
PM
SYN
C
HR
ON
OU
S
GEN
E
RA
TOR
Axi
a
l
-
fl
u
x
PM
SGs
ha
ve a
nu
m
b
er of
di
st
i
n
c
t
adva
nt
ages
, i
.
e. t
h
ey
can
be
desi
g
n
e
d
t
o
ha
ve (i
) hi
ghe
r
p
o
wer- t
o
-
wei
g
h
t
ratio
, resu
l
tin
g
in less co
re m
a
terial, (
ii)
p
l
an
ar an
d easily ad
ju
stab
le ai
r-g
a
ps,
(iii) redu
ced
noi
se a
nd
vi
br
at
i
on l
e
vel
s
. M
o
re
o
v
er, t
h
e
di
rect
i
on
of t
h
e
ai
r gap fl
ux
pa
t
h
can be va
ri
e
d
, so t
h
at
addi
t
i
onal
t
o
p
o
l
o
gi
es can
be de
ri
ve
d. T
h
i
s
pa
per
p
r
ese
n
t
s
a com
p
arat
i
v
e st
u
d
y
bet
w
een t
h
e a
x
i
a
l
-fl
ux sl
ot
t
e
d st
at
or
a
n
d
sl
ot
l
e
ss (ai
r-c
o
r
ed
) st
at
or pe
r
m
anent
-
m
a
gne
t
sy
nchr
on
o
u
s
gene
rat
o
rs f
o
r
a 2 k
W
wi
n
d
t
u
r
b
i
n
e ap
pl
i
cat
i
on.
The m
a
gnet
s
a
r
e
of
hi
g
h
-
ene
r
gy
N
d
FeB
t
y
pe
, an
d a
r
e
gl
ue
d
on
b
o
t
h
si
des
o
f
t
h
e
t
w
o s
o
l
i
d
-
i
ro
n
di
sc-r
ot
o
r
s
.
2.
1.
Double
-
Si
ded
AFP
M
SG
Slotless (Air-Core
d
) Stator
I
n
a co
r
e
less
A
FPM m
ach
in
e th
e stato
r
is
lo
cated
b
e
tw
een
th
e tw
o
oppo
sing
ro
to
r
d
i
scs. Fig
u
r
e
1
sho
w
s
t
h
e m
achi
n
e
has
a si
ng
l
e
st
at
or sa
n
d
w
i
c
he
d
bet
w
ee
n t
w
o
PM
r
o
t
o
r
di
scs [
2
]
.
Th
e ai
r-c
ore
d
(i
r
o
nl
ess)
nat
u
re of t
h
e
st
at
or el
im
i
n
ated t
h
e l
a
m
i
nat
i
on st
am
pi
ng duri
ng t
h
e m
a
nu
fact
u
r
i
n
g p
r
oces
s of t
h
e
st
at
or
win
d
in
g.
Howe
ver, the
r
e is no iron in t
h
e stat
or
of thi
s
m
achine,
inst
ead t
h
e
windings a
r
e
placed i
n
t
h
e air ga
p
and
epoxy enc
a
ps
ulated. T
h
e
abse
nce of
the iron
core
for th
e co
ils
o
f
t
h
e stator
winding creates a l
o
w fl
ux
d
e
nsity in
th
e mag
n
e
tic circuit o
f
th
e co
il,
resu
ltin
g
i
n
a low v
a
l
u
e of indu
ctan
ce
for th
e co
il in
th
e coreless
st
at
or [
3
]
.
Th
e
st
at
or wi
ndi
n
g
o
f
t
h
e
AFPM
m
ach
in
e in
th
is p
a
p
e
r is usin
g
the sing
le-layer trap
ezo
i
d
a
l co
il
sha
p
e. T
h
e a
dvantage
of the
trapezo
i
d
al co
il sh
ap
e is th
at it
allo
ws
for t
h
e
max
i
m
u
m
co
il flux
link
a
g
e
.
Fig
u
re
1
.
Dou
b
le-sid
ed AFPM
m
ach
in
e with
in
tern
al ai
r co
red
stator
Due t
o
the
abs
e
nce
of stator i
r
on
, t
h
e fl
ux
t
r
avel
s f
r
om
t
h
e no
rt
h
-
pol
e
of
one
r
o
t
o
r di
sc
t
h
r
o
u
g
h
t
h
e
air g
a
p
t
o
th
e
so
u
t
h
-
po
le o
f
t
h
e o
t
h
e
r
d
i
sc an
d
return
s
b
y
trav
elling
circum
feren
tially
aro
und
th
e ro
tor b
ack
iron. T
h
e
r
efore
,
in t
h
e m
ach
ine with ai
r-c
ore
d
stator, t
h
e
north-pole of
one
rot
o
r directly faces the
s
out
h-pole
of t
h
e
othe
r
rot
o
r. T
h
e m
achine with ai
r c
o
re
d stator
has t
h
e
sam
e
advanta
g
es as
the
TORUS m
achine
suc
h
as
eli
m
in
atio
n
of cogg
ing
an
d
easy in
tegration
t
o
turb
in
e du
e
t
o
o
u
t
er roto
r
con
f
i
g
uratio
n. In
add
ition
t
h
e
abse
nce
of i
r
on in the
stator el
im
inates stator
iron los
s
es a
n
d increase
s
gene
rator efficiency
.
2.
2. Double
-
Si
ded AFP
M
SG
Slotted
S
t
ator
Th
e d
oub
le-si
d
ed
structu
r
e with
ex
tern
al ro
t
o
r
sim
p
lifies
the m
a
nufac
ture
process
due to easie
r
fix
a
tion
o
f
t
h
e stato
r
ring
s t
o
th
e
fram
e
; it
also
favo
ur
s t
h
e cooling proc
ess beca
use
the m
a
in heat s
o
urce
is
located ne
ar the surface.
Slotted stat
ors increase rem
a
rkabl
y
the a
m
plitude
of t
h
e air ga
p fl
ux
de
nsity due
t
o
sho
r
t
e
r ai
r ga
p
[4]
.
D
u
e t
o
t
h
e sl
ot
t
e
d nat
u
re, t
h
e ai
r ga
p
i
s
sm
al
l
e
r but
t
h
e fl
ux
di
st
ri
but
i
o
n m
a
y cont
ai
n
h
a
rm
o
n
i
c, transmitted
to
th
e lo
ad
as a to
rqu
e
ripp
le.
Asso
ciated
with
th
e slo
tted
core are to
o
t
h
saturation
p
r
ob
lem
s
an
d
ad
d
ition
a
l iro
n
lo
ss in
t
h
e teeth
.
Th
e efficien
cies of th
is
stato
r
d
e
sign
are no
t th
e
h
i
g
h
e
st
achieva
ble.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design of Slotted and Slotless
AFPM Sy
nc
hr
onous Generat
o
rs and
their P
e
rformance …
(
Sai
nt
S
a
i
n
t
So
e)
81
2
Fi
gu
re
2.
D
o
ub
l
e
-rot
o
r
si
n
g
l
e
-
s
l
o
t
t
e
d st
at
o
r
st
ruct
ure
(
A
FPM
SG)
2.
3.
PM
M
o
u
n
t
i
n
g
T
y
pe
f
o
r
Sl
ot
ted
St
at
or
Th
e m
a
g
n
e
tic flux
in
th
ese st
ru
ct
u
r
es are sho
w
ed
in
two
deriv
a
tion
s
, th
e
To
ru
s-NN and th
e To
ru
s-
NS,
as s
h
ow
n i
n
t
h
e
Fi
g
u
r
e
3(
a) a
n
d
Fi
g
u
re
3
(
b
)
.
The
de
pi
ct
ed
fi
g
u
res
sh
o
w
a
sl
ot
t
e
d
st
at
or
,
ho
we
ver t
h
e fl
u
x
di
rect
i
o
ns a
r
e a
l
so
val
i
d
f
o
r st
at
ors
wi
t
h
out
s
l
ot
s.
(a)
N
N
type
(b)
NS type
Fi
gu
re
3.
Di
rec
t
i
on
of
t
h
e
fl
u
x
f
o
r a
x
i
a
l
fl
ux
m
achi
n
es
wi
t
h
sl
ot
t
e
d st
at
o
r
t
y
pe N
N
a
n
d
N
S
2.
4.
C
o
mp
ari
s
on
of
N
N
T
y
p
e
an
d
NS T
y
p
e
There a
r
e t
w
o
t
y
pes of rot
o
r
const
r
uct
i
o
n f
o
r an
AFPMSG. They are NN type rotor and
NS type
rot
o
r.
N
o
rt
h-
n
o
rt
h (
N
N
)
st
r
u
ct
ure
has m
a
i
n
fl
u
x
t
o
fl
ow
ci
rcum
ferent
i
a
l
l
y
al
ong t
h
e
st
at
or c
o
re,
so a
t
h
i
c
k
stator yoke is
requi
red,
hence
increase i
r
on l
o
sses
exists
. NN
stru
ctur
e t
h
us h
a
s less co
pper
lo
sses an
d smaller
external diam
e
t
er, but m
o
re
ir
on
lo
sses an
d lo
ng
er ax
ial.
N
o
r
t
h-
sou
t
h
(N
S) stru
ctur
e
h
a
s m
a
in
f
l
u
x
f
l
ow
ing
axi
a
l
l
y
t
h
rou
g
h
st
at
or, s
o
i
n
pri
n
ci
pl
e, t
h
i
c
k
st
at
or y
oke i
s
un
necessa
ry
. I
r
on l
o
sses are t
hus
red
u
ce
d, b
u
t
l
a
p
wi
n
d
i
n
gs l
e
ngt
hen
en
d
wi
n
d
i
ngs
,
whi
c
h a
g
a
i
n i
n
c
r
ease c
o
p
p
er
l
o
sses
.
By com
p
arison of t
h
e NS and NN st
ruct
ure
,
the s
h
or
ter
stato
r
yok
e i
n
the NS t
o
po
log
y
resu
lts i
n
a
in
creasing
p
o
wer d
e
n
s
ity an
d
lo
wer stato
r
core lo
ss co
m
p
ared
to
th
e
NN t
o
po
log
y
[5
]. The ax
ial th
ick
n
e
ss of
th
e stato
r
can
b
e
less th
an
NN typ
e
m
ach
in
e. Th
e
NS
featu
r
e
resu
lts in
l
e
ss weigh
t
, less iron
lo
ss and h
i
gh
er
efficiency tha
n
NN type m
achine.
He
re
,
NS
const
r
uct
i
o
n
h
a
s bee
n
sel
ect
ed
beca
use as st
ator c
o
re loss is less
th
an
NN
typ
e
.
3.
COMPONENT OF THE
AFPMSG
Thi
s
pa
pe
r i
s
d
e
si
gne
d f
o
r 2
k
W
a
x
i
a
l
-
fl
u
x
perm
anent
m
a
gnet
sy
nch
r
o
n
ous
ge
nerat
o
r
wi
t
h
co
rel
e
s
s
st
at
or an
d sl
ot
t
e
d st
at
or
.
Th
e
mach
in
e con
f
i
g
uration
con
s
i
s
ts o
f
th
e fo
llowing
co
m
p
on
en
ts: two
ro
tor
d
i
scs
and
one st
at
o
r
di
ck.
T
h
ey are external doubl
e-rotor and internal st
ator. The assigned
va
lue param
e
ters of the
AFPM
S
G
f
o
r
s
l
ot
t
e
d st
at
o
r
a
n
d sl
ot
l
e
ss st
at
o
r
are
s
h
o
w
n i
n
Tabl
e
1.
Tabl
e 1. Speci
f
i
cat
i
ons of AF
PM
SG
Para
m
e
ters
Units
Desired
Value
Nu
m
b
er
of phases
-
3
Nu
m
b
er
of pole pair
s
-
16
Fr
equency Hz
50
Rated voltage
V
48
Output power
kW
2
Specif
i
c electro
m
a
gnetic loading
A/
m
12000
Connection o
f
stator
winding
-
star
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
81
0
–
82
0
8
13
3.
1. Desi
gn
E
q
uati
on f
o
r AF
PMS
G
w
i
th Sl
otl
e
ss
St
at
or
The axial-flux perm
anent
magnet m
ach
in
e co
nf
igu
r
ation co
n
s
ists of
ex
tern
al d
oub
le-
r
o
t
or
and
internal ai
r c
o
red stator.
Desi
gn cal
cul
a
t
i
o
n
of
2
k
W
AFPM
SG
wi
t
h
ai
r c
o
red
st
at
or
by
u
s
i
n
g
si
zi
ng
e
q
u
a
t
i
ons
is d
e
scrib
e
d
in
th
is sectio
n.
The e
ffective
a
i
r ga
p
for t
h
e
machine ca
n
be
calcu
lated
b
y
th
e fo
llowing
eq
u
a
tion
,
m
geff
g
s
y
rm
2l
l=
2
l
+
+
h
μ
(1
)
Th
e air g
a
p
flux
d
e
nsity d
u
e
to
m
a
g
n
e
t fo
r the slo
tless stator is th
e
fo
llowing
eq
u
a
tion
,
rm
m
g
rm
g
e
ff
2B
l
B=
μ
l
(2
)
The pea
k
val
u
e
o
f
ai
r
-
ga
p fl
u
x
de
nsi
t
y
,
g
p
23
×
B
B=
π
(3
)
The
stator outer diam
e
t
er
for AFPMSG
ca
n
b
e
calcu
lated
by th
e fo
llowing equ
a
tio
n,
ou
t
3
ou
t
2
ws
g
m
ε
P
D
πλ
kn
B
A
η
co
s
(4
)
The stator i
nne
r
diam
e
t
er for t
h
e
AFPMSG,
i
n
out
D
D=
D
×
K
(5
)
K
D
= rat
i
o
of
i
n
ner
an
d
out
e
r
di
am
et
er of m
achi
n
e
The R
M
S-
val
u
e of t
h
e si
n
u
s
o
i
d
al
p
h
ase
v
o
l
t
a
ge o
f
t
h
e n
o
n
-
o
verl
a
ppi
ng
wi
n
d
i
n
g ca
n be
cal
cul
a
t
e
d
by
th
e fo
llowing
eq
u
a
tion
,
ge
n
e
p
t
e
a
p
d
q2
2
E
ω
BN
r
l
k
k
ap
=
(6
)
The
Stator c
opper losses
,
2
cu
ac
i
P=
3
I
R
(7
)
Th
e
Stato
r
eddy cu
rr
en
t l
o
sses,
42
2
ap
e
t
p
ed
dy
t
π
ld
B
ω
QN
N
P=
32
ρ
(8
)
Out
put
p
o
we
r of
t
h
e ge
nerat
o
r
ca
n be
cal
cul
a
t
e
d
by
,
ou
t
g
e
n
ac
P
=
3E
I
c
o
s
(9
)
In
p
u
t
p
o
w
er
o
f
t
h
e
gene
rat
o
r i
s
gi
ven
by
t
h
e
fol
l
o
wi
n
g
e
q
ua
t
i
on,
in
out
c
u
e
ddy
PP
P
P
= +
+
(1
0)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design of Slotted and Slotless
AFPM Sy
nc
hr
onous Generat
o
rs and
their P
e
rformance …
(
Sai
nt
S
a
i
n
t
So
e)
81
4
Efficiency
of t
h
e
gene
rator ca
n
be calculate
d by,
out
in
P
η
=
×
10
0%
P
(1
1)
The m
echani
cal
desi
gn
par
a
m
e
t
e
rs of t
h
e
do
u
b
l
e
-si
d
e
d
a
x
i
a
l
-fl
u
x
perm
anent
m
a
gnet
sy
nch
r
o
n
o
u
s
gene
rato
r
fo
r a
i
r-co
r
e
d
stato
r
are s
h
o
w
n in
T
a
ble 2
.
Table
2. Mec
h
anical Desi
gn
Param
e
te
rs fo
r
Slotless Stato
r
of
AF
PM
S
G
Para
m
e
ters
Units
Value
Outer
diam
eter of stator
,
cm
52.
8
I
nner
diam
eter
of s
t
ator
cm
30.
5
Outer
r
a
dius of stator
cm
26.
4
I
nner
r
a
dius of stator
cm
15.
3
T
h
e nu
m
b
er
of turn per
coil
tur
n
s
37
The total nu
m
b
er of stator coil
-
24
Air
gap distance
m
m
2
Air
gap flux densit
y
T
0.
657
T
h
e peak value of air
gap flux densit
y
T
0.
724
3.
2. Desi
gn
E
q
uati
on f
o
r AF
PMS
G
w
i
th Sl
ot
ted St
at
or
In a
slotted
AFPM m
achine, the stat
or
outer
diam
e
t
er is ass
u
m
e
d to be t
h
e
sam
e
size as the slotless
stator
oute
r
diameter and is al
so
app
lied
th
e
sam
e
PM ro
to
r d
i
scs.
The ai
r ga
p fl
ux
de
nsi
t
y
due
t
o
m
a
gnet
fo
r
t
h
e sl
ot
t
e
d st
at
or can
be ca
l
c
ul
at
ed by
t
h
e fol
l
o
wi
n
g
equat
i
o
n,
p
m
gr
m
rm
g
e
ff
p
π
b
2l
4
B=
×
B
×
×
s
i
n
μ
l
πτ
(1
2)
The
n
u
m
b
er o
f
sl
ot
per
p
o
l
e
p
e
r
phase
can
be
cal
cul
a
t
e
d
by
t
h
e
fol
l
o
wi
n
g
e
quat
i
o
n,
1
1
Z
q =
2p
m
(1
3)
The a
v
era
g
e
pole pitch ca
n
be calculated
by
,
av
g
p
π
D
τ
=
2p
(1
4)
The RMS
value of the i
n
duced ph
ase
voltage of the
winding can
be c
a
l
c
ul
at
ed by
t
h
e f
o
l
l
o
wi
n
g
equat
i
o
n,
wp
h
g
p
s
ph
4×
f
×
k
×
N
×
B
×
τ
×l
E=
2
(1
5)
Based on the c
a
lculated phas
e curr
ent a
nd
phase resista
n
ce
, the copper
losses in a stator
winding are
calculated as,
2
()
C
u
ph
ph
P=
m
R
I
(1
6)
In t
h
e analytical approac
h
the axial-fl
ux PM
m
ach
in
e is su
bd
i
v
id
ed
in
t
o
yok
e and
teeth
p
a
rts [6
].
There
f
ore, the
iron los
s
es ca
n
be calculate
d a
s
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
81
0
–
82
0
8
15
1.5
1
.5
22
Fe,
y
1
.
0
y
y
F
e,
t
1
.
0
t
t
Fe
ff
P=
k
P
G
B
+
k
P
G
B
50
50
(1
7)
Th
e st
ray lo
ad
lo
sses are
o
f
ten
co
nsid
ered
t
o
be a
f
r
act
i
o
n
o
f
t
h
e
o
u
t
p
ut
po
wer
,
s
t
r
s
t
r
out
P=
k
P
(1
8)
st
r
k
= th
e co
efficien
t fo
r
stray load
losses
The st
ray loss
coefficient m
a
y to
va
ry
bet
w
een
0.
03
an
d
0.
05
f
o
r
m
achi
n
es rat
e
d
u
p
t
o
1
0
k
W
[
7
]
.
Th
e
ou
tpu
t
power of th
e m
a
c
h
in
e can
b
e
calcu
lated
b
y
th
e
fo
llowing
equ
a
tio
n
,
out
p
h
ph
P=
m
E
I
c
o
s
φ
(1
9)
Th
e inpu
t power
of
ax
ial-
f
l
ux
p
e
r
m
an
en
t
mag
n
e
t sy
nc
hr
on
o
u
s gene
rat
o
r f
o
r
sl
otted stator
ca
n be
calculated by
the fo
llowing equation,
in
out
Cu
F
e
str
P
=
P
+
P
+
P
+
P
(2
0)
The m
achine e
fficiency is
obtained
by
us
in
g
the in
put
p
o
we
r a
n
d
o
u
tp
ut
po
wer
as,
ou
t
in
P
η
=
P
(2
1)
The m
echanica
l
design
param
e
ters of t
h
e
AFPM
SG
f
o
r
slotted stato
r
a
r
e s
h
ow
n i
n
Ta
ble
3
.
Table
3. Mec
h
anical Desi
gn
Pa
ram
e
ters fo
r
Slotted Stat
or
Para
m
e
ters
Units
Value
T
h
e nu
m
b
er
of slot per
pole per
phase
-
1
T
h
e nu
m
b
er
of total slot
-
96
T
h
e nu
m
b
er
of coil tur
n
s per
phase
tur
n
s
96
T
h
e nu
m
b
er
of coil per
phase
-
18
T
h
e nu
m
b
er
of turns per
coil
tur
n
s
9
T
h
e axial length of the stator
cm
3
T
h
e y
oke of the stator
cm
1.
7
T
h
e depth of slot
cm
1.
05
T
h
e width of tooth
cm
1.
82
The average slot pi
tch
c
m
2.72
T
h
e width of slot
cm
0.
9
T
h
e air gap flux de
nsity
T
1.
24
T
h
e peak value of air
gap flux densit
y
T
1.
37
The average pole p
itch
c
m
8.2
3.
3.
C
o
mp
ari
s
on
of
De
si
gn
Resul
t
s
f
o
r
A
FPMS
G
w
i
th
Sl
otl
e
ss
St
a
t
or
an
d Sl
ot
ted
S
t
a
t
or
The
output results of th
e
a
x
ial-flu
x
perm
anent m
a
gnet sy
n
c
hr
o
n
o
u
s
ge
ne
rator
f
o
r
slotte
d stato
r
a
n
d
slotless stator a
r
e s
h
ow
n in Ta
ble 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Design of Slotted and Slotless
AFPM Sy
nc
hr
onous Generat
o
rs and
their P
e
rformance …
(
Sai
nt
S
a
i
n
t
So
e)
81
6
Table
4. Electrical Design Re
sults for AFPMSG
Para
m
e
ters
Slotless Value
Slotted Value
T
h
e RM
S value of the induced phase voltage
48.
44V
56V
T
h
e phase cur
r
e
nt
16.
13A
14A
T
h
e per
phase stator
r
e
sistance
0.
11
Ω
0.
109
Ω
T
h
e stator
leakage
inductance
1.
32
m
H
0.
49
m
H
T
h
e eddy
curr
ent losses
73.
74 W
-
T
h
e copper
losses
85.
85W
64.
09W
T
h
e ir
on losses
-
63.
7W
The stra
y
load losses
-
80W
T
h
e input power
2.
16kW
2.
21kW
T
h
e output power
2kW
2 kW
The m
a
chine
ef
f
i
ciency
93%
90%
Accord
ing
to
th
e co
m
p
arison resu
lts, th
e co
pp
er lo
ss in
slo
tless stato
r
is h
i
g
h
e
r th
an th
at o
f
th
e
slo
tted
d
e
si
g
n
. Mo
r
e
o
v
e
r
,
t
h
e air
co
r
e
d
st
ato
r
h
a
s no
iro
n
l
o
ss
b
u
t
it also
h
a
s eddy cu
r
r
e
n
t
lo
ss in
th
e
statorwi
ndi
ng
because the
m
a
gnetic
flux is
directly expose
d to
the
stator winding.
4.
PERFO
R
MA
NCE
A
NAL
Y
S
IS F
O
R
AF
P
M
SG
Fi
ni
t
e
-el
e
m
e
nt
anal
y
s
i
s
al
l
o
ws
m
odel
i
ng
of c
o
m
p
l
i
cat
ed geom
et
ri
es, no
n l
i
neari
t
y
of
t
h
e
st
eel
, i
n
2
D
and
3
D
, a
nd
gi
ves acc
ur
at
e resul
t
s
wi
t
h
o
u
t
st
an
di
n
g
o
n
m
a
ny
rest
ri
ct
i
ng ass
u
m
p
t
i
ons [
8
]
.
T
o
an
al
y
ze a
pr
o
b
l
e
m
,
i
t
shoul
d
ha
ve a
n
a
p
pr
o
p
ri
at
e ge
om
et
ry
, m
a
t
e
ri
al
pro
p
ert
i
e
s,
an
d
exci
t
a
t
i
on
of
a
devi
ce
o
r
sy
st
e
m
of
devi
ces
.
4.
1. Perf
orm
a
nce
A
n
al
ysi
s
o
f
Sl
ot
ted St
at
o
r
Evaluation
of machine perf
orman
ce with the 2D
FEA m
o
dellin
g
ax
ial-flux
m
ach
in
es is
p
o
s
sib
l
e i
n
a
si
m
ilar way as it is with
th
e
an
alytical co
mp
u
t
ation
,
i.e
.,
by usi
ng t
h
e a
v
era
g
e radi
us
of t
h
e m
achine as a
desi
g
n
pl
ane
.
I
n
t
h
i
s
st
udy
,
t
h
e per
f
o
rm
ance of
2
k
W
A
FPM
SG
with
sl
o
tted
stator is
calcu
lated
with
2
D
fin
ite
ele
m
ent analysis. To
run t
h
e
FEA s
o
ftwa
re,
the first ste
p
is to
draw th
e m
ach
in
e
g
e
om
etry with t
h
e cal
culated
desi
g
n
param
e
t
e
rs o
n
t
h
e
w
o
rki
ng
pl
ane
.
A
n
d
t
h
e
n
, m
a
t
e
ri
al
sel
ect
i
on f
o
r eac
h a
n
d e
v
ery
po
rt
i
o
n f
o
r t
h
e
slo
tted
stator
desig
n
. Th
e
n
e
xt step
, m
e
sh
presen
tatio
n is ru
nn
ing
con
d
itio
n wh
ich can
b
e
ad
ju
sted
th
e m
e
sh
size defi
ned in
the prope
rties
of each m
a
terial.
Fi
gu
re 4.
The
m
a
gnet
i
c
fl
u
x
den
s
i
t
y
val
u
es fo
r AFPM
S
G
Fi
gu
re 4 sh
o
w
s t
h
e m
a
gnet
i
c
fl
ux densi
t
y
val
u
es fo
r AFPM
S
G
by
usi
n
g FEM
so
ft
ware
. Aft
e
r
ru
n
n
i
n
g, t
h
ese
m
odel
di
spl
a
y
FEM
res
u
l
t
o
u
t
put
,
fl
ux
de
nsi
t
y
whi
c
h ca
n
be
pl
ot
t
e
d
as a
co
l
o
u
r
densi
t
y
pl
ot
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
JECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
81
0
–
82
0
8
17
Fi
gu
re
5.
The
peak
val
u
e
of
a
i
r ga
p
fl
u
x
den
s
i
t
y
pl
ot
f
o
r
A
FPM
SG
Fi
gu
re 5 i
s
r
u
n
n
i
n
g res
u
l
t
t
h
at
i
s
t
h
e peak va
l
u
e of ai
r
ga
p fl
u
x
de
nsi
t
y
pl
ot
fo
r A
F
PM
S
G
by
usi
n
g
th
e fi
n
ite-elemen
t
an
alysis.
In th
is fi
g
u
re, th
e p
e
ak
v
a
lu
e
of
air g
a
p
flux
d
e
n
s
ity is 1
.
23
8
T.
Fi
gu
re 6.
The
m
a
gni
t
ude
of m
a
gnet
i
c
fl
u
x
den
s
i
t
y
pl
ot
f
o
r
o
n
e pol
e pai
r
s
Fi
gu
re
6 s
h
ows
t
h
e m
a
gni
t
u
de
of
m
a
gnet
i
c
fl
ux
de
nsi
t
y
pl
ot
fo
r
o
n
e
pol
e
p
a
i
r
s o
f
AFPM
S
G
by
usi
n
g
FEA software. In th
is fi
g
u
re, th
e fl
u
x
d
e
n
s
i
t
y in
th
e m
a
g
n
e
t will b
e
h
i
g
h
er th
an
th
e air
g
a
p flux
d
e
n
s
ity and
flux
d
e
n
s
ity in
th
e stato
r
sectio
n.
Fi
gu
re
7.
The
m
a
gni
t
ude
of
m
a
gnet
i
c
fl
u
x
den
s
i
t
y
pl
ot
f
o
r
t
eet
h an
d y
o
ke
Fig
u
re 7
illu
strates th
e
m
a
g
n
e
tic flu
x
d
e
n
s
ity p
l
o
t
for stato
r
teeth
an
d
stator yo
k
e
b
y
using
th
e fin
ite-
ele
m
en
t an
alysis. In
th
is
figu
re, th
e
flux
d
e
nsity in
th
e
teeth (which appears
at 0.75 cm
and the
value is
1.55T)
i
s
sl
i
ght
l
y
hi
gh
er t
h
an t
h
e
fl
u
x
de
nsi
t
y
i
n
t
h
e st
at
or y
oke s
ect
i
on (
w
hi
c
h
appea
r
s at
0.
4
cm
and t
h
e val
u
e i
s
1.
5T)
.
4.
2.
Perf
orm
a
nce A
n
al
ysi
s
o
f
Sl
otl
e
ss
St
at
or
M
o
re
ove
r,
t
h
e
per
f
o
r
m
a
nce of
2
k
W
A
FPM
S
G
wi
t
h
sl
o
tless stato
r
is an
aly
zed
with
2
D
fi
n
ite-elem
e
n
t
analysis (m
ethod).
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Design of Slotted and Slotless
AFPM Sy
nc
hr
onous Generat
o
rs and
their P
e
rformance …
(
Sai
nt
S
a
i
n
t
So
e)
81
8
Fi
gu
re 8.
The
m
a
gnet
i
c
fl
u
x
den
s
i
t
y
val
u
es fo
r AFPM
S
G
Fi
gu
re 8
sh
o
w
s t
h
e m
a
gnet
i
c
fl
ux
de
nsi
t
y
val
u
es
fo
r A
F
PM
SG
by
usi
ng
fi
ni
t
e
-el
e
m
e
nt
anal
y
s
i
s
so
ft
ware. After ru
nn
ing
,
th
ese
m
o
d
e
l with
2D FEA so
ft
ware d
i
sp
lay th
e mag
n
e
tic flu
x
d
e
nsity wh
ich
can
b
e
pl
ot
t
e
d a
s
a c
o
l
o
u
r
de
nsi
t
y
pl
o
t
.
Fi
gu
re
9.
The
peak
val
u
e
of
a
i
r ga
p
fl
u
x
den
s
i
t
y
pl
ot
f
o
r
A
FPM
SG
Fi
gu
re
9 i
s
ru
nni
ng
res
u
l
t
s
t
h
at
are t
h
e ai
r
gap
fl
u
x
de
nsi
t
y
pl
ot
f
o
r
AF
PM
SG
by
usi
n
g t
h
e
fi
ni
t
e
-
ele
m
ent analysis. In this
figure,
t
h
e
pea
k
val
u
e
of
ai
r
gap
fl
ux
de
nsi
t
y
val
u
e i
s
0
.
6
9
8
T.
Fi
gu
re
1
0
. T
h
e
m
a
gni
t
ude
of
m
a
gnet
i
c
fl
u
x
den
s
i
t
y
pl
ot
f
o
r
o
n
e
pol
e
pai
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
I
J
ECE Vo
l.
5
,
No.
4
,
Au
gu
st 2
015
:
81
0
–
82
0
8
19
Figu
re
10
sh
o
w
s the
m
a
gnitude
o
f
m
a
gnetic flux
de
nsity
plot fo
r one
pole pairs
o
f
AFPM
S
G
by
using FEA
software. In this
fi
gure, t
h
e
flux
density in the
m
a
gnet will
be higher than the
air
gap flux density
and
fl
ux
de
nsity
in the
stator
s
ection.
5.
CO
MP
ARI
S
O
N OF LO
S
S
ES A
ND EF
FICIE
N
C
Y
B
ETWEEN SI
Z
I
NG EQUA
TION A
N
D
F
E
A
SOFTW
ARE
Table
5 shows the c
o
m
p
arison
of losses and e
ffici
ency
between t
h
e
o
ret
i
cal sizing e
q
uation
value
s
and
finite ele
m
ent analysis results for slotted
stator
an
d slotless stator o
f
d
o
uble
-
side
d AF
PM
SG. B
y
ap
p
l
y
i
ng
the FE
A m
e
thod, the e
x
act
data of air-gap
flux
de
nsity
is obtaine
d a
n
d
m
achine effi
ciency is recalculated by
m
eans of corre
cted data. He
re
, the efficiency
of m
achin
e is
higher tha
n
the theoretical sizing equation values.
Finite ele
m
ent analysis leads t
o
m
u
ch
m
o
re a
ccurate m
a
gnet
i
c fields s
o
lutions
.
Com
p
are t
o
the
results i.e., the
analytical result of c
o
ppe
r losses, eddy c
u
rre
n
t losses,
iron
losses a
nd t
h
e
m
achine efficiency which is
base
d
on the i
n
itial assum
e
d flux
density data to
the result getting from
the FE
A
soft
ware.
Table
5. C
o
m
p
ariso
n
of
Lo
sse
s an
d E
fficien
c
y
betwee
n Sizi
ng
E
quatio
n a
n
d F
E
A
So
ftwa
r
e
Specif
i
cations
Units
Sizing E
quation
(AFP
MSG)
2D FE
A
(AFP
MSG)
slotted
stato
r
air cored
stator
slotted
stator
air cored
stator
Peak value of air
g
a
p flux density
T
1.
37
0.
724
1.
238
0.
698
I
nductance m
H
0.
49
1.
32
0.
0074
0.
06
Resistance
Ω
0.
109
0.
11
0.
088
0.
094
Copper
losses
W
64.
09
85.
85
51.
744
73.
37
E
ddy
cur
r
ent losses
W
-
73.
74
-
68.
54
I
r
on
losses
W
63.
7
-
60.
21
-
E
fficiency
%
90
93
91.
3
93.
41
6.
CO
NCL
USI
O
N
This pa
per
ha
d
descri
bed the
desig
n
an
d pe
r
f
o
r
m
a
n
ce o
f
ax
ial-
f
l
ux
d
oub
le
-sided perm
a
n
ent m
a
gnet
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r
with slotted stator a
nd sl
otless
stator. The c
o
ppe
r
losses, i
r
on losses, e
d
dy curre
nt
losses a
n
d the
m
achine efficiency bet
w
een
analytical si
zing e
quatio
n a
n
d
FEA
so
ftwa
re
are c
onsi
d
ere
d
in the
per
f
o
r
m
a
nce com
p
arison
o
f
d
o
u
b
le-si
d
ed
A
FPM
SG
de
sig
n
.
A
n
d
the
n
, t
h
e finite elem
ent
m
e
thod
was
use
d
to
com
pute the
flux
de
nsity
in t
h
e
gene
rato
r c
o
m
pone
nts.
According to the FEA software th
e p
e
ak
valu
e of
air gap f
l
ux
d
e
nsity and the
resistance are l
o
we
r
than t
h
e a
n
alytical sizing data
for sl
otted sta
t
or a
n
d sl
otless
stator. B
eca
us
e of
the
red
u
ci
ng
flu
x
de
nsity
, the
eddy c
u
rrent l
o
sses also re
duced
for air c
o
re
d stator
. M
o
re
over, t
h
e ai
r cored
stator
of
AFPM
SG
m
achine
coppe
r
loss is lowe
r tha
n
t
h
at of t
h
e a
n
alytical si
zing equatio
n.
Acc
o
r
d
in
g to
the c
o
m
p
arison r
e
sul
t
s, the
m
achine efficiency is slightly highe
r
tha
n
t
h
at of the a
n
aly
tical sizing e
q
u
a
tion.
And then, the
slotted stator teeth
flux density value is lower than
that of the initial siz
i
ng equati
on
value. By re
ducing the teeth flux
density, the iron losses is also redu
ced.
Whe
n
the
slotted stator
phas
e
resistance is de
creased t
h
an t
h
e theoretical equation
valu
e
,
it causes the c
o
pper losse
s in
decrease. Beca
use of
the com
p
arison
results, th
e m
achine
efficiency
is higher than
t
h
at of
t
h
e
analytical sizing equation. T
h
ere
f
ore,
it can be conc
lude
d that application of FE
A can
perf
orm
a great effort to get a m
o
re accurate m
achine
desig
n
in
g
pr
oc
ess tha
n
usin
g
sizing e
q
uation
s
o
n
ly
. M
o
reo
v
e
r, t
h
e
per
f
o
r
m
a
nce
of
the sl
o
tless stator m
a
chin
e
efficiency is
greater tha
n
that
of
the sl
otted st
ator ty
pe
.
ACKNOWLE
DGE
M
ENTS
First of all, the author woul
d lik
e to express deep
gratitude to Dr
. Yan Aung Oo,
Professor,
Head of
Depa
rtm
e
nt of Electrical Power E
n
ginee
r
ing
,
M
a
n
d
al
ay
Tech
nol
ogical
Uni
v
ersity
, f
o
r
his close
gui
danc
e
,
accom
p
lished supe
rvision,
help, suppor
t and
shari
n
g ideas a
n
d expe
rience
du
ring t
h
e re
se
arch of the
s
is.
Finally
, the a
u
t
h
o
r
w
oul
d like
to e
x
press
her
dee
p
est
great
than
k t
o
her
fa
ther a
n
d m
o
the
r
f
o
r
no
ble
sup
p
o
rt t
o
her
all tim
e
s and th
eir u
n
iq
ue l
ovi
ng
ki
nd
ne
ss to
attain her destina
tion without
any the t
r
ouble.
Evaluation Warning : The document was created with Spire.PDF for Python.