# Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model
## 4 Results and Discussion
### Discussion of xLSTM Results
#### 4.2.2 Seasonal Wind Speed Distribution Prediction Performances
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical Parameter**} & \multicolumn{2}{c}{**Winter**} & \multicolumn{2}{c}{**Spring**} & \multicolumn{2}{c}{**Summer**} & \multicolumn{2}{c}{**Autumnn**} \\ \cline{2-9}  & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** & **SCADA** & **xLSTM** \\ \hline Central Tendency & & & & & & & & \\ Primary Mode (m/s) & 7.8 & 7.5 & 3.4 & 3.6 & 6.4 & 6.5 & 3.5 & 4.8 \\ Secondary Mode (m/s) & – & – & 8.2 & 8.8 & – & – & 10.8 & 10.5 \\ Mean Wind Speed (m/s) & 8.2 & 8.1 & 6.9 & 7.1 & 7.3 & 7.1 & 6.4 & 6.5 \\ Median Wind Speed (m/s) & 7.5 & 7.4 & 5.8 & 6.2 & 6.8 & 6.7 & 5.7 & 5.9 \\ \hline Distribution Shape & & & & & & & & \\ Standard Deviation (m/s) & 4.8 & 4.6 & 5.1 & 5.3 & 4.3 & 4.2 & 4.3 & 4.5 \\ Coefficient of Variation & 0.58 & 0.57 & 0.74 & 0.75 & 0.59 & 0.59 & 0.67 & 0.69 \\ Skewness & 0.67 & 0.64 & 0.78 & 0.74 & 0.59 & 0.56 & 0.42 & 0.39 \\ Kurtosis & 2.87 & 2.91 & 2.71 & 2.65 & 2.59 & 2.63 & 2.65 & 2.72 \\ Bimodality Coefficient & 0.42 & 0.41 & 0.59 & 0.56 & 0.47 & 0.45 & 0.53 & 0.51 \\ Distribution Entropy (bits) & 2.67 & 2.70 & 2.76 & 2.79 & 2.74 & 2.72 & 2.83 & 2.81 \\ \hline Probability Characteristics & & & & & & & & \\ Prob. Density at Primary Mode & 0.092 & 0.088 & 0.116 & 0.095 & 0.099 & 0.102 & 0.106 & 0.104 \\ Prob. Density at Secondary Mode & – & – & 0.045 & 0.061 & – & – & 0.055 & 0.052 \\ Prob. Wind Speed \(<\) 5 m/s & 0.27 & 0.26 & 0.42 & 0.38 & 0.31 & 0.33 & 0.38 & 0.41 \\ Prob. Wind Speed \(>\) 12 m/s & 0.22 & 0.21 & 0.19 & 0.20 & 0.18 & 0.17 & 0.16 & 0.15 \\ \hline Error Metrics & & & & & & & & \\ MAPE in Probability Density (\%) & – & 4.3 & – & 8.7 & – & 5.2 & – & 7.1 \\ RMSE & – & 0.024 & – & 0.038 & – & 0.029 & – & 0.035 \\ \(R^{2}\) & – & 0.987 & – & 0.963 & – & 0.978 & – & 0.971 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of seasonal probabilistic distribution between SCADA measurements with xLSTM predictions of wind speeds. Cross-seasonal comparative analysis reveals systematic patterns in prediction performance. The coefficient of variation demonstrates consistent tracking of seasonal variability, ranging from 0.58 (winter) to 0.74 (spring) in SCADA measurements, with xLSTM following this pattern closely (0.57 to 0.75). Distribution entropy measures show the highest complexity in autumn (2.83 bits for SCADA measurements, 2.81 bits for xLSTM results) and the lowest in winter (2.67 bits for SCADA measurements, 2.70 bits for xLSTM results), with the model capturing these information-theoretic characteristics effectively. The probability of high wind speeds (>12 m/s) shows consistent representation across all seasons, with a maximum deviation of only 5.3% in spring. The comprehensive statistical assessment validates the xLSTM model's capability to capture fundamental properties of wind velocity distributions across varied seasonal patterns. Performance metrics consistently demonstrate strong predictive capability, with \(R^{2}\) values ranging from 0.963 to 0.987 and MAPE values between 4.3% and 8.7%. The xLSTM model exhibits particular strength in representing unimodal distributions (winter and summer) while maintaining acceptable performance for bimodal distributions (spring and autumn). The statistical evidence supports the conclusion that the xLSTM architecture effectively models complex time series data with seasonal dependencies, with minor limitations in capturing exact modal positions in multimodal distributions.