Multi-Objective Optimization and Load-Flow Analysis in Complex Power Distribution Networks

Modern power distribution networks are increasingly challenged with nonlinear operating conditions, the high penetration of distributed energy resources, and conflicting operational objectives such as loss minimization and voltage regulation. Existing load-flow optimization approaches often suffer from slow convergence, premature stagnation in non-convex search spaces, and limited robustness when handling conflicting multi-objective performance criteria under fixed network constraints. To address these challenges, this paper proposes a Fractional Multi-Objective Load Flow Optimizer (FMOLFO), which integrates a fractional-order numerical regularization mechanism with an adaptive Pareto-based Differential Evolution framework. The fractional-order formulation employed in FMOLFO operates over an auxiliary iteration domain and serves as a numerical regularization strategy to improve the sensitivity conditioning and convergence stability of the load-flow solution, rather than modeling the physical time dynamics or memory effects of the power system. The optimization framework simultaneously minimizes physically consistent active power loss and voltage deviation within existing network operating constraints. Extensive simulations on IEEE 33-bus and 69-bus benchmark distribution systems demonstrate that FMOLFO achieves an up to 27% reduction in active power loss, improved voltage profile uniformity, and faster convergence compared with classical Newton–Raphson and metaheuristic baselines evaluated under identical conditions. The proposed framework is intended as a numerically enhanced, optimization-driven load-flow analysis tool, rather than a control- or dispatch-oriented optimal power flow formulation.