Page - 36 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 Table3 illustrates the forecastingaccuracy indexes for theproposedSSVRCCSmodelandother alternativecomparedmodels. It is clearly to see that theMAPE,RMSE,andMAEof theproposed SSVRCCSmodelare0.70%,56.90,and40.79,respectively,whicharesuperiortotheotherfivealternative models. It also implies that theproposedSSVRCCSmodelcontributesgreat improvements in termsof loadforecastingaccuracy. Table3.Forecastingaccuracy indexesof thecomparedmodels forExample1. ForecastingAccuracyIndexes SARIMA(9,1,8)×(4,1,4) GRNN(œ=0.04) SSVRCCS SSVRCS SVRCCS SVRCS MAPE(%) 3.62 1.53 0.70 0.99 1.51 2.63 RMSE 280.05 114.30 56.90 80.42 126.92 217.19 MAE 217.67 88.63 40.79 57.69 87.94 151.72 Finally, toensure thesignificantcontribution intermsof forecastingaccuracy improvement for theproposedSSVRCCSmodel, theWilcoxonsigned-ranktestandtheFriedmantestareconducted. WhereWilcoxonsigned-ranktest is implementedunder twosignificance levels,α=0.025andα=0.05, by two-tail test; theFriedman test is then implementedunderonlyone significance level,α=0.05. The test results inTable4showthat theproposedSSVRCCSmodelalmost reachesasignificance level in termsof forecastingperformance thanotheralternativecomparedmodels. Table4.ResultsofWilcoxonsigned-ranktestandFriedmantest forExample1. ComparedModels WilcoxonSigned-RankTest FriedmanTest α=0.025; W=9264 p-Value α=0.05; W=9264 p-Value α=0.05; SSVRCCSvs. SARIMA(9,1,8)×(4,1,4) 842a 0.00000** 842a 0.00000** H0 : e1= e2= e3= e4= e5= e6 F=23.49107 p=0.000272 (RejectH0) SSVRCCSvs.GRNN(σ=0.04) 3025a 0.00000** 3025a 0.00000** SSVRCCSvs. SSVRCS 2159a 0.00000** 2159a 0.00000** SSVRCCSvs. SVRCCS 3539a 0.00000** 3539a 0.00000** SSVRCCSvs. SVRCS 4288a 0.00000** 4288a 0.00000** aDenotes that theSSVRCCSmodelsignificantlyoutperformstheotheralternativecomparedmodels; * represents that the test indicatesnot toaccept thenullhypothesisunderα=0.05. ** represents that the test indicatesnot to accept thenullhypothesisunderα=0.025. 3.2.5. ForecastingResultsandAnalysis forExample2 Similar toExample1,SVRCSandSVRCCSmodelsarealso trainedbasedontherolling-based procedurebyusingthe trainingdataset fromExample2 (mentionedinSection3.1). Theforecasting results and thesuitableparametersofSVRCSandSVRCCSmodelsare showninTable5. It is also obviously that theproposedSVRCCSmodelhasachievedasmaller forecastingperformance in terms of forecastingaccuracy indexes,MAPE,RMSE,andMAE. Table5.ThreeparametersofSVRCSandSVRCCSmodels forExample2. EvolutionaryAlgorithms Parameters MAPEofTesting(%) RMSEofTesting MAEofTesting σ C ε SVRCS 0.6628 36,844.57 0.2785 3.42 886.67 631.40 SVRCCS 0.3952 42,418.21 0.7546 2.30 515.10 426.42 Figure9alsodemonstrates theseasonal/cyclicchangingtendencyfromtheusedelectric loaddata inExample2. Basedonthehourlyrecordingfrequency, tocompletelyaddress thechangingtendency of theemployeddata, theseasonal length issetas24. Therefore, thereare24seasonal indexes for the proposedSVRCCSandSVRCSmodels. Theseasonal indexes foreachhourarecomputedbasedonthe 576 forecastingvaluesof theSVRCCSandSVRCSmodels in the training(432 forecastingvalues)and validation (144 forecastingvalues)processes. The24seasonal indexes for theSVRCCSandSVRCS modelsare listed inTable6, respectively. 36