TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.1, Jan
uary 20
14
, pp. 20~ 28
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i1.3379
20
Re
cei
v
ed
Jun
e
5, 2013; Re
vised July
8,
2013; Accept
ed Augu
st 26
, 2013
Transient Stability Analysis of Grid-connected Wind
Turbines with Front-end Speed Control via Information
Entropy
Energy Function Method
Haiy
ing Dong*
1,a
, Shuaibing Li
1,b
, Shu
b
ao Li
2
, Hong
w
e
i Li
1,c
1
School of Aut
o
matio
n
& Elec
trical Eng
i
ne
eri
ng, Lanz
ho
u Ji
aoton
g Un
ivers
i
t
y
Anni
ng W
e
st Road, 73
00
70 L
anzh
ou, Ch
ina,
+
86-093
1-4
9
5
610
6
2
Lanzh
ou El
ectric Corpor
atio
n
No.66, Min
l
e R
oad, 73
00
50, L
anzh
ou, Ch
ina,
+
86-093
1-2
8
6
695
1-80
10
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: h
y
don
g@ma
i
l
.lzjtu.cn
a
, lishu
aibi
ng
11
05@
1
63.com
b
,
liho
n
g
w
e
i
@mai
l.lzjtu.cn
c
A
b
st
r
a
ct
Accordi
ng to the char
acterist
ics like ti
me-c
onsu
m
ing a
n
d
can not be q
uantitativ
ely a
naly
z
e
d
o
f
tim
e
domain s
i
mulation in
power system transient stab
ility analysis, a
direct
m
e
thod using
infor
m
ation
entropy c
o
mbi
ned w
i
th transi
ent en
ergy fun
c
tion
meth
od
is
propos
ed i
n
th
is pap
er to an
a
l
y
z
e
the trans
ie
nt
stability
of w
i
n
d
pow
er syste
m
equ
ip
ed w
i
th front
-e
nd sp
eed c
ontro
lle
d
w
i
nd turb
ines
(FSCWT) w
i
th
synchro
nous
g
ener
ators. In which, t
he syste
m
ki
netic e
ner
gy an
d pote
n
ti
al en
ergy ar
e u
s
ed as i
n
for
m
a
t
io
n
source to
mak
eup inf
o
rmation entropy
funct
i
on, then,
a theoret
ic
al
analy
s
is of system
transient stability is
conducted. Based on this, sim
u
la
tions ar
e
carried
out in IEEE 5-ma
chine 14-
bus system
compar
ed wit
h
the ti
me
do
ma
in
’
s
, w
h
ich
veri
fied th
e co
nsis
tency of
i
n
for
m
ati
on
entro
py
en
ergy fu
ncti
on (IEEF
)
met
hod
and
ti
me
do
ma
in
ana
lysis.
Re
sults sh
ow
that
it is
mo
re
i
n
tui
t
ively
and
effe
ctively to
us
e I
EEF
method
f
o
r
wind power system
transient
ana
lysis equiped with FSCWT.
Ke
y
w
ords
: transie
nt stability
,
front-end
sp
eed co
ntroll
ed
w
i
nd turbine
(FSCW
T
), informati
on e
n
trop
y,
ener
gy functio
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With an
ever-incre
asi
ng wind po
we
r pe
ntrati
on
into power syste
m
, the power syste
m
performance
especi
ally transient stabilit
y is infl
uenced inevitablely
[1-5].
The wind
power syst
em
transi
ent sta
b
ility under
se
vere g
r
id faul
t is sun
d
ry, which i
s
affect
ed by diffiere
n
t types of wi
nd
turbine
s
, va
ri
ous gri
d
lo
a
d
mod
e
ls an
d un
equ
al g
r
id-conn
ecte
d
ca
pa
city. The
conve
n
tio
nal
doubly fed in
ductio
n
gen
e
r
ator
(DFIG)
and di
re
ctly
drive syn
c
h
r
o
nou
s gen
erator (DDS
G)
with
back-end inv
e
rter
woul
d consume con
s
idera
b
le re
act
i
ve powe
r
form gird si
de o
n
ce a
severe grid
fault occ
u
rred [6, 7], the FSCWTs
use eletric
a
lly
exc
i
t
ed
s
y
s
n
c
h
ronous
genertors
(EESG) whic
h
can a
c
h
e
vie excelle
nt perf
o
rma
n
ce like
thermal po
wer ge
nerators, relatively sp
eaki
ng. As th
e
FSCWT i
s
of
goo
d gi
rd
ad
aptability an
d
fault
ri
de th
o
ugh
ca
pa
city, ha
s
been
a
p
p
lied
gra
duall
y
.
Therefore, to make
study on tran
sient
stability of FSCWT
with gr
id-connected is
important and
of great sig
n
ifican
ce to the
stabl
e o
peration of the con
necte
d grid.
There have
many scholars investigated on t
r
ansient stability of
wi
nd
power system, in
pape
r [8, 9], the mathem
atical mod
e
ls of
con
s
tant sp
e
ed wind tu
rbi
ne (CS
W
T
)
, DFIG and
DDSG
are e
s
tabili
sh
ed re
sp
ectiv
e
ly and the
critical faul
t clea
ring time
(CCT) u
nde
r tra
s
ient fau
l
t is
determi
ned fo
r tran
sient sta
b
ility analysis in time
domain by simulation,
the generator paramet
er
effect of turbi
ne tran
sie
n
t stability is discussed,
a
dditi
onally. Refe
rence [10] an
alyzed th
e po
wer
system trai
sent stability with an un
consta
nt
voltage-d
epe
nde
n
t
load into energy analy
s
is
inco
rpo
r
ating
comp
re
hen
si
ve
load ch
ara
c
teri
stics
a
n
d
achieved a
d
e
sired re
sult while refe
ren
c
e
[11] con
s
ide
r
ed a dynami
c
load model f
o
r tran
sie
n
t function
con
s
truction in tra
n
s
ient an
anlysi
s
.
As the tim
e
domain
si
mul
a
tion meth
od
emph
asi
s
o
n
qu
alitative analysi
s
, the
ene
rgy
function m
e
th
od can a
c
hie
v
e a qualitativ
e ann
alysi
s
. In refe
ren
c
e [
12], a com
b
in
ation of coin
ci
de
prob
ability function
with transi
ent en
erg
y
func
tion m
e
thod is mad
e
and a
qua
ntitative method
for
transi
ent sta
b
ility analysi
s
is p
r
op
ose
d
from the
probability perspect
ive. In this paper,
th
e
transi
ent stab
ility of power grid with FS
CWT conne
cte
d
in system e
nergy a
s
pe
ct is ann
alyzed
by
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 20 – 28
21
makin
g
a co
mbination of i
n
formatio
n e
n
tropy and
e
nergy fun
c
tio
n
methon p
r
o
posed in [13]
an
d
a time domai
n simulatio
n
is used to veri
fy the corre
ct
ness of pro
p
o
s
ed meth
od.
2. Modeling of FSCSG an
d Po
w
e
r grid
The structu
r
e
of FSCWT can be seen in
Figur
e 1, whi
c
h is
comp
osed by a wind
whe
e
l,
a main ge
arb
o
x, a hydro-d
y
namically
co
ntro
lled
gea
rbox Win
D
rive
and an EES
G as
sho
w
n i
n
figure 2.
M
a
i
n
G
ear
Wi
n
D
r
i
v
e
SG
Grid
Figure 1. Structure of FS
CWT
Figure 2. Structure of Excit
a
tion System
From
refe
ren
c
e [14], we can kno
w
the
relation
shi
p
s
among th
e variabl
e wi
nd
spe
ed,
con
s
tant ge
n
e
rato
r roto
r speed, turbi
ne
spe
ed an
d wi
nd wh
eel spe
ed:
21
2
3
=n
=n
=(1
+
)n
tG
B
R
T
nn
(1)
therefo
r
e, the
torque bal
an
ce eq
uation
can be written as:
1
3
jR
qT
tq
j
B
G
MM
MM
MMM
M
M
(2)
whe
r
e
T
M
,
B
M
and
G
M
stand for the
turbine torq
u
e
, the pumb whe
e
l torqu
e
and the gen
e
r
ator
input torqu
e
, respe
c
tively
.
t
M
,
q
M
and
j
M
sepa
rat
e
ly stand for the torqu
e
of sun gea
r, ring gea
r
and the pla
n
e
t
ary gear, whi
c
h satisfy:
22
::
1
:
:
(
1
)
tq
j
MM
M
(3)
The gen
erato
r
input po
we
r can b
e
derive
d
from equ
ation (1
), (2) a
n
d
equatio
n (3
):
12
3
GG
G
R
R
B
B
B
B
PM
M
M
M
(4)
whe
r
e
1
,
3
stan
d for the tran
smissio
n
ef
ficiency from
wi
nd roto
r to the planeta
r
y carri
er a
n
d
the transmi
ssion ef
ficien
cy from cente
r
wheel to ring g
ear
, sepe
ratel
y
while
2
is the
ef
fcience of
hydro
-
dynami
c
torqu
e
co
nverter.
2.1. Electrica
lly
Excited Sy
nchronous Gener
a
tor M
odel
As the
FSCWT
uses an
EESG, the excitation
sy
st
em shoul
d be taken i
n
to
accunt
of
dynamic m
o
d
e
l, the rotor
motion equ
ation and
stator
voltage equ
ation ca
n be de
scribe
d as:
1
()
s
me
d
dt
d
PP
D
dt
M
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Transient Stability Analysi
s
of Grid-connected
Wind T
u
rbines
with Front
-end ... (Hai
ying
Dong)
22
and
0
cos
q
dd
d
dq
f
dd
dE
xx
x
TE
U
U
dt
x
x
(6)
whe
r
e
D i
s
th
e dam
ping
co
efficient,
is rotor a
ngul
ar,
0
2
s
f
is the
refere
nce
freq
uen
cy. M
is ine
r
tia time
co
nsta
nt of E
ESG,
is the
relative ang
ul
ar
spe
ed in
p.
u..
m
P
and
e
P
s
t
a
nd fo
r
th
e
mech
ani
cal p
o
we
r an
d the
elect
r
oma
g
n
e
tic po
we
r, resp
ectively.
U
is stato
r
volta
ge an
d
f
U
is
the field volt
age,
q
E
stan
ds for tran
sient
voltage.
d
x
a
nd
d
x
are
rea
c
tance
an
d transi
ent
rea
c
tan
c
e of d-axis.
The output p
o
we
r equ
atio
n is:
2
2
11
sin
(
)
s
in
2
2
sin
s
in
2
(c
o
s
)
2
q
e
dq
d
eq
dq
UE
U
P
xx
x
UU
QE
U
x
x
(7)
w
h
er
e
e
Q
is
the output rea
c
tive
po
we
r,
q
E
an
d
q
x
stan
d for i
ndu
ced
pote
n
t
ial and
rea
c
tance o
f
q-axis.
2.2. Grid Model
For ge
neral p
o
we
r syste
m
, it can be de
scrib
ed by DA
E as follows [16]:
(,
)
0(
,
)
x
fx
y
gx
y
(8)
w
h
er
e
x
is a
contin
uou
s v
a
riabl
e a
bout
time a
nd
re
p
r
esents for
continuo
us dy
namic p
r
o
c
e
s
s of
gene
rato
r,
y
stand
s fo
r
alg
ebrai
c varibl
e
s
can
mutate
d like n
ode
v
o
ltage, p
h
a
s
e
angl
e a
nd
et
c.,
and
u
is
control variable. A
n
N nod
e po
wer g
r
id
can
be expre
s
sed
as:
11
12
1
21
22
2
12
n
n
nn
n
n
YY
Y
YY
Y
YY
Y
11
22
nn
UI
UI
UI
(9)
whe
r
e
ii
ii
ii
YG
j
B
stan
ds fo
r self
admittance o
f
node i,
ik
ik
i
k
YG
j
B
is the m
u
tua
l
admittance b
e
twee
n nod
e i and nod
e k.
i
U
is the nod
e voltage vecto
r
of node i to th
e gro
und,
i
I
is the cu
rrent
vector of no
de i inflows t
o
grid. The
r
e
f
or, the powe
r
injecte
d
into node i ca
n
be
descri
bed a
s
:
1
1
[
s
in
(
)
co
s(
)]
[s
i
n
(
)
c
o
s
(
)
]
n
ii
k
i
k
i
k
i
k
i
k
i
k
k
n
ii
k
i
k
i
k
i
k
i
k
i
k
k
PU
U
B
U
U
G
QU
U
G
U
U
B
(10
)
For ea
sy to analysi
s
, seco
nd orde
r model
s are
used fo
r the re
st syn
c
hrono
us
gene
rato
rs i
n
sy
stem, th
e ge
nerator
model
ca
n be conve
r
te
d
to cente
r
of
inertia
(COI)
coo
r
din
a
te in con
s
id
eratio
n
of relative rotor ang
ula
r
an
d angul
ar spe
ed as foll
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 20 – 28
23
i
si
ii
mi
e
i
i
i
COI
T
d
dt
dM
PP
D
P
dt
M
(11
)
whe
r
e
n
2
ei
i
i
i
i
j
i
j
i
j
i
j
i
j
i
j
j=
1
,
j
i
P
=
E
G
+
[
EE
B
s
i
n
(
f
-
f
)
+
EE
G
c
o
s
(
f
-
f
)
]
, in which
i
an
d
i
resp
re
sent fo
r
rotor a
ngul
ar
and an
gula
r
speed a
nd
ii
C
O
I
, where
COI
is the weighted me
an
of
i
.
3. Transien
t Stabilit
y
Analy
s
is Based on Entrop
y
Function
3.1. Configur
ation of Ener
g
y
Function
In wind p
o
wer sy
stem in
cludi
ng FSCWT
s
, def
ine
the kineti
c
e
nergy of
syn
c
hrono
us
gene
rato
r i is
ki
V
, by using eq
uation (5
), we
can get
2
1
=
2
ki
i
i
VM
(12
)
and the sy
ste
m
kinetic e
n
e
r
gy is:
2
11
1
=
2
nn
kk
i
i
i
ii
VV
M
(13
)
whe
r
e
i
is th
e differen
c
e
of rotor ang
u
l
ar sp
eed an
d synchro
n
o
u
s ang
ula
r
speed of SG i.
Whe
n
the fau
l
t is cleared, the tran
sient kinetic en
ergy
of SG i is:
00
2
1
|=
(
)
2
ci
ci
ii
II
i
ki
c
i
i
i
i
m
i
e
i
i
d
VM
M
d
P
P
d
dt
(14
)
Whe
n
the
sy
stem i
s
stea
dy
,
0
ki
V
as
0
i
. By
usin
g
0
as th
e pote
n
tial e
nergy
referen
c
e poi
nt, the potential energy of SG i can be
written a
s
:
0
=(
)
i
i
III
pi
ei
mi
i
VP
P
d
(15
)
From e
quatio
n (14
)
and (1
5), the ene
rg
y function of gene
rato
r i at any moment is:
0
2
1
=(
)
2
i
i
III
ip
i
k
i
i
i
e
i
m
i
i
VV
V
M
P
P
d
(16
)
The sy
stem
transi
ent ki
n
e
tic ene
rgy
,
t
r
an
sient p
o
te
ntial ene
rgy and tra
n
si
ent
energ
y
sho
w
n a
s
eq
uation (1
2), (15) an
d 16 ca
n be co
nverte
d to COI coo
r
dinate:
2
1
=
2
ki
i
i
VM
(17
)
0
=(
)
i
i
i
pi
m
i
e
i
C
O
I
i
T
M
VP
P
P
d
M
(18
)
0
2
1
=(
)
2
i
i
i
ii
i
m
i
e
i
C
O
I
i
T
M
VM
P
P
P
d
M
(19
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Transient Stability Analysi
s
of Grid-connected
Wind T
u
rbines
with Front
-end ... (Hai
ying
Dong)
24
Whe
r
e,
ii
C
O
I
, wh
ere
CO
I
is the weighted me
a
n
of
i
,
T
M
is the inertial time
con
s
tant sum
of all genera
t
ors in syste
m
. The por
ce
dure for syste
m
transient e
nerfy calculat
ion
can b
e
se
en i
n
Figure 3.
1
&0
nn
pp
p
VV
V
1
n
cr
p
VV
|
cr
k
c
VV
Figure 3. Steps of transien
t analysis using PEBS method
3.2. Configur
ation of Infor
m
ation Entr
op
y
Functio
n
W
e
h
a
ve defi
ned info
rmati
on stri
ctly in term
s
of the p
r
oba
bilities
of
events. Th
erefore,
let
us sup
p
o
s
e
t
hat
we have a
set of
pro
b
abilities (a probability
di
stri
bution).
12
{,
,
,
}
n
Pp
p
p
, W
e
define the ent
ropy of the distributio
n P
by [18]
：
1
1
()
l
n
(
)
n
i
i
i
HP
p
p
(20
)
As is sh
own above,
()
HP
can
be use
d
for d
e
scribi
ng verage un
ce
rtain
t
y of probabili
ty
sy
stem, whe
r
e
i
p
is the i
n
formation
sou
r
ce. Each
pa
rt
of the defin
e
d
sy
stem
re
mains a
stabl
e
state in
certai
n rule
s a
s
th
e
r
e
are
correla
t
ions
of e
a
ch
part i
n
p
o
wer
system.
On
ce
a
seve
re
faul
t
occurre
d
, the stable
state would be b
r
o
k
e
n
: the sy
stem
would b
e
co
me cha
o
s if the system te
nds
to instability
and the
syst
em inform
ation entropy
would in
crea
se
, otherwi
se
would d
e
crea
se.
If
we have a
co
ntinuou
s rath
er than di
scre
te proba
bility distrib
u
tion
()
Px
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 20 – 28
25
1
()
(
)
l
n
(
)
()
HP
P
x
d
x
Px
(21
)
In this pap
er,
the power system kin
e
tic energy
k
V
and
potential en
ergy
p
V
is used
as
informatio
n source
1
i
p
an
d
2
i
p
to construct informat
ion
ent
ropy fun
c
tion
()
HP
, thus, to
any
SG
i in system, we can d
e
fine:
1
ki
i
ki
p
i
V
p
VV
，
2
pi
i
ki
p
i
V
p
VV
To a sta
b
le system, there
exsit
1
[0
,
1
]
i
p
,
2
[0
,
1
]
i
p
. According to Gib
b
s inequality, we
know that:
0(
)
l
n
2
HP
n
, the ki
netic e
nergy
an
d p
o
tential e
nergy sati
sfy
0
ki
p
i
VV
and
()
0
HP
when the sy
stem is co
nverge
nt. Once
a severe fau
l
t is cleare
d
, for each gen
erato
r
,
the prob
abilit
y is equal for
system to re
main stabl
e o
r
unsta
ble an
d
12
12
ii
pp
,
()
l
n
2
HP
n
,
accordingly.
During the transient fault,
the potential energy boundary
surface
(PEBS) method [17],
whi
c
h can b
e
se
scribe
d like that: the system
w
oul
d start form t
he stabl
e eq
uilibriu
m
poin
t
of
stable
statu
s
,
if the traj
ect
o
ry is in
side
of
potential
energy bo
un
dary, then
th
e sy
stem g
o
e
s
stable due
to
damping
effect , or
un
sta
b
le if outsi
de
of
potential e
nergy b
oun
d
a
ry. The trasi
ent
stability analy
s
is p
r
o
c
e
ss u
s
ing IEEF me
thod ca
n be g
eneralized a
s
follows:
(1)
cal
c
ulate t
he po
wer flo
w
before syst
em fault.
(2) tracking
system traje
c
tory unde
r sustained fault a
nd cal
c
ul
ate
i
k
V
and
pi
V
real-time
.
(3) cal
c
ulate
()
HP
by using
i
k
V
and
pi
V
.
(4) if
()
l
n
2
HP
n
, stop ca
lculatin
g, retu
rn
()
HP
and calcul
ation time
t
.
Figure 4. IEEE 5-miachine
14-b
u
s
syste
m
4. Simulations and Case
Studies
Form eq
uatio
n (17)
we ca
n kown that whe
n
system
fault occu
rre
d, the kinetic energy
increme
n
tal of generators losing syn
c
hroni
zatio
n
a
r
e more gre
a
ter than the one
s kee
p
ing
in
synchro
n
ization, so, the
informatio
n e
n
tropy
keep
s increa
sing.
Otherwise, the informatio
n
entropy woul
d fluctuate. T
o
a
n
machin
e system, form equation
(19) an
d (2
0)
we can dete
r
mine
that
i
k
V
an
d
pi
V
wo
uld
kee
p
in
creasi
ng if th
e
system
lose synchro
n
ization
a
nd goe
s unsta
ble
,
then the syst
em pro
babilit
y is the bigge
st with inform
ation entro
py
()
l
n
2
HP
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Transient Stability Analysi
s
of Grid-connected
Wind T
u
rbines
with Front
-end ... (Hai
ying
Dong)
26
In this paper
, the IEEE 5-mac
h
ine 14-
b
us
s
y
s
t
em is
us
ed for
s
i
mulation analys
is
whic
h
scheme
can
be
see
n
in
Fi
gure
4, fi
rstly. In
COI
coo
r
d
i
nate, a
s
th
e
kineti
c
e
n
e
r
g
y
increa
se
s
o
f
an
unsta
ble, the
system t
r
an
si
ent sta
b
ility can be
dete
r
m
i
ned by i
n
formation e
n
tro
p
y after a
severe
fault. In order to sho
w
n th
e
relatio
n
shio
of tran
sient
st
ability and
sy
stem inf
o
rmat
ion e
n
tropy, t
he
IEEE 3-machine 9-bus
syst
em and the I
EEE 10-ma
chine 39-bus system is studed, behind.
Figure 5. Information e
n
tro
p
y of IEEE 5-machi
ne 14
-b
us
Figure 6. Power
angle of IEEE 5-
mac
h
ine 14-bus
Figure 5
sho
w
n
s
the
syst
em informatio
n entropy
()
HP
with fault time lasted for 518ms
and 519m
s of
IEEE
5-machine 14-bu
s
sytem during a three
phase fault. And
Figure 6 showns
the traditional
time domain
simulation
with a same fa
ult, it can be see
n
that the IEEF method
has a g
ood
consi
s
ten
c
y wi
th tme domai
n simulatio
n
.
Figure 7. Information e
n
tro
p
y of IEEE 3-machi
ne 9
-
bu
s
Figure 7
s
howns
the information entr
opy of
the IEEE 3-
mac
h
ine
9-
bus
s
y
s
t
em with fault
clea
r time 3
93ms
(the g
r
een lin
e) a
n
d
395m
s (th
e
purpl
e line
)
and Fig
u
re
8 sho
w
n
s
the
infor
m
ation entr
opy of the IEEE 10-
mac
h
ine 39-
b
us s
y
s
t
em
with fault c
l
ear
time 230ms (
t
he
gree
n lin
e) a
nd 2
32m
s
(t
he p
u
rple li
n
e
). It
can
be
se
en
that, if inform
ation
entropy
cl
ose
r
to
ln
2
n
, the system goe
s to unst
able, otherwi
se re
ma
in
s a
stable state
with inform
ation entro
py
var
i
es
.
0
0.
5
1.
0
1.
5
2.
0
2.5
3.0
3.5
0
1
2
3
4
ti
m
e
s
(
s
)
I
n
f
o
r
m
a
t
i
o
n E
n
t
r
op
y
H
(
P
)
(
p
u)
S2
y
m
a
x
S1
0
10
20
30
40
50
60
70
80
-1
0
1
2
3
4
ti
m
e
s
(
s
)
P
o
w
e
r
A
ngel
d
e
l
t
a (
pu)
F
a
u
l
t C
l
ea
r
T
i
m
e
: 51
8m
s
0
10
20
40
60
80
-0
.
4
-0
.
2
0
0.2
0.4
0.6
ti
m
e
s
(
s
)
P
o
w
e
r A
n
ge
l
de
l
t
a
(p
u)
F
aul
t c
l
ear
T
i
m
e
:519m
s
0.5
1.
0
1.
5
2.
0
2.5
3.0
3.5
0
0.
5
1
1.
5
2
2.
5
ti
m
e
s
(
s
)
In
fo
r
m
a
t
i
o
n
E
n
tr
o
p
y
H
(
P
)
(
p
u
)
S1
S2
y
m
a
x
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 20 – 28
27
Figure 8. Information e
n
tro
p
y of IEEE 10-ma
chin
e 39-bus
5. Conclusio
n
s
The tran
sie
n
t stability is cruci
a
l to the stabl
e o
peration of wind p
o
we
r syste
m
. In this
pape
r, the en
ergy fun
c
tion
method i
s
combine
d
with
information
entropy, an
d the pro
c
e
dure of
usin
g thi
s
p
r
o
posed m
e
tho
d
is illu
strate
d. Nu
meri
ca
l
simulatio
n
ve
rifies the vali
dity effectiven
ess
and
co
rrectn
ess of
the
a
nalysi
s
re
sult in
com
apri
s
ion
with tim
e
do
main
si
mulation,
whi
c
h
sho
w
n
s
th
at the IEEF m
e
thod i
s
vali
d f
o
r tran
sient
stability analysis in
po
we
r
system in
cludi
ng
FSCW
Ts a
n
d
the IEEF method is mo
re i
n
tuitiv
e in reflecting the
system transi
ent behavio
r.
Ackn
o
w
l
e
dg
ement
This
wo
rk is
sup
porte
d by
Nation
al Hi
g
h
-t
ech
Devel
opment P
r
og
ram
(86
3
Project) of
Chin
a: Key
Tech
nolo
g
ie
s Re
se
arch
o
n
Desi
gn a
n
d
Man
u
factu
r
e of
Gri
d
-conne
cted
Wi
nd
Turbi
n
e
s
with
Front-end Sp
eed Controll
e
d
Synchrono
us Ge
nerator
(201
2AA052
9
02).
Referen
ces
[1]
Lib
ao S
h
i, S
h
i
q
ia
ng
Dai,
Li
a
ngzh
o
n
g
Ya
o, et a
l
. Impact
of W
i
nd
F
a
rm
s of DF
IG T
y
p
e
o
n
P
o
w
e
r
S
y
stem T
r
ansient Stabil
i
t
y
.
El
ectromag
netic
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is & App
licatio
ns
. 20
10;
2: 475-48
1.
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Eel-H
w
a
n
K
i
m, Jae-Ho
ng K
i
m, Se-Ho Kim,
et al
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i
nd F
a
rms in th
e Jej
u
Islan
d
Po
w
e
r S
y
stem.
Systems Jour
nal, IEEE
. 201
2; 6(1): 134-1
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Durga Gautam, Vijay
Vittal,
T
e
rry
H
a
rb
our.
Impact of Inc
r
ease
d
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netr
a
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of DF
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i
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u
rbine Gener
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r
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ilit
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urn
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uter
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ontr
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hang
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ngg
uan
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hen S
h
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y
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g, et al.
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e T
r
ansi
ent B
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d
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e
r System
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i
th Lar
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a
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u
a
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i
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nra
n
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i
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d
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n
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r Syte
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aj
othi
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a
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i
a
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i
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d
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u
rbine
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i
t
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nchro
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natio
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urn
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uter
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al Engi
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n,
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g
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u
nction-B
a
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o
w
e
r
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stem T
r
ansi
ent Stabi
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y
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ys
is.
Pow
e
r System T
e
ch
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4-1
1
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J Ma, DJ
Hi
ll,
ZY Don
g
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al
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w
e
r
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y
ste
m
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g
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ysis
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porati
ng
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e
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n
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n, T
r
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y
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a
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w
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ur
e-Pres
erved Po
w
e
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r
ansient Stabilit
y Us
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g
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e
r
g
y
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u
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ng
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ope
ng.
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e
r Sy
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n
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n
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0
0.
5
1.0
1.5
2.0
2.5
3.0
3.
5
0
2
4
6
ti
m
e
s
(
s
)
I
n
f
o
r
m
at
i
on E
n
t
r
opy
H
(
P
)
(
p
u
)
S1
S2
y
m
a
x
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Transient Stability Analysi
s
of Grid-connected
Wind T
u
rbines
with Front
-end ... (Hai
ying
Dong)
28
[15]
PM Anderso
n.
Pow
e
r System
Contro
l and St
abil
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, Secon
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ederic
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n
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e
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She
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ang
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.
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i
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ng U
n
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96 (in C
h
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.
[18]
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.
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n
formatio
n
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h
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g
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[19]
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Do
ng C
h
ia
ng; Ca
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i
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iv., et al. F
ound
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he pote
n
tia
l
ener
g
y
bo
un
dar
y surfa
c
e
method
for
po
w
e
r s
y
stem
tra
n
sie
n
t stab
ilit
y an
al
ysis.
IEE
E
T
r
ansacti
on
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u
its
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198
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8.
Evaluation Warning : The document was created with Spire.PDF for Python.