Latitude Based Model for Tilt Angle Optimization for Solar Collectors in the Mediterranean Region

Abstract

This paper inspects the different parameters that intervene in the determination of the optimal tilt angle for maximum solar energy collection. It proposes a method for calculating the optimal tilt angle based upon the values of the daily global solar radiation on a horizontal surface. A computer program using the mathematical model to calculate the solar radiation incident on an inclined surface as a function of the tilt angle is implemented. Four years data of daily global solar radiation on a horizontal surface in 35 sites in different countries of the Mediterranean region is used. The program assumes a due south orientation of the collectors and it determines the optimal tilt angle for maximum solar radiation collection for sites in the Mediterranean region. A regression analysis using the results of the computer simulation is conducted to develop a latitude based tilt angle optimization mathematical model for maximum solar radiation collection for the sites. We tested both a linear and a quadratic model (of the form ax2+bx) for representing the relationship between the annual optimal tilt angle and the site's latitude. The quadratic model is better; it provides very high prediction accuracy. 99.87% of the variation in the annual optimal tilt angle is explained by the variability in site's latitude with an average residual angle of only 0.96° for all 35 sites studied. It also gives an average percentage decrease in the annual solar radiation of only 0.016% when compared with actual optimal tilt angles.