Previous publications suggest that geometrical solar panels are more efficient in terms of using the mounting space than traditional flat static solar panels. However, previous research does not deeply discuss the questions of the distribution of solar cells on the considered segments of cylinders, cones, spheres, and catenoids. To find the best geometry, we optimize the parameters of various curved surfaces, such as cones and catenoids, for the greatest energy produced per square meter. In practice, these curved solar panels are created by packing flexible fixed size square solar cells onto the curved surface. So, we must also optimize our curved surfaces for their ability to be packed efficiently with square solar cells. Using combinatorial methods, we propose sample solar cells packing and approximate energy production to optimize geometrical solar panels at various geographic locations. These techniques allow us to create more efficient static solar panels and improve the overall value of solar energy.
The introduction of flexible solar cells embedded in fabrics motivates the search for more efficient solar cell designs than flat panels. The optimal configuration of solar cells should receive the maximal flux density of sunlight rays over the course of a year. There may also be spatial restrictions which only allow the cells to cover an arbitrary roof or area and surrounding structures which cast shadows in that area. So, it is difficult to analytically find the most efficient way to cover an arbitrary surface on Earth with solar cells. The genetic algorithm was used to find the optimal geometry for solar cells that have constant footprints at various latitudes. Random configurations of solar cells covering a constant area evolved into efficient configurations under the guidance of chosen selection, crossover, and mutation mechanisms. The results allow us to cover arbitrary roofs or areas as efficiently as possible, which greatly increases the value of solar energy.