## 3 Simulation Results
### Minimization of the ENS Criterion  
In this section, for the ENS criterion, the optimal topology for the IEEE 33-bus test network is obtained using the exhaustive approach, GA, and PSO algorithms. Based on the combinatorial formula, the number of solutions to explore in this case is equal to \(\text{Nb}_{\text{sol}}=435.897\) solutions. There are a total of 50,751 radial configurations for this distribution network. Subsequently, using the proposed load-flow program, each of these configurations must be evaluated against the optimization criterion while adhering to all safety constraints.  
Table 1 summarizes the characteristics of the three methods developed to solve the mono-objective optimization problem infindingan optimal configuration for the IEEE 33-bus test system. The PSO approach appears to be the most efficient. In comparison to the AG and exhaustive research, it requires less computational effort.  
The optimal network configuration obtained for the minimization of the ENS criterion is shown in Figure 6. The open branches in this case are [7-9-14-16-27]. The ENS in this radial structure is 4.7304 kWh/year, which is 66.64% less than the initial topology (7.0980 kWh/year).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Optimal Configuration** & **ENS** & **Calculation Time (s)** \\  & **(Open Branches)** & **(kWh/an)** & **Calculation Time (s)** \\ \hline Exhaustive approach & 7-9-14-16-27 & 4.7304 & \(1.296\times 10^{-4}\) \\ GA & 7-9-14-16-27 & 4.7304 & 335.14 \\ PSO & 7-9-14-16-27 & 4.7304 & 150.36 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison between the proposed approaches for the minimization of the energy not supplied (ENS)criterion.  
Figure 5: IEEE 33-bus test system.  
A good voltage profile with regard to the initial topology was obtained by maximizing the reliability (Figure 7). The voltages are as close to the nominal voltage (1 pu) as possible. As a result, voltage profiles were improved in all network nodes. It is also evident that the security constraints are observed.  
In terms of the transited current restriction, we can observe from Figure 8 that all currents passing through the distribution lines were within their allowable limits. We also observed that the profile of the currents per branch was generally lower after the reconfiguration process.  
Figure 8: Currents profiles for the minimization of the ENS criterion (before and after reconfiguration)).  
Figure 6: Optimal configuration for the minimization of the ENS criterion (open branches: 7-9-14-16-27).  
Figure 7: Voltage profiles for the minimization of the ENS criterion (before and after reconfiguration)).  
Figure 9 shows the GA and PSO convergence characteristics of ENS for the IEEE 33-bus test system. From this figure, it is evident that the PSO algorithm outperforms the other algorithms in terms of speed to reach the optimal solution. The difference in terms of iterations in achieving an optimal solution was 25 iterations. Both algorithms achieved an optimal solution. However, compared to GA, the PSO approach appears to be more appealing due to its lower computational effort. This is demonstrated by the fact that, unlike the GA, we do not need to replicate the constraint validation test at each iteration. Therefore, this approach is considered one of the fastest techniques for solving distribution network optimization problems.