Optimization of Parabolic Heliostat Focal Lengths in a Mini-Tower Solar Concentrator System

Solar tower with heliostat mirrors is one of the established setups for utility-scale solar energy harvesting. Advantages of the setup include the capability to reach high temperature, modularity and ease of maintenance for the heliostats, containment of the high temperature zone atop the tower, as well as overall low cost per unit energy. However, downscaling to medium or small scale applications often does not turn out economically feasible with flat mirror heliostats that are the norm in utility-scale systems. This is mainly due to the need to preserve the solar concentration ratio, which in turn means the number of flat mirrors cannot be reduced. Use of parabolic mirrors instead can significantly reduce the required number of mirrors for smaller scale systems, but comes with new challenges. Unlike flat mirrors that have infinite effective focal length, the effective focal length of parabolic mirrors changes with the angle of incidence, which in turn, changes throughout the day and season. The design challenge tackled in this paper is that of optimal selection of the focal lengths of the heliostats in order to maximize the yearly harvested energy while maintaining the concentration ratio within desirable limits. A parameterized system model is developed and a genetic algorithm is implemented for the optimization task. The model is then applied to a demonstration case study of a 10 kW solar concentrator. Results of the study demonstrate the proposed design approach as well as show the promise for effective downscaling of tower and heliostat systems.