Page - 52 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2019,12, 164 thatmorehistorical laggedsamplesareavailable (fine tuning). Thisfine tuninghowever results in greater timeduringexecutionof thealgorithm.Thus, there isa trade-offbetweenconvergencerate andaccuracy. Before feedingtheforecast/predictionmodulewithP, thevaluesofParenormalized. In thisprocess,a localmaximumvalue ‘pcimax’ is computedineachcolumnofP: pcimax=max(p(hi,d1),p(hi,d2),p(hi,d3), . . . ,p(hi,dn)), ∀ i∈{1,2,3, . . . ,m} (2) BylocalnormalizationwemeannormalizationofeachP’scolumnbylocalmaxima(onemaximum ineachcolumn); resultsaresavedinPnrm (rangeofPnrm∈ [0,. . . ,1]). Similarly, thematricesTDP,nrm, TDB,nrm andDT,nrm arenormalizedformsofTDP,TDB andDT, respectively. These inputmatricesPnrm,TDP,nrm,TDB,nrm andDT,nrmnotonlycontain irrelevant featuresbut alsocontainredundant features. Toremovethese twotypesof features,weusemutual information technique that is proposed in [27] and later used in [28] aswell. According to this technique, the relativeamountofmutual informationbetweentwoquantities; inputKandtargetG, isas follows: MI(K,G)=∑ i ∑ j p(Ki,Gj)log2 ( p(Ki,Gj) p(Ki)p(Ki) ) (3) Inreference (3),MI(K,G)=0reflects that the inputandtargetvariablesandindependent,high value ofMI(K,G) reflects that there is a strong relation betweenK andG two and lowvalue of MI(K,G) reflects that there is looserelationbetweenKandG. Byusing (3),we calculateMI(K,G)with thehelpofwhich two types of samples (redundant plus irrelevant)arediscardedfromthegiven inputdatamatricesPnrm,TDP,nrm,TDB,nrm andDT,nrm. Accordingto[27,28], thisMItechniqueachievesacceptableaccuracywhilenot takinghightimefor execution. Remark1. Thedata setused for training ishistorical, i.e., for tomorrow’s load forecastweneedmeasured load valuesofpreviousdays. Yes! Thehistoricaldatawas timedependenthoweverwithrespect to thecurrentday thesevaluesdonotundergoanychange. Inotherwords,wedealwithpreviously recordeddatawhichmeans that the stationaryassumption isnotviolated. Thus, the computationofMI is applicablehere. Remark2. Thepowerconsumption/demandof auser isdifferent fordays suchasholidaysorworkingdays. It evenshowsvariation fordifferenthours suchason-peakandoff-peakhours. Tobetter explainourchoice, letus consider the followingexample: ConsideringmatrixP inEquation (1), let p(h1,d1)be thepredictionvariable. Then thereare twopossible cases for training: (a) TheANNis trainedbyall elementsof thematrixPexcept thefirst row. (b) TheANNis trainedonlyby the1st columnof thematrixPexcept p(h1,d1). The trainingsamples incase (a) lead togreaterpredictionerrordue to thepresenceof outliers.Whereas, the trainingsamples incase (b) lead to smallerpredictionerrorbecause theoutliers are removed. Remark3. To improveaccuracyof a forecast/predictionmodel, the samplesused for trainingmustbea-priori maderelevant.Also,minimizednumberof sampleswill decreasealgorithm’s execution time.Due to these two reasons, we prefer/chose local training for each hour. In our approach, the historical load values are locally normalized by localmaxima. Then the normalized values are binary encodedwith respect to localmedian. This encodingrepresents twoclasses of values: highand low. The classes areused for selecting features only, i.e., themutual information is easily calculated forbinaryvariables. This selectionreduces the computational complexity of themutual information-based feature selection strategy. Once we get rid of redundant and irrelevant samplesare removed fromthedata set, theactualvaluesagainst thebinaryencodedvaluesareused 52