Symmetry-Inspired Comparative Evaluation of Metaheuristic Algorithms for Optimized Control of Distributed Generation Microgrids with Active Loads

Optimizing the control parameters of an islanded microgrid with active load integration presents a challenging operational research problem since current methodologies frequently fail to reach the ideal balance or symmetry between transient response, stability, and efficiency. The conventional methods, such as the canonical Particle Swarm Optimization (PSO), have settling time and voltage ripple minimization constraints, indicating possible improvement scopes. This research addresses this gap by employing advanced metaheuristic algorithms such as Accelerated Particle Swarm Optimization (APSO), Accelerated Particle Swarm Optimization with variable α (APSO α), Accelerated Particle Swarm Optimization with Normal Distribution (APSO_G), Rayleigh Distribution Accelerated Particle Swarm Optimization (RDAPSO), Rayleigh Distribution Accelerated Particle Swarm Optimization with variable α (RDAPSO α), and the Dragonfly Algorithm (DA). The algorithms were tested for their performance by using CEC Standard Benchmark functions from 2017, 2019, and 2022, providing a basis for rigorous and symmetrical testing and validation. The optimized RDAPSO α algorithm showed a significant reduction in voltage ripple, which was reduced from 4 V to 0.47 V, with an 88.25% reduction. It also showed a 46.32% improvement in settling time, which was reduced from 184.2 ms to 98.9 ms compared to PSO. A detailed statistical analysis was conducted to enhance the reliability and symmetry of the outcomes using Multivariate Analysis of Variance (MANOVA), the Mann–Whitney U test, the Friedman test, and the Bonferroni test. The results show that RDAPSO α offers a significant edge over the rest of the algorithms, with improvements that can be declared statistically superior in optimizing microgrids with improved symmetry in performance.