Effect of Circumsolar Radiation on Performance of Focusing Collectors

Abstract

Circumsolar radiation is one of several factors, along with optical errors (contour, tracking, etc.), that determine the size and shape of the solar image at the receiver of a concentrating collector. The sensitivity of a collector to circumsolar radiation depends on insolation conditions and on collector parameters; it increases with geometrical concentration ratio and decreases with threshold. In this paper the Lawrence Berkeley Laboratory (LBL) circumsolar data are used to calculate the effect of circumsolar radiation on both the instantaneous and the long-term average performance of focusing collectors. To speed up the computations, the optical properties of the concentrator are expressed in terms of an angular acceptance function. The angular acceptance function and the brightness distribution of the sun are then convoluted, a procedure which requires, for each circumsolar scan, only 56 multiplications and additions (one for each of the angular intervals at which the brightness has been measured by the LBL circumsolar telescope). While the formalism is applicable to all focusing collectors, only parabolic troughs and dishes are evaluated explicitly in this paper. The instantaneous performance corresponding to particular circumsolar scans is of interest for the analysis of test results of collectors with high concentration. For most predictions of long-term average performance a far simpler approach will, however, be adequate. For this purpose a standard synthetic circumsolar scan has been developed that describes the brightness distribution of the solar disk (“limb darkening”) and of the circumsolar region. The radiation intercepted by a receiver is calculated once for the solar portion and once for the circumsolar portion of this standard sun shape. The long-term average radiation intercepted by the receiver is then obtained by averaging the solar and the circumsolar intercept factors, weighted according to the long-term average circumsolar ratio for the location and period under study. Tested against hour-by-hour simulations, this simple approach was found to have an rms error of only 0.2 percent, negligible compared to typical uncertainties in system performance calculations. This analysis points out the usefulness of the long-term average circumsolar ratio as a simple measure of circumsolar radiation.