Seite - 255 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1678 literature [17]. Sincewewere forecasting theheat loadofanentire city,we tookamore simplified approach. In theAarhusdistrictheatingsystem, theheat load ismost stronglycorrelatedwith the outdoor temperature laggedby4h, compared toother time lagsof the temperature. Theheat load alsocorrelatesmost stronglywith thesolar irradiation laggedby4h. Thereseemedtobenobenefit in laggingthewindspeed.Only includingtwospecific lags, isof courseasimplificationof thedynamics of thesystem,but theresultsof includingthemweresignificantlybetter than justusingsimultaneous (lag0h)weathervariables. Summingup, the followingfiveweathervariableswere includedinthe modeling:Toutt ,v wind t , I sun t ,T out t−4, and I sun t−4. Outdoor temperature and, as a consequence, the heat load varies substantially fromyear to year [18]. Themeanannual temperatures inourdataset spannedarangeof2.5◦C.Comparedto the meanloadof thewholedataset (excluding2016), theannualmeanheat loadwas15%higher in the coldestyearand11%lower in thewarmestyear. 2.4.1.DataScenariosandPre-Processing Inorder toevaluate theeffectof including thevarious typesof inputdata for forecastingheat load, threedifferentdatascenarioshavebeendefined.Wecall thesescenarios: “OnlyWeatherData,” “WeatherandCalendar,”and“Weather,Calendar,andHolidays”. Table1details the inputdataused ineachscenario. Table1. Inputvariablesusedin the threedatascenarios (inbold). OnlyWeatherData WeatherandCalendar Weather,CalendarandHolidays Laggedheat load Pt−24 orPt−48 Pt−168 Weatherdata Toutt vwindt Isunt Toutt−4 Isunt−4 Calendardata Hourofday Dayofweek Weekend Monthofyear Holidaydata Nationalholiday Observance Schoolholiday Toachievethebestperformanceof themodels, the inputdatawerescaledandencodedasfollows. All thecontinuousvariables (laggedheat loadandweather)werestandardizedtohavemean0and standarddeviation1. Thecalendardataandholidaydatawere includedasso-calleddummyvariables. Dummyvariablesareawaytorepresentcategoricalvariablesasbinaryvariables. Forinstance,whether ornotagivenhour fallsonaschoolholidaycanbeencodedasabinaryvariable (0or1). Thedayof weekcanbeencodedassixbinaryvariables: onevariable indicating if it isMonday,one indicating if it Tuesday,etc.Onlysixvariablesareneededtoencodesevendays,because if it isnotanyof thedays fromMondaytoSaturday, then itmustbeSunday.Usingsimilardummyvariablesall thecalendar andholidaydatawas included. Encodingcategoricaldataasdummyvariables isastandardmachine learningmethod[19]. 2.5.MachineLearningModels Webenchmarkedandcomparedthreedifferentmachine learningmodels thathaveallpreviously been proven adequate for heating load forecasting [7,8]: ordinary least squares regression, multilayerperceptron,andsupportvector regression. 255