Computing Optimum Solar Tilt Angles for Photovoltaic Applications Through Python Code Simulation

Carrying out the dual objectives of computing the optimized tilt angles for multiple locations in Pakistan along with recommending a generalized approach for the estimation of optimum tilt angle for any location in country, this study was conducted. Python code was developed for the optimization purpose of daily, monthly, seasonally, biannually and annual solar tilt angle. Detailed analysis was presented for one location (Karachi) and a comparative analysis of optimum tilt angle conditions has been conducted for all investigated sites. Daily optimum tilt angles were found to vary from −12.0° to 55.5°. Similarly, monthly optimized tilt angles were found to vary from −11.5° (in June) to 55.0° (in December). Furthermore, seasonal tilt angles were found as 46.0 °, 2.0 °, 0.5 ° and 45.0 ° in winter, spring, summer and autumn respectively. Finally, annual optimum tilt angle (fixed throughout the year) was found as 25.5° (closer to the latitude value of Karachi). It has been found that daily adjustment of tilt angle causes a gain of 6.85% in annual energy yields when compared with fixed angle throughout the year. Similarly, energy gains were found as 0.15%, 1.24% and 6.83%, when tilt angle was adjusted daily as compared to monthly, seasonal and biannual adjustment cases respectively. The optimum tilt angle for three pairs of locations having comparable latitudes were compared and it was found that the sites having comparable latitudes do not have any marked difference in their optimum tilt angle values.