## 4 Results  
The proposed solution technique for the optimal coordination of OCRs was tested with the network depicted in Figure 3 (adapted from [21]), the parameters of which can be consulted in [40]. This system corresponds to an IEC test network used in several research papers [10; 11; 21; 41; 42]. Furthermore, for comparative purposes with other techniques, the same formulation of [21] was considered. Table 1 summarizes the four scenarios considered. These scenarios refer to different conditions under which the DN is expected to operate. In scenario 1, the DG units are disconnected and the load is met using the main power supply; in contrast, in scenario 2, all DG units are connected and the load is fed using not only the DG plants but also the main power supply. In scenario 3, the DG3 and DG4 units are disconnected, so the load is supplied by the main power supply and also by the DG1 and DG2 units. In scenario 4, the DN is disconnected from the main power grid and the load is fed using the DG units only. Five three-phase line failures were considered. In this case, fault 1 represents a fault on line DL-5; Fault 2 and Fault 3 are failures on lines DL-4 and DL-2, respectively; fault 5 represents a fault on the DL-1 line; and F5 represents a fault on the DL-3 line. The results obtained with the proposed approach were compared with those reported in [10,11]. Additionally, \(CTI\) was set to 0.3 s and IEC normal inverse curves were considered for all relays, which are labeled with numbers ranging from 1 to 15. Figure 3 shows the location of each relay. Switches CB-LOOP1 and CB-LOOP2 remained open for all scenarios under consideration. Several tests were performed to adjust the HS and HS-SA parameters. Such tests were carried out by trial and error based on recommendations reported in [22,34]. The parameters that showed the best performance for both HS and HS-SA algorithms were: number of iterations 1000, harmony memory size 25, number of new harmonies 20, har \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **Main Grid** & **DG1** & **DG2** & **DG3** & **DG4** \\ \hline
1 & ON & OFF & OFF & OFF & OFF \\
2 & ON & ON & ON & ON & ON \\
3 & ON & ON & ON & OFF & OFF \\
4 & OFF & ON & ON & ON & ON \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution network scenarios. Figure 3: Distribution network with DG (adapted from [21]). mony memory consideration rate 0.9, and pitch adjustment rate 0.1. Furthermore, the SA parameters consist of an initial temperature (\(T_{0}\)) of 0.025 and a temperature reduction rate (\(\alpha\)) of 0.99, as recommended in [22]. As regards the parameters of the PSO and GA, these were adopted as suggested in [42] and limited to 1000 iterations. As previously mentioned, PSO, HS, PSO-HS and HS-SA techniques were implemented in order to solve the coordination problem. The results obtained with these techniques are compared with those found in the literature [10; 11; 21]. Table 2 presents the total operating time (\(T(s)\)) obtained with each implemented technique. It is important to highlight that in all scenarios under analysis, HS-SA obtained adequate coordination and lower operating times than reported in [10; 11; 21]; additionally, HS-SA performed better HS, PSO and PSO-HS. Note that for all operative scenarios, HS, PSO and PSO-HS were also able to obtain a proper coordination with lower operational times than those reported in [10; 11]. In conclusion, HS-SA remains an appealing option for solving the optimal coordination problem due to its ease of implementation and high performance. Figures 4-7 show the convergence curves of the implemented algorithms, as well as the curve of the GA proposed in [21]. In Figure 5, GA presents the fastest convergence; nonetheless, the implemented hybrid HS-SA is the algorithm with the shortest operating time (best objective function). Figure 5 depicts the convergence curves for scenario 2. Figure 5: Convergence of different algorithms for Scenario 2. Figure 6: Convergence of different algorithms for Scenario 3.