## 4 Test System Description and Experimental Setup for Algorithmic Benchmarking
### Test System  
This study evaluates the operational performance of a 33-node AC MG test system under both grid-dependent and self-powered modes [38], as illustrated in Figure 3. The analysis incorporates realistic power generation and demand profiles for Medellin, Colombia, derived from operational data provided by Empresas Publicas de Medellin (EPM) [39] and solar irradiance datasets from NASA [35]. This 12.66 kV test system (100 kW base) features a 33-node architecture with 32 distribution lines. The slack bus (Bus 1) operates with dual functionality:  
* Acts as PCC (Point of Common Coupling) in grid-dependent mode;
* Switches to diesel generator control in self-powered mode. The diesel generator connected at the Point of Common Coupling (PCC) has a nominal capacity of 4000 kW, with its dispatch constrained between 1600 kW and 3200 kW (40% to 80% of rated capacity) to ensure reliable performance and extend operational lifespan [33]. This slack bus configuration accurately represents the microgrid's dual-mode operation: in grid-connected mode, Bus 1 acts as the PCC, balancing active and reactive power by exchanging energy with the upstream network to maintain voltage stability; in islanded mode, the diesel generator assumes the slack role, regulating power balance internally without external support. The operational limits prevent the generator from running at zero load or full capacity continuously, avoiding damage and maintenance issues. Consequently, the control algorithm must carefully coordinate energy storage and renewable sources to meet demand while keeping the diesel generator within its safe operating range. This strategy reflects realistic constraints typical of isolated power systems and ensures reliable, efficient microgrid operation. Complete line parameters, including resistance and reactance per kilometer, as well as load demands and current limits, are provided in Table 1[40]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Line** & **From** & **To** & \(R_{ij}\) & \(X_{ij}\) & \(P_{j}\) & \(Q_{ij}\) & \(I_{ij}^{\text{max}}\) \\ \(l\) & **Node _i_** & **Node _j_** & **(G)** & **(G)** & **(G)** & **(G)** & **(G)** & **(G)** \\ \hline
1 & 1 & 2 & 0.0922 & 0.0477 & 100 & 60 & 385 \\
2 & 2 & 3 & 0.4930 & 0.2511 & 90 & 40 & 355 \\
3 & 3 & 4 & 0.3660 & 0.1864 & 120 & 80 & 240 \\
4 & 4 & 5 & 0.3811 & 0.1941 & 60 & 30 & 240 \\
5 & 5 & 6 & 0.8190 & 0.7070 & 60 & 20 & 240 \\
6 & 6 & 7 & 0.1872 & 0.6188 & 200 & 100 & 110 \\
7 & 7 & 8 & 1.7114 & 1.2351 & 200 & 100 & 85 \\
8 & 8 & 9 & 1.0300 & 0.7400 & 60 & 20 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Technical parameters of the 33-node AC microgrid test system. Figure 3: Topological schematic of the 33-node AC microgrid test system in dual-operation modes: Grid-dependent (M\({}_{1}\)) and self-powered (M\({}_{2}\)). The test system integrates three PV generation units with the following distribution:  
* Bus 12: 1125 kW rated capacity;
* Bus 25: 1320 kW rated capacity;
* Bus 30: 999 kW rated capacity. All photovoltaic systems operate under MPPT during the entire simulation horizon. Figure 4 presents the characteristic daily profiles of both solar generation and load demand for the Medellin case study. All values are expressed as percentages relative to the total installed capacity of PV generation available in the system and the total installed demand capacity supplied by the slack node or the corresponding distribution substation. The system includes three lithium-ion BESS units positioned at Buses 6, 14, and 31, as detailed in [41] and categorized as follows:  
* **Type A**: 1000 kW h capacity (4-h charge/discharge);
* **Type B**: 1500 kW h capacity (4-h charge/discharge); \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Line** & **From** & **To** & \(R_{ij}\) & \(\textbf{X}_{ij}\) & \(\textbf{P}_{j}\) & \(\textbf{Q}_{j}\) & \(\textbf{I}^{\text{max}}_{ij}\) \\ \(I\) & **Node \(i\)** & **Node \(j\)** & **(T)** & **(T)** & **(KW)** & **(kV/Av)** & **(A)** \\ \hline  
\hline \end{tabular}
\end{table}