Page - 189 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2008 (a) (b) DNN performs betterANN performs better -5 -4 -3 -2 -1 0 1 2 3 4 5 ANN wmape - DNN wmape 0 5 10 15 20 25 30 Figure6. Thisfigure shows twohistograms: (a)Acomparisonof theperformanceofall 62models between theDNNand the LR. Instances to the left of the center line are those forwhich the LR performedbetter,while thoseontherightareareaswhere theDNNperformsbetter. Thedistance from thecenter line is thedifference inWMAPE. (b)Thesameas (a)butcomparingtheANNtotheDNN. Oneinstance (at10.1) in (b) is cutoff tomaintainconsistentaxes. It isalso interestingtoconsider that insomeareas, theLRandANNforecastersperformbetter than theDNN.This implies that in somecases, the simplermodel is thebetter forecaster. It is also important topointout thatof the13areaswhere theLRoutperforms theDNN,only twohaveLR WMAPEsgreater than5.5,whichmeans that thesimpleLRmodelsareperformingverywellwhen comparedto industrystandards forshort-termloadforecastingofnaturalgasonthoseareas. Figure7compares theperformanceof the twoDNNs.Aswith the twodistributions inFigure6, a left-tailed t-testwasperformedon thehistograminFigure7 resulting inap-valueof 9.8×10−5. Thismeans that theLargeDNNoffersastatisticallysignificantbetterperformanceover the62areas than the smallDNN.However,much like in the comparisonbetween theDNNandothermodels, thesmallDNNperformsbetter insomeareas,whichsupports theearlierclaimthatcomplexmodels donotnecessarilyoutperformsimplerones. Figure7.Acomparisonof theperformanceofall62modelsbetweentheDNNandtheLargeDNN. Instances to the leftof thecenter lineare those forwhich theLargeDNNperformedbetter,while those ontherightareareaswheretheDNNperformsbetter. Thedistancefromthecenter lineis thedifference inWMAPE. 8.Conclusions WeconcludethatDNNscanbebettershort-termloadforecasters thanLRandANNs.Onaverage, over the62operatingareasexamined,aDNNoutperformedanotherwise identicalANNatshort-term load forecasting of natural gas, and a larger DNNoffered even greater performance. However, 189