Adaptive fractional-order moth flame swarm intelligence algorithm for optimal reactive power dispatch and stability enhancement in power grids

This paper presents a fractional-order swarm intelligence optimization framework for solving the optimal reactive power dispatch (ORPD) problem in modern power grids. The proposed method integrates fractional calculus into the moth-flame optimization algorithm to capture the memory and hereditary characteristics inherent in complex power systems. The fractional-order formulation enhances information exchange among candidate solutions and improves the exploitation capability of the search process. The resulting fractional-order moth-flame optimization (FMFO) algorithm was applied to IEEE benchmark power systems to minimize real power losses and voltage deviations while considering flexible alternating current transmission system (FACTS) device constraints. Simulation results demonstrate significant performance improvements, achieving active power loss reductions of 17.53% in the IEEE-30 bus system, 43.32% in the modified IEEE-30 bus network, and 22.5% in the IEEE-57 bus system. Furthermore, voltage deviation was reduced by up to 84% in the IEEE-57 benchmark system. Statistical evaluations confirm the robustness, stability, and superior convergence behavior of the proposed fractional-order swarm optimization framework compared with conventional optimization techniques, demonstrating its effectiveness for intelligent power system operation.