Page - 337 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1282 Owingtothecharacteristicofstrongself-learning,self-adaptingabilityandnon-linearity,artificial intelligencemethodssuchasbackpropagationneuralnetworks(BPNN),supportvectormachine(SVM) aswellas the least squaressupportvectormachine (LSSVM)etc. haveobtainedgreaterattentionand havehadawideapplicationinthefieldofpowerloadforecastingduringthelastdecades[5,6]. Park[7] andhispartnersfirstused theartificialneuralnetwork inelectricity forecasting. Theexperimental resultsdemonstrated thehigherfittingaccuracyof theartificialneuralnetwork (ANNs)compared with the fundamentalmethods. Hernandez et al. [8] successfully presented a short-term electric load forecast architecturalmodelbasedonANNsand the resultshighlighted the simplicityof the proposedmodel. YuandXu[9]proposedacombinationalapproachforshort-termgas-loadforecasting including the improved BPNNand the real-coded genetic algorithmwhich is employed for the parameteroptimizationof thepredictionmodel, andthesimulation illustrated its superiority through thecomparisonsofseveraldifferentcombinationalalgorithms.Huetal. [10]put forwardageneralized regression neural network (GRNN) optimized by the decreasing step size fruit fly optimization algorithmtopredict theshort-termpower load,andtheproposedmodelshowedabetterperformance withastrongerfittingabilityandhigheraccuracy incomparisonwith traditionalBPNN. Yet, the inherent feature of BPNNmay cause lowefficiency and local optimal. Furthermore, the selectionof thenumberofBPNNhiddennodesdependson trial anderror. Asa consequence, it is difficult to obtain the optimal network. On the basis of structural risk, empirical risk and vapnik–chervonenkis (VC)dimensionboundminimizationprinciple, the support vectormachine (SVM)showedasmallerpractical riskandpresentedabetterperformance ingeneral [11]. Zhaoand Wang[12] successfullyconductedaSVMforshort-termloadforecasting,andtheresultsdemonstrated theexcellenceof the forecastingaccuracyaswellascomputingspeed.Consideringthedifficultyof the parameterdeterminationthatappearedinSVM,theleastsquaressupportvectormachine(LSSVM)was putforwardasanextension,whichcantransformthesecondoptimal inequalityconstraintsproblemin original space intoanequalityconstraints’ linearsysteminfeaturespace throughnon-linearmapping andfurther improve thespeedandaccuracyof theprediction [13].Nevertheless,howtoset thekernel parameterandpenalty factorofLSSVMscientifically is still aproblemtobesolved. Huangetal. [14]proposedanewsingle-hiddenlayerfeedforwardneuralnetworkandnameditas theextremelearningmachine(ELM)in2009, inwhichonecanrandomlychoosehiddennodesandthen analyticallydeterminetheoutputweightsofsingle-hiddenlayerfeed-forwardneuralnetwork(SLFNs). Theextremelearningmachine tends tohavebetter scalabilityandachievesimilar (for regressionand binaryclasscases)ormuchbetter (formulti-classcases)generalizationperformanceatmuchfaster learningspeed(uptothousandsof times) thanthe traditionalSVMandLSSVM[15].However, it is worth noting that the inputweightsmatrix andhidden layer bias assigned randomlymay affect thegeneralizationabilityof theELM.Consequently, employinganoptimizationalgorithmsoas to obtain thebestparametersofboththeweightof input layerandthebiasof thehiddenlayer isvital andnecessary. Thebatalgorithm(BA),acknowledgedasanewmeta-heuristicmethod,cancontrol themutual conversion between local search and global search dynamically and performs better convergence[16]. Becauseof theexcellentperformanceof localsearchandglobalsearchincomparison withexistingalgorithmslike thegeneticalgorithm(GA)andparticleswarmoptimizationalgorithm (PSO), researchersandscholarshaveappliedBAindiverseoptimizationproblemsextensively [17–19]. Thus, thispaperadopted thebatalgorithmtoobtain the inputweightmatrixandthehidden layer biasmatrixofELMcorrespondingto theminimumtrainingerror,whichcannotonlymaximize the meritofBA’sglobalandlocal searchcapabilityandELM’s fast learningspeed,butalsoovercomethe inherent instabilityofELM. The importanceof forecastingmethods is self-evident, yet the analysis andprocessingof the original loaddata also cannot be ignored. Somepredecessors have supposedhistorical load and weatheras themost influential factors in their research[20–22].However, selecting thehistorical load datascientificallyornotcancauseastrong impactontheaccuracyofprediction. Inaddition, there arestillmanyotherexternalweather factors thatmayalsopotentially influence thepower load.Only 337