Comparative Study of Short-term Electric Load Forecasting

Transcription

1 2014 Ffth Internatonal Conference on Intellgent Systems, Modellng and Smulaton Comparatve Study of Short-term Electrc Load Forecastng Bon-gl Koo Department of electrcal and computer engneerng Pusan atonal Unversty Busan, Republc of Korea Sang-woo Lee, Woo Km, June ho Par Department of electrcal and computer engneerng Pusan atonal Unversty Busan, Republc of Korea Abstract In ths paper, we performed short-term electrc load forecastng usng three methods and compared each results. We classfed before mang a forecastng model usng K- means and - to elmnate error from calendar based classfcaton. Classfed load data used as nputs of forecastng model. We compared three methods such as A, SES, GMDH. We carred out 1-day ahead predcton for two wees, January 10 to 16, March 14 to 20, 2011 usng hourly Korean electrc load data. The results of forecastng, all methods were mostly good n general wthout applyng meteorologcal data. Most of them, GMDH expressed the most performance n MAPE except for Saturday. A. Load Preparng Electrc loads s expressed n total generated power(hourly). These data are sorted by calendar based and t probably not proper. Generally, they can reflect ther day- auto regresson and fuzzy lnear regresson, neural networ, experts system are frequently adopted to express ther pattern. Keywords-component; formattng;short-term electrc load foreacastng, ARIMA, -, Artfcal eural etwor, Smple Exponental Smoothng, GMDH I. ITRODUCTIO As the capacty of power system has been expendng, grd has become more complcated and needed to more effort to safe operaton n a secure manner. In addton, f power system s n the stuaton that solated and hasn t suffcent spnnng reserve, the mportance of accurate electrc load forecastng become ncrease. There are many economcal and techncal problems n grd operaton, t can be one of soluton that electrc load forecastng usng advanced technques. ormally, t can provde standard for bddng generaton pool, generator mantenance schedulng, unt commtment and also as nputs to load flow study or contngency analyss.[1]-[2] Electrc load forecastng classfed to short-term, longterm forecastng. Short-term electrc load forecastng usually meanng next day forecastng, t dvded nto ther day-type such as weedays(tuesday through Frday), Monday, Saturday, Sunday, holday forecastng. As see the Fg.1, each day-type has ther unque characterstc, forecastng models have to be establshed reflectng ther nherent patterns. weedays model normally has hgh accuracy results from ther defnte tme seres characterstc. However, Monday, Saturday, Sunday relatvely lower accuracy than weedays comes from ther lac of data causng lower contnuty than weedays. For ths reason, exponental smoothng s frequently chosen as method of weedays forecastng and Fgure 1. Weely electc load pattern(mon.-sun.) Electrc load pattern ncludes mplct factors. It normally follows ther prevous load pattern, however, t wll lead to wrong predcton between successve days f the date-type s dfferent compare to prevous day. In addton, seasonal varaton and socal effectveness, meteorologcal such as artemperature and weather are also consdered. Consequently, load classfcaton by ther nherent characterstcs s nevtable procedure. Classcal lnear methods have been used to electrc load forecastng nclude movng average and exponental smoothng, lnear regresson[3]-[7]. However, nowadays, data mnng methods such as Artfcal eural etwor[8]- [11] and SVM(Support Vector Machne) are showng satsfactory results. So, ths paper compare to results of some methods applyng load classfcaton. II. LOAD CLASSIFICATIO /14 $ IEEE DOI /ISMS

2 type fathfully. For example, Comparng weeday loads wth Saturday loads, the level of Saturday loads s relatvely low durng p.m.. The level of Monday loads durng a.m. relatvely low to weedays affected by Sunday brea. However, sometmes some of data show dfferent characterstc other same day-type data. Ths can possbly exst that a data present Monday pattern that lower load durng a.m. compare to weedays actually Wednesday n calendar. For ths reason, ths paper suggests load classfcaton before establshng forecastng model. It dvded nto seasonal and day-type classfcaton. K-mean and - algorthm are used to Seasonal and day-type classfcaton respectvely. B. K-mean algorthm K-mean algorthm was proposed by Cox (1957) and Fsher (1958) and developed by Hartgan (1975) and MacQueen (1967). However, ths algorthm assgn as an nput, and splt the data set nto several clusters now. The data whch was gathered to same cluster have strongly smlar characterstc. However, data smlarty among the ntercluster s relatvely low compare to smlarty among the ntracluster data. The smlarty can be measured by cluster s centrod or center of gravty. Ths can be establshed by followng procedure. [12]. Input : : the number of cluster D: a data set contanng n objects. Output: A set of clusters. Method (1) arbtrarly choose objects from D as the ntal cluster centers (2) repeat (3) (re)assgn each object to the cluster to whch the object s the most smlar, based on the mean value of the objects n the cluster (4) update the cluster means,.e., calculate the mean value of the objects for each cluster (5) It the square-error crteron converges, stop. 2 E p (1) where, 1 E: the sum of the square error for all objects n the data set P: the pont n space representng a gven object m : the mean of cluster C C. -earest eghbor algorthm K-earest eghbor method was frst descrbed n the early 1950s. Ths algorthm wasn t popular before supported by computng technology. Ths method s one of famous technque n the pattern recognton. In bascally, ths algorthm gvng a tag to certan data that we want to classfy. That s, tranng sets are descrbed by n attrbutes. Each set represents a pont n an n-dmensonal space. In ths way, all the tranng data are stored n an n-dmensonal space. When m gven an unnown datum, - model fnds data among traned data by order of the shortest dstance. Fgure 2. K-mean clusterng procedure Dstance s defned n terms of a dstance metrc. In ths paper, we used the Eucldean dstance between two ponts, X 1 = (x 11, x 12,,x 1n ) X 2 = (x 21, x 22,,x 2n ) 2 1 2) (X1 X2) 1 ds (X,X (2) For determne optmal, we selected certan odd startng from 1 and tested comparng the error rate of classfer. Repeatng ths experment, we choose the best whch s the lowest error rate. III. LOAD FORECASTIG A. GMDH(Group Method of Data handlng) GMDH has been developed by A.G.Ivaneno[13]. After ntal development, ts advanced models also have developed to express mult-varable, non-lnear system[14]. The GMDH s one of nductve self-organzaton data drven approach, t s only small data samples. Its basc equaton s called Kolmogrov-Gabor polynomal, expressed by (3) whch s dscrete form of Volterra seres. j j j j a x a x x a x x x (3) a 0 j where, x (=1,2,,) and represent nput and output varable respectvely. Relatonshp between two varables can express = f(x 1,x 2,,x ) and j 464

3 If the structure of model s unnown and nput parameter =4, parameters to estmaton are 70. It also consders tremendous structures. Due to avod ths complexty, ths paper used 1 parameters and 1st-order self-organzed model as seen below y a a x (4) 0 B. SES(Smple Exponental Smoothng) The smple exponental smoothng model s a movng average method that places a greater weght on the recent demand when calculatng the average. F t+1 = F t +α(z t -F t ) (5) F t = αz t-1+ (1- α)f t-1 (6) Where, F t+1 : predcted value at tme pont t+1 Z t : observed value at tme pont t Z F : error : smoothng constant Larger the smoothng constant value (0 1), the greater the weght gven to the recent data. For data wth a partcular pattern, more weght should be gven to recent data, and for data wthout a partcular pattern or wth severe varaton, more past data should be ncluded. In addton, should mnmze error.. The advantage of ths technque s that t needs only three data (the predcton value just obtaned, the observed value, and smoothng constants) whereas the weghted movng average method requres the prevously observed value and the weght. C. A(Artfcal eural etwor) Fgure 4. A two-layer feed-forward neural networ eural networs are mathematcal tools orgnally nspred by the way the human bran processes nformaton. Ther basc unt s the artfcal neuron, schematcally represented n Fg.3. The neuron receves (numercal) nformaton through a number of nput nodes, processes t nternally, and puts out a response. The processng s usually done n two stages: frst, the nput values are lnearly combned, then the result s used as the argument of a nonlnear actvaton functon. The combnaton uses the weghts w attrbuted to each connecton. The actvaton functon must be a non-decreasng and dfferentable [10]. The neurons are organzed n a way that defnes the networ archtecture. The one we shall be most concerned wth n ths paper s the multlayer perceptron (MLP) type, n whch neurons are organzed n layers. The neurons n each layer may share the same nputs, but are not connected to each other. If the archtecture s feed-forward, the outputs of one layer are used as the nputs to the followng layer. The layers between the nput nodes and the output layer are called the hdden layers. Fg.4 shows an example of a networ wth 28 nput nodes, 2 layers (one of whch s hdden), and 24 output neurons. IV. CASE STUDY Fgure 3. An artfcal neuron In ths paper, we carred out for one-day-ahead predcton of hourly electrc load usng electrc load data of Korea. The electrc load data were used except for specal holdays. (Thans gvng day, ew year s day etc.) After that, electrc load data were classfed by K-mean and - algorthm and normalze by (7) L forecasted L L actual actual 100 where, L normal s normalzed load. L max and L mn represent maxmum and mnmum load among the classfed load. Test results were evaluated by MAPE(Mean Absolute Percentage Error). MAPE can be expressed followng equaton. (7) 465

4 24 1 Lforecasted Lactual MAPE 100 (8) 24 Lactual where, L forecasted and L actual represent forecasted load and actual load respectvely. Case studes from the proposed algorthm were carred out for two wees, January 10 to 16, March 14 to 20, We expermented three methods as prevously have been ntroduced to predct. All methods used classfed data as an nput. From Fg.5 to Fg.7 show forecasted load patterns compare to actual load. Table shows the summary of predcton results. For A, we chose a multlayer perceptron wth 28 nputs, 1 hdden layer, 24 outputs. Smoothng constant of SES, we selected 0.75 to mnmze predcton errors. The accuraces of three models are slghtly dfferent. SES s mostly low accuracy for all day- type and max error compare to the other methods. It had also qute large dfference between mn and max error rage. However, GMDH shows 1.055% n MAPE, whch s the best performance among all day-type and methods despte of excludng weather data. A showed mddle performance between other two methods. Fgure 5. Predcton result of SES S E S G M D H A Methods Fgure 7. Predcton result of A TABLE I. MAPE OF PREDICTIO ERRORS MAPE Wee days Mon Sat Sun Mn Max V. COCLUSIO In ths paper, we carred electrc load classfcaton and short-term electrc load forecastng usng A, SES, GMDH. Compare to other two methods, GMDH was the best performance. However, t have to be mproved that the type of load for weeend and Monday are forecasted relatvely hgher MAPE than weedays and large value of maxmum MAPE. These can help to mprove study that usng addtonal meteorologcal data or constructng more sophstcated classfcaton model usng data mnng technques. ACKOWLEDGMET Ths wor was supported by atonal Research Foundaton of Korea(RF-2013R1A1A ). REFERECES Fgure 6. Predcton result of GMDH [1] P. Sharma, Transent Stablty Investgatons of the Wnd-Desel Hybrd Power Systems. Internatonal Journal of Energy, Informaton, and Communcatons.1, 1, pp , [2] D.-J. Kang and S. Par, A Conceptual Approach to Data Vsualzaton for User Interface Desgn of Smart Grd Operaton Tools. Internatonal Journal of Energy, Informaton, and Communcatons. 1, 1,pp , [3] H. Mor and K. Kosemura, Optmal regresson tree based rule dscovery for short-term load forecastng, n Proc. IEEE Power Eng. Soc.Wnter Meetng, Columbus, OH, pp , January

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