Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
6, No. 4, Decem
ber
2015, pp. 759~
771
I
S
SN
: 208
8-8
6
9
4
7
59
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
The Camparison of Harmonic Dist
ortion Self-Excited Induction
Generator with Isolated Sy
nchronous Generator Under
Non-linear Loads
Refdin
al N
a
z
i
r
1
, Krism
a
din
a
t
a
2
, Ri
z
k
a A
m
al
i
a
1
1
Electrical Eng
i
neering
Depar
t
me
nt, Andalas Univ
ersity
, Indonesia
2
Ele
c
tri
cal
Eng
i
neering
Depar
t
m
e
nt,
Padang
State University
, Ind
onesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 31, 2015
Rev
i
sed
No
v
18
, 20
15
Accepted Nov 29, 2015
In this p
a
per
,
th
e harmonic distortion
for
Self-
E
xcited Indu
ctio
n Generato
r
(SEIG) and an isolated s
y
nchro
nous generator (
I
SG) under non-linear load
during s
t
ead
y
s
t
ate cond
itions
are an
al
yz
ed.
The volt
a
ge
and curren
t
harmonics distortion for both g
e
nerators
are c
a
l
cul
a
ted us
ing t
h
e trans
f
e
r
function method
in frequency
do
main
for SEIG and phasor diagram method
for ISG.
This
an
aly
s
is is done in
dependen
t
ly
on
e b
y
one component for
all
harmonic components appear
.
The an
aly
s
is results
for both generators ar
e
verified to the laborator
y
test results.
For loading with the same
non-linear
load to
both g
e
nerators, the har
m
onics
distortio
n on the stator
windings of
S
E
IG was
sm
aller than com
p
are
IS
G.
In addition, the harmonic distortio
n
effec
t
s
on oth
e
r
loads
conn
ect
ed
to P
CC point
o
f
SEIG was lower th
an th
e
other loads
conn
ect
ed
to
IS
G.
Keyword:
Harm
oni
c Di
st
ort
i
o
n
No
n-l
i
near Loa
d
SEIG
Syn
c
hro
nou
s G
e
n
e
r
a
tor
To
tal Harm
o
n
i
c Distortio
n
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
:
Refdinal Nazir,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
And
a
las Un
iv
ersity,
Lim
a
u M
a
ni
s
C
a
m
pus,
Pada
ng
2
5
1
6
3
,
I
n
do
nesi
a.
E-m
a
il: refdi
n
a
l
nazir@y
a
ho
o.
co.id
1.
INTRODUCTION
Cu
rren
tly, th
e
ap
p
lication
s
of Self-Ex
c
ited
In
du
ction
g
e
n
e
rato
r (SEIG) are
m
o
re co
mm
o
n
in
sm
all-
scal
e po
wer
pl
ant
s
usi
n
g
re
ne
wabl
e e
n
er
gy
s
o
u
r
ces, i
n
cl
u
d
i
ng:
wi
n
d
, m
i
ni
/m
i
c
rohy
dr
o,
t
i
d
al
wa
ve,
bi
o
m
ass,
biogas, etc. [1],[2]. Meanwhile, the
i
s
ol
at
ed sy
nc
hr
on
o
u
s
gene
rat
o
rs (I
SG) a
r
e wi
del
y
appl
i
e
d i
n
di
esel
electric g
e
n
e
ratin
g
sets (Gen
set). In
its ap
p
licatio
n
,
th
e t
w
o
gene
rat
o
rs are
oft
e
n em
pl
oy
ed t
o
d
r
i
v
e
no
n
-
l
i
n
ea
r
l
o
ads
,
i
n
cl
u
d
i
n
g:
uni
nt
err
u
pt
i
b
l
e
po
wer s
u
p
p
l
y
(UPS
), va
ri
abl
e
fre
q
u
en
cy
dri
v
es (
V
F
D
), s
w
i
t
c
he
d m
ode
p
o
wer supp
ly (SMPS), en
erg
y
-sav
i
n
g
lam
p
(ESL), etc.
Th
e i
m
p
o
s
itio
n
o
f
gen
e
rat
o
r with
no
n-lin
ear
l
o
ads
will
have a
n
i
m
pact
on t
h
e
gene
ra
t
i
on o
f
ha
rm
on
i
c
curre
nt
s an
d
vol
t
a
ges
di
st
o
r
t
i
o
n
.
The
ge
n
e
rat
i
on
of
har
m
oni
c
cur
r
ent
s
i
n
t
h
e
gene
rat
o
r has
adve
rse ef
fec
t
s up
on i
t
s
pe
rf
orm
a
nce. It
can gi
ve t
h
e effect
o
f
dec
r
easi
n
g
effi
ci
ency
,
hea
t
i
ng a
n
d r
e
d
u
c
i
ng t
h
e l
i
f
e
t
i
m
e of t
h
e
ge
n
e
rat
o
r
[
3
]
-
[
5]
.
Harm
oni
c
di
st
ort
i
o
n
o
f
t
h
e
v
o
l
t
a
g
e
g
e
n
e
rator will b
e
ab
le to
create a h
a
rm
o
n
i
c d
i
stu
r
b
a
n
ce to
o
t
h
e
r lo
ads, wh
ich
are co
nn
ected
in
p
a
rallel to
th
e
sam
e
source.
The l
e
vel
s
of
harm
oni
c
di
st
o
r
t
i
o
n
i
n
c
u
r
r
ed
due
t
h
e em
pl
o
y
e
d o
f
n
o
n
-
l
i
n
ear l
o
a
d
s
o
n
S
E
IG
an
d
IS
G
will b
e
d
i
fferen
t. Th
is lev
e
l
o
f
h
a
rm
o
n
i
c disto
r
tio
n is influ
e
n
c
ed
b
y
th
e equ
i
v
a
len
t
circu
it structu
r
e
o
f
th
e
gene
rator a
n
d
its param
e
ters. Ge
nerat
o
rs
for Ge
nset
us
ual
l
y have
highe
r
the reactance than
t
h
e distri
bution
tran
sform
e
rs on
u
tility n
e
tw
ork
s
[3
]. C
o
nseq
u
e
n
tly, th
e rate for t
h
e
h
a
rm
o
n
i
c d
i
stributio
n
o
f
th
e g
e
n
e
rat
o
r
v
o
ltag
e
is
h
i
gher th
an
t
h
e u
tility so
u
r
ce, if both
sou
r
ces
op
erate with
th
e same n
o
n
-lin
ear l
o
ad. Th
e equ
i
valen
t
ci
rcui
t
st
ruct
ur
e of SE
IG
has
t
h
e com
b
i
n
at
i
on bet
w
een m
a
gnetization inductance a
nd e
x
citation capacitanc
e
t
h
at
can red
u
c
e
t
h
e di
st
ort
i
o
n harm
oni
cs. I
n
t
h
e pre
v
i
o
us
st
udy
, anal
y
s
i
s
of ha
rm
oni
c pr
o
p
agat
i
o
n o
n
SEIG
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6
,
No
.
4
,
D
ecem
b
er
2
015
:
75
9 – 771
76
0
wh
en
its is lo
ad
ed
b
y
non
-linear lo
ad
[6]. T
h
e res
u
lts showed t
h
at SEIG
reject
s t
h
e
hi
g
h
o
r
de
r
harm
oni
cs an
d
at
t
e
nuat
e
s l
o
w
or
der
ha
rm
oni
cs cur
r
e
n
t
s
o
n
i
t
s
st
at
or wi
n
d
i
ngs;
c
o
nseq
ue
nt
l
y
THD
I
is l
o
w
relativ
ely o
n
t
h
e
st
at
or wi
n
d
i
n
gs
.
In t
h
i
s
pa
per, t
h
e cu
rre
nt
an
d
vol
t
a
ge
ha
rm
oni
c di
st
o
r
t
i
on
f
o
r S
E
I
G
an
d I
S
G
un
der
n
o
n
-
l
i
n
ear l
o
a
d
s
d
u
ring
stead
y
state co
nd
itio
ns are an
alysed. Th
e an
alysis resu
lt o
f
h
a
rm
o
n
i
c d
i
stortio
n
fo
r two
g
e
n
e
rat
o
rs is
com
p
ared i
n
o
r
der t
o
s
h
o
w
t
h
e im
pact
of no
n-l
i
n
ea
r l
o
ad
s on t
h
e
bot
h ge
nerat
o
r an
d ot
h
e
r l
o
ads c
o
n
n
e
c
t
e
d t
o
t
h
e sam
e
sourc
e
s. Thi
s
pape
r
i
s
or
gani
ze
d i
n
t
o
7 sec
t
i
o
ns.
I
n
sect
i
o
n 2, t
h
e sy
st
em
descri
pt
i
on
of
pr
o
p
o
se
d
sy
st
em
i
s
prese
n
t
e
d.
M
o
del
i
n
g
an
d a
n
al
y
s
i
s
f
o
r
SE
IG
wi
t
h
no
n-lin
ear lo
ad is d
i
scu
ssed
i
n
sectio
n
3
.
In sectio
n
4, t
h
e
harm
oni
cs di
st
ort
i
on
of
ISG
u
nde
r n
o
n
-l
i
n
ea
r l
o
a
d
s i
s
di
scus
sed
.
T
h
e ex
pe
ri
m
e
ntal
set
-
up i
s
e
x
pl
ai
ned
in
section
5
.
Th
e
section
6
d
i
scu
sses
th
e resu
lts
and
i
t
s
a
n
a
l
y
s
i
s
. C
oncl
u
si
ons
ar
e presen
ted
in section
7
.
2.
SYSTE
M
DESCRIPTIO
N
The
co
n
f
i
g
urat
i
o
n
o
f
st
u
d
i
e
d
sy
st
em
consi
s
t
s
of
a
ge
ne
rat
o
r
,
no
n-l
i
near
l
o
ad
s,
an
d
ot
he
r l
o
ads
t
h
at
are linea
rly
,
as
shown
by Fi
gure
1.
In this
sy
ste
m
,
V
a
riable
Fequency
Drive (V
FD) and
E
n
er
gy-Sa
v
ing
Lam
p
(ESL
) are
ap
pl
i
e
d as
no
n-l
i
ne
ar l
o
a
d
a
n
d
re
si
st
or i
s
em
ployed as the
ot
her loa
d
.
The
harm
onic curre
n
ts,
I
h
,
flow fro
m
th
e
n
on-lin
ear l
o
ads to
the gen
e
rato
r and
o
t
h
e
r load
,
R
L
. I
n
t
h
e S
E
IG
, the
ha
rm
onic cu
rre
nts
flo
w
t
o
th
e stato
r
wind
ing
s
and
th
e ex
citatio
n
cap
acito
rs t
h
at are lo
w im
p
e
d
a
n
ce to
h
i
gh
freq
u
e
n
c
ies,
while th
e
harm
oni
c c
u
r
r
e
n
t
s
fl
o
w
onl
y
t
o
t
h
e st
at
o
r
wi
ndi
ng
s i
n
t
h
e
I
S
G
.
F
u
rt
herm
ore, t
h
e
b
o
t
h
ge
nerat
o
rs
al
so
p
r
o
d
u
ce
t
h
e sm
al
l
harm
oni
c
o
f
vol
t
a
ge
s d
u
e t
o
th
e imp
e
rfectio
n of it
s con
s
tru
c
tion
.
Fi
gu
re 1a
show
s t
h
e co
nf
igur
atio
n of
st
u
d
i
ed
system
u
s
ing
SEIG
.
A
s
sho
w
n
i
n
t
h
is f
i
gu
r
e
, SEIG
is
con
s
t
r
uct
e
d
by
an i
n
d
u
ct
i
on
m
ach
ine and a
n
excitation ca
pacitor
.
Z
im
is th
e in
tern
al imp
e
d
a
n
ce
o
f
i
ndu
ctio
n
mach
in
e, wh
ich
will
b
e
d
e
termin
ed
in
n
e
x
t
sectio
n
.
Me
anwh
ile, t
h
e config
uratio
n
of st
u
d
i
ed
system
u
s
in
g
an
i
s
ol
at
ed
sy
n
c
h
r
on
o
u
s ge
nerat
o
r
i
s
s
h
ow
n by
Fi
gu
re 1
b
.
Th
i
s
stud
y uses a
salien
t
po
le sy
n
c
hro
nou
s
g
e
ner
a
to
r
,
so t
h
e sy
nc
h
r
on
o
u
s i
m
pedance
Z
s
is constructed
by a direct synchronous reacta
n
ce
Z
d
and
qu
adrat
u
re
synchronous re
actance
Z
q
[7]
.
SE
IG
O
t
he
r Lo
ad
Excitation
C
apac
i
t
or
In
duc
ti
on
M
a
ch
in
e
i
h
i
Rh
i
IG
h
i
sh
Is
olate
d
S
y
nch
r
on
ous
Gen
e
rat
o
r
Non
-
Lin
ear
Loa
d
as
Har
m
on
ic Cu
rren
t
So
urce
s
Ot
her Loa
d
i
h
i
Rh
i
SGh
i
sh
Z
s
Z
im
i
Ch
PC
C
PC
C
T
e
rmi
nal
poin
t
Te
rmin
al
po
i
n
t
No
n-Li
nea
r Lo
ad
as
Ha
rmo
n
ic C
u
rre
nt
S
ourc
e
s
a. studied system
using SE
I
G
b.
st
udie
d
system
using IS
G
Fi
gu
re
1.
The
c
o
n
f
i
g
urat
i
o
n
o
f
st
u
d
i
e
d sy
st
e
m
3.
HA
RM
ON
IC
AN
ALY
S
IS
O
F
SEIG
Th
e si
ng
le-phase equ
i
v
a
len
t
circu
it
o
f
SEIG with
non
-li
n
ear lo
ad
is sh
own
in Fi
g
u
re 2
.
In th
is
ci
rcui
t
,
t
h
e
no
n-l
i
n
ea
r l
o
a
d
s
are m
odel
e
d
as a cur
r
e
n
t
f
u
n
d
am
ent
a
l
com
ponent
I
1
, a
nd
ha
rm
oni
c cur
r
en
t
sources:
I
2
,
I
3
,
...
,
I
n
[
8
]
.
Wh
ereas,
SEI
G
m
odel
i
s
co
nst
r
u
c
t
e
d by
th
e ci
rcu
it of indu
ctio
n m
ach
in
e and
the
ex
citatio
n
capacito
r C
e
. Whe
r
e
R
s
,
L
s
,
R
r
’
, and
L
r
’
a
r
e the
stator
resistance, st
ator leakage inductance
, rotor
r
e
s
i
s
t
a
n
c
e
,
an
d ro
tor
le
ak
ag
e inductance
re
s
p
ectively
.
E
g
an
d
σ
are th
e vo
ltag
e
of ai
r
gap
and
slip
.
R
L
is t
h
e
o
t
h
e
r lo
ad
, wh
i
c
h
is t
h
e lin
ear
lo
ad
con
n
ected at PCC po
in
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
The C
a
m
p
aris
on of
H
a
rm
oni
c
Distortion
Se
lf-Excited I
n
duction
Gene
rat
o
r with Is
olate
d
....
(
R
efdinal N
a
zir)
76
1
Fi
gu
re 2.
Singl
e
-phase
e
q
ui
va
l
e
nt
ci
rcui
t
of
s
t
udi
ed
sy
st
em
usi
n
g S
E
I
G
The a
n
al
y
s
i
s
i
s
con
d
u
ct
ed
usi
ng t
h
e si
n
g
l
e
-
p
hase e
qui
val
e
n
t
ci
rcui
t
as sh
o
w
n i
n
Fi
g
u
re
2.
Thi
s
ci
rc
ui
t
contains
non-linear loa
d
a
s
n
u
n
it’
s cu
rren
t so
urces and SEIG as
v
o
lta
ge
s
o
u
r
ces.
B
e
si
de
s t
h
at
,
t
h
e
ot
he
r l
o
a
d
as linear l
o
a
d
R
L
is conn
ected
in p
a
rallel with
th
e
n
on-linear lo
a
d
at
PC
C
p
o
i
n
t
.
T
h
e
r
e
sp
onse
o
f
eac
h s
o
urce
to
th
e ci
rcu
it
o
f
m
ach
in
e stato
r
s and
o
t
h
e
r
lo
ad
are ev
aluated
sep
a
rately
.
Th
e to
tal
resp
on
se can b
e
so
lv
ed
fr
om
t
h
e sum
m
a
t
i
on
of
t
h
e c
u
r
r
ent
res
p
o
n
se
o
f
eac
h s
o
u
r
ce a
n
d
v
o
l
t
a
ge
res
p
ons
e.
3.
1.
Curr
ent Sour
ces
Res
p
onse
For
c
u
r
r
ent
so
urces
res
p
on
se
, t
h
e
anal
y
s
i
s
i
s
pe
rf
o
r
m
e
d by
c
o
nsi
d
e
r
i
n
g
o
n
e
cu
rre
n
t
so
urce,
I
h
.
Meanwhile, t
h
e ot
her current
sources a
n
d
voltage
source
are replace
d re
spectively w
ith
an op
en
circu
it and
i
n
t
e
rnal
i
m
pedance
o
f
SEI
G
.
Fi
gu
re
3a
s
h
o
w
s
t
h
e
eq
ui
val
e
nt
ci
rc
ui
t
fo
r
one
harm
oni
c
cur
r
ent
s
o
u
r
ce.
I
n
t
h
i
s
an
alysis, th
e eq
u
i
v
a
len
t
circuit is
expresse
d
i
n
t
h
e d
o
m
a
i
n
fre
que
ncy
ω
.
In
th
is cond
ition
,
ω
=
h
ω
1,
where
h
and
ω
1
ar
e num
b
e
r
of
h
a
r
m
o
n
i
cs an
d
f
und
am
en
tal f
r
e
qu
en
cy
re
specti
v
ely
.
T
h
e
correlation
betwee
n t
h
e
cu
rren
ts is
p
r
od
u
c
ed b
y
no
n-lin
ear lo
ad
I
(h)
,
th
e
o
t
h
e
r
lo
ad
cu
rr
en
ts
I
L
(h), and
th
e curren
t i
n
t
o
indu
ctio
n
gene
rat
o
r
I
IG
(h) is e
x
pres
sed
as,
I
IG
(h
)
=
I
(h
)-
I
L
(h
)
(1
)
whe
r
e,
t
L
(h)
(h)
=
R
V
I
1
j
ω
C
()
L
h
I
()
I
h
I
G
()
I
C
h
h
()
I
s
h
h
()
I
m
h
h
'
()
I
h
r
1
j
ω
C
()
I
C
0
h
()
I
s
0
h
()
I
m
0
h
a.
one c
u
r
r
ent s
o
urce
res
p
onse
b.
no-
l
oad
res
p
onse
Fi
gu
re
3.
SE
IG
eq
ui
val
e
nt
ci
r
c
ui
t
f
o
r a
n
al
y
s
i
s
From
t
h
e e
qui
v
a
l
e
nt
ci
rcui
t
of
Fi
gu
re
3,
t
h
e i
n
duct
i
o
n m
achi
n
e i
m
pedance
,
Z
im
, can be
expresse
d as,
rh
im
rh
m
s
h
'
'+
R
jL
j
L
R
j
L
Z
s
=
+
/
/
+
︵
︶
(2
)
whe
r
e, a slip,
σ
h
, is de
fine
d as
,
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I
S
SN:
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088
-86
94
I
JPEDS
Vo
l.
6
,
No
.
4
,
Decem
b
er
2
015
:
75
9 – 771
76
2
1r
h
1
-
=
h
h
(3
)
If
mr
m
r
h
=+
'
L
LL
and
r
σ
rh
'=
'
RR
,
the
n
E
q
. 5
ca
n be sol
v
ed
as,
2
r
σ
sm
r
h
s
m
r
r
σ
sm
r
σ
sm
r
im
r
σ
mr
'-
'
+
+
'
+
'
+
=
'+
RR
L
L
L
L
j
R
L
L
R
R
L
Rj
L
Z
(4
)
The t
r
ansfer function
T
s
(
jh
ω
1
) or
T
s
(
h
) as
a curre
nt
gain bet
w
een the
stator c
u
rre
n
t
I
s
(h
) a
n
d th
e
inp
u
t cu
rre
nts
of
SE
IG
I
IG
(h) can be written as,
sC
s
im
C
IG
(h
)
(h)
=
=
+
(h)
IZ
T
ZZ
I
(5
)
Or
r
σ
1m
r
s
22
33
r
σ
1r
σ
me
r
σ
se
s
m
r
e
1
r
σ
s
e
mr
1
s
mr
e
m
r
e
'+
(h
)
=
'-
'
+
'
+
+
'
+
-
+
'
Rj
h
L
Rh
R
L
C
R
L
C
R
L
C
j
h
R
R
C
L
h
L
L
C
L
L
C
T
(6
)
Furt
herm
ore, the stator c
u
rre
n
ts
I
s
(
h
) ca
n
be
sol
v
ed
usi
n
g
the
follo
win
g
e
quatio
ns:
I
sh
(
h
)=
T
s
(
h
)
I
IG
(
h
)
(7
)
The m
a
gnetizing curre
nt
I
m
(
h
) ca
n
be calcul
a
ted as,
r
σ
1r
h
mh
s
r
σ
1m
r
'+
'
(h)
=
(h)
'+
Rj
h
L
Rj
h
L
II
(
8
)
3.
2.
No
-Lo
a
d
Res
p
onse
No
-loa
d
res
p
o
n
se is
use
d
t
o
obtain
the
exci
tation c
u
r
r
ent
f
l
owin
g i
n
t
h
e s
t
ator
win
d
in
gs
to ge
ne
rate
a
g
e
n
e
r
a
tor
vo
ltag
e
.
Th
is
can be do
n
e
thr
ough
d
i
r
ect m
easu
r
em
en
t o
f
t
h
e
stato
r
cu
rr
en
t
at n
o
-
l
o
a
d
cond
itio
n
s
.
At this m
easure
m
ent, the val
u
e of e
x
citation capacit
o
r is
kept c
o
nstant,
while the
rot
o
r spee
d is set to obtai
n
th
e f
und
am
en
tal f
r
e
qu
en
cy of 5
0
Hz.
As sh
own
in
Figu
r
e
3b
,
th
e stator
cur
r
e
n
t
s at n
o
-
l
o
a
d
cond
itio
n
s
I
s0
(h
) is
equal t
o
the c
u
rre
nt of e
x
citation ca
pacitor
I
c
(h) or the
m
a
gnetization current
-
I
m0
(h).
A
ssum
e
d, the c
u
rre
nt
flowing i
n
t
h
e
rotor ci
rcuit i
s
ne
gligi
b
le.
T
h
e
ha
rm
onic c
o
m
pone
nts a
p
peari
n
g at
no-load conditions are
cause
d
by
the i
nhe
re
nt nat
u
re
of
the
ge
nerat
o
r
.
3.
3.
To
t
a
l
R
e
s
p
o
n
s
e
The c
u
rrents
fl
owi
n
g in the
SEIG
circuit a
r
e
obtained
from
the tota
l r
e
spon
se
o
f
th
e cu
rren
t
sour
ces
an
d no-
lo
ad
r
e
sp
on
se,
as
shown b
y
th
e
f
o
llowing
eq
u
a
tion
:
I
s
(h
) =
I
s0
(
h
)-
I
sh
(h);
I
m
(h
) =
I
m0
(h
)+
I
mh
(h)
(9
)
The term
inal votage
of SE
IG
in the
ha
rm
onic disto
r
tion
ca
n
be s
o
lve
d
as
,
V
t
(
h
) =
E
(
h
)-
I
s
(h
)(
R
s
+
jX
s
)
(1
0)
whe
r
e,
E
(
h
)
is
the air
ga
p
volt
a
ge that its
is determ
ined as
(s
ee Fig
u
re
3
b
)
,
E
(h
) =
V
t0
(h
)
+
I
s0
(h)
(
R
s
+
jX
s
)
(1
1)
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I
J
PEDS
I
S
SN:
208
8-8
6
9
4
The C
a
m
p
aris
on
of
H
a
rm
o
n
i
c
Distortio
n
Se
lf-Excited I
n
d
u
c
tion
Gene
rat
o
r w
ith Is
olate
d
....
(
R
efdin
a
l N
a
zir)
76
3
The t
o
tal rm
s of m
a
gnetizing
current
I
m
(rm
s) can
be calc
u
la
ted as
[8],
n
2
mm
h=
1
(rm
s
)
=
(
h
)
II
(1
2)
The
value
of m
a
gnetizing i
n
ductance
L
m
app
lied in t
h
is sect
ion
de
pe
nds
o
n
the
value
o
f
m
a
gnetizin
g
current
I
m
, which its
va
riation is
obtaine
d from
the e
x
pe
ri
m
e
ntal results. In addition, the
val
u
es
of
R
rh
’
and
L
rh
’
f
o
r
dif
f
ere
n
t harm
onic o
r
ders is s
o
lve
d
usin
g the
bloc
k
roto
r test [6]
,
[
9
]
,
[
10]
. T
h
e ex
perim
e
ntal results are
resol
v
ed t
h
rough c
u
rve
fitting
for a
num
ber of data that
obtained
from
th
e
experim
e
ntal test.
This m
e
thod is
i
m
ple
m
ented with
polyfit
state
m
ent in MA
T
L
AB, so
R
r
’(
h),
L
r
’(h
)
and
L
m
(
I
m
) are
obtaine
d as:
R
r
’(
h)
= c
1
h
4
+ c
2
h
3
+ c
3
h
2
+ c
4
h+c
5
;
L
r
’(
h)
=
d
1
h
4
+ d
2
h
3
+ d
3
h
2
+ d
4
h+
d
5
(
1
3
)
L
m
(
I
m
) = e
1
I
m
3
+ e
2
I
m
2
+ e
3
I
m
+ e
4
(1
4)
whe
r
e,
c,d
&
e
ar
e
a
p
o
l
ynomial co
ef
icien
t
th
at its
v
a
lu
es ar
e
g
i
v
e
n in
App
e
n
d
i
x
.
In
th
is an
alysis,
Eq
.
13
&
Eq. 14
a
r
e
applied for ha
rm
onic orde
rs till
20
th
, a
n
d can
b
e
assum
e
d a consta
nt f
o
r
har
m
onic orde
rs a
b
o
v
e
20
th
.
4.
HA
RM
ON
IC
AN
ALY
S
IS
O
F
ISG
The a
n
aly
s
is o
f
ha
rm
onics di
stortio
n f
o
r
IS
G is co
nd
ucte
d usi
ng t
h
e eq
uivalent circ
uit and
p
h
aso
r
diag
ram
that sho
w
n
by
Fig
u
r
e
4 &
5
.
As s
h
ow
n i
n
Fig
u
r
e
4, t
h
e n
o
n
-line
a
r loa
d
is m
o
d
e
lled as a f
u
nd
am
ental
cur
r
ent
c
o
m
ponent
an
d
harm
onic
cu
rr
ent
s
o
u
r
ces.
A
not
he
r l
o
ad
c
u
r
r
ent
that is c
o
nnect
ed t
o
the
sam
e
PC
C
will also be
contam
inated by harm
onic
com
pone
nts
I
L
(h). Because
this study uses the salient pole
syn
c
hr
ono
us
gen
e
r
a
to
r
,
th
e syn
c
hr
ono
u
s
r
e
actan
ce
X
s
is split into the
re
actan
ce in the
direct a
x
is
X
d
and
the
reactance in the qua
drature a
x
is
X
q
, as s
h
o
w
n i
n
Fi
gu
re 5
a
[7]
,
[1
1]
. Li
k
e
wise, the c
u
rr
ent flo
w
s t
h
r
o
ug
h the
stator wi
ndi
ng
s
are also
dec
o
m
posed into t
h
e
current i
n
the direct axis
I
sd
and t
h
e curre
nt in the
quadrature
axis
I
sq
.
T
o
analy
ze the
resp
o
n
se o
f
h
a
rm
onic cur
r
e
n
t so
urce
s, eac
h o
r
de
r
-
by
-o
r
d
er ha
rm
onic com
pone
nt is
evaluate
d
usin
g a
n
e
q
uivalen
t
circuit as
sh
o
w
n
in
Fig
u
re
5
a
. He
re,
E
(h) is the
ha
rm
onic voltage
distortion
of
the air gap, which is the
innate nature
of the ge
ne
rator
.
E
(h) can
be
obtained from
no-l
o
ad test results. T
h
e
correlation bet
w
een the
curre
nts is
pr
o
duce
d
by
n
o
n
-linea
r
loa
d
I
(h), the othe
r l
o
ad c
u
rrents
I
L
(h
),
an
d the
stator c
u
rrent
I
s
(h
) f
o
r
h
th
o
r
de
r c
o
m
pone
nt is give
n a
s
,
Figu
re 4.
Eq
ui
valent circ
uit o
f
stu
d
ied
sy
stem
using I
S
G
I
s
(h
)
=
I
(h
)
-
I
L
(
h
)
(1
5)
w
h
er
e
,
t
h
e
o
t
h
e
r
l
o
ad
cu
rr
en
t
ca
n
b
e
c
a
l
cu
l
a
t
e
d
a
s
,
t
L
L
(h)
(h
)
=
R
V
I
(1
6)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
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088
-86
94
I
J
PEDS
Vo
l.
6
,
No
.
4
,
Decem
b
er
2
015
:
75
9 – 771
76
4
[
I
sq
(
h
),
I
sd
(
h
)]
V
t
(h)
R
L
I
L
(
h
)
X
d
(
h
),X
q
(
h
)
(
h
)
R
s
I
s(
h
)
E
f
(h
)
I
sd
(
h
)
d
-
a
x
i
s
(+
)
j
I
sq
(h
)
I
s
(h)
-
R
s
I
s
(
h
)
V
t
(h)
(h)
-j
X
d
(
h
)
I
sd
(h
)
-
j
X
q
(
h
)
I
s
(
h
)
-
j
X
q
(
h)
I
s
q
(
h)
s
(h)
E
’
(
h
)
E
f
(
h)
q
-a
x
i
s
(
-)
d
-
a
x
i
s
(-
)
a. sim
p
lified equi
valent circ
u
it
b
.
pha
so
r diagram
Figure
5.
Sim
p
lified eq
uivale
nt circ
uit an
d
p
h
as
or
diag
ram
of
IS
G
fo
r
h
th
h
a
rm
onic
or
de
r of
n
o
n
-
linear loa
d
The
phas
o
r di
agram
of sy
nc
hr
o
n
o
u
s
gene
r
a
tor f
o
r
h
t
h
ha
rm
onic
com
ponent of n
o
n
-
linear
l
o
ad
i
s
give
n in
Fig
u
r
e
5
b
.
T
o
determ
i
n
e the
phase
angle
δ
(h),
the following relationshi
p
is use
d
,
E’
(h
)
=
V
t
(h
)-
R
s
I
s
(h
)-
jX
q
(h)
I
s
(h
)
(
1
7
)
whe
r
e,
X
q
(h
)
=
j
h
ω
1
L
q
(
h
) a
n
d
X
d
(h
)=
j
h
ω
1
L
d
(
h
)
Here
,
E’
(h)
i
n
pha
sor form
ca
n be written
as,
()
(
)
hh
''
EE
(1
8)
The c
u
r
r
e
n
t so
urce
ha
rm
onic
in term
s d-a
x
is an
d
q-a
x
is ca
n
be
p
r
esente
d a
s
,
0
sd
s
s
(h)
=
(h)
s
i
n
(h)
-
90
-
(
h)
II
(
1
9)
0
sq
s
s
()
=
(
)
c
o
s
()
-
9
0
-
(
)
Ih
I
h
h
h
(
2
0
)
Furt
herm
ore, the term
inal vol
ta
ge equation c
a
n
be
written a
s
:
E
f
(
h
)=
V
t
(
h
)-
R
s
I
s
(
h
)-
jX
q
(
h
)
I
sq
(
h
)-
jX
d
(
h
)
I
sd
(
h
)
(2
1)
The
harm
onic
com
pone
nt o
f
t
e
rm
inal voltag
e
can
be
sol
v
ed
as:
V
t
(
h
)=
E
f
(
h
)+
R
s
I
s
(
h
)+
jX
q
(
h
)
I
sq
(
h
)-
jX
d
(
h
)
I
sd
(
h
),
for
h
=
2,
3,
4.
...
...
(
2
2
)
w
h
er
e
E
f
(
h
) is
co
ng
en
ital h
a
rm
o
n
i
c co
m
p
o
n
en
t
o
f
th
e in
ductio
n vo
ltag
e
,
wh
ich
is
d
e
termin
ed
th
ro
ugh th
e
n
o
load test.
The i
n
fl
uence
of ha
rm
onics
on t
h
e
direct i
n
ductance,
L
d
(h
),
and
the
q
u
a
d
ra
ture i
n
d
u
cta
n
c
e
,
L
q
(h
),
ar
e
m
easured
base
d
on
the
m
e
thod
m
eansurem
e
nt in
se
veral l
iterature
[
1
1]
,
[
12]
.
T
h
e
variat
ion
o
f
L
d
and
L
q
with
the
harm
ornic
orde
rs h is
resolve
d
t
h
rough c
u
rve
fitting for a
num
b
er
of data
that obtained
from
the
expe
rim
e
ntal test.
T
h
is m
e
th
od is im
ple
m
e
n
ted
with
polyfit
state
m
ent in M
A
TLAB
,
so
L
d
(h
)
an
d
L
q
(h
) is
obtaine
d a
s
:
L
d
(h
) =
k
1
h
4
+ k
2
h
3
+ k
3
h
2
+ k
4
;
L
q
(h
) = m
1
h
4
+ m
2
h
3
+ m
3
h
2
+ m
4
(2
3)
whe
r
e,
k
&
m
are
poly
nom
ial coe
f
icient,
w
h
ich its
values
a
r
e
give
n i
n
Ap
pendix
.
In this analysis, Eq.
23 is
use
d
for
harm
onic orders till 20
th
, a
n
d
ca
n
be
assum
e
d a co
n
s
tant f
o
r
ha
rm
onic o
r
ders
ab
o
v
e
20
th
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
S
SN:
208
8-8
6
9
4
The C
a
m
p
aris
on
of
H
a
rm
o
n
i
c
Distortio
n
Se
lf-Excited I
n
d
u
c
tion
Gene
rat
o
r w
ith Is
olate
d
....
(
R
efdin
a
l N
a
zir)
76
5
5.
E
X
PERI
MEN
T
AL
SETUP
The a
n
aly
s
is r
e
sults o
f
pr
o
p
o
se
d m
odels a
r
e vali
dated t
h
ro
u
gh c
o
m
p
arison
s
betwee
n
analy
s
is an
d
expe
rim
e
ntal test results. Fig
u
re
6 sh
o
w
s th
e testing
circui
t for all the propose
d
configuration system
.
The
expe
rim
e
ntal test contai
ns tw
o step
s, as
sh
o
w
n
in Fi
gu
re
6
.
The
fir
s
t step
is pe
rform
ed the testing of SEIG
un
de
r n
o
n
-line
a
r loa
d
s.
T
h
e t
e
sting
of
IS
G
un
de
r n
o
n
-
line
a
r loa
d
s is done on the
second
step.
For al
l test
conditions, the
fre
quency
fund
am
ental for
both t
h
e ge
ne
rator is
set at its nom
inal value
(50
Hz)
by a
d
justing
the rotor spee
d.
This test
uses t
w
o
gene
rators
using the
m
achines
with
the
sa
m
e
capacity
, nam
e
l
y
:
0.8 kW
, 380
V
,
3-
p
h
a
se, 50 Hz,
4
po
les. SEI
G
is equ
i
pp
ed
with
26
μ
F ca
pacitors that c
o
nnected i
n
Y
.
For two
ge
nerators,
testing sc
hem
e
was
use
d
4
0
5
W
E
n
er
gy
-Sa
v
ing Lam
p
(E
S
L
) a
nd
V
a
riabe
l
Freq
ue
ncy
D
r
ive (
V
F
D
) as
a
no
n
-
linear loa
d
a
nd resistor
900
Ω
as ot
her loa
d
.
The
both m
achines are
ro
tated
by the
DC m
o
tor
with a spe
e
d
of
1536 rpm
for
SEIG an
d 1500 rpm
for ISG
in order t
o
obt
ain the
fre
quency and the termin
al voltage
reaches
its nom
inal value.
T
h
e m
easured m
achine param
e
ter were:
R
s
= 8,20
Ω
a
nd
X
s
= 6,97
Ω
fo
r SE
IG;
R
s
= 1
0
,
60
Ω
fo
r sy
nc
hr
on
ous
g
e
ne
rato
r
.
An
d
othe
r
para
m
e
ters fo
r
bot
h
m
achines has
been
ex
plaine
d
in Sectio
n
3
&
4.
The m
easurem
ent
of ha
rm
onic curre
nt
s
i
s
ca
r
r
i
e
d
o
u
t
on
th
r
e
e br
an
ch, na
m
e
ly:
the non-linear
loa
d
b
r
an
ch
(
P1
), t
h
e
othe
r loa
d
bra
n
c
h
(
P2
),
an
d the
stato
r
wi
ndi
ng
s
br
anch
(
P3
).
In the m
eanwhi
l
e, the
m
easurem
ent of the ha
rm
onic voltage
s is pe
rf
orm
e
d at the
PCC
point. On
this
m
easur
e, the curre
n
t flows in
the bra
n
ches
of non-linea
r
load m
easure
d
in the
di
r
ection of lea
v
ing the loa
d
.
All testing
of ha
rm
onic
distortio
n is
d
o
n
e
usin
g
Po
we
r
Analy
zer
CA
8220 that c
o
nnected to
PC.
Figure
6. The
testing circ
uit for all the
proposed system
6.
RESULTS
A
N
D
DI
SC
US
S
I
ONS
6.
1.
The Harmonic Produced by
The Non-line
a
r L
o
ads
Figu
re
7 s
h
o
w
m
easurem
ent results
fo
r th
e harm
onics
p
r
o
d
u
ced
by
no
n-linea
r loa
d
whe
n
S
E
I
G
encum
b
ere
d
w
ith 40
5
W ES
L. As sh
o
w
n b
y
Figure 7a
, th
e curre
nt wa
ve
fo
rm
has deviated far f
r
om
the ideal
sinusoidal
form
because
of harm
onics ef
fec
t
, but the
volta
ge
wa
veform
is al
m
o
st close
to the
ideal
sinusoi
d
al
form
. This is in line t
h
e re
sul
t
s sh
ow
n
by
Fi
gu
re
7b
that T
H
D
I
and
T
H
D
V
harm
onic
pr
od
uce
d
by
ES
L we
re
47
.0
%
and
4.
3
%
respectively
.
Figu
re 8 s
h
o
w
s m
easurem
ent results f
o
r the ha
rm
onics pr
o
duce
d
by
n
o
n
-
linear
load
whe
n
SE
I
G
enc
u
m
b
ered
with va
riable f
r
eq
ue
ncy
dri
v
e
(VF
D
)
.
As s
h
ow
n by
Fi
gu
re
8, the
value
of
THD
I
will was great
er (56.3%)
w
h
en SE
IG
burdened with VF
D.
T
h
e
c
o
m
pone
nt of ha
rm
onic
curre
nts
sc
attered
from
low order to
high
order,
whe
r
ein the c
o
m
ponent
w
ith t
h
e
highest am
plitude ar
e
on t
h
e orde
r
of 5,7,13.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
6
,
No
.
4
,
Decem
b
er
2
015
:
75
9 – 771
76
6
a. voltage
an
d cu
rre
nt
wa
ve
fo
r
m
b. s
p
ectr
u
m
harm
onic
Figu
re 7.
The
harm
onic pr
od
uced
by
n
o
n
-
linear
loa
d
whe
n
SEI
G
b
u
r
d
e
n
e
d
E
S
L
a.
vo
l
t
a
g
e
and
cu
rr
e
n
t
w
a
v
e
fo
rm
b
.
spectr
u
m
harm
onic
Figu
re
8.
The
harm
onic
pr
od
uced
by
n
o
n
-
linear
loa
d
whe
n
SEI
G
e
n
c
u
m
b
ered
with
V
F
D
Figu
re 9 a
nd
1
0
sh
o
w
m
easurem
ent results f
o
r the
harm
oni
c gene
rated
by
no
n-linea
r loa
d
w
h
en
IS
G
encum
b
ere
d
with
405 W
ESL
an
d VFD
r
e
sp
ectiv
ely.
As shown b
y
these f
i
gu
r
e
,
THD
I
for ISG was
l
o
we
r
t
h
an
SEI
G
, nam
e
ly
: 29.
5 %
(
w
ith
ESL) an
d 2
4
.
2
%
(
w
ith VF
D).
H
o
we
ver
,
THD
V
was bi
gger
whe
n
using IS
G
,
nam
e
ly
:
13.
7 %
(
w
ith ESL
)
and
24
.2%
(
w
i
t
h
V
F
D
)
.
T
h
e Harm
onics ge
n
e
rated by
IS
G with n
o
n
-
linea
r
loa
d
s
m
o
re foc
u
se
d
on
lo
w-
or
de
r
h
a
rm
onic com
pone
nts,
especia
lly
the or
der
of
5 a
n
d
7.
The list of ha
rm
onic com
ponents
pr
od
uce
d
by
n
o
n
-
linea
r loads
fo
r b
o
t
h gene
rato
rs
was use
d
to
analy
ze the harm
onic distortion
on stat
or si
de an
d othe
r load
usin
g anal
y
s
is
m
e
thod in
section 3 & 4
.
The
analysis results will be e
x
plained in
ne
xt subsection.
TH
D
I
=
47.0 %;
T
H
D
V
= 4.3 %
V
rm
s
= 220.2 V;
I
rm
s
=
0.587A
current
voltag
e
current
voltag
e
current
voltag
e
current
voltag
e
V
rm
s
= 224.2 V;
I
rm
s
=
0.582 A
T
H
D
I
=
56.3 %;
T
H
D
V
= 5.1 %
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
S
SN:
208
8-8
6
9
4
The C
a
m
p
aris
on
of
H
a
rm
o
n
i
c
Distortio
n
Se
lf-Excited I
n
d
u
c
tion
Gene
rat
o
r w
ith Is
olate
d
....
(
R
efdin
a
l N
a
zir)
76
7
a.
v
o
ltage a
n
d
c
u
r
r
e
nt wa
ve
fo
rm
b
.
s
p
ectrum
harm
on
ic
Figu
re 9.
The
harm
onic pr
od
uced
by
n
o
n
-
linear
loa
d
whe
n
IS
G
e
n
c
u
m
b
ered with
E
S
L
a.
voltage
an
d
cu
rre
nt wa
ve
fo
r
m
b
.
sp
ectrum
har
m
onic
Figu
re
1
0
. T
h
e
ha
rm
onic pr
o
d
u
ced
by
n
o
n
-
linear
loa
d
whe
n
IS
G
bu
r
d
ene
d
with
VF
D
6.
2.
T
h
e Imp
a
ct
o
f
N
o
n-l
i
n
e
a
r L
o
a
d
s
Ag
ai
ns
t
Harm
oni
c
Di
s
t
or
ti
on
o
n
T
h
e St
at
or
Wi
nd
i
n
gs
The im
pact of
n
o
n
-
linear
lo
ad
on
b
o
th
ge
nerat
o
rs
can
b
e
m
easured
fr
om
the level
of
ha
rm
onic
distortio
n fo
r the
cu
rre
nt
o
f
stator win
d
in
gs. Fig
u
re
1
1
and
1
2
s
h
o
w
the cu
rre
nt an
d v
o
ltage
ha
r
m
onic
distortio
n
on
stator
win
d
in
gs
side an
d term
inals w
h
e
n
SEIG and
I
S
G bu
rd
en
ed
w
ith 405W
ESL
respe
c
tively
.
As shown these figure
,
T
H
D
I
&
T
H
D
V
of the curre
n
t stator windings a
n
d the
term
inals
voltage of SEIG
wa
s
lowe
r tha
n
THD
I
&
T
H
D
V
l
e
vel f
o
r
I
S
G
.
The
SEI
G
has
elim
inated alm
o
st all the harm
onic com
pone
nts
,
except the
harm
onic co
m
ponent orde
r 3
th
, 5
th
, and
7
th
.
Whil
e, the stator c
u
rre
nt
of
ISG still has containe
d 3
th
,
5
th
, 7
th
, 1
1
t
h,
13
th
, 17
th
and 19
th
or
de
r
harm
on
ic com
pone
nt.
V
rm
s
= 221.6 V;
I
rm
s
=
0.479A
T
H
D
I
=
37.9 %;
T
H
D
V
= 16.3 %
current
voltag
e
TH
D
I
=
29.5 %;
T
H
D
V
= 13.7 %
current
voltag
e
current
voltag
e
current
voltag
e
V
rm
s
= 221.4 V;
I
rm
s
=
0.524A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
6
,
No
.
4
,
Decem
b
er
2
015
:
75
9 – 771
76
8
h
a
rm
onic or
de
rs
(
h
)
h
a
rm
onic or
de
rs
(
h
)
a. m
easured
b
.
a
n
aly
zed
Figu
re
1
1
. T
h
e
cu
rre
nt ha
rm
onic dist
ortio
n
o
n
the
stator
wi
ndi
ng
s w
h
e
n
S
E
IG
b
u
r
de
ne
d
with E
S
L
h
a
rm
onic or
de
rs
(
h
)
ha
r
m
onic or
ders
(
h
)
a. m
easure
d
b. a
n
aly
zed
Figu
re
1
2
. T
h
e
cu
rre
nt ha
rm
onic dist
ortio
n
o
n
the
stator
wi
ndi
ng
s w
h
e
n
I
S
G e
n
c
u
m
b
ered
with E
S
L
Figu
re
1
3
a
n
d
14
s
h
o
w
t
h
e c
u
rre
nt h
a
rm
onic disto
r
tio
n on
s
t
ator win
d
in
gs side whe
n
SEI
G
a
n
d
I
S
G
burdene
d
with VFD re
specti
v
ely. Like
a
s
loadin
g t
h
e
bo
th ge
nerat
o
rs
with ESL, the
curre
n
t and
voltage
harm
onic dist
o
r
tion
o
f
the st
ator
win
d
in
gs
and
term
in
als for SE
IG was
lowe
r tha
n
the
curre
n
t and
voltage
harm
onic
disto
r
tion
o
f
the
stator
wi
ndi
ngs
an
d term
inals fo
r
ISG
.
TH
D
I
=
17.25 %;
T
H
D
V
=
16.92%
TH
D
I
=
8.05 % ;
T
H
D
V
= 3.23%
TH
D
I
=
17.80 %;
T
H
D
V
=
14.0 %
TH
D
I
=
10.1 %;
T
H
D
V
= 4.1 %
current
voltag
e
current
voltag
e
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