Page - 277 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 Theoutcomeof thismodel, aspresented inTable3, enhancedthe forecastingaccuracyby34% whenitwascomparedto thebestbase learner,SVR.Moreover, thesecondensemblemodelwasamix ofBPNNasthebase learnerandLRas themeta-learner, thecombinedmodel increasedthe forecasting accuracybydecreasingtheerrorby46%,comparedto thebest singlemodelasmentionedpreviously. Figure4. Illustrated(a)actualandpredictedconsumptionusingSMLElearners(b)errorofSMLEmodels. Table3.SummaryofdifferentevaluatingmeasuresamongallmodelsonGOCdata. Measures SingleModels ClassicEnsembleModels SMLEModels LR SVR BPNN Bagging AR 1stSMLE 2ndSMLE 3rdSMLE MAPE(%) 6.77 2.82 3.15 2.52 5.19 2.27 2.07 1.65 DA(%) 82.59 89.03 89.90 66.17 82.59 88.50 90.69 91.24 ED 0.074 0.035 0.034 0.026 0.059 0.028 0.024 0.020 T-Time 0.04 0.05 0.03 0.06 0.07 0.09 0.13 0.17 Boldnumber indicates thebestvalue inallmeasures. Finally, the thirdensemblemodelwasacombinationofSVRandBPNNasbase learnersandLR as themeta-learner. Theforecastingresultof thismodel indicates that theaccuratepredictivemodel decreasedtheerrorof thebestbasemodelby50%,which ledtoproofof thesuperiorityof the third modeloverboth thesingleandcombinationmodels. Thesimilaritybetweenactualandpredicteddata is showninTable3, the3rdSMLEbased(SVR-BPNN)modelscorewas0.020,while1stSMLEbased (SVR)scorewas0.028, theworst similarity inacrossall themodels.Also, it canbeobservedthatall ensemblemodelhadlessdistancecomparedtosinglemodels. Inthesameaspect, the3rdSMLEperformedbetter thanthebestclassicensemblemodel (bagging) inallmeasures, except for trainingtime(T-Time); thiswasdueto theensemblemodel learning level whichconsumedmore timeandcalculation. 4.Discussion In thissubsection,wepracticallyusedall singleandensemble forecasters tosolve theproblem ofhowtoestimate thefutureOC.For furtherevaluationofSMLEschemestability,allmodelswere examinedin1-aheadand10-aheadhorizonpredictions. FromFigure5andTable4, it is easy tofindthat theproposedSMLEmethodwas thebestone forOC forecasting in all prediction horizons (i.e., 1, 3, 5, 7, and 10-step-ahead), relative to other 277