# Enhanced Wind Energy Forecasting Using an Extended Long Short-Term Memory Model
## 4 Results and Discussion
### xLSTM Results for Wind Energy Forecasting
#### 4.1.2 xLSTM Results
The model slightly underestimates probability density in the 3-4 m/s range while marginally overestimating it in the wind speed range of 10-11 m/s. These deviations likely correspond to the challenges in modeling transitional seasonal patterns characterized by greater meteorological variability. The summer distribution presents a broader, more diffuse pattern with maximum probability density occurring around 6-7 m/s, as shown in Figure 3c. The xLSTM predictions closely track SCADA measurements across most of the distribution range, with particularly accurate modeling of the central peak and the tail behavior beyond 12 m/s. The model captures the characteristic summer wind pattern that typically features moderate velocities with gradual distribution tails. Minor variations appear in the 2-4 m/s range, where the model slightly underestimates probability density compared with actual SCADA measurements. Autumn exhibits the most complex distribution pattern with a primary concentration in the wind speed range of 3-6 m/s and secondary modes at approximately 10-12 m/s, as shown in Figure 3d. Figure 2: Comparison of theoretical, actual, and xLSTM predicted power output of the wind turbine. Figure 3: Seasonal probabilistic distribution of wind speeds: comparative analysis of SCADA measurements and xLSTM predictions in (**a**) winter (December–February), (**b**) spring (March–May), (**c**) summer (June–August), and (**d**) autumn (September–November). This multimodal structure reflects the variable wind conditions characteristic of autumn. The xLSTM model demonstrates strong predictive performance across most velocity ranges, accurately capturing both the primary concentration and the secondary modes. However, there are minor discrepancies in the exact positioning of the peaks, with the model estimating a slightly higher probability density at 5 m/s compared with the measured peak at 4 m/s. The comparative analysis of power output distributions across seasonal patterns offers critical insights into performance characteristics of the xLSTM model for predicting wind turbine power generation, as shown in Figure 4. This analysis examines the probabilistic distribution of power output data across four distinct seasonal contexts, with particular attention to the bimodal distribution patterns that characterize wind turbine power generation. The winter season power distribution exhibits a distinctive bimodal structure with significant probability density concentrations at the extremes of the power spectrum, as shown in Figure 4a. A substantial probability density concentration exists near zero output (0-200 kW), corresponding to wind speeds below the cut-in threshold or turbine curtailment during winter weather events. Simultaneously, a secondary peak appears at rated power (3.5 MW), representing periods of optimal wind conditions. Between these extremes lies an extended transitional region (500-3000 kW) with relatively uniform and low-density distribution. The xLSTM model demonstrates excellent fidelity in capturing this bimodal structure, with a notably accurate estimation of both the near-zero and rated power probability masses. The spring distribution maintains the bimodal characteristics observed in winter but exhibits several distinctive features, as shown in Figure 4b. A more pronounced concentration appears at near-zero output (0-200 kW), with a probability density of approximately 0.002, significantly higher than other seasons. A reduced but still prominent secondary peak exists at the rated power of the wind turbine, with a density of approximately 0.0009. The summer power distribution reveals a modified bimodal pattern with unique characteristics. A reduced but still significant probability density appears at near-zero output (0-200 kW), with a density of approximately 0.00160. A less pronounced secondary peak exists at rated power, with a density of approximately 0.00060.