Page - 260 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1678 The forecastperformance, showninthe topofFigure4, is similar to theperformance thatwas achievedduring trainingandcross-validation. This indicates that themodelshavenotbeenoverfitted andgeneralizewell toout-of-samplepredictions. It isworthpointingout that theperformanceof all thesemodels, even theOLSmodel using onlyweatherdata,exceeds theperformanceof thecommercial forecastingsystemthat iscurrently in operation in theAarhusdistrictheatingsystem.Thiscommercial forecastingsystemhadanRMSEof 41.9MWinyearof2016onthesameforecasthorizons. Inrelative terms, theSVRmodelhasaMAPE of6.4%versus8.3%for thecommercial system. Themodelspresentedhereperformbetter thanall other forecastmodels thathavebeenusedin theAarhusdistrictheatingsystem. 3.2. SeasonalPerformanceVariations Theheat loadvariessignificantlyover theyear,both inmagnitudeandinvariance,asexemplified inFigure2. It canbeachallengeforasinglemodel toadequately forecastbothwinterandsummer heat loads. Therefore, it is relevant to further investigate themodelperformance throughout theyear. Theforecasterrorof thebestmodel,SVRusingweather, calendar,andholidaydata, is illustrated in Figure5. Threedifferenterrormetricsareshown: onthe leftaxes, theRMSE(blue)andMAE(yellow) areshowninMW;ontherightaxes, theMAPE(red) is showninpercent. Thehorizontalaxesshow thehourofday for the forecastedhour, andeachsubplotdepicts amonth in theyear. Thismakes itpossible to see if it isharder to forecast themorningpeakand if the forecasthorizon impacts the accuracy. Keep inmind thatHour 1has the shortest forecast horizon (15h), andHour 24has the longesthorizon(38h), since the forecastsareproducedat10:00a.m. thepreviousday. InspectingFigure5, it is clear that theabsolute errormeasuresRMSEandMAEare largest in winterandsmallest insummer. This isareflectionof theannualheat loadprofileandthe large load with largevarianceduringwinter. In late fall andwinter, theRMSEcanbeabove50MWinsome hours,whereas it canbebelow10MWinsomehours in July. TherelativeerrormetricMAPEbehaves in theoppositeway. Therelativeerror is smaller in thewintermonthsandlarger insummermonths, but it staysbetween2.5%and10.5%.This isaconsequenceof theannual loadvariationsbeing larger thantheannualvariations in theabsoluteerror. There isnoclearpattern in thewaytheerrorchangesduringtheday. Themodeldoesnotseemto performworsebetween7:00and8:00 in themorning,where themorningpeakfalls.Novemberand Mayareexceptions to this rule. Inmanyapplications, theerrorofa forecastmodel increaseswith the forecasthorizon(here thehourofday).Wedonotobserveageneral increasingtrendin theerrorwith thehourofday. This indicates that theweather forecasts thatareusedas inputs tocreate the forecast arenot significantlyworseat the longesthorizoncompared to theshortesthorizon. Itmayalsobe duetoweather forecastingaccuracyhavingaminor impactontheheat loadforecastingerror,aswe sawfromFigure4. Ifwewere to increase the forecasthorizonfurther, the forecasterrorwouldmost likely increase. Theforecasterrorvariessignificantlyover theyear,butaggregatederrormetricssuchasRMSE, MAE,orMAPEdonot tell the full story.Maximumerrorscanberelevant forunit commitment in the productionplanningandforevaluatingriskregardingtradingintheelectricitymarket. Figure6shows histogramsfor thehourlyerror foreachmonthof theblindtestyear2016. The10%and90%quantiles havebeen indicated ineachplot. It is clear that thewidthof theerrordistributionvariessubstantially frommonthtomonth.Duringthesummer, the forecasterror isquiteconfined,but thedistribution widens in late fall andbecomeswidest inDecember. InTable2,asummaryof theerrordistribution isshown.The99%and1%quantilesof theerror distributionare indicationsof themaximumerrors thatcanbeexpected.Ninety-eightpercentof the forecastedhourshave forecasterrorsbetweenthe1%andthe99%quantile. Thebestmonth is July with 98%of the errors fallingbetween−16.0and25.8MW. Theworstmonth isDecember,where there isa1%riskof the forecastovershootingbymore than115.0MWanda1%riskof the forecast 260