Applications of Particle Swarm Optimization Algorithm to Solving the Economic Load Dispatch of Units in Power Systems with Valve-Point Effects"

Abstract

The Economic Load Dispatch (ELD) problem is a cornerstone of power system operation, aiming to allocate generation among thermal units to minimize total fuel cost while satisfying load demand and operational constraints. The presence of valve-point effects, which arise from the multi-valve characteristics of steam turbines, introduces non-linear, non-smooth, and multi-modal cost functions that render conventional optimization methods such as lambda iteration or quadratic programming ineffective. This paper presents a comprehensive analysis of Particle Swarm Optimization (PSO) and its advanced variants for solving the ELD problem with valve-point effects. Standard PSO, while simple and fast, exhibits premature convergence in the presence of multiple local minima. To address this limitation, hybrid approaches integrating evolutionary strategies, differential evolution, harmony search, and biogeography-based optimization are evaluated, demonstrating improved exploration-exploitation balance. Additionally, quantum-inspired PSO frameworks leverage probabilistic position updates to enhance global search capability and effectively navigate complex non-convex landscapes. The study systematically synthesizes results from multiple PSO-based strategies, including chaotic PSO, hybrid PSO, artificial bee colony-assisted PSO, and firefly algorithm hybrids, highlighting their convergence characteristics, cost minimization performance, and robustness against parameter variations. Findings indicate that quantum-behaved PSO consistently achieves superior fuel cost reduction and faster convergence compared to classical and hybrid methods (Zhisheng, 2010). The paper further critically examines the limitations of these approaches, including sensitivity to control parameters, computational overhead in large-scale systems, and trade-offs between convergence speed and solution accuracy. Realistic simulations on benchmark multi-unit test systems validate the practical applicability of these methods, demonstrating that hybrid and quantum-inspired PSO algorithms can achieve cost reductions of up to 2–3% compared to conventional techniques, while maintaining operational feasibility under generator constraints. By consolidating and analyzing these advanced PSO methodologies, the study provides a robust framework for power system operators and researchers to implement effective, adaptive, and reliable ELD solutions in the presence of valve-point effects. The insights gained from this research are critical for improving economic efficiency, optimizing operational performance, and facilitating integration with modern energy management systems, including renewable energy sources. The findings also highlight future research directions, emphasizing the need for adaptive parameter tuning, real-time implementation, and multi-objective optimization encompassing both economic and environmental objectives.