## 4 Test System Description and Experimental Setup for Algorithmic Benchmarking
### Comparison of Optimization Methodologies and Parameter Calibration  
All optimization approaches were calibrated using a PSO algorithm with a swarm size of 100 particles. Both the cognitive and social coefficients were set to 1.494, while the inertia weight decreased linearly from 1 to 0. The stopping condition was defined as a maximum of 300 iterations. This algorithm has been widely adopted in the literature to improve energy management strategies in systems incorporating distributed energy resources [47]. In this study, its role is to identify the optimal parameter set that allows each control strategy to reach its highest performance. During the tuning process, tailored parameter configurations were defined for each optimization method under both grid-dependent and self-powered conditions. Specifically, for the MVO algorithm, the grid-dependent scenario employed a population size (N\(\hat{n}\)) of 100 agents and a maximum of 1964 iterations (T\(Max\)). The inertia weight varied linearly from 0 to 1 (WEP\(Min\) and WEP\(Max\)), with the exponential constant (\(p\)) set to 10. In contrast, the self-powered configuration used 200 agents, 2000 iterations, the same inertia range, and a reduced exponential constant of \(p=8\). To assess the effectiveness of the PMVO/SA-based EMS, comparative analyses were carried out against two alternative metaheuristic algorithms: the Chu & Beasley Genetic Algorithm (CBGA) [48] and the Vortex Search Algorithm (VSA) [49]. All methods were implemented using the same power flow solver (SA), ensuring a consistent evaluation framework. For the Chu & Beasley Genetic Algorithm, the grid-dependent configuration used 10 individuals (N\(\hat{n}\)) over 2000 iterations (T\(Max\)), applying three mutation operations per generation (\(N_{m}\)). In the self-powered mode, the population size was increased to 200 individuals with 4000 iterations, while the number of mutations per generation was reduced to one. Regarding the Vortex Search Algorithm, the grid-dependent setup employed a population (N\(\hat{n}\)) of 100 individuals and a maximum of 1000 iterations (T\(Max\)), while the self-powered case utilized 233 individuals and 4000 iterations. The decay rate (\(\chi\)) was adapted to each scenario, with values of -9.0645 for the grid-dependent mode and -11.4285 for the self-powered case. Moreover, to significantly accelerate computations, this study incorporates a parallel processing scheme into the proposed optimization methodologies, giving rise to the Parallel Vortex Search Algorithm (PVSA) and Parallel Multi-Vorse Optimizer (PMVO). These enhanced versions leverage all available CPU cores to simultaneously evaluate multiple BESS operation schemes per iteration using the Successive Approximations (SAs) method [50], dramatically reducing computation time by distributing power flow analyses across multiple threads [51; 52]. In contrast, the Chu & Beasley Genetic Algorithm (CBGA) maintains a sequential approach, evaluating only one solution per iteration due to its inherent structure, underscoring the superior efficiency of the parallelized methods for large-scale optimization problems [48]. To ensure robustness, consistency, and reproducibility, all optimization algorithms were executed under identical conditions, using the same power flow solver, system configuration, demand and PV generation profiles, and tuning methodology. Each method was tested over 100 independent runs in both grid-connected and self-powered modes. The performance evaluation reports the best, average, and standard deviation values for energy losses and CO\({}_{2}\) emissions, as well as the average computation time per method. Additionally, violin-scatter plots are included to illustrate the variability and distribution of the results. In this analysis, two approaches were considered: (i) a scenario without BESS operation (base case) and (ii) a scenario with BESS actively operated using the proposed optimization methodologies.