A Theoretical Optimum Tilt Angle Model for Solar Collectors from Keplerian Orbit

Tong Liu,Guochang Xu,Li Liu,Mengfei Sun,Jian Liu,Yufang He

doi:10.3390/en14154454

Abstract

Solar energy has been extensively used in industry and everyday life. A more suitable solar collector orientation can increase its utilization. Many studies have explored the best orientation of the solar collector installation from the perspective of data analysis and local-area cases. Investigating the optimal tilt angle of a collector from the perspective of data analysis, or guiding the angle of solar collector installation, requires an a priori theoretical tilt angle as a support. However, none of the current theoretical studies have taken the real motion of the Sun into account. Furthermore, a complete set of theoretical optimal tilt angles for solar energy is necessary for worldwide locations. Therefore, from the view of astronomical mechanics, considering the true orbit of the Sun, a mathematical model that is universal across the globe is proposed: the Kepler motion model is constructed from the solar orbit and transformed into the local Earth coordinate system. After that, the calculation of the optimal tilt angle solution is given. Finally, several examples are shown to demonstrate the variation of the optimal solar angle with month and latitude. The results show that for daily fixed solar collectors, the altitude angle of the collector should be about 6° above the noon solar altitude angle in summer and 6° lower in winter. For annual fixed collectors, the tilt angle should be slightly higher than the latitude. In summary, this study demonstrates that when a location is specified, this model can be used to calculate the theoretical optimum tilt angle of solar collectors for that position.

Highlights

IntroductionIn addition to improving the conversion efficiency from solar to chemical energy [1], one of the key points for solar energy to be fully utilized is the optimized design of the tilt angle (or its complementary angle: elevation angle) of the solar collector
As a green energy source, solar energy has been widely used around the world
One is to change the elevation angle of the solar collector periodically to ensure that more direct sunlight is obtained: Yakup [2] showed that changing the inclination angle 12 times a year can improve the utilization rate by 5%; this method has been proven to be effective by experiments [3]

Summary

Introduction

In addition to improving the conversion efficiency from solar to chemical energy [1], one of the key points for solar energy to be fully utilized is the optimized design of the tilt angle (or its complementary angle: elevation angle) of the solar collector. One is to change the elevation angle of the solar collector periodically to ensure that more direct sunlight is obtained: Yakup [2] showed that changing the inclination angle 12 times a year can improve the utilization rate by 5% (latitude = 4.90◦ N and longitude = 115◦ E); this method has been proven to be effective by experiments [3]. Not all solar collectors have the ability to adjust their angle automatically, especially when deployed over a large area. It is especially critical to set the optimal tilt angle at the beginning

Methods

Results

Conclusion