Seite - 231 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1893 Another interestofclustering is forecasting,morepreciselybottom-upforecastingwhichmeans forecastingthe total consumptionofasetofcustomersusing individualmetereddata. Forecasting is an obvious need for optimisation of the grid. As pointedpreviously, it becomesmore andmore challengingbutalsocrucial to forecastelectricityconsumptionatdifferent“spatial”scale (adistrict, a city, a region but also a segment of customers). Bottom upmethods are a natural approach consistingofbuildingclusters, forecastingmodels ineachclusterandthenaggregatingthem. In [19], clusteringalgorithmsarecomparedaccordingto their forecastingaccuracyonadatasetconsisting of6000residential customersandSMEinIreland.Goodperformancesarereachedbut theproposed clusteringmethodsaredefinedquite independentlyof themodelusedfor forecasting.Onthesame data set,Ref. [20] associate a longitudinal clusteringanda functional forecastingmodel similar to KWF(see [21]) for forecasting individual loadcurves. Aclusteringmethodsupervisedbyforecastingaccuracyisproposedin[22]toimprovetheforecast of the total consumptionofaFrench industrial subsetobtainingasubstantialgainbutsufferingfrom high computational time. In [23], a k-meansprocedure is applied on features consisting ofmean consumptionfor5well chosenperiodsofday,meanconsumptionperdayofaweekandpeakposition into theyear. Ineachclusteradeep learningalgorithmisusedfor forecastingandthenthebottom up forecast is the simple sumof clusters forecasts. Results showing aminimumgain of 11% in forecast accuracyareprovidedon the Irishdata set andsmartmeterdata fromNew-York. On the Irishdataagain,Ref. [3]propose tobuildanensembleof forecasts fromahierarchical clusteringon individualaverageweeklyprofiles, coupledwithadeep learningmodel for forecasting ineachcluster. Different forecasts corresponding todifferent sizesof thepartitionareat theendaggregatedusing linearregression. Weproposehere anewapproach, following thepreviousworkof [24], to build clusters and forecastingmodels that areperformant for thebottom-up forecastingproblemaswell as fromthe computationalpointofview. Thepaper isorganizedas follows.After thisfirst section introducingthe industrial contextanda state-of-the-art reviewof individualelectricaldataanalysis,Section2provides thebigpictureofour proposal forbottom-upforecastingfromsmartmeterdata,without technicaldetails. Thenext three sections focusonthemaintools:wavelets (Section3) torepresent functionsandtodefinesimilarities between curves, the nonparametric forecastingmethod KWF (Section 4) and thewavelet-based clustering tools to deal with electrical load curves (Section 5). Section 6 is specifically devoted to the upscaling issue and strategy. Section 7 describes an application for forecasting a French electricitydataset. Finally,Section8collects someelementsofdiscussion. It shouldbenotedthatwe tried towrite thepaper in suchaway that eachsectioncouldbe read independentlyof eachother. Conversely, somesectionscouldbeskippedbysomereaders,withoutaltering the local consistencyof theothers. 2.Bottom-UpForecastingfromSmartMeterData: BigPicture We present here our procedure to get a hierarchical partition of individual customers, schematically represented in Figure 1. On the bottom line, there areN individual customers, say I1, . . . , IN. Eachof themhasanindividualdemandcodedintoanelectrical loadcurve.At the topof theschema, there isonesingleglobaldemandGobtainedbythesimpleaggregationof the individual ones at each time step, i.e., G = ∑n In. We look for the construction of a set ofKmedium level aggregates, A1, . . . ,AK such that they formapartition of the individuals. Each of the considered entities (individuals,mediumlevelaggregatesandglobaldemand)canbeconsideredas timeseries since theycarry important timedependent information. 231