The increasing adoption of light-emitting diode (LED) technology in Nigeria and across Sub-Saharan Africa has delivered measurable gains in energy efficiency; yet these gains are substantially eroded by the power quality degradation inherent in conventional switch-mode LED driver circuits. This study presents a comprehensive modelling, simulation, and optimisation framework for evaluating power factor correction (PFC) strategies in 75 W LED lighting systems operating on a 220 V/50 Hz supply characteristic of the Nigerian grid. Five correction techniques were implemented and benchmarked across a structured parameter-sweep study of 900 simulation evaluations: series inductor passive PFC, LC filter passive PFC, active boost-converter PFC, a passive–active hybrid scheme, and a Particle Swarm Optimisation (PSO)-tuned hybrid. The baseline system without PFC exhibited a power factor of 0.50–0.70 and total harmonic distortion (THD) exceeding 50%, consistent with the behaviour of nonlinear rectifier-capacitor loads. The PSO-tuned hybrid achieved a power factor of 0.9999, THD of 1.65%, and efficiency of 98.24%, satisfying IEEE 519-2014 and IEC 61000-3-2 compliance thresholds. The active PFC stage alone attained a power factor of 0.9815, THD of 19.50%, and efficiency of 99.00%, confirming its practical adequacy for grid-connected LED deployment. All modelling, simulation, and optimisation were implemented in Python using the NumPy and SciPy scientific-computing libraries, with Average Current Mode Control (ACMC) applied to the boost stage. Findings demonstrate that active PFC delivers the strongest power-quality improvement per unit of circuit complexity for grid-connected LED systems, while PSO-based hybrid tuning offers a pathway to near-ideal harmonic compliance where regulatory demands are stringent. A full economic comparison of the strategies is identified as future work.