## 4 Simulation and Results
### The IEEE Test Systems (33-Bus and 69-Bus)  
The optimization for the 33-bus test network is conducted with regard to the acquired economic data. The results are demonstrated in Table 3. In addition, the convergence behavior of two targeted methods in reaching the optimal solution is illustrated in Figure 7. Accordingly, the LAPO method has reached the optimal solution with fewer iteration. In terms of accuracy, the results of LAPO are better than the ABC algorithm. As can be seen, at the early hours of the time horizon (at midnight), when there is no solar power generation, a battery energy storage unit can supply the demand of internal loads of the microgrid as it is clear that the battery power is negative during these hours, which indicates that it is discharged. The battery starts charging after 8:00 and reaches its maximum charge level at 11:00. Therefore, no power is stored in it until it starts discharging again at 18:00. It is recharged at 19:00 and fully discharged at 20:00 due to the high volume of consumption. The diesel generator commits at 8:00 and stops power exchange at 9:00. These conditions continue until 20:00, and after that, it continues to serve the loads until midnight. Due to the significant amount of solar production, a large volume of this production is sold to the distribution network, and the obtained profit improves the objective function. As it is evident, the network is designed in such a way that no load is interrupted during the day and all the loads are completely satisfied. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Jan.** & **Feb.** & **Mar.** & **Apr.** & **May** & **Jun.** & **Jul.** & **Aug.** & **Sep.** & **Oct.** & **Nov.** & **Dec.** \\ \hline
5.45 & 5.73 & 6 & 6.01 & 5.65 & 5.26 & 4.81 & 4.78 & 5.15 & 5.63 & 5.84 & 5.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The mean solar radiation for each month for both radiation systems. [45]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Load Level** & **\begin{tabular}{c} **Price of Residential** \\ **Load (\(\upupup\)/MW)** \\ \end{tabular} & **\
\begin{tabular}{c} **Price of Industrial** \\ **Load (\(\upupup\)/MW)** \\ \end{tabular} & **
\begin{tabular}{c} **Percent of** \\ **Peak Load** \\ \end{tabular} \\ \hline Low & 35 & 2000 & 50 \(<\) L \\ Middle & 49 & 2800 & 50 \(<\) L \(<\) 70 \\ Peak & 70 & 3050 & L \(>\) 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The electricity price for different load types and various demand levels for both distribution systems. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Level** & **\begin{tabular}{c} **Price of Residential** \\ **Load (\(\upup)/MW)** \\ \end{tabular} & **\
\begin{tabular}{c} **Price of Industrial** \\ **Load (\(\upup)/MW)** \\ \end{tabular} & **
\begin{tabular}{c} **Percent of** \\ **Peak Load** \\ \end{tabular} \\ \hline Low & 35 & 2000 & 50 \(<\) L \\ Middle & 49 & 2800 & 50 \(<\) L \(<\) 70 \\ Peak & 70 & 3050 & L \(>\) 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The electricity price for different load types and various demand levels for both distribution systems. With regard to the economic data provided in the previous section, the optimization problem is simulated on the 69-bus test system. The optimized results of the simulation are presented in Table 3. In addition, the convergence behavior of both optimization techniques employed in this study is depicted in Figure 8. As can be seen, it is evident that the LAPO approach not only has reached the optimal solution in less iteration, but also it has found a better solution in comparison with the ABC method. The behavior of the microgrid in August is illustrated in Figure 9. As can be perceived, in the early hours at midnight, while the sunrise has not occurred, the battery is responsible for maintaining power for the microgrid. Thus, the power battery is negative in these hours, which implies that the battery is discharging. The battery starts to be charged at 8:00 in the morning, and it will be fully charged at 11:00.