Page - 109 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 3442 Figure8.PlotbetweenGDPperCapitaandTEC. 3.4. SimpleExponentialSmoothing If the timeseriesvaryaboutbase level, simpleexponential smoothingmightbebring intoplay tofindgoodestimatesorupcomingvalueof thesameseries. Todepict thisphenomenon, letAt the smoothedaverageofa timeseries. Subsequent toobservingxt,At is theanticipate for thevalueof the timeseriesduringanyupcomingperiod. • At=smoothedaverageat theendof theepoch • t= ft, • k=for the forecastperiod(t+k)at theendof theepocht. Chooseαso that itminimizes theMAD. Thekey inequation insimpleexponential smoothing is that At=αxt + (1−α)At−1 (1) In theEquation (1),αwillbe thesmoothingconstant that suit 0<α>1. Tostart the forecasting process,wehavegot tosetavalue forA0beforesurveyingx1. Typically,we letA0be theexperiential value for theperiodrightawayprior thefirstperiod.Asamongmoving-average forecasts,we let ft,k be theestimate forxt+k readyat thefinalperiodt.Then At=ft,k (2) Pretentious thatweattempt to forecastoneperiodahead, theerror for forecastingxt is Et =xt− ft−1,1 =xt−At−1 (3) Thesmoothingconstantvalueconsideredfor theanalysis isα=0.3,0.4and0.5. TheTECfor2015wasfoundtobe746,882MWwhenα=0.3and793,765MWwhenα=0.4and 823,941.3MWwhenα=0.5. 109