Page - 152 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2080 Figure11showstheevolutionofaccuracyandsimulationtimeagainst thenumberofneurons in thehidden layer. It canbeseenthat theexecution time isalmostconstantandtherefore thenumberof neurons isnotan issueregardingcomputationalburden. Inaddition,accuracyonregulardaysdoes not improvewithmorecomplexnetworks. Specialdays,however, showadeteriorationas thenumber ofneurons increases.Apossibleexplanationto this is thatamorecomplexnetwork isable tooverfit the trainingdataandlosegenerality. This isespeciallyobviousonthespecial-daycategorydueto the scarcityofdata. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1.00% 1.20% 1.40% 1.60% 1.80% 2.00% 2.20% 2.40% 2.60% 3 4 5 10 15 20 Number of Neurons Overall Accuracy and Exec. Time vs number of neurons OVERALL REGULAR SPECIAL Time (s) Figure11.Overall forecastingerror (RMSE)andexecutiontimewithdifferentnumberofneurons. 4.5. RedundancyofNeuralNetworks The use of a redundant number of NN reduces themodel’s dependency of random initial conditions. Furthermore,eliminatingextremevaluesalsoreduces theoverall error. Table6showsthe resultsofusingfrom3to25redundantnetworks for theNNmodel. Table6.Forecastingerror (RMSE)andexecutiontimewithdifferent redundantnetworks. TypeofDay NumberofNetworks 3 5 10 11 12 14 15 16 20 25 Overall 1.67% 1.62% 1.55% 1.56% 1.54% 1.54% 1.54% 1.55% 1.55% 1.56% Regular 1.55% 1.51% 1.46% 1.48% 1.46% 1.45% 1.46% 1.46% 1.45% 1.46% Special 2.51% 2.30% 2.10% 2.08% 2.08% 2.11% 2.12% 2.13% 2.18% 2.22% Hot 2.02% 1.97% 1.93% 1.98% 1.92% 1.94% 1.92% 1.93% 1.92% 1.94% Cold 1.54% 1.57% 1.45% 1.43% 1.45% 1.43% 1.44% 1.46% 1.47% 1.44% Time(s) 0.839 1.09 1.686 1.746 1.868 2.039 2.228 2.333 2.713 3.363 Testconditions: 7YT,4N,5TL,12MF,7/14LAG. There isan improvementusingupto10redundantnetworks.However, there isnotsignificant error reduction from10 to 25 networks. The execution time shows an increase, although for the optimumamount of 10 networks the computational burden is still manageable. As a reference, wehaveusedtheexecutiontimefor theARmodel,which is0.835s. Inaddition, inFigure12 it canbe seenthat the typeofdays thatbenefit themost fromincreasingnumberofnetworks from3to10are specialdays.Again, this isprobablyduetothehighervariability in theoutput fromdifferentnetworks for this scarcer typeofdays. 152