Page - 345 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1282 Table4.Resultsofantcolonyclusteringalgorithm. Classification DateNumber Class1 3→21→25→28→45→51→54→56→59 Class2 1→7→8→9→10→15→16→26→39→43→44→49→53→57 Class3 5→12→13→17→19→20→29→31→34→35→37→40→41→42→46→47→48→55→60 Class4 2→4→6→11→14→18→22→23→24→27→30→32→33→36→38→50→52→58 3.5.ApplicationofBA-ELM Toverify therationalityofdataprocessing, theBA-ELMmodelwasconductedonYangquanCity loadforecasting. In thispaper, therelativeerror (RE),meanabsolutepercentageerror (MAPE),mean absoluteerror (MAE)androot-mean-squareerror (RMSE)areemployedtovalidate theperformance of themodel. Theformulasdefinitionareexpressedas follows, respectively: RE(i)= ŷi−yi yi ×100% (12) AE(i)= ∣∣∣∣ŷi−yiyi ∣∣∣∣×100% (13) MAPE= 1 n n ∑ i=1 ∣∣∣∣ŷi−yiyi ∣∣∣∣ (14) RMSE= √ 1 n n ∑ i=1 (ŷi−yi)2 (15) MAE= 1 n n ∑ i=1 |ŷi−yi| (16) wherenstands for thequantityof the test sample, ŷi is the real load,whileyi is thecorresponding predictedoutput. Moreover, thepaper compared theELMwith thebenchmarkmodel’sLSSVMand theBPNN todemonstrate thesuperiorityof theproposedmodel. Theparametersof themodelsareshownin Table 5. Figure 6 shows the iterationsprocessofBA.Fromthefigurewecan see thatBAachieves convergenceat350 times. Theoptimalvaluesof theparametersareshowninTable6. Table5.Parametersofmodels. Model Parameters BA-ELM n=10,N_iter=500,A=1.6, r=0.0001, f= [0,2] ELM N=10,g(x)= ‘sig’ LSSVM γ=50; σ2=2 BPNN G=100;hidden layernode=5; learningrate=0.0004 Table6.Theoptimalparameters. Parameter Value Theinputweightmatrix ωij= ⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝ −5.12 −5.12 −5.12 −2.62 −5.11 5.12 5.12 −5.05 −5.12 −3.61 −0.52 −1.50 5.12 5.12 −5.11 −0.13 −5.12 −5.12 1.14 −5.12 4.77 −5.12 5.12 −0.06 −0.61 2.08 −3.05 −2.03 5.12 4.26 4.92 0.03 5.12 2.74 3.37 2.28 −0.44 2.33 5.12 −1.72 5.12 0.54 1.38 3.48 4.83 5.12 −4.59 −5.12 −5.12 2.56 0.49 1.32 4.03 1.46 3.18 4.87 5.12 5.10 2.65 2.19 −5.12 1.06 4.63 2.66 −5.12 −3.91 −5.12 5.12 2.16 5.12 −5.12 −2.09 3.86 −5.12 1.85 5.12 −1.44 −5.12 5.12 1.97 5.00 0.30 5.12 −4.42 −5.12 4.08 −4.79 5.12 −5.12 −5.12 ⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ 345