Seite - 297 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1561 3. ProposedIntervalPredictionModelforShort-TermLoadForecasting(STLF) Inthispaper,weproposedahybridmodel for intervalpredictionbasedonthedatapreprocessing, multi-objectiveoptimizationalgorithmandLUBEtosolve theproblemofSTLF.Thishybridmodel consistof twostages: datade-noisingandmodelprediction. Inthefirststage, themaintaskis torefinetheoriginaldata. Therawpowerloaddataisaffectedby manyinternalandexternal factors in thecollectionprocess. Therefore,a lotofunrelated information is integrated in thedata. Severalpiecesof informationwill further affect thequalityof thepower loaddata,andincrease thedifficultyofaccurate forecastingof thepower load. In theneuralnetwork model, the performance of themodel is directly affected by the quality of the data. As a type of machine learningalgorithm, theneuralnetworkuses itsmultilayeredstructure to learntherelevant interdependenciesof thedataanddetermine thestructuralparametersof thepredictionmodel, soas toachievefittingandforecasting.However, if the inputsetof themodelcontains toomuchnoiseand “false information”, themodelwillbeseriouslyaffected in the trainingprocess,andsomeproblems willemerge,suchastheoverfittingproblem.Therefore,weintroducedCEEMDANtoeliminateuseless information in the rawdata. Asmentionedabove,CEEMDANcandecompose thedataseries into several IMFswithdifferent frequencies, as showninFigure2. Because the IMFsareextractedwith envelopecurvesdependingontheextremum,someof the IMFshavehigher frequencies, justas the first fewIMFsthatareshowninFigure2. Inaddition, theother IMFsalsohave lower frequenciesand represent the trendfactors, therebyformulating thevitalbasis for time-seriesprediction. In theactual operations,wecanremovetheIMFswithhigherfrequencies,whicheffectivelyrepresentnoisetorefine theoriginaldata. Inorder todeterminewhichIMFsought tobeabandoned,wecalculated theentropy ofeachIMFandremovedtheIMFswith lowerentropy.After thedenoisingprocess, therefineddata are transferredtonextstageas the inputdata for training in thepredictivemodel. In the secondstage, themain intervalpredictionmodelwasproposed. Inourhybrid interval predictionmodel, thePI is outputdependentonLUBE,which isbasedon themulti-outputof the Elmanneuralnetwork(E–LUBE). In the trainingprocess, the inputsetofE–LUBEisconstructedas indicatedinFormula(16),whiletheoutputset isconstructedasindicatedinFormula(17),wheremand s respectivelydenote thenumberof featuresandthenumbersofsamples,andαdenotes the interval widthcoefficient. In thecaseof theSTLFproblem,m indicates thenumberofprevious time-points that weuse to forecast thepredictivevalue. Inputset : ⎡⎢⎢⎢⎢⎣ x1 x2 · · · xm x2 x3 · · · xm+1 ... ... ... ... xs xs+1 · · · xs+m ⎤⎥⎥⎥⎥⎦ (16) Outputset : ⎡⎢⎢⎢⎢⎣ xm+1×(1−α) xm+2×(1−α) ... xm+s+1×(1−α) xm+1 xm+2 ... xm+s+1 xm+1×(1+α) xm+2×(1+α) ... xm+s+1×(1+α) ⎤⎥⎥⎥⎥⎦ (17) Accordingtoatrainedmodel,whenanewseriesXi, i=1, . . . ,m, is inputintothemodel,Xm+1with anupperboundXUm+1 andalowerboundX L m+1willbeoutput. This is thebasicmechanismof interval prediction for STLF in this study. However, in traditionalmulti-output neural networks, the loss function isalways themean-square-error (MSE),which isakeycriterionforpoint forecasting. In this study,weintroducedtwonewcriteria (PIWandCP) toconstruct the loss function, consideringthe mainpurposeofour intervalprediction. The traditionalneuralnetworkparametersweredetermined byusingagradientdescentalgorithm,but for twoof thesetcriteria, thecalculationof thegradient 297