TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
0
2
~ 651
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.467
1
6502
Re
cei
v
ed O
c
t
ober 1
0
, 201
3; Revi
se
d May1
9, 2014;
Acce
pted Jun
e
10, 2014
An improved Grey-based Approach for Short-Term
Wind Power Prediction
Bin Zeng*, Hong-bing Xu,
Jian-xiao Zo
u, Kai Li, Xia
o
-shu
ai Xin
Schoo
l of auto
m
ation e
ngi
ne
erin
g,
Univers
i
ty of Electro
n
ic
Scienc
e an
d T
e
chn
o
lo
g
y
of C
h
in
a,
No.20
06, Xi
yu
an Ave, W
e
st Hi-T
e
ch Z
one, Che
ngd
u 61
17
31, Sichu
an, C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zengb
in
200
6
@
12
6.com
A
b
st
r
a
ct
W
i
th the expa
nsio
n of w
i
nd farm insta
l
l
a
tio
n
s in
most co
untries a
ll ove
r
the w
o
rld, the pow
er
gen
eratio
n
has
alre
ady
sig
n
ifi
c
antly
influ
enc
ed
on th
e st
a
b
ility a
n
d
secur
i
ty of the
pow
e
r
grid
after
gri
d
-
conn
ectio
n
. W
i
nd pow
er fore
casting is an
effectiv
e met
h
od for guar
ant
ees stabi
lity of the pow
er output
from w
i
nd far
m
. T
h
is pap
er pr
opos
ed a
n
i
m
p
r
oved GM(1,1)
base
d
pre
d
icti
on
meth
od, a
n
d
focuses
on t
h
e
w
i
nd pow
er
o
n
lin
e pr
edicti
o
n usi
ng th
e r
e
lati
onsh
i
p
bet
w
een the w
i
n
d
spe
ed
and
the w
i
nd
po
w
e
r
gen
eratio
n. T
h
e si
mulati
on
re
sults h
a
ve
verif
i
ed
that
th
e
de
velo
ped
a
ppr
o
a
ch, w
i
th GM r
o
lli
ng
mech
an
i
s
m,
d
a
t
a
p
r
e
p
r
o
c
e
s
si
n
g
a
n
d
ba
ckg
r
o
u
n
d
va
l
u
e
o
p
t
im
i
z
ing
h
a
s
b
e
tte
r p
r
e
d
i
ctio
n
p
r
e
c
i
s
io
n ove
r
th
e
trad
i
t
i
onal
GM rolli
ng
mo
del
an
d d
a
ta s
e
ries s
m
ooth
i
n
g
mod
e
l. F
i
n
a
l
l
y, utili
z
e
d
a c
a
se stu
d
y at
A
z
u
o
q
i
w
i
nd
far
m
locate
d in Inn
e
r
Mongo
lia pr
o
v
ince of Ch
ina,
w
h
ich obv
io
usl
y
reali
z
e
d
w
i
nd
pow
er gen
erat
ion pr
edicti
on f
o
r
opti
m
i
z
i
n
g the
w
i
nd pow
er co
ntrol in the w
i
n
d
farm in r
eal ti
me.
Ke
y
w
ords
: Grey theory, GM(1,1), predicti
o
n
,
w
i
nd pow
er
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
No
wad
a
ys, wind power ge
neratio
n is un
derg
o
ing
the
fastest rate o
f
growth of any form
of elect
r
icity
gene
ration i
n
the wo
rld. T
he po
we
r
ge
neratio
n from
the win
d
farms h
a
s
sig
n
ificant
influen
ced o
n
the stability and security of the power
grid
after grid
-co
nne
ction. For
a certai
n type
of wind tu
rbin
e, max output
power i
s
fixed unde
r
certai
n wind
sp
eed
. In other words, wi
nd po
wer
c
a
n in
d
i
r
e
c
t
ly p
r
ed
ic
ted
by fo
r
e
ca
s
t
ing w
i
nd
s
p
e
e
d
at
the hub
height of
ea
ch win
d
turbi
ne,
throug
h the
manufa
c
ture’
s
po
we
r cu
rv
e [1-4]. T
he
physi
cal ap
proach investe
d
for win
d
sp
eed
forecastin
g,
whi
c
h u
s
e
s
t
opog
rap
h
ical
informatio
n
of
the site to
d
e
scrib
e
the
wind flow i
n
de
tail
applying flui
d
dynami
c
s eq
uation
s
[5].
Wind
speed
predi
ction
is an
effe
ctive method
fo
r p
o
wer
control.
In re
cent d
e
cade
s, seve
ral
time-seri
e
s-
b
a
se
d mo
dels
have be
en
studied fo
r
win
d
sp
eed
forecastin
g,
such
a
s
a
u
toregre
s
sive
(AR), m
o
ving
a
v
erage
(MA
)
algorith
m
. Art
i
ficial intellig
e
n
ce
and hyb
r
id m
odel
s, incl
udi
ng ad
aptive
netwo
rk ba
se
d Fu
zzy inte
rferen
ce
syste
m
(ANFIS) a
nd
radial b
a
si
s functio
n
(RBF
), are also in
volved for ho
urly wind sp
eed fore
ca
sti
ng [6-9]. The
s
e
model
s requi
re la
rge
set
of histori
c
al
data fo
r thei
r para
m
eters
estimation,
strong m
a
chin
e
learni
ng abilit
y or compli
cated comp
uting process, which
limited application in real wind farm
.
Grey syst
em theory is suited to predi
ct with
poo
r dat
a [10]. More and mo
re sch
o
lars ha
s
tried to take
GM(1,1
) mo
del into the
study of pre
d
iction
whe
n
lacki
ng of l
a
rge
numb
e
r of
histori
c
al d
a
ta for learning
and com
puti
ng po
wer
i
s
limited [11, 12]. While the traditional GM
(1,1)
model i
s
ap
prop
riate fo
r steady d
e
velopme
n
t
tenden
cy of p
r
edi
ction b
a
ckgroun
d, lots of
transfo
rmatio
n method
s p
r
opo
sed a
nd
most of them
can
not wo
rk
well
when th
e discrete series
cha
nge
ra
pidl
y. Wind
sp
ee
d in
win
d
p
o
w
er pla
n
t al
ways
cha
nge
s
sha
r
ply,
so, it
is
ne
ce
ssary
to
find a more ef
ficient metho
d
for wind
sp
eed fore
ca
sti
ng.
In this
pap
e
r
, an
imp
r
ov
ed G
M
(1,1
) model
p
r
op
ose
d
fo
r p
r
edictin
g
win
d
po
we
r
continuously. First, rolling
mech
ani
sm i
n
troduced for forecastin
g wind
speed cont
inuously, and
only four hist
orical value
s
need
ed in on
e predi
ct
ion
cycle. Secon
d
, we pre
p
ro
ce
ss d
a
ta se
ries
with smoothi
ng meth
od a
nd optimi
z
e
b
a
ckgroun
d va
lue of tra
d
itio
nal alg
o
rithm,
whi
c
h im
pro
v
ed
predi
ction accuracy
in the very great
degree. Fi
nall
y, the proposed appr
oach is
illustrated b
y
impleme
n
ting
it in the win
d
sp
eed a
n
d
active
po
we
r predictio
n
of a middle
-
size
wind p
o
wer
plant.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An im
proved
Gre
y
-ba
s
ed
Appro
a
ch for Short-T
e
rm
Wind Po
we
r Predi
ction (Bi
n
Zeng
)
6503
2. Rese
arch
Metho
d
The
comm
on
pro
c
e
s
se
s o
f
traditional
GM(1,1
)
algo
rithm for wi
n
d
spee
d fore
ca
sting
listed a
s
belo
w
[10].
2.1. Accum
u
lated G
e
ner
a
ting Ope
r
ation (AG
O
)
Serve the sa
mple data of wind
spee
d, colle
cted
fro
m
wind turbi
n
e, as the inpu
t data set
(0)
(
0
)
(0)
(
0)
(
1
),
(
2
),
...,
(
)
VV
V
V
n
for the GM
(1,1) mo
delin
g, and at lea
s
t four d
a
ta i
n
clu
ded
in the data set. Then, a
new accum
u
lated ro
w matrix
(1
)
V
generated by the first-o
r
de
r
Accu
mulate
d Gene
rating O
peratio
n (1
-A
GO).
(1
)
(
1
)
(1
)
(
1
)
(
1
)
,
(
2
)
,
...,
(
)
VV
V
V
n
(
1
)
(1
)
(
0
)
(1
)
(
0
)
1
(1
)
(
1
)
1
,
2
,
...
,
()
(
)
i
k
VV
in
Vi
V
k
(
2
)
2.2. Grey
Differen
t
ial Equ
a
tion and Pa
ram
e
te
rs Ide
n
tifica
tion
The definition
of GM(1,1)
Model is fo
rm
ulated a
s
:
(0
)
(
1
)
()
Va
z
i
b
(
3
)
Whe
r
e
(1
)
z
, the backgroun
d value, can b
e
e
x
presse
d as f
o
llow,
(1
)
(
1
)
(
1
)
1
(
)
(
)
(
1
)
2
,
...,
2
z
i
Vi
Vi
i
n
(
4
)
And the first-orde
r whitene
d di
fferential
equatio
n expressed a
s
:
(1
)
(1
)
dV
Vb
di
(
5
)
2.3. Param
e
t
e
rs Identi
fic
a
tion of t
h
e
GM(1,1
) Mod
e
l
The pa
ramet
e
rs a a
nd b can be calcula
t
ed with the least squa
re
method a
s
follow:
1
()
T
TT
ab
B
B
B
Y
(
6
)
Whe
r
e the m
a
trixes B and
Y can be exp
r
esse
d by:
(1
)
(1
)
(1
)
(2
)
1
(3
)
1
...
...
()
1
z
z
B
zn
(
7
)
(0)
(0
)
(0
)
(2
)
(3
)
...
()
V
V
Y
Vn
(
8
)
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ISSN: 23
02-4
046
TELKOM
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Vol. 12, No. 9, September 20
14: 65
02 – 651
0
6504
2.4. Calculate Prediction
Value
Finally, the
predi
cted tim
e
-seri
e
s
data
(1
)
V
can
be o
b
tained
by me
thod of inve
rse
accumul
a
ted gene
rating
o
p
e
ration (IAG
O):
(0
)
(
1
)
(0
)
(0
)
(
)
(1
)
(
1
)
(1
)
(
1
)
(
1
)
1
,
2
,
...,
aa
i
VV
b
Vi
e
V
e
a
in
(
9
)
2.5. Prediction Precision
The preci
s
io
n
of predictio
n
can be te
ste
d
by
the size
of residu
als
and rel
a
tive errors.
Relative error
()
i
can be calculated a
s
is shown in Equa
tion (10
)
:
(0
)
(
0
)
(0
)
ˆ
()
()
(
)
1
,
2
,
...,
()
Vi
Vi
ii
m
Vi
(
1
0
)
Whe
r
e m is t
he numb
e
r of
predi
cted val
ues. And ave
r
age e
r
ror
()
av
g
is expre
s
sed a
s
:
1
1
(
)
(
)
1
,
2
,
..
.,
m
i
av
g
i
i
m
m
3. Im
prov
ed
GM(1,1
) Alg
o
rithm
3.1. Rolling Modeling an
d Wind Spee
d Prediction
The tradition
al GM(1,1
) model ca
n only
be
used for
predi
cting lim
ited numbe
r of data
seri
es,
and
rolling m
odeli
ng me
ch
ani
sm is involve
d
for p
r
edi
ctin
g the
contin
u
ous
win
d
sp
eed
data
se
ries [
10]. The
met
hod
of rolling
modeli
ng i
s
refre
s
hi
ng th
e real
wind
speed
data
se
ries
(0
)
V
, which h
a
s f
our d
a
ta in this wo
rk, by re
moving the ol
dest value a
n
d
inse
rting int
o
the latest
one. Wh
en th
e pre
d
iction fi
nish
ed with d
a
ta se
rie
s
be
gin with
(0
)
()
Vi
, and
(0
)
V
will changed as
follow by rolli
ng.
(0
)
(
0)
(0
)
(
0)
(
1
)
,
(
2
)
,
...,
(
)
VV
i
V
i
V
i
n
(
1
2
)
Above ope
rat
i
ons repe
ated
as long a
s
n
e
we
r win
d
sp
eed value exi
s
ted.
3.2. Optimizing the Back
ground Valu
e
From th
e p
r
e
d
iction
pro
c
e
ss
of GM
(1,1
), we
ca
n se
e that predi
ction p
r
e
c
isio
n
depe
nd
s
on paramete
r
s a an
d b, i.e. precisi
o
n is
clo
s
ely related to original data serie
s
(0
)
V
and
backg
rou
nd value
(1)
()
zi
.
In traditional
GM(1,1
) alg
o
rithm, Equa
tion
(4
) is
ch
ose
n
to de
scribe the
ba
ckgroun
d
value b
a
sed
the a
s
sumpti
on that th
ere
is
no
muta
ti
ons ap
pea
re
d in
a ve
ry short time
inte
rval.
Ho
wever, bei
ng a sho
r
t pe
riod of time,
∆
t is only a re
lative concept
ion. In this period of time, the
cha
nge of wi
nd sp
eed ma
y include mut
a
tions, a
s
is shown in Figu
re 1.
A integral
eq
uation
can b
e
obtain
ed from traditio
nal
GM(1,1
) mo
del in Equ
a
tion (3
) at
regio
n
1,
ii
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An im
proved
Gre
y
-ba
s
ed
Appro
a
ch for Short-T
e
rm
Wind Po
we
r Predi
ction (Bi
n
Zeng
)
6505
(1
)
(1
)
Vi
(1
)
()
Vi
i
1
i
(1
)
()
Vt
Figure 1. Erro
r of Backgrou
nd Value
(1
)
(1
)
11
ii
ii
dV
dt
a
V
dt
b
dt
i.e.
(0)
(
1
)
1
()
i
i
Vi
a
V
d
t
b
(
1
3
)
Comp
ari
ng Equation (13)
with GM(1,1)
model in
Equ
a
tion (3
), it is easy to find out that
error come
s from re
pla
c
em
ent
(1
)
1
i
i
Vd
t
by
(1
)
z
.
In orde
r to eliminate the error,
(1
)
z
can be calcul
ated a
s
follows,
(1
)
(
1
)
(1
)
()
1
(
)
(
)
(
)
(
1
)
zi
i
V
i
i
V
i
(
1
4
)
Whe
r
e
determined by met
hod of ‘avera
ge syste
m
slo
pe’ [13] with the followi
ng rules:
1)
02
()
2
1
11
2,
3
,
.
..,
1
i
ii
i
ki
ik
i
k
i
ki
in
2)
()
1
n
And the relati
ve position
s
i
k
determi
ned b
y
the followin
g
formula:
(0)
(
0
)
ln
(
)
(
1
)
ln
i
av
g
Vi
V
k
(
1
5
)
Whe
r
e the av
erag
e slo
pe coefficient
av
g
calculate
d
as foll
ow:
(0
)
(1
)
(0)
()
(1
)
n
avg
Vn
V
(
1
6
)
3.3. Smoothing the Origi
n
al Data Series
Equation (14
)
develope
d with the assum
p
tion t
hat ori
g
inal data
se
ries i
s
ba
se
d
on the
homog
ene
ou
s expon
ential
law, and
sm
oothne
ss ch
a
r
acte
ri
stic of
origin
al data
seri
es i
s
the
main
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
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KA
Vol. 12, No. 9, September 20
14: 65
02 – 651
0
6506
factor that inf
l
uen
ce
s the predi
ction p
r
eci
s
ion. Th
u
s
, it is necessary to prep
ro
ce
ss the o
r
igi
nal
data, to make
it more smo
o
t
hness an
d cl
ose
to the ch
ara
c
teri
stic of
exponential l
a
w.
Functio
n
1
bx
ae
was
utilized to improve the sm
oot
hness of original
seri
es,
thus
predi
ction
a
c
curacy
imp
r
o
v
ed [12]. But
lots of
non
se
nse
p
r
edi
ctive value
s
app
ear wh
en
we
use
this function f
o
r pre
d
ictin
g
wind spee
d conti
nually. So, the sum of
mean value
and max differ
value se
rved
as re
du
ction
buffer ope
rat
o
r
redu
c
d
to eliminate the abnormal pre
d
ictio
n
results.
For
kee
p
ing
con
s
i
s
ten
c
y of the equ
ations
as
before, the origi
n
al win
d
spee
d se
rie
s
expre
s
sed a
s
(0
)
X
, instead of
(0
)
V
. Before op
er
ation (1
-AGO
) in (1
), s
e
rie
s
(0
)
V
establishe
d
from
(0
)
X
by the formul
a:
(0
)
(0
)
()
1
()
re
d
u
c
bX
i
Vi
d
ae
(
1
7
)
Whe
r
e
red
u
c
d
can b
e
cal
c
ulate
d
as:
1
(0
)
(
0
)
(0
)
11
1
1
()
m
a
x
(
)
(
)
nn
n
r
e
duc
ii
j
i
dV
i
V
i
V
j
n
(
1
8
)
Acco
rdi
ngly, the final pre
d
i
c
tion data
will
expresse
d a
s
:
(0
)
(0
)
(0
)
(1
)
(1
)
l
n
(1
)
1
red
u
c
Vi
Xi
b
d
aV
i
(
1
9
)
Once colle
cted the
curre
n
t
wind
spe
e
d
value, wind
spe
ed of n
e
xt time interva
l
can
be
predi
cted
wit
h
the im
proved al
gorithm.
Figu
re
2 sh
ows
the
pred
iction pro
c
e
s
s
b
a
sed on
t
he
improve
d
GM
(1,1)
rolling m
odel for wi
nd
spe
ed predi
ction.
(1)
(
1
)
(1
)
(
1)
(
1
),
(
2
),
..
.
,
(
)
XX
X
X
n
(0)
(0)
()
1
()
re
du
c
bX
i
Vi
d
ae
(1
)
(
0
)
(1
)
(
0
)
1
(1
)
(
1
)
()
(
)
i
k
VV
Vi
V
k
(1
)
(
1
)
(1
)
()
1
(
)
(
)
(
)
(
1
)
z
ii
V
i
i
V
i
(0
)
(
1
)
(0
)
(0
)
(
)
(1)
(
1)
(1
)
(
1
)
(
1
)
aa
i
VV
b
Vi
e
V
e
a
(0
)
(0
)
(0
)
(1
)
(1
)
l
n
(1
)
1
r
e
duc
Vi
Xi
b
d
aV
i
Figure 2. Flow Ch
art of Wi
nd Speed Pre
d
ic
tion
with Improve
d
GM(1,1) Algorith
m
4. Results a
nd Analy
s
y
s
Sample data
of wind sp
ee
d and po
wer
colle
cted fro
m
Azuoqi wi
n
d
farm locate
d in Inner
Mongoli
a
pro
v
ince of Chi
n
a. The rate p
o
we
r of wi
n
d
turbine i
s
1.5
M
W, whi
c
h i
s
cha
r
a
c
teri
ze
d by
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
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An im
proved
Gre
y
-ba
s
ed
Appro
a
ch for Short-T
e
rm
Wind Po
we
r Predi
ction (Bi
n
Zeng
)
6507
a cut in
win
d
sp
eed
of 3
m
/s, rate
d
wi
nd
spe
ed
of
11.7m/s and
a cutting o
u
t win
d
spe
e
d
of
25m/s.
Original wi
nd speed data
was sampled every 100 millis
econds from anem
ometers
mounted
on
cabi
n of the wind tu
rbin
e, and the me
an value in 5
minutes
cal
c
ulated for a
c
t
i
ve
power predi
ction. In order t
o
ensu
r
e the
pre
c
isi
on
of predi
ction, 3 d
e
cimal di
gits retaine
d
in the
mean
value
of 5 mi
nute
s
. A whole
day
’s
sam
p
le
dat
a set of
win
d
sp
eed
an
d
power coll
ect
e
d
from one
win
d
turbine, a
s
pre
s
ente
d
in Figure 3.
Figure 3. Sample Data Se
t of Wind Spe
e
d
From Fi
gure
3, we
can
se
e that wind
speed
kee
p
s
stable rel
a
tively betwee
n
po
int 41th
and 6
0
th, wh
ile co
ntinue
s
cha
nge
sh
arply betwe
en
point 16
0th a
nd 24
0th in
the
sampl
e
d
a
ta
set. So, we will verify the algorithm p
r
edi
ction
p
r
e
c
isio
n not only with the wind
sp
eed data
se
ri
es
of whole d
a
y and in the co
ndition of sta
b
le and rape
d
chan
ging.
4.1. stable Wind Simulation
We sele
cted real wind
spe
ed
data set
from
41th
to
60th as S1 to
verify the algorithms
,
and S2={5.32
, 5.35, 5.28,
5.45, 5.
74, 5.78, 5.59, 5.83, 6.25, 6.72,
6.37, 6.79, 6.65, 6.03, 6.12
,
6.02, 6.63, 6.05, 5.86, 6.77
}.
Predictio
n result
s with dif
f
erent metho
d
s liste
d in Table 1.
Table 1. Pred
iction Result whe
n
Win
d
Speed
Cha
nge
Gently
Time point
real w
i
nd
speed
(m/s
)
predicted
w
i
nd speed(m/s) a
nd M
R
E
Traditional GM
(1
,1)
Smooth
GM
(1,1)
Improved
GM(1,
1
)
45th
5.74
5.46(4.85
%)
5.45(4.98
%)
5.45(5.07
%)
46th
5.78
5.97(3.24
%)
5.95(2.86
%)
5.81(0.59
%)
47th
5.59
5.99(7.19
%)
6.01(7.50
%)
5.87(5.07
%)
48th
5.83
5.56(4.70
%)
5.55(4.87
%)
5.56(4.69
%)
49th
6.25
5.78(7.45
%)
5.78(7.60
%)
5.81(7.07
%)
50th
6.72
6.58(2.07
%)
6.54(2.71
%)
6.35(5.47
%)
51th
6.37
7.21(13.1
6
%)
7.17(12.6
3
%)
6.89(8.18
%)
52th
6.79
6.57(3.31
%)
6.58(3.14
%)
6.45(5.00
%)
53th
6.65
6.70(0.73
%)
6.68(0.38
%)
6.76(1.67
%)
54th
6.03
6.88(14.1
6
%)
6.92(14.6
8
%)
6.67(10.6
3
%)
55th
6.12
5.77(5.66
%)
5.69(6.98
%)
5.90(3.55
%)
56th
6.02
5.74(4.57
%)
5.81(3.53
%)
5.98(0.62
%)
57th
6.63
6.05(8.80
%)
6.05(8.81
%)
6.03(9.09
%)
58th
6.05
6.79(12.2
9
%)
6.69(10.5
5
%)
6.65(9.84
%)
59th
5.86
6.26(6.87
%)
6.25(6.59
%)
6.09(3.99
%)
60th
6.77
5.44(19.6
4
%)
5.49(18.9
6
%)
5.69(15.8
9
%)
MRE
-
7.42%
7.30%
6.03%
From the val
ue of mean relative erro
r (MRE
), we
ca
n see that improved G
M
(1
,1) has
better p
r
edi
ct
ed re
sult a
n
d
the pre
c
i
s
ion
of predi
ction
improve
d
18
.7%, 17.4%, 0.5% com
paring
with tradition
al, smooth, a
nd ada
ptive al
pha-ba
sed G
M
(1,1)
algo
risms re
sp
ectiv
e
ly.
0
50
100
15
0
200
250
30
0
0
5
10
15
i
n
t
e
rv
al
s
(
5
m
i
nut
es
) f
r
om
0:
00 t
o
23:
55
（）
W
i
nd S
peed
m
/
s
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TELKOM
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Vol. 12, No. 9, September 20
14: 65
02 – 651
0
6508
4.2. Rapid Changing Win
d
Simulation
The
wind
sp
e
ed data
set from 20
6th to
225t
h in
ra
pi
d ch
angi
ng
wind spee
d
se
ction a
r
e
sele
cted
as S2, and
S2={9.5
4
,8.5
7,7.58,8.45,6.
18,
12.83,8.1
1
,
8.52,6.93,10.
16,8.31,
12.1
4
,
10.23,8.32,7.
86,10.99,1
0
.3
,8.92,10.74,9.
44}. Predi
ctio
n result of using
the ab
o
v
e mentione
d method
s base
d
on rolli
ng
modelin
g techniqu
e to pre
d
ict win
d
sp
e
ed value
s
list
ed in Table 2.
Table 2. Pred
iction Result whe
n
Win
d
Speed
Cha
nge
Rapidly
Time point
real w
i
nd
speed
(m/s
)
predicted
w
i
nd speed(m/s) a
nd M
R
E
Traditional GM
(1
,1)
Smooth
GM
(1,1)
Improved
GM(1,
1
)
210th
6.18
8.08(30.6
7
%)
8.06(30.4
)
8.34(35.0
0
%)
211th
12.83
6.19(51.7
6
%)
5.64(56.0
7
%)
5.98(53.4
1
%)
212th
8.11
15.32(88.
94%
)
8.25(1.76
%)
10.75(32.
50%
)
213th
8.52
10.75(26.
12%
)
13.48(58.
19%
)
8.15(4.40
%)
214th
6.93
5.94(14.2
2
%)
7.42(7.00
%)
8.23(18.7
5
%)
215th
10.16
6.79(33.2
0
%)
6.40(37.0
0
%)
6.74(33.6
9
%)
216th
8.81
10.49(19.
04%
)
8.65(1.79
%)
9.64(9.40
%)
217th
12.14
10.50(13.
49%
)
12.22(0.6
8
%)
10.23(15.
69%
)
218th
10.23
12.68(23.
91%
)
10.78(5.3
6
%)
11.79(15.
21%
)
219th
8.32
11.77(41.
46%
)
13.02(56.
46%
)
11.63(39.
84%
)
220th
7.86
6.95(11.5
2
%)
7.17(8.83
%)
7.64(2.78
%)
221th
10.99
6.63(39.7
1
%)
6.98(36.5
3
%)
7.44(32.3
0
%)
222th
10.3
12.26(19.
00%
)
10.08(2.1
6
%)
10.57(2.6
5
%)
223th
8.92
12.23(37.
09%
)
13.99(56.
85%
)
11.60(30.
08%
)
224th
10.74
8.19(23.7
8
%)
8.06(24.9
1
%)
8.61(19.8
0
%)
225th
9.44
10.46(10.
80%
)
10.06(6.6
1
%)
9.92(5.07
%)
MRE
-
30.30%
24.41%
21.91%
Whe
n
win
d
spe
ed chan
g
e
s rapidly, the pr
eci
s
io
n
of predi
ctio
n based o
n
improve
d
GM(1,1
) in
creased 2
7
.7% and 1
0
.2%, comp
ari
ng
wi
th
that of trad
itional GM
(1,
1
) alg
o
rithm
and
smooth
GM(1
,1) algo
rithm respe
c
tively.
4.3. Whole d
a
y
w
i
nd spe
e
d simulatio
n
In orde
r to e
v
aluate the a
c
tual result o
f
these p
r
edi
ction meth
od
s, all data
se
t of 13th
May 2013 u
s
ed for fore
ca
sting. The mea
n
absolute error (MA
R
) an
d
MRE listed i
n
Table 3.
Table 3. Statistic of wh
ole
Day Win
d
Speed Pre
d
ictio
n
Prediction algorithm
MAE
MRE
traditional GM(1
,
1
)
1.43
19.24%
smooth GM(
1
,1)
1.39
19.05%
improved GM
(1,
1
)
1.18
16.01%
In Table 3, t
he sm
ooth G
M
(1,1)
mod
e
l
i
ng ma
ke o
u
t non
sen
s
e p
r
edict valu
es i
n
som
e
points
ch
angi
ng sha
r
ply, whi
c
h
re
sult i
n
the la
r
ge
e
rro
r. The
imp
r
oved
GM(1,1) mo
del in
this
work u
s
in
g b
o
th data
set
smoothi
ng a
n
d
ba
ckgro
u
n
d
value o
p
timizing te
ch
nol
ogie
s
ha
s hi
g
her
predi
ction
preci
s
e
com
paring with
the
smooth
GM
(1,1)
rolling
m
odel, with
its MAE and
M
R
E
redu
ce
d by 1
5
.1% and 1
5
.96%, so th
e i
m
prove
d
GM
(1,1) rolling m
odel h
a
ve the
best p
r
e
d
icti
on
pre
c
isi
on am
ong the thre
e
models.
4.4. Wind Pow
e
r
Predic
tion
Wind tu
rbi
ne
has
win
d
spe
ed-p
o
wer
cu
rve in theo
ry, whi
c
h
can
be
use
d
for
cal
c
ulatin
g
the active
po
wer by relatio
n
shi
p
bet
wee
n
win
d
spee
d
and
wind
po
wer. So, th
e
predi
ctive
wind
power
pre
d
P
can be
expresse
d a
s
belo
w
,
0[
3
,
2
5
]
[
17.
5
,
25
]
[3,
1
7
.
5
}
pr
e
d
r
a
t
e
cu
r
v
e
v
PP
v
Pv
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
An im
proved
Gre
y
-ba
s
ed
Appro
a
ch for Short-T
e
rm
Wind Po
we
r Predi
ction (Bi
n
Zeng
)
6509
Whe
r
e
pre
d
P
is p
r
edicte
d
wi
nd
power,
rat
e
P
the
rate p
o
wer
o
f
wind tu
rbin
e,
curv
e
P
the
queri
ed wi
nd
power a
c
cord
ing to power-spe
ed curve, v the predicti
v
e wind spee
d.
However, re
al situation o
f
wind turbi
n
e, such as
mech
ani
cal p
r
ope
rty and
electri
c
al
cha
r
a
c
ter, is different fro
m
theory values
whic
h were calculate
d
in the peri
od of desig
ni
ng.
Figure 4 sho
w
s the comp
arison of the
theory cu
rv
e and re
al wind spe
e
d
-
po
wer p
o
ints, real
value clo
s
e to
theory value on the cu
rve but not one a
nd the sam
e
.
Figure 4. Power in T
heo
ry vs. Real Power
The cu
rve
ex
pre
s
ses
the relation
ship b
e
twee
n wind
sp
eed and
output
p
o
wer
ca
n
be
establi
s
h
ed b
y
methods a
s
below.
1)
Se
rve
the
power
val
ue as refe
ren
c
e value
at eve
r
y wind
sp
eed
interval
of 0.
1m/s o
n
theory cu
rve.
2) Colle
ct the
wind
sp
eed
and o
u
tput p
o
we
r from
wi
nd turbi
ne, a
nd re
move a
bnormal
points.
3)
Gro
up th
e
real
po
we
r
values on
wi
nd
spe
ed i
n
terval a
s
befo
r
e, an
d
statistic offset
from theo
ry curve.
4) Revi
se referen
c
e valu
e
s
acco
rdin
g o
ffset value an
d freque
ncy o
f
occu
rren
ce.
The co
ntinuo
us predi
cted power
calcul
ated by the predi
cted wi
nd
speed d
a
ta with the
MAE value of
136.20
and
MRE value
of 23.72%. Co
mpari
s
o
n
bet
wee
n
predi
cted po
we
r an
d
real
power sho
w
n
as Figu
re 5.
Figure 5. Win
d
spe
ed-po
wer cu
rve in th
eory
5. Conclusio
n
The com
putin
g powe
r
and
histori
c
al d
a
ta are limited in most wind
power pla
n
t,
so a poo
r
data req
u
ire
d
short
-
term wi
nd power p
r
e
d
iction alg
o
rit
h
m is necessary for wind p
o
we
r pre
d
icti
on
0
50
100
15
0
200
25
0
300
-2
00
0
20
0
40
0
60
0
80
0
100
0
120
0
140
0
160
0
i
n
t
e
r
v
a
l
s
(
5
m
i
nut
es
)
f
r
om
0:
0
0
t
o
23
:
5
5
）
W
i
nd P
o
w
e
r
(
K
W
pr
ed
i
c
t
e
d
po
w
e
r
r
eal
pow
er
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
02 – 651
0
6510
and cont
rol. An
improved
GM(1,1
) rolli
ng
p
r
edi
ct
ion
model
pro
p
o
s
ed i
n
thi
s
p
aper with
bet
ter
perfo
rman
ce
in the ve
ry short-te
rm
pre
d
iction
comp
ared
to oth
e
r GM(1,1) ba
sed
simil
a
r type
method
s with
actu
al wind
spe
ed at
a mi
ddle-si
zed
wi
nd fa
rm. F
r
o
m
the te
st
re
sults of
real
case,
it can
be
see
n
that p
r
edi
ction p
r
e
c
isi
on
of t
he imp
r
ov
ed alg
o
rithm
are
18.7% a
n
d
27.7% hi
gh
er
than that of t
r
adition
al alg
o
rithm u
nde
r relatively ge
ntle win
d
sp
eed a
nd
rapi
d ch
angi
ng
wind
spe
ed
re
spe
c
tively. The
wind
po
we
r
predi
ction
re
sult o
b
tained
ba
sed
on t
he relation
sh
ip
betwe
en the wind
spee
d and win
d
po
wer
with MR
E value of 23.72%, which
confirm that
the
improve
d
GM
(1,1)
mod
e
l i
s
favorable f
o
r imp
r
ov
ing
the
accu
ra
cy of
wi
nd sp
ee
d
predictio
n and
achi
eving win
d
power p
r
edi
ction.
Referen
ces
[1]
Z
hang Z
Z
,
Z
o
u
JX, Z
h
e
ng G.
Ultra-Sh
o
rt T
e
rm W
i
n
d
Pow
e
r
Predicti
on M
o
del B
a
se
d o
n
Modifi
ed Grey
Mode
l Method
for Pow
e
r Control in W
i
n
d
F
a
rm
. W
i
nd e
ngi
n
eeri
ng. 20
11; 3
5
(1): 55-6
8
.
[2]
Z
hang
YC, L
i
u
HJ, Z
han
g HJ
, Z
hao
X. P
e
rformanc
e An
al
ysis of D
o
u
b
l
y
Excite
d Br
ushl
ess Gen
e
rat
o
r
w
i
t
h
Outer Rotor for Wi
nd
Po
w
e
r App
l
i
c
ation.
T
E
LK
OMNIKA T
e
lecommunic
a
tio
n
Computi
n
g
Electron
ics an
d Contro
l
. 201
2; 10(3): 47
1-4
76.
[3]
Karki R, T
hapa
S, Billi
nton
R.
A simpl
i
fied r
i
s
k
-base
d
meth
o
d
for sh
ort-term
w
i
n
d
p
o
w
e
r
commitment.
Sustain
abl
e En
ergy
. 201
2; 3(3
)
: 498-50
5.
[4]
Moha
ndas S, Cha
nde
l AK.
T
r
ansi
ent stabil
i
ty en
ha
ncem
en
t of the po
w
e
r s
y
stem
w
i
th
w
i
nd ge
ner
atio
n
.
T
E
LKOMNIKA T
e
leco
mmunic
a
tion C
o
mputi
n
g Electron
ics a
nd Co
ntrol
. 20
11: 9(2): 26
7-2
78.
[5]
T
ogelou A, Sid
e
ratos G, Hatziarg
yrio
u ND. W
i
nd Po
w
e
r F
o
recasti
ng in th
e Absenc
e of Historica
l Data.
IEEE Transactions on
sust
ainable energy
. 2
012; 3(3): 4
16-
421.
[6]
Hua
ng Z
,
Cha
l
abi Z
S
. Use
of time-series
an
al
ysis to mo
de
l
and for
e
cast
w
i
nd s
p
e
ed.
Jo
urna
l of W
i
n
d
Engi
neer
in
g an
d Industria
l Aer
odyn
a
m
ics
. 19
95; 56(2): 3
11–
322.
[7]
Kamal L,
Jafri YZ.
T
i
me
series
mode
ls to s
i
mulate
an
d for
e
cast h
ourl
y
av
erag
ed
w
i
n
d
sp
eed
in
Quetta
,
Pakistan.
Sol
a
r
Energy
. 19
97; 61(1): 23
–3
2.
[8]
Ale
x
i
adis MC, Doko
pou
los P
S
, Sahsaman
o
g
lo
u HS,
Mano
usari
d
is IM. Short-term forecasting of
w
i
n
d
spee
d an
d rela
ted electric p
o
w
e
r
. Solar En
e
r
g
y
. 1
998; 6
3
(1
): 61–68.
[9]
Li S, Wunsch
DC, Ha
ir EO
, Giesselmann MG.
Neural
netw
o
rk for w
i
nd p
o
w
e
r gen
eratio
n w
i
th
compressi
ng fu
nction
. Proc. Int. Conf. Neural
Net
w
orks. Ho
u
s
ton. 199
7; 1: 115
–1
20.
[10]
Den
g
JL. T
he
Gre
y
Contr
o
l S
y
stem. W
u
h
an:
Pr
ess of
Hu
az
hon
g U
n
ivers
i
ty
of Scie
nce
&
T
e
chnolo
g
y
.
199
3.
[11]
W
ang Y, Song
QB, MacDone
ll S,
Shep
perd
M, Shen JY. Integrate
the GM
(1,1) and V
e
rh
ulst Mode
ls
to Predict Soft
w
a
re Stage
Effort.
IEEE transactions
on system
,
m
a
n and cy
bernetics-part c
:
app
licati
ons a
n
d
review
s
. 200
9; 39(6): 64
7-6
58.
[12]
Liu R
C
, Yang
AP, Dai W
Z
.
GM (1, 1)
Mode
l bas
ed
on the transfo
rmati
on of fun
c
tion
1
bx
ae
.
Procee
din
g
s o
f
2007 IEEE Internatio
na
l C
onfere
n
ce
o
n
Gre
y
S
y
stems
and Intell
ig
e
n
t Services.
Nanj
in
g. 200
7: 440-
444.
[13]
Yao W
L
, Chi
SC, Chen JH.
An improve
d
Gre
y
-b
as
e
d
ap
proac
h for ele
c
tricit
y
d
e
man
d
forecastin
g
,
Electric Power System
s Res
e
arch
. 200
3; 67(
3): 217–
22
4.
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