Int
ern
at
i
onal
Journ
al of
P
ower
El
ectr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
3
,
Septem
be
r 2020
, pp.
1211
~
1219
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
3
.
pp
1
2
1
1
-
1219
1211
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Effect
analysis
of resi
dual magn
etism
availabilit
y le
ve
l
on th
e
success o
f voltage
genera
tion pr
ocesses in
self
-
excite
d inducti
on
generat
ors
Ref
din
al
N
azir
,
Sya
fii,
An
di
Paw
awoi
,
F
aj
ri
l Akbar
,
Yudi
A
r
fa
n
Depa
r
tment
o
f
E
le
c
tri
c
al E
ngin
eering,
Anda
la
s U
nive
rsity
,
Indon
e
sia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
N
ov
1
6
, 201
9
Re
vised
Feb
4
,
20
20
Accepte
d
Apr
26
, 20
20
The
voltage
ge
ner
ation
pro
ce
s
s
is
a
v
ery
cr
uci
a
l
ini
t
ia
l
sta
ge
for
th
e
succ
essful
op
er
at
ion
of
the
s
elf
-
exc
i
te
d
induct
ion
gen
erator
(
SEIG).
Th
e
ava
i
la
bi
li
ty
of
r
esidua
l
m
agne
t
ism
and
th
e
ade
q
uac
y
o
f
exc
i
ta
t
i
on
ca
p
acitor
val
ue
ar
e
fa
ct
ors
that
de
te
r
mi
ne
t
he
succ
ess
of
th
e
vol
ta
ge
gen
erati
on
pro
ce
ss
on
the
SEIG.
T
his
pap
er
ana
l
y
z
es
the
eff
e
ct
of
the
availa
b
il
i
ty
of
residu
a
l
ma
gne
ti
sm on
th
e
rotor's
ma
gn
et
i
c
cor
e. With a
si
mpl
e
appr
oa
ch, the
t
erm
in
al
volt
ag
e
on
the
SEIG
c
an
be
s
olve
d
through
t
he
int
e
rsec
t
ion
bet
wee
n
the
ma
gne
ti
z
at
ion
c
urve
(Xm)
and
the
ex
ci
t
at
ion
c
urve
(X
ce
)
.
The
shape
and
equa
t
ion
of
the
ma
gne
ti
z
at
ion
c
urve
wil
l
b
e
aff
ec
t
ed
by
the
av
ai
l
abi
lity
of
residua
l
m
agne
t
i
sm.
The
ch
ange i
n
r
esidua
l
m
agn
et
ism
av
ai
l
abi
l
ity
will c
ause
a
ch
ange
in
the
i
nte
rsec
ti
on
po
int
bet
we
en
the
magnetiza
t
ion
cur
v
e
(Xm)
and
the
excitation
c
urve
(Xc
e),
wh
ic
h
will
de
te
rm
ine
the
va
lue
of
voltage
gene
ra
te
d
by
th
e
gen
era
tor
.
In
thi
s
study,
New
ton
Rhapson's
me
thod
wi
th
nume
ri
ca
l
itera
t
i
on
appr
oac
h
has
bee
n
used
to
an
al
yz
e
the
eff
ec
t
of
cha
nges
in
the
avail
abi
l
ity
of
residual
m
a
gnet
ism
on
the
succ
e
ss
of
vol
ta
g
e
gen
era
t
ion
on
th
e
SEIG.
T
he
analysis
resu
lt
s
h
ave
be
en
show
n
that
the
av
ai
l
abi
lity
of
residua
l
m
agneti
sm
with
residu
al
voltage
v
al
ues
bel
ow
1
.
04
Volt
will
ca
use
the
f
ai
lur
e
of
the
SEIG
to
gen
erate
th
e
t
erminal
v
olt
ag
e
a
t
i
ts
nom
ina
l
v
al
u
e.
M
ea
nwhile,
the
availa
b
il
i
ty
of
residua
l
ma
gn
etism
in
SEIG
with
r
esidua
l
volt
ag
e
va
lue
s
a
bove
1.
04
Volt
,
will
suc
ceed
in
gene
ra
ti
ng
te
r
minal
vo
lt
ag
e
at
i
ts
nomi
n
al
v
al
ue
.
For
SEIG
used
as
the
object
of
thi
s
study,
the
va
lue
of
Ere
s =
1.
04
Volt
is a c
r
it
i
cal
va
lu
e
of the
av
ai
l
abi
l
it
y
of
residu
al
m
agne
t
ism.
Ke
yw
or
d
s
:
Excit
at
ion
c
urv
e
M
a
gn
et
iz
at
ion
curve
Re
sidu
al
m
ag
ne
ti
sm
SEIG
Vo
lt
age
g
e
ne
ra
ti
on
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
:
Re
fd
inal
Nazir
,
Dep
a
rtme
nt of
Ele
ct
rical
En
gi
neer
i
ng,
Andalas
U
niv
e
rsity, I
ndonesi
a
Jal
an Dr.
M
oh
ammad
H
at
ta
Pada
ng 25
163, I
ndonesi
a
.
Emai
l:
refdinal
nazir@
ya
hoo.c
o.
id
1.
INTROD
U
CTION
Currentl
y,
the
app
li
cat
io
n
of
i
nductio
n
gen
e
r
at
or
s
i
n
po
wer
plants
is
in
crea
sing
l
y
ri
valing
the
us
e
of
sy
nc
hro
nous
ge
ner
at
or
s
,
espe
ci
al
ly
in
small
scal
e
power
pl
ants
that
are
dri
ven
by
renew
able
ene
rgy
s
ources
,
su
c
h
as
micr
o hyd
ro
po
wer
pl
ants, w
in
d
po
w
er,
biomass
po
wer,
et
c.
[
1
-
4].
This
is
m
ai
nly
due
t
o
t
he
i
nduction
gen
e
rato
r
(s
quirrel
-
ca
ge
ro
t
or)
has
a
num
be
r
of
ad
va
ntag
es
ove
r
s
ynch
r
onous
ge
ner
at
or
s
,
i
nclu
ding:
str
ong
and
sim
ple
r
ot
or
co
ns
tr
uctio
n,
mi
nimal
mai
ntena
nce,
sim
pl
e
operati
on,
ha
s
the
abili
ty
t
o
sel
f
-
protect
ion.
In
add
it
io
n,
i
nduc
ti
on
gen
e
rato
rs
are
m
or
e
r
esi
sta
nt
to
ha
r
monic
cu
rr
e
nt
s
ge
ner
at
e
d
by
non
-
li
nea
r
l
oads
or
el
ect
ro
nic
lo
a
d
co
ntr
ollers
(
ELC)
[
5
-
8].
T
her
e
a
re
2
op
erati
ng
patte
r
ns
of
i
nductio
n
gen
e
rato
rs
a
ppli
ed,
namely:
opera
ti
on
as
a
s
ta
nd
-
al
on
e
ge
nerat
or
a
nd
ope
r
at
ion
as
a
ge
ner
at
or
c
onne
ct
ed
to
t
he
gri
d
[
3,9]
.
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
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
12
11
–
12
19
1212
The
operati
on
of
a
sta
nd
-
al
one
in
duct
io
n
ge
ner
at
or
,
bette
r
known
as
t
he
Self
-
Excit
ed
I
nductio
n
Ge
ner
at
or
(S
E
IG),
is
ge
ne
rall
y
us
e
d
in
small
-
scal
e
po
wer
pla
nts
in
off
-
gr
i
d
a
reas
.
W
hile
the
op
erati
on
of
i
nduction
gen
e
rato
rs
wit
h
gr
i
d
-
c
onnect
ed
patte
r
ns
is
gen
e
rall
y
ap
plied
t
o
t
he
distr
ibu
te
d
gen
e
rati
on
(
D
G)
in
on
-
gri
d
areas.
The
stu
dy in
this
pa
per
is fo
c
us
e
d
t
o
a
nalyze t
he o
perat
ion
of SE
IG.
Be
sides
the
rot
at
ion
of
the
pr
ime
move
r,
there
a
re
tw
o
var
ia
bles
that
determi
ne
the
su
ccess
of
the
S
EI
G
ope
rati
on,
namel
y:
the
a
vaila
bil
it
y
of
the
res
idu
al
mag
neti
sm
at
the
ti
me
of
init
ia
ti
on
an
d
the
ade
quacy
of
the
reacti
ve
powe
r
durin
g
t
he
excit
at
ion
pr
ocess.
The
rea
ct
ive
powe
r
ne
eds
of
t
he
in
du
ct
ion
gen
e
rato
r
a
re
use
d
to
ge
ne
rate
a
ma
gn
et
ic
fiel
d
in
t
he
ai
r
ga
p,
w
hich
is
nee
ded
to
pro
du
c
e
the
in
duced
volt
age
[10]. I
n
S
EI
G, the
r
eact
ive po
wer
re
quireme
nts
a
re
s
upplie
d
from
the
e
xcita
ti
on
ca
pacit
or, which
is
c
onnected
in
par
al
le
l
wit
h
t
he
ge
ner
at
or
te
r
minal.
Th
e
avail
abili
ty
of
resid
ual
ma
gnet
ism
i
n
the
i
ron
c
ore
of
the
SE
IG
ro
t
or
is
abs
olut
el
y
necessar
y
to
ge
ner
at
e
the
init
ia
l
vo
lt
age
of
the
gen
e
rat
or
(
E
res
),
a
nd
t
hen
as
a
tri
gg
e
r
f
or
the
init
ia
l
e
xcita
ti
on
cu
rr
e
nt
(
I
e0
)
[
11]
.
The
unavail
abili
ty
of
resi
du
al
ma
gn
et
ism
or
the
re
du
ct
io
n
in
it
s
value
lowe
r
t
han
th
e
crit
ic
al
value
will
cause
t
he
f
ai
lure
of
t
he
vo
lt
age
gen
e
rati
on
proces
s
i
n
th
e
SE
IG.
The
va
lue
of
resid
ual
ma
gne
ti
sm
avail
abili
ty
in
the
SEIG
can
be
c
hange
du
e
to
short
ci
rcu
it
fa
ul
t,
e
xtr
a
reacti
ve
l
oad,
an
d
it
s o
pe
rated
at
it
s cr
it
ic
al
p
oi
nt [12,1
3].
The
e
ff
ect
of
t
he
a
vaila
bili
ty
of
resi
du
al
ma
gn
et
ism
on
the
su
cce
ss
of
vo
l
ta
ge
gen
e
rati
on
on
S
EI
G
is
analyze
d
in
th
is
pa
pe
r.
G
ra
phic
al
ly,
the
ge
ner
at
io
n
of
S
EIG
te
r
minal
vo
lt
age
s
at
n
omi
nal
value
s
can
be
determi
ned
fro
m
the
intersect
ion
betwee
n
th
e
mag
netiz
at
ion
cu
rve
(
X
m
)
a
nd
t
he
excit
at
ion
c
urve
(
X
ce
)
[14]
.
The
ma
gnet
iz
at
ion
cu
r
ve
eq
ua
ti
on
will
be
a
ff
ect
ed
by
the
avail
abili
ty
of
the
resid
ual
m
agn
et
ism
,
w
hile
the
excit
at
ion
cu
rve
eq
ua
ti
on
is
de
te
rmin
e
d
by
t
he
value
of
th
e
excit
at
io
n
ca
pacit
or.
T
he
c
hange
in
the
r
esi
du
a
l
mag
netism
a
va
il
abili
ty
will
c
ause
a
c
ha
nge
in
th
e
i
ntersect
ion
poi
nt
betw
een
t
he
ma
gn
e
ti
zat
ion
c
urve
(
X
m
)
and
t
he
excit
at
ion
c
urve
(
X
ce
)
,
w
hich
will
de
te
rmin
e
the
a
m
oun
t
of
volt
age
gen
e
rated
by
t
he
ge
nerat
or.
I
n
this
study,
New
t
on
Ra
ph
s
on's
met
hod
with
a
numerical
a
ppr
oa
ch
is
a
pp
li
ed
t
o
anal
yze
the
ef
fect
of
c
hanges
in
the
avail
abili
ty of
resid
ual ma
gne
ts o
n vo
lt
age
generati
on
by S
EIG.
2.
THE
PROCE
SS
O
F
VOLT
AGE
GENE
R
ATIO
N
O
N S
EIG
In
the
in
duct
ion
gen
e
rato
r
connecte
d
t
o
the
gr
i
d,
the
vo
lt
age
gener
at
ion
proces
s
can
occur
immediat
el
y
w
hen
the
ge
ner
a
tor
is
pa
rall
el
ed
to
the
gri
d.
This
happe
ns
because
the
re
act
ive
po
wer
ne
eds
fo
r
the
excit
at
ion
process
a
re
dir
ect
ly
pro
vid
e
d
by
t
he
gr
i
d
sys
te
m.
U
nlike
th
e
inducti
on
ge
ner
at
or
c
onnec
te
d
to
the
gri
d,
the
re
act
ive
pow
er
s
upply
in
t
he
S
EIG
is
ob
ta
ine
d
from
t
he
e
xc
it
at
ion
capaci
t
or.
And
t
he
e
xc
it
at
ion
process
i
n
S
E
IG
be
gin
s
wit
h
the
avail
abil
it
y
of
re
sid
ual
mag
netism
i
n
it
s
ro
t
or.
T
he
r
ef
or
e
,
the
vol
ta
ge
gen
e
rati
on
pro
cess
in
SE
IG
c
an
be
bro
ke
n
dow
n
int
o
t
wo
sta
ges,
namel
y:
s
yn
c
hro
nous
operati
on
sta
ge
a
nd
asy
nchron
ous
op
e
rati
on sta
ge
[15
-
17
].
2.1.
Synchro
nous
mod
e
o
p
era
tio
n
The
e
xcita
ti
on
process
at
the
sy
nc
hro
nous
op
e
rati
ng
m
ode
sta
ge
is
tr
igge
red
by
t
he
av
ai
la
bili
ty
of
resid
ual
ma
gnet
ism
in
the
S
EIG.
T
he
avai
la
bili
ty
of
residu
al
ma
gnet
ism
can
be
c
hec
ked
from
t
he
vo
lt
age
gen
e
rated
at
th
e
machi
ne
te
r
minals
it
caus
ed.
M
eas
urem
ent
of
t
he
mac
hin
e
te
rmin
al
vo
lt
age
cau
sed
by
th
e
resid
ual
ma
gnet
ism
is
perfor
med
i
n
the
c
onditi
on
t
hat
the
machine
has
not
bee
n
c
onne
ct
ed
to
the
e
xc
it
at
ion
capaci
tor
a
nd
it
s
ro
to
r
is
r
otate
d
in
s
yn
c
hr
onous
r
otati
on
,
as
sho
wn
in
fig
ur
e
1.
T
he
value
of
t
he
volt
age
gen
e
rated
by
t
he
resid
ual
ma
gn
et
ism
in
t
he
sta
tor
is
pr
opor
t
io
nal
to
the
resid
ual
ma
gn
et
ism
de
ns
it
y
and
the
numb
e
r
of
r
otor
r
otati
on
.
Fi
gure
2b.
sho
ws
the
wa
veform
of
the
te
rmin
al
vo
lt
age
due
to
resid
ual
mag
ne
ti
sm
for
mac
hin
es
us
e
d
as
stu
dy
ob
je
ct
s
a
nd
ro
t
at
ed
at
synch
r
onous
r
otati
on.
The
re
sid
ual
mag
netism
is
f
orm
ed
because
of
the
ma
gn
et
iz
in
g
process
that
ha
s
be
en
car
rie
d
out
befor
e
t
he
machi
ne
is
op
e
rated
,
as
s
how
n
i
n
fig
ur
e
2.
For
ge
ner
at
or
s
,
t
he
mag
netiz
ing
pr
ocess
is
usual
ly
im
pleme
nted
unti
l
it
reac
he
s
the
fl
ux
sat
urat
ion
value
(
ψ
s
).
W
hen
the
ma
gne
ti
zat
ion
cu
r
re
nt
is
re
du
c
ed
to
zer
o,
the
re
is
sti
ll
a
mag
netic
flu
x
sto
red
on
t
he
mag
netic
c
or
e
of
mac
hin
e
ro
t
or.
T
he
re
main
ing
fl
ux
in
the
ma
gn
et
ic
co
re
is
know
n
as
t
he
rema
ne
nce
flu
x
(
ψ
r
)
.
T
he
co
m
par
is
on
betwe
e
n
the
m
ag
nitu
de
of
t
he
re
man
ence
fl
ux
with
the
sat
ur
at
i
o
n
f
lux
is
known
a
s
the
rema
nen
ce
fac
tor
(
K
r
)
[
18].
The
rema
ne
nc
e
facto
r
value
of
a
n
in
duct
ion
ge
ne
rato
r
i
s
deter
mine
d
by
th
e
mag
netic
c
or
e
mate
rial
use
d
[
19
-
21].
T
he
m
agn
it
ude
of
th
e
ma
gn
et
iz
at
io
n
c
urre
nt
will
aff
ect
t
he
a
moun
t
of
resid
ual
ma
gn
e
ti
sm,
w
hich
a
ut
om
at
ic
al
ly
al
so
af
fects
th
e
m
agn
it
ude
of
vol
ta
ge
that
it
s
f
or
ms.
Fi
gure
3
s
how
s
the
va
riat
ion
be
tween
the
ma
gn
et
iz
at
io
n
cu
r
ren
t
I
m
a
nd
t
he
vo
lt
age
ge
nerat
ed
at
the
ma
chine
te
r
minal
du
e
t
o
resid
ual
ma
gn
et
ism
E
res
.
As
this
fi
gure
s
ho
ws,
the
ma
gn
it
ud
e
of
volt
age
due
t
o
t
he
re
sidu
al
mag
neti
sm
is
pro
portion
al
t
o t
he
ma
gnit
ude
of c
urren
t i
nject
ed
into
one
of the
phase
windin
gs
of mac
hin
e stat
or.
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
Eff
ect
a
naly
sis
of resid
ual m
agnetis
m ava
il
abil
it
y
le
vel
o
n
t
he
s
uccess
o
f v
oltag
e
…
(
Ref
di
na
l N
az
ir
)
1213
(a)
(b)
Figure
1. V
oltage
du
e
to
t
he
i
nductio
n of res
idu
al
ma
gnet
ism
(a
)
e
qu
i
vale
nt
ci
rc
uit (
b)
volt
age
wav
e
f
orm
Figure
2. The
process
of
for
ming resi
du
al
mag
netism
Figure
3. M
a
gne
ti
zi
ng
cu
rr
e
nt
(
Im
) ver
su
s
th
e volt
age
du
e
to resi
dual
mag
netism
(Eres)
2.2.
Asynchr
onous
Mode
Oper
ati
on
The
as
ynch
ronous
operati
ng
m
ode
of
SEIG
in
t
he
vo
lt
a
ge
ge
ne
rati
on
proces
s
sta
rts
after
the
e
xcita
ti
on
capaci
tor
(Ce)
is
co
nnect
ed
on
t
he
ge
nerat
or
te
r
minal.
T
he
SE
IG
e
quival
ent
ci
rc
uit
i
n
t
he
no
-
load
c
onditi
on
and the a
sync
hro
nous o
pe
rati
ng m
od
e
is s
hown in Fi
gure
4.
In
no
-
l
oad
c
on
diti
on
s
,
the
r
oto
r
c
urre
nt
is
ve
ry
s
mall
an
d
c
an
be
ig
nore
d.
In
t
his
co
ndit
io
n,
t
he
r
otor
ci
rcu
it
branc
h
becomes
a
n
open
ci
rc
uit,
s
o
t
hat
the
e
quival
ent
ci
rc
uit
of
S
EIG
can
b
e
simpli
fied
as
s
how
n
i
n
Figure
4b.
I
n
t
his
ci
rc
uit,
I
m
=
I
s
=
I
e
ap
plies.
T
he
ai
r
gap
vo
lt
age
c
urve
(
E
g
)
a
s
a
f
un
ct
ion
of
I
m
is
obta
ined
from
the
sat
ur
at
ion
te
st
res
ul
ts.
T
he
te
r
min
al
volt
age
c
ur
ve
(
V
t
)
as
a
f
unct
ion
of
I
m
c
an
be
so
l
ved
t
hro
ugh
the
f
ollo
wing e
qu
at
io
n:
2
s
m
2
s
m
g
t
)
(
)
(
R
I
X
I
E
V
+
+
=
(1)
Figure
5
s
how
s
the
relat
ion
s
hi
p
betwee
n
the
ma
gnet
iz
at
ion
cu
r
ve
(
X
m
)
a
nd
t
he
excit
at
io
n
c
urve
(
X
ce
)
in
the
volt
age
gen
e
rati
on
pro
cess
of
SE
IG.
M
a
gn
et
iz
at
ion
curves
can
be
expresse
d
i
n
te
rms
of
ai
r
gap
vo
lt
ag
e
(
E
g
)
ve
rsus
ma
gn
et
iz
in
g
c
urr
ent
(
I
m
)
or
te
r
minal
vo
lt
age
(
V
t
)
ve
rs
us
m
a
gn
et
iz
in
g
c
urr
ent
(
I
m
),
as
show
n
i
n
Figure
5a
.
For
the
same
ma
c
hin
e,
th
e
i
niti
al
valu
e
of
the
mag
netiz
at
ion
curve
will
c
ha
ng
e
acc
ordin
g
to
the
value of
t
he
vo
lt
age g
ene
rated
d
ue
t
o
re
si
du
a
l magn
et
ism
. The e
xcita
ti
on
curve is a li
nea
r
cu
rv
e
with c
ha
ng
e
s
directl
y
pro
por
ti
on
al
to
the
e
xcita
ti
on
react
ance
(
X
ce
)
or
inv
e
rsely
propo
rtion
al
to
t
he
e
xcita
ti
on
ca
pac
it
ance
(
C
e
).
T
he
vo
lt
age
ge
ne
rati
on
process
i
n
S
EIG
ca
n
be
c
omplet
ed
f
r
om
the
in
te
rsecti
on
of
the
ma
gnet
iz
ing
curve
with
t
he
excit
at
ion
cu
r
ve
[15,22],
as
s
how
n
in
Fig
ur
e
5b.
The
po
i
nt
of
intersect
io
n
of
these
tw
o
curves
can
occ
ur
in
th
e
re
gion
of
sat
ur
at
io
n,
li
near
or
init
ia
l
re
gion.
The
vo
lt
age
gen
e
rati
on
pro
cess
is
cl
ai
me
d
to
be
su
c
cess
fu
l
i
f
th
e
intersect
io
n
of
the
t
wo
cu
r
ves
occ
ur
s
in
t
he
sat
ur
at
io
n
r
egio
n.
If
the
two
cu
r
ves
inte
rsect
in
a
li
near
reg
i
on,
i
ntersecti
on
will
occ
ur
at
ma
ny
po
i
nts,
w
hich
tri
gg
e
rs
t
he
volt
age
ge
ner
at
i
on
pr
ocess
t
o
be
come
un
sta
ble.
M
ean
wh
il
e,
if
t
he
in
te
r
sect
ion
occ
urs
in
the
i
niti
al
area,
the
n
the
gen
e
rato
r
will
on
l
y
ge
ne
rate
a
ver
y
small
volt
age.
jX
s
R
s
jX
m
E
r
e
s
E
g
V
t
I
m
I
s
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
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
12
11
–
12
19
1214
(a)
(b)
Fig
ure
4. The
SEIG e
qu
i
valent circ
uit o
n
th
e asy
nc
hrono
us o
per
at
in
g mo
de
(a)
e
quivale
nt circ
uit o
n no load
conditi
ons, (b
) si
mp
li
fied
eq
ui
valent circ
uit
(a)
(b)
Figure
5
.
The
re
la
ti
on
sh
i
p between
the
mag
ne
ti
zat
ion
curve
(
X
m
)
and t
he
e
xcita
ti
on
c
urve
(
X
ce
)
in
t
he vo
l
ta
ge
gen
e
rati
on
pro
cess of S
EI
G.
(
a)
ma
gnet
iz
ing cu
rv
e
in
te
r
ms
E
g
an
d
V
t
(
b)
i
ntersecti
on
of the ma
gnet
iz
at
ion
curve
with se
ve
ral exc
.
C
ur
ve
s
3.
ANALY
SIS
A
ND EXPE
RI
MENT
AL SE
T
-
UP
3.1.
Analy
sis
As
disc
us
se
d
i
n
se
ssio
n
2.2,
the
process
of
volt
age
ge
ne
r
at
ion
at
the
S
EIG
ca
n
be
simply
s
olv
e
d
from
t
he
inter
s
ect
ion
betwee
n t
he
ma
gnet
iz
at
ion
c
ur
ve (
X
m
) a
nd the e
xcita
ti
on curve
(
X
ce
).
The fu
nctio
n o
f
the
mag
netiz
at
ion
curve ca
n be
de
fine
d
by the
f
ollow
i
ng equat
ion
:
X
m
:
V
t
=
g
(
I
m
)
;
X
ce
:
V
ce
=
h
(
I
m
)
(2)
If
the
ma
gn
et
i
zat
ion
c
urve
e
qu
at
io
n
is
a
ppr
ox
imat
e
d
by
t
he
poly
nomial
interp
olati
on
method,
t
he
n
it
s f
unct
ion ca
n be e
xpresse
d by the
f
ollow
i
ng e
qu
at
io
n:
g
(
I
m
)
=
a
0
+
a
1
I
m
+
a
2
I
m
2
+
a
3
I
m
3
++
a
n
-
1
I
m
n
-
1
+
a
n
I
m
n
(3)
The
c
onsta
nt
values
of
a
1
,
a
2
,
a
3
,
……
…
.,
a
n
-
1
,
a
n
ca
n
be
s
olv
e
d
us
i
ng
the
poly
fi
t
f
un
ct
io
n
in
M
A
TLAB
[2
3].
T
he
e
xcita
ti
on
c
urve ca
n be
expresse
d b
y
t
he follo
wing
f
un
ct
io
n:
h
(
I
m
)=
X
ce
I
m
(4)
The
dif
fer
e
nce
bet
ween
the
mag
netiz
at
ion
curve
an
d
the
excit
at
io
n
c
urve
ca
n
be
s
ol
ved
by
this
fo
ll
owin
g
e
qua
ti
on
:
f
(
I
m
)
=
g
(
I
m
)
-
h
(
I
m
)
(5)
The
i
ntersect
ion
of
the
se
two
c
urves
can
be
s
olv
e
d
by
de
te
rmin
in
g
t
he
r
oo
t
of
the foll
owin
g
e
qu
at
io
n:
L
s
R
s
L
m
E
r
e
s
E
g
V
t
C
e
i
m
i
e
L
s
R
r
i
r
i
s
jX
s
R
s
jX
m
E
r
e
s
E
g
V
t
-
jX
ce
I
m
I
e
I
s
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
Eff
ect
a
naly
sis
of resid
ual m
agnetis
m ava
il
abil
it
y
le
vel
o
n
t
he
s
uccess
o
f v
oltag
e
…
(
Ref
di
na
l N
az
ir
)
1215
f
(
I
m
) =
a
0
+(
a
1
-
X
ce
)
I
m
+
a
2
I
m
2
+
a
3
I
m
3
++
a
n
-
1
I
m
n
-
1
+
a
n
I
m
n
=
0
(
6)
w
hile,
f’
(
I
m
)
=
(
a
1
-
X
ce
)
+
2
a
2
I
m
+3
a
3
I
m
2
+.+(n
-
1)
a
n
-
1
I
m
n
-
2
+n
a
n
I
m
n
-
1
(7)
To
determi
ne
t
he
r
oot
of
e
qu
a
ti
on
(
6),
New
t
on
Ra
phs
on
's
i
te
rati
on
meth
od
is
use
d,
wit
h
the
eq
uatio
n
for
s
olv
i
ng eac
h
it
erati
on as
foll
ows [2
4,25]:
)
(
'
)
(
m
m
m
m
I
f
I
f
I
I
n
e
w
−
=
(8)
I
m
new
=
value o
f
ma
gnet
iz
at
ion
c
urren
t at
t
he
k
-
it
erati
on
I
m
=
value o
f
magneti
zat
ion cu
rr
e
nt at the
(
k
-
1)
-
it
erati
on
Ov
e
rall
,
the
a
na
lysis
of
the
e
f
fect
of
resi
du
al
mag
net
avail
a
bili
ty
on
the
ge
ner
at
io
n
of
S
E
IG
te
r
minal
vo
lt
age
s
is
co
mp
le
te
d
th
rou
gh
the
ste
ps
a
r
range
d
in
the
flo
wch
a
rt
in
F
igure
6.
As
s
how
n
i
n
Fi
gur
e
6,
th
e
mag
netiz
at
ion
curve
data
in
var
ia
ti
ons
of
E
g
(i)
an
d
I
m
(i)
are
obta
ine
d
f
rom
sat
urat
ion
measu
reme
nts
(se
e
Appe
nd
i
x).
W
her
eas
the
ma
gnet
iz
at
ion
c
urv
e
data
i
n
t
he
va
riat
ion
V
t
(i)
with
I
m
(i
)
is
c
al
culat
ed
th
r
ough
(
1).
The
deter
minat
ion
of
t
he
valu
e
of
t
he
e
xcita
ti
on
capaci
to
r
by
operati
ng
t
he
ge
ner
at
or
wit
h
t
he
a
vaila
bili
ty
of
su
f
fici
ent
r
esi
dual
ma
gnet
ism
an
d
ze
ro
loa
d
conditi
ons,
s
o
that
the
te
r
min
al
vo
lt
a
ge
rea
c
hes
a
nomi
nal
value.
The
fr
e
quenc
y
val
ue
of
the
vo
lt
age
gen
e
ra
te
d
by
the
ge
ne
rat
or
is
set
at
50
Hz.
I
n
thi
s
it
erati
on,
t
he
init
ia
l
conditi
on
I
0
ca
n
be
set
t
o
zer
o
.
For
eac
h
it
e
rati
on
ste
p
k
,
a
ne
w
value
of
the
I
m
new
ma
gn
et
iz
at
ion
cu
rr
e
nt
is
cal
culat
ed.
T
he
it
erati
on
proc
ess
is
stoppe
d,
if
|
I
m
-
I
m
new
|
reach
small
er
or
equ
al
to
,
w
he
re
in
the
proc
ess
of
this
diag
ram
s
et
=
10
-
5
.
Th
e
analysis
proc
ess
is
carried
out
for
a
va
riet
y
of
re
sid
ual
m
agn
et
ism
c
ondi
ti
on
s,
rangin
g
from
the
a
vaila
bili
ty
of
str
ong
resid
ual
ma
gnet
ism
to
the
avail
abil
it
y
of
very
l
o
w
resid
ual
mag
ne
ti
sm,
so
t
hat
no
m
ore
vo
lt
a
ge
ca
n
be
gen
e
rated
.
I
n
t
his
st
udy,
the
re
a
re
6
ef
fects
of
the
av
ai
la
bili
ty
of
re
sidu
a
l
mag
net
co
nd
it
ion
s
a
nalyze
d
on
the
ge
ne
rati
on
vo
lt
a
ge
of
SE
I
G.
Al
l
resu
lt
s
of
t
he
anal
ys
is
w
il
l
be
discusse
d i
n
se
ssion 4
.
Fig
ure
6
.
Flo
w
ch
a
rt for
ef
fec
t analysis
of th
e resid
ual m
ag
netism a
vaila
bili
ty to
the volt
age
g
e
ne
rati
on pro
c
ess
S
t
a
r
t
|
I
m
–
I
m
n
ew
|
<
I
m
=
I
m
n
e
w
E
n
d
No
Y
e
s
k
,
I
m
,
V
t
C
a
c
u
l
a
t
e
:
V
t
(
I
m
)
(
Eq
.
1
)
P
o
l
y
n
o
m
i
a
l
I
n
t
e
r
p
o
l
a
t
i
o
n
:
V
t
(
I
m
)
:
g
(
I
m
)
=
a
0
+
a
1
I
m
+
a
2
I
m
2
+
+
a
n
I
m
n
D
a
t
a
M
a
g
n
e
t
i
z
i
n
g
C
u
r
v
e
:
I
m
(
i
)
,
E
g
(
i
)
Ex
c
i
t
a
t
i
o
n
C
u
r
v
e
:
V
ce
(
I
m
)
:
h
(
I
m
)
=
X
ce
I
m
f
(
I
m
)
=
g
(
I
m
)
-
h
(
I
m
)
S
e
t
E
x
c
.
C
a
p
a
c
i
t
o
r
&
f
r
e
q
u
e
c
y
:
C
e
&
f
g
X
ce
=
2
π
f
g
C
e
a
a
k
=
k
+
1
I
m
=
I
m
n
ew
V
t
(
I
m
)
=
a
0
+
a
1
I
m
+
a
2
I
m
2
+
+
a
n
I
m
n
I
n
i
t
i
a
l
C
o
n
d
i
t
i
o
n
:
I
m
=
I
0
;
k
=
0
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
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
12
11
–
12
19
1216
3.2.
Ex
peri
menta
l
set
-
up
In
order
to
veri
fy
the
res
ults
of
the
a
nalysis,
a
series
of
ex
per
ime
nt
a
re
c
onduct
ed
in
th
e
la
borat
ory.
This
te
st
a
pp
li
es
the
s
quirrel
-
cage
in
du
ct
io
n
mac
hin
e
of
1.5
kW,
380
V,
3
-
phase,
50
Hz,
4
pole
s,
wh
ic
h
i
s
equ
i
pp
e
d
with
12
mF
e
xcita
ti
on
ca
pacit
ors
t
hat
co
nn
ect
e
d
in
delta
.
T
his
machine
pa
ra
mete
rs
obta
ine
d
f
rom
the test
r
es
ults
are
R
s
=
4,3
8
an
d
X
s
=
3,61
.
The
la
borato
ry
te
sti
ng
proces
s
be
gin
s
with
the
dema
gnet
iz
at
ion
process
of
the
SE
IG
thr
ough
loa
di
n
g
the
gen
e
rato
r
a
t
it
s
crit
ic
al
po
int,
s
o
that
t
h
e
ge
ne
rator
volt
age
dro
ps
to
z
ero
s
udde
nly
.
I
n
t
his
c
onditi
on,
the
vo
lt
age
ca
us
ed
by
the
resi
du
a
l
mag
netism
is
cl
os
e
t
o
zer
o.
The
ne
xt
proc
ess,
the
dc
cu
r
ren
t
is
i
nject
ed
int
o
on
e
of
the
sta
t
or
ph
ase
windi
ng
s
from
the
S
EIG,
so
that
E
r
es
can
be
obta
ined
at
the
e
xp
e
ct
ed
value
.
Th
en,
the
ro
t
or
of
SEIG
is
r
otate
d
with
the
m
otor
at
1506
r
pm
an
d
E
res
are
meas
ur
e
d.
Ne
xt,
the
ex
ci
ta
ti
on
ca
pacit
or
is
switc
he
d
on
t
he
SE
IG
te
rmi
nal
unde
r
no
-
load
c
onditi
on,
and
t
he
te
rmi
nal
volt
age
ge
ner
at
e
d
(
V
t
)
a
nd
t
he
mag
netiz
at
ion
current
(
I
m
)
is
measu
red.
T
he
te
sti
ng
proces
s
is
re
peated
,
each
for
t
he
a
vaila
bili
ty
of
s
tro
ng
,
weak, a
nd criti
cal
r
esi
dual
ma
gn
et
ism
.
4.
RESU
LT
S
AND
DI
SCUS
S
ION
4.1.
The
analy
sis
resul
ts
of
volt
age
ge
nera
tion
processe
s
und
er
strong
resi
dua
l
m
agnetis
m
availabil
it
y
cond
i
tion
s
Figure
7
has
sh
ow
n
t
he
a
na
lysis
re
su
lt
s
of
the
volt
age
ge
ner
at
io
n
pr
ocess
in
t
he
SEIG
unde
r
conditi
ons
of
a
vaila
bili
ty
of
s
tro
ng
resi
dual
mag
netism,
na
mely
Eres
=
4.27
Vo
lt
s
a
nd
E
res
=
2.73
V
ol
ts.
A
s
sh
ow
n
in
fig
ure
7,
the
i
nterse
ct
ion
of
the
c
urve
only
occur
s
in
the
sat
urat
ion
reg
i
on
a
re
a,
namel
y:
at
(
Im
=
2,831
A,
Vt
=
220,
07
V
olts)
for
Ere
s
=
4.2
7
Vo
lt
s
a
nd
at
(Im
=
2,7
99
A,
Vt
=
217,
54
V
olts)
f
or
Eres
=
2.73
Vo
lt
s.
Wh
e
r
eas
in
the
init
ia
l
reg
i
on,
t
he
tw
o
c
urves
do
not
inter
sect
.
T
his
has
sho
wn
that
the
volt
ag
e
gen
e
rati
on
pro
cess at
SE
IG ha
s b
ee
n
s
ucces
sfu
l
f
or
both c
onditi
ons
of the
avail
abili
ty of
resid
ual ma
gne
ti
sm.
Fig
ure
7
.
The
a
nalysis
res
ults
of volt
age
ge
ne
rati
on pro
c
ess
und
e
r
st
ron
g
r
esi
du
al
mag
netism a
va
il
abili
ty co
ndit
ion
s
4.2.
The
resul
t
s
of
th
e
analy
sis
of
volt
ag
e
ge
nera
tion
pr
oc
esses
u
nder
cri
tical
resi
du
al
m
agnetism
availabil
ity
c
ondi
tions
The
a
nalysis
r
esults
of
the
volt
age
gen
e
rati
on
proce
ss
on
the
SE
IG
i
n
c
onditi
ons
of
c
riti
cal
residu
a
l
mag
netism
ava
il
abili
ty,
namel
y
Ere
s
=
1.0
4
Vo
lt
s
a
nd
E
res
=
0.993 V
olts,
are
sho
wn
i
n
f
igure
8.
As
s
ho
wn
i
n
this
fig
ur
e
,
f
or
Eres
=
1.0
4
Vo
lt
s,
t
he
proc
ess
of
volt
age
gen
e
rati
on
is
s
ti
ll
su
ccessfu
l
because
at
the
init
ia
l
area
do
e
s
no
t
occ
ur
at
th
e
intersect
io
n
of
the
cu
rv
e
.
Howe
ver,
wh
e
n
t
he
resid
ual
volt
age
of
re
sidu
al
mag
netism
dec
reases
t
o
Er
es
=
0.9
93
V
olts,
the
volt
age
ge
ner
at
io
n
proce
ss
can
not
ha
ve
reac
hed
the
e
xpect
ed
value
(n
omi
nal
value
).
This
ha
pp
e
ns
beca
use
there
a
re
2
i
nt
ersecti
on
poin
ts
of
t
he
c
urve,
namel
y
in
the
init
ia
l
area (Im
1
=
0.
109 A,
V
t
1
=
8.4
7 Vo
lt
s)
and
the satu
rati
on a
rea (Im
2
=
2.761 A
, Vt2 =
21
4.58 V
olts).
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
Eff
ect
a
naly
sis
of resid
ual m
agnetis
m ava
il
abil
it
y
le
vel
o
n
t
he
s
uccess
o
f v
oltag
e
…
(
Ref
di
na
l N
az
ir
)
1217
Figure
8. The
a
nalysis
res
ults
of volt
age
ge
ne
rati
on pro
c
ess
und
e
r
c
riti
cal
r
esi
du
al
mag
netism a
va
il
abili
ty co
ndit
ion
s
4.3.
The
analy
sis
resul
ts
of
vo
l
tage
ge
ne
rat
i
on
pr
oces
s
under
weakening
resi
d
ua
l
ma
gn
e
tis
m
availabil
ity
c
ondi
tions
Figure
9
have
sh
ow
n
the
an
al
ys
is
res
ults
of
the
ge
ner
at
io
n
vo
lt
age
proces
s
on
the
SEIG
unde
r
wea
k
resid
ual
ma
gnet
ism
avail
abili
ty
co
nd
it
io
ns
,
namel
y
E
res
=
0.4
87
V
olts
a
nd
E
res
=
0.0
88
Vo
lt
s.
As
show
n
i
n
fig
ur
e
9,
f
or
both
c
onditi
ons,
the
inters
ect
io
n
of
t
he
ma
gn
et
iz
at
ion
cu
rv
e
an
d
the
e
xcita
ti
on
c
urve
occ
ur
s
at
two
points.
T
he
refor
e
,
i
n
bo
t
h
of
the
se
c
on
diti
on
s
,
t
he
ge
ner
at
or
only
ge
ner
at
es
a
s
ma
ll
vo
lt
age
,
nam
el
y
V
t
=
10.54
Vo
lt
s
in
the
resi
du
al
mag
netism
sta
te
with
E
res
=
0.487
Vo
lt
s
a
nd
V
t
=
10.
54
Vo
lt
s
in
t
he
r
esi
du
al
mag
netism
sta
te
with
E
res
=
0.088
V
olts.
T
his
mea
ns
that
the
volt
age
ge
ner
at
io
n
proc
ess
to
reac
h
nomina
l
vo
lt
age
w
a
s
not success
fu
l
f
or both c
onditi
on
s of the
r
esi
du
a
l mag
netism a
va
il
abili
ty.
Figure
9. The
a
nalysis
res
ults
of volt
age
ge
ne
rati
on pro
c
ess
und
e
r wea
k
re
sidu
al
mag
netism a
va
il
abili
ty co
ndit
ion
s
4.4.
Co
m
pa
ri
s
on
of
an
alysi
s
an
d
test
in
g
res
ults
The
e
xp
e
rimen
ta
l
te
sts
are
con
duct
ed
t
o
che
ck
the
validit
y
of
the
res
ults
of
the
anal
ys
is
di
scusse
d
i
n
sessions
4.1
t
o
sessio
n
4.3
.
Fi
gure
10
s
how
s
the
co
mp
a
rison
bet
wee
n
the
analysis
resu
lt
s
and
the
te
st
re
su
lt
s
for
va
rio
us
va
r
ia
ti
on
s
in
t
he
a
vaila
bili
ty
of
r
esi
du
al
ma
gnet
ism
to
the
volt
age
gen
e
rated
by
SEIG.
As
s
how
n
in
this
fig
ure,
t
he
sim
ulati
on
r
esults
an
d
ex
pe
riment
r
esults
bo
t
h
s
how
tha
t
the
gen
e
rato
r
fail
ed
to
gen
e
rate
a
te
rmin
al
volt
age
at
it
s
nomin
al
value
f
or
a
n
E
res
value
below
1.0
4
V
olt.
At
E
re
s
values
above
1.04
volt
,
bo
t
h
curves
hav
e
i
nd
ic
at
ed
t
he
ge
ner
at
or
s
ucce
eded
i
n
ge
nerat
ing
it
s
te
r
minal
volt
age
at
no
minal
valu
e.
T
he
simulat
ion
res
ults
an
d
the
te
st
resu
lt
s
sho
w
that
the
crit
ic
al
value
of
the
re
mainin
g
mag
netic
avail
abili
ty
occurs at t
he
va
lue of
E
res
=
1.0
4 Vo
lt
. Fr
om t
he
de
scri
ptio
n
a
bove,
t
he
a
na
lysis res
ults a
re in
li
ne
w
it
h
t
he
te
st
resu
lt
s,
so the
validit
y of t
he mo
del and t
he a
nalysis
meth
od a
re suf
fici
ent
ly test
ed.
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
.
11
, N
o.
3
,
Se
ptembe
r
2020
:
12
11
–
12
19
1218
Figure
10. T
he
com
pa
rison
of simulat
io
n
a
nd test
r
e
su
lt
s
5.
CONCL
US
I
O
N
The
ef
fect of
t
he
avail
abili
ty
o
f
re
sid
ual ma
gn
et
ism
o
n
t
he
s
uccess
of
the
terminal v
oltag
e
ge
ne
rati
on
process
f
or
S
EIG
on
it
s
no
minal
val
ue
ha
s
bee
n
s
ucce
ssfu
ll
y
a
nalyze
d
us
in
g
New
t
on
Ra
phs
on
's
it
erati
on
method.
T
he
a
vaila
bili
ty
of
r
esi
du
al
mag
net
ism
with
resid
ual
volt
age
val
ues
belo
w
1.0
4
Vo
lt
will
ca
us
e
the
fail
ur
e
of
t
he
SEIG
to
gen
e
r
at
e
the
te
rmina
l
vo
lt
age
at
it
s
nominal
value.
M
ea
nwhile
,
the
avail
a
bili
ty
of
resid
ual
mag
ne
ti
sm
in
SEIG
with
resid
ua
l
vo
lt
age
values
ab
ove
1.0
4
V
olt,
will
su
cc
eed
i
n
ge
ne
rati
ng
te
rmin
al
volt
ag
e
at
it
s
nomi
na
l
value
.
F
or
S
E
IG
us
e
d
as
t
he
ob
je
ct
of
this
s
tudy,
the
value
of
E
res
=
1.04
Vo
lt
is
a
c
riti
cal
value
of
the
a
vaila
bili
ty
of
resi
dual
ma
gnet
s
(
E
critical
).
T
he
dec
rease
i
n
E
res
va
lue
of
SE
IG
ca
n
be
cause
d
by
v
ari
ou
s
c
onditi
ons,
su
c
h
as:
s
hort
ci
rcu
it
fa
ult,
la
ck
of
reacti
ve
powe
r,
operati
on
of
the
ge
nerat
or
at
the
crit
ic
al
point
et
c.
The
refor
e
,
f
or
the
vo
lt
age
ge
ner
at
io
n
process
i
n
S
EIG
to
be
s
uc
cessf
ul,
it
m
ust
be
ens
ur
e
d
that t
he
r
esi
dual
vo
lt
a
ge value
must
be
a
bove
it
s c
ri
ti
cal
v
al
ue
.
ACKN
OWLE
DGE
MENTS
Au
t
hor
w
ould
l
ike
than
ks
to
A
nd
al
as
Un
i
ver
s
it
y
for
the
fi
na
ncial
su
pp
or
t
t
his
w
ork,
th
r
ough
PDUPT
Fund
i
ng (N
o.
T/5/U
N.16.1
7/
PT.
01.03/P
D
-
EET/
2019)
.
REFERE
NCE
S
[1]
Li
Wa
ng
,
Ping
-
Yi
Li
n
,
“Ana
lys
is
of
a
Com
me
r
ci
a
l
Biog
as
Gen
era
t
ion
Sys
te
m
Us
ing
a
Gas
E
ngine
Indu
ct
ion
Gene
rat
or
Set
,
I
EE
E
Tr
ansacti
o
ns on
Ene
rg
y
Co
nve
rs
ion
,
vo
l.
24
,
no
.
1
,
pp
.
230
-
239,
2009
.
[2]
E.
Mulja
d
i,
C.
P.
Butt
erf
i
el
d
,
H.
Rom
anowit
z
,
R
.
Yinger
,
“
Self
Exc
i
ta
t
ion
and
Har
moni
c
s
in
Wi
nd
Po
wer
Gene
ration”
,
Na
ti
onal Re
n
ewa
bl
e
En
erg
y
La
bor
a
tory,
Nove
mbe
r
2004.
[3]
R.
C.
B
ansa
l
,
“
Thre
e
-
Phase
Sel
f
-
Exc
i
te
d
Indu
ction
Gene
r
at
ors:
An
Overvi
ew”
,
IEE
E
Tr
ansacti
ons
on
Ene
rgy
Conve
rs
ion
,
Vol
.
20
,
No.
2,
June
2005.
[4]
M.
Benm
e
zi
an
e,
S.
Ze
bir
at
e
,
A.
Chake
r1,
and
Z
.
Boudje
ma,
“Fu
zz
y
slidi
ng
mod
e
cont
ro
l
of
dou
bly
-
fed
indu
ct
io
n
gene
ra
tor
driv
en
by
wind
turb
in
e”
,
Inte
rnat
ional
Journal
of
Pow
er
El
e
ct
roni
cs
a
nd
Dr
iv
e
Syst
em
(IJ
P
EDS),
Vol.
10,
No.
3,
pp.
15
92
-
1602,
2019
.
[5]
Refdi
na
l
Na
zi
r,
Krismad
inata,
a
nd
Riz
k
a
Ama
lia
,
“
The
Cam
p
ari
s
on
Of
Harm
oni
c
Distorti
on
Self
-
Exc
ited
Indu
ct
io
n
Gene
rat
or
with
Isolat
ed
Synch
ronous
Gene
rator
Under
Non
-
Li
ne
ar
Lo
ads”
,
Inte
rnationa
l
Journal
of
Pow
er
El
e
ct
ronics
and
Dr
iv
e
Syst
em
(I
J
PE
DS
)
,
vo
l.
6,
n
o.
4
,
pp
.
759
-
77
1,
2015
.
[6]
Refdi
na
l
Na
zi
r
,
Syafii
,
Andi
Pa
wawoi,
Fa
jri
l
A
kbar
and
Ax
el
Dorinz
a,
“Dif
fer
enc
es
in
the
impact
of
har
monic
distort
ion
due
to
th
e
installation
of
e
lectr
oni
c
load
con
trol
l
er
in
s
el
f
-
ex
ci
t
ed
indu
ct
ion
gen
erator
and
synch
ronou
s
gene
ra
tor”,
Int
er
nati
onal
Journal
of
Powe
r
E
lect
ronics
and
Dr
ive
Syst
em
(IJ
PED
S),
vol
.
10
,
no
.
1
,
pp.
104
-
116
,
2019
.
[7]
Refdi
na
l
Na
zi
r
,
“Ana
lysis
of
Harm
onic
Curr
ent
s
Propag
at
io
n
on
the
Self
-
Exc
ited
Induc
t
i
on
Gene
r
at
or
with
Nonline
ar
Lo
ads”
,
J El
e
ct
r
Eng
T
ec
hnolog
y
,
Vol.
9,
No.
6
,
pp
.
193
5
-
1943,
2014
.
[8]
Refdi
na
l
Naz
ir,
Andi
Pawawoi,
Riska
Amalia
,
“
Harm
onic
Eff
e
cts
Analysis
of
Elec
tron
ic
Loa
ds
Control
le
r
on
Se
lf
Exc
ited
Indu
ct
i
on
Gene
ra
tor
(S
EIG)
Opera
t
ion
s”,
Indone
sian
Journal
of
Elec
tric
al
Engi
n
ee
ri
ng
and
Comput
er
Sci
en
ce
,
vol
.
8
,
no.
2
,
pp
.
273
-
2
80,
2017
.
[9]
Raj
ase
kh
ara
R.
C.
,
et
a
l.,
“Per
f
orma
nc
e
of
a
S
el
f
-
Ex
ci
t
ed
Indu
ct
ion
Gene
r
at
or
with
DS
TATCOM
-
DTC
Drive
-
Based
Volt
age and Freque
ncy
C
ontrol
ler”,
IE
EE
Tr
ansacti
ons on Energy
Con
ve
rs
i
on
,
vol
.
29
,
no
.
3
,
2014
.
[10]
Jinn
-
Chang
Wu
,
“Nove
l
C
irc
u
it
Configura
ti
on
fo
r
Compe
nsat
ing
for
the
R
eact
iv
e
Pow
er
of
Induc
ti
on
Gene
rat
or
”,
IEE
E
Tr
anscti
on
s on
Ene
rgy
Con
ve
rs
ion
,
vo
l. 23,
no.
1
,
Mar
ch
20
08.
[11]
Hayde
r
Hus
sein
Kadhum,
et
al
.
,
“T
he
infl
u
enc
e
o
f
iron
losses
on
sele
c
ti
ng
th
e
minimum
exc
i
tatio
n
ca
p
ac
i
ta
nc
e
fo
r
self
-
excite
d
ind
uct
ion
g
ene
r
at
or
(SEIG)
with
w
ind
turbi
n
e”,
In
donesian
Journ
al
of
Elec
tri
cal
Engi
n
ee
ring
a
nd
Computer
Scien
ce
,
Vol.
19,
No.
1,
pp
.
11
-
22
,
20
20
.
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
Eff
ect
a
naly
sis
of resid
ual m
agnetis
m ava
il
abil
it
y
le
vel
o
n
t
he
s
uccess
o
f v
oltag
e
…
(
Ref
di
na
l N
az
ir
)
1219
[12]
Loke
sh
Varshne
y,
R.
K.
Saket,
“
Rel
ia
b
il
i
ty
ev
al
u
at
ion
of
SEIG
r
otor
cor
e
m
agnetizat
ion
wi
th
m
i
nim
um
ca
p
ac
i
ti
v
e
exc
i
ta
t
ion
for
un
reg
ulated
r
ene
w
abl
e
ene
rgy
applications
in
r
em
ot
e
ar
ea
s”
,
A
in
Sh
ams
Engi
nee
rin
g
Journal
,
vo
l.
5,
pp.
751
–
757
,
20
14
.
[13]
Rishike
sh
Chou
dhar
y
and
R
.
K.
Saket
,
“A
cr
it
i
cal
rev
i
ew
on
th
e
s
el
f
-
ex
ci
t
at
ion
pr
oce
ss
and
ste
ady
stat
e
analysis
of
an
SEIG dri
ven by wind
turb
ine”
,
R
ene
wab
le
and
Sustainable
En
e
rgy
Revi
ews
,
vol
.
47
,
pp
.
344
-
35
3,
2015
.
[14]
D.B.
W
at
son, et al
.
,
“Con
trol
l
able
d.
c.
powe
r
supply
from
wind
-
d
rive
n
se
lf
-
excited i
nduction
m
achine
s”,
Proc. I
E
E
,
Vol.
126
,
No.
12
,
De
ce
mb
er
197
9.
[15]
El
der
,
J.M.;
Boy
s,
J.T
.
&
Wood
ward,
J.L
.
“
Se
lf
-
Exc
ited
Indu
ct
io
n
in
induction
g
e
ner
at
ors.
”,
IEE
Proce
ed
ings
.
Vo
l.
130,
Pt.
B.
,
No
.
2,
pp
.
103
-
108,
1
984
.
[16]
Refdi
na
l
Naz
ir,
“De
vel
op
me
n
t
o
f
Self
-
Ex
ci
t
ed
I
nduct
ion
G
ene
r
at
or
for
Vari
ab
l
e
Speed
and
Lo
ad
Condit
ions”,
Ph.D.
Diss
ert
a
tion.
Univer
si
ti T
e
knologi
Ma
la
ysi
a,
1999
.
[17]
We
jd
an
S.
A.,
a
nd
Annet
te
M.
,
“Sel
f
-
Ex
ci
t
at
ion
and
St
abi
l
it
y
a
t
Speed
Tra
nsi
en
ts
of
Self
-
Exc
i
ted
Singl
e
-
Phase
Rel
uctanc
e
Gen
e
rat
ors”,
IE
EE Tr
anscti
ons on
Sus
tai
nable E
n
ergy
,
vol. 4, no. 1, Ja
nuar
y
2013.
[18]
Wi
ll Knape
k
,
“R
esidua
l
Magne
t
ism”
,
Omi
cro
n,
20
12.
[19]
Maure
r
Magn
et
i
c
AG
,
“Me
asuri
ng
Residual
Ma
gnet
ism
of
Ferro
ma
gne
ti
c
Parts”
,
©
Maur
er
Magn
et
i
c
AG
04.
2014
.
[20]
Maure
r
Magn
et
i
c
A
G, “Dem
agn
et
i
za
t
ion
of
la
rg
e
surfac
e
obj
ects”
,
©
Maure
r
Mag
net
i
c
AG
04.
201
5.
[21]
Orian
o
Bott
ausc
io,
e
t
a
l.
“Rol
e
of
Magne
tic
Ma
te
ri
al
s
in
a
Novel
E
le
c
trica
l
Mo
toge
ner
at
or
for
t
he
More
E
le
c
tric
Airc
raf
t
”,
IE
EE
Tr
anscti
ons on Magnetics
,
vo
l.
50,
no
.
4
,
April
201
4.
[22]
Julia
no
B
.
Pad
ilha,
et
a
l.,
“Ve
ctor
Hys
te
resis
M
odel
As
sociate
d
with
FEM
in
a
Self
-
Excite
d
Ind
uct
ion
Gene
r
at
o
r
Modeli
ng”
,
I
EEE
Tr
anscti
ons o
n
Magne
t
ic
s
,
vol
.
52
,
no
.
3
,
Mar
c
h
2016.
[23]
Math
Wor
ks
,
SI
MU
LINK
-
M
ATLAB
Li
br
ary
,
20
12.
[24]
Steve
n
Ch
apr
a
a
nd
Raym
ond
P.
Cana
l
e, “
Numer
i
ca
l
Methods
for
Engi
ne
ers”
,
Mc.
Graw
-
Hill
,
2015
.
[25]
Stani
sław
Rosło
nie
c
,
“Fundame
nta
l
Numer
ical
Methods
for
El
e
ct
ri
ca
l
Engi
n
ee
ring
”,
Spring
er
-
Verl
ag
,
Ber
lin
Heide
lb
erg
,
200
8.
Evaluation Warning : The document was created with Spire.PDF for Python.