Page - 31 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 3.NumericalExamplesof theProposedSSVRCCSModel 3.1.DataSet ofNumericalExamples Todemonstrate thesuperioritiesof the tentchaoticmappingfunctionandseasonalmechanismof theproposedSSVRCCSmodel, thispaperuses thehalf-hourelectric loaddata fromtheQueensland regionalmarketof theNationalElectricityMarket (NEM,Queensland,Australia) [47],namedExample 1,andtheNewYorkIndependentSystemOperator(NYISO,NewYork,NY,USA)[48],namedExample 2. Theemployedelectric loaddatacontainsa totalof768half-hourelectric loadvalues inExample1, i.e., from00:3001October2017 to00:0017October2017. BasedonSchalkoff’s [49] recommendation that theratioofvalidationdataset to trainingdataset shouldbeapproximatelyoneto four, therefore, the electric loaddata set is divided into three sub-sets. The training set has 432half-hour electric loadvalues (i.e., from00:3001October2017 to00:0009October2017). Thevalidationset contains 144half-hourelectric loadvalues(i.e., from00:3009October2017to00:0013October2017). Thetesting sethas192half-hourelectric loadvalues (i.e., from00:3013October2017 to00:0017October2017). Similarly, inExample2, theusedelectric loaddataalso contains a total of 768hourly electric load values, i.e., from00:00 01 January 2018 to 23:00 1February 2018. The electric loaddata set is also divided into three sub-sets. The training sethas432hourlyelectric loadvalues (i.e., from00:0001 January20182017 to23:0018 January2018). Thevalidationsethas144hourlyelectric loadvalues (i.e., from00:0019 January2018 to23:0024 January2018). The testingsethas192hourlyelectric load values (i.e., from00:0025 January2018 to23:001February2018). Tobebasedonthesamecomparison conditions,all comparedmodels thushavethesamedatadivisionsets. Duringthemodelingprocesses, in the trainingstage, therolling-basedprocedure,proposedby Hong [28], is alsoapplied toassistCCSalgorithmto implementwell searching for anappropriate parameter combination (σ,C, ε) of an SVRmodel. Specifically, theCCSalgorithmminimizes the empirical risk,asshowninEquation(4), toobtain thepotentialparametercombinationbyemploying thefirstn electric loaddata in the training set; then, it receives thefirst forecastedelectric loadby the SVRmodelwith these potential parameter combination, i.e., the (n+1)th forecasting electric load. For thesecondround, thenextnelectric loaddata, from2ndto (n+1)thelectric loadvalues, are then used by the SVRmodel to obtain newpotential parameter combination, then, similarly, the (n+ 2)th forecasting electric load is receive. This procedurewould never be stopped till the totally432 forecastingelectric loadarecomputed. Thetrainingerrorandthevalidationerrorarealso calculated ineach iteration. Onlywith thesmallestvalidationandtestingerrors, apotentialparametercombinationcould be finalized as the determined parameter combination of an SVRmodel. Then, the never used testingdata setwouldbe employed todemonstrate the forecastingperformances, i.e., eventually, the192half-hour/hourlyelectric loadwouldbeforecastedbytheproposedSSVRCCSmodel. 3.2. TheSVRwithChaoticCuckooSearch (SSVRCCS)ElectricLoadForecastingModel 3.2.1. EmbeddedParameterSettingsof theCCSAlgorithm TheembeddedparametersofCCSalgorithmformodelingaresetas follows: thenumberofhost nests is set tobe50; themaximumnumberof iterations is setas500; the initialprobabilityparameter pa is set as0.25. During theparameteroptimizingprocessofanSVRmodel, the searching feasible rangesof the threeparametersaresetas following,σ∈ [0.01, 5], ε∈ [0.01, 1], andC∈ [0.01,60,000]. Inaddition, considering that the iteration timewouldaffect theperformanceofeachmodel, thegiven optimization time for each model with an evolutionary algorithm is set at the same inasmuch aspossible. 31