NURBS values based on multi-objective particle swarm optimization algorithm for optimal power flow problem in power system

The research on Optimal Power Flow (OPF) problems in power systems has undergone significant development, yet a significant gap persists in effectively addressing the multi-objective nature of these problems, particularly within the context of modern power systems characterized by increasing renewable energy integration. This study posits that the incorporation of the Non-Uniform Rational B-Spline (NURBS) curve concept into the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm can significantly enhance its performance in resolving OPF problems. This paper introduces a novel methodology, termed NURBS-MOPSO, which capitalizes on the geometric structure of the Pareto front to facilitate co-evolution among subpopulations of particles. This approach aims to optimize the OPF problem within power systems, with the objectives of minimizing generation costs, reducing pollution emissions, balancing line loads, and maintaining node voltage stability simultaneously. Comprehensive simulations are conducted on the IEEE 30- bus and 57-bus systems, demonstrating the superior performance of the proposed algorithm.