## 3 Results and Discussion
### Optimal Solutions for the LP Optimization Model  
Tests were carried out for the 20 years of average wind turbine life for each possible scenario concerning the battery lifetime, \(pb\). Scenarios 1, 2, 3, and 4 correspond, respectively, to the battery life, \(pb\), equal to 5, 10, 15, and 20 years. For scenarios 1, 2, 3, and 4, the ESS was replaced 3, 2, 1, and 0 times, respectively. In this way, if possible, the LP model will determine four optimal solutions, one for each scenario. The results are presented in Table 5. It is easily identified which turbine and the tariff to be adopted for each scenario and the number of batteries used for the 20 years period. In either scenario, the optimal solution corresponds to the use of the horizontal axis turbine, Aeolos-H 20 kW, and the optional tariff. These are the choices that guarantee the best performance to the problem created. Concerning the batteries, there is a consensus on adopting the 8 kWh battery for scenarios 1, 2, and 3. However, for scenario 4 it is more profitable to adopt the 13 kWh battery. Figure 8 shows the original real load profile for the building under study, represented by the black bar, together with the load profile's obtained with the optimization of energy purchased from the grid and necessary investments. There was a considerable reduction in the energy purchase from the grid from 14:00 to 21:00. According to the legal summer or wintertime, this period can correspond to peak or full time. The period with the most significant reduction in the energy purchase from the grid was 17:00 h, where the purchase of energy suffered a reduction between 18.16% and 20.45%. An economic analysis of the optimal solution for each scenario is performed to assess the feasibility of integrating wind and storage systems in the building. The optimal solution for each scenario is based on the lifespan of the adopted batteries. Therefore, it is necessary  
Figure 8: Energy purchased from the grid for the scenarios presented. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Scenario 1** & **Scenario 2** & **Scenario 3** & **Scenario 4** \\ \hline Optimal value & 221,023.49 EUR & 431,492.59 EUR & 663,920.59 EUR & 920,959.21 EUR \\ Tariff & Optional tariff & Optional tariff & Optional tariff & Optional tariff \\ Wind turbine & Aeolos-H 20 kW & Aeolos-H 20 kW & Aeolos-H 20 kW & Aeolos-H 20 kW \\ Battery & BYD 8 kW & BYD 8 kW & BYD 8 kW & LG Resu 13 kW \\ N. of batteries & 4 & 3 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal solutions for each scenario. to determine the amortization value of the annual investment and extend it to the lifespan of the turbine, which is 20 years. As shown in the graph in Figure 9, the balance sheet values are between approximately \(-\)30,000 EUR, corresponding to the initial investment of the project, and 80,000 EUR, which represents the savings over the 20 years of the integration of the wind and storage project in the building. Therefore, it is quickly concluded that scenario 4 is the scenario with the highest profitability and that for the analysis period, it guarantees greater savings over the 20 years. Scenario 1, which concerns the scenario where the battery lifespan is five years, is the worst performance regarding the speed of amortizing the investment made and total revenue for the period under analysis. Note that in the sixth year, there was practically no amortization due to the new investment in batteries, because after five years, the replacement of the batteries is necessary. Focusing now on scenario 4, the main differences observed between it and the other scenarios are the adoption of a different ESS and the absence of reinvestment in the analysis period. Given that the adopted turbine and the energy tariff the same across the different scenarios, the notable difference between them is the use in terms of the maximum allowed cycles per year of the batteries, in this case, 300 cycles per year for a total of 6000.