Page - 53 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2019,12, 164 for training and optimization in the rest of themodules to prevent information loss. Thus, we have used a compromisingapproachbetweencomputational complexityand information loss. Remark4. Feature selection isdoneatbeginning, andthe selected featuresare thenused for trainingduring theoperational life of the technique. Fromsimulations,weconclude the following: (i) If thedata set size is small (≤1month), feature selectionhasnosignificant impacton thecomputational complexityof theoverall strategy. (ii) If the data set size is moderate (≥1 month and≤3 months), feature selection somehow affects the computational complexityof theoverall strategy. (iii) If thedata set size is large (≥3months), feature selectionhasasignificant impacton thecomputational complexityof theoverall strategy. 3.2. ForecastModule From theworks discussed in Section 2, it is concluded that anyDALF strategymust ensure non-linearpredictioncapability. Therefore,wechooseANNsbecause thesecancapture thehighly volatilecharacteristicsof load-timeserieswithreasonableaccuracy. ForDALF, twostrategiesareused;direct forecastinganditerative forecasting[28].However, it isdiscussed in [41] that thefirst strategymayintroducesignificant roundofferrorsandthesecond one introduces large forecasterrors. Toovercomethese imperfections, reference [28]has introduced the ideaofcascadedstrategy. Thus,ourproposedforecastmodule implements thecascadedstrategy. OurforecastmoduleconsistsofanANN;24consecutivecascadedforecasterssuchthateachoneof the 24forecastershasanoutput for forecastinganhour’s loadof theupcomingday. It isworthmentioning that the24h’ forecasters/predictorsaremodeledexplicitly insteadofasingle implicit/complexone. These24onehouraheadforecastersallowimprovement in termsofaccuracy [28]. ThecascadedANN forecast structure isacombinationofdirectanditerativestructuressuchthat loadofeachhourof the nextday isdirectlypredictedandeachforecasteryieldsexactlyoneoutput. In the forecastmodule, eachforecaster isanANthat implementssigmoidfunctionforactivation. We have chosen sigmoid activation function because for enabling ANs in terms of capturing the highly volatile (non-linear) SG’s time variant load characteristics. To update the weights during trainingprocessof theANN,differentalgorithmshavebeenusedpreviously. Forexample, reference [42] includeGradientDescent BackPropagation algorithm. Similarly, references [27,28] suggestLevenberg-Marquardtalgorithmas it cantrain theANN1–100 times faster thantheGradient DescentBackPropagationalgorithm. Weusemultivariate auto regressivealgorithm(MARA) [43] because it can train theANNfaster thanLevenberg-MarquardtalgorithmandGradientDescentBack Propagationalgorithm[42].AccordingtoKolmogrovtheorem, if theANNisprovidedwithproper numberofANsthenit cansolveaproblembyadoptingonehiddenlayer. Thus,wehaveconsidered onehiddenlayer in thecascadedANNstructureofall 24ANs. FromtheselectedfeaturesSf(.)of the pre-processingmodule, the forecastmoduleconstructs trainingandvalidationsamples,ST=Sf(i, j) and SV = Sf(1, j), respectively (where i ∈ [2,m] and j ∈ [1,n]). These samples illustrate that the training ofANNby all the candidate inputs except the last/final one. The set of last samples of historical load-timeseries isused forvalidationpurpose. In fact, thevalidation set is apart of the training loadsetconstructedfromit the training. Thus, thevalidationsetbecomesunseenforANN. Tomakethevalidationerrorasa truerepresentativeof the forecasterror,validationsetneeds tobe as close to the forecasthorizonaspossible. While forecasting tomorrow’s loadwechooseoneday backwardsamplesdueto tworeasons: (i)dailyperiodicity;and(ii) short-runtrend[44]. Thus,eachof the24ANsis trainedaspermulti-variateMARAusingtheaforementionedtrainingandvalidation sets. Furtherdetailsof the trainingprocess toupdate theweightscanbefoundin[43]andpictorial viewof the learningprocess is showninFigure4. 53