Page - 25 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 papers [5,28,29], electric load data, particularly short term load data, illustrate an obvious cyclic tendency, thus, the seasonalmechanismproposed in theauthors’previouspapers [5,28,29]would be further improvedandcombinedwith the SVRCCSmodel. Finally, theproposed seasonal SVR withCCS,namely theSVRwithchaotic cuckoosearch (SSVRCCS)model, is employed to improve theforecastingaccuracy levelbysufficientlycapturingthenon-linearandcyclic tendencyofelectric loadchanges. Furthermore, the forecastingresultsof theSSVRCCSmodelareusedtocompare them withotheralternativemodels, suchas theSARIMA,GRNN,SVRCCS,andSVRCSmodels, to test the forecastingaccuracy improvementsachieved. Theprincipal contributionof thispaper is incontinuing tohybridize theSVRmodelwitha tentchaoticcomputingmechanism,CSalgorithm,andeventually, combineaseasonalmechanism,towidelyexploretheelectric loadforecastingmodel toproducehigher accuracyperformances. The remainderof this article is organizedas follows: thebasic formulationof anSVRmodel, theproposedCCSalgorithm,seasonalmechanism,andthemodelingdetailsof theproposedSSVRCCS modelaredescribed inSection2.Anumericalexampleandforecastingaccuracycomparisonsamong theproposedmodelandotheralternativemodelsarepresented inSection3. Finally, conclusionsare given inSection4. 2.TheProposedSVRwithChaoticCuckooSearch(SSVRCCS)Model 2.1. SupportVectorRegression (SVR)Model Themodelingdetails of anSVRmodel arepresentedbrieflyas follows. The trainingdata set, {(xi,yi)}Ni=1, ismapped into a highdimensional feature space by a non-linearmapping function, ϕ(x).Then, in thehighdimensional featurespace, theSVRfunction, f, is theoreticallyusedtoformulate thenonlinearrelationshipsbetweenthe input trainingdata (xi)andtheoutputdata (yi). Thiscanbe shownasEquation(1): f(x)=wT ϕ(x)+b (1) where f(x) represents the forecastedvalues; theweight,w, andthecoefficient,b, arecomputedalong withminimizingtheempirical risk,asshowninEquation(2): R(f)=C 1 N N ∑ i=1 Θε(yi, f(xi))+ 1 2 wTw (2) Θε(y, f(x))= { 0, if|f(x)−y|≤ ε |f(x)−y|−ε, otherwise (3) where Θε(y, f(x)) is so-called ε-insensitive loss function, as shown inEquation (3). It is used to determinetheoptimalhyperplanetoseparatethetrainingdataintotwosubsetswithmaximaldistance, i.e.,minimizingthe trainingerrorsbetweenthese twoseparatedtrainingdatasubsetsandΘε(y, f(x)), respectively.C isaparameter topenalize the trainingerrors. Thesecondterm, 12w Tw, is thenusedto represent themaximaldistancebetweenmentionedtwoseparateddatasubsets,meanwhile, it also determines thesteepnessandtheflatnessof f(x). Then, theSVRmodelingproblemcouldbedemonstratedasminimizingthe total trainingerrors. It isaquadraticprogrammingproblemwith twoslackvariables,ξandξ∗, tomeasure thedistance betweenthe trainingdatavaluesandtheedgevaluesofε-tube. Trainingerrorsunder εaredenotedas ξ∗,whereas trainingerrorsabove εaredenotedasξ, as showninEquation(4): Min w,ξ,ξ∗ R(w,ξ,ξ∗)= 1 2 ‖w‖2+C N ∑ i=1 (ξi+ξ ∗ i ) (4) with theconstraints: 25