A new approach to seasonal energy consumption forecasting using temporal convolutional networks

Zayed University Zayed University

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9-1-2023

A new approach to seasonal energy consumption forecasting A new approach to seasonal energy consumption forecasting using temporal convolutional networks

using temporal convolutional networks

Abdul Khalique Shaikh Sultan Qaboos University Amril Nazir

Zayed University Nadia Khalique

Sultan Qaboos University Abdul Salam Shah Universiti Kuala Lumpur Naresh Adhikari Slippery Rock University

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Shaikh, Abdul Khalique; Nazir, Amril; Khalique, Nadia; Shah, Abdul Salam; and Adhikari, Naresh, "A new approach to seasonal energy consumption forecasting using temporal convolutional networks" (2023). All Works. 5947.

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Results in Engineering 19 (2023) 101296

Available online 17 July 2023

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Results in Engineering

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Research paper

A new approach to seasonal energy consumption forecasting using temporal convolutional networks

Abdul Khalique Shaikh

^a,∗

, Amril Nazir

^b

, Nadia Khalique

^a

, Abdul Salam Shah

^c

, Naresh Adhikari

^d

aDepartmentofInformationSystems,SultanQaboosUniversity,Muscat,123,Oman

bDepartmentofInformationSystemsandTechnologyManagement,ZayedUniversity,AbuDhabi,144534,UnitedArabEmirates

cDepartmentofComputerEngineering,UniversityofKualaLumpur(UniKl-MIIT),KualaLumpur,50250,Malaysia

dDepartmentofComputerScience,SlipperyRockUniversity,1MorrowWay,SlipperyRock,PA 16057,USA

A RT I C L E I N F O A B S T R A C T

Keywords:

Energyforecasting Seasonalenergy Smartgrids

Temporalconvolutionalnetworks

Therehasbeenasignificantincreaseintheattentionpaidtoresourcemanagementinsmartgrids,andseveral energyforecastingmodelshavebeenpublishedintheliterature.Itiswellknownthatenergyforecastingplays acrucialroleinseveralapplicationsinsmartgrids,includingdemand-sidemanagement,optimumdispatch,and loadshedding.A significantchallengeinsmartgridmodelsismanagingforecastsefficientlywhileensuringthe slightestfeasiblepredictionerror.A typeofartificialneuralnetworkssuchasrecurrentneuralnetworks,are frequentlyusedtoforecasttimeseriesdata.However,duetocertainlimitationslikevanishinggradientsand lackofmemoryretentionofrecurrentneuralnetworks,sequentialdatashouldbemodeledusingconvolutional networks.Thereasonisthattheyhavestrongcapabilitiestosolvecomplexproblemsbetterthanrecurrent neural networks.Inthis research,a temporalconvolutionalnetwork isproposedtohandle seasonalshort- termenergyforecasting.Theproposedtemporalconvolutionalnetworkcomputesoutputsinparallel,reducing thecomputationtimecomparedtotherecurrentneuralnetworks.Furtherperformancecomparisonwiththe traditionallongshort-termmemoryin termsof MADandsMAPEhasprovedthatthe proposedmodel has outperformedtherecurrentneuralnetwork.

1. Introduction

Differentsmartcityinitiativesbygovernmentandprivateorganiza- tionshaveincorporatedinformationandcommunicationtechnologies (ICTs)tomeetcities’growingchallenges.Internationalpoliciesandsci- entificliteraturehavewidelyembracedthesmarthomes,smartgrids, andoverallintelligentcityconcept.Thisconceptmakescitiessmarter for citizensbyutilizingmany ICTinnovationshitting usalarmingly.

Accordingtoscientificevidence,smartcitiesarebasedonthefollow- ing foundational theories: ICTs, urbanplanning, environmental con- siderations,living labs,andcreativeindustries[16]. Inaddition,the associatedconceptsillustratehowICTcanassistinaddressingalmost everyurbanchallenge.ThelatestICTtrendsidentifiedintheliterature analysisaresmartgrids,IoT,bigdata,opendata, ande-government [20,32,45].Thetopicofconsiderationforthisstudyissmartgrids.The world’surbanpopulationmakesupabouthalfofthetotalpopulationof theentireplanet[59].Citiesareincreasinglycrowded,resultinginde-

*

Correspondingauthor.

E-mailaddress:shaikh@squ.edu.om(A.K. Shaikh).

cliningqualityandquantityofservicesfortheirresidents.Theincreased populationhascausedchallengesfortheenergysectortoproduceen- ergyasperfuturedemand[12].Thepredictionofenergyconsumption isessentialforeffectivedemand-sidemanagement.

Themodelsofenergyconsumptionpredictionmostlyusestatistical andmachinelearningmodels[1,46].Thepreviouslyrecurrentneural network-basedmodelshavebeenappliedforshort-termenergypredic- tion,whiletheseasonalfactorhasnotbeenconsidered[34].Traditional statisticalmodelshaveperformedbetterwiththesmallamountofdata, buttheenergyconsumptiondatahasdrasticallyincreasedwiththein- creaseintheurbanpopulation[41].Thestatisticalmodelshavecertain limitations;hencethedeeplearningmodelshavebeenwidelyadopted tohandlethetimeseriesenergyconsumptiondata.Recurrentneural networksareessentialalgorithmsforforecastingenergyconsumption [40].Theothermostprominentalgorithmsaretemporalconvolutional neuralnetworks(TCNs).Thegovernmentsfocusonprovidingeffective

https://doi.org/10.1016/j.rineng.2023.101296

Received31March2023;Receivedinrevisedform10July2023;Accepted11July2023

Results in Engineering 19 (2023) 101296

2 A.K. Shaikh, A. Nazir, N. Khalique et al.

solutionstothepeopleforacomfortablelife.Intermsofcomfort,the heating,ventilation,andairconditioning(HVAC)systeminanyhouse plays significant importance, andpeopleare readytospendenough for abetterstandardof HVAC.Themaintenanceof HVACstandards requiresenoughamountofenergytobeproducedbythesmartgrids [29,47].Energyproductionalwaysremainsacostlysolution;hencere- searchershavefocusedonanalternativeforenergyproduction.Based on historical energyconsumption data, thedeep learningprediction modelscanavoidenergywastageandproductionoftheexactamount inthegridenvironment[39].

The prediction methods remainedtypical for future energycon- sumption forecasting in the smart grids. Deep learning, specifically recurrentneuralnetworks,successfullymanagedtheextensiveenergy consumption data.Themost commonproblemwithrecurrentneural networksisthevanishinggradientsandlackofmemoryretention[9].

Thetemporalconvolutionalnetworks (TCN)haveastrongcapability tohandlesequentialdata.Thispaperproposesanenergyconsumption predictionmodelusingaTCN.Intraditionalmodels,energyconsump- tionforecastsarebasedontheoverallpatterns,whileseasonalpatterns vary;hence,anapproachforseasonalenergyconsumptionforecasting isneeded.TheperformancecomparisonwiththeLSTMhasprovedthat thetemporalconvolutionalnetworkcanhandlethetimeseriesdatabet- ter.

Thereareseveralbenefitsassociatedwiththismodel.

• TCNsolvesthevanishinggradientandmemoryretentionproblem, reducingcomputationtimeforeffectiveenergyconsumptionman- agementthroughparallelcomputation.

• ComparedtoatraditionalRNN,TCNstrainandevaluatelongin- putsequencestogetherratherthansequentiallyandmaintainthe customer’sseasonalenergyconsumptionpatternsovertime.

• SinceTCNfiltersonlyshareasingleback-propagationpathamong layers,theyareanexcellentalternativetoRNNsforsequencesof arbitrarylength.

• Differentperformanceevaluationindicatorsareusedtodetermine howwelltheproposedTCNprocedureperformsandsomeconven- tionalmethods,suchasLSTM.

Theremainingpaperisorganizedas:section2providesrelatedwork, section 3containsresearch designandmethodology.Theresultsare presentedinsection4,thediscussioninSection5,andfinallythecon- clusionispresentedinsection6.

2. Relatedwork

The traditional methodsof energyconsumption forecasting have used deep learningandrecurrentneuralnetworks,along withother machinelearningalgorithms.Deeplearningsignificantlyimprovedthe prediction intimeseriesdataassuggestedin asurveyconductedby Torreset al. [43].Thefocusincludesthesmartgriddemandsideman- agementandenergyconsumptionpredictionatsmarthomes.Themost recentmodelusedNBEATSfortheenergyconsumptionforecastingof multiplecustomersinasmartgridenvironment[40].Themodelhas performedbetter,butithasnotconsideredtheseasonalfactorofthe energy consumptionprediction. Deeplearningremainssignificant in optimization-basedstudiesfocusingonenergyoptimizationwhileim- provingthecomfortindex[14].Theneuralnetwork-basedmodelshave handledtheenergypredictionproblemtosomeextentwithhigherac- curacybuthavefailedtotacklethecomplexseasonalpatternsofthe data[13].Unlikethetraditionalmodel,thedeepgenerativeshort-term loadforecastingmodelbyLangevinet al. [21] usedtheappliances’en- ergyconsumptionconsumedin thepastandthefutureconsumption.

Thefocusonappliances’energyconsumptionbenefitsmorethanhis- toricalforecasts.

Additionally,Wahid et al. [48] proposesamulti-layer perceptron andrandomforesttechniqueforclassifyingbuildingsashighor low

powerconsumers.TheMLPremainscomputationefficientforsmaller datasets;hencemanyauthorspreferitoverdeeplearningmodelswhile havingsmallerdatasets.Oldewurtelet al. [35] usedindoorweatherpre- dictiontousethethermalcapacityofbuildingsefficientlyusingmodel predictivecontrol(MPC).Theweatherpredictionaimedtoavoidusing high-costactuatorsandreducewaste. Zenget al. [57] usedahybrid approach based on an extremelearning machine andswitching de- layedparticleswarm optimization (SDPSO)algorithm forshort-term load forecasting. The SDPSO has the enhanced capability of global searchingtoreachtheoptimalsolutionforoptimizinghiddennodepa- rametersoftheextremelearningmachine.Liet al. [26] evaluatedthe impactofnonlinearityandresponsetimeontheaccuracyofthesystem identificationprocessoftheenergyforecastingmodelforbuilding.The modeltriedtosolvethescalingproblemsofbuildingsbecausetheper- formanceofthesystemsdesignedforsmallcommercialbuildingswas notsatisfactorywiththelargerbuildings.Byaddingelectricvehicles, themodeldevelopsapower-pollutiondynamicloaddispatchalgorithm thatsolvesamulti-objectiveoptimizationprobleminanattempttore- duceboth fuelcostsandpollution emissionsatthesame time[51].

ThemodelbyAraghianet al. [4] optimizeseconomicanddiscomfort metricsthroughintegratedenergymanagement.Residents’dissatisfac- tionwithindoortemperaturesismeasuredusinganovelmetriccalled discomfortdegree-day,whichtakesbothmagnitudeanddurationinto account.Thehybridshort-termenergyconsumptionmodelbySekhar andDahiya [38] useddifferentrecurrentnetworksandthegraywolf optimizationalgorithm.

Theoptimizationalgorithmhasbeenutilizedtoselecttheoptimal parametersofBi-LSTMandCNN.Aneffectivetimeseriesfeatureex- tractionmethodisbasedonaone-dimensionalCNN.Basedonaneural networkwithalearningprocesscontrolalgorithm,a methodisdevel- opedforpredictingwindspeedinanisolatedpowersystem.Anhourly retrospectivemeteorologicaldatasetofwindspeedobservationsisused tomakepredictionsforfourseasonsthroughouttheyear[28].Modeling ofrenewableenergysources,energystoragedevices,electricvehicles, anddistributedgenerationsystemswasconductedheretooptimizethe managementofaVPP.Aswellastheforecastingofwindspeed,electric- ityprice,loaddemand,andthebehaviorofelectricvehiclesisexamined byusingamethodbasedontwo-waylongshort-termmemorynetworks [2].Animprovedmethodisproposedinthispaper,whichusesatwo- stageprocesswhichcanbeusedtoforecastgridloadatthesystem-wide level.Thefirstbenefitofthismethodisthatitreducestheoriginalnet loadbyremovingthelow-frequencycomponentswhoseenergyisquite insignificant[58].

This paperproposes anapproach forselecting theoptimalsetof featuresforshort-termloadforecasting(STLF)problemsusinghybrid featureselection(HFS).TheHFSusesahybridgeneticalgorithm(EGA) combinedwitharandomforestmethodasacomponentofits online featureselectionalgorithm,combiningtheelitistgeneticalgorithmand randomforestmethods[42].Thesmartgridenergyoptimizationmeth- odsusingdeeplearningarepresentedinthispaperusingthenewtype of wild horseoptimization algorithm[31]. Theresults of this study demonstratethatthereshouldbeaconsiderationofthefactorsthataf- fectthegenerationofrenewableenergy,alongwithaqualitativemodel forhowthegenerationofrenewableenergywillaffectelectricityprices.

Thismodelisbasedonrandomforestsandimprovedmahalanobisdis- tance[50].

Thestudy addressesthe challenge of impreciseenergy efficiency servicesandinsufficienthouseholdresponsetoenergyusethroughady- namicload-priorityschedulingstrategy[54].Modelpredictivecontrol- basedreinforcementlearningandShapleyvaluesareusedinthispaper toproposeanenergymanagementstrategyforresidentialmicro-grid systems[7].ThemodelproposedbyVelimirovi´cet al. [44] isanevident exampleoftheentropy-basedfuzzymodelsfortheproblemofshort- termenergyforecasting.Toestimatetheenergyproduction,twodiffer- entapproacheswereusedduringtheanalysis:thefirstuserdataand artificialintelligencetechniquestoestimateenergyproduction,specifi-

callymultilayerperceptronsinconjunctionwithradialbasisfunctions;

andthesecondusedmodelstoestimateenergyproduction[11].This paperpresentsanovelencodingmethodbasedonneuralordinarydif- ferentialequationsthatcanbeviewedascontinuousresidualnetworks (ResNets)forlearningtimeseriesdynamicsofelectricityload[18].

Thisstudyproposesacombinedframeworkforsolvingtheproblem oflowpredictionaccuracyinelectricityloadforecastingwithamodi- fiednoiseprocessingstrategy,a multi-objectiveoptimizationalgorithm, anddeepneuralnetworkstoresolvetheproblemoflowpredictionac- curacy [52]. Severalefficient algorithms have been applied toDSM methodology for a residentialcommunity that aims to reduce peak energy consumption, including binary orientation search algorithms (BOSA),cockroachswarmoptimization(CSO),andsparrowsearchal- gorithms(SSA).A smartgridDSMoptimizedonalgorithmswillreduce electricityconsumptioncostswhileincreasingsmartgridefficiency.Us- ingaload-shiftingtechnique,theproposedDSMmethodologyisableto achieve theabove objective.Usingrenewableenergysourceson-site, theproposedsystemwillreduceelectricitycostsandreducepeakingat powerplants[19].Alrwashdeh [3] conductedstudyconsideringlocal climate,averagemonthlyenergyconsumption,andelectricityratesin Jordantodeterminethemostprofitablewaytoinstallaphotovoltaic (PV)systemonaresidentialbuilding.

Thisreviewaddressesseveraldimensions,butmajorityofthestud- ies haveconsideredthenormalenergyconsumptionforecasting.The divisionsbaseonshort,mediumandlongtermpredictions.Energystor- agehasalwaysbeenviewedascriticalinreducingenergycosts.Asa partofthestudies,greenenergywasalsoconsideredfromapollution reductionperspective.Inmostpredictionproblems,deeplearningand reinforcementlearningtechniqueshavebeenusedtobuildmodels.The implementationofasmartgridrequiresdevelopingamodeltopredict energyaccordingtotheseason.

3. Researchdesignandmethodology

Mostofthemodelsarebasedonsyntheticdata,whichmeansthey do not accuratelyreflect the real smartgrid environment andoften don’t perform wellwhenimplemented.The proposedstudyis based on different experiments using theenergyconsumption dataset.The modelhasthreemainlayers,i.e.,pre-processing,prediction,andperfor- manceevaluation.Theexperimentaldesignisbasedonseasonalenergy consumption,wherethemodelpredictsthefourseasons’energycon- sumptionbasedonhistoricaldata.Thepre-processingstepsarehelpful fortheremovalofnoiseandirregularitiesinthedatawhilethemain responsibilityreliesonthepredictionmodule,wherethetemporalcon- volutionalnetworkpredictsenergyconsumption.

3.1. Databaseacquisition,pre-processinganddescription

Thedatasethasbeenacquiredhavingenergyconsumptiondatafor the customers of Londonhouseholds. Thesame data hasbeen used inourpreviousenergyforecastingmodel[34,40].Overthecourseof November2011toFebruary2014, datawascollectedfrom different householdcustomers.Theobjectiveoftheproposedmethodisseasonal energyconsumptionforecasting;henceafteranalysis,theunnecessary datahasbeeneliminated[10].Theproposedstudyconsiders150cus- tomers,withonlyseasonaldataof12monthsforeachcustomeranda dynamictime-of-usepricingstrategy(dToU).Theexperimenthasbeen carried out withdaily consumption datain kWh units. Thetraining datahas75%whiletherest25%usedtoevaluatethemodelintermsof theprediction.Byusingthemovingaverage,themodelhasbeenable toeliminatetheoutliersthatcauseloweraccuracy.UsingthePython packageNumPy,outliershavebeenidentifiedasobservationsloweror higherQ1+1.5IQR[34,40].Weused(1) and(2) tonormalizeand denormalizethedataintoa0–1scale.

𝑁(𝑎) = 𝑥(𝑎) − min(𝑎)

max(𝑎) − min(𝑎) (1)

Table 1

ParametersettingofLSTMandTCN.

Parameter LSTM ConvolutionalNetwork

(Temporal)

Activation function ReLU ReLU

Hidden Dim/Size/Widths 10

Number of Layers 1 6

Random State 42 0

Training length/Input chunk length 30 30

Output chunk length 15 15

No of epochs val period 1

Batch size 32 512

Learning rate 1–3 1–3

Epochs 150–250 200–250

Dilation base 2

Kernel Size 5

Number of Filters 3

Dropout rate 0.1 0.1

Future/Past covariates Day Series Day Series

𝐷(𝑎) =𝑁(𝑎) ∗ (max(𝑎) − min(𝑎)) + min(𝑎) (2) Wherethedataafternormalizationhasbeendenotedby𝑁(𝑎),once thetrainingiscompletedandthedataisdenormalizedanddenotedas 𝐷(𝑎).Thedataunderconsiderationforthenormalizationisrepresented as𝑥(𝑎).These conversionsuse theminimumandmaximumvaluesof thedatasetdenotedbymin(𝑎)andmax(𝑎)respectively.

3.2. Predictionmodule

Thepredictionmodulecontainsatemporalconvolutionalnetwork that takes the pre-processed input data of energy consumption and trainsthenetwork.TheTCN providesvariousadvantagesover tradi- tionalconvolutionalneuralnetworks(CNN).Incomputervision,con- volutionalneuralnetworksarecommonlyusedtorecognizeandclassify objectsinimagesorvideos.Basedonstudiesofthevisualcortex,con- volutionalneuralnetworkswerefirstproposedin1979.Recently,ithas beenusedforpredictiontasksinvariousareas,includingweatherand energyconsumptionprediction.Convolutionalneuralnetworks(CNNs) canhandlesequentialdatawithtemporalaspectsandlargereceptive fields; however, temporalconvolutional networks dependon casual convolutionsanddilations.Asaresultofitsinherentlimitations,CNNs areunsuitablefortime-seriespredictionduetoconstraintssuchasa fixed-sizeinputvectorandinconsistentinputandoutputsizes[15,24].

At the sametime, the TCN resolves thelimitations of CNN models andremains suitablefor theproposed energy consumptionforecast- ingmodel.Asacrucialfactorindefiningneuralnetworks’architectural configuration,thenumberofhiddenlayersbecomescriticaltothefinal result.Thenumberoflayersindeeplearningnetworkshasbeenwidely acknowledgedasanimportantfactorincapturingintricatefeaturesand achievingrelativelyhighaccuracylevels.Toenhanceperformance,ad- ditionallayersarecommonlyaddedtoneuralnetworkstoincreasetheir size[25].Intheproposedmodelwehaveusedrandomsearchasitcan bearguedthatrandomsearchisafundamentalimprovementovergrid search.The hyper-parametersareexploredrandomizedtodetermine potentialparametervaluesbysamplingfromspecificdistributions[30].

Assoonasthedesiredlevelofaccuracyisreached,thesearchprocess continues.Randomsearchhasconsistentlyproducedbetterresultsthan gridsearch, despitebeing similartoit,althoughitis similartogrid search.TheparametersselectedforTCNandLSTMalgorithmscanbe seeninTable1.

PyTorchforecastingisusedtoimplementTCNinthemodel.Input chunksareusedaspastcovariates,andoutputchunksareusedasfu- turecovariates[27].Futurecovariatesareusedasmandatoryinputsfor multi-headattentionqueries.Furthermore,encoderswereusedtoauto- maticallygeneratethedaycovariates(futurecovariates)inadditionto thepastcovariates.

Results in Engineering 19 (2023) 101296

4 A.K. Shaikh, A. Nazir, N. Khalique et al.

Fig. 1.Proposed TCN model.

3.2.1. Temporalconvolutionalnetwork(TCN)

Like traditionaldeeplearningnetworks,the convolutionalneural networksalsocontainthreeprominentlayers,i.e.,input,hidden,such astheconvolutionallayer,andanoutputlayer.Theinputandoutput layersizedependsonthenumberofinputvariablesanddesiredoutput variable.Thedetailsoftheselayershavealreadybeendefinedinthe Table 3. IntheproposedTCNmodel,thehiddenlayersareresponsi- blefortheconvolutions.Theconceptofconvolutioniscommonlyused inmathematics,whereitreferstotheconversionoftwofunctionsinto a new functionthat expresseshow onefunction’sshape is modified byanother[37].Tocalculatetheintegraloftheproductoftwofunc- tions,oneofwhichisreversedandshifted,itisnecessarytotaketwo functionsandcalculatetheintegraloftheirproducts.Usingtheconvo- lutionfunction,wecanexpresshowonefunctionchangestheshapeof another.Theconvolutionissimilartocross-correlationinvolvingtwo similar seriesor sequences[36].Itis thehiddenlayers thatperform computations,whileitisthepoolinglayersthatconsolidateandcollect theresultsfromthehiddenlayers.Constructingafullyconnectedlayer mapstheinputandoutputvaluesusinganonlinearfunction.Inaddi- tiontoRNNs,TCNshavecostorlossfunctionsthatareminimizedto reduceerrorsinprediction[17].IntheTCN,theinputnode’sreceptive fieldisalsoknownasapatchincomputervisionterminology.Inputsare receivedfromalimitedareaofthepreviouslayerofthenetwork,the node’sreceptive field.A featuredetectionalgorithmprimarilyworks byapplyingfilterstotheinputtomakedetectingthefeatureseasierfor theTCN.Thesefiltersaremadeupofneuronsornodes[55].Similarly, somefiltersconnecttootherfeatures.Itisessentialtoisolatethetrend orseasonalityofatimeseries.Duringtraining,theTCNcalibratesthe filters’valuesbasedonthelossfunctiontominimizepredictionerror.

Usingthefilterslearned,theTCNpredictsfutureenergyconsumption.

Trendandseasonalitypatternscanberecognizedbyitwhendealing withtimeseries[8].Featuremapsaregeneratedbythenodes,indicat- ingwherefeaturesarelocated.A filterscansaninputpatchtocheck ifthefeatureispresent.A featuremapiscreatedbasedontheresults.

A kernelisanarrayofweightsarrangedintwodimensions.Astheker- nelmovesthroughareceptivefield,itdetectsthefeatures[33].The

strideofthefilterdetermineshowfaritmovesacrosstheinput.Anac- tivationfunctionisappliedtotheextractedfeaturesbyfullyconnected layers.Nodesinthislayerreceiveinformationfromnodesinprevious layers,soitsnamearisesfromconnectingthemall:inafullyconnected layer,a nodereceivesinformationfromallthenodesinpreviouslay- ers[56]. Throughthefullyconnectedlayer,featuresofearlierlayers aretied togetherinatypicallynonlinearmanner.TCNslearntosort outunimportantfeaturesfromessentialoneswithsuccessivetraining epochs –feed-forwardfollowedbyback-propagation.TheTCNensures causalconvolution.Valuesatthebeginningoftheinputsequencemust determineanoutputvalue.A TCNdilationexpandsanode’sreceptive fieldtoencompass moreperiods of history[23,53]. A typical resid- ualblockofTCNcanbeseeninthefollowingFig.1.Thecomputation andmathematicalexpressionsofthelayersandresidualblockhasbeen adoptedfromBaiet al. [5], Lässig [22].

Ifwehaveone-dimensionalsequenceinput𝑋∈𝑅^𝑛 havingafilter 𝑓∶ {0,…,𝑘−1}→𝑅,wecandefinethe𝐹_𝑠dilatedconvolutionoperation asin(3).

𝐹(𝑠) = (𝑋∗𝑑𝑓)(𝑠) = Σ^𝑘_𝑖=0⁻¹𝑓(𝑖)⋅𝑋𝑠−𝑑⋅𝑖 (3) Thedilationfactorcanbedefinedby𝑑,thefiltersizeisrepresented by𝑑,andthedirectionofthepastisdenotedby𝑠−𝑑⋅𝑖asdefinedin (4).

𝑑_𝑖= 2^𝑖,1≤𝑖≤𝑛 (4)

Generalizing,a 1Dconvolutionalnetworkwith𝑛layersand𝑘ker- nelshasareceptivefield𝑟asin(5).

𝑟= 1 +𝑛∗ (𝑘− 1) (5)

Wecan calculatethenumberof layers𝑛by settingthereceptive fieldsizetoinputlength𝑙asin(6).

𝑛=

⌈(𝑙− 1) 𝑘− 1

⌉

(6)

Fig. 2.Comparison of spring season energy consumption.

Bycomputing𝑑asafunctionof𝑖,wecancomputethedilationofa particularlayerbasedonitsdilationbaseinteger𝑏asin(7).

𝑑=𝑏∗∗𝑖 (7)

Wherein𝑖representsthenumberoflayers.Asaresultoftheseobserva- tions,wecancalculatehowmanylayersournetworkneedstoprovide fullhistoricalcoverage.Ifwetakeakernelwithsizek,a dilationbase b,wherekforeachbaseequalsb,andaninputlengthl,thenwecan statethefollowinginequalityusing(8).

1 + (𝑘− 1). 𝑏^𝑛− 1

𝑏− 1 ≥𝑙 (8)

Theminimumnumberoflayersrequiredcanbecalculatedbysolving for𝑛using(9).

𝑛=

⌈ 𝑙𝑜𝑔_𝑏

((𝑙− 1).(𝑏− 1) (𝑘− 1) + 1

)⌉

(9) Wecancomputethenumberofzero-paddingentries𝑝neededfor ourcurrentlayergiventhedilationbase𝑏,kernelsize𝑘,andthenumber oflayersbelowitusing(10).

𝑝=𝑏^𝑖.(𝑘− 1) (10)

Basedondilationbase𝑏andkernelsize𝑘𝑥𝑏,wecancomputethe totalsize𝑟ofthereceptivefield𝑟foraTCNusing(11).

𝑟= 1 +

∑𝑛−1 𝑖=0

2.(𝑘− 1).𝑏^𝑖= 1 + 2.(𝑘− 1). 𝑏𝑏^𝑛−1− 1 (11) Thus,therewillbeaminimumnumberofresidualblocks 𝑛forafull historycoverageofinputlength𝑙asin(12).

𝑛=

⌈ 𝑙𝑜𝑔_𝑏

((𝑙− 1).(𝑏− 1) (𝑘− 1).2 + 1

)⌉

(12) The^𝑡ℎlayerofthenetworkhasbeendenotedby𝑖totaldilatedcon- volutionallayersarerepresentedbythe𝑛asin(13).

𝑘𝑖+1=𝑑𝑖∗ (𝑘𝑖− 1) + 1,1≤𝑖≤𝑛, 𝑘1𝜖𝑁^∗ (13) The ^𝑡ℎ layer of the networkhas been denoted by 𝑖total dilated convolutionallayersarerepresentedbythe𝑛.Datasituationsusually determinetheinitialsizeofthefilter,thedefaultis𝑘_𝑖= 2.However,it canbeadjustedtoothervaluesifnecessary.

3.3. Performanceevaluationmetrics

For time seriesdata, thesmaller the error value, the better the accuracywith themeanabsolutedeviation(MAD)[6,49]. Usingthe MADformula,a predictionismade,andtheactualvalueiscalculated atleastoneperiodahead.Inthefollowingequation,youcanseethe

MAD’smathematicalexpression(14).Theotherperformancemetricis thesMAPE,asexpressedin(15).

𝑀𝐴𝐷= 1 𝑁

∑𝑛 𝑖=1

|𝐴_𝑖−𝑚(𝑋)_𝑖| (14)

𝑠𝑀𝐴𝑃 𝐸=100%

𝑁

∑𝑛 𝑖=1

|𝑃_𝑖−𝐴_𝑖|

|𝐴_𝑖|+|𝑃_𝑖|

2 (15)

Where𝑚(𝑋)denoteaveragevalueofthedataset,𝑥𝑖isthedataval- uesintheset.The𝑁standsfortotalobservations,𝐴foractualvalues, and𝑃 forpredictedvalues.

4. Results

4.1. Seasonalpowerconsumption

Theproposedmodelaimstoforecastthesmartgrids’seasonalen- ergyconsumptiontoproduceenergyconsumptionperthecustomers’

seasonaldemand.Thedatasetforevaluatingtheproposedmodelbe- longs tothe customers of England, where typical weather has four seasons,i.e.,spring,summer,autumn,andwinter.Thespringseason startsfromMarchtoMay.Ifweobservethegraphofthespringsea- son,thehighestenergyconsumptionof randomlyselected customers is11 kWh.Hence,theLSTMandproposedTCNmodelhasperformed better,althoughtheactualenergyconsumptionhashigherfluctuations, andthemodelhasbeentrainedonenergyconsumptiondataofmul- tiplecustomershavingdifferentenergyconsumptionbehaviors;hence thereistheprovisionoftheimprovementinthegraphs.Overall,the LSTMgraphshowsthatithasstruggledwiththefrequentfluctuations ofenergyconsumption,whileontheotherhand,theTCNhasabetter energyconsumptiongraph.

IntheFig.2duringthespring,thetemperaturevariesbetween1 to30centigrade;henceboththeheatingandcoolingsystemsoperate.

WhilefromMarchtoMay,thehighesttemperaturekeepsincreasing.

Theincreasedtemperatureusuallycauseshigherenergyconsumption asmostresidentsstartoperatingcoolingsystemswhichisevidentfrom theabovegraph.ThesummerseasonstartsfromJunetoAugustandis consideredthetimeofoutingsandholidaysbymostresidents.While theweathermostlyremainshot,thesummer’senergyconsumptionis higherthaninspring,asseeninthegraph.Thehighesttemperature duringAugustmonthevenreaches38centigrade.Thehighestenergy consumptionduringthisperiodisduetothecoolingsystemsoperating inthehouses.

TheFig. 3forthe summer show thatduring June,thecustomer consumedhigherenergy,sotheLSTMandTCNhavepredictedhigher, whereinbothalgorithmshaveshownasimilar pattern,whichmeans thefluctuationsarechallengingforthealgorithms.Atthesametime, thehighestenergyconsumptioncan benoticedduringJuly.Theau- tumnseasonhasnormalweatherwherefromSeptembertoNovember,

Results in Engineering 19 (2023) 101296

6 A.K. Shaikh, A. Nazir, N. Khalique et al.

Fig. 3.Comparison of summer season energy consumption.

Fig. 4.Comparison of autumn season energy consumption.

Fig. 5.Comparison of winter season energy consumption.

thetemperaturegraduallyreduces;henceFig.4showsthesametrend as duringSeptembertheenergyconsumptionis highwhilewiththe passageofdays,itreducestotherangeof5to10kWh.Thereasonis typicalweatherandareductionintheusageofcoolingsystems.Here theLSTMandTCNalgorithmshaveshownbetterperformancewithlin- eargraphsofthesamepatternwithouttoomanyfluctuations.Overall, theTCNhasperformedbetterthanLSTM.

The winter lasts from December toFebruary, and most weather remainscold,withsnowandfrosteverywhere.TheFig.5showsacon- stantpatternofenergyconsumptionduringthesethreemonthsbecause most oftheusersoperateheatingsystemsduringthewinter,andthe systemsoperateforthedayandnight;hencethesameamountofen- ergyisconsumeddaily.Thegraphofpredictedenergyconsumptionby LSTMandTCNshowsthatbothalgorithmshaveperformedbetterwith thewinterseasonpredictionthantheotherthreeseasons.Thereason

isasimilarpatternduringthethreemonths.Soitisevidentthatdeep learningmightrequiremoredataforthesamecustomerstoperform withbetteraccuracy.

5. Discussion

AcomparativeanalysishasbeencarriedoutwiththeLSTMmodel compared to the proposed TCN model based on customers’ energy consumptiondatainEngland. Combiningthesedatahasenabled the proposedTCNmodeltobetestedandevaluated.Thereisnodoubtthat bothdeeplearningalgorithmscanhandleenergyconsumptionforecast- ingproblemsinasmartgridenvironmentwhenlookingattheMADand sMAPEerrorsofbothalgorithms.Theperformanceofbothalgorithms seemstodifferslightlyfromoneanother.Duetoitsstrongcapabilities andparallelcomputations,theTCNmodelhasperformedbetterinMAD

Table 2

ComparisonofseasonalMADandsMAPEerror.

Model Season

Spring Summer Autumn Winter

MAD sMAPE MAD sMAPE MAD sMAPE MAD sMAPE

LSTM 1.346 0.189 2.307 0.192 2.83 0.292 1.702 0.219

TCN 1.291 0.184 2.295 0.190 2.43 0.256 1.69 0.215

andsMAPE.Thereisalsoasignificantdecreaseintrainingtimeforthe TCN modelcomparedtotheLSTMmodel.AnevaluationoftheTCN basedonmodifiedparametershasbeenconductedtoevaluateitseffec- tiveness.Modificationshavebeenmadetoepochs,learningrates,batch sizes,andrandomstates.A closeexaminationoftheresultsrevealed thatthebatchsizedramaticallyimpactsthecomputationtime,andthe accuracyhasbeenreducedwithlargerbatches.Themoderateapproach was adoptedfortheexperimentationtoavoid theextracomputation time, eventhough theslowerlearningrateimproveditsignificantly.

Therewasanimprovementinaccuracyduetotheincreaseinepoch, butafteracertainlevelofadvancement,therewasnofurtherimprove- ment; asaresult,themaximumsizewasselectedoncetherewasno moreimprovement.A significantproblemwiththedatawasthatitfre- quentlyfluctuated,ultimatelycreatingchallengesforthedeeplearning algorithmsastheyattemptedtoanalyzeit.Althoughnormalizationwas applied,itwaslimitedtoacertainextenttokeeptheoriginalpattern ofenergyconsumptionsincethemodelwasdesignedforasmartgrid environment whereeach userconsumesenergydifferently.Sincethe modelusesbatchsizes,ithascertainlimitations;therefore,ifnewdata isaddedtoitinfuturework,ithastoberetrained.Asnewdataisadded toamodelinrealtime,theweightsandbiaseswillbeupdated,andthe modelwillberetrainedtopredictdatainlinewiththecustomer’sre- quirements.

5.1. ComparisonofMADandsMAPEerrors

TheperformancecomparisonoftheproposedseasonalTCNmodel withtheLSTMhasbeencarriedout,wherethedatahasbeendistributed accordingtothefourseasons.TheMADbyLSTMduringspringmonth is1.346andsMAPE0.189,whiletheTCNmodelhasperformedbetter withslightlylesserror.ThereasonisthattheTCNmodelcanobserve thetrendsinlargedatasets.Thereisaveryslightimprovementinthe sMAPEerror.TheLSTMandTCNbothhavestrongcapabilitytotackle thepredictiontasks.ThesummerseasonhasslightlyhigherMADand sMAPEerrorsbytheLSTMcomparedwiththespringseason.Therea- son isthattherearefluctuations inthetemperatureduringsummer;

hencetheenergyconsumptionbehavior ofthecustomerschangesac- cordingly. Mostusers operatecooling systemsduring theday while nighthasstandardenergyconsumptionpatterns;therefore,thefluctu- ationsintheenergyconsumptionhavecausedchallengesfortheLSTM andTCNmodels.Autumnhasasimilarrangeoferrordifferences,al- thoughithasincreasedcomparedtothesummerduetothesamereason ofdifferentiationintheenergyconsumptionbehaviorbytheresidents ofhomes.Tables2and3showtheTCN’ssmallesterrorscalecompared tothefourcomparativemethods.

Thewinterseasonhasagainnormalizedtheerrordifferencebecause theenergyconsumptionpatternremainsthesamethroughouttheday while itmayreducefurtheratnight.SotheMADandsMAPEerrors havereducedcomparedtothesummerandautumnseasons.TheTCN modelhasperformedbetterwiththedataofallfourseasons;hencethe modelcanhandletheseasonaldataalongwiththenormaloverallor customer-basedenergyconsumptioninthesmartgridenvironment.

5.2. Comparisonofenergyconsumption

Table3providesanoverviewoftheperformanceoftheproposed TCNmodelintermsoftheactualenergyconsumptionvs.forecastby

Table 3

Comparisonofseasonalenergyconsumption.

Model Energy Consumption in kWh

Spring Summer Autumn Winter

Actual 647.89 1095.00 833.17 680.41

LSTM 694.03 1082.78 886.04 724.41

TCN 679.59 1099.03 869.92 723.77

theLSTM andTCN.Itcan be seenthat thecustomerhas consumed higherenergyduringthesummerduetohotweatherandtheoperation ofthecoolingsysteminsidethehomes. Theactualenergyconsump- tionduringsummerwas 1095.00,whiletheTCNhaspredicteditas 1099.03.Henceitcanbeconcludedthatforseasonalenergyconsump- tion,theLSTMandTCNmodelsarereliabletobeimplementedinthe smartgridenvironmentforfuturedemandprediction.Theadvantageof theTCNmodeloverLSTMisthatitcanhandlelargerdatasets,anddue toparallelcomputation, itcan providehigheraccuracy.Theautumn seasonalsohashigherconsumption;hence,theTCNandLSTMhave slightlypredictedhigherconsumptionthantheoriginal.Theautumn seasonalsohashotweather;therefore,peoplestilloperatethecooling systems,consuming considerableenergy.Thespring andwinter sea- sonshaveasimilarrangeofenergyconsumptionduetocoldweather comparedtothesummerandautumn;hencemostlyduringthewinter season,peopleoperateheatingsystemstomaintaintheinsideweather conditionsunderanacceptablerange.

TheperformanceanalysisshowsthattheTCNandLSTMhaveper- formedbetterwiththesummerdataduetoasimilarpatternofoper- atingelectricalequipment.Atthesametime,thereisenoughprovision toimprovetheresultsforthespring,autumnandwinter.Still,ifwe considerthethreemonthsdurationforeachseason,thedifferenceis acceptableandsmartgridscan avoidenough energyoverproduction usingtheproposedTCNandLSTMmodels.

6. Conclusion

Variousenergyconsumptionmodelshavebeenproposedinthelit- eraturefocusedonshort,mediumandlongtermenergyconsumption prediction.Duetolimitationsofthedata,mostmodelsdonotconsider theseasonalfactorforenergypredictions.Intraditionalrecurrentneu- ralnetworkbasedmodels,energyconsumptionhasbeenpredictedwith certainaccuracy,butthecomplexityofthedataremainsachallenge.It isdifficultforthealgorithmstoproperlytrainduetothenoiseandthe differentpatternsofenergyconsumptionamongthecustomers.Using temporalconvolutionalnetworks,wehavedevelopedaseasonalenergy forecastingmodelthatavoidstheseissues.Thismodelis newinthat itusesatemporalconvolutionnetworkaswellasaseasonalcompo- nent,astraditionalmodelsonlyconsidershort,medium,andlong-term forecastsofenergyconsumption.Forsmartgridenvironments,seasonal predictioncanbeusedinsteadofpredictingenergyconsumptionannu- allytoproduceenergybasedon theseasons.A comparisonof TCN’s performancewiththatofLSTMhasshownthatTCNgenerallyperforms betterthanLSTM.Withsmoothingofthedata,themodel’sperformance canfurtherbeimproved,buttheactualpatternofenergyconsumption willbeaffected.Ourfutureworkwillexaminehowsmoothingaffects energyconsumptiondatabycomparingactualwithsmootheddata.

Results in Engineering 19 (2023) 101296

8 A.K. Shaikh, A. Nazir, N. Khalique et al.

Real-timeforecastscanbeperformedusingTCNmodelsduetotheir ability to process data in parallel. The energy sector is particularly relevant,wherereal-timepredictionensuresstablepowersupply,opti- mizationofelectricitygrids,andmanagementofelectricitygrids.Grid stability, loadbalancing,anddemand responsecan be improvedus- ingTCNmodels.Solarandwindgenerationfromintermittentsources suchassolarandwindcanbeintegratedwiththepowergridbyusing TCNmodels.Gridoperatorscantakeproactivemeasurestomaintain grid stability byforecasting renewableenergyproduction accurately andbalancingsupplyanddemand.Itcanbeconcludedthattheprimary practicalimplicationsofTCNenergyforecastingmodelslieintheirabil- itytodeliveraccurate,real-time,andscalablepredictionsregardingthe consumptionandgenerationofenergyaswellasthedynamicsofthe energymarket.Toputforwardamoresustainableandefficientenergy future,thesemodelsempoweractorsandstakeholdersinvolvedinthe energyindustrytomake informedchoices, optimizeenergysystems, andreducecarbonemissions.

CRediTauthorshipcontributionstatement

The authorshereby confirmthat we allhave madea substantial contribution tocomplete this article.Amril Nazir: Ideageneration, methodologyand,engagedinwritingpaper.AbdulKhaliqueShaikh:

Methodology,writing,reviewingandediting.NadiaKhalique:proof- readingandstructuring.AbdulSalamShah:Experimentandresults.

NareshAdhikari:Guidanceandsupervision.Weallreadandapproved thefinalmanuscript.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinfluence theworkreportedinthispaper.

Dataavailability

Datawillbemadeavailableonrequest.

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