TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5022 ~ 50
3
6
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.470
9
5022
Re
cei
v
ed O
c
t
ober 1
1
, 201
3; Revi
se
d March 11, 201
4
;
Accepte
d
March 26, 201
4
A Novel SSR Mitigation Method Based on GCSC in
DFIG with Series Connected Compensator
Zakieldee
n
Elhassan
1
, Li Yang*
2
, Tang
Yi
3
Schoo
l of Elect
r
ical En
gin
eeri
ng, South
east Univers
i
t
y
,
Chin
a, Jian
gsu
,
Nanji
ng 2
100
96
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zakide
enz
ain
@
gmai
l.com
1
, li_
ya
ng@s
eu.e
du.cn
2
, tang
yi
@seu.e
du.cn
3
A
b
st
r
a
ct
This paper presents a novel study for SSR m
i
tigating in the wind pow
er system
s bas
ed on DFIG
usin
g
GCSC (
G
ate control
l
e
d
series c
apac
itor). T
he GC
SC
is co
mp
osed
o
f
three pa
irs of
anti-p
a
ral
l
el G
T
O
T
h
yristors (Gat
e T
u
rn-
off) co
nnecte
d
in
par
alle
l w
i
th
a fix
ed c
a
p
a
citor.
T
he GCSC
is
app
lie
d to
re
d
u
ce
inrus
h
curre
nt in cap
a
citor co
mp
ens
ator dur
i
ng the
tra
n
sie
n
t
operati
on by
executi
ng a
pr
oper firi
ng a
n
g
l
e
control of thyri
s
tor gates. In order to re
ali
z
e SSR
osci
llati
on w
hen th
e transi
ent op
erati
on occurr
ed, t
h
e
DF
IG turbine
i
s
con
necte
d th
roug
h th
e sh
aft turbin
e
mo
de
l
.
T
he si
mulati
o
n
res
u
lts sh
ow
n that th
e GC
SC
devic
e is suita
b
le a
nd reas
o
nab
le for supp
ressin
g
SSR
cause
d
by torsi
ona
l interacti
o
n (T
I) and torque
amplific
atio
n (
T
A) and
a
l
so
da
mp
ing
the
s
ubsync
h
ron
ous
osci
llati
on
as
w
e
ll. T
h
e
tra
n
sie
n
t si
mu
lati
on
s
have b
e
e
n
carr
ied o
u
t usin
g P
S
CAD/EMT
D
C
progra
m
to
d
e
m
o
n
strate the
capa
bil
i
ty of
the GCSC dev
ic
e in
miti
gati
ng SSR
.
Ke
y
w
ords
:
subsync
h
ron
o
u
s
reson
anc
e
SSR, series
c
apac
itor co
mpens
ator, ve
ct
or contro
l
me
thod,
dou
bly fed i
ndu
ction ge
ner
ator
DF
IG, interpol
ated firin
g
pu
ls
e
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
SSR phen
o
m
enon mi
gh
t take pla
c
e
in the system with a
seri
es
com
pen
sated
transmissio
n
line
whe
n
th
e tra
n
si
ent o
peratio
n
h
a
p
pene
d in
the
po
we
r
syste
m
. Beca
use, the
intera
ction b
e
t
ween th
e se
ries compe
n
sated net
work elect
r
ical
o
s
cillation, a
nd
the me
chani
cal
oscillation of the
generator
drive train
produces tors
ional torques.
This to
rsional torque may
be
led to the shaft fatigue whe
n
the sy
stem ha
s tra
n
sie
n
t mode
operatio
ns.
Therefore, S
S
R
mitigation
ha
s gotten mo
re attention a
nd sig
n
ific
a
n
t care study i
n
orde
r to avoid the probl
ems
asso
ciated
wi
th SSR, and it continue
s to
be a subj
ect
of rese
arch a
nd develo
p
m
ent. Referring
to
that, many
st
udied
a
r
e
do
ne in
SSR mi
tigation, e
s
pe
cially whe
n
th
e
DFIG wa
s employed
a
s
the
gene
rato
r in
win
d
e
nerg
y
. The ba
si
c study
of
th
e SSR
qua
n
t
itie’s calcula
t
ion an
d te
sts i
s
pre
s
ente
d
in [1]. The work [2] discusse
s
clea
rl
y the DFIG co
ntrol
strategy usi
ng the voltage
comm
and i
n
the control l
o
o
p
s of the
grid
side
co
nvert
e
r (GSC) to d
a
mping SS
R. More
over, th
e
SSR definitio
n, classification and mitiga
tion have got
great inte
re
st in variou
s pa
pers su
ch a
s
[3-
5].
Re
cently, the
SSR mitigati
on u
s
ing
flexible
AC t
r
an
smissi
on
syst
ems
(FA
C
TS
) in the
seri
es-comp
e
n
sate
d wi
nd
energy ha
s been
demo
n
strate
d in t
he literatu
r
e.
These FACTS
device
s
in
clu
de the
static
sync
hro
nou
s
seri
es
co
mpe
n
sato
r (SSS
C), thyri
s
tor-controlle
d seri
es
cap
a
cito
r (T
CSC), static va
r com
pen
sat
o
r (SVC
) and
(STATCOM
). In a modern paper [6] the
SSR s
t
udy modified IEEE
firs
t benc
hmark model
is
mitigated by
using SSSC. E
v
en though, t
he
more recentl
y
resea
r
ch wa
s orie
nted
to SSR damping u
s
ing
the subsyn
chrono
us
current
s
u
ppress
or
with the SSSC [7]. The
TCS
C
is
app
lied in many
modes
of SSR
s
u
ppress
i
on s
t
udy
either i
n
the f
r
equ
en
cy sca
nning
or im
p
edan
ce
meth
od a
s
in [8
-1
0]. Moreove
r
,
the TCS
C
h
a
s
useful
ap
plication in
the
d
a
mping
of SS
R
study
exactly in the
sca
nning
freq
ue
ncy m
e
thod
[11].
The ap
plying
of SVC in th
e SSR dam
pi
ng ha
s b
een
impleme
n
ted
and di
scu
s
se
d in [12]. Both
[13] and [14]
explained
a n
o
vel co
ntrol f
o
r mi
tigatin
g SSR
in
the wind
farm and wind park with
seri
es
com
p
e
n
sate
d by usi
ng STATCO
M controller.
On the
othe
r hand, th
e
GCSC devi
c
e pres
ents a
s
n
e
w
FACT
S device
s
fo
r seri
es
comp
en
satio
n
of tran
smi
s
sion li
ne
s
stu
d
y as i
n
[15]. Up to
no
w, the G
C
SC i
s
rarely appli
e
d
to
mit
i
gat
e su
bs
y
n
chr
ono
us
r
e
so
nan
ce,
u
n
les
s
some
r
e
se
ar
che
r
s f
o
cu
s t
hei
r r
e
sea
r
c
h
e
s
in t
h
is
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel SSR
Mitigation Me
thod Base
d o
n
GCS
C
in DFIG with Seri
es…
(Za
k
ield
een Elha
ssan
)
5023
field. Among them, the Jesus et al. [16] pre
s
ent
e
d
the SSR mitigation usin
g G
C
SC devi
c
e, and
they were applied IEEE first benchmark model to
test the GCSC operation. In this study, the
GCSC gate
control i
s
a
c
hi
eved by
a zero-cro
ssi
ng de
tector, whi
c
h use
s
the syst
em
po
we
r
a
s
a
feedba
ck sig
nal cont
rol in
stead of the frequ
en
cy
deviation. Additionally, this study was obtai
ned
a good result, but it needs
more
spe
c
ific control in the
GCSC firin
g
angle
s
.
It’s demo
n
st
rated that
all
d
e
vice
s a
pplie
d in
SSR
ana
lysis
and
da
mping
to e
n
h
ance the
power
syst
em stability and
cont
ro
l
are mitigated
SSR problem
s, but t
hey have some li
mite
d
appli
c
ation
s
.
For exampl
e, the TCSC ha
s so
m
e
disadvanta
g
e
s like it g
enerates a
new
rea
c
tan
c
e bet
wee
n
the ca
p
a
citor, a
nd th
yristor
cont
rol
l
ed rea
c
tan
c
e
at the norma
l frequen
cy fo
r
kno
w
n
blo
c
ki
ng a
ngle
of t
he thyri
s
tor.
Furthe
rmo
r
e,
the va
riation
of rea
c
tan
c
e
in th
e T
C
SC is
s
lightly narrow [15]. The
SSSC c
o
mpens
a
tor has
us
eful applic
at
ion,
but the
cos
t
is very high
becau
se it include
s co
nvert
e
rs in
sid
e
.
Therefore, thi
s
pape
r prese
n
ts
the GCS
C
with simpl
e
con
s
tru
c
tion
and flexible o
peration
to achieve S
S
R
supp
re
ssion in
the
wind p
o
wer
system b
a
se
d
on
DFIG
with the
se
rie
s
-
comp
en
sated
tran
smi
ssi
on
line. T
h
is rese
ar
ch
con
s
ide
r
s SSR
study u
s
in
g
one
of the
S
S
R
analytical too
l
s, namely is an ele
c
trom
agneti
c
Tra
n
sient
s Prog
ra
m (EMTP). T
he EMTP is
a
prog
ram for
nume
r
ical integratio
n of the system differential e
qua
tions and its
suitabl
e for SSR
study in dyn
a
mic o
p
e
r
ati
on. The SS
R ph
enom
en
on was
discussed th
rou
g
hout the
system
model stu
d
y with and with
out GCSC d
e
v
ice. The re
sults sh
ow tha
t
the GCSC has bee
n able
to
alleviate the SSR probl
em
s and imp
r
ov
e sub
s
yn
chro
nou
s oscillati
ons.
2. SSR Defi
nition
SSR is a
d
y
namic even
t of attention
in
p
o
wer systems that
have
cert
ain
sp
eci
a
l
cha
r
a
c
teri
stics. Th
e fo
rmal
definition
of
SSR p
r
ovid
e
s
by
the IEE
E
a
s
a
n
electric
po
wer sy
stem
con
d
ition
wh
ere
the
ele
c
tric n
e
two
r
k ex
cha
nge
s
ene
rgy with
a tu
rb
ine g
ene
rato
r at on
e o
r
mo
re
natural f
r
eq
u
enci
e
s
of the combi
ned
system bel
o
w
the syn
c
hron
ous fr
equ
en
cy of the syst
em
[17]. The definition incl
ude
s any syste
m
conditio
n
tha
t
provides th
e
opportu
nity for an ex
chan
ge
of energy at a given sub
synchrono
us f
r
equ
en
cy. The most co
m
m
on exampl
e of the natural
mode of
sub
s
ynchro
nou
s
oscillation i
s
due to the
serie
s
capa
cit
o
r comp
ensa
t
ed tran
smi
s
sion
lines. The
s
e li
nes, with thei
r se
rie
s
LC
combi
natio
ns,
have natural frequ
en
cie
s
are defined by:
f
π
f
(1)
Whe
r
e
f
is the SSR frequen
cy asso
ci
ating with LC transmissi
on,
f
is the base
freque
ncy a
n
d
X
L
, X
C
are the indu
ctive and capa
citi
ve rea
c
tan
c
e
s
, re
spe
c
tivel
y
. The
f
in the
SSR freq
uen
cy which ha
s a
corre
s
p
o
n
d
ing
com
pon
ent ind
u
ced i
n
the
roto
r
ci
rcuit
s
with th
e
freque
ncy (
f
f
),
f
is the fre
que
ncy of rotatin
g
sp
eed. So i
n
this
study, the SSR freq
uen
cy
con
s
id
er
s is (
f
f
) whi
c
h di
re
ctly related to the network
in
teractio
n with
seri
es
comp
ensator.
Thus, the effe
ctive tran
smission imp
eda
n
c
e X
eff
with se
ries
cap
a
citiv
e
comp
en
sati
on is given a
s
:
X
X
X
1K
X
(2)
Whe
r
e X is the total line reacta
nce, and
K is
the degree of se
rie
s
comp
en
sati
on,
K
, 0
K1
,
and K usuall
y
between 2
5
%
to 75%.
SSR is a
resonant
co
nditi
on, with
fre
q
uen
cie
s
b
e
lo
w the
n
o
min
a
l fre
que
ncy,
whi
c
h
i
s
related
to
an
ene
rgy
exchang
e b
e
twe
en the
ele
c
trical
and
the
mech
ani
cal
system, coupl
ed
throug
h the g
enerator. The
SSR can be
divided in
to two main p
a
rti
c
ula
r
group
s [9, 18]:
1.
Steady state
SSR in
clu
des: In
du
ction
g
ene
rato
r effe
ct (IG
E
) an
d torsional
intera
ction (TI
)
2.
Tran
sie
n
t torque
s or torqu
e
amplificatio
n (TA).
The IGE is
rarely ha
ppe
n
ed in the
se
ries
comp
en
sa
t
ed po
wer
sy
st
em
s.
Ho
we
v
e
r,
t
h
e
SSR cau
s
ed
by TI and TA are dang
ero
u
s conditi
on
s that must be avoided in power sy
ste
m
s
and u
s
ually h
appe
ns in
series compe
n
sated po
wer
systems.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5022 – 50
36
5024
3.
Sy
stem Stud
ied Model
The
config
uration of th
e
studie
d
syste
m
ha
s b
een
sho
w
n
in Fi
g
u
re
1. Thi
s
fi
gure, i
s
basi
c
ally modified from the IEEE
first benchmark model as in [
19]. It consists of wind turbine
based on DFIG with ba
ck t
o
back conve
r
ters, tran
sformer, po
wer g
r
id and
se
ries compe
n
sate
d
transmissio
n l
i
ne. The p
a
ra
meter d
a
ta of
DFIG a
r
e
a
r
range
d a
s
in table I an
d it's taken from t
h
e
[20]. The DFIG s
haft s
y
s
t
em c
o
ns
is
t
s
of three ma
sse
s
: a high pre
s
sure turb
ine (HP) to represe
n
t
turbine
blad
e
s
, an inte
rme
d
iate sta
ge p
r
essure turbin
e (IP) (gea
rb
ox) and
a lo
w pre
s
sure turbine
(LP) (hub
). All masses a
r
e
mech
ani
cally con
n
e
c
ted to
gether u
s
in
g elasti
c sh
afts. The DFIG a
nd
conve
r
ters
are protecte
d b
y
voltage limi
t
s an
d a
n
ov
er-cu
r
rent ‘
c
rowb
ar’
circuit
.
The
conve
r
t
e
r
system e
nabl
es vari
able
speed o
p
e
r
ati
on of the
win
d
turbin
e by de-cou
p
ling t
he po
we
r system
electri
c
al f
r
eq
uen
cy and th
e roto
r me
ch
anical fr
eq
ue
ncy. To
stud
y SSR mitigation, the GCSC
device i
s
con
necte
d in
se
ries
with a tran
smissio
n
line
to red
u
ce
the
transi
ent volt
age th
roug
h t
he
cap
a
cito
r by
i
n
se
rting
the
GCSC
cap
a
citor
w
hen
the
syste
m
h
a
s
a dyna
mic m
ode
by ap
plying
prop
er firin
g
angle
control.
Figure 1. Studied System
Config
uratio
n
4. Wind
Po
w
e
r
Expressio
n
The win
d
turb
ine mechani
cal output po
wer is given by
[21-24]:
P
ρπ
R
C
β
,
λ
V
(3)
Whe
r
e
P
is the mechani
cal
extraction wi
nd power,
ρ
is the air den
sity (1.225kg/m
3
),
R
is the rotor
ra
dius,
V
is the
wi
nd spee
d in
m/s,
λ
is the ti
p sp
eed
ratio,
β
is the bl
ade
pitch a
ngle
in deg
ree
(
β
is usu
a
lly set a
s
0 for th
e m
a
ximum valu
e of
C
),
C
is the
power
coefficient as a
function of bo
th tip-spe
ed ratio
λ
and the b
l
ade pitch an
gle
β
. The tip speed ratio
λ
,
defined by:
λ
Ω
(4)
Her
e
Ω
is th
e turbine rot
o
r spe
ed (ra
d
/s) at a specific win
d
speed (m/
s
). The
theoreti
c
al m
a
ximum valu
e of
C
is give
n by the Betz’s limit, (ab
o
u
t
0.593
) [25]. But there
are
many nume
r
i
c
al eq
uation
s
have been
develop
ed to
calculate the
C
for identified values of
λ
and
β
as
in [24].
C
λ
,
β
0
.
7
3
λ
0
.
5
8
β
.
1
3
.
2
e
.
λ
(5)
Whe
r
e,
λ
λ
.
β
.
β
(6)
Acco
rdi
ng to these e
quatio
ns mentio
ned
above,
the pitch angl
e co
ntrol is built i
n
sid
e
of
the PSCAD
wind
turbi
ne
packa
ge to
a
c
hieve
maxi
mum
wind tu
rbine to
rqu
e
a
nd
controller
data
is set in Ta
ble 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel SSR
Mitigation Me
thod Base
d o
n
GCS
C
in DFIG with Seri
es…
(Za
k
ield
een Elha
ssan
)
5025
5.
DFIG Ma
the
m
atical Mod
e
l
The
DFIG
sta
t
or an
d rotor
voltage eq
uat
ions refe
rri
ng
to the di
re
ct
and q
uad
ratu
re
(dq
)
referen
c
e fra
m
e can b
e
written as [20
]
, [26
-
27]:
V
R
i
p
λ
ω
λ
;
V
R
i
p
λ
ω
λ
(7)
V
R
i
p
λ
ω
ω
λ
;
V
R
i
p
λ
ω
ω
λ
(8)
Here p is the derivative
,
ω
is synchro
n
o
u
s sp
eed,
ω
is rotor spe
ed and the term
(
ω
ω
is defined a
s
slip sp
eed
ω
.
The d&q axes flux in both
stator and rotor (
λ
,
λ
,
λ
and
λ
) are very difficult to
estimate t
hese pa
ram
e
ters, so th
ese flu
x
es
can
be
written with
the
stato
r
a
nd
ro
tor ind
u
cta
n
ces.
Reg
a
rdi
ng to that, the DFIG dynamic e
quation
s
are written a
s
[25
]:
pi
D
L
v
L
v
R
L
i
D
ω
ω
L
i
R
L
i
ω
L
L
i
pi
D
L
v
L
v
R
L
i
D
ω
ω
L
i
R
L
i
ω
L
L
i
pi
D
L
v
L
v
R
L
i
D
ω
ω
L
L
i
R
L
i
ω
L
L
i
(9)
pi
D
L
v
L
v
R
L
i
D
ω
ω
L
L
i
R
L
i
ω
L
L
i
Whe
r
e,
D
(10)
The stato
r
an
d rotor voltag
es an
d cu
rren
ts can b
e
cal
c
ulated a
s
:
V
V
j
V
,
V
V
j
V
,
ı
i
j
i
and
ı
i
j
i
(11)
The stato
r
act
i
ve powe
r
P
an
d rea
c
tive po
wer
Q
are give
n
by:
P
V
i
V
i
;
Q
V
i
V
i
(12)
Here, the qua
dratu
r
e stato
r
voltage
V
set to 0, so that the Equation (1
2) re
written a
s
:
P
V
i
;
Q
V
i
(13)
The motion a
nd ele
c
trom
a
gnetic torque
equatio
ns a
r
e
given by:
T
i
i
i
i
p
ω
T
T
(14)
Whe
r
e P is th
e numbe
r of pole pai
rs.
6.
DFIG Co
nv
erters
Con
t
rol
Generally,
the
DF
IG
model
co
ntains
a
b
a
ck-to
-
ba
ck
co
nverter
b
a
se
d
on
two
-
lev
e
l
conve
r
ters. The two- level
conve
r
te
rs are modelle
d wi
th ideal swit
ches that allo
w current flows in
both di
re
ction
s
. In thi
s
exp
o
sition, th
e controlle
d
sem
i
con
d
u
c
tor
wit
h
a di
ode
in a
n
ti-pa
r
allel
used
is an i
n
sulate
d gate bi
pola
r
tran
sisto
r
(IG
B
T). T
he
DFI
G
co
nverte
rs
control is
ado
pted by u
s
ing
a
vector
co
ntrol
method
as in
the [20, 26].
The ve
ct
or
co
ntrol meth
od i
s
de
eply ap
pl
ied in th
e gri
d
side
converte
r GS
C
and
ro
tor
side
conv
erter RS
C.
T
he [28]
prese
n
ts a
ne
w pro
posed
metho
d
of
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5022 – 50
36
5026
DFIG vec
t
or
c
ontrol based on the inverse s
y
s
t
em
and variable s
t
ruc
t
ure s
l
iding
mode(VSS).
The
RSC is u
s
e
d
to regulate th
e slip po
we
r in orde
r to co
ntrol the gen
erato
r
sp
eed
and torq
ue whil
e
the GSC ma
intains
a
con
s
tant
DC li
n
k
voltage
in
the gri
d
side
. The GS
C i
s
in
ch
arge
of
controlling part of the power flow of the DFIG.
T
h
is power i
s
i
n
completely del
i
vered through
RSC, DC lin
k and fin
a
lly is tran
smitted
by the
GCS
to the grid [25], [29-30].
There are m
any
control strate
gies of
GSC whe
n
it's appl
ied
in
t
he
DFI
G
win
d
turbin
e, and the
m
o
st mo
del of t
h
is
purp
o
se ca
n be found in the [31]. However, in
this pape
r, the co
mpre
hen
sive equatio
ns to get
the referen
c
e
values of the
GSC and
RSC
are
written
based on [20,
25] as belo
w
,
V
V
V
K
i
K
i
X
(15)
V
i
i
K
i
X
I
= (
Q
Q
K
(16)
I
rq
ref
= (
ω
m
ω
ref
K
pqr
K
iqr
s
The q-axis cu
rre
nt referen
c
e i
qs
ref
can be o
b
tained fro
m
:
i
qs
ref
Q
s
1
.
5V
ds
(17)
Whe
r
e th
e K
pdc
, K
pd
s
, K
pq
s
, K
pdr
, K
pq
r
and K
idc
, K
ids
, K
iqs
, K
idr
, K
iqr
are
propo
rtional a
nd inte
gral
gain
s
of DC
link voltage, stator an
d ro
tor dire
ct an
d quad
rature
current
s re
spectively. These
para
m
eters a
r
e playing a
great role in
enhan
ci
ng t
he voltage control. Thu
s
,
the values are
desi
gne
d accordin
g to system comp
on
ents an
d DF
I
G
paramete
r
s to reali
z
e
specify co
ntrol
of
conve
r
ters in
both si
de
s.
The X
T
is th
e
cou
p
ling t
r
a
n
sformer re
a
c
tan
c
e a
nd t
he Q
g
ref
is th
e gri
d
reac
tive power whic
h is
s
e
t to z
e
ro value.
g
s
L
g
s
L
Figure 2. DFI
G
GSC an
d RSC Blo
ck
Di
agra
m
Co
ntro
l
7.
Shaft Mo
del Equations
The shaft model in this
study is a
s
sumed a
s
an
elastic m
u
ltimass mod
e
l with fou
r
masse
s
in
clu
d
ing th
e
DFI
G
. Thi
s
mo
de
l ca
n b
e
g
r
ap
hically
sh
own
in Fi
gure 3.
The
shaft m
o
del
is rep
r
e
s
e
n
te
d by linear m
a
thematical e
quation
s
and
the masse
s
are sele
cted
as thre
e ma
sse
s
according to the refe
ren
c
e
[33]. The mathematical
eq
uation
s
of the turbine
-
ge
ne
rator
referring
to
the [34, 35] are written as:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel SSR
Mitigation Me
thod Base
d o
n
GCS
C
in DFIG with Seri
es…
(Za
k
ield
een Elha
ssan
)
5027
2H
1
d
ω
1
dt
K
12
δ
1
δ
2
D
12
ω
1
ω
2
T
1
(18)
2H
2
d
ω
2
dt
K
12
δ
2
δ
1
K
23
δ
2
δ
3
D
12
ω
2
ω
1
D
23
ω
2
ω
3
T
2
(19)
2H
3
d
ω
3
dt
K
23
δ
3
δ
2
K
34
δ
3
δ
4
D
23
ω
3
ω
2
D
34
ω
3
ω
4
T
3
(20)
2H
g
d
ω
g
dt
K
34
δ
4
δ
3
D
34
ω
4
ω
3
T
m
T
e
(21)
Whe
r
e H i
s
the inertia con
s
tant of each turbin
e blad
e in se
c, K is the spri
ng con
s
tant in N.m/ra
d
,
ω
is the me
chani
cal
spee
d in ra
d/se
c,
D is th
e mu
tual dampi
ng
in N.m-s/ra
d
,
δ
is the roto
r
angle in ra
d, T
m
is the mecha
n
ical torq
ue in N.m an
d T
e
is the electro
m
ag
neti
c
torqu
e
in N.m.
We n
o
tice
h
e
re th
e ma
sse
s
self
-dam
ping a
r
e
omi
tted from
the
s
e
eq
uation
s
for line
a
ri
zing
. In
addition
al, the comm
on d
y
namic eq
uat
ion of the
generato
r- tu
rbi
ne model
co
uld be written in
se
con
d
ord
e
r
equatio
n to ith row a
s
:
J
i
δ
i
K
i
δ
i
D
i
δ
i
T
i
(22)
J
i
2H
i
(23)
Whe
r
e i = 1,
2, 3 , here (i ) is the numbe
r of masse
s
.
If we comp
are the equatio
n (22
)
with st
anda
rd secon
d
orde
r eq
uat
ion sol
u
tion
s, we get
natural frequ
enci
e
s of the
shaft model a
s
:
f
i
1
2
π
K
i
2H
i
(24)
The Equ
a
tio
n
(2
4) i
s
u
s
ed to o
b
tain
the shaft m
odel p
a
ramet
e
rs when th
e natu
r
al
freque
ncy of t
he shaft mod
e
l is kno
w
n.
Ho
wever,
in t
h
is
study, the
eigenvalu
e
method i
s
u
s
ed to
obtain the m
a
sse
s
natu
r
al
freque
nci
e
s
by using
th
e Matlab prog
ram. From the
imagina
ry parts
of eigenval
ue
s, the m
u
ltimass nat
u
r
al
freque
nci
e
s
na
mely are
calculated a
s
: 1
0
.64, 21.10
2 a
n
d
29.523Hz
respec
tively. The s
h
aft
model s
y
s
t
em data are
modified from IEEE firs
t benc
h
mark
and liste
d in Table 3.
Figure 3. Equivalent Shaft
Model Di
ag
ra
m
8. GCSC
Dev
i
c
e
The GCSC
consi
s
ts of a fi
xed capacitor in
shunt with GTO thyristo
r has the capabilities
to turn on a
nd off upon
control a
c
tio
n
. The GCS
C
is
ap
plied
to control voltage acro
ss the
cap
a
cito
r
at given
line
cu
rrent
by usi
n
g
GTO
valves,
accordin
g
to the
gate
op
en
an
d
clo
s
e. The capa
citor
is
bypasse
d wh
en the va
lve is clo
s
e
d
and
when it
o
pen
s
the cu
rre
nt
is
followed
through th
e ca
p
a
citor. F
u
rthe
rmore, t
he bi
dire
ctional
G
T
O thyristo
rs have a pa
ral
l
el
snu
bbe
r cap
a
c
itor ci
rcuit
to
exec
ute the
system
prote
c
tion [2
0]. Fig
u
re
4
sho
w
s t
he G
C
SC ba
sic
circuit topol
o
g
y with com
p
ensator tra
n
smissi
on li
ne
element
s. Th
e main go
al of using
a G
C
SC
device i
s
to
mitigate the
SSR proble
m
s by
red
u
ci
ng in
ru
sh
cu
rre
nt cau
s
ed
by the tran
sient
operation tha
t
takes pla
c
e
when the th
ree ph
ase
fault occurs in
the system.
GCSC h
a
s t
h
e
same
work
a
c
tion
with TS
SC (thyri
sto
r
- switch
ed
se
ries
ca
pa
citor) whi
c
h
ap
plie
s to
co
ntrol t
h
e
AC voltage throug
h ca
pa
citor at the given line cu
rrent [36]. Howeve
r, the differen
c
e bet
wee
n
two
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5022 – 50
36
5028
model
s that the TSSC uses thyristo
r a
nd the
GCS
C
use
s
the gate turn-off thyristor (GT
O
).
Furthe
rmo
r
e,
the GCS
C
has
bee
n ab
le to vary the rea
c
tan
c
e
from zero to
the maximu
m
comp
en
satio
n
rel
a
ted to
the fixed
cap
a
citor value.
The G
C
S
C
must b
e
o
p
e
r
ated
with
prope
r
GTO firing angle control which automati
cally closes
a
nd ope
n acco
rding to control action. So the
equatio
n of GCSC could b
e
written referr
ing to [15], [16], [36] and [37] as:
V
C
α
1
C
Ic
os
ω
t
ω
t
α
dt
I
ω
C
sin
ω
t
sin
α
(25)
Whe
r
e V
C
α
is the voltage acro
ss the ca
pa
ci
tor, I
is
the maximum value of line current
and
α
is the thyristo
r firing
angle which
interval is
α
ω
t
π
α
. The turn-off angle(
α
is
measured f
r
o
m
the
ze
ro
crossing
of
th
e line cu
rre
nt and the comp
e
n
satio
n
level of the GCSC is
determi
ned b
y
the fundamental co
mp
onent of the
voltage V
C
α
on the GCSC.
The GCS
C
rea
c
tan
c
e va
ries from ma
ximum value
at
α
π
2
radia
n
to zero
value for
α
π
radian
[37, 38].
Referrin
g to that, the equivalent rea
c
tan
c
e of the GCSC as a fun
c
t
i
on of
α
can be
expresse
d a
s
:
X
C
α
X
C
π
2
α
2
π
sin2
α
(26)
Acco
rdi
ng to
the Eq
uatio
n (2
6) the
reacta
nce of
the capa
citor ca
n b
e
cha
nged
to
variou
s value
s
relate
d to the firing angl
e of thyris
tor, b
u
t we notice here all the reacta
nce values
must be
positive value, so that
the firing a
ngle u
s
ually le
ss t
han
π
. Figure
5 sho
w
s th
e
impeda
nce value pe
r unit
of the GCS
C
a
s
a fun
c
tion of the firing angl
e
α
and Figure 6
grap
hically explaine
d the re
lationship bet
wee
n
the ca
p
a
citor voltag
e
and turn
-off delay angle.
In order to co
ntrol the GCS
C
ope
ration, the app
rop
r
iat
e
firing angle
circuit is de
si
gned to
enabl
e the thyristo
r gate
con
d
u
c
ting
or not
con
d
u
c
t. Thereby the interpolat
ed firing
pul
se is
applie
d to rel
ease the G
T
O Thyri
s
tors
gate en
able
after re
ceivin
g the alp
ha a
ngle
α
from the
pha
se l
o
cke
d
loop
(PL
L
).
The p
h
a
s
e l
o
cked l
oop
PI controlle
r g
a
i
n
s
are
obtai
n
ed by
usi
ng t
r
ial
and erro
r me
thod. This PLL gene
rate
s a ramp sign
al of angle
α
variation b
e
tween (0 an
d
360°
), syn
c
hronized o
r
locked in
pha
se,
to the input voltage V
th
which i
s
mea
s
ured
acro
ss t
h
e
cap
a
cito
r. The initial angle
α
0
adjusted to suitable value, then it compare
s
with ram
p
signal
α
in the inte
rpol
ated firing
pul
se to e
nabl
e
thyris
tor ope
ration.
Figu
re 7
sh
ows
the control sche
me
model
of G
C
SC. Hen
c
e,
the
GCS
C
can be
o
perated in volta
ge control
o
r
compe
n
sating
rea
c
tan
c
e co
ntrol acco
rdi
n
g to the appli
ed co
ntrol.
Figure 4. GCSC Equivalen
t
Circuit
with Comp
en
sato
r Line Param
e
ters
Figure 5. GCSC Impeda
nce as a Fu
ncti
on of Angle
α
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel SSR
Mitigation Me
thod Base
d o
n
GCS
C
in DFIG with Seri
es…
(Za
k
ield
een Elha
ssan
)
5029
0
10
20
30
40
50
60
70
80
90
0
0.
2
0.
4
0.
6
0.
8
1
Al
p
ha
[
de
g
re
e
]
V
c
(a
l
p
h
a
) [
p
u
]
)
(
C
V
2
1
2
si
n
1
1
Figure 6. Fun
damental
Co
mpone
nt of the Seri
e
s
Ca
p
a
citor Volta
g
e
Against Tu
rn
-off Delay
Angle
Figure 7. Sch
e
me Co
ntrol
Model of the GCSC
9.
Simulation Results a
nd Discussion
Figure 1
is u
s
ed
to ve
rify the SSR mi
ti
gation b
a
se
d on
the
GCSC, an
d the
system
model was
constructe
d an
d impleme
n
te
d in the PSC
AD pro
g
ra
m.
Initially, the system is ru
nn
ing
unde
r
stea
dy state
an
d 3
Φ
fault o
c
curred
at 8
s
e
c
with d
u
ration
time 0.1
1
se
c. Th
e
GCS
C
i
s
con
n
e
c
ted i
n
se
rie
s
with
the comp
en
sated tran
smi
ssi
on li
ne to
mitigate SS
R effe
cts du
e to
transi
ent mo
d
e
occu
rren
ce
in the p
o
wer
system.
T
he
adju
s
ted firi
n
g
angl
e of G
C
SC i
s
set to
the
comp
uted val
ue (
0
60°
).
Und
e
r
the above ci
rcu
m
stan
ce
s, serie
s
com
p
a
r
ative
results
with and
without
GCSC
have been pl
otted from the PSCAD &
MATLAB to describe
system b
eha
vior.
The DFI
G
sta
t
or real
and reactive po
we
rs
a
r
e viewed
in Figure 8(a
)
and
(b).
As
we hav
e
s
e
en
in F
i
gu
re
8(
a
)
without GCS
C
, the
P
s
duri
ng th
e
fault i
s
d
e
cre
a
se
d to
a
ne
gative value
and
after fault
cle
a
ring
do
es no
t return to th
e
sa
me valu
e
before
tra
n
si
e
n
t mode
which indi
cate
s th
at
the system l
o
st syn
c
h
r
oni
sm and thi
s
l
ead
s to
unst
able op
eratio
n. Whilst wit
h
GCS
C
, the P
s
cha
r
a
c
teri
stic curve t
r
an
sie
n
t is mo
re
saf
e
ty
beca
u
se the G
C
SC p
r
o
duced a
ne
ce
ssary requi
re
d
power to co
mpen
sate
system re
activ
e
pow
er du
ring dynami
c
mode to prevent the SSR
occurre
d
. Figure 8
(
b) i
s
cl
early sh
own the stator rea
c
tive powe
r
Q
s
whic
h wit
h
GCSC i
s
more
linear an
d
sta
b
le. Thi
s
in
di
cate
s that th
e
GCS
C
cha
n
ges the
syste
m
re
acta
nce
to ne
w value
b
y
addin
g
the G
C
SC re
acta
n
c
e
X
GCSC
. Th
ese
re
sult
s a
r
e
confi
r
med
again
in the
DFIG
active
and
rea
c
tive po
wers,
whi
c
h a
r
e sh
own in Fi
gure
9(a) a
n
d
(b)
re
spe
c
tively. The DFI
G
rea
c
tive po
wer
with GCS
C
is always mai
n
tained to ze
ro to ensu
r
e a
DFIG unity power facto
r
whi
c
h is di
re
ctly
improve
d
voltage sta
b
ility control.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5022 – 50
36
5030
Figure 8. Stator Power Respon
se: (a) a
c
tive power, (b
) rea
c
tive po
wer
Figure 9. DFI
G
Powe
r Re
spon
se : (a) a
c
tive power
(b) reactive po
wer
On the oth
e
r
han
d, the
DFIG ele
c
tro
m
agneti
c
torque a
nd me
cha
n
ical torq
ue are
pre
s
ente
d
in
Figure 1
0
(a
)
and
(b
). Fro
m
Figu
re
10
(a), the
T
e
wit
hout G
C
SC a
fter fault
clea
ring
contai
ns hi
gh
er value
s
be
cause the roto
r cu
rrent
is very high, which may be le
d to shaft fatigue
whil
st with G
C
SC i
s
mo
re
stable
and n
o
dange
ro
us t
o
the sh
aft turbine
syste
m
. The me
cha
n
i
c
al
torque
T
m
foll
ows the
sa
m
e
beh
avior of
T
e
at a
stea
dy state, but
a
fter tra
n
si
en
t there i
s
a b
i
g
differen
c
e b
e
twee
n them,
whi
c
h lea
d
to
abno
rmal
system ope
ration
. In additional
, the intere
sting
result is to t
a
ke
the el
ect
r
oma
gneti
c
t
o
rqu
e
sign
al
and
analy
s
i
s
it by u
s
in
g
on-li
ne
scan
ner
freque
ncy. Th
is esse
ntially use
d
fast Fou
r
ier tr
a
n
sfo
r
m
to get the harmoni
c freq
ue
ncy of the (T
e
)
as in Fig
u
re
11. From thi
s
figure,
the m
a
ximum harm
onic freque
ncy of the T
e
without GCS
C
is
about 44.39
7
4
Hz whi
c
h in
dicate
s that the SSR
wa
s happeni
ng i
n
this syste
m
, but when
th
e
GCSC was
adde
d to th
e
syste
m
, the
frequ
en
cy l
e
ss tha
n
1
H
z. Rega
rdin
g
to these
re
sults
,
the SSR phe
nomen
on wa
s occu
rri
ng in
the system
case stu
d
y, and
the
G
C
SC mitigated
the
SSR effec
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel SSR
Mitigation Me
thod Base
d o
n
GCS
C
in DFIG with Seri
es…
(Za
k
ield
een Elha
ssan
)
5031
The mo
st im
portant results are the sha
ft m
odel syst
em cu
rves
which a
r
e illu
st
rated in
Figure 1
2
(a
)-(c). Fig
u
re
12
(a) sho
w
s th
e torque
bet
wee
n
ma
ss2
-
1 T
12
, Figu
re
12(b
)
th
e to
rque
betwe
en ma
ss3-2 T
23
, and
Figure
12(c) the torque
b
e
twee
n ma
ss3-4 T
34
. Fro
m
these figu
res,
the shaft torque
s with G
C
SC are sta
b
le and t
he oscillation
p
r
odu
ced from
SSR
has
b
een
dampe
d.
Figure 10. DF
IG T
e
and T
m
Simulation Result
s: (a) el
e
c
trom
agn
etic
torque T
e
(
b
)
mech
ani
cal
torque T
m
Figure 11. Electro
m
ag
neti
c
Torque
(T
e
)
Freq
uen
cy Harmo
n
ics u
s
i
ng On-li
ne Scanne
r Fre
que
ncy
(fast Fou
r
ie
r tran
sform F
F
T
)
: (a)
without
GCSC; (b
) with GCSC
Figure 12. Shaft Model Re
sults: (a) To
rque bet
wee
n
mass
1-2
T
12
(b) Torque bet
wee
n
mass
2-3
T
23
(c) Torque b
e
t
ween ma
ss
3-4
T
34
Evaluation Warning : The document was created with Spire.PDF for Python.