Geometric Optimization of Concentrating Solar Collectors using Monte Carlo Simulation

This paper presents an optimization algorithm for designing linear concentrating solar collectors using stochastic programming. A Monte Carlo technique is used to quantify the performance of the collector design in terms of an objective function, which is then minimized using a modified Kiefer-Wolfowitz algorithm that uses sample size and step size controls. This process is more efficient than traditional “trial-and-error” methods, and can be applied more generally than techniques based on geometric optics. The method is validated through application to the design of three different configurations of linear concentrating collector. INTRODUCTION With the growing demand for energy and its increasing impact on our ecosystem, solar collectors are becoming an increasingly important substitute for conventional thermal and electrical sources. Accordingly, the development of a fully customizable, comprehensive, and straightforward procedure for determining optimal collector geometry would be of great benefit to industry. Highly-reflective specular surfaces are commonly used to redirect or concentrate solar radiation in collectors. These devices are traditionally designed using a combination of “trial-and-error” and non-imaging optics techniques like the edge-ray method [1]. In this approach design aspects such as acceptance angle or concentration ratio must first be decided, which then dictate the concentrator geometry based on existing ideal designs. These designs are optimal only under restrictive conditions including specular reflection, blackbody absorption, or collimated incoming radiation, however, none of which prevail in real-world scenarios. Numerical simulation allows the designer to account for these realistic optical phenomena. Haeberle et al. [2], for example, used a ray-tracing based software package [3] to perform a series of univariate parametric studies on a linear concentrating Fresnel collector. They determined the optimal collector length based on realistic weather data and material properties, including mirror reflectivity, absorber surface absorptivity, heat loss coefficient, and mirror manufacturing error. Unfortunately, univariate parameter studies neglect nonlinear interactions between the design variables. Muschaweck et al. [4] optimized the reflector geometry for a non-tracking linear (trough) solar collector, based on calculated maximum yearly average utilizable power