Page - 247 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1893 viewpoint: detailsandapproximationsof thedaily loadcurvesareclusteredseparately leadingto twodifferentpartitionswhichare thenfused. • thePAMalgorithmandthehierarchical clusteringtobuild theclustersareofverycommonuse andwell adapted to their specific role in thewholestrategy. It shouldbenoted that theuseof PAMto construct the super customersmustnecessarily bebiased towards a largenumberof clusters (definingthesupercustomers) so it isuseless to includesophisticatedmodel-selection rulestochooseanoptimalnumberofclusterssincethestrategyisusedonlytodefineasufficiently largenumberofclusters. • theKernel-Wavelet-Functional (KWF)method to forecast time-series. The global forecasting scheme is clearly fullymodular and then, KWF could be replaced by any other time-series model forecasting. Themodelmustbeflexibleandeasytoautomaticallybe tunedbecause the modelingand forecastingmustbeperformed ineach cluster in a ratherblindway. Themain difficultywithKWFis to introduceexogenousvariables.Wecouldimagineto includeasingleone quiteeasilybutnotaricher family in fullgenerality.Nevertheless, it ispreciselywhendealing withmodelscorrespondingtosomespecificclusters that it couldbeof interest touseexogenous variablesespecially informative, forexampledescribingmeteoata local levelorsomespecific marketsegment. Therefore, somealternativescouldbeconsidered, suchasgeneralizedadditive models (see [37] forastrategywhichcouldbepluggedintoourscheme). 8.2.MultiscaleModelingandForecasting In fact, sucha forecasting strategy combining clustering in individuals and forecastingof the total consumptionofeachclustercanbealsoviewedasamultiscalemodeling. Indeedaby-product is a forecastingatdifferent levels of aggregation fromthe super customers to the total population. Therefore, insteadofrestrictingourattentionontheforecastingoftheglobalsignal foragivenpartition wecould imagine to combine in time thedifferentpredictionsgivenbyeachpieceof thedifferent partitions insuchawaythatall the levelscouldcontribute to thefinal forecasting. Thewaytoweight thedifferentpredictions couldbefixed for all the instants (see [38] for a large choiceofproposals) or,onthecontrary, time-dependentaccordingtoaconvenientchoiceof theupdatingpolicy (see the sequential learningstrategiesalreadyusedintheelectricalcontext in[39]).Anattempt inthisdirection canbefoundin[40]. Another related topic is individual forecastingorprediction. Itmust bementionedsince it is interesting tohavesomeideasabout thekindofstatisticalmodelsorstrategiesused in thisespecially hardcontext,due toextremevolatilityandwildnonstationarity. Ref. [41]examine theshort-term(one hour) forecastingof individualconsumptionsusingasparseautoregressivemodelwhich iscompared againstwell-knownalternatives(supportvectormachine,principalcomponentregression,andrandom forests). Ingeneral,exogenousvariablesareusedtoforecastelectricityconsumptions,butsomeauthors focusonthereverse. Ref. [42,43]are interested indetermininghouseholdcharacteristicsorcustomers informationbasedontemporal loadprofilesofhouseholdelectricitydemand. Theyusesophisticated deeplearningalgorithmfor thefirstoneandmoreclassical tools for thesecondone. In thecontextof customerssurveys,Ref. [44]usesmartmeterdataanalytics foroptimalcustomerselection indemand responseprograms. 8.3.HowtoHandleNonStationarity? Evenif themodelKWFiswell suitedtohandlenonstationarities in the time-domain, it remains that theclustersofcustomersarealsosubjected tosomedynamicswhichcouldbeof interest tomodel in order to control these changes. Afirst naivepossibility is to periodically recompute the entire process includinganewcalculationof thesuper-customersanddecide,at somestage if thechange issignificant tobe takenintoaccount.Asecondpossibilitycouldbetodirectlymodel theevolution of theclusters. Forexample, in [45]a time-varyingextensionof theK-meansalgorithmisproposed. Amultivariatevectorautoregressivemodel isusedtomodel theevolutionofclusters’ centroidsover 247