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<p>Renewable energy sources like wind, solar PV, and tidal energy are increasingly impacting power system operations, creating uncertainty and intermittency that make traditional deterministic Optimal Power Flow (OPF) formulations insufficient. This paper introduces a stochastic Multi-Objective Optimal Power Flow (MOOPF–PET) framework that minimizes four conflicting objectives: (i) total generation cost, (ii) emissions, (iii) active power loss, and (iv) voltage deviation. Wind speed, solar irradiance, and tidal flow uncertainties are modeled with Weibull, lognormal, and Gumbel distributions, respectively, allowing for a realistic representation of renewable variability in the MOOPF formulation. A hybrid <i>gbestABC–NSGA-II</i> algorithm is proposed to effectively tackle high-dimensional, nonlinear, and constrained optimization problems by combining the global exploration strength of the Artificial Bee Colony algorithm with the elitist non-dominated sorting and diversity preservation features of NSGA-II. A Diversity-Enhanced Tri-Stage Constraint-Handling (DEST) strategy is used to improve feasibility and robustness under complex constraints, while Pareto archive management with crowding-distance sorting enhances convergence and distributes Pareto-optimal solutions effectively. The framework is validated on standard ZDT and DTLZ benchmarks and the modified IEEE 30-bus, Standard IEEE 57-bus and IEEE 118-bus test system across various renewable penetration scenarios. Comparative studies with top multi-objective algorithms like MOGWO, MOPFA, NSGA-II, MOPSO, MOMVO, MOAHA, and MOSSA show consistent performance gains. The proposed approach reduces generation costs by about 5–12%, emissions by 6–15%, and active power losses by 4–10%, while enhancing voltage profiles in all cases studied. The performance evaluation with Inverted Generational Distance (IGD), Spacing (SP), and Wilcoxon signed-rank tests shows the proposed hybrid algorithm’s clear superiority in convergence accuracy, solution diversity, and robustness. The <i>gbestABC–NSGA-II</i> framework effectively addresses stochastic MOOPF problems, ensuring secure, economical, and sustainable operation of renewable-integrated power systems while aiding global net-zero emission goals.</p>

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A hybrid gbestABC–NSGA-II metaheuristic framework with tri-stage constraint handling for stochastic multi-objective optimal power flow in cleaner energy systems

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • A. B. Katkar,
  • H. T. Jadhav

摘要

Renewable energy sources like wind, solar PV, and tidal energy are increasingly impacting power system operations, creating uncertainty and intermittency that make traditional deterministic Optimal Power Flow (OPF) formulations insufficient. This paper introduces a stochastic Multi-Objective Optimal Power Flow (MOOPF–PET) framework that minimizes four conflicting objectives: (i) total generation cost, (ii) emissions, (iii) active power loss, and (iv) voltage deviation. Wind speed, solar irradiance, and tidal flow uncertainties are modeled with Weibull, lognormal, and Gumbel distributions, respectively, allowing for a realistic representation of renewable variability in the MOOPF formulation. A hybrid gbestABC–NSGA-II algorithm is proposed to effectively tackle high-dimensional, nonlinear, and constrained optimization problems by combining the global exploration strength of the Artificial Bee Colony algorithm with the elitist non-dominated sorting and diversity preservation features of NSGA-II. A Diversity-Enhanced Tri-Stage Constraint-Handling (DEST) strategy is used to improve feasibility and robustness under complex constraints, while Pareto archive management with crowding-distance sorting enhances convergence and distributes Pareto-optimal solutions effectively. The framework is validated on standard ZDT and DTLZ benchmarks and the modified IEEE 30-bus, Standard IEEE 57-bus and IEEE 118-bus test system across various renewable penetration scenarios. Comparative studies with top multi-objective algorithms like MOGWO, MOPFA, NSGA-II, MOPSO, MOMVO, MOAHA, and MOSSA show consistent performance gains. The proposed approach reduces generation costs by about 5–12%, emissions by 6–15%, and active power losses by 4–10%, while enhancing voltage profiles in all cases studied. The performance evaluation with Inverted Generational Distance (IGD), Spacing (SP), and Wilcoxon signed-rank tests shows the proposed hybrid algorithm’s clear superiority in convergence accuracy, solution diversity, and robustness. The gbestABC–NSGA-II framework effectively addresses stochastic MOOPF problems, ensuring secure, economical, and sustainable operation of renewable-integrated power systems while aiding global net-zero emission goals.