Hybrid Osprey-Salp Swarm Optimization Algorithm for Single and Multiobjective Optimal Power Flow in Smart Grids With Renewable Energy Integration

Abstract

The increasing integration of renewable energy sources into smart grids presents substantial challenges in solving the nonlinear and nonconvex optimal power flow (OPF) problem. This paper proposes a comprehensive OPF model that incorporates conventional thermal generators, solar photovoltaic generators, and hydroelectric power generators, while effectively addressing the uncertainties associated with renewable power generation. A lognormal probability distribution models solar irradiance variability in solar generators, while a Gumbel distribution captures water availability fluctuations in hydro generators. The paper proposes a novel hybrid optimization approach, hybrid osprey-salp swarm optimization (HOSSO), to solve this complex OPF problem. The HOSSO leverages the exploration–exploitation balance of Osprey Optimization alongside the adaptive leadership and follower dynamics of Salp Swarm Optimization. The proposed methodology is validated on Institute of Electrical and Electronics Engineers 30-, 57-, and 118-bus test systems across five distinct optimization scenarios: economic cost minimization, emission cost minimization, combined economic–environmental cost minimization, voltage deviation penalty cost minimization, and renewable generation uncertainty penalty cost minimization. The model incorporates reserve and penalty costs for renewable generation uncertainty and integrates carbon emission taxation to enhance grid reliability and sustainability. Comparative analysis against classical and hybrid optimization techniques demonstrates the superior performance of HOSSO across most test scenarios, consistently achieving competitive solutions while satisfying system constraints and stability requirements. The algorithm delivers improvements ranging from 0.4% to 17% in cost minimization, 3%–23% in voltage deviation minimization, and 2%–8% in uncertainty management over competing methods, with performance advantages becoming increasingly pronounced as system scale grows. The algorithm exhibits rapid convergence within 20–50 iterations, effectively avoids local optima, and proves well-suited for both single- and multiobjective OPF problems in renewable energy-integrated power systems. The results highlight HOSSO's potential for real-time power system applications and its adaptability to smart grids with high renewable energy penetration.