Page - 324 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1449 coefficientapproach,distanceorcloseness.Anabsolutevalue indexmethodis introducedhere [28], asexpressed inEquation(2). rij= exp(− m ∑ k=1 ∣∣∣x′ik−x′jk∣∣∣), (i=1, 2, ..., n; j=1, 2, ..., n; k=1, 2, ...,m) (2) Thenthe transitiveclosureR∗ofRcanbeobtainedbysquaresynthesis. (3)Dynamicclustering. Selectanappropriate thresholdL toseparateR∗. Theclusteringresults areupto the levelofL.WhenLdrops from1to0,adynamicclusteringgraphisobtainedbychanging theroughclassification toafineone. ThebestvalueofLcanbeacquiredbasedonitschangerate [29]. Ci= Li−1−Li ni−ni−1 (3) where i is theclusteringorderofL inadescendingform;ni andni−1 are thenumberofelements in i and i−1clusters, respectively;Li andLi−1 are theconfidence levels in iand i−1clusters, respectively. IfCi =max(Cj), Li is treatedas thebest threshold. Thus,n samples canbe separated into several categoriesandeachtypecontainsadifferentnumberofsamples. (4) Classification recognition. The category consistent with the forecasted day needs to be identified after sample classification. TheEuclideandistance is calculated between thepredicted dayandtheabovecategoriesonebyone[26]: dij= 1√ m √ m ∑ k=1 (x′ik−x′jk)2 (4) wherex′ik is thecharacteristicvectoronthepredictedday,x ′ jk represents thecharacteristicvectorof eachcategory. Thispaper takes the typewiththeshortestEuclideandistanceas theclassificationof the forecasteddaytomaketheprediction. 3.2. LeastSquaresSupportVectorMachine AsanextensionofSVM,LSSVMtransforms the inequality constraints intoequalityonesand converts quadratic programming problems into linear equation ones, which is conducive to the improvementofconvergencespeed[30]. Set the training samples as T = {(xi,yi)}Ni=1, where N is the total number of samples. Theregressionmodelcanbeexpressedas follows[31]: y(x)=wT×ϕ(x)+b (5) where ϕ() is a function thatmaps the training samples into a highlydimensional space,w and b represent theweightandbias, respectively. ForLSSVM,theoptimizationproblemcanbedefinedasEquation(6) [32]: min 1 2 wTw+ 1 2 γ N ∑ i=1 ξ2i (6) s.t. yi=wTφ(xi)+b+ξi, i=1,2,...,N (7) whereγ is the regularizationparameter that balances the complexity andprecision of themodel. ξi equals theerror. 324