Seite - 232 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1893 Figure1.Schematic representationofahierarchyofcustomers. Seasonalunivariate timeseriescannaturallybepartitionedwithregards to time. Forexample, electrical consumptioncouldbeviewedasasequenceofconsecutivedailycurveswhichexhibit rich information related to calendar,weather conditionsor tariff options. Functionaldataanalysis and forecasting is thenaveryelegantmethodtoconsider. Ref. [25]proposeanon-parametric functional methodcalledKWF(Kernel+Wavelet+Functional) tocopewithnonstationarytimeseries. Briefly, themain idea is tosee the forecastsasaweightedmeanof futuresofpast situations. Theweightsare obtainedaccordingtoasimilarity indexbetweenpastcurvesandactualones. Patternresearch-basedmethodsreposeonafullynonparametricandthusmoregeneral frame thanpredictionapproachesmoreadaptedtoelectricity loaddemand.Thispointcanbeseenasboth aweaknessandastrength. Specificmodelscanbetterexpress theknowndependencesofelectricity demand to long-term trend, seasonal components (due to the interaction of economic and social activities)andclimate.However, theyusuallyneedmorehumantimetobecalibrated. Thearrivalof newmeasurement technologiesstructureof intelligentnetworks,withmore localandhighresolution information,unveils forecastingelectricityconsumptionat local scale. Several arguments can be given to prefer bottom-up approaches with respect to some descendingalternatives. Letusbrieflymentiontwoof them.Thefirst is relatedtoelectrical individual signals themselveswhich need to be smoothed and themost natural and interpretableway is to definesmallaggregatesof individuals leadingtomorestablesignals, easier toanalyseandto forecast (see [17]). Thesecondreason ismorestatistically relatedandrefers todescendingclusteringstrategies which involvesupervisedstrategieswhichappear tobeespecially timeconsuming(see [22]). Bottom-upforecastingmethodsarecomposedof twosuccessivesteps: clusteringandforecasting. In theclusteringstep, theobjective is to inferclasses fromapopulationsuchthateachclasscouldbe accurately forecast. Typically, eachclasscorresponds tocustomerswithspecificdaily/weeklyprofile, differentrelationshipstotemperature, tariffoptionsorprices(seee.g., [26]regardingdemandresponse). Thesecondstepconsists inaggregating forecasts topredict the totaloranysubtotal. In thecontext ofdemandresponseanddistributiongridmanagement it couldbe forecasting theconsumptionof adistrict, a townorasubstationonthedistributiongrid. Recently,Ref. [24] suggestedaclusteringmethodachievingbothclusteringandforecastingof apopulationof individual customers. Theydecompose the total consumption such that the sum of disaggregated forecasts improves significantly the forecast of the total. The strategy includes threesteps: in thefirstonesuper-consumersaredesignedwithagreedybutcomputationallyefficient clustering, then a hierarchical partitioning is done and amongwhich the best partition is chosen accordingtoadisaggregatedforecast criterion. Thepredictionsaremadewith theKWFmodelwhich allowsonetouse itasaoff-the-shelve tool. Inconcrete,data foreachcustomer isasetofP timedependent (potentiallynoisy) recordsevenly sampledatarelativelyhighfrequency(e.g., 1/4,1/2orhourlyrecords). Then,weconsider thedata for each individual as a time series thatwe treat as a functionof time. Wavelets areused to code the informationabout theshapeof thecurves. Thanks tonicemathematicalpropertiesofwavelets, 232