Page - 254 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1678 2.4.DataExploration Figure2 shows theaveragehourlyheat load for theexampleyearof 2010. Noticehowmuch theheat loadvariesover theyearboth inmagnitudeandinvariance. Thezoomedinset in theplot showstheheat loadvariationsoveraweekinMarch.Acleardailypatterncanbeobserved,witha sharpmorningpeakbetween7:00and8:00onweekdaymornings. Themorningpeak isawell-known phenomenoninthedistrictheatingcommunityandiscausedbymanypeopleshoweringaroundthe sametimeeverymorning.Onweekends,morningpeakscanbeobservedlater in themorningand tendtobelesssharpcomparedtoweekdays. Fromtheinset, it isclear that thedaily loadpatternvaries substantiallywithin justoneweek. Figure2.Timeseriesforthehourlyheat loadintheyear2010.TheinsetshowsazoomofaweekinMarch. Theheatdemandhaspeaks in itsautocorrelationfunctionat24h,48h,72h,andsoon. This is duetothestrongdailypattern. There isalsoanotablepeakat168h(oneweek). Inordertocapturethis behavior, laggedvaluesof theheat loadwereusedas inputvariables in themodeling. Specifically,we includedtheheat loadlaggedwith24h,48h,and168h. LookingatFigure1,wesee that the forecast horizonvaries between15hand38h. Theheat load in thefirst hourof theday canbe forecasted with theshortesthorizon,andthe lasthourofeachday is forecastedwith the longesthorizon.When forecastinghourswitha forecasthorizonof24hor less, theheat loadlagged24hcanbeused.When forecastinghourswitha longerhorizonthan24h, theheat load laggedwith48hmustbeused instead. Apowerspectrumanalysisconfirmedstrongpeaksat frequencies1/12h−1 and1/24h−1,but12h is shorter thantheshortest forecasthorizonandwasthusdiscarded. The twolags thatbest capturedthe dailyandweeklypatternof theheat loadwere included.Wedenote the laggedheat loadbyPt−24, Pt−48, andPt−168, respectively. Themost important weather variable whenmodeling district heating loads is the outdoor temperature,because there isastrongnegativecorrelationbetweentheheatdemandandtheoutdoor temperature. Dependingon the specificdistrict heating system, solar irradiationandwind speed can also be significant predictors for the heat load [2]. Due to the thermalmass of the buildings inadistrictheating system, there is a certain inertia in theheat loadwhenchanges in theweather occur.Onthe individualbuilding level, this inertia ishandled ingreatdetail in thecivil engineering 254