Mathematical Modelling and Optimizing Design of Heliostat Field

Abstract

The heliostat field is a form of solar thermal power plant, and establishing a heliostat field is of great significance for reducing carbon emissions. This paper focuses on the mathematical modelling and optimization design problem of the heliostat field. For three different design scenarios, firstly, based on the data provided by the China Undergraduate Mathematical Contest in Modeling 2023, a geometric optical efficiency model is proposed to determine the annual average optical efficiency and output thermal power under specific heliostat field design parameters. Secondly, aiming at the optimal design parameters of the solar furnace field under the condition of rated annual average output thermal power is 60\(\text{M}\text{W}\), Particle Swarm Optimization (PSO) combing with efficiency model are utilized to determine the optimal design parameters of the heliostat field. Finally, this paper uses Quasi -Monte Carlo ray tracing (QMCRT) model to perform simulation, exploring how to obtain the optimal design parameters of the heliostat field with the goals of maximizing the output thermal power and ensuring high efficiency. On this basis, the influence of normal disturbances on the annual average output thermal power is further explored.