Investigation of the Effect of Albedo in Photovoltaic Systems for Urban Applications: Case Study for Spain

Rooftop photovoltaic generation can help cities become key players in the transition to clean energy. The optimal solar photovoltaic production on rooftops depends on two angles: tilt angle and azimuth angle. It is accepted in all studies that the ideal orientation of photovoltaic modules is toward the south (north) in the northern hemisphere (south). In contrast, the determination of the optimum tilt angle is more complex, and there are different equations for its calculation. Most of these equations do not take albedo into account. In this work, 47 Spanish province capitals representing the most populated cities have been studied with different equations for the calculation of the optimum annual tilt angle (Technical report by the Spanish Institute for the Diversification and Saving of Energy (IDAE), Lorenzo's and Jacobson's equation) and different types of albedo. Accounting for the geographical and the meteorological conditions of the cities, we analyzed the optimum tilt angle through a Mathematica (c) optimization code. The influence that different variables have on optimum tilt angle has been quantified by means of the term relative energy harvested. The use of the equations as a function of latitude increases the annual relative energy harvested by increasing the albedo. When the albedo is 0.2, the annual relative energy harvested is very similar in all equations. Comparing to the method that maximizes the total irradiation incident on a tilted surface, the minimum and maximum value of the percentage of relative energy harvested per year were 0.01 and 2.50% for the IDAE guideline, 0.00 and 2.38% for Lorenzo's equation, 0.00 and 2.46% for Jacobson's equation. A simplified polynomial regression model to estimate optimum tilt angle as a function of latitude, altitude and albedo has been proposed as well.

Automated summary

Rooftop photovoltaic generation plays a crucial role in cities' transition to clean energy. The determination of the optimal tilt angle for solar photovoltaic modules is complex and depends on various factors such as albedo. This study analyzed 47 Spanish province capitals using different equations and albedo types to calculate the optimum annual tilt angle. The results showed that using equations as a function of latitude increased the annual relative energy harvested by increasing the albedo. Comparisons with the method of maximizing total irradiation incident on a tilted surface revealed variations in the percentage of relative energy harvested per year. Additionally, a simplified polynomial regression model was proposed to estimate the optimum tilt angle based on latitude, altitude, and albedo.