Page - 68 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 3433 VMDAlgorithm 1. Foreachmode,vk, compute theassociatedanalytic signalusingtheHilbert transformtoobtain theunilateral frequencyspectrum; 2. Foreachmode,vk, shift themodefrequencyspectrumtothebaseband(narrowfrequency)by mixing itwithanexponential tunedto thecorrespondingestimatedcenter frequency; 3. Estimate thebandwidthusingtheGaussiansmootheddemodulatedsignal. Theresultingconstrainedvariationalproblemisexpressedas: min vk,wk { K ∑ k ∥∥∥∥∂t[(δ(t)+ jπt ) ∗vk(t) ] e−jwkt ∥∥∥∥2 2 } (1) subject to K ∑ k vk=Wp(t). (2) whereWp(t) is the pweekly loadprofilewithmodevand frequencyw, δ is theDiracdistribution, k is themode index,K is the total number ofmodes and thedecomposition level, and ∗denotes convolution.Modevwithhighorderk represents lowfrequencycomponents. Incontrast to thatof EMD, thedecomposition levelofVMD,k,mustbepre-determined[22–25]. 2.4.Decomposition forFeatureSelection Figure1showstheproposedloadprofiledecompositionmethod.Thebuilding loadprofilehas similarweekdaypatterns,andthe loadismeasuredat5-min intervalsbyAMI.Toclassifyseasonal patterns, the typical loadprofile (xt) of the building is decomposedonaweekly basis forweekly seasonality features (xpt ). The typical loadprofile is decomposed into twodimensions. The load variationscanbeextracted if theyareperiodicbecause theVMDdecomposes the loadprofile in terms of the frequency(xpk,t). Thus,all the IMFsexhibitperiodiccharacteristics.AseachIMFhasaspecific frequency, theVMDidentifiesperiods that cannotbe identified in the typical loadprofile and the weekly loadprofile.Asaresult, the typical loadprofile isdecomposedinto three-dimensionaldata accordingto time,weeklyseasonality,andIMF-level. Thefeaturedecompositionprocessof the load profilecontributes to the loadcharacteristicswithoutexternaldata, suchas thecalendar information aboutholidays, temperature,andhumidity. Figure1.Loadprofile featuredecompositionprocess. 68