Short Term Load Forecasting Using Artificial Neural Network And Imperialist Competitive Algorithm

Transcription

1 Short Term Load Forecastig Usig Artificial eural etwork Ad Imperialist Competitive Algorithm Mostafa Salamat, Javad Mousavi, Seyed Hamid Shah Alami, Paper Referece umber: Abstract I last two decades, statistical methods have bee usual techiques for short-term load forecastig. But today, much research has bee carried out o the applicatio of Artificial eural etwork techiques to Short-Term Load-Forecastig (STLF) problem. I this paper, The time of STLF is reduced by idetifyig of effective parameters i STLF by usig of imperialist competitive algorithm. Key words: Imperialist Competitive Algorithm, Artificial eural etwork, Short-Term Load- Forecastig 1. ITRODUCTIO Load forecastig is oe of the cetral fuctios i power systems operatios ad it is extremely importat for eergy suppliers ad other participats ivolved i electric eergy geeratio, tramissio, distributio, ad supply. Load forecasts ca be divided ito three categories: short-term forecasts, medium-term forecasts ad log-term forecasts. Short-term load forecastig (STLF) is a importat part of the power geeratio process. Previously it was used by traditioal approaches like time series, but ew methods based o artificial ad computatioal itelligece have started to replace the old oes i the idustry. Artificial eural etworks are provig their supremacy over other traditioal forecastig techiques. This etwork uses cotiuously valued fuctios ad supervised learig, the actual umerical weights assiged to elemet iputs are determied by matchig historical data (such as time ad weather) to desired outputs (such as historical loads) i a pre-operatioal traiig sessio. The model ca forecast load profiles from oe to seve days. But, because of the umbers of iput parameters to eural etwork is high, Therefore the time of learig ad forecastig icreased. I this paper, The time of STLF is reduced by idetifyig of effective parameters i STLF by usig of imperialist competitive algorithm. Like other evolutioary algorithms, the proposed algorithm starts with a iitial populatio. Populatio idividuals called coutry are i two types: coloies ad imperialists that all together form some empires. Imperialistic competitio amog these empires forms the basis of the proposed evolutioary algorithm. Durig this competitio, weak empires collapse ad powerful oes take possessio of their coloies. Imperialistic competitio hopefully coverges to a state i which there exist oly oe empire ad its coloies are i the same positio ad have the same cost as the imperialist. Applyig

2 the proposed algorithm to STLF problem, shows its ability i dealig with differet types of optimizatio problems ad improvemet of load forecastig time. 2. IMPERIALIST COMPETITIVE ALGORITHM Figure 1 shows the flowchart of the proposed algorithm. Like other evolutioary oes, the proposed algorithm starts with a iitial populatio (coutries i the world). Some of the best coutries i the populatio are selected to be the imperialists ad the rest form the coloies of these imperialists. All the coloies of iitial populatio are divided amog the metioed imperialists based o their power. The power of a empire which is the couter part of the fitess value i GA, is iversely proportioal to its cost. After dividig all coloies amog imperialists, coloies start movig toward their relevat imperialist coutry. The total power of a empire depeds o both the power of the imperialist coutry ad the power of its coloies. We will model this fact by defiig the total power of a empire by the power of imperialist coutry plus a percetage of mea power of its coloies. The the imperialistic competitio begis amog all the empires. Ay empire that is ot able to succeed i this competitio ad ca t icrease its power (or at least prevet decreasig its power) will be elimiated from the competitio. The imperialistic competitio will gradually result i a icrease i the power of powerful empires ad a decrease i the power of weaker oes. Weak empires will lose their power ad ultimately they will collapse. The movemet of coloies toward their relevat imperialists alog with competitio amog empires ad also the collapse mechaism will hopefully cause all the coutries to coverge to a state i which there exist just oe empire i the world ad all the other coutries are coloies of that empire. I this ideal ew world coloies, have the same positio ad power as the imperialist.

3 Fig 1 : Flow chart of proposed algorithm 1 Imperialist Competitive Algorithm The goal of optimizatio is to fid a optimal solutio i terms of the variables of the problem. We form a array of variable values to be optimized. I GA termiology, this array is called chromosome, but here the term coutry is used for this array. This array is defied by coutry [ p1, p2, p3,..., p ] (1) The variable values i the coutry are represeted as floatig poit umbers. The cost of a coutry is foud by evaluatig the cost fuctio f at the variables ( p1, p2, p3,..., p ).The cos (c ) (,,,..., ) t f outry f p1 p2 p3 p ( 2 ) To start the optimizatio algorithm we geerate the iitial populatio of size imp. we select of the most powerful coutries to form the empires. the remaiig col of the populatio will be the coloies each of which belogs to a empire. the we have two types of coutries; imperialist ad coloy. to form the iitial empires, we divide the coloies amog imperialists based o their power. That is the iitial umber of coloies of a empire should be directly proportioate to its power. To divide the coloies amog imperialists proportioally, we defie the ormalized cost of a imperialist by, C c maxc i Where c is the cost of th imperialist ad C is its ormalized cost. Havig the ormalized cost of all imperialists, the ormalized power of each imperialist is defied by, ( 3 ) p C i1 imp C i From aother poit of view, the ormalized power of a imperialist is the portio of coloies that should be possessed by that imperialist. The the iitial umber of coloies of a empire will be,. C roud p. ( 5 ) col (4) Where.C is the iitial umber of coloies of th empire ad col is the umber of all coloies. To divide the coloies, for each imperialist we radomly choose..c of the coloies ad give them to it. These coloies alog with the imperialist will form th empire. Figure 2 shows the iitial populatio of each empire. As show i this figure bigger empires have greater umber of coloies while weaker oes have less. I this figure imperialist 1 has formed the most powerful empire ad has the greatest umber of coloies.

4 Fig 2 : Geeratig the iitial empires: The more coloies a imperialist possess, the bigger is its relevat mark 2 Imperialist competitio As metioed i sectio II, all empires try to take possessio of coloies of other empires ad cotrol them. This perialistic competitio gradually brigs about a decrease i the power of weaker empires ad a icrease i the power of more powerful oes. We model this competitio by just pickig some (usually oe) of the weakest coloies of the weakest impires ad makig a competitio amog all empires to possess these (this)coloies. Figure 6 shows a big picture of the modeled imperialistic competitio. Based o their total power, i this competitio, each of empires will have a likelihood of takig possessio of the metioed coloies. I other words these coloies will ot be possessed by the most powerful empires, but these empires will be more likely to possess them. Fig 3 : Imperialistic competitio To start the competitio, first, we fid the possessio probability of each empire based o its total power. The ormalized total cost is simply obtaied by,. T. C T. C max T. C ( 6 ) i Where T.C ad.t.c are respectively total cost ad ormalized total cost of th empire. Havig the ormalized total cost, the possessio probability of each empire is give by,

5 p p. T. C imp i1. T. C i To divide the metioed coloies amog empires based o the possessio probability of them, we form the vector P as, P p, p, p,..., p p1 p2 p3 p imp The we create a vector with the same size as P whose elemets are uiformly distributed radom umbers. R r1, r2, r3,..., r imp The we form vector D by simply subtractig R from P. D p r, p r, p r,..., p r p1 1 p2 2 p3 3 p imp imp Referrig to vector D we will had the metioed coloies to a empire whose relevat idex i D is maximum. 3 Covergece After a while all the empires except the most powerful oe will collapse ad all the coloies will be uder the cotrol of this uique empire. I this ideal ew world all the coloies will have the same positios ad same costs ad they will be cotrolled by a imperialist with the same positio ad cost as themselves. I this ideal world, there is o differece ot oly amog coloies but also betwee coloies ad imperialist. I such a coditio we put a ed to the imperialistic competitio ad stop the algorithm. Some of bechmark problems i the realm of optimizatio. The mai steps i the algorithm are summarized i the pseudo code show i figure 4. (7) ( 8 ) ( 9 ) (10 ) Fig 4 : Pseudo code for the proposed algorithm

6 3. EXPERIMETAL STUDY For our eural etwork model we used a Back propagatio etwork with a sigle hidde layer. The activatio fuctio used i the hidde ad output layer was Ta-sigmoid ad Pure liear. The A was implemeted usig MATLAB. The data employed for traiig ad testig the eural etwork were obtaied from the EMMCO website for the period Jue-July Like other evolutioary algorithms, The competitive algorithm also requires a buch of settigs that have bee selected i the followig calculatios The umber of iitial states: 100 umber of early empires: 5 umber of coloies: 95 umber of decades (algorithms repeati): 90 umber of etries: 21 umber of variables to be selected: 8 I the proposed algorithm, the data used as iput to the eural etwork was used oce, after beig ormalized i the form of a Excel file ito the MATLAB program. For example, This data icludes the time (1 to 24 represet the hours of the day), day (from 1 to 31 for six moths ad 1 to 30 for 5 i the first moth ad the last moth of 1 to 29 was cosidered.), Moth (from 1 to 12 ), day of week (Saturday to Friday from 1 to 7),workig day(0 for holiday,0.5 for Thursday ad 1 for other days), miimum temperature, maximum temperature, Wid, humidity,the cosumed curret load,. The ed result of optimal respose i STLF problem is show i figure 5. Calculatio error is obtaied by mea square error ad equal to e-004. As ca be see, the etwork is able to solve STLF problem with good accuracy. The oly differece is i the peak load forecast ad the actual value.this differece ca fixed by output feedback etworks. Fig 5 : Comparig betwee actual ad forecastig load

7 4. COCLUSIO I this paper, A optimizatio algorithm based o modelig the imperialistic competitio is proposed for STLF. The algorithm is tested ad the results show that the time of STLF problem is reduced. I other words, The result of STLF problem show that our expectatios regardig our proposed method is able to satisfy most of load forecastig problem. 5. REFRECES [1] I. Moghram, S.Rahma, Aalysis ad evaluatio of five short-term load forecastig techiques, IEEE trasactio of power system, 4(4), 1989,pp [2] J. W. Taylor, P. E. McSharry, Short-term load forecastig methods: A evaluatio based o Europea data, IEEE Trasactio o Power System, o. 22, pp , [3] ] M. Peg,.F. Hubele, ad G.G applicatio Advacemet i the"karady. Of eural etworks for Short-Term Load Forecastig. IEEE Trasactios o Power Systems, 7: , [4] Esmaeil Atashpaz-Gargari, Caro Lucas, "Imperialist Competitive Algorithm: A Algorithm for Optimizatio Ispired by Imperialistic Competitio", IEEE Cogress o Evolutioary Computatio (CEC), Sigapore, , [5] R. L. Haupt ad S. E. Haupt, Practical Geetic Algorithms, Secod Editio, ew Jersey: Joh Wiley & Sos, 2004 [6] P. Fishwick, eural etwork models i simulatio: A compariso with traditioal modelig approaches Workig Paper, Uiversity of Florida, Gaiesville, FL,1989. [7] M. Shahidehpour, H. Yami, ad Z. Li, Market Operatios i Electric Power Systems: Forecastig,Schedulig, ad Risk Maagemet, ew York:Wiley, [8] S. Hayki, eural etworks, A comprehesive foudatio, Pretice-Hall, ew Jersey, [9] Website for historical load data. [10] Website for historical weather.