## 6 Experimental Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline
**WPP Method** & **Winter** & **Spring** & **Summer** & **Fall** & **Average** \\ \hline Persistence & 2.37 & 2.30 & 0.48 & 2.73 & 1.97 \\ BP-FFANN & 1.61 & 1.54 & 0.29 & 1.91 & 1.34 \\ GA-FFANN & 1.52 & 1.34 & 0.27 & 1.65 & 1.19 \\ PSO-FFANN & 1.44 & 1.11 & 0.23 & 1.40 & 1.05 \\ WT-ACO-FFANN & 1.32 & 0.75 & 0.18 & 1.02 & 0.82 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of normalized mean absolute error (NMAE) results (%) by various WPP methods. Figure 11: Hourly absolute errors for a spring day (5 April 2016). Figure 12: Hourly absolute errors for a summer day (21 July 2016). Figure 10: Hourly absolute errors for a winter day (4 January 2016). Beyond the MAPE and the NMAE criteria, the invariability of WPP results is a key indicator of the prediction performance of WPP methods. Table 6 provides the comparison of the devised dual-step WT-ACO-FFANN WPP method and the other four methods with respect to the variance of the forecast error. As presented in Table 6, the average variance of the forecast error achieved by the devised WT-ACO-FFANN WPP method is the smallest one, revealing the lowest variability of forecasts. The devised method's average error variance improvements over the other four methods are 75.44%, 57.58%, 39.13%, and 30%, respectively. The FS is also a key index for performance comparison among various WPP methods. It indicates the merit of a WPP technique by evaluating its accuracy values with reference to a persistence prediction. Table 7 gives the comparison of the devised WT-ACO-FFANN WPP method and the other four methods regarding the FS index. As given in Table 7, the devised WT-ACO-FFANN WPP method achieves an improved FS for all the test days. This further verifies the enhanced quality of the WPP method devised in this paper. For a broader performance comparison of the various WPP methods evaluated in this paper, the values of the accuracy criteria for the complete testing year (2016) are provided hereafter, in Table 8. \begin{table}
\begin{tabular}{c c c c c c} \hline
**WPP Method** & **Winter** & **Spring** & **Summer** & **Fall** & **Average** \\ \hline Persistence & 0.0083 & 0.0129 & 0.0007 & 0.0011 & 0.0057 \\ BP-FFANN & 0.0044 & 0.0078 & 0.0003 & 0.0009 & 0.0033 \\ GA-FFANN & 0.0023 & 0.0059 & 0.0004 & 0.0008 & 0.0023 \\ PSO-FFANN & 0.0023 & 0.0046 & 0.0003 & 0.0008 & 0.0020 \\ WT-ACO-FFANN & 0.0023 & 0.0026 & 0.0001 & 0.0008 & 0.0014 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of forecast error variance by various WPP methods. \begin{table}
\begin{tabular}{c c c c c c} \hline
**WPP Method** & **Winter** & **Spring** & **Summer** & **Fall** & **Average** \\ \hline Persistence & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ BP-FFANN & 30.56 & 29.60 & 38.96 & 27.25 & 31.59 \\ GA-FFANN & 39.13 & 39.07 & 39.59 & 35.93 & 38.43 \\ PSO-FFANN & 41.59 & 48.02 & 47.71 & 43.67 & 45.25 \\ WT-ACO-FFANN & 45.33 & 63.55 & 61.31 & 54.67 & 56.21 \\ \hline \end{tabular}
\end{table} 
Table 7: Comparison of forecast skill (FS) results (%) by various WPP methods. Figure 13: Hourly absolute errors for a fall day (11 October 2016). As verified by the annual MAPE results in Table 8, the MAPE values are almost similar (even better in some of the months) to the values obtained for the individual testing days in the respective seasons, which shows the consistency and the robust prediction performance of the devised WPP technique in this work. Above all, the devised technique gives an improved annual MAPE over the other four examined methods. In summary, the devised dual-step WT-ACO-FFANN integrated ML WPP method achieves improved 24 h-ahead wind power forecast results. It outperforms the other four evaluated WPP methods with respect to MAPE, NMAE, variance, and FS performance indicators.