Page - 182 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2008 NotethekinkinthetrendofFigure1atabout65◦F.Attemperaturesgreaterthan65◦F,residential andcommercialusers typicallystopusingnaturalgas forheating.At temperaturesgreater than65 ◦F, only thebaseloadremains. Thus,heatingdegreedays (HDD)areusedas inputs to forecastingmodels, HDD=max(0,Tref−T), (1) whereT is thetemperature,andTref is thereferencetemperature[3]. Referencetemperatureis indicated byconcatenating it toHDD, i.e.,HDD65indicatesareference temperatureof65 ◦F. Severalotherweather-based inputscanbeused in forecastingnaturalgas, suchaswind-adjusted heatingdegreeday(HDDW);dewpoint temperature (DPT),whichcaptureshumidity;andcooling degreedays (CDD), CDD=max(0,T−Tref) (2) andisusedtomodel temperature-relatedeffectsaboveTrefasseen inFigure1. In addition to weather inputs, time variables are important for modeling natural energy demand[4]. Figure2illustratesthedayoftheweek(DOW)effect.Weekends(Friday–Sunday)haveless demandthanweekdays (Monday–Thursday). ThehighestdemandtypicallyoccursonWednesdays, while the lowestdemandgenerallyoccursonSaturdays. Adayof theyear (DOY)variable is also important. Thisallowshomeownerbehaviorsbetweenseasons tobemodeled. InSeptember,a50 ◦F temperaturewill cause fewnaturalgascustomers to turnontheir furnaces,while inFebruaryat50 ◦F all furnaceswillbeon. -40 -20 0 20 40 60 80 65 - Temperature (°F) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 10 5 Sunday Monday Tuesday Wednesday Thursday Friday Saturday Figure2.Thesamedataas inFigure1coloredbydayof theweek. 3. PriorWork Multiple linear regression (LR) and autoregressive integratedmoving average (ARIMA) are common models for forecasting short-term natural gas demand [5]. Vitullo et al. propose a five-parameter linear regressionmodel [5]. Let sˆbe thedayahead forecastednatural gasdemand, HDD65bethe forecastedHDDwithareference temperatureof65 ◦F,HDD55bethe forecastedHDD withareference temperature55 ◦F,andCDD65bethe forecastedCDDwithareference temperature 65 ◦F.LetΔHDD65bethedifferencebetweentheforecastedHDD65andthepriorday’sactualHDD65. Then,Vitullo’smodel isdescribedas sˆ= β0+β1HDD65+β2HDD55+β3ΔHDD65+β4CDD65. (3) β0 is the natural gas load not dependent on temperature. The natural gas load dependent on temperature is captured by the sumof β1 and β2. The two reference temperatures bettermodel thesmoothtransitionfromheatingtonon-heatingdays. β3 accounts for recencyeffects [5,6]. Finally, β4modelssmall,butnot insignificant, temperatureeffectsduringnon-heatingdays. 182