Fractional Calculus and Adaptive Balanced Artificial Protozoa Optimizers for Multi-Distributed Energy Resources Planning in Smart Distribution Networks

This paper presents two enhanced variants of the Artificial Protozoa Optimizer (APO), namely the Adaptive Balanced Artificial Protozoa Optimizer (AB-APO) and the Fractional Calculus-Enhanced Artificial Protozoa Optimizer (FC-APO), for optimal multi-Distributed Energy Resources (DERs) planning in smart radial distribution networks. The proposed framework addresses the coordinated allocation of Electric Vehicle Charging Stations (EVCSs), photovoltaic (PV) units, and Battery Energy Storage Systems (BESS). The AB-APO introduces an adaptive balancing mechanism that dynamically regulates exploration and exploitation to improve convergence stability and robustness, while the FC-APO incorporates fractional-order dynamics to embed long-memory effects, enhancing numerical stability and search smoothness. The proposed optimizers are evaluated on the IEEE-33 and IEEE-69 bus systems under eight DERs penetration scenarios. Simulation results demonstrate significant reductions in real and reactive power losses, improved voltage profiles, and effective mitigation of EV-induced network stress. Real power loss reductions exceeding 54%, 38.53%, 53.78%, 38.20%, 61.68%, and 60.72% are achieved for the IEEE-33 system, while reductions of 64.32%, 63.51%, 64.33%, 63.51%, 67.31%, and 67.04% are obtained for the IEEE-69 system across Scenarios 3–8. Overall, the results highlight the effectiveness of adaptive balancing and fractional-order modeling in strengthening APO-based optimization and confirm the suitability of the AB-APO and FC-APO as efficient planning tools for future smart distribution networks.