# The Forecast of the Wind Turbine Generated Power Using Hybrid (LTC + XGBoost) Model
## 5 Results
### Comprehensive Economic Error Analysis
Extra revenue is calculated by summing the differences between factual generated power and predicted power, multiplied by Nord Pool price, only in cases where factual generated power exceeds the predicted power (see Equation (7)):  
\[\sum Extra\ Revenue\ Loss=\sum_{i=1}^{n} \begin{cases}(GP_{i}-PP_{i})\times NPHP_{i},&if\ GP_{i}>PP_{i}\\ 0,&otherwise\end{cases}  \tag{7}\]  
where: PP--Predicted Power, GP--Generated Power, NPHP--Nord Pool Hour Price  
Extra revenue losses (see Table 13) indicate that the least revenue is lost according to the XGBoost model results, while the LTC model underestimated the most, leading to an extra revenue loss of 83,251.19 EUR. The hybrid model incurs a revenue loss of 74,431.06 EUR, positioning it between XGBoost and LTC models in terms of performance. This is connected to the previous calculations (see Table 11), since the XGBoost model had the largest overestimation but the smallest underestimation. On the other hand, the LTC model had the largest additional revenue loss, even though it underestimated power generation at a medium rate (in between XGBoost and Hybrid) based on the number of days. This was because of the undervaluation of the LTC model aligned with high energy prices in the Nord Pool market, resulting in the highest extra revenue shortage. To fully assess these estimation errors, earnings should be calculated by subtracting the previously determined penalties and extra revenue losses from potential earnings (see \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Extra Revenue Loss** & **Percentage of** & **Earnings After Extra** \\  & **(Eur in Thousands)** & **Potential Earnings (\%)** & **Revenue Loss** \\  & & **(Eur in Thousands)** & **(Eur in Thousands)** \\ \hline XGBoost & 56 & 15.61 & 301 \\ LTC & 83 & 23.34 & 273 \\ Hybrid & 74 & 20.87 & 282 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Extra revenue loss comparison across XGBoost, LTC, and Hybrid models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Penalties (Eur in** & **Percentage of** & **Earnings After Penalties** \\  & **Thousands)** & **Potential Earnings (\%)** & **(EUR in Thousands)** \\ \hline XGBoost & 113 & 31.56 & 244 \\ LTC & 73 & 20.36 & 284 \\ Hybrid & 57 & 15.87 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Penalties comparison across XGBoost, LTC, and Hybrid models. Figure 16), which comes to a total of 356,619.66 EUR. This provides a clear understanding of the overall financial impact of each model's estimation errors. Total earnings are calculated as follows (see Formula (8)):  
\[\sum Earnings=\sum Potential\ Earnings-\sum Penalties-\sum Extra\ Revenue\ Loss, \tag{8}\]  
Table 14 demonstrates calculations of total earnings for each model. The Hybrid model has the highest earnings among all models. The hybrid model's earnings are 16.47% higher than those of the XGBoost model and 11.01% higher than those of the LTC model, leading to maximized revenue. Figure 16 provides a detailed breakdown of the potential composition of profits, showing once again how the accuracy of each model's prediction can affect the financial results. From the information presented, reducing the nMAE error by 1% resulted in a profit increase of \(\ell\)14,739.27, representing 4.13% of total earnings.