With the rapid development and growth in technology, the

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1 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) DEMAND FORECASTING BY USING GENERALIZED REGRESSION NEURAL NETWORK Deept Arela 1, Shlpa Agrawal M.Tech Scholar, Sobhasara Group of Insttutons, Skar 1 Faculty Member, Sobhasara Group of Insttutons, Skar deeptarelapce@gmal.com 1, a_shlpa15@yahoo.co.n Abstract: Wth the ncreases n compettve busness envronment, forecastng of demand s drectly lnked up wth the portfolo of the generatng companes and consdered as an mportant parameter of power system regulaton. To take decsons lke bddng of the power blocks n a pool market, trade decsons, generaton schedules, dspatch and unt commtment operatons requre precse knowledge of the system demand. It s also essental to consder an accuracy of load forecastng to mantan balance n power system regulaton. In ths paper we propose senstvty analyss wth an applcaton of adaptve supervsed learnng technque Generalzed Regresson Neural Network (GRNN) to know the effect of the change n parameters n forecastng engne performance. Dfferent nputs are changed unformly and far comparson s carred out on the bass of standard error ndex Mean Absolute Percentage Error (MAPE). Keywords Load Forecastng, Power system regulaton, Senstvty Analyss, GRNN, MAPE I INTRODUCTION Wth the rapd development and growth n technology, the demands of electrc energy hghly ncrease, correspondngly the load forecastng becomes more and more mportant and close attenton s ncreasngly pad to contnuous power supply by both electrc ndustry and consumers. The major duty of any electrcal utlty s to supply relable power to ts customers. The predcton of future actve loads at varous load buses n power system s known as load forecastng [1].The man objectve of load forecastng s to provde the load predcton for generaton schedulng, power system securty, generaton reserve of the system, and proper market operaton. For a restructured power system, Generaton Company would have to forecast the system demand to make a sutable market decson. To satsfy the load demand t s necessary to predct the load for future []. Accurate load determnaton s necessary for applcaton lke automatc generaton control [3], contngency rankng [4], stablty assessment [5] and prce forecastng [6] Load forecastng can be classfed n three categores dependng upon the tme span used for forecastng. The long term forecastng s done for more than one year, medum term (ntermedate) forecast s done for few weeks to one year and short term load forecastng belongs to an hour to few days. The mportant factors whch are to be consdered manly are tme, weather parameters and categorzed consumer classes [7]. Fgure 1 shows the general model archtecture of load forecastng. It s shown n the fgure that varous numbers of nput parameters are consdered for predcton of the load. Evaluaton of these nput parameters s very tme consumng and as well as cost effectng for load forecastng. Sometmes large no of parameters are not much responsble for precse load forecastng. By avodng such parameters, we can also do a good load forecastng. It s essental to know the effect of each nput parameter on load forecastng. The process to know the effect of these parameters on load forecastng s known as senstvty analyss. The man object of senstvty analyss s to study the mpact of dfferent nput factors on the proposed archtecture for load forecastng. The senstvty analyss s also performed to dentfy the sgnfcant nputs. Electrcal load s hghly senstve to the weather condtons such as temperature, humdty, wnd cover, sunshne, etc n whch temperature,wnd speed and humdty are the most sgnfcant but other parameters shall also be consdered whch depends upon the geographcal condtons of the forecastng regon [8]. There s a functonal relatonshp between electrcal load and temperature. As 39

2 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) saturaton level and per capta consumpton ncreases, to reflect the wde- spread use of weather-senstve devces, t s necessary to nclude weather effects n forecastng future load requrements [9]. II FORECAST TECHNIQUES There are several tradtonal methods lke wavelets, neural networks; grey theory, genetc algorthm predcton etc are used for predcton the load. Some of them are: Tme seres and regresson technques Fgure 1 Model Archtecture of Load Forecastng Intellgent methods lke Neural network approach and fuzzy systems Hybrd structures wth neural and fuzzy systems, neural networks and genetc algorthms etc. These determnstc methods are conventonal model of load and nput varables. Curve fttng, data extrapolaton and smoothng methods are ncludng n these methods [10-15]. Fgure Classfcaton of Dfferent Electrcty Load Forecastng Methods 40

3 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) Fgure shows the classfcaton of dfferent electrcty load forecastng methods. Although these methods are used to forecastng the load from the years, yet they cannot satsfy the requrement of forecast precson. So the new researchers put forward some methods accordng to the naccuracy of these tradtonal methods. Dfferent forecastng methods have been employed n power systems for achevng forecastng accuracy. Some of the models are regresson, statstcal and state-space methods. [16].Jhang et.al. [17] proposed the support vector machne (SVM) optmzed by mproved frut fly algorthm and the smlar day method used for optmze and auto select parameters of SVM, n the meantme, a smlar day method (SDM) was used to reduce the number of tranng samples, boost tranng speed and ncreased the forecast precson. Nkta et.al.[18] suggested an applcaton of statstcal forecastng method for predctng the demand of smlar days. It also presents a comparson of dfferent statstcal load forecastng methods namely trend analyss, decomposton and movng average method. A.Hemlatha et.al. [19] worked on senstvty analyss of load forecastng by usng a mxed model of artfcal neural networks and fuzzy logcto know the effect of changes n nput varables on system outputs. Among the models are regresson, statstcal and state-space methods. In addton, artfcal ntellgence-based algorthms have been ntroduced based on expert system, evolutonary programmng, fuzzy system, artfcal neural network (ANN), and a combnaton of these algorthms. Among these algorthms, ANN has receved more attenton because of ts clear model, easy mplementaton, and good performance. One of the keys to a good archtecture n ANN s choosng approprate nput varables. III ARTIFICIAL NEURAL NETWORKS An ANN s a method to perform non-lnear modelng and adaptaton whch s based on tranng the system wth past load data as nput and current load data as target. The ANN learns from experence and generalzes from prevous examples to new ones [0].There are three types of learnng strateges are used supervsed,unsupervsed and renforced learnng.the number of hdden layers,number of teratons to perform neural network and learnng rate are the key factors whch s used to consder for accurate load foreacstng. The modfcaton of the weghts and bases of a neural network can be done by learnng rule.the man purpose of these learnng rules s to tran the network to perform some task. The supervsed learnng provded a set of tranng data of proper network behavor[1]. IV ALGORITHM OF GRNN The generalzed regresson neural network s a new method whch s used to overcome the lmtatons of the other methods used for short term load. The GRNN gves the hgher accuracy and stablty as compared to other neural networks. It s the nonlnear regresson analyss. The regresson analyss of the non- ndependent varable Y wth respect to the ndependent varable x s to calculate the maxmum probablty value of y. So the jont probablty densty functon of random vector x and random varable y s f (x, y), the condtonal mean value s gven by [] yf ( X, y) dy ˆ( ) [ / ] Y X E y X f ( X, y) dy Where the observed value of x s X, the Y s relatve to the regresson of X. Specht scholars ponted out that the contnuous probablty densty functon can be estmated from the observaton k 1 1 ( XX )( XX ) ( YY ) ˆf( XY, ) exp[ ]exp[ ] p1 ( p 1) k 1 ( ) () where X and Y are the sample observaton value of random varable x and y, s the smoothng parameter, p s the dmenson of random varable x, k s the sample number. (1) Use f ˆ( x, y ) nstead of f ( x, y ) the condtonal mean value can be obtaned by D exp( ) k Y 1 ˆ( ) k D exp( ) 1 Y X Where Y ˆ( X ) s the weghted average of all observaton value Y, D s the Eucldean dstance T, D ( X X ) ( X X ).The structure of GRNN s shown n the fgure 3.It s composed of four layers, the nput layer, the pattern layer, the summaton layer and the output layer. Correspondng network nput s X =[x 1, x,,xm], ts output s Y=[y 1,y,, ym]. (3) 41

4 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) Fgure 3 General structure of GRNN V SENSITIVITY ANALYSIS For the predcton of accurate load t s very essental to know the effect of varous nput parameters on t. The process to know the effect of these parameters on load forecastng s known as senstvty analyss. The man motve of senstvty analyss s to study the mpact of dfferent nput factors on the proposed archtecture for load forecastng. The method s used to calculate senstvty analyss.the man purpose of the use of method s to analyze the senstvty of ANN by perturb the ANN nput wth a small amount ( ).The analyss of senstvty of ANN represents the nput output mappng, to the nput by checkng the varaton of the output ( ). VI PROBLEM FORMULATION For STLF the nputs can be classfed n tme, weather and hstorcal load. From these nputs weather and hstorcal load are much responsble for accuracy of predcton the load. To contnue and satsfy the load demand, t s requred to know the effect of nput parameters on load forecastng so that the mportant nput parameters can be consdered nstead of least nput parameters. To analyss the mpact of each nput parameter on load forecastng, senstvty analyss wll be appled on each nput. Sometmes t s also dependent on customer behavor. Customer load demand does vary because of human actvtes follow daly, weekly, and monthly cycles. The load demand s generally hgh durng the day tme and lower n the late evenng and early mornng.smlarly load demand does also vary n weekdays, weekends and some specal days (holdays) because of the human actvtes are dfferent n these days. The nputs used for predcton of load demand s also non lnear n behavor. Wth the all consderaton of above, senstvty analyss s done n ths work. The nput data s collected from Australa Electrcty Market [3] of year 006 to 009 of whch s segregated nto three folds namely week days, weekends and specal days. From Monday to Frday, the fve days of week are consdered as weekdays and the two days Saturday and Sunday are consdered as weekends. The four days also consdered as specal days for load predcton as the load demand s fluctuated dfferently n these days, are: New Year day (1 st January) Good Frday Chrstmas day (5 th December) New Year eve (31 st December) Thus the whole data s dvded n eleven days.e. seven weekdays and four specal days. The nput parameters are humdty, temperature (Wet bulb measurement, Dry bulb measurement, Dew pont measurement) and electrcal prce. The system load s consdered as target. For forecastng the load ANN s used because of the ablty to handle the nonlnear relatonshps between load and the factors affectng t drectly from hstorcal data. Among the all ANN methods generalzed regresson analyss model s used as our nputs are nonlnear n nature. The data of each year s from 006 to 009 dvded n two parts as tranng and valdaton (test data) sets.by usng GRNN topology tranng would be easer and results wll be more accurate. To analyss the mpact of each nput parameter on load forecastng, senstvty analyss wll also be appled n whch the each nput parameter s changed by 1 percent. By applyng the senstvty analyss t would be easer to fnd the mpact of each nput. The senstvty of each nput parameter s decded wth the calculatng of Mean Absolute Percentage Error (MAPE) of each changed one percent nput of each day. The formula of MAPE s: M n t 1 A F t A t t *100 Where A t s the actual system load and F t s the forecast load. VII SIMULATION RESULTS To analyze the senstvty GRNN s constructed for the data of 11 days: 5 week days, weekend days and 4 specal days.e. holdays of year 006 to 009 of Australan Electrcty Market. Sx models are desgned for all 11 days by changng 1 % ncrement n each nput parameter. The strategy of desgnng of models are shown n fgure 4 n whch frst block shows the forecaster model wth actual nputs and the other fve blocks from -6 are desgned wth changed nputs. Thus total 66 models are desgned n ths work. All these changed nput parameters along wth the model whch s desgned wth orgnal nputs. The output (Forecastng Load) calculated from the traned network for a partcular day s the result obtaned for the same day of 010.Model 1 s consdered wth the modfcaton of 1 % humdty, model s consdered wth the modfcaton of 1 % (4) 4

5 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) dry bulb, model 3 s consdered wth the modfcaton of 1 % dew pont, model 4 s consdered wth the modfcaton of 1 % prce and model 5 s consdered wth the modfcaton of 1 % wet bulb. MAPE s also calculated for each model. The Average value of MAPE s also calculated of all sx models for the proposed technology for the Weekdays and Weekends. The comparatve table s shown gven below. Table 1 shows the average value of MAPE of a week of all sx models of GRNN topology. The senstvty of nputs are judged by the average value of MAPE of each nput of a week. The hghest value of MAPE s obtaned from Fgure 4 Block dagram representaton of Modfed Inputs modfed humdty, than from prce, dew pont, than wet bulb and last from dry bulb respectvely. These results show the senstvty n decreasng order.e. humdty, prce, dew pont, wet bulb and dry bulb. Table 1 COMPARATIVE TABLE OF AVERAGE VALUE OF MEAN ABSOLUTE PERCENTAGE ERROR OF ALL SIX MODELS FOR PROPOSED TOPOLOGY DAY MAPE MAPE 1 MAPE MAPE 3 MAPE 4 MAPE 5 Mon Tue Wed Thurs Fr Sat Sun Avg.Value Table shows the average value of MAPE of a four specal days of all sx models of GRNN topology. Senstvty s also calculated from average value of MAPE.Agan the sequence of hghest senstvty to lowest senstvty s obtaned from humdty, than from prce, than dew pont, than wet bulb and last from dry bulb. Thus the senstvty n ths case also obtaned n decreasng order.e. humdty, prce, dew pont, wet bulb and dry bulb. 43

6 Volume 3 Issue February 018 ISO 397:007 Certfed ISSN (Onlne) Table COMPARATIVE TABLE OF AVERAGE VALUE OF MEAN ABSOLUTE PERCENTAGE ERROR OF ALL SIX MODELS FOR PROPOSED TOPOLOGY DAY MAPE MAPE 1 MAPE MAPE 3 MAPE 4 MAPE 5 NEW YEAR DAY GOOD FRIDAY CHRISTMAS DAY NEW YEAR EVE Avg.Value VIII CONCLUSION For the contnuous and smooth operaton of electrcal ndustry precse load forecastng s essental. In ths paper an applcaton of ANN, GRNN s used for predcton the load estmaton wth senstvty analyss. From the proposed topology, the followng results are concluded of: a) The Mean Absolute Percentage Error (MAPE) s mnmzed when there s no change n nput data.e. the actual data. b) Then the each nput data s erroneous by 1%, MAPE s ncreased. The mnmum value of MAPE s obtaned by changng n Dry bulb measurement. c) The Maxmum value of MAPE s ncreased from changng n humdty. From ths analyss t can be concluded that Dry bulb measurement method of temperature measurement s a least senstve varable as the MAPE obtaned n model s low and the varaton of the MAPE from the orgnal values are very low. On the other hand, t can be concluded that the values of MAPE s hgher as compared to the orgnal values when the humdty s vared wth 1%. From ths fndng we can suggest that humdty s a senstve parameter n load forecastng. Senstvty analyss can become most accurate wth changng nput parameters by % to 5%. REFERENCES [1]M.Amrthavall, Fuzzy Logc and Neural Networks, SCITECH Publcatons, 004. []Moh.Shahdehpour, HatmYamn, Zuy L, Market OperatonnElectrc Power Systems: Forecastng, Schedulng and Rsk management IEEE, New York, Wley Interscence, 00. [3]. Gupta, Esha, and Akash Saxena. "Grey wolf optmzer based regulator desgn for automatc generaton control of nterconnected power system." Cogent Engneerng 3.1 (016): [4] Son, Bhanu Pratap, Akash Saxena, and Vkas Gupta. "A least square support vector machne-based approach for contngency classfcaton and rankng n a large power system." Cogent Engneerng 3.1 (016): [5] Saxena, Akash, and Ankt Kumar Sharma. "Assessment of Global Voltage Stablty Margn through Radal Bass Functon Neural Network." Advances n Electrcal Engneerng 016 (016). [6]. San, Deepak, and Akash Saxena. "Electrc Prce Forecast usng Interbreed Approach of Lnear Regresson and SVM." Indonesan Journal of Electrcal Engneerng and Computer Scence.3 (016): [7]H. K. Alfares, M. Nazeeruddn, Electrc load forecastng: lterature survey and classfcaton of methods,internatonal Journal of Systems Scence, 33(00), pp [8]A.Hemalatha, G.Moulka, E.Harka, Hemachandra, Senstvty Analyss n Load forecastng usng Computatonal Intellgence, Helx Vol. 7(5), 1 September, 017, PP No [9] Nahd-Al-Masood, Mehd Z. Sad, Shohana Rahman Deeba and Faeza Hafz, Temperature Senstvty Analyss of Bangladesh Electrcal Load: A Lnear Regresson Based Approach. 009 [10] Mttal, Nkta, and Akash Saxena. "Layer Recurrent Neural Network Based Power System Load Forecastng" Indonesan Journal of Electrcal Engneerng and Computer Scence 16.3 (015): [11] M. T. Hagen and S. M. Behr, The tme seres approach to tme seres load forecastng, IEEE Trans.,1987, PRWS- (3), pp [1] S. R. Haung, Short Term Load Forecastng usng Thresold Autoregressve Models, IEE Proc. Gener. Trans. Dstrb., Vol. 144, No.5, Sept.1997, pp [13] D. Sngh, S. P. Sngh and O. P. Malk, Numercal Taxonomy Short Term Load Forecastng usng general exponental smoothng Network for Short-Term Load Forecastng, Jour. Electrc Power Components and Systems, No. 30, 00, pp

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