wind energy

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Keywords:Wind speed forecasting

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Swarm Optimization (PSO) as an intelligent optimization algorithm to optimize the parameters of the

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it hard to predict when wind power will be brought into the grid,and energy transportation becomes difcult, as well [1]. An effec-tive way to resolve this problem is wind speed forecasting, whichcan improve the power grid efciency. Therefore, wind speed fore-casting 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

network-based 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.E-mail 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 well-known, one of the primary reasons for the low utilization rate ofwind power is the volatility of the wind speed. This volatility makes

least-squares method, time series analysis, wavother algorithms have been widely applied [6]. Tare all time series-based. Pousinho et al. [7] pubing model using particle swarm optimizatiohttp://dx.doi.org/10.1016/j.enconman.2014.05.0580196-8904/ 2014 Elsevier Ltd. All rights reserved.recast-aptive-singlecuracyspeed.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 pollution-free [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 70-m area near the ground

perform poorly in the short-term, such as Mesoscale Model 5(MM5), Consortium for Small Scale Modeling (COSMO), WeatherResearch Forecast (WRF) and High Resolution Model (HRM). Thetime series-based model (which is the subject of this paper) usesonly historical wind data to build statistical models and providesa suitable short-term 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 over-tting. 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, includ-ing thermal, frictional and convection effects. Several of theseapproaches are good for long-term 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 wind-related 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 non-stationary 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 PSO-optimized ARIMA models arewell-suited to capture short range correlations [5], another limita-tion 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 over-come 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 time-series 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 accu-racy. 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 thePSO-optimized 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 perfor-mance 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 short-range 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 Jen-kins [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 society-based 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 PSO-based 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 gener-ations. However, compared to genetic algorithms, the advantagesof PSO are easier to actualize and possess fewer parameters to reg-ulate [24]. At the same time, PSO, compared to differential evolu-tion, is an important characteristic from an end-user 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 n-dimensional 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 pop-ulation. 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 con-sumable 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, real-world 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 non-stationary 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 speci-ed: 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 glo-bal state of the modeling approach through a dynamically consis-tent interpolator based on information from the measurements[2729]. Al-Hamadi and Soliman [30] researched short-term elec-tric load forecasting using a moving window weather model basedon the Kalman ltering algorithm. Tsiaplias [31] explored factorestimation using MCMC-based Kalman lter methods. Anotherhybrid wavelet-Kalman lter method for forecasting was proposedby Zheng et al. [32] in 2000.

The Kalman lter also could be described as an approach con-sisting 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 n-dimensional system states; A(t) denotes n nstate transition matrix; Z(t) denotes m-dimensional measurementvector; H(t) denotes m n output matrix; w(t) denotes n-dimen-sional system error; and v(t) denotes m-dimensional measurementerror.

The noise vectors w(t) and v(t) are white noise. Known covari-ance matrices

EwtwTt Q ; EvtvTt R; 10

where Q and R are positive denite and positive semi-denitematrices, 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 P-cycles are shown in Fig. 1. Then, the loop isbegun again in the head of project and continued until all measure-ments have been adopted; then, X(t) is calculated.optimized hybrid model combining the Kalman lter and PSO-optimized 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 low-height 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 algo-rithm until the optimum particle was calculated (the denition

Fig. 1. Main cycle in Kalman lter.anagement 85 (2014) 443452 445applied to change the non-stationary 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 low-order 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 bet-ter 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 PSO-optimized 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 opti-mized by a PSO algorithm, and the tting and forecasting resultsare shown in Fig. 5.

The PSO-optimized 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 differ-ences 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 informa-tion. 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 fore-casting 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 fore-casting 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 PSO-opti-mized 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 PSO-optimized 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 zero-medianmed(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 sign-test 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 dis-tribution 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 signed-rank test

A related distribution-free procedure that demands the symme-try of the error differential is the Wilcoxons signed-rank test. Thetest statistic is as follows:

~S XTt1

Idtrankjdt j; 33

The accurate nite-sample crucial values of the testing statistic areconstant to the distribution of the error differential, which has beentabulated only as zero-mean and symmetric. Moreover, the stan-dard 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

dPSO-optim

ized

ARIM

APSO-optim

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 test-ing 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 PSO-optimized ARIMA in Zhangye, three testsshowed a rejection, but because the MGN test showed an accep-tance. 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 pre-cisely, according the measures dened above, the indices of differ-ent 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 thePSO-optimized ARIMA model but are reduced to 34.8% in the opti-mized 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 PSO-optimized 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 PSO-optimized ARIMA model, which is, in turn,superior to the basic ARIMA model.

In Tables 24, which compares the basic ARIMA model and thePSO-optimized 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 per-formance 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 infor-mation. 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 pre-dicting 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 auto-kinetic and a non-requirement for making complexdeterminations regarding the denite form for the models in eachcase. Based on the above-mentioned reasons, it is suggested thatthe proposed optimized hybrid model has better forecasting accu-racy and ability.

Wind speed forecasting is a difcult issue. Currently, forecastingerrors are generally observed in between 25% and 40% of short-term 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 dif-ferent 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, permit-ting 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 Foun-dation 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 signed-rank test3.3.4 The MorganGrangerNewbold test

3.4 Predictive result analyses

4 ConclusionsAcknowledgementReferences