Mathematical modeling of shading by obstacles and prediction of optimal energy generation from a solar pv system per unit area over the year

Abstract

There is an exponential growth and growing popularity of solar photovoltaic technology for energy generation in comparison with the conventional and other renewable energy sources. But the massive utilization of this technology is hindered by space constraints. And that is why optimal use of space with solar PV modules is a pre-requisite for optimal energy generation per unit area. In this research, the sunpath diagram, surrounding obstacles shading, optimal PV module row spacing have been analyzed and a mathematical model have been developed which is solved using Mat lab. This study shows that the optimal module row spacing is about 1 meter considering comparatively effective sunshine hour (9:00am to 3:00pm) for commercial systems. The minimum module row spacing calculated from sun-path diagram is about 1 meter under the same condition. Deviation between the values of module row spacing calculated from these two method is only 1.05%. Power generation per unit area by minimum module row spacing calculated from our proposed model is about 250 kWh per square meter land area. Return rate of money due to the use of minimum row spacing is about 20%. Moreover in this research a shading diagram has been proposed to study the effect of obstacles over the year on a solar system drawn by the overlaying of horizontal-profile over sun-path diagram which will provide information about which obstacles may cause shading at a specific time of day and year. It can be analyzed from the shading diagram that which obstacle may affect by shading at specific time over the year. The mathematical model is solved by Mat lab.