This study proposes an integrated control–optimization framework for harmonic mitigation in two-level, grid-connected inverters with battery energy storage operating under unbalanced grid conditions. A proportional–resonant controller in the stationary $\alpha \beta$ frame and a proportional–integral controller in the synchronous $dq$ frame are compared, with controller gains optimized using PSO, GA, and a hybrid PSO–GA approach. The hybrid method achieves superior trade-offs among THD, convergence speed, and computational effort. For the PR controller, hybrid PSO–GA reduces THD to 1.07%, satisfying IEEE 1547 and IEC 61727 standards, while for the PI controller it achieves 2.70%, outperforming standalone PSO (4.12%) and GA (3.38%). The hybrid-optimized gains further minimize tracking error indices (IAE, ISE, ITAE, ITSE), ensuring precise steady-state current regulation. Convergence analysis shows that hybrid PSO–GA attains optimal solutions within three iterations for both controllers, faster than GA and comparable to PSO for the PR case. Simulation studies on the IEEE 13-bus unbalanced feeder in DIgSILENT PowerFactory validate the proposed framework. Results confirm that the PR controller delivers a 60.36% THD reduction and tenfold ISE improvement over the optimized PI design, establishing a robust and scalable solution for harmonic suppression in unbalanced grid-tied energy systems.

This paper presents the Multi-Objective Reptile Search algorithm for identifying ideal rating and location of distributed generation in unbalanced grids, focusing on minimizing power losses, total costs, and carbon emissions. The proposed methodology integrates DIgSILENT PowerFactory and Python platforms to evaluate unbalanced IEEE distribution feeders under varying power factor conditions. The results demonstrate that optimal DG configurations involve strategically positioning multiple units to enable both active and reactive power injection, significantly improving overall system performance across multiple objectives and voltage deviation index. The analysis identifies an optimal PF range between 0.75 and 0.89, with unity power factor operations yielding suboptimal outcomes. Moreover, increasing the number of DG units generally enhances grid efficiency and reduces power losses, although a trade-off emerges between cost savings and carbon emission reductions, particularly when fewer DG units are deployed. The findings highlight the importance of balancing these objectives based on system operator priorities for sustainable and efficient power system management. A comparative study validates that proposed algorithm outperforms the Multi-Objective Particle Swarm Optimization method, demonstrating efficient capabilities in addressing the complexities of multi-objective DG optimization.