Page - 145 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2080 thisparameter,as it isassociatedto itsability tomodelnon-linearbehaviors.Anetworkwitha low numberofneurons in itshidden layerwouldfail to learncomplex,non-linear relationsbetween input andoutput. On theotherhand, thenumberofneurons increases the computationalburdenof the trainingandforecastingprocessand, therefore it shouldbeminimized if thesystemisworkingonline andhasaresponse timelimit. Inaddition, theneuralnetworktrainingalgorithmreliesonarandominitializationof theneurons’ weights. Therandomnesscauses thenetwork’soutput tocontainarandomcomponent. Inorder to minimizetheeffectof thisrandomness, theworkingmodel includesaredundantdesign. Eachnetwork is replicatedn times toobtainndifferentoutputs foreachforecast. Thefinaloutput isobtainedthenby discardingthe lowestandhighestvaluesandaveragingtherest. Increasing thenumberof replicas costsa linear increaseof computationalburdenwhile it reduces therandomnessof theoutputand reduces thevariabilityof theoutput,minimizingthemaximumerrorofa forecastedperiod. The response timeof the system is a critical feature. If the forecast is not producedon time, thenthewholeeffortcouldbeuseless. Inorder totesthowthelimitof timeresponseaffects themodels thenumberofneurons is set from3to20andthenumberof redundantnetworks from3to25.As the neural networkmodel is the onewithhigher computational burden it is the only one affectedby this limitation. 2.2.5. FrequencyofTraining As itwill be furtherdiscussed inSection3, the loadseries evolveover timedue tochanges in factors like economic growth or shifts in consumer behaviors. This causes forecastingmodels to becomeobsolete if thedatausedduring trainingno longer follows the current trends. Therefore, inorder tokeepupwith loadshiftingbehavior, forecastingmodelsneedtobe frequentlyretrained withnewdata. The trainingprocessmayhaveheavycomputational requirements thatmake itunpractical to increase frequencyneedlessly. Therefore, theperiod inbetweentrainings isa factor thatmayalter the accuracyof themodel. In this research, bothARandNNmodels have been testedwith training frequencies of 3, 6, 12and24months. Ineachof these tests, all sub-modelswere retrainedusing themost recentdata. Inaccordancewith this, for frequencieshigher than12months, thesimulationperiodofoneyearwas split intoseparateblocksas theTable1shows. Toevaluate theresults, allblocks fromeachfrequencyareaddedtogether intoasingleone-year period and the corresponding Root Mean Square Error (RMSE) is calculated for both AR and NNmodels. Table1.Trainingandsimulationperiodsusedfor testing theeffectof trainingfrequency. Frequency(Months) Block TrainingPeriod SimulationPeriod Start End Start End 3 1 1 January2010 31December2016 1 January2017 31March2017 2 1April2010 31March2017 1April2017 30 June2017 3 1 July2010 30 June2017 1July2017 30September2017 4 1October2010 30September2017 1October2017 31December2017 6 1 1 January2010 31December2016 1 January2017 30 June2017 2 1 July2010 30 June2017 1July2017 31December2017 12 1 1 January2010 31December2016 1 January2017 31December2017 24 1 1 January2009 31December2015 1 January2017 31December2017 145