Seite - 127 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 3283 (3) Calculate the7-steperroronthe forecast for timeh+7+i−1; (4) Compute the forecastaccuracybasedontheerrorsobtained. 4. PerformanceMetrics Toanalyze the forecastmodelperformance, severalmetrics, suchasmeanabsolutepercentage error (MAPE), rootmeansquareerror (RMSE),andmeanabsoluteerror (MAE),areused,whichare well-knownforrepresentingthepredictionaccuracy. 4.1.MeanAbsolutePercentageError MAPEisameasureofpredictionaccuracyforconstructingfittedtimeseriesvalues instatistics, specifically in trendestimation. Itusuallypresentsaccuracyasapercentageof theerrorandcanbe easier tocomprehendthantheotherstatisticssince thisnumber isapercentage. It isknownthat the MAPEishuge if theactualvalue isveryclose tozero.However, in thiswork,wedonothavesuch values. Theformula forMAPEisshowninEquation(3),whereAt andFt are theactualandforecast values, respectively. Inaddition,n is thenumberof timesobserved. MAPE= 100 n n ∑ t=1 ∣∣∣∣At−FtAt ∣∣∣∣ (3) 4.2. RootMeanSquareError RMSE(alsocalledtherootmeansquaredeviation,RMSD)isusedtoaggregate theresiduals intoa singlemeasureofpredictiveability. Thesquarerootof themeansquareerror,asshowninEquation(4), is the forecastvalueFt andanactualvalueAt. Themeansquarestandarddeviationof the forecast valueFt for theactualvalueAt is thesquarerootofRMSE.Foranunbiasedestimator,RMSEis the squarerootof thevariance,whichdenotes thestandarderror. RMSE= √ ∑ni=1(Ft−At)2 n (4) 4.3.MeanAbsoluteError Instatistics,MAEisusedtoevaluatehowclose forecastsorpredictionsare to theactualoutcomes. It is calculatedbyaveraging theabsolutedifferencesbetween thepredictionvaluesand theactual observedvalues.MAEisdefinedasshowninEquation(5),whereFt is the forecastvalueandAt is the actualvalue. MAE= 1 n n ∑ i=1 |Ft−At| (5) 5. ExperimentalResults Toevaluate theperformanceofourhybridforecastmodel,wecarriedoutseveralexperiments. We performed preprocessing for the dataset in the Python environment and performed forecast modelingusingscikit-learn [50],TensorFlow[51], andKeras [52].Weusedsixyearsofdailyelectrical loaddata from2012 to 2017. Specifically, weused electrical loaddata of 2012 to configure input variables fora trainingset.Data from2013to2015wasusedas the trainingset, thedataof2016was thevalidationset, andthedataof2017was the test set. 5.1.DatasetDescription Table2showsthestatisticsof theelectricconsumptiondataforeachcluster, includingthenumber ofvalidcases,mean, andstandarddeviation. Asshownin the table,ClusterBhasahigherpower consumptionandwiderdeviationthanclustersAandC. 127