The optimization of heliostat paraboloid canting via differentiable ray tracing

Abstract

In solar power systems, large-scale heliostats are typically constructed by assembling multiple rectangular facets into a paraboloid configuration. Existing researches still face substantial challenges in achieving efficient and reliable optimization of heliostat facet canting angles. To address the problem, a novel heliostat paraboloid canting optimization method based on differentiable ray tracing is proposed in this paper. To improve the concentration efficiency, this method formulates the minimization of the spot area $S_{95}$ (the area enclosing 95% of the flux) as the optimization objective. An optimization model for the canting angles of the facets in the paraboloid heliostat is established, and high-precision simulations of the flux spot are conducted using a differentiable full-path Monte Carlo ray tracing algorithm, while simultaneously and automatically computing the gradient of the simulation process. The gradient is then used for iterative optimization to determine the optimal canting parameters. Furthermore, this method is efficiently implemented via GPU parallel computation. Experimental results show that, compared to the improved particle swarm algorithm, the new method reduces the optimization time for a single paraboloid heliostat from 45 min to just 1 min. More importantly, the new method can be extended to simultaneously optimize thousands of heliostats across the heliostat field. Furthermore, when compared to on-axis heliostats, the optimized paraboloid heliostat achieves a reduction of 1.5%-9.7% in the annual average $S_{95}$ for a single heliostat, and in the case of the Gemasolar field, the annual average $S_{95}$ of the entire heliostat field is reduced by 2.33%.