# The Forecast of the Wind Turbine Generated Power Using Hybrid (LTC + XGBoost) Model
## 5 Results
### Comprehensive Economic Error Analysis  
The errors in wind power forecasts have a great impact from an economic perspective. Larger and more frequent errors result in greater income losses. There are a few types of economic impact estimations: income that will not be received due to insufficient energy supply to the Nord Pool market exchange, and the penalties for undelivered energy. The aspects of these calculations are explained in more detail below. During 2023, the wind turbine Enercon E82/2000 generated 4,587,000.43 kWh or 4587.00 MWh of energy. XGBoost predicted a total energy generation of 5,033,260.61 kWh (5033.26 MWh), which is 10% more than the factual energy generated. The LTC model predicted 4,307,797.35 kWh (4307.79 MWh) of energy, i.e., 6% less than the actual generation. The Hybrid model also predicted 4.2% less energy than the total amount of energy generated (4,393,924.05 kWh or 4393.92 MWh). These results indicate potential financial losses, as overestimations may lead to penalties for undelivered energy (e.g., XGBoost) and lost revenue due to underestimations (e.g., LTC and Hybrid models). From Table 10, it is visible that the XGBoost model overestimates more than it underestimates, while the LTC and Hybrid models do the opposite. Earlier discussed over- and under-estimations in hours can be compared from a power perspective (see Table 11). The hybrid model overestimates 75.6% less power than the XGBoost model, but only 15.5% less compared to the LTC model. Additionally, the Hybrid model underestimates 17.6% more power than the XGBoost model, but 22% less than the LTC model. The hybrid model significantly reduces overestimation compared to XGBoost and underestimation compared to LTC, making it a more balanced and accurate power estimation model overall. For both overestimation and underestimation calculations, the Nord Pool day-ahead hourly prices of Lithuania in 2023 were used. The total potential earnings were calculated by multiplying the factual electricity produced by the Nord Pool day-ahead prices (see Equation (5)), which resulted in a total amount of EUR 356,619.63. \[\sum Potential\ Earnings=\sum_{i=1}^{n}GP_{i}\times NPHP_{i} \tag{5}\]  
where: GP--Generated Power, NPHP--Nord Pool Hour Price. \begin{table}
\begin{tabular}{c c c c} \hline  & **XGBoost** & **LTC** & **Hybrid** \\ \hline Overestimations in hours & 5544 h & 4655 h & 4435 h \\ Underestimations in hours & 3168 h & 4054 h & 4277 h \\ Exact estimations in hours & 0 h & 3 h & 0 h \\ \hline \end{tabular}
\end{table} 
Table 10: The number of overestimated and underestimated hours resulting from the prediction of XGBoost, LTC, and Hybrid models. \begin{table}
\begin{tabular}{c c c c} \hline  & **XGBoost** & **LTC** & **Hybrid** \\ \hline Overestimations (MWh) & 1139 & 749 & 649 \\ Underestimations (MWh) & 693 & 1028 & 842 \\ \hline \end{tabular}
\end{table} 
Table 11: Calculated total amount of overestimated and underestimated energy resulting from the prediction of XGBoost, LTC, and Hybrid models. To calculate the economic impact (penalties) of overestimations, we need to identify the days when overestimation occurred and multiply those days by the Nord Pool day-ahead price for that day (see Equation (6)):  
\[\sum Penalty=\sum_{i=1}^{n} \begin{cases}(PP_{i}-GP_{i})\times NPHP_{i},&if\ PP_{i}>GP_{i}\\ 0,&otherwise\end{cases}  \tag{6}\]  
where: PP--Predicted Power, GP--Generated Power, NPHP--Nord Pool Hour Price. Table 12 shows the penalties for the model's underestimation. The Hybrid model generated 49.69% fewer penalties than the XGBoost model and 22.05% fewer penalties than the LTC model, demonstrating its superiority in terms of reducing penalty costs. Another economic aspect that should be considered is the extra revenue loss. It happens when the model underestimates power generation, leading to missed opportunities to sell energy.