A COMBINED FORECASTING METHOD OF WIND POWER CAPACITY WITH DIFFERENTIAL EVOLUTION ALGORITHM

Transcription

1 Joural of Theoretcal ad Appled Iformato Techology 0 th Jauary 03. Vol. 47 No JATIT & LLS. All rghts reserved. ISSN: E-ISSN: A COMBINED FORECASTING METHOD OF WIND POWER CAPACITY WITH DIFFERENTIAL EVOLUTION ALGORITHM JIANJUN WANG, HONGYANG ZHANG, ZHANGYI PAN, LI LI School of Ecoomc ad Maagemet Admstrato, North Cha Electrc Power Uversty, Bejg 006, Cha School of Ecoomcs & Busess Admstrato, Bejg Iformato Scece & Techology Uversty, Bejg 00085, Cha ABSTRACT As wd power s a mature ad mportat reewable eergy, wd power capacty forecastg plays a mportat role reewable eergy geerato s pla, vestmet ad operato. Combed model s a effectve load forecastg method; however, how to determe the weghts s a hot ssue. Ths paper proposed a combed model wth dfferetal evoluto optmzg weghts. The proposed model ca mprove the performace of each sgle forecastg model of regresso, BPNN ad SVM. I order to prove the effectveess of the proposed model, a applcato of the Cha s wd power capacty was evaluated from 000 to 00. The expermet results show that the proposed model gets the maxmum mea absolute percetage error (MAPE) value.79%, whch s better tha the results of regresso, BPNN ad SVM. Keywords: Capacty Forecastg, Dfferetal Evoluto Algorthm, Wd Power. INTRODUCTION Reewable eergy geerato s a mportat way for electrcty power dustry to acheve the eergy savg goal, whch helps Cha fsh the promse of decreasg the carbo emssos per ut of GDP by 40-45% 00 compared wth 005. As wd power geerato s the most mature reewable eergy techology the reewable eergy geerato, t has bee developed rapdly. From 000 to 008, the creasg rate of wd power geerato ma developed coutry has bee mproved more tha 0%. Wd power forecastg problem s oe of the load forecastg problems, whch s a tradtoal ssue but a dffcult problem, because t always flueced by may factors. May of coutres the world have focused o the load forecastg the last decades such as the regressve method [], autoregressve movg average model (ARMA)[] ad tellget load forecastg algorthms. The artfcal eural etworks (ANNs) became oe of the most popular tellgece methods last decade because t ca cosder the o-lear factors ad oly a three-layer eural etwork ca acheve ay accuracy degree of ay cotuous fucto mappg by the Kromogols theorem. M. Beccal proposed a group of eural etworks for a suburba areas electrc demad forecastg ad obtaed a good forecastg accuracy [3]. I ths feld, Herque Steherz Hppert gave a very excellet revew o the eural etworks for load forecastg [4], ad the revew, he poted out that the back propagato artfcal eural etwork (BPNN) s the most popular algorthm the ANNs. Furthermore, wth support vector regresso (SVR) method proposed by Vapk 998, SVR become the other popular method for load forecastg. Support vector regresso (SVR) uses the structural rsk mmzato prcple to mmze the geeralzato errors prcple ad overcome the local optmal soluto problem. B.J. Che wo a load forecastg competto orgazed by EUNITE etwork 00 by a SVR model [5]. P.F. Pa ad W.C. Hog combed several tellgece algorthms such as geetc algorthm (GA), smulated aealg (SA) ad mmue algorthm wth the SVR model to forecast Tawas aual electrc load, ad they obtaed a very good performace case study, t also shows that SVR models outperform ARIMA ad ANN models [6]. Recetly, there are may researches o the wd power forecastg such as wd speed forecastg ad wd power forecastg, ad the forecastg methods clude the autoregressve model, 33

2 Joural of Theoretcal ad Appled Iformato Techology 0 th Jauary 03. Vol. 47 No JATIT & LLS. All rghts reserved. ISSN: E-ISSN: ARIMA[7] model, ANN model[8,9], GMDH model[0] ad so o. It regrets that few researches pay atteto to the forecastg problem about wd power capacty, whch plays a mportat role for the wd power costructo pla, vestmet ad operato. Ad these papers are all focused o usg a sgle model to solve the wd power forecastg, some forecastg scholars have bee poted out that a sgle model s performace s worse tha combed models. The reasos are as follows: frst, the combed model ca reduce dsadvatage of ay a sgle model; secod, the errors of combed model are always smaller tha each sgle model s. Therefore, ths paper proposed a combed forecastg model of wd power capacty wth dfferetal evoluto algorthm to solve the problem. Ths paper s orgazed as follows. I secto, the combed forecastg model wth dfferetal evoluto algorthm s gve. I secto 3, the expermetal results of comparg the algorthm proposed ths paper wth other algorthms are preseted. Fally, our work of ths paper s summarzed the last secto.. A COMBINED FORECASTING MODEL WITH DIFFERENTIAL EVOLUTION ALGORITHM I practce, a load forecastg problem ca use dfferet load forecastg models, so the load forecastg accuracy are also dfferet. How to choose the best forecastg model s a dffcult problem. Usg combed forecastg model ca solve the above problem. A combed forecastg model cossts of two or more forecastg models ad each model has a certa weghts, a combed forecastg model ca be descrbed as follows: Suppose that f s forecastg results of the th method, y s the actual data. The combed forecastg model ŷ ca be expressed by yˆ = wf () = I whch, w s the weght of the th method, ad a optmzato problem of the combed model eed satsfy the followg model. M : MSE( y w f ) () = = st.. w = ; w 0 The key problem of the combed model s to determe the weght. The weght determe methods ca be dvded to two categores, oe s fxed weght method, whch determed the weght as a fxed umber, ad the other s trasformable weght method, whch determed the weght as a fucto of the tme. The fxed weght determed model s the most popular method because t s smple ad easy to apply, ad t s sutable for usg tellgece algorthm such as geetc algorthm, partcle swarm optmzato to solve the problem. Dfferetal evoluto (DE) algorthm s oe of the evolutoary algorthms, whch was proposed by Stor ad Prce order to solve the Chebychev Polyomal fttg problem at frst, t becomes oe of the most popular optmzato algorthms. As other evoluto algorthms such as geetc algorthm (GA), DE s also populato based algorthm, whch cotas mutato, crossover ad selecto steps. However, compare wth other evoluto algorthms, DE s easy to mplemet, t eeds fewer parameters ad exhbts fast covergece. The detal workg steps are as follows []: Step.Parameters talzato The ma parameters of DE algorthm are populato sze N, legth of the chromosome D, the mutato factor F, the crossover rate C ad the maxmum geeratos umber g. the mutato factor F s selected [0, ], the crossover rate C s selected [0, ] ad the larger C s always easy to premature ad covergece faster. Step.Populato talzato Set g=0. Geerate a N*D matrx wth uform probablty dstrbuto radom values. The geerato method s X j = rad ( hgh[ j] low[ j]) + low[ j] (3) I whch, =,,, N, j =,,, D,rad s a radom umber wth a uform probablty dstrbuto, ad hgh[j], low[j] s the upper boud ad lower boud of the jth colum, respectvely. Step 3.Populato evoluto Calculate ad record ftess values of all the dvduals. Step 4.Mutato operato Ths operato uses two radom chose vectors X b,x c to produce a mutat X a vector as follows: X = X + F( X X ) () a a b c 34

3 Joural of Theoretcal ad Appled Iformato Techology 0 th Jauary 03. Vol. 47 No JATIT & LLS. All rghts reserved. ISSN: E-ISSN: I whch, F s the mutato factor the rage [0,], abc,, {,,, N} are radomly chose ad they must keep dfferet from each other. Step 5.Crossover operato Crossover operato ca crease the dversty of the populato, ad the equato s show as follows. X b( j) = X a( j) f rad( j) C or j = rad( j) (6) X b( j) = X a( j) otherwse Where j s the gee locato of a populato, rad(j) s a radom umber ad rad(j) s also a radom teger the rage of [,D], esures that at least oe elemet of the populato ca get the crossover operato. C s the crossover rate [0,]. Step 6.Selecto operato Selecto operato retas the better offsprg the ext geerato. The selecto prcple s the ftess values, f the offsprg s ftess value f(u,g ) s better tha the paret s f(x,g ), the offsprg U,G would select, otherwse, the paret X,G would reta. UG, f f ( UG, ) < f ( X G, ) X G, + = () X G, otherelse DE algorthm has the better performace tha GA ad PSO algorthms the examato of the 34 wdely used bechmark fuctos []. Accordg to the study, DE algorthm s stable ad t ca obta a better soluto tha other algorthms, ad the expermet results are also show that DE ca get the earest optmal soluto the PSO ad GA algorthm. Therefore, the DE algorthm wll be used to solve the weght determg problem, whose ftess fucto s employed the mea absolute percetage error fucto (MAPE), whch s commo used load forecastg performace evaluato. A () F() MAPE = 00% () = A () Where A() s the actual value, F() s the forecastg value ad s the total umbers. 3. A NUMERIC EXAMPLE I ths case, we use the aual wd power capacty of Cha from 000 to 00, whch s show Fgure. Load(MW) 4.5 x Fgure : The wd power capacty of Cha from 000 to 00 It s clearly see that the curve appears a expoetal curve character, so we are usg the l(x) value as the depedet varable the sgle forecastg models. Ad the sgle forecastg models are chose as regresso model, back propagato eural etwork (BPNN) ad support vector mache(svm) models, because these models are all the popular sgle models load forecastg. I BPNN forecastg model, the ode umber of put layer s x t-3, x t-, x t-, the hdde layer umber s fve ad the output ode s x t. I SVM forecastg model, the put varables are also x t-3, x t-, x t-, ad the output ode s also x t, the same as BPNN model, but the parameters s δ = 0., C = 000, µ = 0.5, because these three parameters are best performaces the expermets. The proposed combed weght of regresso, BPNN ad SVM, whch determed by DE algorthm wth default parameters, are 0, ad respectvely. The fal results are all show Table ad Fgure. Table. The Actual Load Ad Forecastg Results Of Regresso, ANN, SVM Ad Combed Model Actual load Regresso BPNN SVM Combed Model

4 Joural of Theoretcal ad Appled Iformato Techology 0 th Jauary 03. Vol. 47 No JATIT & LLS. All rghts reserved. ISSN: E-ISSN: MAPE %.793%.97%.79% From the determed weght of DE algorthm, t ca be clearly see that BPNN model gets the maxmum weght, SVM follows, ad the regresso model s weght s zero. The better the performace s, the greater the weght s. It proves that DE algorthm s effectve. 4. CONCLUSION mprove the load forecastg performace. I the expermet, the proposed method gets the mmum MAPE values, whch verfes the proposed method s effectveess wd power capacty forecastg. ACKNOWLEDGEMENTS Ths work was supported by NSFC uder Grat No , ad the Fudametal research fuds for the cetral uverstes (QN7). The proposed combed model tegrates the regresso, BPNN ad SVM models. Wth usg DE algorthm to determe the weght, t ca 5 x 04 Load(MW) Actual load Regresso BPNN SVM Combed Model Fgure : The Forecastg Results Of Regresso, ANN, SVM Ad Combed Model 36

5 Joural of Theoretcal ad Appled Iformato Techology 0 th Jauary 03. Vol. 47 No JATIT & LLS. All rghts reserved. ISSN: E-ISSN: REFERENCES: [] A. Goa, C. May, G. Fusa, Fuctoal clusterg ad lear regresso for peak load forecastg, Iteratoal Joural of Forecastg, Vol.6, No. 4, 00, pp [] S.Sp. Pappas, L. Ekoomou, D.Ch. Karamousatas, G.E. Chatzaraks, S.K. Katskas, P. Latss, Electrcty demad loads modelg usg AutoRegressve Movg Average (ARMA) models, Eergy, Vol. 33, No 9, 008, pp [3] M. Beccal, M. Cellura, V. Lo Brao, A. Marvugla, Forecastg daly urba electrc load profles usg artfcal eural etworks, Eergy Coverso ad Maagemet, Vol. 45,No. 8-9, 004,pp [4] H. S. Hppert, C. E. Pedrera, R. C. Souza, Neural etworks for short-term load forecastg: a revew ad evaluato, IEEE Trasactos o Power Systems,Vol.6, No., 00, pp [5] B.-J. Che, M.-W. Chag, C.-J. L, Load forecastg usg support vector maches: A study o EUNITE Competto 00, IEEE Trasactos o Power Systems, Vol.9, No.4, 004, pp [6] W.-C. Hog, Electrc load forecastg by support vector model, Appled Mathematcal Modellg,Vol.33, No.5, 009, pp [7] E. Erdem, J. Sh, ARMA based approaches for forecastg the tuple of wd speed ad drecto, Appled Eergy, Vol.88, No. 4, 0, pp [8] M. Mofared, H. Rastegar, H. M. Kojabad, A ew strategy for wd speed forecastg usg artfcal tellget methods, Reewable Eergy, Vol. 34, No. 3, 009, pp [9] Z. H. Guo, W. G. Zhao, H. V. Lu, J. Z. Wag, Mult-step forecastg for wd speed usg a modfed EMD-based artfcal eural etwork model, Reewable Eergy, Vol. 37, No., 0, pp [0] R.E. Abdel-Aal, M.A. Elhaddy, S.M. Shaahd, Modelg ad forecastg the mea hourly wd speed tme seres usg GMDH-based abductve etworks, Reewable Eergy, Vol. 34, No. 7, 009, pp [] J.J. Wag, L. L, D.X. Nu, Z.F. Ta, A aual load forecastg model based o support vector regresso wth dfferetal evoluto algorthm, Appled Eergy, Vol. 94, 0, pp [] L. dos Satos Coelho, V. C. Mara, Combg of chaotc dfferetal evoluto ad quadratc programmg for ecoomc dspatch optmzato wth valve-pot effect, IEEE Trasactos o Power Systems,Vol., No., 006, pp