Seite - 13 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2226 Table3.Normalizationvaluesof loaddata forGEFCom2014(July). Time 1July 2July 3July 4July 5July 6July 7July 01:00 0.1562 0.1612 0.1583 0.2747 0.2636 0.1699 0.1063 02:00 0.0728 0.0882 0.0763 0.1302 0.1266 0.0857 0.0394 03:00 0.0238 0.0348 0.0232 0.0456 0.0554 0.0302 0.0054 04:00 0.0000 0.0000 0.0000 0.0000 0.0063 0.0000 0.0000 05:00 0.0222 0.0186 0.0181 0.0190 0.0000 0.0021 0.0302 06:00 0.0945 0.0957 0.1040 0.0589 0.0554 0.0154 0.1187 07:00 0.2811 0.2781 0.3143 0.2091 0.1872 0.0955 0.2972 08:00 0.4692 0.4736 0.5172 0.4316 0.4153 0.2521 0.4903 09:00 0.6244 0.6212 0.6637 0.6873 0.7008 0.4459 0.6424 10:00 0.7396 0.7516 0.7733 0.8878 0.9017 0.6131 0.7476 11:00 0.8306 0.8479 0.8722 0.9734 0.9561 0.7163 0.8425 12:00 0.8979 0.9209 0.9389 1.0000 0.9561 0.7570 0.9051 13:00 0.9378 0.9673 0.9678 0.9876 0.9111 0.7809 0.9434 14:00 0.9737 1.0000 0.9938 0.9287 0.8515 0.7928 0.9865 15:00 0.9879 0.9829 1.0000 0.8546 0.8243 0.8111 0.9995 16:00 0.9970 0.9290 0.9881 0.8032 0.8462 0.8574 1.0000 17:00 1.0000 0.8564 0.9423 0.8004 0.9195 0.9199 0.9962 18:00 0.9960 0.8101 0.9005 0.8279 0.9937 0.9853 0.9833 19:00 0.9687 0.7567 0.8672 0.8203 1.0000 1.0000 0.9579 20:00 0.9176 0.6907 0.7756 0.7386 0.9435 0.9579 0.9213 21:00 0.9044 0.6489 0.7377 0.6787 0.9362 0.9417 0.8975 22:00 0.8291 0.5461 0.6354 0.5428 0.8692 0.8687 0.7875 23:00 0.6138 0.3572 0.4262 0.3279 0.6883 0.6426 0.5701 24:00 0.4095 0.1678 0.2272 0.0913 0.4341 0.4213 0.3927 3.2. ForecastingAccuracy IndexesandPerformanceTests 3.2.1. ForecastingAccuracyIndex Thisstudyuses theMAPE (mentionedinEquation(28)), therootmeansquareerror (RMSE),and themeanabsoluteerror (MAE)as forecastingaccuracy indexes. TheRMSEandMAEaredefinedas in Equations (33)and(34), respectively: RMSE= √√√√∑Ni=1(fi(x)− fˆi(x))2 N (33) MAE= 1 N N ∑ i=1 ∣∣∣fi(x)− fˆi(x)∣∣∣, (34) whereN is thetotalnumberofdatapoints; fi(x) is theactualvalueatpoint i;and fˆi(x) is theforecasting valueatpoint i. 3.2.2. ForecastingPerformanceImprovementTests Todemonstrate the significant forecastingperformancesof theproposedmodel,Dieboldand Mariano [48] andDerrac et al. [49] suggest that, for a small data size (24-h load forecasting) test, aWilcoxonsigned-ranktest [50] is suitable. Thus,wedecidedtoapply theWilcoxonsigned-ranktest. For thesamedatasize,aWilcoxontestdetects thesignificanceof thedifference (i.e., the forecasting errorsfromtwoforecastingmodels) inthecentral tendency. Therefore, letdibetheabsoluteforecasting errorsfromanytwomodelsonithforecastingvalue:R+bethesumofranksthatdi>0;R− thesumof ranks thatdi<0. Ifdi=0, then, removethiscomparisonanddecrease thesamplesize. Thestatistics ofWilcoxontest,W, is calculatedas inEquation(37): W=min { R+,R− } . (35) 13