Page - 246 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1893 Bottom-upforecast is the leadingargumentofusingthe individual loadcurveclustering.Wetest theappropriatenessofourpropositionbygettingforafinalnumberofclusters rangingfrom2to20, 50,100and200 therespectiveaggregates in termsof loaddemand. Then,weuseKWFasanautomatic predictionmodelforbothstrategies: predictionoftheglobaldemandusingtheglobaldemand,andthe onebasedonthebottom-upapproach. Weuse the secondyear on thedataset tomeasure thequality of thedailypredictionusing a rolling basis. Figure 13 reports theprediction error using theMAPE for both the two forecasting strategies. The fullhorizontal line indicates theannualmeanMAPEusingthedirectmethodandso it is independentof thenumberofclusters. Fordifferentchoicesof thenumberofclusters, thedashed linerepresent theassociatedMAPE.Allpossibleclusteringsproduce thenbottom-upforecasts thatare better thantheoneobtainedfromdirectglobal forecasting. 1XPEHU RI FOXVWHU *OREDO %RWWRPí8S Figure13. MAPEfor theaggregatedemandbynumberofclasses for the twostrategies: directglobal demandforecast (full)andbottom-upforecast (dashed). 8.Discussion In thisfinalsection,wediscuss thevariouschoicesmadeaswellassomepossibleextensionto copewithmultiscalemodelpointofviewandhowtohandlenonstationarity. 8.1. ChoiceofMethods Thethreemaintoolsare: • the wavelet decomposition to represent functions and compute dissimilarities. Of course, several other choices could be interesting, such as splines for bases of functionswhich are independent of the data or even some data-driven bases like those coming from functional principal component analysis. With respect to these two classical alternatives, (more or less related toamonoscale strategy) thechoiceofwaveletsallowssimultaneouslyaparsimonious representationcapturing local featuresof thedataaswell as redundantonedeliveringamore accuratemultiscale representation. In addition, from a computational viewpoint, DWT is a veryfast: of linearcomplexity. So todesignthesuper-customers thediscrete transformisgood enough, for thefinal clusters, the continuous transform leads tobetter results. Letus remark that combiningwavelets and clusteringhas recently been considered in [36] fromadifferent 246