Development in solar photovoltaic (PV) technology has made it possible to manufacture curved or shaped panels. However, little research has been done on the topic of solar resource for curved surfaces. This project aims to develop a numerical program to estimate solar resource for a curved cylindrical panel on Earth and Mars. Numerical calculations of solar resource were performed through MATLAB using Typical Meteorological Year (TMY) empirical irradiance data for New York City. This data was used as inputs for the code and the solar resource for a cylindrical panel of different curvatures and orientation was calculated using the MATLAB program. The cylindrical surface will be discretized into segments of flat surfaces. The isotropic diffused sky solar irradiance model was then used to calculate total solar resource for the given surface. It was found that as the curvature of the panel increased, the total solar resource per unit surface area decreased while the total solar resource per unit footprint area, which is the area an object occupies on a horizontal surface, increased. In addition to quantifying the performance of a curved surface on Earth and Mars, this work shows the potential of highly efficient non-tracking curved surfaces for collecting solar resource in volume limited situations such as space travel or urban applications. The resource estimation algorithm can also be used to estimate solar resource for commercial applications and system sizing.
The long-term goal of the project is to create and justify a reliable mathematical model that expresses the efficiency of geometrical shapes of non-tracking flexible solar panels. However, the amount of solar energy absorbed by a non-tracking flexible solar panel depends on many parameters: the direction of the sun beam, reflected light, and temperature, etc., which would make a complete model mathematically complicated. In the current model, we limit our consideration to the direction of the sunbeam. In order to simulate the exposure of the panel, we describe the trajectory of the Sun and base the model on the mathematical flux that uses the sun rays as the vector field. To be precise, the efficiency of a geometrical panel is defined as the flux density, which is the ratio of the mathematical flux and the surface area. Our current model was evaluated for the latitude of New York City and we determined the efficiency of the optimized at panels, cylindrical panels, and conical panels. The analysis was largely done through geometrical studies and numerical integration with software programs Python, Maple, Mathematica, and MATLAB.
The purpose of this research is to analyze mathematically cylindrical shapes of flexible solar panels and compare their efficiency to the flat panels. The efficiency is defined to be the flux density, which is the ratio of the mathematical flux and the surface area. In addition we describe the trajectory of the Sun at specific locations: the North Pole, The Equator and a geostationary satellite above the Equator. The calculations were performed with software: Maple, Mathematica, and MATLAB.
The purpose of this study is to analyze various surfaces of flexible solar panels and compare them to the traditional at panels mathematically. We evaluated the efficiency based on the integral formulas that involve flux. We performed calculations for flat panels with different positions, a cylindrical panel, conical panels with various opening angles and segments of a spherical panel. Our results indicate that the best efficiency per unit area belongs to particular segments of spherically-shaped panels. In addition, we calculated the optimal opening angle of a cone-shaped panel that maximizes the annual accumulation of the sun radiation per unit area. The considered shapes are presented below with a suggestion for connections of the cells.