Seite - 190 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2008 these improvements to theperformancearenotpresent forall 62operatingareas. Forsome,eventhe much simpler linear regressionmodel is shown toperformbetter than theDNN.For this reason, it is concludedthat,althoughtheDNNisapowerfuloptionthat ingeneralwillperformbetter than simpler forecasting techniques, itmaynotdoso foreveryoperatingarea. Therefore,DNNscanbe usedasa tool inshort-termloadforecastingofnaturalgas,butmultipleother forecastingmethods shouldbeconsideredaswell. Author Contributions: G.D.M. and R.J.P. conceived and designed the experiments G.D.M. performed the experiments; G.D.M. and R.J.P. analyzed the data; R.H.B. contributed reagents/materials/analysis tools; G.D.M.andR.J.P.wrote thepaper. Funding:This researchreceivednoexternal funding. Acknowledgments:TheGasDaylabatMarquetteUniversityprovidedfundinganddata for thiswork. Conflictsof Interest:Theauthorsdeclarenoconflictsof interest. Nomenclature b bias termofaneuralnetworknode c thebias termofarestrictedBoltzmannmachine (RBM) CDD coolingdegreedays DPT dewpoint Dth dekatherm h vectorofhiddennodesofaRBM HDD heatingdegreedays hj jthhiddennodeofaRBM MAPE meanabsoluteerror o outputofaneuralnetworknode RMSE rootmeansquareerror s naturalgasdemand T temperature indegreesFahrenheit Tref reference temperature forHDDandCDD v vectorofvisiblenodesofaRBM vi ithvisiblenodeofaRBM W weightmatrixofaneuralnetwork wi weightof the ith inputofaneuralnetworknode WMAPE weightedmeanabsolutepercentageerror xi ith input to thenodeofaneuralnetwork References 1. NaturalGasExplained.Availableonline: https://www.eia.gov/energyexplained/index.php?page=natural_ gas_home(accessedon24July2018). 2. Merkel,G.D.;Povinelli,R.J.;Brown,R.H.Deepneuralnetworkregressionforshort-termloadforecastingof naturalgas. InProceedingsof the InternationalSymposiumonForecasting,Cairns,Australia,25–28June 2015;p.90. 3. Asbury, J.G.;Maslowski,C.;Mueller,R.O.SolarAvailability forWinterSpaceHeating:AnAnalysisof theCalendar Period,1953–1975;ArgonneNationalLaboratory:Argonne, IL,USA,1979. 4. Dahl,M.;Brun,A.;Kirsebom,O.;Andresen,G. Improvingshort-termheat loadforecastswithcalendarand holidaydata.Energies2018,11, 1678. [CrossRef] 5. Vitullo, S.R.; Brown, R.H.; Corliss, G.F.; Marx, B.M.Mathematical models for natural gas forecasting. Can.Appl.Math.Q.2009,17, 807–827. 6. Ishola, B. ImprovingGasDemand Forecast during ExtremeCold Events. Master’s Thesis, Marquette University,Milwaukee,WI,USA,2016. 7. Haida,T.;Muto,S.Regressionbasedpeakloadforecastingusingatransformationtechnique. IEEETrans. PowerSyst. 1994,9, 1788–1794. [CrossRef] 190