TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 391 ~ 4
0
0
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.993
391
Re
cei
v
ed
No
vem
ber 1
2
, 2014; Re
vi
sed
March 8, 201
5; Acce
pted
March 25, 20
15
Flicker Measur
e
ment and Grey Disaster Prediction of
Grid-Connected Wind Turbines
Zhanqian
g Zhang
1
, Keqil
a
o Meng
2
, Li Zhang
3
Coll
eg
e of Information En
gi
ne
erin
g, Inner Mo
ngo
lia U
n
ivers
i
t
y
of T
e
chnolo
g
y
, H
ohh
ot 010
080,
Inner Mon
g
o
lia
Autonomo
u
s
Regi
on, Ch
in
a
e-mail: dz
xzz
q
@16
3
.com
1
, mengk
e0
0@a
l
i
y
un.com
2
, 540
2
161
07@
qq.co
m
3
A
b
st
r
a
ct
Grid-con
necte
d oper
ation of l
a
rge-sc
ale w
i
n
d
tu
rbin
es (W
Ts) w
ill have an
impact on p
o
w
e
r qua
lity
of electric
power system
s. Th
erefore, on the basis
of
analy
z
ing the International
Electrot
echnical standar
d
IEC 6140
0-2
1
, w
e
describe
d
the meas
ure
m
e
n
t, evaluati
on
meth
od of the flicker of
W
T
s a
nd pro
pose
d
th
e
meth
od
of gr
e
y
disast
er pr
ed
iction.Active
p
o
w
e
r, reac
tive power,
flicker coefficien
t and flicker s
e
verit
y
of
the W
T
s
w
e
re tested on the
actual w
i
nd far
m
accor
d
i
ng to
IEC 61400-
21
standard. W
e
beli
e
ve
d that the
flicker sev
e
rity
w
a
s a d
i
sast
er, so us
ed th
e grey
dis
a
ste
r
pred
ictio
n
to
pred
ict the
o
ccurrenc
e ti
me
of
excessiv
e
flick
e
r.Analys
is of
t
he test data
of flicker w
a
s
necess
a
ry, w
h
ich co
uld
det
e
r
mi
ne th
e U
p
p
e
r
disaster thres
h
old of the flick
e
r.
T
he disaster
seque
nce w
a
s ma
de up
of the excess
ive fl
icker val
ues. T
h
e
date s
equ
enc
e
w
a
s extracte
d fro
m
the
dis
a
ster se
que
nc
e. Establ
ishi
ng
GM (1,1)
mo
del f
o
r the
da
te
sequ
enc
e w
a
s to pred
ict
the
future dis
a
ste
r
date se
qu
en
ce.T
he exp
e
ri
me
ntal r
e
sults
show
ed th
at the
relativ
e
accur
a
cy of the dis
a
ster pre
d
ictio
n
mode
l r
eac
he
d 9
4
.87%, w
h
ich
w
a
s suitabl
e fo
r long-t
e
rm fl
ic
ker
disaster pr
edict
ion.
Ke
y
w
ords
:
W
i
nd T
u
rbi
nes, F
licker, IEC 614
00-2
1
, Grey Disaster Predicti
on, GM (1,1)
1. Introduc
tion
As a
kind
of rene
wa
ble e
n
e
rgy, wi
nd p
o
we
r is
on
e
of the impo
rtant alternative ene
rgy
sou
r
ces of th
e fossil fuel.
Becau
s
e
wi
n
d
po
we
r is random
an
d u
n
stabl
e. With
grid
-conn
ect
ed
operation
of large
-
scale WT
s,
pow
er
fluctuation of
WTs
will b
r
i
ng neg
ative effects to po
wer
quality; flicker is one of the main influen
ce [1]-[3].
The pu
rp
ose
of this pa
rt of
IEC 6140
0 [4
] is
to provide
a uniform m
e
thodol
ogy which
will
ensure
co
nsi
s
ten
c
y and
a
c
cura
cy in th
e pre
s
e
n
tatio
n
, testing a
n
d
asse
ssmen
t
of powe
r
q
u
ality
cha
r
a
c
teri
stics of grid
-con
necte
d WT
s.
The po
wer
quality cha
r
a
c
teri
stics he
re inclu
de wi
nd
turbine
spe
c
i
f
ication
s
, voltage quality (emission
s
of flicker an
d harmo
nics), voltage drop
respon
se, p
o
w
er
co
ntrol,
grid p
r
ote
c
tio
n
and recon
nectio
n
time. The re
se
arch focu
s was to
measure, asse
ss an
d pre
d
ict t
he flicker of grid-co
nne
cted WT
s under conti
nuou
s ope
rat
i
on.
Acco
rdi
ng to
IEC 614
00-2
1
stan
da
rd th
e refe
ren
c
e [
5
] pro
p
o
s
ed
a stan
da
rd e
v
aluation met
hod
whi
c
h
wa
s b
a
se
d on
testi
ng the fli
c
ker co
efficient
)
,v
c(
ψ
a
a
of a
single
WT
s.The
metho
d
coul
d
estimate th
e
sum
of flickers of mo
re
WT
s conn
ecte
d to PCC (Point
of Comm
on
Cou
p
ling
)
,whi
ch
proved
the
rationality of
WT
s flicke
r
measur
ement
and
evaluati
on meth
od
s.The
referen
c
e [6]
establi
s
h
ed t
he virtual
gri
d
mod
e
l and
evaluated
th
e
power
qualit
y of WTs fro
m
two a
s
p
e
ct
s of
contin
uou
s o
peratio
n a
n
d
switchin
g o
peratio
n.
Th
e refe
ren
c
e
[7] prop
osed
the meth
od
of
contin
uou
s wavelet transf
o
rm to re
cog
n
ize the po
wer quality disturban
ce
s. T
he refe
ren
c
e
[8]-
[10] asse
sse
d
po
we
r qu
ali
t
y comprehe
n
s
ively ba
sed
on the th
eori
e
s of
grey
rel
a
tional a
naly
s
is,
grey clu
s
te
rin
g
and optima
l
combin
ation
of wei
ghts.
The refe
re
nce [11]
used t
he grey
syst
em
theory and
radial ba
sis f
unctio
n
neu
ral netwo
rk to
predi
ct the flicker value
s
according to
th
e
Jap
ane
se
10
∆
v
ind
e
x and o
b
tai
ned the
bett
e
r p
r
edi
ction
results. Th
e
referen
c
e [12
]
used
the
grey mod
e
l to predi
ct the failure nu
mbe
r
of wind turbi
n
e blade
s.
This pa
per d
e
scrib
ed the measurement
and ev
aluati
on method
s of the flicker
based on
studying
IEC
6140
0-2
1
sta
ndard. Th
e fli
c
ker coeffici
e
n
t of the
a
c
tu
al wi
nd fa
rm
wa
s m
e
a
s
ure
d
to
cal
c
ulate th
e
flicke
r valu
es.
Grey
disa
ste
r
predi
ction
was to fo
re
ca
st
the date
se
q
uen
ce
s of th
e
flicke
r whi
c
h
excee
ded the
standa
rd val
ues. Firs
t, we
identified the upper di
sa
st
er se
que
nce by
studying
the
disaste
r
se
quen
ce
of
the flicke
r. T
hen
we
stud
ied
the
re
gu
larity of di
sa
ster
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 391 – 40
0
392
seq
uen
ce
an
d predi
cted t
he date
sequ
ences
of di
saster. Finally,
we esta
blish
ed
the disast
er
seq
uen
ce G
M
(1,1) mo
de
l and reali
z
e
d
grey
disa
ste
r
predi
ction of the flicke
r.
2. Measurem
e
nt and a
sse
ssment me
thods of flic
k
e
r
The mea
s
u
r
ement pro
c
e
dure
s
are valid for a si
ngle WT
s wi
th a three-p
hase grid
con
n
e
c
tion. The mea
s
u
r
em
ent pro
c
ed
ures a
r
e valid
for any si
ze of
WTs, thou
gh
this part of IEC
6140
0-2
1
o
n
l
y requi
re
s
wind
turbi
n
e
types i
n
ten
ded fo
r P
C
C.Power qu
ality cha
r
a
c
teri
stics
measured at for exampl
e a test site ca
n be
co
nsi
dere
d
valid also at
other site
s.
2.1. Flicker Measur
e
men
t
Procedu
r
es
Und
e
r co
ntin
uou
s
op
eration
of
WT
s, the me
asure
m
ent an
d a
s
se
ssm
ent p
r
oce
s
s of
flicke
r [4] is shown in Figu
re 1.
()
m
ut
()
m
it
,
,3
0
,
5
0
,
7
0
8
5
kf
i
c
k
S
和
,
ka
Cv
（）
(t
)
fi
c
u
,
s
tf
i
c
P
)
k
C
（
(c<x)
t
P
,
kf
i
c
S
,,
kk
a
Sv
,
s
tl
t
PP
6/
,
7
.
5
/
,
8
.
5
/
,
1
0/
a
vm
s
m
s
m
s
m
s
Figure 1. Measu
r
em
ent an
d asse
ssm
en
t proce
d
u
r
e
s
for flicker
durin
g co
ntin
uou
s ope
ratio
n
of WTs
Measurement
s shall be
ta
ken so
that at
l
east five
10 min tim
e
-seri
e
s of po
wer are
colle
cted fo
r
each 1m/
s
wind
spee
d bi
n
betwe
en
cut-
in win
d
spe
e
d
and
15
m/s.The test
sh
o
u
ld
be ta
ken
at l
east five time
s.The fifteen
10min ti
me
serie
s
of in
sta
n
taneo
us volt
age a
nd
cu
rrent
measurement
data
(t)
u
m
and
(t)
i
m
are
colle
cted,
whe
r
ein
the
averag
e wi
nd
spe
ed i
s
10
min.
Each
set of
measured tim
e
-seri
e
s i
s
u
s
ed a
s
inp
u
t to simulate t
he
voltage fluctu
ations,
(t)
u
fic
on a
fictitious gri
d
with an ap
prop
riate sh
ort-circuit ap
pare
n
t powe
r
(t)
S
fic
k,
and for four different
netwo
rk im
p
edan
ce p
h
a
s
e angle
s
k
ψ
(blo
ck 1 i
n
Figu
re 1).The tim
e
se
rie
s
of instanta
neo
us
simulate
d voltage
(t)
u
fic
is inp
u
t to the voltage
flicke
r alg
o
rit
h
m de
scrib
e
d
in IEC 61
000
-4-15[13
]
to generate the flicker emi
ssi
on value
fic
st,
P
( block 2 in Fig
u
re 1
)
.
The flicker m
e
ter’s fun
c
tio
n
s can be divi
ded into two
parts:
1)
It simulates the light-eye
-b
rain
resp
on
se
when the in
stantaneo
us v
o
ltage
(t)
u
fic
fluctuates by
establi
s
hi
ng a
mathematica
l
model;
2)
It counts the flicker severity
online, and
calcul
at
es the
10min of the sho
r
t-te
rm flicker valu
e.
fic
st,
P
is
cal
c
ulate
d
from th
e v
o
ltage flu
c
tu
ation of
(t)
u
fic
und
er fou
r
different po
we
r
netwo
rk impe
dan
ce p
h
a
s
e
angle
s
k
ψ
to obt
ain the fli
c
ker value.Each
fic
st,
P
value i
s
n
o
rma
lized t
o
a f
licke
r co
ef
f
i
cient
)
c(
ψ
k
(block 3
in Figure 1
)
.
S
k,
fic
c(
ψ
)=
P
ks
t
S
n
(1)
In the equ
ation (1),
fic
k,
S
is sh
ort-circuit
cap
a
c
ity of the virtual gri
d
,
n
S
is ra
ted app
are
n
t
power of
a si
ngle
WT
s. To
ensure
the fli
c
ker m
e
a
s
ure
m
ent in
strum
ent within th
e
ran
ge
spe
c
ified
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TELKOM
NIKA
ISSN:
1693-6
930
Flicker Measurem
ent and
Grey
Di
saster Prediction of Grid
-Connect
ed .... (Zhanqiang Zhang)
393
in IEC61
000
-4-15,
we
sh
o
u
ld ad
opt th
e ap
pro
p
riate
sh
ort-circuit
ratio
n
fic
k,
/S
S
. IEC 6
1400
-21
stand
ard
re
co
mmend
s the
sho
r
t-circuit ratio is betwee
n
20-5
0
.
For
ea
ch
net
work i
m
pe
da
nce
ph
ase a
ngle
k
ψ
,the wei
ghting
pro
c
e
dure
calculat
es th
e
weig
hted a
ccumulated
distribution fun
c
tions of the f
licker
coeffici
ent
x)
(c
P
r
,assumin
g fou
r
different
win
d
di
stributio
n
s
.For ea
ch
a
c
cumulate
d
distrib
u
tion,th
e 99%
pe
rce
n
tile
)
,v
c(
ψ
a
k
is
repo
rted
(blo
ck 4 and bl
ock 5 in Figure 1
)
.
2.2. Flicker Ass
essme
n
t Procedure
s
If you get a
flicke
r co
efficient
)
,v
c(
ψ
a
k
, you can cal
c
ulate flicker
st
P
or
lt
P
on any
spe
c
ified
site
through the
param
eters
of
k
S
,
k
ψ
and
a
v
.The flicker emi
s
sio
n
from a sin
g
le WT
s
durin
g co
ntin
uou
s ope
ratio
n
shall b
e
esti
mated applyi
ng the equ
ation (2
) belo
w
.
n
st
l
t
k
a
k
S
P=
P
=
c
(
ψ
,v
)
S
(2)
In ca
se mo
re
WT
s are con
necte
d to the
PCC,
the flicker emi
s
sion from the sum o
f
them
can b
e
estim
a
ted from the
equation (3)
belo
w
.
wt
N
2
st
Σ
lt
Σ
ik
a
n
,
i
i=
1
k
1
P=
P
=
(
c
(
ψ
,v
)
S
)
S
(3)
If the wind farm use
s
the same mod
e
l of WTs,
the flicker
emissio
n
fr
om the su
m of them
can b
e
simplif
ied as the e
q
uation (4
) bel
ow.
n,
i
st
Σ
lt
Σ
ka
W
T
k
S
P=
P
=
c
(
ψ
,v
)
N
S
(4)
Whe
r
e
wt
N
is the numbe
r of WTs conne
cted
to the PCC.
3. Flicker Te
st
3.1. Sy
stem
Des
c
ription
In this pa
pe
r, the test d
a
ta we
re m
easure
d
on
the BAIYUN wind fa
rm
in Inne
r
Mongoli
a
.The
wind farm center is lo
cat
ed about
10
9°56'
40" ea
st
longitude , 41°4
4'46" no
rth
latitude
, with
the avera
ge altitude
of 15
65m.The
a
n
n
ual
wind
spe
ed of
this site
at h
ub
heigh
t is
estimated to
be 8 m/
s.The
averag
e wi
nd
power d
e
n
s
ity is 523.6
W
/
m
2
.The total installe
d capa
city
of the
wind
farm i
s
49M
W, the rated
p
o
we
r fo
r a
si
ngle
WT
s i
s
810KW,
the
output voltag
e i
s
0.69KV.The
wind
farm
in
stalled the
do
uble
arm
a
ture hybri
d
ex
citation
WT
s,which
combin
e
the
advantag
e of
VSCF(Va
riabl
e Spee
d
Con
s
tant F
r
eq
ue
ncy) gen
erato
r
an
d CSCF
(Con
stant
Sp
e
ed
Con
s
tant F
r
e
quen
cy) g
ene
rator.T
he ge
n
e
rato
r ha
s hi
gh po
we
r ge
neratio
n effici
ency a
nd si
m
p
le
control fe
atu
r
es.
O
n th
e
wind
farm
a ste
p
-up transfo
rme
r
substatio
n
with 22
0KV was
con
s
tru
c
ted.
The main
wiri
ng diag
ram of
the wind farm is sh
own in
Figure 2.
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ISSN: 16
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930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 391 – 40
0
394
Figure 2. Main wirin
g
diag
ram of the win
d
farm
Powe
r quality
measureme
n
ts were ta
ke
n from
a
singl
e WT
s termi
n
al on the lo
w
voltage
side of the transfo
rme
r
T
R
1, whi
c
h
was
sho
w
n at
point A in Figure
2.We
could calculat
e the
flicke
r of mult
iple WTs
co
n
necte
d to PCC by
the e
q
u
a
tion (4
).Th
e
measurement
wa
s carried
out
from 16:10 o
n
Novemb
er
26,201
3 to 12
:00 Novemb
e
r
26,201
3,whi
c
h ha
d 120
0 minutes in tot
a
l.
3.2. Flicker Test
The me
asure
m
ent data
of 10 min time
serie
s
of in
sta
n
taneo
us volt
age a
nd
cu
rrent we
re
colle
cted.Th
e
voltage and
current sam
p
le frequ
en
cy was 10.2
4
KHz, the win
d
spe
ed sam
p
le
freque
ncy wa
s 5Hz an
d accura
cy of the anemo
m
et
er wa
s ±0.2
m/s. In acco
rdan
ce with I
E
C
6140
0-2
1
sta
ndard, the measure
m
ent
data of three
-
pha
se volta
ge and
curre
n
t were u
s
e
d
to
cal
c
ulate
the flicker coeffici
ent.T
he
system was in
equilibrium
by ana
lyzing the test data,
so the
data of pha
se
1 were u
s
e
d
only.
3.2.1. Activ
e
and Re
activ
e Po
w
e
r Tes
t
The a
c
tive a
nd rea
c
tive p
o
we
r of the
WT
s were
te
sted u
nde
r th
e co
ntinuo
us
operation
state.The
tre
nd of
the
act
i
ve and
rea
c
tive po
we
r h
a
d
con
s
iste
ncy,which
coul
d be
see
n
from
Figure 3.There was a
cert
ain pro
portio
nal relati
o
n
sh
ip betwee
n
the active po
wer a
nd re
active
power,
Q/P
tan
, where
φ
wa
s the
power fa
ctor
angle. With
i
n
the rang
e of
rated wi
nd
speed,
the output po
wer of
WTs in
cre
a
s
ed with i
n
crea
sing
win
d
spe
ed.
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TELKOM
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ISSN:
1693-6
930
Flicker Measurem
ent and
Grey
Di
saster Prediction of Grid
-Connect
ed .... (Zhanqiang Zhang)
395
Figure 3. Active Power a
n
d
Rea
c
tive Power
3.2.2. Relatio
n
ship bet
w
e
e
n Wind Spe
e
d and Flick
e
r Coe
fficie
n
t
It can be se
en from Fig
u
re 4 that the f
unctio
n
relati
on between fl
icker
coeffici
ent and
wind
spee
d
whe
n
the
net
work i
m
pe
da
nce
ph
ase a
ngle
k
ψ
are
30
°,50°,70
°
an
d85
°, the
sho
r
t-
circuit ratio i
s
50.The la
rge
r
grid impe
dan
ce ph
as
e ang
le is, the grea
ter flicker coe
fficient is .
Figure 4. Rel
a
tionship bet
wee
n
Win
d
Speed a
nd Flicker
Coeffici
en
t
3.2.3. Measu
rement o
f
Short-term Flic
ker
The flicker of
WTs can b
e
measure
d
from
two asp
e
cts of continuou
s ope
rat
i
on and
swit
chin
g op
eration. In th
is pa
per
we
studie
d
the
measurement
of f
licke
r u
n
der
contin
uo
us
operation.Th
e gen
eratio
n
of flicke
r un
d
e
r continu
o
u
s
operation
wa
s cau
s
ed by
cha
nge
s in
wind
spe
ed, whi
c
h
ca
used
th
e cha
nge
s of
reactive
and
active p
o
wer.
The m
e
a
s
ure
m
ent pe
rio
d
of
sho
r
t-time fli
c
ker is 10
mi
nutes,the
me
asu
r
em
ent p
e
riod
of lo
ng
-time flicke
r i
s
2
hou
rs.In
the
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93-6
930
TELKOM
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Vol. 13, No. 2, June 20
15 : 391 – 40
0
396
contin
uou
s o
peratio
n
state,
st
P
and
lt
P
have t
he
same
flicker valu
e. If the flicke
r val
ue of
WT
s
excee
d
s th
e l
i
mit value (
st
P
=1), it wo
uld a
ffect the op
erati
on of the
power
syste
m
. The
upp
er
limit values
of
st
P
=1 and
st
P
=
0
.5
w
e
re mark
ed in Figur
e
5.
st
P
=0.5 wa
s th
e
uppe
r di
sa
ste
r
limit
value of flicke
r grey di
sa
ste
r
pre
d
ictio
n
.
Figure 5. Measu
r
em
ents o
f
Short-term
Flicker
4. Model of F
licker Gre
y
Disas
ter Pre
d
iction
The thoug
hts of flicker
g
r
ey disaste
r
pr
edi
ction
we
re a
s
follo
ws: The mea
s
u
r
eme
n
t
values of flicker
st
P
we
re
finit
e
,it met that grey syste
m
used
the
"poor info
rm
ation" as the
resea
r
ch obj
ect. The
thre
shol
d value
of flicker
wa
s set
0.5 a
c
co
rding
to the
measured va
lue.
Becau
s
e in th
e stable o
peration of WT
s, and wh
en th
e mea
s
ureme
n
t time was
short, more than
1 of the value of
st
P
wa
s less.The less da
ta could affe
ct
the establi
s
hme
n
t of grey disa
ster
predi
ction m
o
del, so we chose
st
P
=0.5 a
s
the threshol
d. If the valu
e of the origi
nal se
que
nce
excee
ded
the
thre
shol
d, th
en the
di
sa
ster
points were sele
cted to
co
nstitute
a
seq
uen
ce
tha
t
wa
s c
a
lled di
sa
st
er
seq
u
e
n
ce.
Th
e di
s
a
st
er
se
que
n
c
e
wa
s mad
e
up of the
exce
ssive flicker
value.The d
a
t
e seq
uen
ce
wa
s mad
e
u
p
acco
rdin
g t
o
the o
c
currence time of
each excessive
flicke
r valu
e.
Establishing
GM (1,1) m
o
del for t
he d
a
te seque
nce
to predi
ct the future
di
sa
ster
date se
que
nce[14].
4.1. Method
of Grey
Disaster Predic
ti
on
Time se
rie
s
d
a
ta of grey disa
ster p
r
edi
ct
ion are a
s
foll
ows:
(
0
)
(
0)
(
0
)
(
0)
X
(
t)
=
{
X
(
1
)
,
X
(
2
)
,
...,
X
(
N)
}
(5)
If the thre
sh
old value
λ
a
r
e give
n , th
e num
bers i
n
(t)
X
(0)
whi
c
h i
s
la
ge
r than
λ
(up
p
e
r-
disa
ster valu
e)
or le
ss tha
n
λ
(d
own-di
saster valu
e)
are
re
ga
r
ded
as a
bno
rmal
value
s
.And t
hen
we
sel
e
ct th
e
ab
no
rmal v
a
lue
s
whi
c
h f
o
rm
a n
e
w d
a
ta sequ
en
ce
, whi
c
h i
s
cal
l
ed the
di
sa
ster
seq
uen
ce.
(0
)'
(0
)
(
0
)
(0
)
12
m
X
(t)
=
{
X
(
i
)
,
X
(
i
)
,
.
..
,
X
(i
)}
,
m
<
N
(6)
The sequ
en
ce of disaste
r
time is m
ade
up a
c
cordi
ng
to occurre
n
ce
time of each
data in
the formula (7).
(0)
(
0
)
(0)
(
0)
Q(
t
)
=
{
Q(
1
)
,
Q
(
2
)
,
.
.
.
,
Q
(
m
)
}
,
m
<
N
(7)
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TELKOM
NIKA
ISSN:
1693-6
930
Flicker Measurem
ent and
Grey
Di
saster Prediction of Grid
-Connect
ed .... (Zhanqiang Zhang)
397
We u
s
e the
(t)
Q
(0)
date se
que
nce to establi
s
h
GM (1,1
) mo
del to pre
d
ict
the occu
rre
nce
time in the future. The G
M
(1,1) m
odel is de
scribe
d a
s
follows.
Den
o
te the original data
se
quen
ce a
s
:
(0
)
(
0
)
(
0
)
(
0
)
X
(
t
)
=
{
X
(
1
)
,
X
(
2
)
,
...,
X
(
n
)
}
(8)
Whe
r
e n is th
e numbe
r of
st
P
observed.
The AGO formation of
(t)
X
(0)
is d
e
fined a
s
:
(1
)
(
1
)
(
1
)
(
1
)
X
(
t
)
=
{
X
(
1
)
,
X
(
2
)
,
...,
X
(
n
)
}
(9)
W
h
er
e
k
(1
)
(
0
)
i=
1
X
(
k
)
=
X
(
i
)
,
i
=
2
,
3
,
...,
n
(10)
GM (1,1
) m
o
del can b
e
co
nstru
c
ted
by
establi
s
hi
ng
a first o
r
d
e
r d
i
fferential eq
u
a
tion for
(t)
X
(1)
as:
(1)
(1
)
dx
+a
x
=
b
dt
(11)
The sol
u
tion
of (11)
can b
e
obtaine
d by
using the le
a
s
t squ
a
re m
e
thod. That is,
(0
)
-
a
k
bb
x
(
k
+
1
)
=
[x
(1)
-
].e
+
aa
(12)
W
h
er
e
T
a=(
a
,
b
)
(13)
The value
s
of a and b are
given usi
ng the lea
s
t squ
a
r
es m
e
thod.
T-
1
T
a=(
B
B
)
B
Y
(14)
W
h
er
e
(0
)
(0
)
(0
)
x
(2
)
x
(3
)
Y=
...
x
(n
)
(15)
(1
)
(
1
)
(1
)
(
1
)
(1
)
(
1
)
1
-(
x
(
1
)
+
x
(
2
)
)
1
2
1
-(
x
(
2
)
+
x
(
3
)
)
1
B=
2
...
1
-(
x
(
n
-
1
)
+
x
(
n
)
)
1
2
(16)
The sim
u
latio
n
values of
(k)
X
(0)
is
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93-6
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15 : 391 – 40
0
398
(0
)
(
1
)
(1
)
x
(k
+
1
)
=
x
(
k
+
1
)
-
x
(k)
(17)
4.2. Flicker disaste
r
date forec
a
s
t
The data of e
s
tabli
s
hin
g
the disa
ster p
r
edict
io
n mod
e
l were take
n
from the test data of
st
P
. The origin
al data se
que
nce wa
s:
(0)
X
(
t)
=
{
0.25
34,
0.2541,
0.2
652,
0.2727
,
.
..,
0
.77
09,
1.1
797,
0.8404
,
.
..,
0
.2
275,
0.2443
,
0
.2
442}
(18)
Acco
rdi
ng to
the actu
al test conditio
n
s
o
f
the system,t
he di
sa
ster i
s
happ
ened
when the
value of
st
P
is greater than o
r
equal to 0.5.
The procedu
re
s of flicker d
i
sa
ster
p
r
edi
ction [15]-[16]
are sho
w
n a
s
follows:
1) The val
ue,
whi
c
h is
gre
a
t
er than o
r
eq
ual to t
he thresh
old of 0.5,
are
sele
cted f
r
om the o
r
igi
nal
data
(t)
X
(0)
.This di
saster
seq
uen
ce
s are fo
rme
d
as follo
ws:
(0
)'
X
(
t
)
=
{
0
.7
709,
1
.
1797,
0.8404,
0.631
,
0
.7
22,
0.5468,
0.616
9,
0.5
929,
0.6457,
0.506,
0.547
9
}
(19)
2) The di
sa
st
er se
que
nce is:
(0
)'
(0
)
(
0
)
(0
)
(
0
)
(0
)
(0
)
(
0
)
(0
)
(
0
)
(0
)
(
0
)
X
(
t
)
=
{
X
(
32
)
,X
(
33
)
,X
(
34
)
,X
(
42
)
,X
(
46
)
,
X
(
55
)
,X
(
63
)
,X
(
65
)
,X
(
69
)
,X
(
78
)
,X
(
79
)}
(20)
3) The
seq
u
e
n
ce of di
sa
ster time is:
(0)
Q
(
t)
=
{
32,
33,
34,
4
2
,
46,
5
5
,63
,
65,
69,
78
,
79}
(21)
4) Establi
s
hi
n
g
the GM (1,1
) model for th
e seq
uen
ce o
f
disaste
r
time. The 1-AG
O seq
uen
ce i
s
:
(1)
Q
(
t
)
=
{
32,
65
,
99,
1
41,
1
87,
242,
305
,
3
70,
439,
517,
5
96}
(22)
Next gene
rati
on se
que
nce is:
(1)
Z
(
t)
=
{
48.
5,
82,
120
,
1
6
4
,
214
.5
,
2
73.
5,
33
7.
5,
40
4.
5,
478
,
5
5
6
.
5
}
(23)
We u
s
e the le
ast-squ
a
res
method to sol
v
e the a and b,then we
ca
n obtain:
a
-
0.096
6
a=
=
b
30.
5236
(24)
The GM (1,1) model is:
(1)
0.
09
6
6
t
Q
(
t
+
1
)
=
3
47
.9
8e
-
3
15
.98
(25)
The re
du
cing
value is:
(0
)
0.0966t
Q
(
t
+
1)
=
3
2.04
e
(26)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Flicker Measurem
ent and
Grey
Di
saster Prediction of Grid
-Connect
ed .... (Zhanqiang Zhang)
399
5. Results a
nd Discu
ssi
on
In the pa
pe
r we me
asu
r
ed th
e flicker
coeffici
ent
and
win
d
spe
ed
whe
n
k
ψ
wer
e
30°,50
°
,70°
a
nd85
°,whi
c
h
coul
d be se
e
n
from Figure 4.
st
P
could b
e
cal
c
ulate
d
by the equation
(2).T
he 1
20 d
a
ta we
re
obt
ained
as sho
w
n in
Figu
re
5.
We co
uld predi
ct
the occurre
n
ce
time
of
exce
ssive flicker by the eq
uation (2
6)
which
coul
d be
seen from the Table 1.
Table 1. Error che
ck tabl
e
ser
i
al
number
O
r
iginal
data
(0
)
Qt
Analog
data
(0
)
Qt
Residual
error
(0)
(0)
kQ
t
Q
t
Relative error
(0)
k
k
Qt
1 32
32.0000
0
0
2 33
35.2914
-2.2914
6.94%
3 34
38.8703
-4.8703
14.32%
4 42
42.8120
0.8120
1.93%
5 46
47.1535
1.1535
2.51%
6 55
51.9353
3.0647
5.56%
7 63
57.2020
5.798
9.20%
8 65
63.0028
1.9972
3.07%
9 69
69.3918
0.3918
0.57%
10 78
76.4287
1.5713
2.01%
11 79
84.1793
5.1793
5.56%
Thro
ugh
ana
lysis
of the t
e
st d
a
ta a
n
d
disa
s
t
er
pr
ed
ic
tio
n
,
w
e
dr
e
w
co
nc
lus
i
o
n
s
as
follows
:
1)
The
calculati
on of flicker coeffici
ent i
s
cl
osely rel
a
ted to the
netwo
rk i
m
p
edan
ce
pha
se
angle
s
an
d a
nnual ave
r
ag
e wind
spe
e
d
.
2)
In orde
r to i
m
prove th
e a
c
cura
cy of flicke
r
p
r
e
d
ictio
n
,we shoul
d measure
the more data
to
establi
s
h the
disa
ster p
r
e
d
i
c
tion mod
e
l.
3)
The p
r
edi
ctio
n re
sults
sh
o
w
ed that
the
averag
e rel
a
tive erro
r wa
s
11
k
k=
2
1
∆
=
∆
=
5
.13%
10
,the
relative accu
racy wa
s 94.8
7
%,which th
e fitting res
u
lt is
s
a
tis
f
ac
tory.
4)
The d
e
velop
m
ent coeffici
ent of GM
(1,
1
) mo
del
wa
s a=
-0.09
66,T
he literature [
17] co
ncl
ude
d
that GM (1,1) model co
uld
be used to predict
the lon
g
-
term flicke
r d
i
sa
ster when
-a
≤
0.3.
6. Conclusio
n
Acco
rdi
ng to
IEC 6140
0-21 sta
nda
rd,
w
e me
asur
e
d
the short
-
term flicke
r a
nd flicker
coeffici
ent of
a sin
g
le
WT
s
on the
win
d
farm, an
d
g
o
t the flicker val
ues
of multi-WT
s through
the
flicke
r asse
ssment p
r
o
c
e
dure
s
. We
should fully
consi
der the i
n
fluen
ce of wind
spee
d on the
measurement
value, and
ensure the
reliability of
t
he test. We
tested th
e
short term fli
c
ker
st
P
values a
nd p
r
edi
cted the
occurre
n
ce time of excessive flicker
b
y
using the
grey syste
m
theory.The
re
lative accu
ra
cy of the m
o
del was hi
gh
er. Its fitting result
wa
s b
e
tter, whi
c
h
sui
t
ed
the long-te
rm
predi
ction for flicker
disa
st
er.
Ackn
o
w
l
e
dg
ments
This pa
pe
r was supp
orted
by National
Natural Sci
e
n
c
e Found
ation
of China (5
1
1670
11,
5146
7016
), Inner Mo
ng
olia sci
en
ce
and techn
o
logy plan
proje
c
t (20
1
3030
3) an
d
the
coo
peration p
r
oje
c
t of Chin
a and Denma
r
k (200
9DFB
6025
0).
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