This research aims to experimentally improve the overall efficiency of solar photovoltaic (PV) panels by coating them with hydrophobic SiO₂ nanomaterial. Also, an accurate mathematical model was used to estimate the parameters of the PV panel, which is a non-linear optimization problem. Based on the experimental data and using the particle swarm optimization (PSO) algorithm, the optimal five parameters of a single diode model of a PV panel were determined in this study. This experimental work was conducted and carried out in the Renewable Energy Laboratory of Assiut University, Egypt. A comparative analysis was completed for three identical solar PV panels; the first panel was coated with hydrophobic SiO₂ nanomaterial, so it was considered to be a self-cleaning panel; the second panel was uncoated and cleaned manually on a daily basis; and the third panel was kept dusty all the time through the experimental investigation, and was used as a reference. Experimentally, the output power of the PV panels was monitored for each panel in this study. Also, the anti-static and anti-reflection effects of coating solar PV panels with hydrophobic SiO₂ nanomaterial were investigated experimentally. According to the obtained experimental results, it was found that the use of SiO₂ coating for PV panels results in the better performance of the PV panels. The overall efficiency of the coated panel increased by 15% and 5%, compared to the dusty panel and the uncoated panel which was manually cleaned daily, respectively.