Online Short Term Load Forecasting by Fuzzy ARTMAP Neural Network

Transcription

1 Online Short Term Lod Forecsting by Fuzzy ARTMAP Neurl Network SHAHRAM JAVADI Electricl Engineering Deprtment AZAD University Tehrn Centrl Brnch Moshnir Power Electric Compny IRAN Abstrct: This pper presents the ppliction of Fuzzy ARTMAP neurl network for evluting on-line lod forecsting in short term cse. A new pproch using rtificil neurl networks (ANNs) is proposed for short term lod forecsting. To forecst lods of dy, the hourly lod pttern nd the mximum nd minimum nd verge of temprture must be determined. To demonstrte the effectiveness of the proposed neurl network, short term lod forecsting is performed on the IRAN power system. Test results indicte tht the specil neurl network is very effective in improving the ccurcy of the forecst hourly lods. Keywords: Power Systems, Lod Forecsting, Short Term, Fuzzy ARTMAP Neurl network 1. Introduction A number of lgorithms hve been suggested for the lod forecsting problem. Previous pproches cn be generlly clssified into two ctegories in ccordnce with techniques they employ. One pproch trets the lod pttern s time series signl nd preicts the future lod by using vrious time series nlysis techniques [1-7]. The ide of the time series pproch is bsed on the understnding tht lod pttern is nothing more thn time series signl with known sesonl, weekly, nd dily periodicities. These periodicities give rough prediction of the lod t the given seson, dy of the week, nd time of the dy. The difference between the prediction nd the ctul lod cn be considered s stochstic process. By the nlysis of this rndom signl, we my get more ccurte prediction. The techniques used for the nlysis of this rndom signl include the Klmn filtering [8], the Box-Jenkins method, the utoregressive moving verge (ARMA) model [9], nd spectrl expnsion technique. The Klmn filter pproch requires estimtion of covrince mtrix. The possible high nonsttionrity of the lod pttern, however, typiclly my not llow n ccurte estimte to be mde. These methods re very time consuming nd difficult. More recently the ppliction of neurl network hs developed in mny of engineering problems. One of these problems is forecsting of lod hourly by bck propgtion method [10] or KOHONEN neurl network clssifier. In this pper, different pproch is proposed for lod forecsting. This pproch is bsed on Fuzzy ARTMAP network. Becuse of self-orgnized chrcteristic of these networks, they cn

2 be used online in power systems for lod forecsting. Section 2 introduces brief description of Fuzzy ARTMAP network t level tht is necessry to understnd the min results of this pper. The experiments re discussed nd the results re presented in section 3. Finlly, the conclusions re drwn in section The Fuzzy ARTMAP network Fuzzy ARTMAP is network with n incrementl supervised lerning lgorithm, which combines fuzzy logic nd dptive resonnce theory (ART) for recognition of pttern ctegories nd multidimensionl mps in response to input vectors presented in n rbitrry order. It relizes new minimx lerning rule, which jointly minimizes the predictive error nd mximizes code compression, nd therefore generliztion [11]. A mtch trcking process tht increses the ART vigilnce prmeter chieves this by the minimum mount needed to correct predictive error. The Fuzzy ARTMAP neurl network is composed of two Fuzzy ART modules, nmely Fuzzy ART nd Fuzzy ART b, which re shown in figure (1). After network is trined nd clusters re creted, then it is plced in prllel with power system to evlute stbility indices s shown in figure (2). The Fuzzy ARTMAP in prediction mode is shown in figure (3). The interction medited by the mp field F b my be opertionlly chrcterized s follows: ) ART nd ART b The inputs to ART nd ART b re in the complement code form: For ART, I=A=(, c ); For ART b, I=B=(b,b c ); For ART, let x ={x 1,,x 2M } denotes the F 1 output vector, y ={y 1,,y N } denotes the F 2 output vector, nd w j ={w j1,,w j2m } denotes the jth ART weight Vector. Also for ART b, let x b ={x b 1,,x b 2Mb } denotes the F b 1 output vector, y b ={y b 1,,y b b Nb } denotes the F 2 output vector, nd w b k ={w b k1,,w b k2mb } denotes the kth ART b weight vector. For the mp field, let x b ={x b 1,,x b Nb } denotes the F b output vector nd w b j ={w b j1,,w b jnb } denotes the weight vector from the jth F 2 note to F b. b) Mp Field Action The mp field F b is ctivted whenever one of the ART or ART b ctegories is ctive. If node J of F 2 is chosen, then its weight w b j ctivte F b. If node K of F b 2 is chosen, then the node K in F b is ctivted by 1-to-1 pthwys between F b 2 nd F b. If both ART nd ART b re ctivted, then F b becomes ctive only if ART predicts the sme ctegory s ART b vi the weight w b j. c) Mtch trcking At the beginning of ech input presenttion to the ART, vigilnce prmeter ρ equls bseline vigilnce ρ 0. The mp field vigilnce prmeter is ρ b. If x b < ρ b y b (1) Then ρ is incresed until it is slightly lrger thn A w J A -1, where A is the input to F 1 in complement coding form. And x = A w J < ρ A (2)

3 Where J is the index of the ctive F 2 node. When this occurs, ART serch leds either to ctivtion of nother F 2 node J with: x = A w J ρ A (3) Input Power System Lod Forecsted + Error nd x = y b w J b ρ y b (4) Fuzzy ARTMAP - Or, if no such node exists, to the shutdown of F 2 for the reminder of the input presenttion. d) Mp Field Lerning Lerning rules determine how the mp field weights w b jk chnge through time. b This cn be done s follows: Weights w jk in F 2 F b pths initilly stisfy: W b jk (0) = 1 ART F2 Y F1 X F0 A=(,') Fig.2. On-Line Trining Wi b P Mp Field Fb Xb Mtch Trcking Pb F2b Yb Trget Cl OutPut During resonnce with the ART ctegory J ctive, w b J pproches the mp field vector x b. With fst lerning, once J lerns to predict the ART b ctegory K, tht ssocition is permnent, i.e., w b jk = 1 for ll time. F2 F1 F0 ART Y X A=(,') Wi b P Mp Field Fb Xb Pb Mtch Trcking F2b F1b F0b Yb Xb B=(b,b') b ARTb Pb Fig.1. A typicl Fuzzy ARTMAP rchitecture Fig.3. Fuzzy ARTMAP network for clssifiction 3. Simultions In order to test the lgorithm for its effectiveness in Lod Forecsting of power system, we chose dt which is obtined from disptching center of TAVANIR Co. We study 2 cses. In cses 1, we use Fuzzy ARTMAP Network nd in cse 2, Perceptron Network is used. Finlly the obtined results re compred. In ech cse, performnce error of neurl network is clculted ccording to the following formul [17]: 1 N 2 E di i N = i= 1 Where, y di : Desired output of NeurlNetwork. y i : Actul output of Neurl Network. N : Number of Dt Set for Trining. ( y y ) (5)

4 Cse 1 (Fuzzy ARTMAP network): In this cse we use Fuzzy ARTMAP neurl network to predict lod of next dy ccording current dy. In this test, prmeter ρ ws chosen to be ρ =0.95, ρ b =0.95, ρ b =0.94. A set of 1000 trining ptterns ws selected from the entire set. After trining the network with 1000 ptterns, the set of 1000 remined ptterns ws used to test network. Summery of obtined results is given in tble (1). Trining Error of this test is bout 0.769% nd is shown in figure (4). Cse 2 (Perceptron network): In this cse we used 3-lyer Perceptron Neurl-Network with bckpropgtion m ethod of trining. Also we used the sme input bit ptterns. Error in this cse is higher thn the bove cses nd computing time for trining is too high. A plot of error in this cse is shown in figure (6). Fig.6. Error plot of MultiLyer Perceptron network with 1000 dt set (Cse 2) Fig.4. Error plot of Fuzzy ARTMAP network with 1000 dt set (Cse 1) Menwhile the ctul lods for one dy during this entire dt set is ploted nd the lso forecsted lod is ploted in figure Conclusion In this pper new pproch bsed on Fuzzy ARTMAP NeurlNetwork for estimted Lod hs been presented. For on-line trining, the fuzzy ARTMAP network ws found to tht is better choice thn other neurl-network trining method. It ws shown tht Fuzzy ARTMAP network, hs low sensitivity reltive to the selection of number of dt set feed to it for trining nd lso reltive to the number of input bits. These could be regrded s n dvntge of this network. As result lower number of dt set for trining could be selected which tkes less time for computing in off-line mode. Fig.5. Actul Lod respected to Predicted Lod by FAM neurl network

5 Tble 1, Summery of Test Results Fuzzy ARTMAP Test Dt Set Input Bit ptterns For Neurl Network ART Node ARTb Node % Error Temp & Lod % p pb pb 3 lyers Percepteron Test Dt Set Input Bit ptterns For Neurl Network Hidden Node Neuron Type Temp & Lod 25 BSF Lerning Rtes n1 = n2 = 0.1 % Error 1.82 % References: [1] J. Toyod, M. Chen, nd Y. Inoue, An Appliction of Stte Estimtion to short- Term Lod Forecsting, Prtl:Forecsting Modeling, Prt2: Implementtion, IEEE Tr. on Power App. nd Sys., vol. PAS-89. pp. 167S-1688, Oct., 1970 [2] S. Vemuri. W. Hung. nd D. Nelson. On-line Algorithms For Forecsting Hourly Lods of n Electric Utility, IEEE Tr. on Power App. nd Sys., vol., PAS- 100, pp , Aug., 1981 [3] G.E. Box nd G.M. Jenkins, Time Series Anlysis-Forecsting nd Control, Holden-dy, Sn Frncisco, 1976 [4] S.Vemuri, D. Hill, R. Blsubrmnin, Lod Forecsting Using Stochstic Models, Pper No. TPI-B, Proc. of 8th PICA confercnce, Minnepolis, Minn., pp.31-37, 1973 [5] W. Christinse, Short-Term Lod Forecsting Using Generl Exponentil Smoothing, IEEE Tr. on Power App. nd Sys., vol. PAS-90, pp , Apr., 1971 [6] A. Sge nd G. Hus, Algorithms for Sequentil Adptive Estimtion of Prior Sttistics, Proc. of IEEE Symp. on Adptive Processes, Stte College, P., Nov., 1969 [7] R. Mehr, On the Identifiction of Vrince nd Adptive Klmn Filtering, Proc. of JACC (Boulder, Cob.), pp , 1969 [8] P. Gupt nd K. Ymd, Adptive Short-Term Forecsting of Hourly Lods Using Wether Informtion, IEEE Tr. on Power App. nd Sys., vol. PAS91, pp , 1972 [9] C. Asbury, Wether Lod Model for Electric Demnd Energy Forecsting, IEEE Tr. on Power App. nd Sys., vol. PAS-94, no.4, pp , [10] D.C. Prk, M.A. El-shrkwi, R.J. Mrks II, L.E. Atls nd M.J. Dmborg, Electric Lod Forecsting Using An Artificil Neurl Network, IEEE Trn. On PWS, vol. 6, No. 2, pp , My 1991 [11] G.A. Crpenter, S. Grossberg, N. Mrkuzon, J.H. Reynolds, D.B. Rosen, fuzzy ARTMAP: A Neurl Network Architecture for Incrementl Supervised Lerning of Anlog Multidimensionl Mps, IEEE trnsction on neurl networks, Vol. 3, No. 5, Sep. 1992, PP