A Hybrid DE–NSGA-II Framework for Stochastic Multi-Objective Optimal Power Flow Considering Wind Uncertainty: Pareto-Based Analysis on a Real Transmission System

Abstract

Abstract: This paper proposes a stochastic multi-objective optimal power flow (MO-OPF) framework that incorporates wind power uncertainty using a scenario-based modeling approach. A hybrid Differential Evolution–Non-dominated Sorting Genetic Algorithm II (DE–NSGA-II) is introduced to enhance convergence speed and solution diversity compared to conventional NSGA-II. The proposed model simultaneously minimizes generation cost, transmission losses, and emission levels while satisfying system operational constraints. The methodology is validated on a real transmission network representing the Sulawesi power system. Simulation results show that the proposed approach achieves significant performance improvements, where generation cost is reduced from 10,101 to 3,740.7, transmission losses decrease from 62.955 to 24.65, and emission levels are lowered from 14,571 to 4,101.9 across the obtained Pareto solutions. These results demonstrate the capability of the model to effectively balance conflicting objectives under wind power uncertainty. Furthermore, the generated Pareto front exhibits a well-distributed and non-linear structure, indicating strong diversity and robustness of the hybrid DE–NSGA-II algorithm in exploring the solution space. The obtained solutions reveal clear trade-offs among economic, technical, and environmental objectives, providing flexibility for system operators in decision-making. These findings confirm that the proposed framework is effective and suitable for modern power system operation with high penetration of renewable energy sources.