Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
7, N
o
. 3
,
Ju
n
e
201
7, p
p
. 1
145
~115
3
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v7
i
3.p
p11
45-
115
3
1
145
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
Embedded Simple Excited Auto
m
o
tive Alt
ern
at
or Modelin
g
using M
agn
etic Equivalent Circu
i
ts
Mo
ufi
d
a Kl
ac
h
1
, Helmi
Aloui
2
, R
a
fik
Ne
ji
3
, Mohamed
Gabsi
4
, Miche
l
Lecrivain
5
1,3
Laborator
y
of
Electronics and
I
n
formation Tech
nologies, Univer
sity
of Sfax
,
ENI
S
, Tunisia
2
Laborator
y
of
Advanced
Electr
onic S
y
s
t
ems an
d Sustaiab
le
Ene
r
g
y
, Unive
r
sit
y
o
f
S
f
ax,
ENET’C
o
m
,
Tunisia
4,5
Labora
t
oire
S
y
s
t
èm
es
et
Applic
ations
d
e
s
T
echn
o
logies
d
e
l
’Info
rm
ation e
t
d
e
l
’
E
n
ergie
,
ENS
-
Cac
h
an, F
r
an
ce
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 12, 2016
Rev
i
sed
No
v
28
, 20
16
Accepted Dec 12, 2016
This paper
pres
ents the modeling b
y
Magn
etic Equivale
nt Cir
c
uit model
(M
EC) of a S
i
m
p
le Excit
e
d
Autom
o
tive Alt
e
rnator (S
E2A)
where DC-
exci
tat
i
on windi
ng is
trans
f
err
e
d
from
rotor s
i
de
to s
t
atoron
e ra
t
h
er than
in
conventional automotive
claw pole
alter
n
ators,
to ov
ercome th
e
disadvantages of
the ring-brush sy
stem. Followin
g
the resolution of the MEC
using Newthon-Raphson numerical method,
th
e altern
ator perfo
rmances at
both no-load an
d under resistiv
e load reg
i
mes is achiev
e
d con
s
idering th
e
s
a
turat
i
on eff
e
c
t
.
It h
a
s
been
fou
nd that
a
ltern
ato
r’s
perform
ances
carr
i
ed ou
t
using the proposed MEC are with closed
proximity
to experimen
t
al records
on a bu
ilt proto
t
y
p
e of
the considered
alternator.
Keyword:
Claw po
le altern
ator
Ex
citatio
n
i
n
t
h
e stator
Ex
peri
m
e
nt
al
test
s
M
a
gnet
i
c
e
qui
val
e
nt
ci
rc
ui
t
si
m
p
le ex
citati
o
n
Copyright ©
201
7 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
:
Moufida Klach,
Lab
o
rat
o
ry
of El
ect
roni
cs
an
d In
fo
rm
at
i
on
Tech
nol
ogi
es
,
Uni
v
ersity
of Sfax,
EN
IS
,
BP W
,
30
38
S
f
ax
,
Tun
i
sia.
Em
a
il: m
o
u
f
ida_
k
l
ach
@
yah
o
o
.
fr
1.
INTRODUCTION
Thr
o
ug
h t
h
e l
a
st
y
ears seve
ral
wo
rk
s, [
1
-
3
]
,
sh
owe
d
st
a
ndi
ng
of cl
aw
pol
e st
ru
ct
ure
ado
p
t
e
d i
n
co
nv
en
tio
n
a
l
au
to
m
o
tiv
e altern
ators
po
wer
g
e
n
e
ration
.
Du
e esp
eci
ally to
its si
m
p
licit
y an
d lo
w
manufact
uri
n
g costs, t
h
e cla
w
pole alternat
or
has t
h
e
m
o
st popular elect
rom
echan
ical autom
o
tive
source of
electrical en
erg
y
[4
].
In
reality, th
e h
e
tero
-p
o
l
ar stru
ctu
r
e
o
f
its ro
tor offering
th
e in
tegratio
n
a
h
i
gh
po
le p
a
ir
n
u
m
b
e
r in
a redu
ced
vo
lume, lead
in
g
so
to
an
in
terestin
g
g
e
n
e
rat
i
o
n
cap
ab
ilities. Sev
e
ral claw po
le
al
t
e
rnat
o
r
s st
r
u
ct
ures
ha
ve
be
en
pr
o
pose
d
a
n
d
st
u
d
i
e
d
i
n
bi
bl
i
o
gra
p
hy
a
n
d
di
ffe
r a
r
e
m
a
i
n
l
y
especi
al
l
y
by
th
eir ex
citatio
n fo
rm
s [5
], [6
]. Th
e d
i
sadv
an
t
a
g
e
o
f
th
is m
a
ch
in
e is a cru
c
ial
m
a
in
ten
a
n
c
e p
r
ob
lem
as
a r
e
su
lt
of
b
r
u
s
h
-ri
ng
s
y
st
em
[7]
,
[
8
]
.
To
di
sca
r
d t
h
i
s
di
sa
dv
ant
a
ge
, s
u
ch
ap
p
r
oac
h
c
o
nsi
s
t
s
i
n
t
r
ansm
i
t
t
i
ng t
h
e
fi
el
d
wi
n
d
i
n
g
fr
om
r
o
t
o
r t
o
st
at
or
.The
rem
o
v
a
l
of
t
h
e
b
r
us
h-
ri
n
g
sy
st
em
m
a
kes i
t
po
s
s
i
b
l
e
t
o
achi
e
ve
hi
g
h
reliab
ility an
d
cru
c
ial co
st as well as it im
p
r
ov
es
g
r
eatly
th
e av
ailab
ility
o
f
th
e claw
po
le altern
at
o
r
.In
th
is
co
n
t
ex
t, an
emb
e
dd
ed
Sim
p
le Ex
cited Au
tom
o
t
i
v
e
Al
t
e
r
n
at
or (SE
2
A
)
w
h
ere
t
h
e DC
-e
xci
t
a
t
i
on wi
n
d
i
ng
i
s
lo
cated
i
n
th
e stato
r
attracts cu
rren
tly an in
creasing
a
tten
tion
an
d rep
r
esen
t
s
a fertile research do
m
a
in
[9]
.
The present work com
e
s to append
a
n
anal
y
t
ical
t
ool
based o
n
rel
u
ct
ant
m
odeli
ng o
f
a
n
em
bedded
Sim
p
l
e
Excit
e
d Aut
o
m
o
t
i
v
e Al
t
e
rnat
or (SE2
A). I
n
w
h
at
fol
l
ows, a st
udi
ed
SE2A
prot
ot
y
p
e i
s
fi
rst
l
y
descri
bed.
Aft
e
r t
h
at
, fl
ux
l
i
n
es t
h
rough
SE2A’s m
a
gnet
i
c
ci
rcui
t
ar
e anal
y
zed and
m
a
gnet
i
c
equi
val
e
nt
rel
u
ct
ant
net
w
or
k
o
f
th
is stru
ctu
r
e is elab
o
r
ated
. Fin
a
lly, es
tab
lish
e
d
m
odel is resolved and obtained res
u
lts are co
m
p
ared to
experi
m
e
nt
al
records
perf
orm
e
d o
n
a t
e
st
ben
c
h.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
7,
No
. 3,
J
u
ne 2
0
1
7
:
11
4
5
– 11
53
1
146
2.
STRU
CT
UR
E AN
D
DES
C
RIPTIO
N
OF
FLU
X
LI
NK
AGE
OF TH
E SE2
A
The SE
2A prototype is a
m
o
dified conve
n
tional cl
aw po
le altern
ato
r
wh
ere DC-ex
c
itatio
n
wi
nd
ing
is tran
sferred fro
m
ro
tor t
o
st
ato
r
. Also
, it is equ
i
pp
ed
b
y
a th
r
e
e-
ph
a
s
e a
r
ma
tu
r
e
w
i
n
d
i
ng
an
d in
clud
es
tw
elv
e
claws leadi
ng t
o
a si
x
pole
pa
ir struct
ure
.
T
h
e stator
m
a
gne
tic circuit is com
posed of t
w
o parts
connected i
n
seri
es. T
h
e
fi
rs
t
part
i
s
t
h
e
us
ual
l
a
m
i
nat
e
d cy
l
i
nder c
o
ns
ists o
f
iro
n
sh
eets and
con
s
ecrated
to th
e i
n
sertio
n
of
al
t
e
rnat
o
r
arm
a
t
u
re.
Th
o
u
g
h
,
t
h
e sec
o
nd
o
n
e
i
s
a m
a
ssi
ve cy
l
i
nder s
u
rr
ou
ndi
ng
l
a
m
i
nat
e
d
part
,
com
m
itt
ed t
o
in
du
ctor flux
’s flo
w
i
n
g
an
d
called
“stato
r yo
k
e”
[10
]
. Th
e d
e
scrib
e
d
co
ncep
t illu
strated in
Fig
u
re 1
is called
Sim
p
le Excited Autom
o
tive
Alternator (SE2A),
because
it has a
single excitation source (only wound
inductor).View that the indu
c
t
or is
placed i
n
the stator, the
field wi
nding
results from
two
ring s
h
a
p
e
d
coils
connected in s
e
ries a
n
d introduce
d
es
peci
al
l
y
i
n
t
o
bot
h si
des
of
t
h
e
m
a
ch
ine
bet
w
een the stator y
oke
and the
a
r
ma
t
u
r
e
e
n
d
w
i
n
d
i
n
g
s
.
Figure 2
illu
strates
flu
x
p
a
th
s b
e
t
w
een
stato
r
and
ro
tor th
rou
g
h
th
e SE2
A
m
a
g
n
e
tic
circuit. They are characterized by
t
w
o
ki
nds:
useful
an
d usel
ess. In fact
,
descri
bed fl
u
x
es ar
e:
a.
A 2D
fl
ux, c
o
n
s
i
d
ered as l
eakage fl
uxes caus
e
d by
hom
opol
ar l
i
nkage bet
w
een rot
o
r m
a
gnet
i
c
ci
rcui
t
s
an
d
stator,
b.
A 3
D
fl
u
x
co
n
n
ect
i
ng t
w
o
po
l
e
s and crossi
n
g
b
o
t
h
st
at
or a
nd r
o
t
o
r m
a
gn
et
i
c
ci
rcui
t
s
. It i
s
dedi
cat
ed to
EM
F generat
i
on i
n
al
t
e
rnat
or’
s
arm
a
t
u
re.
Fi
gu
re
1.
St
ruct
ure
o
f
t
h
e
SE
2
A
.
Lege
n
d
:
(a
)
st
at
or,
(
b
)
r
o
t
o
r
,
(
1
)
hal
f
of t
h
e
st
at
or
DC
-e
xci
t
a
t
i
on
ri
n
g
wind
ing
,
(2
) armatu
re en wi
nd
ing
,
(3
)
no
n-mag
n
e
tic core
Fi
gu
re
2.
Fl
u
x
pat
h
s
t
h
r
o
ug
h t
h
e m
a
gnet
i
c
ci
rcui
t
of t
h
e S
E
2A
. Le
ge
nd:
(1
) t
o
(
5
)
sam
e
as i
n
Fi
g
u
re
1,
(6
):
hal
f
of
t
h
e st
at
or DC
-e
xci
t
a
t
i
on wi
n
d
i
n
g, (7
):
arm
a
t
u
re
e
n
d
-
wi
n
d
i
n
g, (8
):
n
o
n
-m
agnet
i
c
co
re hol
di
n
g
t
h
e
t
w
o m
a
gnet
i
c
r
i
ngs
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Em
bed
d
e
d
Si
m
p
l
e
Exci
t
e
d
Aut
o
m
o
t
i
ve Al
t
e
rn
at
or
Mo
del
i
n
g
usi
n
g M
a
gnet
i
c …
.
(
M
o
u
f
i
d
a
K
l
ach)
1
147
3.
MA
GNETI
C EQUI
VALE
N
T
CI
RC
UIT OF
THE SE2
A
In
literatu
re, accu
racy an
d
calcu
l
atio
n
ti
m
e
are g
e
n
e
rally th
e m
a
in
creteri
o
n
s
ado
p
t
ed
for th
e cho
i
ce
of a
n
anal
y
t
i
cal
m
odel
i
ng m
e
t
h
o
dol
ogy
am
ong
ot
he
rs. T
h
e
m
a
g
n
e
t
i
c
e
q
u
i
v
a
l
e
n
t
c
i
r
c
u
i
t
(
M
E
C
)
m
o
d
e
l
i
n
g
i
s
a
rapi
d anal
y
t
i
cal
form
ul
at
i
on
m
ean t
h
at present
s
short
calcul
a
t
i
on t
i
m
e
wi
t
h
adequat
e
preci
si
on, u
s
ed
for
m
o
d
e
lin
g
of
nu
m
e
r
o
u
s
m
ach
in
es
[
11]
. Su
ch
am
et
hod co
nsi
s
t
s
on t
h
e dec
o
m
posit
i
on of
m
achi
n
es st
ruct
ure t
o
fl
ux t
ubes. T
h
e
s
e fl
ux t
ubes re
present
rel
u
ct
ances, M
M
F
sources and, i
f
av
ai
l
a
bl
e, per
m
anent
m
a
gnet
s
sources.
Also
, th
e MEC ap
p
r
o
ach
is
b
a
sed
on
th
e mag
n
e
tic Oh
m law resu
ltin
g
fro
m
th
e an
alo
g
y b
e
tween
mag
n
e
tic
circuits and electric ones.
In s
e
ve
ral
w
o
r
k
s, as
[
12]
a
n
d [
1
3]
, fl
e
x
i
b
l
e
M
E
C
m
odel
s
ha
ve
been s
u
c
c
e
s
s
f
u
l
l
y
i
n
v
e
s
t
i
g
a
t
e
d
a
n
d
presented through detailed and
synthetic de
scription. In
thepresent study, in order
to
prepare an accurate and
rapi
d t
ool
fo
r t
h
e opt
i
m
i
z
at
i
o
n of t
h
e p
r
o
pos
ed aut
o
m
o
ti
ve al
t
e
rnat
or, t
h
e M
E
C
m
e
t
hod i
s
adopt
ed t
o
es
t
i
m
a
te
perf
orm
a
nces o
f
th
e SE2
A
proto
t
yp
e.
3.
1.
No-Load
Ope
r
ati
o
n
Model
Fi
gu
re 3 s
h
o
w
s t
h
e co
rre
s
p
o
n
d
i
n
g M
E
C
of t
h
e S
E
2
A
a
t
n
o
-
l
o
a
d
r
e
g
i
m
e
,
t
a
ki
ng i
n
t
o
acc
ou
nt
satu
r
a
tion
eff
e
ct.
C
onsi
d
eri
n
g Park
’s t
r
ansf
orm
a
t
i
on, de
ve
l
oped bac
k
-E
M
F
can be decom
posed i
n
di
rect
and
quad
r
at
ure co
m
ponent
s t
h
at
corresp
on
d, res
p
ect
i
v
el
y
,
t
o
t
h
e pol
ar an
d i
n
t
e
r-p
ol
ar axi
s
el
em
ent
s
, as expressed
i
n
Equat
i
on
(1
)
and E
quat
i
on
(
2
):
(
1
)
with
:
‖
‖
,
(
2
)
Where
Id
i
s
t
h
e di
rect
com
ponent
o
f
arm
a
t
u
re’s cu
rrent
,
Iq
i
s
t
h
e qua
drat
ure com
ponent
of
arm
a
t
u
re’s
current
,
and If is alternator’s field current.
In t
h
e
case o
f
no-l
o
a
d
operat
i
on,
al
t
e
rnat
or
EM
F i
s
gi
ven
onl
y
by
di
rect
fl
ux c
o
m
ponen
t
.
As
a
result
, the
no-
l
o
ad EM
F, can
be cal
cul
a
t
e
d as i
n
Equat
i
ons
(3) a
nd
(4
):
0
so
(
3
)
Then
√
Φ
(
4
)
Where
is th
e nu
m
b
er o
f
tu
rn
s p
e
r arm
a
tu
re p
h
a
se,
ω
is the angular fre
quency, and
is th
e m
a
x
i
mu
m
fl
ux cr
ossi
ng a
phase w
h
i
c
h i
s
obt
ai
ned usi
n
g
t
h
e M
E
C
.
Because of the nonlinear be
havior of the S
E
2A,
due
to sa
turating
m
a
terials, a nu
m
e
rical procedure
based on Ne
w
t
on-R
a
phs
on
m
e
t
hod has been adopt
ed i
n
order t
o
reso
l
v
e prop
osed r
e
l
u
ct
ance
m
o
d
e
l
and
calculate needed value of flux crossi
ng al
t
e
rnat
or’s arm
a
t
u
re [14]
. The nu
m
b
er of Equat
i
ons t
o
be resol
v
ed i
s
sam
e
as i
ndependent
l
o
o
p
s i
n
co
nsi
d
ered
m
a
gnet
i
c
ci
rcu
i
t
.
In general
,
i
f
a net
w
o
r
k i
n
cl
udes:
NR
rel
u
ct
ances
and N
N
no
des,
i
t
encl
oses:
NIl
p
(= NR
–
N
N
+ 1) i
ndepe
ndent
l
o
ops
.
L
e
t
us consi
d
er
our case, t
h
e
p
r
op
osed
MEC includes
21 bra
n
ches a
nd 12 nodes which lead to
10 indepe
ndent
loops, as illustrated in MEC
of the
SE2A s
h
o
w
n i
n
Fi
gu
re 3.
In
th
e case of no
n
-
saturated
mag
n
e
tic circu
it,
o
b
t
ai
ned sy
st
em
i
s
expressed
by
Equat
i
on
(5
).
Ψ
F
(
5
)
The loop m
a
trix S is built cons
idering following values
of e
ach
com
ponent: Sij is equal to:
a.
-1
: in
th
e case
wh
ere th
e
flu
x
o
f
b
r
an
ch
j
is i
n
th
e op
po
site d
i
rectio
n
o
f
th
e o
r
ien
t
atio
n
o
f
lo
op
i,
b.
0: in the case where the flux of bran
ch
j is n
o
t
in
clu
d
e
d
in
loop
i,
c.
1
:
in
th
e case wh
ere th
e flux
of b
r
an
ch
j is in
th
e same d
i
recti
o
n
o
f
th
e
o
r
ien
t
atio
n
o
f
loo
p
i.
Ho
wev
e
r,
wh
en
m
a
teria
l
s ar
e satu
rated
,
th
e in
v
e
rsio
n
of
m
a
tr
ix
is not possible because
rel
u
ct
ances depend
o
n
fl
u
x
e
s
whi
c
h
are n
onl
i
n
ear.Fo
r
t
h
at
, t
h
e sol
u
t
i
on co
nsi
s
t
s
on
defi
ni
ng
a vec
t
or
C
expressed
by
E
quat
i
on (
6
).
So
, t
h
e cal
cul
a
ti
on p
r
ocess i
s
st
o
pped
w
h
en C
t
u
rns t
o
be
nul
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
7,
No
. 3,
J
u
ne 2
0
1
7
:
11
4
5
– 11
53
1
148
Ψ
(
6
)
Wh
ere F is loo
p
m
.
m
.
f v
ecto
r
,
S is th
e top
o
l
og
ical
m
a
tri
x
and
i
s
l
o
o
p
fl
uxes
vect
or,
and R
i
s
a
di
ago
n
al
matr
ix containing the
reluctances.
Reluctances ar
e calculated using E
quation
(
7
)
:
(
7
)
Fi
gu
re
3.
M
E
C
o
f
t
h
e
SE
2A
whe
r
e t
h
e
ori
e
nt
at
i
ons
of the
bra
n
c
h
es a
n
d the loops a
r
e indicated.
3.
2.
L
oad
O
p
era
ti
on
M
o
del
Un
d
e
r lo
ad
op
eratio
n
,
th
e p
r
op
o
s
ed
n
e
two
r
k
is illu
stra
t
e
d
in
Fig
u
r
e 4
.
It in
clu
d
e
s th
e effect o
f
ar
m
a
ture’s
m
a
gnetic reaction, in
both d a
n
d q axis.I
ndee
d
, s
u
ch a
reac
tion is taken i
n
to account
by the
i
n
t
e
grat
i
on of a
n
arm
a
t
u
re sou
r
ce nam
e
d
and
expresse
d by
Equat
i
on (
8
).
(
8
)
To take into account the effe
ct of claws geom
etry
on ar
m
a
ture reaction Kr is replaced with a new
coeffi
ci
ent
:
Kri
[1
4]
, expresse
d by
Eq
uat
i
on (
9
):
(
9
)
Where
is
th
e
ex
tern
al ro
to
r rad
i
u
s
,
is the claw length,
is
the Carter coefficient,
is
th
e t
h
ick
n
e
ss
of t
h
e
ai
r
gap
bet
w
een t
h
e
cl
aws and the
stator teeth,
is th
e po
le p
a
ir num
b
e
r,
i
s
t
h
e wi
dt
h
of t
h
e
claw base,
is t
h
e wid
t
h
of th
e claw tip
,
is th
e stator active length,
i
s
t
h
e num
ber of con
d
u
ct
ors
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Em
bed
d
e
d
Si
m
p
l
e
Exci
t
e
d
Aut
o
m
o
t
i
ve Al
t
e
rn
at
or
Mo
del
i
n
g
usi
n
g M
a
gnet
i
c …
.
(
M
o
u
f
i
d
a
K
l
ach)
1
149
by
sl
ot
,
i
s
t
h
e t
h
i
c
kness of t
h
e ai
r gap
bet
w
een t
h
e col
l
ector an
d t
h
e m
a
gnet
i
c
ri
ng,
is th
e in
tern
al
m
a
gnet
i
c
coll
ect
o
r radi
us, a
n
d
is th
e co
llecto
r
th
ick
n
e
ss.
Fig
u
re
4
.
SE2A relu
ctan
ce network with
i
n
t
h
e
d
-
ax
is
acc
o
unt
i
n
g
f
o
r t
h
e a
r
m
a
t
u
re
m
a
gne
t
i
c
react
i
on a
n
d t
h
e
satu
ration
.
The di
rect
co
m
ponent
of al
t
e
rnat
or EM
F
(
E
d
) i
s
obt
ai
ned
usi
n
g
t
h
e SE
2
A
’s
rel
u
ct
ant
m
odel
under
load operation. Besides,
qua
drature com
p
onent (E
q
) i
s
d
e
duced
usi
ng
t
h
e phase di
a
g
ram
of Fi
gur
e 5,
corresp
on
di
ng
t
o
t
h
e si
ngl
e-p
h
ase schem
e
o
f
a sy
nchr
on
ou
s
m
achi
n
e. In
fact
, referri
ng
t
o
t
h
i
s
di
agram
,
t
h
e
t
o
t
a
l
EM
F of the al
t
e
rnat
or can be cal
cul
a
t
e
d usi
ng E
quat
i
on (
10)
. B
e
si
des, referri
ng t
o
p
h
a
se di
agra
m
of t
h
e
SE2A,
t
h
e pr
oj
ect
i
on of t
h
e E
M
F on
d an
d
q axi
s
, l
eads t
o
t
h
e ex
pressi
o
n
s o
f
neede
d
c
o
m
ponent
s gi
v
e
n by
Eq
u
a
tio
n
(1
1).Fin
ally,
th
e b
l
oc d
i
ag
ram
fo
r th
e reso
lu
tio
n
of th
e estab
lish
e
d
MEC is il
lu
st
rated
in
Fig
u
r
e
6
.
Figure
5. Phas
e diagram
of t
h
e SE
2A in t
h
e
case of a
resistiv
e lo
ad
Fi
gu
re
6.
B
l
oc
k
di
ag
ram
of t
h
e n
u
m
e
ri
cal
pr
oced
u
r
e
devel
ope
d
f
o
r t
h
e
resol
u
t
i
o
n
o
f
t
h
e
SE
2A
m
odel
ME
C
(i
n
d
-
a
x
is
)
El
ect
ri
c c
i
rcu
i
t
mode
l
P
h
a
s
or d
i
agra
m
A
r
matu
re r
e
a
c
tion
in
q-ax
i
s
Eq
= Lq.
ω
.I
q
I
f
E
d
E
q
I
q
I
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
7,
No
. 3,
J
u
ne 2
0
1
7
:
11
4
5
– 11
53
1
150
̅
(
1
0
)
0
0
(
1
1
)
Where
Is is the armature’s curr
en
t, V is th
e ph
ase’s vo
ltag
e
, R
is the phase’s resistance, and
is th
e leak
a
g
e
i
nduct
a
nce.
4.
EX
PER
I
M
E
NTA
L
VA
LIDA
TION
In
orde
r to
validate the propose
d MEC, both accur
acy and robust
n
ess
of the elaborated m
odel are
t
a
rget
ed
. C
o
ns
eque
nt
l
y
, seve
ral
t
e
st
s have
been m
a
nage
d
and e
xpe
ri
m
e
nt
al
l
y
val
i
d
at
ed u
s
i
n
g
a
t
e
s
t
b
e
n
c
h
b
u
ilt arou
nd
an SE2
A
’s
p
r
o
t
o
t
yp
e, illu
strated in
Fi
g
u
re
7
.
Op
erated
tests are:
a.
At
n
o
-
l
o
a
d
ope
rat
i
on:
1.
Al
t
e
rnat
or
’s
no
-l
oa
d c
h
aract
er
i
s
t
i
c
at
10
00
r
p
m
(Fi
gure
8
(
a)
),
2.
EM
F ve
rs
us t
r
ai
ni
ng
s
p
eed
f
o
r a
fi
el
d c
u
r
r
e
n
t
of
5
A
(Fi
g
u
r
e
8
(
b
)
)
.
b.
At short-circu
it op
eration
:
armatu
re
cu
rr
en
t ver
s
u
s
f
iled cur
r
en
t,
f
o
r
a
sp
eed of
1
000
rp
m
(
F
ig
ur
e
9
)
,
c.
Und
e
r resistiv
e lo
ad op
eratio
n
:
arm
a
tu
re
v
o
ltag
e
ve
rs
us
arm
a
ture cu
rr
ent,
fo
r a
field c
u
r
r
ent
o
f
4
A
r
e
sp
ectiv
ely at
1
000
r
p
m
an
d
at 2
800
r
p
m
(
F
ig
ur
e
1
0
(
a
) and Figu
r
e
10
(b)
)
.
Fi
gu
re
7.
Ex
pe
ri
m
e
nt
al
t
e
st
bench
o
f
t
h
e SE
2A
.
Analyzing obtained curves,
we su
mm
arize
d
the error bet
w
een m
odel values and expe
rim
e
ntal ones
i
n
Ta
bl
e 1
,
usi
n
g
E
quat
i
o
n
(1
2)
.
%
(
1
2
)
Tabl
e
1. E
r
r
o
r
rat
e
f
o
r
pe
rf
or
m
e
d t
e
st
s
No-
l
oad oper
a
tion
Shor
t-
cir
c
uit
Resistive load
(
1000 r
p
m
)
Resistive load
(
2800 r
p
m
)
I
(A)
Erro
r
(%)
sp
eed
(rp
m
)
Erro
r
(%)
I
(A)
I
(A)
I
(A)
Erro
r
(%)
I
(A)
Erro
r
(%)
1 5
700
14.
43
1
0.
25
0.
25
2.
6
0 0.
51
2 0.
4
1000
5.
83
1.
5
0.
4
0.
4
0.
4
0.
83
1.
74
3 1.
8
1500
0.
97
2
0.
6
0.
6
0.
7
1.
5 1.
93
4 6.
6
2000
1.
01
2.
5
0.
95
0.
95
3.
5
1.
75
0.
05
5 1.
4
2500
3
3
1.
15
1.
15
2.
7
2.
25
5.
26
6 2.
3
2800
3.
15
3.
5
a1.
66
1.
66
1.
8
- -
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Em
bed
d
e
d
Si
m
p
l
e
Exci
t
e
d
Aut
o
m
o
t
i
ve Al
t
e
rn
at
or
Mo
del
i
n
g
usi
n
g M
a
gnet
i
c …
.
(
M
o
u
f
i
d
a
K
l
ach)
1
151
Based
o
n
th
ese resu
lts we can no
tice th
e
fo
ll
o
w
i
n
g
:
a.
At no-loa
d regi
m
e
,for a co
nstant speed(Figure 8(a)) error values
do not
exceed 7%
. In addition, for a
constant field current (Figure
8(
b)) EMF e
r
ror does not exceed
6%,
e
x
c
e
pt starting point.Furthe
r
m
o
re,
refe
rrin
g
t
o
Fi
gu
re
8(a
)
, m
a
gnetic circuit o
f
the SE
2A
is sa
turated
f
o
r a
field cu
rre
nt o
f
6A
. H
o
weve
r,
in
t
h
e case
of t
h
e
con
v
e
n
t
i
onal
al
t
e
rnat
o
r
, sat
u
ra
t
i
on a
ppea
r
s at
fi
el
d cu
rre
nt
of
3A
. C
o
nse
q
ue
nt
l
y
, m
odi
fi
ed
altern
ator co
u
l
d
b
e
co
nsid
ered
as seri
o
u
s
can
d
i
d
a
te to
fo
r au
to
m
o
tiv
e g
e
neratin
g app
licatio
n
s
.
b.
At short-circu
it reg
i
m
e
,erro
r
on
arm
a
tu
re cu
rren
t is less th
en
2
%
.
c.
Unde
r
loa
d
regim
e
and for bot
h
c
o
nsidere
d
s
p
eed
s, e
r
ror on arm
a
ture voltage
doe
s
not e
x
ceed
6%.
(a).
Ω
=
1
0
0
0
r
p
m
(
b
)
.
I
F
=
5A
Fi
gu
re
8.
EM
F
o
f
t
h
e
SE
2A
a
t
no
l
o
a
d
ope
ra
t
i
on
regi
m
e
.
Fi
gu
re
9.
A
r
m
a
t
u
re s
h
ort
-
ci
rcu
i
t
e
d cu
rre
nt
ver
s
us t
h
e
fi
el
d c
u
rre
nt
,
fo
r a
spe
e
d
of
1
0
0
0
r
p
m
.
As an
issu
o
f
th
is co
m
p
ariso
n
,
we can
con
c
lud
e
that t
h
e elaborated
ME
C
pr
o
v
i
d
es
val
u
e
s
wi
t
h
cl
osed
pr
o
x
i
m
i
t
y
t
o
experi
m
e
nt
al
wi
t
h
a sat
i
s
fy
i
ng a
ccuracy
,
un
de
r di
f
f
ere
n
t
o
p
e
rat
i
on
regi
m
e
s and
exci
t
a
t
i
on. T
h
us,
rapi
di
t
y
of
est
a
bl
i
s
he
d
m
odel
coul
d
be ex
pl
oi
t
e
d t
o
i
n
vest
f
u
t
u
r
e
wo
r
k
s ai
m
e
d t
o
t
h
e
opt
i
m
i
zati
on
o
f
t
h
e
al
t
e
rnat
or
’s
per
f
o
r
m
a
nce an
d t
o
p
o
logy. More
over, c
o
m
p
ared to
conv
en
tion
a
l claw po
le
altern
ator, [1
5], in
in
tro
d
u
c
ed
SE2A th
e bru
s
h
-
ring
system is
eli
m
in
ate
d
lead
ing
to
th
e i
m
p
r
ov
em
e
n
t of
altern
ator’s availab
ility
th
ro
ug
h
t
h
e
d
i
scard
ofsystemic
m
a
in
ten
a
n
ce,
[16
]
.
0
1
2
3
4
5
6
7
8
0
10
20
30
40
50
60
70
80
90
f
i
el
d
cu
r
r
en
t
(
A
)
EM
F
(
V)
M
E
C
r
esu
l
t
s
exp
er
i
m
en
t
a
l
r
esu
l
t
s
0
50
0
1
000
150
0
2
000
250
0
3000
0
50
100
150
sp
eed
(
r
p
m
)
EM
F
(
V)
M
E
C
r
esu
l
t
s
exp
er
i
m
en
t
a
l
r
esu
l
t
s
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
0
0.
5
1
1.
5
2
2.
5
3
3.
5
f
i
el
d
cu
r
r
en
t
(
A
)
A
r
m
a
tu
re
s
h
o
r
t-
c
i
rc
u
i
te
d
c
u
rr
e
n
t (A
)
M
E
C
r
esul
t
s
expe
r
i
m
en
t
a
l
r
esu
l
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
7,
No
. 3,
J
u
ne 2
0
1
7
:
11
4
5
– 11
53
1
152
(a).
Ω
=
100
0rp
m
(
b
)
.
Ω
=
28
00
rp
m
Figu
re
1
0
.
Ar
m
a
ture v
o
ltage
ve
rsus
arm
a
ture c
u
r
r
ent
fo
r
a f
i
e
l
d
cu
rr
en
t of
4
A
(
i
n th
e ca
se of
resistive l
o
ad).
5.
CO
NCL
USI
O
N
In
ord
e
r to imp
r
ov
e th
e
g
e
n
e
ratio
n cap
ab
ilities o
f
au
t
o
m
o
ti
v
e
altern
ato
r
s,
n
e
w con
c
ep
ts
an
d d
e
si
g
n
s
of
these
m
achines
a
r
e require
d
. This pa
per was de
vote
d
to stud
y an
alytically an
d
e
x
peri
m
e
nt
al
l
y
a
m
odi
fi
ed
al
t
e
rnat
o
r
wi
t
h
t
h
e aim
of carr
y
out
a ro
b
u
st
t
ool
t
o
pre
d
i
c
t
el
ect
rom
a
gnet
i
c
beha
vi
o
r
an
d
per
f
o
r
m
a
nce of ne
w
enha
nce
d
st
r
u
c
t
ures. E
s
t
a
bl
i
s
h
e
d t
o
ol
i
s
a per
m
eance ne
t
w
or
k base
d
on m
a
gnet
i
c
eq
ui
val
e
nt
ci
rcui
t
m
e
t
h
od
. It
was app
lied
on
a Sim
p
le Excited
Au
to
m
o
tiv
e Altern
ator
(SE
2
A)
w
h
e
r
e field
wi
ndi
n
g
is t
r
ans
f
e
rre
d
fr
o
m
r
o
to
r
to
s
t
a
t
o
r
si
d
e
r
a
th
e
r
th
an
u
s
u
a
l
a
u
to
mo
t
i
v
e
a
l
t
e
rn
a
t
o
r
s
.
In
fi
rst
,
base
d
on
fl
u
x
pat
h
s t
h
r
o
u
g
h
t
h
e
m
a
gnet
i
c
ci
rc
ui
t
,
SE
2A
rel
u
ct
ant
net
w
or
k m
odel
was
est
a
bl
i
s
hed
at
no
-l
oa
d a
n
d
un
der
l
o
a
d
ope
rat
i
ons
. A
f
t
e
r
t
h
at
, ad
o
p
t
e
d
n
u
m
e
ri
cal
m
e
t
hod
base
d
on t
h
e
N
e
wt
o
n
-
R
a
phs
o
n
pr
oce
d
u
r
e
fo
r t
h
e
re
sol
u
t
i
o
n
o
f
obt
ai
ned
Eq
uat
i
o
n sy
st
em
i
s
pr
ovi
ded
.
Fi
nal
l
y
, seve
ral
t
e
st
s
ha
ve
been m
a
nage
d
and
ex
peri
m
e
nt
al
l
y
val
i
d
at
ed s
h
o
w
i
n
g
hi
g
h
sat
i
s
fy
i
n
g p
r
eci
si
on a
nd
r
o
bust
n
ess
of
o
u
r
m
odel
un
de
r di
f
f
e
r
ent
ope
rat
i
o
n re
gi
m
e
s and e
x
ci
t
a
t
i
on.
As a
n
o
u
t
c
om
e of pe
rf
or
m
e
d wo
r
k
s,
A
u
t
h
ors
pl
an
t
o
expl
oi
t
est
a
bl
i
s
hed t
o
o
l
for t
h
e st
u
d
y
and sh
o
w
t
h
at
t
h
e SE2A ca
n be en
ha
nced
t
o
a hy
bri
d
al
t
e
rnat
or
wi
t
h
hi
g
h
g
e
n
e
ration
capab
ilities,
m
a
k
i
n
g
it a seri
o
u
s
can
d
i
d
a
te to equ
i
p
fu
tu
re au
t
o
m
o
t
i
v
e
s.
REFERE
NC
ES
[1]
D. Arumugam,
P. Logamani,
S. Karuppiah, “Design and Implementation of
Claw Pole Alternator for Aircraf
t
Applica
tion,
”
ACES JOURNAL
, Vol. 31, no.5
,
p
p
. 582-590
,
May
2016.
[2]
M. Hecquet, P.
Brochet,
“Modeling of
a Claw Pole Altern
ator
usi
ng Permeance Network Cou
p
led with
Electr
i
c
Circuits
,",
I
E
EE Trans.
Magn.
, v
o
l. 31
, no
. 3
,
pp
.
2131-2134, 199
5.
[3]
V.
Ostovic, J.
M
.
Miller,
V.
Garg,
R.
D
.
Sc
hultz, S.
Swa
l
e
s
"A
Ma
gne
tic
E
q
ui
va
l
e
nt
C
i
rc
u
i
t B
a
se
d
Pe
r
f
o
r
m
a
n
ce
Computation of
a Lund
ell Altern
ator,"
IEEE Trans. Magn
, vol. 3
5
, no
. 4
,
pp
. 825
- 830, July
/Augu
st 1999.
[4]
Z.
Zhang
,
H.
Liu, T. Song, “Op
timi
zation Desig
n
and Performance Analy
s
is
of
a PM Brushless Rotor Claw Pole
Motor with FE
M,”
Ma
chines
, v
o
l. 4
,
no. 3, pp. 2
-
9,2016.
[5]
S
.
H
.
L
e
e
,
S
.
O
.
K
w
o
n
,
J
.
J
.
L
e
e
,
J
.
P
.
H
o
n
g
,
“
C
h
a
racte
r
is
ti
c
Anal
y
s
is
of
Cla
w
-Pole Machin
e using Improved
Equivalent Mag
n
e
t
ic
Ci
rc
ui
t,
”
I
EEE Transactio
ns on Magnetics
, Vol. 45, No. 10
, pp. 4570-4573,
Octobre 2009
.
[6]
P.
G.
Dickinson,
A. G.
Jack
and B. C. Mecrow,
"
I
mproved
Permanent Ma
gnet Ma
chines
with Claw
Pole
Armature
s,
"
CD-ROM of the International Conference on
El
ectr
ical Machines
, Br
uges-Belgium,
August 2002.
[7]
R. G.
S
h
riwas
t
a
v
a, M
.
B.Diag
av
ane,
S
.
R.Va
is
hnav, “
L
iter
a
tur
e
Review of
Permanent Magnet A
C
Motors Drive
for
Autom
o
tive App
lic
ation
,
”
Bulletin of
Electrical
Engineering
and I
n
formatics
, Vol.1, No.1
, pp
. 7-14
, Mar
c
h 2012
.
[8]
J. Mostafapour
,
J. Reshadat
, M.
Farsadi, “Improved Rotor Speed Brus
hless DC Motor Using Fuzzy
Con
t
roller,”
Indonesian Jour
nal of Electrical
Engineering and
Informatics
, Vo
l. 3
,
No
. 2
,
pp
. 7
8
-88, June 2015.
[9]
H. Aloui, A
.
Ibala, A
.
Masmoudi, M. Ga
bsi, M.
Lecr
ivain
,
“Relu
c
tan
t
Networ
k b
a
sed Investig
atio
n of a Claw Pole
Alterna
t
or with
dc Exci
ta
tion in
the Stator
,"
in I
n
ter. Journal for
Computation and Mathematics
in Electrica
l
an
d
Electronic Engin
eering,
vol. 27
,
no. 5
,
pp
.1016-1
032, 2008
.
0
0.
5
1
1.
5
2
0
5
10
15
20
25
30
35
40
45
A
r
ma
tu
re
c
u
r
r
e
n
t
(A
)
A
r
m
a
t
u
r
e
vo
l
t
ag
e (
V
)
ME
C
re
s
u
l
t
s
exp
e
r
i
m
en
t
a
l
r
e
su
l
t
s
0
0.
5
1
1.
5
2
0
50
100
150
A
r
ma
t
u
re
c
u
rr
e
n
t
(
A
)
A
r
mat
u
r
e
vo
l
t
ag
e (
V
)
ME
C
re
s
u
l
t
s
ex
p
e
r
i
m
e
n
t
al
r
esu
l
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Em
bed
d
e
d
Si
m
p
l
e
Exci
t
e
d
Aut
o
m
o
t
i
ve Al
t
e
rn
at
or
Mo
del
i
n
g
usi
n
g M
a
gnet
i
c …
.
(
M
o
u
f
i
d
a
K
l
ach)
1
153
[10]
S. Mouellef
,
A.
Bentounsi, H. B
e
na
lla, “Optimal Design of Switched Re
luctance Motor using PSO Based FEM-
EMC Modeling,”
Internationa
l Journal of Elect
rical and Computer Engineering
, Vol. 2, No.5, pp. 621-631,
October 2012
.
[11]
H. W
.
Derbas,
J.
M. W
illi
am
s, A. C. Koenig
, S.
D. Pe
karek
,
“
A
Com
p
arison of Nodal- and Mes
h
-Based Magne
t
i
c
Equivalent Circu
it Models,”
IEEE Transactions
on Energy Conversion
, vol. 24
, n
o
. 2
,
June 2009.
[12]
S Hlioui,
L Vido,
Y Amara,
M
Gabsi,
A Miraoui,
M Lécriv
ain
,
“Magnetic
Equivalen
t
Circu
it M
odel of
a H
y
brid
Excitation S
y
nchronous Machine,”
The In
ternational Journal for
Computa
tion and Mathematics
in Electrical an
d
Electronic Engin
eering
, vol. 27
,n
o. 5
,
pp
. 1000-1
015, 2008
.
[13]
L. Albert
, C. C
h
ille
t, A. Jarosz
, J. Rousseau, F. W
u
rt
z, “
S
izin
g of Autom
o
tive Claw-pole Al
t
e
rnator b
a
sed on
Anal
yti
cal
M
ode
ling,
”
E
l
e
c
tromotion
, vol. 12
, no
. (5/6), pp.749
-77
2
, 2005
.
[14]
A.
Delale, L.
Albert, L.
G
e
rbau
d
,
F.Wurtz, “Automatic Ge
n
e
ration of Sizing
Models for the Optimization
of
Electromagnetic Devices
usin
g
R
e
luctance Networks,”
I
EEET
rans .Magn
, vol. 40
,
no. 2
,
Mar
c
h 20
04.
[15]
L. Albe
rt, “
M
od
elling
and Opti
m
i
zation of
Cla
w
Pole A
ltern
at
ors Applied to
Autom
o
tive S
y
s
t
em
s (in French
),”
PhD Dissertatio
n, Institut N
a
tion
a
l Po
ly
techn
i
que de Gr
enoble, Fr
ance, 2004
.
[16]
H. Aloui, A. Masmoudi, M.
Lecrivain et M. Gab
s
i,
“A New Claw Pole Synchro
nous Machine with DC Excita
tio
n
in the Stator: A Comparison with the
Conventio
nal Claw Pole Alternator,”
Inter
n
ation
a
l Confere
n
ce on Ele
c
tri
c
a
l
Machines (IC
EM), CD-ROM,
Ch
ania-Greece, September
2006
.
Evaluation Warning : The document was created with Spire.PDF for Python.