# Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model
## 4 Results and Discussion
### Comparative Performance Analysis with Other Forecasting Models  
To properly contextualize the predictive capabilities of the xLSTM architecture, a systematic comparison against other time series forecasting models was conducted, including both traditional statistical approaches and contemporary machine learning methods. All models were trained and evaluated using identical datasets, preprocessing techniques, and evaluation metrics to ensure fair comparison. Table 9 presents the comprehensive performance metrics for all models across different wind speed regimes for a representative 72-h period. The traditional statistical ARIMA model demonstrates limited predictive capability (\(R^{2}=0.682\)), particularly for turbulent wind conditions, with an overall MAPE of 17.35%. This reflects the inherent limitations of linear models in capturing the non-linear relationships in wind SCADA data. The standard neural network models, e.g., LSTM and GRU, show marked improvements over ARIMA, with the recurrent architectures achieving \(R^{2}\) values between 0.864-0.871 and MAPE scores between 10.95-11.23%. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Model** & **Overall \(R^{2}\)** & **MAPE \(\epsilon\) (\%)** & **RMSE \% (kW)** & **Low Wind \(R^{2}\)** & **Medium Wind \(R^{2}\)** & **High Wind \(R^{2}\)** & **Training Time (min)** \\ \hline ARIMA & 0.682 & 17.35 & 63.7 & 0.584 & 0.693 & 0.712 & 0.5 \\ LSTM & 0.864 & 11.23 & 42.3 & 0.801 & 0.845 & 0.892 & 3.8 \\ GRU & 0.871 & 10.95 & 41.5 & 0.813 & 0.851 & 0.897 & 3.5 \\ BiLSTM & 0.885 & 10.21 & 38.9 & 0.826 & 0.864 & 0.917 & 4.6 \\ Transformer & 0.902 & 9.37 & 36.1 & 0.835 & 0.886 & 0.936 & 7.2 \\ xLSTM & 0.923 & 8.47 & 34.6 & 0.886 & 0.901 & 0.954 & 5.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance comparison of xLSTM against benchmark forecasting models. Advanced architectures, such as BiLSTM and Transformer, demonstrate further performance gains, with the Transformer model achieving an \(R^{2}\) of 0.902 and MAPE of 9.37%, representing the strongest baseline performance. This highlights the value of the attention mechanism in capturing long-range dependencies in wind power data. The proposed xLSTM architecture consistently outperforms all baseline models across every evaluation metric, with statistically significant improvements (\(p<0.01\)). The performance gain is particularly pronounced in high wind speed regimes, where xLSTM achieves an \(R^{2}\) of 0.954 compared with 0.936 for the Transformer model, representing a 7.4% reduction in unexplained variance. This demonstrates the effectiveness of the exponential gating and matrix memory mechanisms for capturing the complex temporal dynamics of wind power generation during high-velocity conditions. The error distributions reveal that while the Transformer and BiLSTM models achieve competitive performance during stable wind conditions, they exhibit wider error distributions during transitional periods (particularly around cut-in and rated speeds). The xLSTM model demonstrates more consistent error patterns across all operating regimes, with notably narrower error distributions during rapid wind fluctuations. This consistency can be attributed to the sLSTM model's enhanced ability to revise storage decisions through exponential gating, particularly valuable during transitional wind conditions. Statistical analysis of error distributions using a Kolmogorov-Smirnov test confirms that the xLSTM error distribution is significantly different from those of baseline models (\(p<0.01\)), with lower kurtosis values indicating fewer extreme prediction errors. This reduced propensity for outlier predictions represents a substantial practical advantage for grid management applications, where extreme forecasting errors can trigger costly balancing measures. When analyzing the relationship between model complexity, computational requirements, and predictive performance, the xLSTM architecture demonstrates a favorable efficiency frontier.