Page - 146 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2080 2.2.6.NumberofAuto-RegressiveLags As itwasaforementioned,bothmodelspresentanauto-regressivecomponent. Thispartof the model introduces thepreviousvaluesasa feedback inorder toenable to forecastingengine toreduce errorsduetounaccountedfactors thatarepersistent in time. Thekeyparameter toconfigure thisaspectof themodels is thenumberof lags,whichrepresents howmanypreviousvaluesare fedback into themodel. Intuitively, themost recentvaluescarry the most informationwhile the further back in time thatwe reach, the less relevant thedata become. Inaddition, theARmodelusesa linear relation to capture the laggedresultswhile theNNmodel allowsnon-linearity. Therefore, it ispossible thatonemodel isable touseadifferentamountof lags thantheother. Theauto-regressiveorderofeachmodelhasbeentestedfrom0to25. The loadseries ishighly self-correlatedonlagsmultipleofsevenduetotheweeklypatterns,asit isshowninFigure4. Therefore, lagsaround7,14and21wereexplored.Auto-correlationmeasures thecorrelationbetweenyt andyt+k, anditscalculation isdescribed in [43]. 0 5 10 15 20 25 -0.2 0 0.2 0.4 0.6 0.8 Lag Sample Autocorrelation Function Figure4.SampleautocorrelationfunctionforNational loadat18h. It isworthmentioning that the objective of this paper is not toprovide or suggest analytical or statisticalmethods to determine the order of auto-regressivemodels like [44,45] but to offer a comparisonbetweenARandNNbasedmodels tounderstandtheeffect that theauto-regressiveorder hasonthe forecastingaccuracy. 2.3. TypesofDays Eachof theproposedparametersandconditionsunderwhichthe forecastingmodelsare tested willcausetheforecastingaccuracytochangeoverthewholeone-yearsimulatingperiod. Thisvariation, however,mayaffect sometypeofdaysmore thanotherand, therefore, itmayseemirrelevantwhenit isaveragedover thewhole testingperiod. Inorder toavoid thiserror, it is important todissect the results andanalyze theaccuracyof themodelsondifferent categoriesofdays todeterminewhich conditionsaffectwhichtypeofdaysandhowtheydoit. There are two aspects to classify the days: social character and temperature. The first one considersdaysasspecial if theyareaholiday,are inbetweentwoholidaysorweekend,orareaffected byDaylightSavingTimeor thevacationalperiodsatChristmasorEaster.Amoredetaileddescription of thedaysconsideredspecial is foundinSection3. Temperature isusedtoclassifydaysashotandcold. Foreachcategory, the top20andbottom 20days fromthe temperatureseriesareconsidered. Ifoneof the20days isalsoaspecialday, then it is 146