Abstract
This paper presents a comprehensive analytical and computational study to determine the optimum tilt angle for south-facing photovoltaic (PV) panels installed in Tripoli, Libya (latitude L ≈ 32.9°N). The study employs the classical solar radiation model, which accounts for direct beam, diffuse, and ground-reflected radiation components striking an inclined collector surface. An insolation model carefully integrates essential solar geometric parameters, including the declination angle, hour angle, altitude angle, azimuth angle, and air mass ratio, ensuring precision and comprehensive analysis. The optimum tilt angle is obtained analytically by differentiating the total collector insolation with respect to the tilt angle Σ. Real measured data of solar irradiance [W/m²] and ambient temperature [°C], recorded every 10 minutes over 30 consecutive days in September 2025 in Tripoli, were used to validate the theoretical results. The findings confirm that the maximum annual solar energy is captured when the fixed surface faces due south at a tilt angle approximately equal to the local latitude. For autumn/winter conditions, slightly higher tilt angles are recommended, while spring/summer conditions favor lower tilt angles. These results provide actionable guidelines for the optimal deployment of PV installations across the North African Mediterranean region.