Page - 165 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2038 wasconsideredasaninput in theforecastingmodel,asprovidedbyAEMET(AgenciaEspañolade Meteorología) for thecityofCartagena(where thecampusuniversity is located), from2011to2016. Besides, dependingon the end-usesof the customer in study, someother features canbe relevant for the load. For example, in this case study,different typesofholidaysor specialdayshavebeen distinguishedthroughoutbinaryvariables (seeTable2 foradetaileddescription). Table2.Descriptionof thepredictors. Predictors Description H2,H3, . . . H24 Hourlydummyvariablescorrespondingto thehourof theday WH2,WH3, . . . WH7 Hourlydummyvariablescorrespondingto thedayof theweek MH2,MH3, . . . ,MH12 Hourlydummyvariablescorrespondingto themonthof theyear FH1 Hourlydummyvariablescorrespondingto themonthof theyear FH2 HourlydummyvariablecorrespondingtoChristmasandEasterndays FH3 Hourlydummyvariablecorrespondingtoacademicholidays (patronsaint festivities) FH4 Hourlydummyvariablecorrespondingtonational, regionalor localholidays FH5 Hourlydummyvariablecorrespondingtoacademicperiodswithno-classesandno-exams(tutorialperiods) Temperature_lag_i Hourlyexternal temperature lagged“i”hours.Dependingonthepredictionhorizon,different lagswillbeconsidered. LOAD_lag_i Hourly load lagged“i”hours.Dependingonthepredictionhorizon,different lagswillbeconsidered. Threedifferentmeasurementsgiven in (9), (10), and(11)wereusedtoobtain theaccuracyof the forecastingmodels: therootmeansquareerror (RMSE), theR-squared (percentageof thevariability explainedbytheforecastingmodel), andthemeanabsolutepercentageerror (MAPE).Althoughthe MAPE is themost used errormeasure, see [1], the squared errormeasuresmight bemorefitting because the loss function in Short TermLoadForecasting is not linear, see [13]. Somedescriptive measuresof theerrors (suchas themean, skewness,andkurtosis)werealsoconsideredtoevaluate the performanceof the forecastingmethods. Therootmeansquareerror isdefinedby: RMSE = √√√√ n∑ t= 1 (yt− yˆt)2 n (9) theR-squared isgivenby: R−squared = 1−∑ n t= 1(yt− yˆt)2 ∑nt= 1(yt−y)2 (10) andthemeanabsolutepercentageerror isdefinedby: MAPE = 100 n n ∑ t= 1 ∣∣∣∣yt− yˆtyt ∣∣∣∣ (11) wheren is thenumberofdata,yt is theactual loadat time t, and yˆt is the forecasting loadat time t. 3.3. ForecastingResults Datafrom1January2011to31December2015wereselectedas the trainingperiodinallmethods, whereasdata from1January2016 to31December2016constitutedthe testperiod. In this subsection, firstlyapredictionhorizonof48h isestablished,whose forecastingresultswillbeused in thenext sectiondealingwithDirectMarketConsumers. In thiscase,weconsider53predictors (seeTable2): 165