Article A Hybrid Method for Short-Term Wind Speed Forecasting

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1 Arcle A Hybrd Mehod for Shor-Term Wnd Speed Forecasng Jnlang Zhang 1,2, *, YMng We 2,3, Zhong-fu Tan 1, Wang Ke 2,3 and We Tan 4 1 School of Economcs and Managemen, Norh Chna Elecrc Power Unversy, Bejng , Chna; anzhongfubejngbj@163.com 2 Cener for Energy and Envronmenal Polcy Research, Bejng Insue of Technology, Bejng , Chna; we@b.edu.cn (Y.W.); wangkebejng@163.com (W.K.) 3 School of Managemen and Economcs, Bejng Insue of Technology, Bejng , Chna 4 School of Managemen and Economcs, Illnos Insue of Technology, Chcago, IL 60616, USA; anwe@homal.com * Correspondence: zhangjnlang1213@163.com; Tel.: ; Fax: Academc Edors: Lexun Yang, Peng Zhou and Nng Zhang Receved: 23 January 2017; Acceped: 7 Aprl 2017; Publshed: 12 Aprl 2017 Absrac: The accuracy of shor-erm wnd speed predcon s very mporan for wnd power generaon. In hs paper, a hybrd mehod combnng ensemble emprcal mode decomposon (EEMD), adapve neural nework based fuzzy nference sysem (ANFIS) and seasonal auo-regresson negraed movng average (SARIMA) s presened for shor-erm wnd speed forecasng. The orgnal wnd speed seres s decomposed no boh perodc and nonlnear seres. Then, he ANFIS model s used o cach he nonlnear seres and he SARIMA model s appled for he perodc seres. Numercal esng resuls based on wo wnd ses n Souh Dakoa show he effcency of hs hybrd mehod. Keywords: shor-erm wnd speed forecasng; ensemble emprcal mode decomposon (EEMD); adapve neural nework based fuzzy nference sysem (ANFIS); seasonal auo-regresson negraed movng average (SARIMA) 1. Inroducon Wnd energy has been consdered o be one of he mos mporan knds of clean energy. As a renewable energy resource, he use of wnd energy can save fossl energy and reduce greenhouse gases emsson. In recen years, he nsalled capacy of wnd power has been ncreasng rapdly. However, he use of wnd power generaon s very challengng for curren power sysem operaons. One reason for hs s ha wnd power s an nermen energy, whch has srong randomness and nsably. Anoher reason s ha wnd power s a non-dspachable energy source, whch canno be conrolled by operaors n he same way as oher generaon resources [1]. These problems can be effecvely resolved f wnd speed can be predced accuraely [2]. Therefore, mprovng he accuracy of shor-erm wnd speed forecasng s crucal for he operaon of wnd power plans. Dfferen mehods have been proposed o predc wnd speed, ncludng physcal mehods [3 5], spaal correlaon mehods [6 9], convenonal sascal mehods [10 14], and arfcal nellgence mehods [15 21]. Physcal mehods ake no accoun physcal nformaon such as emperaure, pressure and opography o predc he wnd speed, and hese mehods have become essenal for shor-erm and very shor-erm wnd speed predcon [22]. However, he necessary physcal nformaon s no avalable o all marke parcpans. Spaal correlaon mehods predc wnd speed based on he wnd speed seres of he suded se and s neghborng ses; however, he measuremen of he spaal correlaed ses wnd speed s dffcul. Compared wh spaal correlaon mehods, convenonal sascal mehods ulze only hsorcal daa o Susanably 2017, 9, 596; do: /su

2 Susanably 2017, 9, of 10 buld predcon models; however, hs mehod presens dffcules n forecasng he complcaed nonlnear componens n a gven wnd speed seres. Arfcal nellgence mehods, such as arfcal neural neworks (ANN), have been wdely used for wnd speed predcon. I has been proved ha he precson of arfcal nellgence mehods s hgher han oher mehods for shor-erm wnd speed forecasng [23]. Alhough ANN has nonlnear modelng capably, also has he drawback of beng wha s consdered as a black box, and he rules of ANN are no easly undersandable [24]. These rules can be undersood by fuzzy logc, bu has dffcules dealng wh oo many varables [25]. Therefore, adapve neural nework based fuzzy nference sysem (ANFIS) was proposed [26]. ANFIS ncorporaes he self-learnng capably of a neural nework and he lngusc expresson funcon of fuzzy logc nference, whch, combned, hus exhbs a superory over each of hem employed separaely. A wnd speed seres has noably random flucuaon and perodc varaon properes [27]. The ANFIS model s good a nonlnear forecasng, whle he seasonal auo-regresson negraed movng average (SARIMA) model s good a perodc forecasng [28]. Modelng he nonlnear componen of a wnd speed seres usng ANFIS model wll change he perodc componen. Thus, ensemble emprcal mode decomposon (EEMD) mehod s appled o decompose he orgnal wnd speed seres no some perodc seres and some nonlnear seres. EEMD s easly undersood, and he man dea of hs mehod s o separae he nonlnear componens and perodc componens by usng he Hlber-Huang ransform. Hence, n hs paper, a hybrd mehod combnng EEMD, ANFIS and SARIMA s proposed for he shor-erm wnd speed forecasng. Numercal es resuls show he effcency of he proposed mehod. The res of hs paper s organzed as follows. Secon 2 provdes a descrpon of he EEMD, ANFIS and SARIMA models. The proposed mehod s presened n Secon 3. Numercal resuls are presened n Secon 4. Secon 5 concludes hs paper. 2. Mehodology 2.1. EEMD Emprcal mode decomposon (EMD) s effecve n exracng he characersc nformaon from an orgnal wnd speed seres, whch can be decomposed no a se of nrnsc mode funcons (IMFs). The IMFs ndcae he oscllaory mode of he orgnal wnd speed seres. EMD s a self-adapve me seres processng mehod, whch can be perfecly used for complcaed processng [29]. The man drawback of EMD s s mode mxng problem. To resolve he mode mxng problem, EEMD mehod was proposed n [30]. The procedure of EEMD s descrbed as follows: (1) Inalze he number of ensemble M and he amplude of he added whe nose, se 1. (2) Add a whe nose seres o he orgnal wnd speed seres x (). x () x() n () (1) where n () denoes he -h added whe nose seres, and x () denoes he seres wh he added whe nose. (3) Decompose he seres x () no J IMFs c j () ( j 1, 2,, J ) by EMD mehod. Where c j () s he j -h IMF afer he -h ral, and J s he number of IMFs. (4) If M hen go o Sep (2) wh 1. Repea Sep (2) and (3) wh dfferen whe nose seres. (5) Calculae he ensemble mean cj () of he M rals for each IMF of he decomposon as he fnal resuls: 1 M 1 c j ( ) cj ( ), 1,2,..., M, j 1,2,..., J. (2) M where cj (), ( j 1,2,, J) s he j-h IMF componens usng he EEMD mehod.

3 Susanably 2017, 9, of ANFIS ANFIS s a mullayer feed forward nework, whch negraes he mers of neural neworks and fuzzy nference sysems [31]. In hs paper, ANFIS wh ype-3 reasonng mechansms s appled. The ypcal ANFIS wh ype-3 reasonng mechansms consss of fve layers, whch are shown n Fgure 1, he dealed descrpons of whch are gven n Reference [31]. The funcons of each layer are gven as follows. Layer 1: The oupus of hs layer are defned as: or: where x or y denoes he wnd speed seres, { 2 O1, ( x), 1, 2 (3) A O1, ( y), 3, 4 (4) B 2 O, B 1, B }, and (x) or (y) s he membershp funcon. The followng membershp funcon s ulzed: where ( x) s he Gaussan funcon; c and A 1 s he membershp degree of fuzzy se { A 1, A2} or ua ( x) exp[ 0.5{( x c)/ }], 1, 2 (5) are he mean and sandard devaon of he membershp funcon, respecvely. Layer 2: Ths layer s he operaon layer. Layer 3: All he npu varables are normalzed n he layer, and he oupu of hs layer s calculaed as: W O3, W W 1 W 2, 1, 2 (6) where O 3, s he oupu of Layer 3, and W s he ncenve srengh of rule. Layer 4: The followng node funcon s appled n hs layer: z W f W ( p xq y r), 1, 2 (7) where { p, q, r } s he parameer se of he nodes. Layer 5: The sngle node n hs layer summarzes all ncomng seres: z W1z1 W2z2 (8) x y x A 1 A 2 W 1 M W 1 z 1 z y B 1 W 2 M W 2 z 2 B 2 x y Fgure 1. The archecure of adapve neural nework based fuzzy nference sysem (ANFIS) nework wh ype-3 reasonng mechansms SARIMA SARIMA s he mos popular mehod for perodc me seres predcon, whch s descrbed as follows:

4 Susanably 2017, 9, of 10 s d s D F ( B) U ( B )(1 B) (1 B ) Z Q( B) V ( B ) e (9) s where F ( B), U( B ) denoes non-perodc and perodc auoregressve polynomal, respecvely. s Q ( B), V( B ) denoes non-perodc and perodc movng average polynomal, respecvely. Z denoes he wnd speed seres, and e represens he whe nose seres. d s he level of negraon, D s he level of perodc negraon, s s he order of perodcy, and B s he back-shf operaor. More deals abou SARIMA can been found n Reference [32]. In order o use he SARIMA model, he frs sep s o esmae he values of d and D. For hourly daa, a perodc dfference wh s = 24 and 168 are used o remove mos of he perodcy. The values of p and q are esmaed usng Auocorrelaon Funcon (ACF) and Paral Auocorrelaon Funcon (PACF). 3. The Proposed Mehod Due o he random feaures of wnd resource from me o me and from locaon o locaon, wnd speed forecasng s very challengng. Therefore, a deep nsgh no he orgnal wnd speed seres s mporan for provdng more accurae resuls. Fgure 2 shows he flowchar of he proposed mehod. As menoned above, a wnd speed seres has he complcaed feaure of nonlneary and perodcy. The hybrd mehod, whch has boh nonlnear and perodc modelng capables, wll be a good choce for wnd speed forecasng. By usng EEMD, he orgnal wnd speed seres s decomposed no some perodc seres and some nonlnear seres. Then, he ANFIS model s used o forecas he nonlnear seres and he SARIMA model s appled for he perodc seres. Wh he proposed mehod, boh he perodc and nonlnear componens of he wnd speed seres can be capured. The procedure s gven as follows. (1) The wnd speed seres s frsly decomposed no some IMFs and one resdual seres. n 1 s X () C() Rn() (10) where X () s he wnd speed seres, and C () and Rn () are he IMFs and he resdual seres, respecvely. (2) If he seres of C () and Rn () have he feaures of perodcy, hen hese seres are defned as Sj () ; oherwse, hey are defned as N (). Then, he orgnal wnd speed seres can be defned as: m n j n 1 jm1 (11) X () N () S () R () where N () and Sj () presen he nonlnear and perodc componen of he wnd speed seres, respecvely. (3) As for he seres of N () and Rn (), he ANFIS model s appled o forecas he seres of N () and Rn (). The forecasng resuls are defned as N ^ () and R ^ n (). The SARIMA model s used o forecas he seres of S j, and he forecasng resul s defned as ^ ^ (4) The wnd speed forecasng resul s he sum of N (), S j () ^ m ^ n ^ ^ j n 1 jm1 X () N () S () R () ^ S j (). and R ^ n () : (12) where ^ X () s he predced wnd speed.

5 Susanably 2017, 9, of 10 Fgure 2. Procedure of he proposed mehod. 4. Numercal Resuls 4.1. Daa Source The 10-mn wnd speed daa of wo ses n Souh Dakoa, USA was used o evaluae he effecveness of he proposed mehod. The daa of wo ses were recorded connuously and were averaged over every 10 mn o oban he wnd arbues. Wnd speeds were measured a 80 m above he ground. The wnd speed daa for four monhs, correspondng o February, May, Augus, and November, were seleced for he wner, sprng, summer, and fall seasons, respecvely. The wnd speed daa of he las day of each monh were used as he esng samples, whle he en days before he las day of each monh were used as he ranng samples. The mean, sandard devaon, mnmum velocy and maxmum velocy of wnd speed for he year 2006 are gven n Table Case Sudes Table 1. Sascal measures of he wnd speeds for he wo suded ses. Ses Mean (m/s) SD (m/s) Mn.Vel (m/s) Max.Vel (m/s) Se Se To verfy he accuracy of he proposed mehod, he forecasng resuls were compared wh oher mehods such as ANFIS and SARIMA. In hs sudy, he error crera, such as mean absolue error (MAE), roo mean square error (RMSE) and mean absolue percenage error (MAPE), are used o measure he predcon error. The mahemacal defnons of MAE, RMSE and MAPE are gven as follows: 1 T ^ T 1 MAE y y (13) 1 RMSE y y T ^ 2 ( ) (14) T 1

6 Susanably 2017, 9, of 10 1 ^ 1 T y y MAPE T (15) y where y and y ^ represen he acual and he forecas value, respecvely, and T s he me perod. For he sake of brevy, he procedure of he EEMD mehod o decompose he wnd speeds on 28 February 2006 for se 1 s used as an example, and oher esng days have hen been decomposed wh he same procedure Wnd Speed Seres Decomposon. The orgnal wnd speed seres s decomposed no nne IMFs and one resdual seres usng he EEMD mehod. The amplude of he added nose and ensemble number are 0.01 and 100, respecvely. The resuls can be seen n Fgure 3. Fgure 3. Decomposon resuls of he wnd speed seres usng EEMD.

7 Susanably 2017, 9, of Sub-Seres Forecasng As shown n Fgure 3, he perodc behavor s observed n IMF4, IMF5, IMF6, IMF7, IMF8 and IMF9, whch flucuae n dfferen perods. Thus, hey can be predced by he SARIMA model. Frs, he dfference and perodc dfference are used o make hese sub-seres more sable. Then, he ACF and he PACF are appled o denfy he parameers of p and q. Fnally, he SARIMA model s used o forecas he seres of IMF4, IMF5, IMF6, IMF7, IMF8 and IMF9. ANFIS s appled for he nonlnear sub-seres of IMF1, IMF2, IMF3 and he Resdual. Wh 5-pon Lker ype scales, hese seres are dvded no fve fuzzy subses, whch mples ha here are 25 rules. In hs sep, he generalzed bell-shaped membershp funcons are used o calculae he consequen parameers. Then, he nal value of sep lengh for he ranng s se o The selecon of he npu varables s crucal for achevng accurae forecasng resuls and he ACF and PACF are used for he npu varables selecon Comparsons of ANFIS, SARIMA and he Proposed Mehod In hs secon, he forecasng resuls obaned from he proposed mehod are compared wh hose from ANFIS and SARIMA. Because of he dfferen feaures of wnd speed n dfferen regons, he proposed mehod s appled o wo ses n Souh Dakoa. Furhermore, a dfferen forecas horzon wll also affec he predcon accuracy. Thus, forecas horzons of 3, 6, 12 and are used o demonsrae s effecveness. The MAE, RMSE and MAPE values of ANFIS, SARIMA and he proposed mehod for he wo ses are gven n Tables Predcon Resuls for From Tables 2 and 3, can be seen ha he MAE, RMSE and MAPE values of he proposed mehod are lower han oher mehods. The descrpon of he effecveness of he proposed mehod s presened as follows based on he predcon resuls of se 1. The MAPE value of he proposed mehod for he wner day s below 0.7%, whle he MAPE values for ANFIS and SARIMA are 1.87% and 1.83%, respecvely. The MAE value for he proposed mehod s 0.05, whch s smaller han ha obaned by ANFIS and SARIMA, whch are 0.15 and 0.14 respecvely. The RMSE value for he proposed mehod s 0.06, whch s also sgnfcanly smaller han ha obaned by ANFIS and SARIMA. For he sprng day, he proposed hybrd mehod s no as good as for he oher es days. However, accuracy s accepable wh he MAPE value below 2.4%. MAPE values for ANFIS and SARIMA are 3.98% and 5.06%, respecvely. The sprng day s no accuraely predced due o he sgnfcan varaon of wnd speed durng hs season. The proposed hybrd mehod s less accurae on he summer day han on he wner and fall days. However, he accuracy s accepable wh MAPE below 0.9%, whle he MAPE values for ANFIS and SARIMA are 1.44% and 2.92% on he summer day, respecvely. The proposed hybrd mehod s prey good for he fall day, wh MAPE below 0.7%, whereas he MAPE values for ANFIS and SARIMA are 1.17% and 1.30%, respecvely. Overall, he MAPE values obaned from all es days for ANFIS range from 1.17% o 3.98%, hose for SARIMA range from 1.30% o 5.06%, and hose for he proposed mehod range from 0.68% o 2.57%. The resuls demonsrae ha by combnng dfferen models, he forecasng accuracy ncreases noably. Table 2. Comparson of he predcon resuls of he hree mehods for se 1. Forecas Horzon Error ANFIS SARIMA Proposed Mehod 28 February May 2006 MAE RMSE MAPE (%) MAE RMSE MAPE (%)

8 Susanably 2017, 9, of Augus November 2006 MAE RMSE MAPE (%) MAE RMSE MAPE (%) Table 3. Comparson of he predcon resuls of he hree mehods for se 2. Forecas Horzon Error ANFIS SARIMA Proposed Mehod 28 February May Augus November Predcon Resuls for 3, 6 and 12 h MAE RMSE MAPE (%) MAE RMSE MAPE (%) MAE RMSE MAPE (%) MAE RMSE MAPE (%) To prove he superory of he proposed mehod, dfferen forecas horzons of 3, 6 and 12 h, whch are randomly seleced, have also been used for esng he proposed approach. 168 h prevous o he begnnng of each forecas horzon s used as he ranng samples. As can been seen from Tables 4 and 5, he MAPE values of he proposed mehod for all forecas horzons are obvously lower han he resuls obaned from oher mehods. The average MAPE value of se 1 for he proposed mehod s 1.38%, whch s less han ha obaned usng ANFIS (2.63%) and SARIMA (3.91%) echnques. Ths fndng shows he superor capably of hs proposed mehod, whch can capure he characerscs of seasonaly and nonlneary. Therefore, he proposed mehod could provde a consderable mprovemen n wnd speed forecasng. Table 4. Dfferen forecas horzons of he hree mehods for se 1. Proposed Forecas Horzon Error ANFIS SARIMA Mehod MAE h RMSE /02/2006 MAPE (%) MAE h RMSE /05/2006 MAPE (%) h 31/08/2006 Average MAE RMSE MAPE (%) MAE RMSE MAPE (%)

9 Susanably 2017, 9, of 10 Table 5. Dfferen forecas horzons of he hree mehods for se 2. Forecas Horzon Error ANFIS SARIMA Proposed Mehod 3 h 28/02/ h 31/05/ h 31/08/2006 Average MAE RMSE MAPE (%) MAE RMSE MAPE (%) MAE RMSE MAPE (%) MAE RMSE MAPE (%) Conclusons In hs paper, a new mehod combnng EEMD, ANFIS and SARIMA s proposed for shor-erm wnd speed forecasng. EEMD s used o decompose he orgnal wnd speed seres no perodc seres and nonlnear seres. The ANFIS model can more easly capure he nonlnear seres, whle he SARIMA model can capure he perodc seres. Suable npu varables are seleced for each sub-seres by usng he ACF and PACF. The proposed mehod has been examned by usng he daa of wo wnd ses n Souh Dakoa. Emprcal resuls show ha he proposed mehod can provde more accurae and effecve predcon resuls. Acknowledgmens: The auhors would lke o hank he suppor of Chna Naonal Scence Foundaon (No ). Auhor Conrbuons: Jnlang zhang had he orgnal dea and wre he paper. Oher auhors conrbued equally o he language of hs paper. Conflcs of Ineres: The auhors declare no conflc of neres. References 1. Erdem, E.; Sh, J. ARMA based approaches for forecasng he uple of wnd speed and drecon. Appl. Energy 2011, 88, Lu, H.P.; Sh, J.; Erdem, E. Predcon of wnd speed me seres usng modfed Taylor Krgng mehod. Energy 2010, 35, Wason, S.J.; Landberg, L.; Hallday, J.A. Applcaon of wnd speed forecasng o he negraon of wnd energy no a large scale power sysem. IEE Proc. Gener. Transm. Dsrb. 1994, 141, Landberg, L. Shor-erm predcon of he power producon from wnd farms. J. Wnd Eng. Ind. Aerodyn. 1999, 80, Negnevsky, M.; Johnson, P.; Sanoso, S. Shor erm wnd power forecasng usng hybrd nellgen sysems. In Proceedngs of he IEEE Power Engneerng General Meeng, Chcago, IL, USA, June 2007; pp Alexads, M.C.; Dokopoulos, P.S.; Sahsamanoglou, H.S.; Manousards, I.M. Shor erm forecasng of wnd speed and relaed elecrcal power. Sol. Energy 1998, 63, Damouss, I.G.; Alexads, M.C.; Theochars, J.B.; Dokopoulos, P.S. A fuzzy model for wnd speed predcon and power generaon n wnd parks usng spaal correlaon. IEEE Trans. Energy Convers. 2004, 19, Barbouns, T.G.; Theochars, J.B. A locally recurren fuzzy neural nework wh applcaon o he wnd speed predcon usng spaal correlaon. Neurocompung 2007, 70, Beccal, M.; Grrncone, G.; Marvugla, A.; Serpora, C. Esmaon of wnd velocy over a complex erran usng he generalzed mappng regressor. Appl. Energy 2010, 87, Brown, B.G.; Kaz, R.W.; Murphy, A.H. Tme seres models o smulae and forecas wnd speed and power. J. Clm. Appl. Meeorol. 1984, 23,

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