Page - 331 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1449 Figure10.REof forecastingapproaches: (a)REofSpringtest; (b)REofSummertest; (c)REofAutumn test; (d)REofWinter test. FromFigures 9and10, it canbe seen that thepredictionerror rangeofFC-WPA-LSSVMwas controlled towithin [−3%+3%],where theminimumerror (7:00 in thespring test)andthemaximum error (18:00 in theautumntest)were0.08%and−2.98%,respectively.Amongthem,10errorpoints of theresultswerewithin [−1%,1%],namely7:00,11:00and16:00 in thespringtest, 1:00,2:00,9:00, 16:00, 23:00 in the summer test, 6:00 in theautumntest, 19:00 in thewinter test; the corresponding valuesofREwere0.08%,−0.49%,−0.52%,−0.71%,−0.98%,−0.74%,−0.85%,0.71%,−0.81%and 0.31%,respectively. Inaddition,19errorpointsofWPA-LSSVMwerecontrolled towithin [−3%,3%], while thecorrespondingnumber forLSSVMwas17,ofwhich2pointsofWPA-LSSVMwerewithin the range [−1%, 1%], namely at 10:00 in the spring test (RE=−0.86%) and9:00 in thewinter test (RE=−0.79%), but all error points of LSSVMwere outside the range [−1%, 1%]. Theminimum errors ofWPA-LSSVMandLSSVMwere−0.79%and−1.07% respectively,while theirmaximum errorswere6.6%and−7.59%, respectively. Theerrorsof theBPNNmodelweremostlywithin the ranges [−6%,−4%]or [4%,6%],where themaximumandminimumofREwere individuallyequal to 1.36%and8.73%,respectively. In this regard, the forecastingaccuracyrankedfromthehighest to the lowestwas: FC-WPA-LSSVM,WPA-LSSVM,LSSVM,andBPNN.Hence,FCcaneffectivelyavoidthe blindness in theselectionofsimilardays throughexperience. IncontrastwithLSSVM,administering WPAimprovesthepredictionprecisionbyvirtueoftheparameteroptimizationofLSSVM.It iswithout doubt that the forecastingaccuracyofsomepoints inFC-WPA-LSSVMisworse thantheother three approaches; for instance, theerrorofFC-WPA-LSSVMwas1.76%at22:00 in thespringtest,whichwas greater thanWPA-LSSVMandBPNN. The performance comparison results of the forecasting models were measured by RMSE, MAPEandAAE,aspresentedinFigure11. Thisdemonstratesthattheproposedapproachoutperforms the other models in terms of all the evaluation criteria, of which RMSE, MAPE and AAE of FC-WPA-LSSVMwere equal to 2.20%, 2.09% and 2.09%, respectively. This ismainly due to the fact thatFCcanovercometheadverseeffectsofunconventional loaddatacausedbyfactormutationon LSSVMtraining,andWPAimproves thegeneralizationabilityandpredictionaccuracybyparameter 331