Page - 257 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1678 MLP, is theriskofoverfittingandthat theyrequirecareful tuningofseveralhyperparameters. Finally, theSVRmodelhas theadvantageofbeingrobust tooutliersandthat thefinalmodeldependsonlyon asubsetof the trainingdata. TheSVRmodel,however, is sensitive to thescalingof the inputdataand thecorrect tuningof regularizationandkernelparameters. 2.6.ModelSelectionandTesting Agoodforecastmodel isonethatperformswellonpreviouslyunseendata.This is thegeneralization abilityof themodel. Inorder toaccuratelymeasure thegeneralizationperformanceof themodels,we dividedthefulldataset (sevenyearsofhourlydata) intoa trainingandvalidationsetandatest set. Allmodelselectionandtrainingwasperformedontheyears from2009to2015(2011not included). This is the trainingandvalidationset. Theentireyearof2016wasusedasablindtest set toestimate thegeneralizationperformanceof the forecasts. The threemodelswerechosenandtheirhyperparameters tunedbasedonsixfoldcross-validation ontheyears2009,2010,2012,2013,2014,and2015.Usingsix foldsensuredthateachfoldcontainedan entireyearandthusrepresentedthe fullannualvariationof theheat load. In thecross-validation, the differentmodelsanddatascenarioswerescoredaccordingtothehourlyrootmeansquareerror(RMSE) RMSE= √ 1 N∑t (Pˆt−Pt)2 (1) where Pˆt is the forecastedheat loadforhour t, andN is thenumberofhours. TheOLSmodeldoesnothaveanyhyperparameters to tune,butamodelwithanonzeroconstant termwas chosen. In theMLPmodel,we tuned thenumber of neurons in thehidden layerusing a grid search on the cross-validation scores. AMLPmodelwith one hidden layer consisting of 110hiddenneuronswas chosen, and theL2 regularizationparameterαwas set to 0.1. In theSVR model, thebestchoices for theregularizationparameterandthekernelparameterwere foundtobe C=4.3andγ=0.2.AllmodelinghasbeenperformedinPython2.7using thescikit-learn framework (version0.19.0) [23]. All results presented in the following sectionwere produced using the blind test year 2016. Thisyearwasnotused foranyof the training,dataexploration, ormodel selection. In theResults section,weemploytwoother forecasterrormetrics, inaddition to theRMSE.Themeanabsoluteerror (MAE) is alsoanabsolute errormetric (here inunitsofMW),but it is less sensitive to largeerrors, comparedto theRMSE.TheMAEisdefinedas MAE= 1 N∑t ∣∣Pˆt−Pt∣∣ . (2) Finally,weusetherelativeerrormetricmeanabsolutepercentageerror (MAPE)tofacilitateeasier comparisonbetweendifferentdistrictheatingsystems. TheMAPEisdefinedas MAPE= 1 N∑t ∣∣∣∣Pˆt−PtPt ∣∣∣∣ . (3) 3.Results Theheat load in adistrict heating systemhas been forecastedusing three differentmachine learningmodels,described in theprevioussection:OLS,MLP,andSVR.Theperformanceof these modelshavebeentestedby letting themproducea forecast for the followingdayusingthe inputdata availableeachdayat10:00a.m.Themodelshavebeentrainedexclusivelyondataprior to the testyear 2016tobeable toaccuratelygaugetheirgeneralizationperformance. Figure3showsanexampleof 257