Seite - 56 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2019,12, 164 ThenewlyproposedMI+ANN+mEDEmodel is testedagainst the twoexistingmodels in termsof threeperformancemetrics: (i) accuracy;and(ii) executiontimeorconvergencerate. • Accuracy: Accuracy(.)=100−MAPE(.).Wehavemeasuredthismetric in%. • Variance: Var(i) = 1m ∑mj=1 |pf(i, j)−pa(i, j)|. Where pa(i, j) is the mean value of pa(i, j). Monthly variance is calculated by using the same formulawhile considering the calculated dailyvariances. • Execution time:Duringsimulations, the timetakenbythesystemtocompletelyexecuteagiven forecast strategy. Thestrategyforwhichexecution time is small convergesmorequicklyandvice versa. Insimulations,wehavemeasuredexecutiontimeinseconds. Table2.Parametersusedinsimulations. Parameter Value Forecasters 24 Hiddenlayers 1 Maximumiterations 100 Neurons (in thehiddenlayer) 5 Bias 0 Initialweights 0.1 Momentum 0 Loaddata (historical) 1year Maximumgenerations 100 ReferringtoFigure6a–fandTables3–6,whicharegraphical/tabular illustrations/representations of the proposed MI+ANN+mEDE-based forecast model versus the two existing DALF models: MI+ANNand bi-level. From Figure 6a,b, it is clear that the proposedMI+ANN+mEDEmodel effectively predicts/forecasts the future loadof the two selected SGs. TheANN-based forecaster captures thenon-linearities in thehistory load-timeseries. Thisnon-linearpredictioncapability is notonlyduetosigmoidactivationfunctionbutalsodueto theselectedtrainingalgorithm;MARA. Whenwelookat thehourly forecast results inFigure6c,d, the%errorof theMI+ANN-basedforecast model is3.8%and3.81%forDAYTOWNandEKPC,respectively. The%errorof thebi-level forecast model is 2.2% and 2.23% forDAYTOWNandEKPC, respectively. The% error of the proposed MI+ANN+mEDE-basedforecastmodelis1.24%forbothDAYTOWNandEKPC,respectively. Similarly, thedaily forecast resultsof the twosimulatedmodels for January2015areshowninTables3and5for thetwoselectedUSAgrids, respectively. Fromtheseresults, it isclear that theexistingMI+ANN-based forecastmodelpredicts the future loadwiththehighest%errorandthehighestvariance.Also, the monthly forecast results of the three simulatedmodels for January–December 2015 are shown in Tables 4 and6 forEKPCandDAYTOWN, respectively. FromTables 4 and6, it is evident that the proposedMI+ANN+mEDEmodel forecasts the future loadwith the leastpredictionerrorand the leastvarianceascomparedto theother twoexistingmodels. This result isobviousduetoabsenceof optimizationmodule inMI+ANN-basedforecastmodel. Tominimize this forecasterror, thebi-level forecastmodelusesEDEalgorithm. Subject to furtherminimizationof the forecast error,wehave integratedanmEDEoptimizationtechnique. PleasenotethatmEDEisourmodifiedversionofexisting EDEalgorithmfordownscaling forecast error. Results showthat integrationofmEDEalgorithm yields fruitful results; theMI+ANN+mEDE-basedDALFmodel is relativelymoreaccurate thanthe other twoexistingDALFmodels. Thesefiguresshowthepositive impactofoptimizationmoduleon the forecasterrorminimizationbetweentargetcurveandthe forecast curve. It isobvious that theerror curvedecreasesas thenumberofgenerationsof themEDEalgorithmare increased.As theproposed MI+ANN+mEDEforecastmodelcomparestheforecastcurve’serror(nextgeneration)withtheexisting one(existinggeneration)andupdates theweights if the forecast curve’serror is less thantheexisting one (survival of thefittest). Thus, as expected, the forecast error is significantlyminimizedas the 56