Page - 57 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2019,12, 164 forecaststrategyissubjectedtostepaheadgenerations.However,duringsimulations,weobservedthat from89thto100thgeneration, the forecasterrordoesnotexhibit significant improvement. Therefore, theproposedandtheexistingforecastmodelsarenotsubjectedto furthergenerations. Thereexistsa possibletrade-offbetweenaccuracyofaforecaststrategyanditsconvergencerate(refertoSections1–3). This trade-off is showninFigure6c–f. Fromthesefigures, it is clear that thebi-level forecastmodel improves the accuracy ofMI+ANN forecastmodelwhile paying cost in terms of relatively slow convergence rate. On the other hand, the newlyproposedMI+ANN+mEDEmodelmodifies the EDEalgorithmtofurther improvetheaccuracyof thebi-level forecastmodel.More importantly, the MI+ANN+mEDEmodel improves thepredictionaccuracybynotpaying surplus cost in termsof executiontime.However, theexecutiontimeofourproposedforecastmodel is stillgreater thanthe MI+ANNforecastmodeldueto integrationofoptimizationmodule. Figure7showsthe impactofdataset size (numberof trainingdatasamples)onerrorperformance (seeFigure7a)andexecution time(seeFigure7b)of the threeselectedmodels. ByobservingFigure7a, an improvementoferrorperformance forall thecomparedSTLFmodels isevidentwhenthenumber of laggedinputsamples increase from30to120. This result followsEquation(1), i.e., theANNismore finely tunedbyincreasingthevalueofn (30 to120)which improves theforecasterrorperformance. However, this improvement isnot significantatmuchhigher tuningwhen thenumberof training samplesare increasedfrom60to120 (stabilitycanbeseen in thecurves).Ontheotherhand,Figure7b shows the cost of high execution timepaidby thefine tuning to achieve relative improvement in forecastaccuracy. This isobviousbecause trainingof theANNtakesadditional timewhenthenumber of trainingsamplesare increase. FromFigure7a,b, it is clear that theproposedmodularmodel ismore scalable (relativelyhigherdegreeofstabilitycanbeseenforMI+ANN+mEDEforecast)ascompared to theother twomodels. The reasons for this higher scalability are: usageof selected features for trainingof theANN, training theANNviaMARAalgorithmwith localnormalization, andusage mEDEalgorithmforerrorminimization. Table7showstherelationshipbetweenMAPEandthenumberof iterationsof thethreecompared STLFmodelswhentestedonDAYTOWNandEKPCdatasets. Theconvergencecharacteristics (i.e., thenumberof iterations) indicate that theproposedMI+ANN+mEDEmodelandthebi-levelmodel convergeatanoptimalvalueinalmostthesamenumberof iterations.Ontheotherhand, theMI+ANN model takesonly20–23 iterations forconverging intoanoptimal targetvalue. This result isobvious dueto theaddedcomputationalburdeninthebi-levelandtheMI+ANN+mEDEmodels (i.e., these modelsusetheoptimizationmodule)whichisnotthecaseinMI+ANNmodel(i.e., thismodeldoesnot use theoptimizationmodel). Inotherwords, theMI+ANNmodelachieves its targetof therequired training, testing,andvalidationwith the leastnumberof iterations.However, this least computational burdenisachievedbypayingthehighcostof forecastaccuracy. In this regard,aregressionanalysis of thenetworkwasperformedtoevaluateconfidence intervalof the training, testingandvalidation performance of the compared forecastmodels, and the results are shown inTable 7. Clearly, the proposedMI+ANN+mEDEmodelachieves thehighestconfidence interval (i.e., 98%)ascompared to bi-level (i.e., 97%) andMI+ANN(i.e., 96%)models. Thismeans that only 2%of the estimated data isnot statisticallysignificant for thenetwork incaseof theproposedMI+ANN+mEDEmodel. Asaresult, the forecasted loaddemandof theproposedMI+ANN+mEDEmodel is rathercloser to its actualvalueascomparedto theother twomodels (seeFigure6a,b). 57