Voltage stability analysis of power transmission systems using multi-index framework of hybrid whale and particle swarm optimization technique

Abstract

The persistent increase in grid collapse has necessitated the need for robust solutions for stability. Hybrid whale and particle swarm optimization (WAPSO) algorithm integrated with multi-index stability indices (MIS) has been applied to enhance voltage stability in this paper. The method is tested on the Nigeria 48-bus, 330 kV transmission system and simulated in MATPOWER embedded in MATLAB. The WAPSO algorithm is optimized with parameters w = 0.4, c₁ = 1.4 and c₂ = 1.5. The outcome achieved 98.84% reduction in mean MIS from 0.3959 to 0.0048 and a robustness index of 0.0051. This depicts low variability of 0.057 and 100% success rate across five dynamic scenarios explored such as gradual load growth with 98.79%, sudden spikes achieved 98.84%, cyclic fluctuations at 98.67%, renewable uncertainty at 98.74%, and N-1 contingencies at 98.84% improvement, respectively. Critical lines, 34-35 and 24-33 exhibit more than 99% MIS improvement, while weak lines, 21-22 and 24-40 achieved 85–87% enhancement, indicating areas for further reinforcement. The LSI and FVSI are reduced to 0.0048 and 0.1477 showing 56.79% improvement respectively as against the 38.9% MIS improvement obtained with the PSO-GA. This demonstrates WAPSO as a highly robust and adaptable technique offering a scalable solution for enhancing grid reliability under dynamic conditions.