
ell
ao
6023Aust
Keywords:Wind speed forecasting
d iss. Ao w
Swarm Optimization (PSO) as an intelligent optimization
algorithm to optimize the parameters of the
is, the utial ap
it hard to predict when wind power will be brought into the
grid,and energy transportation becomes difcult, as well [1]. An
effective way to resolve this problem is wind speed forecasting,
whichcan improve the power grid efciency. Therefore, wind speed
forecasting is a key issue in achieving the management of wind
farms.
In recent studies, there have been two primary methods ofwind
speed prediction, which are based upon the weather
elet analysis andhe above modelslished a fon and ad
networkbased fuzzy inference system, as the use of astatistical
method cannot always satisfy forecasting acdue to the complex
nonlinearity and seasonality of windBoth theoretical and empirical
research projects have suggestedthat different prediction models
can supplement the capturingproperties of data sets; thus, a
combination method may performmuch better than any individual
forecasting model [810]. In thispaper, a hybrid forecasting model
is built for daily wind speedforecasting in the Gansu Corridor,
employing both statisticaland articial intelligence methods.
Corresponding author. Tel.: +86 15339864602.Email address:
wjz@lzu.edu.cn (J. Wang).
Energy Conversion and Management 85 (2014) 443452
Contents lists availab
n
lse[4]. Thus, the analysis and estimation of wind energy in this
areais a meaningful but notably difcult task for research. As is
wellknown, one of the primary reasons for the low utilization rate
ofwind power is the volatility of the wind speed. This volatility
makes
leastsquares method, time series analysis, wavother algorithms
have been widely applied [6]. Tare all time seriesbased. Pousinho
et al. [7] pubing model using particle swarm
optimizatiohttp://dx.doi.org/10.1016/j.enconman.2014.05.05801968904/
2014 Elsevier Ltd. All rights
reserved.recastaptivesinglecuracyspeed.inuence of higher oil
prices in many countries [1]. In this regard,wind power has been
increasingly recognized as a signicantsource of renewable energy
that is clean and pollutionfree [2].Currently, wind power
represents approximately 10% of theenergy consumption in Europe and
over 15% in Germany, Spainand the USA [3]. In China, abundant wind
energy resources exist,especially in the Gansu Corridor, which
annually produces over1.5 1015 kW h/m2 of power over a 70m area
near the ground
perform poorly in the shortterm, such as Mesoscale Model
5(MM5), Consortium for Small Scale Modeling (COSMO),
WeatherResearch Forecast (WRF) and High Resolution Model (HRM).
Thetime seriesbased model (which is the subject of this paper)
usesonly historical wind data to build statistical models and
providesa suitable shortterm forecasting result for wind farms
[5]. Amongthe statistical approaches, many models have been used
toadvance the accuracy of prediction. The regression
method,ARIMAKalman lterParameter optimizationIntelligent
optimization
1. Introduction
Considering theworld energy crisis becoming an increasingly
essenARIMA model, which develops a hybrid model that is best
adapted to the data set, increasing the ttingaccuracy and avoiding
overtting. The proposed method is subsequently examined on the
wind farms ofwestern China, where the proposed hybrid model is
shown to perform effectively and steadily.
2014 Elsevier Ltd. All rights reserved.
se of renewable energyproach to reduce the
forecasting and the time series. The former uses
hydrodynamicatmospheric methods and contains physical phenomena,
including thermal, frictional and convection effects. Several of
theseapproaches are good for longterm wind speed forecasting
butAvailable online 21 June 2014 optimized hybrid method based on
the Autoregressive Integrated Moving Average (ARIMA) and Kalmanlter
is proposed to forecast the daily mean wind speed in western China.
This approach employs ParticleA new hybrid model optimized by an
intfor wind speed forecasting
Zhongyue Su a, Jianzhou Wang b,, Haiyan Lu c, Ge ZhaCollege of
Atmospheric Sciences, Lanzhou University, Lanzhou, Gansu 730000,
Chinab School of Statistics, Dongbei University of Finance and
Economics, Dalian, Liaoning 11c Faculty of Engineering and
Information Technology, University of Technology,
Sydney,dDepartment of Statistics, University of South Carolina,
29201, USA
a r t i c l e i n f o
Article history:Received 25 September 2010Accepted 8 May
2014
a b s t r a c t
Forecasting the wind speemanagement of wind farmforecasting
errors related t
Energy Conversio
journal homepage: www.eigent optimization algorithm
d
,Chinaralia
indispensable in windrelated engineering studies and is
important in thes a technique essential for the future of clean
energy systems, reducing theind speed has always been an important
research subject. In this paper, an
le at ScienceDirect
and Management
vier .com/ locate /enconman

Erdem published a technique based on ARIMA in wind
speedforecasting [9]. The ARIMA model was initially presented
by
d MBoxJenkins [10] and was successfully used in such
applicationsas forecasting economic, marketing and social problems.
However,the main disadvantage of the ARIMA method is that it has
lowaccuracy in forecasting nonstationary or uctuating time
series.Based on a PSO algorithm proposed by Eberhart and
Kennedy[11], an optimized ARIMA model has been developed by us
afterthe basic model. The advantage of this optimized model is
thatfew assumptions are needed, and no a priori postulation of
themodels is required. Furthermore, with the constant adjustment
ofthe ARIMA parameters in the modeling process, the features ofthe
data can be better explored.
Although the basic and the PSOoptimized ARIMA models
arewellsuited to capture short range correlations [5], another
limitation of the ARIMA model is the difculty of adjusting the
modelsparameters when the time series contains new information.
Tosolve this problem, it was proposed to test the ARIMA model
incombination with a Kalman lter; this testing constitutes the
mainobjective of this paper. The Kalman lter, which is proposed
byKalman [12], is a sequential algorithm for minimizing state
errorvariance. Along with an extended version, the Kalman lter
hasbeen used successfully by several researchers [13]. The
primaryadvantage of the Kalman lter is that the method can be
appliedin both linear and nonlinear systems [14] and thus is able
to overcome the shortcomings of the ARIMA model.
Recently, considerable research has focused on wind
speedforecasting, and several hybrid methods have a good
performancein this area. In the hybridization of articial neural
networksachieved by Sancho et al. [15,16], the superiority of the
hybridmodel is demonstrated and found to be successful and
feasible.In this paper, the ideas of parameter optimization and
informationmining have been manifested. Combining the Kalman lter
withthe ARIMA model, the basic steps taken were as follows.
First,the basic ARIMA model was established based on historical
data;as a standard timeseries method, the ARIMA model has
goodproperties for forecasting. Second, the ARIMA models
parameterswere optimized by the PSO algorithm. PSO is a useful
method inselecting a models parameters and improving its
forecasting accuracy. As used by Marcela et al. [16] on the
reactive power dispatchof wind farms, this algorithm has been
tested to be effective andoptimal. Finally, a model combining the
Kalman lter with thePSOoptimized ARIMA method was established for
wind speedforecasting. As time goes on, more wind speed
informationobtained, more accurate wind speed characteristic will
be derivedby forecasting models, the new information on the wind
speed isabsorbed by this hybrid optimized model. Therefore, the
performance of this hybrid, optimized model will be stable and
accurate.
The remaining sections are arranged as follows. The
preparationmethods and main modeling process are described in
Section 2.Section 3 predicts the wind speed of the Gansu Corridor
usingthree different methods and provides the forecasting results
andanalyses. Finally, the conclusion is presented in Section 4.
2. Preparation methods for forecasting and modeling process
2.1. ARIMA modelConsidering that the Autoregressive Integrated
Moving Average(ARIMA) model is suitable for capturing shortrange
correlationsand has been used widely in a variety of forecasting
applications[5], the ARIMA model is taken as a basic model in this
study. Ergin
444 Z. Su et al. / Energy Conversion anThe ARIMA model, which is
among the most popularapproaches, was introduced for use in
forecasting by Box and Jenkins [10]. Hybrid forecasting method,
which generally employs anARIMA model as a linear model to predict
the linear componentand employs nonlinear model to predict the
other component intime series. It is always valid to improve the
forecastingperformance of wind speed [1]. The applications of ARIMA
model[1719] also demonstrate its superiority in many areas.
A general ARIMA (p,d,q) model describing the time series
iswritten as follows:
/Brdxt hBet ; 1where xt and et represent wind speed and random
error at time t,correspondingly. B is a backward shift operator
dened by Bxt = xt1,and related to ; d is the order of differencing;
= 1 B, d =(1 B)d. /(B) and h(B) are autoregressive (AR) and moving
averages(MA) operators of orders p and q, separately, that are
dened asfollows:
/B 1 /1B /2B2 /pBp; 2
hB 1 h1B h2B2 hqBq; 3where /1, /2, . . . ,/p are the
autoregressive coefcients and h1, h2,. . . ,hq are the moving
average coefcients.
The time series xt can also be represented as a linear
transferfunction of the noise series:xt luBet ; 4where
uB 1u1Bu2B2 : 5/(B) can be computed as u(B) = h(B)//(B).
2.2. PSO algorithm
Particle Swarm Optimization (PSO) is a societybased
swarmalgorithm that was initially developed by Kennedy and
Eberhart[11]. Bonabeau et al. [20] gave a detailed description and
analysisof swarm intelligence in 2000. At the same time, some PSO
modelshave also been applied in forecasting. Zhao and Yang [21]
proposeda PSObased single multiplicative neuron model in the
forecastingeld. Hong Kuo et al. [22] discussed an improved method
based onfuzzy time series and PSO for forecasting enrollments. Hong
[23]researched chaotic PSO algorithms using support vector
regressionin electric load forecasting.
The procedure is dened by a population of random solutionsthat
then searches for an optimal state through renovating generations.
However, compared to genetic algorithms, the advantagesof PSO are
easier to actualize and possess fewer parameters to regulate [24].
At the same time, PSO, compared to differential evolution, is an
important characteristic from an enduser attitude,according to
which a clustering algorithm must not only be exactbut also must
propose reproducible and reliable results [25].
In this paper, the particle of PSO is autoregressive
coefcientsand moving average coefcients in ARIMA model. Let m
representsthe number of particles and n is the number of
optimizedparameters. Thus, the ith particle xi(t) is xi(t) = (xi1,
xi2, . . . ,xin)(i = 1, 2, . . . ,m) in the search space. The ith
particles velocity is alsoa ndimensional vector that is
represented as vi(t) = (vi1, vi2, . . . ,vin)(i = 1, 2, . . . ,m).
There are two best values during the optimizationprocess, called
Pbest and Gbest, respectively, which are the bestvalue obtained by
each single particle or by all particles in the population. The
sensitivity analysis experiment was carried out bychanging the
number of particles and the number of iterations inorder to assure
the convergence to a minimum of the PSO swarm.
The PSO algorithm can be displayed by the following
equations:
anagement 85 (2014) 443452v it 1 w v it c1rand1Pbesti xi
c2rand2Gbest xid6

of PSO is the square root of the mean square error (RMSE) in
this
parameters of the PSO optimization are calculated after
three
ltering is an effective approach to regulating real time series
of
T T 1
of the parameters is given in the next paragraph). Finally,
the
of the China Meteorological Administration, the supposedly
consumable wind resources of potential power generation
capacityare over 4300 GW, and the supposedly consumable wind
resourcesamount to 297 GW [34]. Especially in the Hexi Corridor of
China,the abundant wind energy theoretically amounts to 2105 MW;
thisregion is famous for acting as a global leader in wind
energyresources [35]. In this article, realworld experiments are
appliedto the wind speed forecasting of ve sites situated on ve
differentareas along the Gansu Corridor of China. These include the
Jiuquan,Mazong Mountain, Zhangye, Wuwei and Minqin regions, which
areshown in Fig. 3. The historical wind speed data of the ve areas
in2005 were used in this case study. To show the consistency of
themodels in different areas, the 120 samples from the wind
speeddata of the ve areas is selected from April 10, 2005 to July
28,2005.
3.2. The forecasting of wind speed for Gansu corridor
One of the most important parts in the evolution of a
satisfyingtime series prediction model is choosing the input data
that decidethe structure of the model [36]. As wind speed time data
havesome nonstationary properties, so different methods must
be
nd MKt Ptjt 1H tHtPtjt 1H t Rt ; 13
X^t X^tjt 1 KtZt HtX^tjt 1; 14
Pt I KtHtPtjt 1: 15Before the Kalman lter is used to determine
an optimal esti
mation of the time series X(t), certain quantities should be
specied: A(t), H(t), R(t) and Q(t). After updating X(t), the two
mainwind speed, as it is calculated from unbiased minimum
varianceestimates. This lter can accomplish the prime estimation of
statevariables in the approach while simultaneously updating the
global state of the modeling approach through a dynamically
consistent interpolator based on information from the
measurements[2729]. AlHamadi and Soliman [30] researched
shortterm electric load forecasting using a moving window weather
model basedon the Kalman ltering algorithm. Tsiaplias [31] explored
factorestimation using MCMCbased Kalman lter methods.
Anotherhybrid waveletKalman lter method for forecasting was
proposedby Zheng et al. [32] in 2000.
The Kalman lter also could be described as an approach
consisting of a state equation and a measurement equation
[33].
System state equation:
Xt AtXt 1 wt; 8Measurement equation:
Zt HtXt vt; 9
where X(t) denotes ndimensional system states; A(t) denotes n
nstate transition matrix; Z(t) denotes mdimensional
measurementvector; H(t) denotes m n output matrix; w(t) denotes
ndimensional system error; and v(t) denotes mdimensional
measurementerror.
The noise vectors w(t) and v(t) are white noise. Known
covariance matrices
EwtwTt Q ; EvtvTt R; 10
where Q and R are positive denite and positive
semidenitematrices, correspondingly. The basic Kalman lter
algorithm couldbe suggested by the following equations.
Time update equation:
X^tjt 1 AtX^t 1; 11
Ptjt 1 AtPt 1ATt Q ; 12State update equation:experiments.
2.3. Kalman lter
Compared with some of the other forecasting methods,
Kalmanpaper, and the iteration limit is set to 50 in this paper.
And thexit 1 xit v it 1 7
In the above equations, the parameters c1 and c2 are
constantscalled acceleration coefcients, and w is the inertia
coefcient. c1and c2 are set to 1.49445 in this paper [26]. The
objective function
Z. Su et al. / Energy Conversion acirculation X and Pcycles
are shown in Fig. 1. Then, the loop isbegun again in the head of
project and continued until all measurements have been adopted;
then, X(t) is calculated.optimized hybrid model combining the
Kalman lter and PSOoptimized ARIMA was established. The entire
modeling process isshown in Fig. 2.
3. Case studies and results
3.1. Region description and data collection
China has plentiful wind resources across its long coastline
andlarge land mass. According to the lowheight wind speed
estimates2.4. Main modeling process
The modeling process was organized as follows. First, the
basicARIMA model of wind speed series was calculated; second,
theparameters of the ARIMA model were optimized by the PSO
algorithm until the optimum particle was calculated (the
denition
Fig. 1. Main cycle in Kalman lter.anagement 85 (2014) 443452
445applied to change the nonstationary properties. The basic
ARIMAmodel parameters, which are shown in Table 1, are
calculatedaccording to the Akaike Information Criterion (AIC) [37],
which is

Fig. 2. Flow chart of the main method.
Fig. 3. Topographic map of the Gansu Corridor.
446 Z. Su et al. / Energy Conversion and Management 85 (2014)
443452

a measure of complexity and model performance that uses
windspeed data from ve areas in the Gansu Corridor.
The experimental results suggest that forecasting
functionsshould be created by the loworder difference equation
modelsshown in Table 1.
Z. Su et al. / Energy Conversion and MThe forecasting equations
calculated by ve ARIMA model areas follows:
xt 1:890xt 1 0:484xt 2 0:246xt 3 0:258xt 4 0:26xt 5 0:35xt 6
0:996xt 1 x^t 1; 16
xt 0:638xt 1 0:398xt 2 0:331xt 3 0:297xt 4 0:403xt 5 0:015xt 6
0:358xt 7; 17
xt 0:243xt 1 0:182xt 2 0:344xt 3 0:231xt 4; 18
xt 0:343xt 1 0:316xt 2 0:419xt 3 0:200xt 4 0:065xt 5 0:178xt 6
0:006xt 7 0:252xx 8 0:263xt 9; 19
xt 0:869xt 1 0:365xt 2 0:182xt 3 0:343xt 40:055xt 5 0:450xt 6;
20
where x(t) represents the wind speed data, and x^t, the
forecastingdata. Because the ARIMA model parameter is q = 1 in the
Jiuquanregion, formula (14) contains x^t.
The wind speeds of the ve regions can be predicted using
theseequations. Model tting and forecasting results are displayed
inFig. 4, in which the forecasting data are arranged from 101 to
120.
It is obvious to recognize that the ARIMA model is able
todescribe the variation of the time series in Fig. 4. To achieve a
better presentation of the learning parts, it is necessary to
determinewhich indices should be used to measure the training
performance.Traditional performance indices, such as the average
relative error(ARE), the square root of the mean square error
(RMSE) and themean absolute error (MAE) are used as measures for
predictionaccuracy. These indices are shown as follows:
RMSE Xn
i1yi y^i2=n
q; 21
MAE Xni1
jyi y^ij,
n; 22
ARE Xni1
jy^i yij=yi,
n; 23
where yi is the real value, and y^i is the forecasted value of
yi.The wind speed forecasting results of the ARIMA model have
been given, and the indices are shown in Table 2.Although the
basic ARIMA model has a good performance for
the description of wind speed variation, the forecasting
accuracy
Table 1ARIMA model parameters of ve areas in Gansu Corridor.
ARIMA Jiuquan Mazong Mountain Zhangye Wuwei Minqin
p 3 5 3 7 4
d 3 1 1 2 2q 1 0 0 0 0of the basic ARIMA still cannot satisfy
the demand for wind powergeneration. To better predict the wind
speed, PSO is suggested tooptimize the parameters of the ARIMA
model.
In the PSOoptimized process, the parameters of the ARIMAmodel,
which were given in formulas (14)(18), are regarded asthe particles
of the PSO. For instance, if x(t) = a1x(t 1) + a2x(t 2) + + anx(t
n), which is based on the process of ARIMAmodel, then a = (a1, a2,
. . . ,an) is regarded as a particle of PSO. Fordifferent regions,
the parameters of the ARIMA model are optimized by a PSO
algorithm, and the tting and forecasting resultsare shown in Fig.
5.
The PSOoptimized ARIMA model describes the changes batterin the
time series from Fig. 5.
In Figs. 4 and 5, it can be ascertained that each model
displayssimilar trends to those of the real data. However, greater
differences between the data predicted from the basic ARIMA
modeland the real data are noticeable. The evaluation indices are
shownin Table 3.
The main idea of the proposed model is to combine the ARIMAmodel
with the Kalman lter, thus achieving the aim for the modelto be
able to forecast the wind speed with the updated information. The
advantage of the Kalman lter is to correct the estimatedvalue
immediately according to the latest observed values.
Beforeattaining the forecasting results in the Kalman lter, the
stateequation and measurement equation must be derived. The
ARIMAmodel optimized by PSO will be rewritten as follows:
x1t xt; x2t xt 1; . . . ; xnt xt n: 24
x1t 1 a1x1t a2x2t anxnt wt 1; 25Therefore, the state equation
will be written as follows:
x1t 1x2t 1...
xnt 1
266664377775
a1 an1 an1 0 0... . .
. ... ..
.
0 1 0
266664377775
x1tx2t...
xnt
266664377775
10...
0
266664377775wt 1;
26The measurement equation will be the following:
zt 1 1 0 0
x1t 1x2t 1...
xnt 1
266664377775 vt 1: 27
According to the formula (8), the error covariance is dened
asR(t) = 1 and as Q(t) = 1. After the Kalman lter iteration, the
newlyforecast results are shown in Fig. 6.
So far, experimental research has shown that wind speed
forecasting is a very difcult issue, and there is no one effective
anduniversal forecasting method to tackle it [38]. Bunn and
Farmer[39] suggested a 10 million operating cost of a 1% increase
in forecasting error for wind farms. Similarly, in wind power
generation, atiny improvement of the wind speed forecasting
accuracy can yieldenormous economic benets. Thus, this optimized
hybrid model,which decreases the forecasting error on the basis of
a PSOoptimized ARIMA model in all ve regions, represents an
importantimprovement for wind speed forecasting in the Gansu
Corridor.The detailed indices are shown in Table 4.
3.3. Predictive accuracy testing
anagement 85 (2014) 443452 447Considering the apparent
credibility of a statistical approach incomparing forecasting
accuracies, a casual manner is critical to thisproblem. Before
measuring the forecasting error, predictive

Fig. 4. Fitting and forecasting results of ARIMA model.
Table 2Indices of ARIMA model.
Jiuquan Mazong Mountain Zhangye Wuwei Minqin
ARE 43.32% 39.83% 30.33% 36.43% 45.18%MAE 0.7824 1.4045 0.6351
0.5511 1.0283RMSE 0.9867 1.8575 0.7254 0.7147 1.3530
Fig. 5. Fitting and forecasting results of the PSOoptimized
ARIMA model.
Table 3Indices of the ARIMA model optimized by PSO.
Jiuquan Mazong Mountain Zhangye Wuwei Minqin
ARE 41.47% 28.99% 28.18% 33.50% 39.08%MAE 0.6957 1.1036 0.6116
0.5286 0.9850RMSE 0.9115 1.3763 0.7001 0.6460 1.2144
448 Z. Su et al. / Energy Conversion and Management 85 (2014)
443452

f th
nd MFig. 6. Forecasting results o
Table 4Indices of optimized hybrid model.
Jiuquan Mazong Mountain Zhangye Wuwei Minqin
ARE 34.80% 27.69% 27.44% 29.82% 36.62%Z. Su et al. / Energy
Conversion aaccuracy testing should be adopted to test the
differences amongthe three methods. This is very important because,
as well asknown, the stability of a forecasting method is
determined bythe distribution of its forecasting error. The gyt ;
y^it is written asthe forecast error; that is, gyt ; y^it geit. The
null hypothesis offorecasting accuracy for two equal variables is
E[g(eit)] = E[g(ejt)],or E[dt] = 0, where dt = [g(eit) g(ejt)] is
the error differential.
3.3.1. The sign testThe null hypothesis is a
zeromedianmed(g(eit) g(ejt)) = 0. The
test statistic is the following:
S XTt1
Idt; 26
where
Idt 1 if dt > 00 otherwise
27
The importance may be estimated using a table calculating
thecumulative binomial distribution. The signtest statistic is
standardnormal:
S S 0:5T0:25T
p N0;1 28
3.3.2. The asymptotic testConsider that dt is stationary
covariance with a short memory
and that the result will be applied to gure out the asymptotic
distribution of the sample mean error differential.
Therefore,T
pd l!d N0;2pfd0; 29
MAE 0.6628 1.0568 0.5952 0.4632 0.9254RMSE 0.8664 1.3355 0.6942
0.5674 1.1366where
d 1T
XTt1
geit gejt 30
is the sample mean error differential, and
fd0 12pX1s1
cds 31
is the spectral density at frequency 0 in the error
differential.cd(s) = E[(dt l)(dts l)] is the covariance of the
error differentialat s, and l is the population mean error
differential. When d is
e optimized hybrid model.anagement 85 (2014) 443452
449distributed with mean l and variance 2pfd(0)/T, the null
hypothesisfor equal forecasting accuracy is
S d
2pbfd 0T
r ; 32where bfd0 is a consistent estimate of fd(0).3.3.3. The
Wilcoxons signedrank test
A related distributionfree procedure that demands the symmetry
of the error differential is the Wilcoxons signedrank test.
Thetest statistic is as follows:
~S XTt1
Idtrankjdt j; 33
The accurate nitesample crucial values of the testing statistic
areconstant to the distribution of the error differential, which
has beentabulated only as zeromean and symmetric. Moreover, the
standard normal is as follows:
S eS TT14TT12T1
24
q N0;1: 34
3.3.4. The MorganGrangerNewbold testLet xt = (eit + ejt) and zt
= (eit ejt), and let x = (eit + ejt) and
z = (eit ejt). Then, the null hypothesis of forecasting accuracy
is

Table5
Theresultscontrastingthetestingmetho
ds.
ARIM
Aan
dOptim
ized
hyb
ridmod
elARIM
Aan
dPSOoptim
ized
ARIM
APSOoptim
ized
ARIM
Aan
dOptim
ized
hyb
ridmod
el
Jiuqu
anMazon
gMou
ntain
Zhan
gye
Wuwei
Minqin
Jiuqu
anMazon
gMou
ntain
Zhan
gye
Wuw
eiMinqin
Jiuqu
anMazon
gMou
ntain
Zhan
gye
Wuwei
Minqin
Thesign
test
Rejected
Accep
ted
Rejected
Accep
ted
Accep
ted
Rejected
Accep
ted
Rejected
Accep
ted
Accep
ted
Rejected
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Theasym
ptotic
test
Accep
ted
Accep
ted
Accep
ted
Rejected
Rejected
Accep
ted
Accep
ted
Rejected
Accep
ted
Rejected
Rejected
Rejected
Accep
ted
Accep
ted
Rejected
TheWilcoxo
nssign
ed
ranktest
Rejected
Accep
ted
Rejected
Accep
ted
Accep
ted
Rejected
Accep
ted
Rejected
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Accep
ted
TheMorganG
ranger
New
bold
test
Accep
ted
Rejected
Accep
ted
Rejected
Accep
ted
Accep
ted
Rejected
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Accep
ted
Rejected
Accep
ted
450 Z. Su et al. / Energy Conversion and Mequal to the zero
correlation with x and (zi.e., qxz = 0), and the testing statistic
is as follows:
MGN q^xz1q^2xzT1
q 35The statistical tests with 95% degrees of condence, which
were
described in the last paragraph, reect the discrepancy and
errordistribution of the different methods. For the ve selected
areas,each forecasting method was tested mutually with each
othermethod. Comparing the nal results in Table 5, a part of
thehypothesis tests were rejected, indicating that there are
signicantdifferences between the three methods. For example, in the
case ofthe ARIMA and PSOoptimized ARIMA in Zhangye, three
testsshowed a rejection, but because the MGN test showed an
acceptance. There are obvious differences between these two
methods.However, in some areas, the answer was accepted, indicating
thatthe tests cannot effectively distinguish among their the
predictiveresults.
3.4. Predictive result analyses
To evaluate the performance of the developed approach
precisely, according the measures dened above, the indices of
different models at ve regions are shown in Fig. 7.
For example, consider the ARE in Jiuquan, in which the valuesare
between 40% and 45% on the basic ARIMA model and thePSOoptimized
ARIMA model but are reduced to 34.8% in the optimized hybrid
model. In another example of RMSE in MazongMountain, the value of
the basic ARIMA model is 1.8575. AfterPSO optimization, the RMSE of
the PSOoptimized ARIMA modelis already reduced to 1.3763, and the
RMSE of the optimized hybridmodel is 1.3355. The experiments from
different areas alwayspresent the same results, namely that the
optimized hybrid modelis superior to the PSOoptimized ARIMA model,
which is, in turn,superior to the basic ARIMA model.
In Tables 24, which compares the basic ARIMA model and
thePSOoptimized ARIMA model, the precision of the optimizedhybrid
model is improved. As an example of Jiuquan, Tables 24shows that
all of the RMSE (0.8664), MAE (0.6628) and ARE(34.8%) of the
optimized hybrid model are the smallest of the threeevaluation
indices. Similarly, in the other four regions, the RMSE,MAE and ARE
of the optimized hybrid model are also the smallest.Hence, all of
the indices imply that the optimized hybrid model caneffectively
decrease the error of the forecasted values compared tothe other
two forecasting methods.
4. Conclusions
A new optimized hybrid forecasting method based on ARIMAand the
Kalman lter has been described by this research. The performance
of the optimized hybrid model was evaluated by the veexamples
above, and the results of the optimized hybrid modelwere excellent
in forecasting. These results also suggest that thePSO algorithm
and Kalman lter are valuable methods of designingand optimizing the
ARIMA model in wind speed forecasting.
There are several advantages of using the proposed method.First,
the use of the Kalman ltering technique ameliorates thedisadvantage
of the ARIMA model, which is unable to adjust thearchitecture of
the model when the time series contains new information. Second,
the proposed ARIMA model as optimized by thePSO suggests preferable
improvements that are more satisfactoryin the current study. In
certain cases, the original parameter in
anagement 85 (2014) 443452the ARIMA is sufciently complex that
it is not effective for predicting wind speed; in such cases, the
idea of combining PSO withARIMA is highly important. Third, the
proposed hybrid model is

Eng 1960;82(Series D):3545.
ent m
nd Mvirtually autokinetic and a nonrequirement for making
complexdeterminations regarding the denite form for the models in
eachcase. Based on the abovementioned reasons, it is suggested
thatthe proposed optimized hybrid model has better forecasting
accuracy and ability.
Wind speed forecasting is a difcult issue. Currently,
forecastingerrors are generally observed in between 25% and 40% of
shortterm forecasts and are related not only to the forecasting
methodsbut also to the forecasting period and the characteristics
of theobservation site [40]. Thus, the optimized hybrid model,
combiningARIMA with the Kalman lter, provides a valid method
for
Fig. 7. Indices of differZ. Su et al. / Energy Conversion
aresearching wind speed forecasting. The differing results in the
different regions indicate that the approach developed in this
study isefcient and easy to implement. With a prepared setting,
thismethod can be extremely benecial for economic dispatchingand
electricity market bidding strategies for wind power, permitting
better scheduling of services. Therefore, these improvementscan
expedite the integration of wind power into ordinary powersystems,
developing a useful, renewable energy source.
Acknowledgement
This work was supported by the National Natural Science
Foundation of China (Grant No. 71171102).
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452 Z. Su et al. / Energy Conversion and Management 85 (2014)
443452
A new hybrid model optimized by an intelligent optimization
algorithm for wind speed forecasting1 Introduction2 Preparation
methods for forecasting and modeling process2.1 ARIMA model2.2 PSO
algorithm2.3 Kalman filter2.4 Main modeling process
3 Case studies and results3.1 Region description and data
collection3.2 The forecasting of wind speed for Gansu corridor3.3
Predictive accuracy testing3.3.1 The sign test3.3.2 The asymptotic
test3.3.3 The Wilcoxons signedrank test3.3.4 The
MorganGrangerNewbold test
3.4 Predictive result analyses
4 ConclusionsAcknowledgementReferences