Optical Analysis and Optimization of Line

SUMMARY The optical analysis of a solar concentrator is usually carried out by means of computer ray tracing, a microscopic method that provides an enormous amount of detailed information but obscures functional relationships. This paper describes a macroscopic approach that yields all the parameters needed for the optical design of line focus parabolic troughs in closed analytical form, requiring only minimal computation. The goal of the optical analysis developed in this report is to determine the flux a t the receiver as a function of concentrator configuration, receiver size, width of sun, and optical errors (e.g., tracking, reflector contour). All causes of image spreading are quantified as angular standard deviation. Ray tracing with a real reflector and a real sun is shown to be equivalent to convoluting the angular acceptance function of a perfect concentrator with an effective radiation source. This effective source, in turn, is obtained by convoluting the distribution function of optical errors with the angular profile of the sun. The problem is reduced to two dimensions by projecting the three-dimensional motion of the sun on the plane normal to the tracking axis. In this frame the apparent width of the sun increases as l/cos 8 with incidence angle 8. A formula is derived for the optimal geometric concentration ratio, maximizing net power output as a function of all relevant variables (all-day average insolation, optical errors, effective transmittance-absorptance, heat loss, and concentrator configuration). Graphical solution of this equation consists of finding the intersection between a universal curve and a straight line representing a critical intensity ratio. In the last section, which is written as a self-contained users guide, the results are summarized and illustrated by specific examples.