Page - 187 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2008 as targetoutputs,andasetof featuressuchas temperature,windspeed,dayof theweek,andprevious loadsareusedas the inputs.After thebackpropagationtraining, theDNNfunctions identically toa largeANN. 5.Data Onecommonproblemwith trainingany typeofneural network is that there is always some amountof randomness in the results [27]. Thismeans that it is difficult toknowwhether a single trainedmodel isperformingwellbecause themodelparametersaregoodorbecauseof randomness. HansonandSalamonmitigatedthisproblemusingcrossvalidationandanensembleofsimilarneural networks [27]. Theytrainedmanymodelsonthedifferentpartsof thesamesetofdataso that they couldtest theirmodelsonmultiplepartsof thedata. This paper mitigates this problem by using data sets from 62 operating areas from local distributioncompaniesaroundtheUnitedStates. Theseoperatingareascomefrommanydifferent geographical regions includingtheSouthwest, theMidwest,WestCoast,Northeast, andSoutheastand thusrepresentavarietyofclimates. Thedatasetsalso includeavarietyofurban, suburbanandrural areas. Thisdiversedatasetallowsforbroaderconclusions tobemadeabout theperformanceof the forecastingtechniques. Foreachof the62operatingareas, severalmodelsare trainedusingat least10yearsofdata for trainingand1year for testing. The inputs to thesemodelsare thosediscussedinSection2. Thenatural gasflowisnormalizedusingthemethodproposedbyBrownetal. [28].All theweather inputs in this experimentareobservedweatherasopposedto forecastedweather for thesakeofsimplicity. 6.Methods Thissectiondiscusses themodelsat thecoreof thispaper. Fourmodelsarecompared: a linear regression(LR)model [5], anANNtrainedasdescribedinReference [26], andtwoDNNstrainedas described inSection3. ThefirstDNNisashallowneuralnetworkwith thesamesizeandshapeas the ANN.TheotherDNNismuchlarger. TheANNhas two hidden layers of 12 and four nodes each and is trained using aKalman filter-basedalgorithm[29]. ThefirstDNNhas the samearchitectureas theANNbut ispretrained using contrastive divergence. The purpose of using thismodel is to determine if the contrastive divergencealgorithmcanoutperformtheKalmanfilter-basedalgorithmonthese62datasetswhenall othervariablesareequal. EachRBMis trainedfor1000epochs,and20epochsofbackpropagationare performed.Despite its small size, thecontrastivedivergence trainedneuralnetwork is referredtoasa DNNtosimplifynotation. Inadditionto thesemodels,whichrepresent thestate-of-the-art inshort-termloadforecasting ofnaturalgas,a largeDNNwithhiddenlayersof60,60,60,and12neurons, respectively, is studied. Thepurposeof thismodel is to showhowmuch improvement canbemadebyusing increasingly complexneuralnetworkarchitectures.All forecastingmethodsareprovidedwith thesameinputs to ensurea fair comparison. 7.Results Toevaluate theperformanceof therespectivemodels,weconsideredseveralmetrics toevaluate theperformanceofeachmodel. Thefirstof these is therootmeansquarederror: RMSE= √√√√ 1 N N ∑ n=1 [sˆ(n)−s(n)]2, (11) for a testing vector of lengthN, actual demand s, and forecasteddemand sˆ. RMSE is a powerful metric for short-term load forecastingofnatural gasbecause it naturallyplacesmorevalueon the 187