A COMPARATIVE STUDY OF FOUR PARTICLE SWARM OPTIMIZATION VARIANTS FOR SOLVING THE ECONOMIC DISPATCH PROBLEM

Abstract

Economic Dispatch (ED) is a fundamental optimization problem in power-system operation, whose objective is to determine generator outputs that minimize total fuel cost while satisfying load demand and operating constraints. Although classical deterministic methods are effective for smooth convex ED, transmission losses and additional non-convex operating features can complicate the formulation. Population-based metaheuristics, particularly Particle Swarm Optimization (PSO), therefore provide flexible alternatives for such extensions. In this paper, four representative PSO variants, namely standard PSO (PSO-std), PSO with linearly decreasing inertia weight (PSO-w), PSO with constriction factor (PSO-CF), and PSO with time-varying acceleration coefficients (PSO-TVAC), are systematically compared on a three-unit ED test system with transmission losses at a load demand of 850 MW. To eliminate the equality constraint, an N−1 encoding is adopted: P1 and P2 are treated as control variables, whereas P3 is recovered analytically from the power-balance equation. Two experiments are conducted: (i) varying the population size from 10 to 50 with 50 fixed iterations, and (ii) varying the iteration count from 20 to 120 with a fixed population size of 10. For each configuration, 50 independent runs are performed and statistical indicators are reported. The results show that all four variants reach the same optimal cost of 8344.5927 USD/h, but their convergence behaviors differ markedly. Under limited iteration budgets, PSO-TVAC achieves the smallest standard deviation, followed by PSO-w, PSO-CF, and PSO-std. On this benchmark, the findings show that the choice of inertia and acceleration schedules materially affects convergence speed and run-to-run consistency under limited iteration budgets.