Page - 350 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1282 point(3.52%)ofBPNNon29Juneandonepoint(−3.50%)ofLSSVMon30Junearebeyondtherangeof [−3%,3%],which indicates that theaccuracy is increasedafter theprocessof reducingdimensionsand clustering. (2)Most relativeerrorpointsof theBA-ELMlocate in therangeof [−1%,1%]onall three days. Bycontrast,mostpointsof theELMarebeyondtherangeof [−1%,1%],whichcandemonstrate that theBAapplied inELMincreases theaccuracyandstabilityofELM.(3)On28June, calledDay1 inthispaper, theELMhas14predictedpointsexceedtherangeof [−1%,1%],andthere isonlyone point (2.12%)beyondtherangeof [−2%,2%]at21:00; theBPhasadozenpredictedpointsoutside the rangeof [−1%,1%],andthere isonepredictedpoint (−2.05%)beyondtherangeof [−2%,2%]at11:00; theLSSVMhas14predictedpointsbeyondtherangeof [−1%,1%],andtherearesixpredictedpoints beyondtherangeof [−2%,2%],whichare−2.38%at11:00,−2.76%at12:00,−2.07%at16:00,−2.85% at17:00,−2.17%at18:00and−2.7%at19:00. (4)On29June, calledDay2 in thispaper, theELMhas 10predictedpointsexceedtherangeof [−1%,1%],andthere isonlyonepointsbeyondtherangeof [−2%,2%],which is2.52%at21:00; theBPhas16predictedpointsexceedingtherangeof [−1%,1%], andthereare threepredictedpointsbeyondtherangeof [−2%,2%],whichare3.52%at7:00,−2.03% at12:00and−2.03%at14:00; theLSSVMhas13predictedpointsbeyondtherangeof [−1%,1%],and thereare fourpredictedpointsoutside therangeof [−2%,2%],whichare−2.25%at12:00,−2.27%at 16:00,−2.77%at15:00and−2.17%at19:00. (5)On30June, calledDay3 in thispaper, theELMhas 15predictedpoints exceed the rangeof [−1%,1%], and thereare threepointsbeyond the rangeof [−2%,2%],whichare−2.48%at8:00,−2.19%at17:00and−2.61%at19:00; theBPhas19predicted pointsexceedtherangeof [−1%,1%],andtherearesixpredictedpointsbeyondtherangeof [−2%, 2%],whichare2.91%at7:00,−2.43%at10:00,−2.85%at12:00,−2.73%at14:00,−2.3%at15:00and −2.05%at22:00; theLSSVMhas18predictedpointsbeyondtherangeof [−1%,1%], andthereare ninepredictedpointsoutside the rangeof [−2%,2%],whichare−2.17%at12:00,−2.03%at13:00, −2.59%at 14:00,−2.41%at 15:00,−3.5%at 16:00,−2.19%at 17:00 and−2.78%at 18:00. Fromthe globalviewof relative errors, the forecastingaccuracyofBA-ELMisbetter than theothermodels, since ithas themostpredictedpoints in theranges [−1%,1%], [−2%,2%]and[−3%,3%].Compared withBPNNandLSSVM, therelativeerrorsofELMare low. Thereason is that theBPNNcanhave advantageswhendealingwith thebig sample, but its forecasting results arenot verygoodwhen dealingwith a small sampleproblem like short-term load forecasting. Thekernel parameter and penalty factorsettingmanuallyofLSSVMaredifficult toconfirm,whichhasasignificant influenceon the forecastingaccuracy. Thenumberofpoints thatare less than1%,2%,3%andmore than3%andthecorresponding percentageof theminthepredictedpointsareaccountedfor, respectively. Thestatistical resultsare shown inTable 10. It canbe seen that there are 61predictedpointswhose theAEof theBA-ELM model is less than1%,whichaccounts for84.72%of the totalamount;and10predictedpoints in the rangeof [1%,2%],accountingfor13.89%of the totalamount;andonly1predictedpoint in therange of [2%,3%],accountingfor1.39%of the totalamount.Moreover, therearenopredictedpointswhose AEismore than3%,accountingfor0%of the totalamount. It canbeconcludedthat the forecasting performanceof theproposedmodel is superior,anditsaccuracy ishigher,whichmeans theBA-ELM model is suitable forshort-termloadforecasting. TheaverageRMSEandMAPEof theBA-ELM,ELM,BPNNandLSSVMmodels are listed in Table11. Inorder toshowthecomparisonsclearly, theRMSE,MAEandMAPEof four forecasting models in three testingdaysareshowinFigures14–16. It canbeconcludedthatbothof theRMSE, MAEandMAPEofBA-ELMare loweronthree testingdays.On28June, theRMSE,MAEandMAPE ofELMareslightlybigger thanBP,butsmaller thanthatofLSSVM.On29June, theRMSE,MAEand MAPEofELMaresmaller thanthatofBPandLSSVM.TheRMSE,MAEandMAPEofBPareclose to thatofLSSVM.On30June, theRMSE,MAEandMAPEofELMaresmaller thanBPandLSSVM’s, andthatofBParesmaller thanLSSVM’s. Tosumup,combiningthiswith theTable11, theaverage behaviorof fourmodelsareBA-ELM,ELM,BPNNandLSSVMfromlowtohighsuccessively. 350