Page - 214 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1900 theestimatedvalueof thedesiredtargetcanbeapproximatedbythestochasticsimulationmethod. Asthenumberofsimulations increases, theexpectedaccuracyof the target isgradually increased. 2.1.1. ThePrincipleof theMCM TheTheoremofLargeNumbersandCentralLimits inProbabilityTheoryare the theoreticalbasis of theMCM[25]. Theprincipleof theMonteCarlosimulationmethodis thatwhentheproblemor the object itselfhasaprobability feature, a samplingresult canbegeneratedbyacomputersimulation method. Thestatisticor thevalueof theparametercanbecalculatedaccordingto thesampling. Basedonthese twotheorems, the functioncanbeexpressedas follows. Assumingthe function[26]: Y= f(X1,X2, · · · ,Xn), (1) where theprobabilitydistributions of thevariablesX1,X2, . . . ,Xn areknown. Thevalues (x1, x2, . . . ,xn)ofeachsetof randomvariables (X1,X2, . . . ,Xn)areobtainedbydirector indirect sampling, thenthevalueyiof the functionYcanbedeterminedaccordingtoFormula (2) [26]: yi= f(xi1,xi2, · · · ,xin) (2) Samplingmultiple times (i=1,2, . . . ,m) repeatedlyandindependently,wecanobtainabatchof samplingnumbersy1,y2, . . . ,ynof the functionY,whichare inaccordancewith thecharacteristicsof thenormaldistribution. Foreachoutput,mpossible resultsareobtained[20]: Y= ⎡⎢⎢⎢⎢⎣ y1 y2 ... ym ⎤⎥⎥⎥⎥⎦= ⎡⎢⎢⎢⎢⎣ f(x11,x12, . . . ,x1n) f(x21,x22, . . . ,x2n) ... f(xm1,xm2, . . . ,xmn) ⎤⎥⎥⎥⎥⎦, (3) 2.1.2. TheStepsof theMCM First, a statistical analysis tool, suchas IBMSPSSStatistics 19.0 software (19.0, IBM,Armonk, NY,USA), isused toanalyze theprobabilitydistributionof theerrorsof theweather forecastdata and the real data. A statisticalmodel related to theproblem isdetermined, ofwhich the solution is regardedas theprobabilitydistributionandmathematical expectationof theconstructedmodel. Generally, anappropriate theoreticaldistribution (e.g.,Uniformdistribution,Normaldistribution, Binomial distribution, Poisson distribution, Triangular distribution, etc.) is used to describe the empiricalprobabilitydistributionof randomvariables. If there isno typical theoreticalprobability distribution thatcanbedirectlyquoted, it isnecessary toestimatean initialprobabilitydistributionof theresearchobjectbasedonhistorical statisticsandsubjectiveprediction. Second, it is important togenerate randomnumbers tosimulate therandomchangesofvariables. Therearemainly twomethods togenerate randomnumbers.Wecanuseanexistingrandomnumbers table,or theycanbecalculatedbyusingacomputerprogram. In thispaper, theprogramof theMCM for theresearchwaswritten intoMATLABto implement theMonteCarlorandomsamplingaccording to theprobabilitydistributionobtainedbythepreviousstep.Aftermultiplesampling,wecangetm possible results, suchasEquation(2). Finally, when the number of simulations is sufficiently large, the probability distribution of the functionY and the concerned digital feature information can be close to the actual situation. Stableconclusionscouldbeobtainedbyaveragingthestatisticsorestimatesof theparameters. 214