Page - 30 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 Step8: StopCriteria. Ifthenumberofsearchiterationsaregreaterthanagivenmaximumsearchiterations, then,thebest nestposition,x(t)k,best, amongthecurrentpopulation isdeterminedasparameters (C, σ, ε)ofanSVR model;otherwise,gobacktoStep2andcontinuesearchingthenext iteration. 2.3. SeasonalMechanism As indicated in existingpapers [5,28,29] the short termelectric loaddata oftendisplay cyclic tendenciesdueto thecyclicnatureofeconomicactivities (production, transportation,operation,etc.) or theseasonalclimate inNature (airconditionersandheaters insummerandwinter, respectively). It isusefultoincreasetheforecastingaccuracybycalculatingtheseseasonaleffects(orseasonal indexes) toadjust theseasonalbiases. Several researchershaveproposedseasonaladjustmentapproaches to determine theseasonaleffects, suchasKocandAltinay[42],GohandLaw[43],andWangetal. [44], whoall apply regressionmodels todecompose the seasonal component. Martens et al. [45] apply a flexible Fourier transform to estimate the daily variation of the stock exchange, and compute a seasonal estimator. Deoet al. [46] composed twoFourier transforms inacyclicperiod to further identify theseasonalestimator.Comparingtheseseasonaladjustmentmodels,Deo’smodelextends Martens’smodel for application togeneral cycle-lengthdata, particularly for hour-basedor other shortercycle-lengthdata.Consideringthat thispaperdealswithhalf-hourbasedshort termelectric load data, this paperwould like to employ the seasonalmechanismproposed byHong and his colleagues in [5,28,29]. That is,firstlyapply theARIMAmodel to identify theseasonal lengthof the target timeseriesdataset; secondly, calculate theseseasonal indexes toadjustcycliceffects toreceive moresatisfiedforecastingperformances,asshowninEquation(16): Seasonratioq= ln ( aq fq )2 =2 ( lnaq− ln fq ) (16) where q= j, l+ j, 2l+ j, . . . , (m− 1)l+ jwithm seasonal (cyclic) periods and l seasonal length in eachperiod. Thirdly, theseasonal index(SI) foreachseasonalpoint j ineachperiodiscalculatedas Equation(17): SIj= exp ( 1 m (m−1)l+j ∑ q=j Seasonratioq ) /2 (17) where j=1,2, . . . l. Theseasonalmechanismisdemonstrated inFigure2. f f fl fl f l f l f l f l fQl fQl f P l f P l ɃɃ ɃɃ ɃɃ ɃɃ ɃɃ ɃɃ 7UDLQLQJ GDWD VHW a a al al a l a l a l a l aQl aQl a P l a P l ɃɃ ɃɃ ɃɃ ɃɃ ɃɃ ɃɃ ɃɃɃɃɃɃɃɃɃɃ ɃɃSeasonratio Seasonratio SeasonratioQ SeasonratioP ( )tt t t q faf aoSeasonrati OQOQ OQ −=¸¸¹ · ¨¨© § = H[S ¸¸¹ · ¨¨© § = ¦+− = jlm q qj oSeasonratim SI 9DOLGDWLRQ GDWD VHW fl al Ƀ Ƀ fl+l al+l f l+l a l+l f l+l a l+l fQl+l aQl+l f P l l a P l l Figure2.Seasonalmechanism. 30