Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1292~
1
303
I
S
SN
: 208
8-8
7
0
8
1
292
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
The Dynamic of Synchronous
Generator under Unbalanced
St
e
a
dy
St
a
t
e
O
p
er
at
io
n:
A
Case of Virt
ual Generator
Laboratory
Sugi
a
rto Kadiman,
Ari
f
B
a
s
uki, Myth
a Ar
ena
Department o
f
Electrical E
ngin
e
ering, Seko
lah
Tinggi Te
knologi Nasional,
Yog
y
akarta
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 29, 2015
Rev
i
sed
Au
g
22
, 20
15
Accepte
d
Se
p 4, 2015
The purpose of
this stud
y
is to
design and d
e
velop a s
y
nchrono
us generato
r
virtual
laborator
y
for undergr
a
du
ate studen
t
cour
ses, which can b
e
treated as
an accessorial tool for enhancin
g instru
ction
.
Firstl
y, the stud
y
reviews the
general concept and algorithm of sy
n
c
hronous generator model. Second
ly
,
the simulation
method of this
s
y
stem
is d
i
scussed. Finally
,
the p
a
per
introduces its example and
an
aly
s
is. One of th
e ma
jor objectives of this
project is the d
ynamics of s
y
nch
r
onous generato
rs connected to
the
500 k
V
EHV Jamali (Jawa-Madura-B
a
li) S
y
st
em under unbalan
ced stead
y
state
condition th
at could be modeled as
a balanced sy
n
c
hronous generator’s
model with unbalan
ced voltage
inputs.
The balanced s
y
n
c
hrono
us generator
m
odel based on the rotor’s qd0 referen
ce fram
e
was chosen to substitute
generator’s mod
e
l embeded in
loadflow
analy
s
is. The verif
i
cation of the
proposed gener
a
tor’s model was check
ed b
y
comparing it
with a PSS
Tecqu
i
ment NE9070 simulator. The unbala
nced
voltag
e
inputs of generato
r
were der
i
ved
uti
lizing
th
e lo
adfl
ow an
al
ysis b
y
determ
ining
the
phase
and
sequence cur
r
ents, and averag
e bus voltages of the 500 kV EHV
Jamali grid
considering
unb
alan
ced por
tion
vari
ations.
Me
anwhile
, th
e lo
ad loc
a
t
i
ons
having signif
i
cant eff
ect
on the test g
e
ner
a
tors
are ob
tain
ed b
y
using
the
electricity
tr
acin
g
method. The develo
p
e
d vir
t
u
a
l laborator
y
with a g
i
ven
example d
e
monstrated
the usef
ulness
of the
to
ol for stud
y
i
ng
s
y
nchronous
generator und
er
unbalan
ced
stead
y
-state oper
a
tio
n.
Keyword:
50
0 K
V
E
H
V
Jam
a
li Syste
m
qd
0 refe
re
nce
f
r
am
e
Syn
c
hro
nou
s gen
e
r
a
t
o
r
Tecq
ui
m
e
nt
NE9
0
7
0
si
m
u
l
a
t
o
r
Unbalance
d
steady
state
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
:
Su
gi
art
o
Ka
di
m
a
n,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Sek
o
l
a
h
Ti
n
ggi
Tek
n
o
l
o
gi
Na
si
onal
,
Jl
. B
a
ba
rsari
,
C
a
t
u
r T
u
ng
gal
,
De
po
k,
Sl
em
an,
Y
ogy
a
k
art
a
55
2
8
1
,
In
d
one
si
a.
Em
a
il: su
g
i
arto.k
ad
im
an
@sttn
as.ac.id
1.
INTRODUCTION
In electrical engi
neeri
ng e
d
ucation, written exerci
ses are
necessa
ry for un
de
rgraduate stude
nts
to
gras
p c
o
ncept
i
on
w
h
i
l
e
ex
per
i
m
e
nt
at
i
ons e
m
phasi
ze t
h
e un
de
rst
a
n
d
i
n
g
of t
h
e s
u
b
j
ect
.
R
eal
expe
ri
m
e
nt
s are
essen
tial for
d
e
v
e
lop
i
ng
sk
ills to
d
eal
with
i
n
stru
m
e
n
t
atio
n
and
ph
ysical
p
r
o
cesses and
n
o
dou
b
t
that n
o
t
h
i
ng
will replace synchronous learning throug
h face to face interaction
[1]. Vi
rtua
l Laboratory can be treated as an
accessorial tool of real la
boratory to e
nha
nce inst
ructi
on
for conventional on-cam
pus stude
nts,
whic
h ca
n
en
ab
le stud
en
t
s
to
i
m
p
r
ov
e the sk
ills b
e
fo
re
g
o
i
n
g
t
o
th
e actu
al lab
o
r
ato
r
y
,
to
learn
b
r
eakin
g
th
e lim
i
t
ati
o
n
o
f
real
l
a
b
o
rat
o
ry
deal
i
n
g
wi
t
h
adva
nce
d
t
opi
c
s
, s
u
ch
as
u
n
b
a
l
a
nced
o
p
erat
i
on i
n
sy
nch
r
o
n
o
u
s
ge
nerat
o
r
s
. S
o
,
Vi
rt
ual
Lab
o
ra
t
o
ry
ca
n e
ffect
i
v
el
y
hel
p
t
o
ove
rc
om
e
th
e b
a
rriers im
p
o
s
ed
b
y
th
e traditio
n
a
l edu
catio
n by
u
s
ing
an
inn
ovativ
e co
m
b
in
at
io
n
of a n
e
w ap
pro
ach
to
education and the applicatio
n of
new t
ech
n
o
l
o
g
i
es [2]
-
[4]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
The
Dy
na
mi
c
o
f
Sync
hr
o
n
o
u
s
Gene
rat
o
r
un
d
e
r U
n
b
a
l
ance
d
St
ea
dy
St
at
e
O
p
er
at
i
on…
(
S
u
g
i
a
rt
o K
a
di
m
a
n)
1
293
Man
y
stu
d
i
es co
n
s
i
d
eri
n
g
u
nbalan
ced
stead
y
state o
p
e
rating
co
nd
itio
ns o
f
syn
c
hrono
u
s
g
e
n
e
rat
o
rs as
a source electrical energy ha
ve done
using
the analytical
approaches
. T
h
e
nat
u
re o
f
t
h
e un
bal
a
nce c
o
m
p
ri
ses
une
q
u
al
vol
t
a
g
e
m
a
gni
t
udes a
t
t
h
e fun
d
am
ent
a
l
of bot
h sy
st
em
freque
ncy
and
phas
e
angl
e devi
at
i
o
n
.
O
n
e o
f
cont
ri
b
u
t
i
n
g
fa
ct
ors i
s
t
h
e a
p
peara
n
ce
of
u
n
b
al
ance
d l
o
ads
of
t
h
e
ge
nerat
o
r
.
I
n
c
r
uci
a
l
un
bal
a
nce
d
sy
st
em
s,
negative
seque
n
ce c
u
rrent m
a
y cause
o
v
e
rh
eatin
g of th
e m
ach
in
eries;
zero
seque
n
ce
curre
n
t m
a
y cause
im
proper acti
o
n
of the
protect
ive relaying
[5].
Un
bal
a
nce
d
s
h
ort
-
ci
rcui
t
s
cal
cul
a
t
i
ng o
f
sy
nch
r
on
o
u
s ge
n
e
rat
o
r
un
de
r st
eady
st
at
e operat
i
on
has
been
com
p
l
e
t
e
l
y
un
derst
o
o
d
[6]
-
[
7]
.
A
n
al
y
s
i
s
base
d
o
n
math
em
at
ical th
eo
ry
wh
ich
i
n
clu
d
e
s
sing
le lin
e-t
o
-
n
e
u
t
ral fau
lt and
th
e lin
e-to
-li
n
e fau
lt, is b
e
en
u
tilized
. B
u
t an
o
t
h
e
r
p
r
ob
lem o
f
th
e
u
n
b
a
l
a
n
ce wh
en
th
e
syste
m
is con
n
ected
the grid
s
h
a
s no
t
b
een tho
r
ou
gh
l
y
so
lv
ed
[8
].
Un
til n
o
w th
ere is n
o
t
h
eoret
i
c
m
a
th
e
m
a
tics
m
o
d
e
ls o
f
sy
nch
r
on
ou
s
g
e
n
e
rato
rs u
s
ed
to
an
alyze th
is
ki
n
d
of
pr
o
b
l
e
m
s
m
e
nt
i
one
d
abo
v
e. I
f
t
h
e
r
e i
s
a st
udy that addresses
the issue, it requi
res an exha
usted
equat
i
o
n, s
u
c
h
as Sal
i
m
who anal
y
zed t
h
e sm
al
l si
gnal
dy
nam
i
c perf
orm
a
nce of sy
nch
r
on
o
u
s ge
n
e
rat
o
r
co
nn
ected to
t
h
e lo
ad
u
n
d
e
r an
y unb
alan
ced
o
p
e
ratio
n co
nd
itio
ns. Su
ch
m
o
d
e
l u
s
es
d
i
fferen
tial alg
e
b
r
aic
equat
i
o
ns
(D
A
E
) w
h
i
c
h i
s
co
m
posed by
di
f
f
e
rent
i
a
l
eq
uat
i
ons
of
ge
nerat
o
rs
(el
ect
ri
cal
and m
echani
c
a
l
part
s)
and
i
t
s
co
nt
r
o
l
s
(
vol
t
a
ge
an
d
s
p
eed
re
g
u
l
a
t
i
on)
, a
n
d
by
al
ge
brai
c e
q
uat
i
o
n
s
fr
om
gene
rat
o
r, i
t
s
c
ont
rol
,
a
n
d
t
h
e
net
w
or
k. The
exam
i
n
ed sy
st
em
i
s
S
i
n
g
l
e Ma
ch
in
e In
fin
ite Bu
s
or SM
I
B
. The res
u
lts are frek
u
e
n
si (f
) a
n
d
dam
p
i
ng rat
i
on
(
of the electromechanical m
o
del calculated i
n
eac
h studied
case of unbalanced scena
r
io
[9-
10]
.
A
not
her
r
e
searche
r
s,
su
c
h
as
R
a
m
y
a and
Sel
v
i
a
r
e al
so
foc
u
se
d
on
SM
IB
. Sy
nch
r
on
o
u
s
gene
rat
o
r m
odel
u
s
es Heffro
n-Ph
illip
s Mod
e
l with
/witho
u
t
am
ort
i
s
eu
r
wi
n
d
i
n
g
. An
alysis fo
cu
ses
o
n
small s
i
g
n
a
l stab
ility,
suc
h
as t
h
e i
n
com
i
ng o
f
c
h
angi
ng
v
o
l
t
a
ge
refe
re
nce a
nd step cha
n
ge in
the m
echani
cal torque
. T
h
e
resul
t
s
p
r
esent
resp
onse c
u
r
v
es o
f
t
e
rm
i
n
al
vol
t
a
ge, fi
e
l
d vol
t
a
ge
, rot
o
r s
p
eed
, and
angl
e [1
1]
. An
ot
h
e
r
researc
h
er
s ha
d f
o
cu
sed
on
t
h
e i
s
ol
at
ed
sel
f-exci
t
e
d i
n
d
u
ct
i
on
ge
n
e
rat
o
r
(SE
I
G
)
bal
a
nce
d
/
u
nb
al
ance
d
co
nd
itio
ns
o
f
l
o
ads [12
-
14
].
Ach
a
[15
]
sugg
ests th
at lo
adflow
analysis can be
use
d
to
analyze
un
bal
a
nced st
ea
dy
-st
a
t
e
pro
b
l
e
m
s
o
f
syn
c
hrono
us g
e
n
e
rator as lo
ng
as m
o
re realistic syn
c
hro
n
o
u
s
gene
rat
o
r
m
odel
i
s
im
plem
ent
e
d. So t
h
e g
o
al
of t
h
i
s
pa
per i
s
t
o
o
b
t
a
i
n
a co
m
p
rehensi
v
e
m
a
t
h
em
at
i
c
al
m
odel
of bal
a
n
ced sy
nc
hr
o
n
o
u
s ge
ne
rat
o
r o
p
erat
e
d
u
n
d
e
r un
b
a
lanced
stead
y state co
n
d
ition
.
It is in
d
i
sp
en
sab
l
e syn
c
hrono
u
s
g
e
n
e
rator
m
o
d
e
l wh
ich h
a
s a
com
p
l
e
t
e
l
y
en
ou
g
h
f
r
am
ewo
r
k
f
o
r a
n
al
y
z
i
n
g t
h
e
sm
all
-
si
gnal
dy
nam
i
c perf
orm
a
nce o
f
po
we
r sy
st
em
s u
nde
r
u
n
b
a
lan
c
ed con
d
ition
s
and
al
so
can
acco
m
m
o
d
a
te th
e lo
ad
fl
o
w
an
alysis to
d
e
term
in
e v
a
lu
es of
g
e
n
e
rato
r’s
termin
al in
pu
ts wh
en th
e ch
ang
i
ng
lo
ad
s h
a
pp
en
ed
on
th
e co
nn
ecting
g
r
i
d
s.
Th
e
p
r
esen
ted
stu
d
y
co
n
s
i
d
ers sev
e
r
a
l typ
i
cal syn
c
h
r
ono
u
s
g
e
n
e
r
a
tor
s
w
h
ich
ar
e co
nn
ected
to
500
k
V
EHV Jam
a
li Syste
m
, In
do
n
e
sia. Th
e stu
d
y
was carried
ou
t th
roug
h
th
e “h
ybrid
” meth
od
b
y
co
m
b
in
atio
n
b
o
t
h
un
b
a
lan
c
ed
lo
adflow un
d
e
r EDSA
20
00
to
an
alyze th
e g
r
id
an
d to
d
e
term
in
e
th
e in
pu
ts o
f
t
h
e test
gene
rat
o
r an
d
t
h
e rot
o
r
’
s
qd0
referen
ce fra
m
e
o
f
syn
c
hro
nou
s g
e
n
e
rato
r m
o
d
e
l to
su
b
s
titu
te th
e l
o
adflow
gene
rat
o
r’s m
odel
[
1
6-
17]
.
The ve
ri
fi
cat
i
o
n of t
h
e
pr
o
p
o
se
d
m
odel
w
a
s checke
d
by
com
p
ari
ng i
t
wi
t
h
a
Tecq
ui
m
e
nt
N
E
9
0
7
0
si
m
u
l
a
tor
.
The de
vel
o
ped m
odel
i
s
a
m
a
i
n
subsy
s
t
e
m
of sy
nchr
o
n
ous
gene
rat
o
r vi
rt
ua
l
lab
o
rato
ry.
Thi
s
w
o
rk i
s
o
r
ga
ni
zed a
s
f
o
l
l
o
ws.
A
b
r
i
e
f
expl
a
n
at
i
o
n ab
out
t
h
e co
nce
p
t
s
and al
go
ri
t
h
m
s
i
nvol
vi
n
g
th
e u
n
b
a
lan
c
ed
con
d
ition
of balan
ced
syn
c
h
r
o
nou
s g
e
n
e
rat
o
r
is d
e
fi
n
e
d o
n
Section
1
.
Sectio
n
2
p
r
esen
t
s
th
e
revi
e
w
conc
ep
t
s
and al
go
ri
t
h
m
.
The sim
u
l
a
t
i
on m
e
t
hods a
r
e prese
n
t
e
d
o
n
Sect
i
on 3
.
S
ect
i
on 4 p
r
ese
n
t
s
t
h
e
resu
lts and
co
nclu
sion
.
2.
REVIEW
C
O
NCEPTS
A
N
D
ALGO
RIT
H
MS
A
bri
e
f
di
sc
us
si
on c
o
nsi
d
e
r
i
n
g
t
h
e
o
p
erat
i
o
n
o
f
po
we
r s
y
st
em
wi
t
h
sy
nch
r
on
o
u
s
gen
e
rat
o
r
s
un
der
steady state unbalance
d c
o
ndi
tions is
present
e
d in the
prese
n
t section.
2.
1.
Ste
a
dy
State Unbalanced Operation
Many large sy
nchronous ge
nerators
conne
c
t
ed to the pow
er grid are
us
ually
found in
recent powe
r
syste
m
, w
h
ich is co
mm
o
n
in sev
e
r
a
l co
un
t
r
ies arou
nd
t
h
e wo
r
l
d
,
i
n
clud
ing
I
ndo
n
e
sia. Th
e 500
k
V
EHV
Jam
a
li Syste
m
s is o
n
e
of
an ex
am
p
l
e. Synch
r
on
ou
s
gene
rators
often operates on unbalance
d
three
-
phase
loading. That is the stat
or
c
u
rrents ha
ve differen
t am
plitudes, and t
h
eir
phase
displacement di
ffe
rs from
120
O
[18]. These
phase curre
nts ca
n
be
de
c
o
m
posed
i
n
positive, negative
a
n
d
z
e
ro se
que
nce c
u
rrents according t
o
Fo
rtesqu
e’s t
r
an
sform
.
At ro
tor speed, the po
sitiv
e sequ
en
ce co
m
p
onen
t
s pro
d
u
ce
a forward
-
travelin
g
m
a
gnet
o
m
o
t
i
v
e f
o
rce a
n
d a
r
e
o
n
l
y
ap
peare
d
i
n
bal
a
nce
d
op
erat
i
o
n
o
f
t
h
e s
y
nch
r
o
n
ous
ge
nerat
o
r.
At
u
nbal
n
ce
d
ope
rat
i
o
n, a
r
m
a
t
u
re c
u
r
r
ent
prese
n
t
s
negat
i
ve an
d ze
ro
seq
u
ence c
o
m
p
o
n
e
n
t
s
t
h
e
negat
i
v
e se
q
u
e
n
ce com
p
o
n
en
t
s
. Negat
i
v
e se
que
nce
pr
od
uc
es
MMF that travels at op
posite ro
to
r sp
eed
,
the
zero se
q
u
ence
com
pone
nt
s p
r
od
uce a zer
o t
r
avel
i
n
g fi
el
d i
n
an ai
r
-
g
a
p a
nd
d
o
n
o
t
i
n
t
e
r
act
wi
t
h
t
h
e r
o
t
o
r i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1292 –
1303
1
294
term
of the fundam
e
ntal com
ponent. Bot
h
, positive
and
negative se
que
n
ce com
p
onents under
unbal
a
nced
stead
y state co
nd
itio
n pro
duce a n
e
t m
a
g
n
e
to-m
o
tiv
e force with a sinu
so
i
d
al v
a
riatio
n of its m
a
x
i
m
u
m
a
m
p
litu
d
e
and will also
appear a sinu
so
idal v
a
riati
o
n
with
a freq
u
e
n
c
y. Co
n
s
equ
e
n
t
ly, th
e sp
eed
o
f
t
h
e
g
e
n
e
rator
will n
o
t
b
e
con
s
tan
t
in
stead
y
state con
d
ition
.
2.
2.
Sync
hronous Generator Dyna
mic Mathe
m
atic
al
Model
Fo
r all of usual g
e
n
e
rator ap
p
lication
,
th
ere is
m
o
re t
h
a
n
one
ge
nerat
o
r
o
p
erat
i
n
g i
n
paral
l
e
l
t
o
supply dem
a
nded by t
h
e loads.
To analy
ze the
dynamic of
ge
nera
t
o
rs under
unba
l
anced steady
state
ope
rat
i
o
n, w
h
i
c
h i
s
po
we
r angl
e o
r
l
o
a
d
a
ngl
e c
h
aract
eri
s
t
i
c
, a “hy
b
ri
d
”
m
e
t
hod by
c
o
m
b
i
n
at
i
on be
t
w
een
unbalance
d
t
h
ree phase l
o
a
d
fl
ow analys
is and rotor’s
q
d0
refe
re
nc
e fram
e
of
ge
nerat
o
r m
odel
w
h
ich
su
bstitu
tes th
e
m
o
d
e
l o
f
g
e
n
e
rato
r i
n
lo
ad
flow an
alysis can
b
e
u
s
ed
.
The dy
nam
i
c
m
a
t
h
em
at
i
c
al
m
odel
of a bal
a
nced sy
nc
hr
on
o
u
s ge
nerat
o
r
wi
t
h
o
n
e q-
axi
s
dam
p
i
n
g
wi
n
d
i
n
g
i
s
c
o
m
posed
by
t
h
e set
o
f
di
f
f
ere
n
t
i
a
l
eq
uat
i
o
ns
as
rese
nt
ed i
n
Fi
g
u
r
e
1 a
n
d
al
so
bel
o
w
[
1
9]
.
Fi
gu
re 1.
I
nne
r
bl
oc
k o
f
bal
a
n
ced
t
h
ree-
p
h
as
e
sy
nc
hr
on
o
u
s gene
rat
o
r [1
7]
Th
e
d
i
fferen
tial eq
uatio
n
s
of
electrical d
y
n
a
mic th
at d
e
sc
ri
b
e
the stator an
d ro
tor
wind
i
n
g
s
an
d are written
in
qd
0
refe
re
nce fram
e are, shown in (1).
(1
)
The fi
rst
t
h
ree
equat
i
o
ns de
sc
ri
be t
h
e st
at
or
wi
n
d
i
n
g (s
ubsc
r
i
p
t
s
) and
th
e fo
llowing
th
ree eq
u
a
tion
s
descri
be t
h
e
ro
t
o
r wi
ndi
n
g
(s
upe
rsc
r
i
p
t
r
). Th
e su
b
s
crip
t
k
i
s
used
fo
r t
h
e dam
p
i
ng
wi
ndi
ng
s (
kq
fo
r
q
-a
xis
dam
p
i
ng wi
n
d
i
n
g
an
d
kd
fo
r
direct ax
is) wh
ile th
e sub
s
cri
p
t
f is
u
s
ed
for the field
wind
ing.
In
these
v
r
e
pr
esen
ts th
e voltag
e
of
w
i
nd
i
n
g
s
,
I
desc
ribes the
electrical curre
n
t fl
owing i
n
the
win
d
in
g,
re
pr
esent
s
t
h
e
m
a
gnet
i
c
fl
u
x
c
o
nn
ect
i
ng t
h
e
wi
n
d
i
n
g,
p
re
prese
n
ts diffe
rential
o
p
erat
or (
d/
dt
),
and
a
r
e an
gu
la
r s
p
e
e
d
o
f
th
e ro
tor r
e
fe
r
e
d to a two po
le g
e
n
e
r
a
to
r an
d
r
e
f
e
r
e
n
c
e
ang
u
l
ar
sp
e
e
d
corres
ponded t
o
t
h
e
rated fre
que
nc
y, resp
ectiv
ely. Th
e m
a
g
n
e
tic
flux
fo
r eac
h
wi
n
d
i
n
g i
s
re
pre
s
ent
e
d i
n
(2
).
Si
nce
t
h
e
dam
p
i
ng
wi
n
d
i
ngs
are
s
h
o
r
t
-
c
i
rcui
t
e
d s
o
t
h
e
val
u
e
o
f
and
are
null.
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
The
Dy
na
mi
c
o
f
Sync
hr
o
n
o
u
s
Gene
rat
o
r
un
d
e
r U
n
b
a
l
ance
d
St
ea
dy
St
at
e
O
p
er
at
i
on…
(
S
u
g
i
a
rt
o K
a
di
m
a
n)
1
295
Whe
r
e
,
,
,
,
,
,
,
,
and
are the electric
a
l fundam
e
ntal param
e
ters o
f
synchronous
generat
o
r. T
h
e
direct-a
xis reac
tance
and the
qua
drature
-
a
x
is reactanc
e
are
gi
ve
n
by
(3
).
(3
)
The m
echani
c
a
l
part
of
t
h
e
ge
nerat
o
r i
s
desc
r
i
bed
by
t
w
o
di
f
f
ere
n
t
i
a
l
eq
uat
i
ons
as
desc
ri
be
d i
n
(
4
)
.
(4)
In
E
quatio
n
(
4
),
H
is an
inertia co
n
s
tan
t
o
f
th
e t
u
rb
in
e-g
e
n
e
rat
o
r set,
is th
e m
ech
an
ical to
rq
u
e
o
f
the
tu
rb
in
e an
d
is a d
a
m
p
in
g
t
o
rq
u
e
. Th
e
d
a
mp
ing
torqu
e
rep
r
esen
ts th
e rotatio
n
a
l lo
sses
o
f
t
h
e ro
tatin
g
p
a
rts
wh
ich
con
s
ist of t
h
e m
a
g
n
e
tic losses an
d th
e m
ech
an
i
cal lo
sses.
2.
3.
Balance
d
S
y
n
c
hron
ous
Ge
n
erator with
Unbal
a
nced
Loads
The
bal
a
nce
d
t
h
ree
-
p
h
ase sy
n
c
hr
o
n
o
u
s
gene
rat
o
r
’
s m
odel
i
s
sh
ow
n i
n
Fi
gu
re
2.
It
i
s
cl
ear t
h
at
t
h
e
g
e
n
e
rator is
d
r
i
v
en b
y
t
h
e
u
nbalan
ced
vo
ltage in
pu
ts; thu
s
:
cos
cos
cos
(5)
Fi
gu
re
2.
B
a
l
a
nced
ge
ne
rat
o
r
wi
t
h
u
nbal
a
nc
ed i
n
p
u
t
s
,
[17]
2.
4.
Electricity Tr
acing
The t
r
aci
n
g
el
ect
ri
ci
t
y
i
s
t
r
aci
ng t
h
e
rel
a
t
i
ons
hi
p bet
w
ee
n ge
ne
rat
o
r a
n
d l
o
a
d
s
usi
n
g
a l
o
ad
fl
o
w
analysis. It could be
diffic
u
lt to realize because the
cha
nging on a dem
a
nd
of ge
ne
rator for eve
r
y node will
pr
o
duce t
h
e c
h
an
gi
n
g
st
i
m
u
l
at
ed on ge
ne
rat
i
on w
h
i
c
h pr
o
duce
d
by
a swi
n
g
-
bus
. One
of t
h
e i
d
eas o
f
electricity tracing calle
d the
co
mmo
n
m
e
thod
i
s
s
h
ari
n
g i
n
f
l
ow
of t
h
e
no
d
e
s di
vi
ded
p
r
o
p
o
r
t
i
o
nal
l
y
am
on
g t
h
e
out
fl
o
w
of t
h
e
no
des
[
20]
.
The
com
m
on
m
e
thod
will ca
tegorize buses
and bra
n
ches
w
ithin t
h
e
net
w
orks int
o
se
veral groups:
1)
Do
m
a
i
n
of
ge
n
e
rat
o
rs
is
defi
ned as t
h
e set
of buses
wh
ic
h a
r
e
reache
d
by power produced
by
th
is g
e
n
e
rati
o
n
.
2)
Po
wer f
r
o
m
a gene
rat
o
r rea
c
hes a pa
rt
i
c
ul
ar b
u
s i
f
i
t
i
s
pos
si
bl
e t
o
fi
n
d
a pat
h
t
h
r
o
u
gh t
h
e
net
w
or
k
fr
om
the g
e
ne
rat
o
r t
o
t
h
e b
u
s
fo
r
wh
i
c
h t
h
e
di
rec
tion
of trav
el is al
ways co
n
s
istent with
th
e
d
i
rectio
n
of
t
h
e
fl
o
w
as
com
put
ed
by
a
po
we
r fl
ow
p
r
og
ram
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
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08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1292 –
1303
1
296
3)
Co
mmon
s
i
s
defi
ned as a
set
of nei
g
h
b
o
r
i
n
g b
u
ses
sup
p
l
i
e
d by
t
h
e sam
e
generat
o
rs
.
Unc
o
nnect
e
d
s
e
t
s
of
buse
s
s
u
ppl
i
e
d
by
t
h
e
s
a
m
e
gene
ra
tors
are t
r
eated a
s
separate
commons
.
A
bus t
h
erefore
bel
o
ng
s t
o
co
m
m
on. The ra
nk
of a com
m
on i
s
t
h
e n
u
m
b
er o
f
ge
nerat
o
rs s
u
p
p
l
y
i
ng
po
we
r t
o
t
h
e bus
es
com
p
ri
si
ng t
h
i
s
com
m
on.
4)
Links
is
one
or
m
o
re external
bra
n
c
h
es c
o
nnecting the same
common
fo
r
m
.
5)
St
at
e gra
p
h
is
the state of the
syste
m
can be
re
prese
n
ted
by a directed, a
c
yclic graph;
co
mmo
n
are re
presente
d as
nodes a
n
d
li
n
k
s
as
branc
h
e
s
.
The c
o
nt
ri
b
u
t
i
o
n
t
o
t
h
e l
o
ad
of
a c
o
m
m
on i
s
o
b
t
a
i
n
e
d
by
usi
n
g t
h
e
defi
n
i
t
i
on o
f
t
h
e
in
f
l
o
w
and t
h
e
o
u
tflo
w
of c
o
m
m
ons. T
h
e
in
flo
w
is the s
u
m
of the powe
r injected
by
s
o
urces c
o
nnect
ed to
buses l
o
cated i
n
t
h
i
s
com
m
on and
o
f
t
h
e
po
we
r i
m
port
e
d i
n
t
h
i
s
com
m
on fr
om
ot
her com
m
ons by
l
i
nks
.
An
d t
h
e
ou
tflo
w
of
com
m
ons i
s
eq
ual
t
o
t
h
e s
u
m
of t
h
e p
o
w
er e
x
p
o
r
t
e
d t
h
r
o
u
g
h
l
i
n
k
s
f
r
om
t
h
i
s
com
m
on t
o
com
m
ons of
hi
ghe
r
rank
.
Th
e in
fl
ow
o
f
a co
mm
o
n
is eq
u
a
l t
o
the su
m
o
f
its
o
u
tflo
w and
o
f
all th
e lo
ad
s co
nn
ected
t
o
th
e bu
ses
com
p
ri
si
ng t
h
e
com
m
on.
The e
q
uat
i
o
n
s
of
co
nt
ri
b
u
t
i
o
n
ge
nerat
o
r i
n
t
o
l
o
ad a
r
e:
∗
(6)
∑
(7)
∑
(8)
W
h
er
e
and
are c
ont
ri
but
i
o
n
g
e
nerat
o
r
i
i
n
to lo
ad
s
an
d ou
tflo
w o
f
the
comm
on j
d
a
n
k, r
e
sp
ectiv
ely.
and
are the
flows
at the
lin
k
bet
w
ee
n
comm
on
- j
and
k
an
d th
e
f
l
ow
s at
lin
k
bet
w
ee
n
co
mmo
n j
and
k
,
respectively.
3.
SIMU
LA
TION
M
ETHOD
OF
SY
NCHRON
O
U
S
GENER
A
T
OR
DYN
AM
IC
To st
udy
t
h
e
dy
nam
i
c of s
y
nch
r
o
n
ous
ge
nerat
o
r
fr
om
the sm
al
l
-
si
gna
l
poi
nt
o
f
vi
ew, se
ve
ral
sim
u
l
a
t
i
ons we
re pe
rf
orm
e
d un
de
r ED
SA
2
0
0
0
a
nd M
a
t
l
a
b/
Si
m
u
l
i
nk. T
h
e p
r
oc
ess o
f
num
eri
cal
sim
u
l
a
t
i
o
n
m
e
t
hod ca
n b
e
prese
n
t
e
d
b
y
t
h
e bl
oc
k di
agram
of Fi
g
u
r
e 3, i
n
w
h
i
c
h
t
h
e rol
e
a
n
d
cont
e
n
t
of t
h
e bo
x
si
m
p
ly illu
strat
e
d
a
fo
llo
ws:
Fi
gu
re
3.
Si
m
u
l
a
t
i
on
fl
o
w
c
h
art
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
The
Dy
na
mi
c
o
f
Sync
hr
o
n
o
u
s
Gene
rat
o
r
un
d
e
r U
n
b
a
l
ance
d
St
ea
dy
St
at
e
O
p
er
at
i
on…
(
S
u
g
i
a
rt
o K
a
di
m
a
n)
1
297
The
un
bal
a
nc
ed T
h
ree
-
p
h
as
e Newt
on
-R
a
phs
o
n
L
o
adfl
ow, EDSA
2000, is
use
d
to analyze
u
n
b
a
lan
c
ed
stead
y state conditio
n
of t
h
e
50
0 kV EHV Ja
m
a
li Syste
m
s
.
The su
b
s
titu
t
i
o
n
o
f
th
e l
o
ad
fl
o
w
gene
rat
o
r’s
m
odel
c
o
nsi
s
t
e
d
of
act
i
v
e a
n
d
reactiv
e
po
wer inj
ection
s
b
y
th
e ro
tor’s
qd
0
re
fe
rence
f
r
a
m
e of
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r m
odel
i
s
i
n
t
e
nded t
o
fi
nd t
h
e
p
h
en
o
m
enon i
n
fl
ue
n
ced by
u
n
b
al
an
ced t
h
ree
-
phas
e
. T
o
det
e
rm
i
n
e t
h
e
veri
fi
e
d
m
odel
,
t
h
e
p
r
o
p
o
sed
gene
rat
o
r m
o
d
e
l
of
bal
a
nced
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r i
s
co
m
p
ared
with PSS Tec
h
qui
pm
ent NE
9070
through sim
i
larity of
their trends
. The results of
loa
d
fl
ow a
n
alysis are then
use
d
as t
h
e i
n
p
u
t
s
of
bal
a
nce
d
sy
nc
hr
on
o
u
s
g
e
nerat
o
r
’
s m
o
d
e
l
whi
c
h
uses
qd
0
re
fere
nce
fr
am
e.
4.
R
E
SU
LTS AN
D ANA
LY
SIS
4.
1.
The 500
kV
E
H
V
Ja
ma
li Syst
em
The st
udied
syste
m
is the 500
kV E
H
V Ja
m
a
li Syste
m
that
c
o
m
p
ri
ses
4-
regi
on
s, s
u
c
h
as
R
e
gi
on
I
Banten-
J
aka
r
ta
, Regio
n
II
W
e
st Java, Regio
n
III Central Ja
v
a
-Y
o
g
y
a
karta,
and Regio
n
I
V
East Java-B
ali. It
also
h
a
s
71
li
n
e
n
o
d
e
s, 27
li
n
e
s
o
f
in
ter
buses, an
d 9 g
e
ner
a
to
r nod
es
,su
c
h as Sur
a
laya 24
50
M
W
,
Cir
a
ta
14
0
0
M
W
, M
u
ara Tawa
r
50
0
M
W
, Sa
g
u
l
i
n
g
45
0 M
W
,
Grat
i
75
0 M
W
, an
d
Gresi
k
2
9
8
M
W
, s
h
ow
n i
n
F
i
gu
re
3
.
I
n
th
is syste
m
, Paito
n
’
s bu
s is th
e sw
in
g n
o
d
e
an
d
o
t
h
e
r
s
ar
e th
e PV
n
o
d
e
s. Syste
m
cap
acity
is
1
0
0
,
000
M
VA.
T
h
e Tes
t
gene
rat
o
rs a
r
e Tan
j
un
g Jat
i
B
’
s p
o
w
er
pl
a
n
t
.
4.
2.
L
oad
fl
ow
C
a
l
c
ul
ati
o
n
Th
e sch
e
m
e
d
e
fin
itio
n
is un
balan
ced
cond
itio
n. Acco
rd
ing
to
th
is p
l
an
, u
s
in
g
EDSA
2
000
software
pr
o
g
ram
based
on
Ne
wt
o
n
-R
aph
s
o
n
m
e
t
hod we ca
n
get
t
h
e fl
o
w
cal
cu
l
a
t
i
on res
u
l
t
s
i
n
Fi
g
u
re
4.
Ta
bl
e 1
p
r
esen
ts a three-ph
ase
v
o
l
at
ge v
a
lu
es
o
f
g
e
n
e
rat
o
r term
in
al b
e
fo
re and
after lo
ad
ing
co
nd
itio
ns. It is sho
w
n
th
at v
o
ltag
e
variato
n
s
o
f
th
e g
e
n
e
rator termin
al in
fluenc
ed by unbalanced loa
d
and the phenom
enons are
happe
n
t at thei
r a
ngle
phases
whic
h a
r
e sw
un
g fr
o
m
th
eir
or
ig
in v
a
l
u
es.
(a) Sin
g
le-line diag
ram
(b
) Distrib
u
tio
n of
flo
w
calc
u
lation
Fi
gu
re
4.
The
50
0
k
V
E
H
V
J
a
m
a
l
i
Sy
st
em
Tab
l
e 1
.
Valu
es
of Gen
e
rator Term
in
al
Vo
ltag
e
s
Condition
Phase
Tanjung Jati B
Stand-
alone
a
1∠0
O
b
1∠120
O
c
1∠240
O
Connected gr
id an
d all of I
B
T
s
are balanced
a
1∠
1
2
O
b
1∠120
O
c
1∠240
O
Connected gr
id an
d all of I
B
T
s
ar
e 5% of unbalanced
Va =0.
273 V
Vb=0.
383 V Vc=
0.
334 V
a
1∠
13.5
O
b
1∠120
O
c
1∠240
O
Connected gr
id an
d all of I
B
T
s
ar
e 7.
5% of unbalanced
Va =0.
258 V
Vb=0.
408 V Vc=
0.
334 V
a
1∠
13.8
O
b
1∠120
O
c
1∠240
O
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1292 –
1303
1
298
4.
3.
Generator’s
Contri
buti
o
n Calculation
B
y
usi
n
g t
h
e
co
mmo
n
m
e
t
h
od
, t
h
e
Jam
a
li Sy
st
em
can
be
di
vi
de
d i
n
t
o
13 c
o
m
m
ons, s
u
ch a
s
6
com
m
ons of s
u
p
p
l
i
e
d en
er
gy
by
gene
rat
o
r f
r
om
t
h
e one b
u
s
and 7 c
o
m
m
ons
of s
u
ppl
i
e
d ene
r
gy
by
ge
nerat
o
r
fr
om
di
ffere
nt
bus
es,
sh
o
w
n
i
n
Fi
gu
re
5.
T
h
e det
a
i
l
o
f
l
i
n
e
-fl
o
w
i
s
s
h
o
w
n
i
n
Ta
bl
e
2.
A
not
her
i
n
fo
rm
at
i
on i
s
gene
rat
o
r d
o
m
a
i
n
sh
ow
n at
Tabl
e 3. Ta
bl
e
4 rep
r
ese
n
t
s
t
h
e i
n
f
o
rm
at
i
o
n
abo
u
t
common
, ra
n
k
an
d g
r
ou
p o
f
bus
. Meanwhi
l
e, Table 5 re
presents the inform
ation about
lin
k
. Figu
re 6
repre
s
ents the
sta
t
e-
graph
di
a
g
ram
t
h
at
desc
ri
bes
l
i
n
e fl
ow
bet
w
e
e
n
bu
ses.
Fi
gu
re 5.
Flow
s
and
com
m
on
s
u
nde
r
bal
a
nce
d
co
nd
itio
n
Fi
gu
re 6.
St
at
e-g
r
ap
h di
ag
ram for t
h
e
balanc
ed case
Tabl
e 2.
Li
ne
Fl
ow
Det
a
i
l
Fro
m
Bus
To Bus
Flo
w
(MW)
Fro
m
Bus
To Bus
Flo
w
(MW)
Bandun
g Selatan
M
a
ndir
a
ncang
-
375
Depok
T
a
sik
-
304
Bandun
g Selatan
Saguling
-
748
Gandul
Sur
a
lay
a
-
1960
Bekasi Cawang
90
Ga
ndul
Kem
b
angan
666
Bekasi Cibinon
g
-
820
Gr
ati W
e
st
Surabay
a
1024
Cawang M
u
ar
a
T
a
war
-
572
Gr
ati
Paiton
-
1128
Cibatu Cir
a
ta
-
516
Gr
esik
W
e
st
Surabay
a
65
Cibatu M
u
ar
an
Tawar
251
Kedir
i
Paiton
-
734
Cibinon
g
Cilegon
-
96
Kedir
i
Pedan
444
Cibinon
g
Depok
-
683
M
a
ndir
a
ncang
Ungar
a
n
-
410
Cibinon
g
M
u
ar
a
T
a
war
-
375
Pedan
T
a
sik
313
Cibinon
g
Saguling
253
W
e
st
Surabay
a
Ungar
a
n
392
Cilegon
Sur
a
lay
a
-
1250
T
a
njung Jati B
Ungar
a
n
821
Cir
a
ta Saguling
-
2
Ungar
a
n
Pedan
313
Depok
Gandul
-
701
Tabl
e 3.
D
o
m
a
i
n
I
n
f
o
rm
ati
on of
t
h
e Sy
st
em
Co
m
m
o
n
Rank
Buses
Co
m
m
o
n
Rank
Buses
1
2
Cilegon,
Gandul,
Kem
b
angan,
Sur
a
lay
a
8
2
Kedir
i
,
Paiton
2
1
W
e
st Bandung,
Mandir
a
ncang,
Saguling
9
1
Gr
esik
3
2 Cir
a
ta
10
2 W
e
st
Surabay
a
4
1
Cawang,
M
u
ara Tawar
11
1
T
a
njung jati B
5
4
Bekasi,
Cibinong,
Depok,
T
a
sik
12
8
Pedan
6
3 Cibatu
13
4 Ungar
a
n
7 1
Gr
ati
Tabl
e
4.
I
n
f
o
r
m
at
i
on o
f
t
h
e
C
o
m
m
on, R
a
n
k
, a
n
d B
u
s
Generator
Buses w
h
ich supplied by generator
Sur
a
lay
a
1-
2
Bekasi,
Cibinong,
Cilegon,
Depok,
Ga
ndul,
Kem
b
angan,
Pedan,
Suralaya,
and T
a
sik
Cirata
Cibatu, and Cirata
M
u
ar
a
T
a
war
Bekasi,
Cawang,
C
i
batu,
Cibinong,
Depok,
M
u
ar
a
T
a
war
,
Pedan, and T
a
sik
Saguling
W
e
st Bandung,
Cibatu,
Cir
a
ta, M
a
nd
ir
ancang,
Pedan,
Saguling,
and Unga
r
a
n
T
a
njung Jati B
T
a
njung Jati B,
Un
gar
a
n,
and Pedan
Grati
Grati,
Kediri
, Paito
n, Peda
n,
W
e
st Surabay
a
, and Ungar
a
n
Gr
esik
Gr
esik,
Pedan, West Sur
a
bay
a
,
and Sur
a
bay
a
Paiton
Kedir
i
,
Paiton,
and Pedan
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
The
Dy
na
mi
c
o
f
Sync
hr
o
n
o
u
s
Gene
rat
o
r
un
d
e
r U
n
b
a
l
ance
d
St
ea
dy
St
at
e
O
p
er
at
i
on…
(
S
u
g
i
a
rt
o K
a
di
m
a
n)
1
299
Tabl
e
5.
I
n
f
o
r
m
at
i
on o
f
t
h
e
Dom
a
i
n
o
f
Sy
s
t
em
Link No.
Fro
m
Co
mm
o
n
To Co
m
m
o
n
Link Flow
(MW)
Link No.
Fro
m
Co
mm
o
n
To Co
m
m
o
n
Link Flow
(M
W)
1
1
5
965 + 711
8
7
8
1128
2 2
3
2
9 7
10
1028
3 2
5
253
10
8
12
444
4 3
6
516
11
9
10
659
5
4
5
170 + 375
12
10
13
392
6 4
6
251
13
11
13
821
7 5
12
237
14
12
13
-
313
Tabl
e
6. C
ont
ri
but
i
o
n
Fact
o
r
o
f
Ta
nj
u
n
g
Jat
i
’
s Ge
nerat
o
r
Co
m
m
o
n
No.
Percen
tage of con
t
ribution
(
%
)
Co
m
m
o
n
No.
Percen
tage of con
t
ribution
(
%
)
1 0 8
0
2 24.
97
9
0
3 0
10
0
4 0
11
100
5 1.
81
12
28.
03
6 0
13
67.
79
7 0
The cal
cul
a
t
i
o
n of eac
h ge
ne
rat
o
r i
n
t
o
fl
o
w
s and l
o
a
d
s can
be do
ne usi
ng
Eq
uat
i
on (
8
).
The res
u
l
t
s
i
s
sho
w
n i
n
Ta
b
l
e 6.
Acc
o
r
d
i
n
g
t
o
Fi
g
u
re
4 a
n
d
Ta
bl
e
6, i
t
ca
n
be e
v
i
d
e
n
ced
t
h
at
West
B
a
n
d
u
n
g
, a
n
d
M
a
ndi
ra
nca
n
g
bu
ses (
c
o
mm
on
n
o
.
2
)
,
Pe
da
n b
u
s
(
common
n
o
.
1
2) a
n
d
Un
ga
ran
b
u
s (
com
m
on
no
. 13
)
ar
e
bus
es
w
h
i
c
h
sup
p
l
i
e
d
m
o
re ene
r
gy
t
h
e
n
ot
he
rs
by
Ta
n
j
u
n
g
Jat
i
B
b
u
s.
C
onse
q
ue
nt
l
y
,
W
e
st
B
a
nd
u
n
g
,
M
a
ndi
ra
nca
n
g
,
Pedan
,
an
d
Un
ga
ran
bus
e
s
are i
n
fl
uenc
i
ng b
u
ses t
h
at
cont
ri
but
e e
n
ergy
si
g
n
i
f
i
c
a
n
t
l
y
t
o
Tanjung Jati B
’
s
power pla
n
t.
4.
4.
Sync
hronous Generator Model
Verific
a
ti
on
Fi
gu
re 6.
Desi
gne
d Si
m
u
l
a
t
o
r
wi
t
h
G
U
I
Fi
gu
re 7.
The
m
a
i
n
wi
n
d
o
w
of
t
h
e de
vel
o
p
e
d
t
o
ol
Fig
u
r
e
8
.
Th
e
w
i
nd
ow
of
inser
tin
g th
e i
n
p
u
t
s
f
o
r
b
a
lan
c
ed
gen
e
r
a
t
o
r
and
un
b
a
lan
ced
inputs
Fig
u
r
e
9
.
PSS Tecqu
i
p
m
en
t
N
E
9
070
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1292 –
1303
1
300
A so
ft
ware
pa
ckage
whi
c
h em
bedded i
n
g
e
nerat
o
r vi
rt
ua
l
l
a
borat
o
r
y
and a
ppl
i
e
d M
a
t
l
a
b’s G
U
I
facilities h
a
s
b
een created
fo
r an
alysis sy
n
c
hro
nou
s
g
e
nerato
r und
er un
b
a
lan
ced stead
y
-state cond
i
tio
n
s
(Fi
g
ure
6).
M
a
t
l
a
b’s
GU
I i
s
a g
r
ap
hi
cal
di
spl
a
y
t
h
at
c
ont
a
i
ns
devices
,
or com
p
onents, t
h
at e
n
able a
user t
o
p
e
rform
in
teractiv
e task
s [21
]
. As an
ex
am
p
l
e
o
f
u
s
ing Matlab
’
s GUI cap
ab
ilities,
m
e
n
u
and
p
l
o
ttin
g
com
m
a
nds a
r
e
i
m
pl
em
ent
e
d i
n
a
scri
pt
fi
l
e
t
o
pr
ovi
d
e
in
teractiv
e wi
n
dows.
Th
e main
m
e
n
u
,
wh
ich
is
d
i
sp
layed af
ter ru
nn
ing
t
h
e f
i
l
e
, sh
ow
n in Fi
g
u
r
e
7
and
Fi
gu
r
e
8.
The
veri
fi
cat
i
o
n o
f
t
h
e ge
ne
ra
t
o
r m
odel
i
s
j
u
dge
d t
h
r
o
u
g
h
c
o
m
p
ari
ng
bet
w
een
gene
rat
o
r’
s res
p
o
n
by
PSS Tec
qui
pm
ent NE
9070, s
h
own in Figure 9 and
by th
e
propose
d
sim
u
lator
unde
r no load, bala
nc
ed, and
u
n
b
a
lan
c
ed
con
d
ition
s
, resp
ectiv
ely.
Fig
u
r
e
10
. Th
e ou
tpu
t
of
PSS
Tecqu
i
p
m
en
t N
E
90
70
Fig
u
r
e
11
.
Ou
tp
u
t
s of
th
e PSS Tecqu
i
p
m
en
t N
E
90
70
Un
de
r no
l
o
a
d
,
t
h
e out
put
re
spo
n
s
o
f
P
SS Tech
qui
pm
ent
NE
90
7
0
a
r
e n
o
n
-
si
n
u
s
o
i
d
al
wi
t
h
vari
e
d
ex
citatio
n
s
, even
tho
ugh
th
e
P.F
v
a
lu
e is
m
o
re th
an
0.8, sh
own
in
Fi
gu
re
10
. Th
e gen
e
rat
o
r’s ou
t
p
u
t
s are
always
no
n-sinu
so
i
d
al u
n
d
e
r
stan
d
a
lon
e
op
eratio
n
.
Th
e
waveform
o
f
it will ch
an
g
e
in
to sin
u
s
o
i
d
a
l fo
rm
when
the ge
ne
rator i
s
connected t
o
the grids
.
Th
e
r
e
su
lts of pr
opo
sed g
e
ner
a
to
r’
s m
o
d
e
l
sim
u
lat
i
on c
o
nsi
d
e
r
i
n
g P
.
F
vari
at
i
o
ns a
r
e
descri
bed
i
n
Fi
gu
re
12
. It
i
s
sh
ow
n t
h
at
o
u
t
put
re
sp
o
n
s ar
e i
n
n
o
n
-si
n
u
s
oi
dal
f
o
rm
s al
tho
u
g
h
t
h
e
val
u
e of
P.F
exci
t
a
t
i
on i
s
reache
d
up
to 0.9.
C
o
m
p
aring bot
h
Fi
gure 10
and Figure
12
concludes
that the
output
respons of
propos
ed
gene
rat
o
r m
o
d
e
l
have
si
m
i
l
a
r t
r
en
d t
o
t
h
e
o
u
t
put
o
f
P
SS Tec
h
q
u
i
p
m
e
nt
NE
90
7
0
.
Fi
gu
re 1
1
p
r
es
ent
s
t
h
e out
put
resp
ons
of PS
S Techq
u
i
p
m
e
n NE
90
7
0
.
When sy
nc
hr
o
n
o
u
s gene
rat
o
r
is u
n
d
e
r
u
n
b
a
lan
ced
lo
ad
co
nd
itio
n, its stead
y state resp
on
will o
s
cill
ates less th
an
u
n
d
e
r b
a
lanced
lo
ad
co
nd
itio
n. Th
e o
s
cillatio
n
m
a
g
n
itud
e
o
f
un
balan
ced
load
du
ri
n
g
tran
sien
t co
nd
ion
is big
g
e
r th
an
b
a
l
a
n
c
ed
lo
ad
s coun
terpart.
Fi
gu
re
1
2
. T
h
e
o
u
t
p
ut
o
f
pr
o
p
o
se
d st
an
dal
o
n
e
ge
n
Fi
gi
re
1
3
. T
h
e
out
put
s
o
f
t
h
e
pr
o
pose
d
c
o
nn
ect
ed
gen
Thi
s
c
o
n
d
i
t
i
o
n
i
s
al
so
occ
u
r
e
d
du
ri
n
g
si
m
u
l
a
t
i
o
n
o
f
t
h
e
pr
o
pose
d
sy
nc
hr
o
n
o
u
s
m
o
d
e
l
sh
ow
n i
n
Fig
u
re 13
. The o
s
cillatio
n
o
f
stato
r
vo
ltage o
f
syn
c
h
r
on
ou
s g
e
n
e
rato
r d
u
r
i
n
g
in
terco
n
n
ecting
with
7
.
5%
un
bal
a
nce
d
g
r
i
d
i
s
bi
gge
r t
h
a
n
i
t
i
s
connect
e
d
t
o
bal
a
nc
e
d
gri
d
. C
oncl
u
d
e
l
y
, t
h
e pro
p
o
s
e
d m
odel
i
s
val
i
d
as
a
syn
c
hr
ono
us
gen
e
r
a
t
o
r
test m
o
d
e
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
The
Dy
na
mi
c
o
f
Sync
hr
o
n
o
u
s
Gene
rat
o
r
un
d
e
r U
n
b
a
l
ance
d
St
ea
dy
St
at
e
O
p
er
at
i
on…
(
S
u
g
i
a
rt
o K
a
di
m
a
n)
1
301
4.
5.
Dynamic
Sim
u
lati
on
of Un
ba
lace
d S
t
e
a
d
y
-s
ta
te
C
o
ndit
i
on
Accord
ing
to th
e Tab
l
e
1
,
it
was seen
t
h
at a th
ree-
phase
unbala
nced loa
d
(of t
h
e
gri
d
s)
causes a
s
h
ift
i
n
t
h
e a
ngl
e
of
pha
se-
a
of
g
e
n
e
rat
o
r term
in
al at stead
y state co
nd
itio
n. Th
e p
e
rcen
tag
e
o
f
un
b
a
lan
ced
lo
ad
is
p
r
op
ortio
n
a
l t
o
th
e
v
a
lu
e
of
phase a
n
gle shi
f
t.
(Stato
r vo
ltag
e
m
a
g
n
itu
d
e
)
(St
a
t
o
r
cu
rre
nt
m
a
gni
t
ude
)
(Ge
n
erate
d
acti
v
e
powe
r)
(
G
en
e
r
a
t
ed
r
e
ac
tiv
e
po
w
e
r
)
Fig
u
r
e
14
. Th
e stead
y-
state
dyn
amic o
f
vo
ltag
e
, cur
r
e
n
t
, an
d pow
er of
sy
n
c
hro
nou
s
g
e
ner
a
to
r
An in
crease i
n
th
e p
e
rcen
tag
e
o
f
un
b
a
lanced
lo
ad
on
t
h
e en
tire IBTs o
f
th
e
grid
s
b
y
5
%
will
increase in the
phase
-s
hift angle of
1.5
O
;
a f
u
rt
her
perce
n
t
a
ge i
n
cre
a
se by
2.
5% w
o
ul
d
on
l
y
i
n
crease t
h
e shi
f
t
of the
phase a
n
gle of
0.3
O
.
The
un
bal
a
nc
e
d
l
o
a
d
doe
s n
o
t
affect
t
o
vari
abl
e
s o
f
gene
ra
t
o
r,
nam
e
l
y
st
at
or
vol
t
a
ge
m
a
gni
t
u
de a
n
d
t
h
e r
o
t
a
t
i
onal
s
p
eed
o
f
t
h
e r
o
t
o
r
.
H
o
we
ve
r, a
si
gni
fi
ca
nt
i
n
f
l
uence
occ
u
rs i
n
ot
her
vari
a
b
l
e
s t
h
at
are ge
n
e
rat
o
r
st
at
or cu
rre
nt
,
gene
rat
e
d act
i
v
e po
wer a
n
d re
act
i
v
e po
we
r.
Gene
rated acti
v
e power
has the greatest infl
uence
on
t
h
e e
ffect
s
o
f
7.
5%
un
bal
a
n
ce t
h
at
i
s
up
t
o
0.
52
p
.
u
.
In t
h
e phase
-
a
,
t
h
e g
r
i
d
e
xpe
r
i
enced a m
o
m
e
nt
o
f
l
o
a
d
i
n
g,
bot
h i
n
bal
a
nc
e and
u
nbal
a
nc
e;
t
h
e zero
-
axi
s
i
n
crease
s
fr
om
poi
nt
0 p
.
u t
o
t
h
e
poi
nt
0.6
p.
u. I
n
c
o
nt
rast
, b
o
t
h
t
h
e phase
-
b
a
n
d pha
se-
c
are ac
tually
d
eclin
ing
,
from
th
e
po
in
t 0
p.u
t
o
-0.6
p.u.
Evaluation Warning : The document was created with Spire.PDF for Python.