Solar Energy Vol. 31, No. 6, pp. 537-543, 1983 0038-092X/83 $3.G0+ .0~) printed in Great Britain. © 1983 Pergamon Press Ltd THE UTILIZABILITY FUNCTION--II VALIDATION OF THEORY AGAINST DATA-BASED CORRELATIONS J. M. GORDON and Y. ZARMIt Applied Solar Calculations Unit, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Israel (Received 4 December 1981; accepted 4 January 1983) Abstract--The results of a new theoretical approach to the calculation of annual utilizability are illustrated and validated against utilizabilities that are based on detailed meteorological data. The theory is applied to concentrat- ing solar collectors with tracking about two axes, the polar axis, the horizontal east-west axis, and the horizontal north-south axis, for a wide range of clearness index values. A new simple analytic formula for annual utilizability and its accuracy for the case of concentrating collectors are presented. The ultimate power of the theoretical results lies in the fact that with a knowledge of the annual average clearness index only, one can accurately predict utilizability curves for concentrating solar collectors in any climate. This would be particularly valuable for geographical locations and climates which are not covered by existing correlations or for which years of detailed meteorological data do not exist. I. INTRODUCTION In the preceding paper[l], a new approach for a quasi- first principles derivation of the utilizability function was presented. The purpose of this paper is three-fold: (a) To illustrate how the results of the preceding paper are used to calculate the annual utilizability as a function of threshold, for the case of concentrating solar collec- tors. (b) To validate the theoretical results against the util- izability calculated using actual meteorological data. (c) To present a new simple analytic formula for utilizability that turns out to be rather accurate. In Section 2, we briefly review the formalism developed in the preceding paper, with emphasis on the computational procedure rather than the derivation of the formulae. The applicability of these results limits their use to concentrating collectors only. The com- parison with existing correlations based on detailed meteorological data is presented in Section 3 for con- centrating collectors with tracking about: two axes, the polar axis (the north-south axis but with tilt angle equal to latitude), the horizontal east-west axis, and the horizontal north-south axis. The results are presented for climates varying from low annual clearness index (/~T -- 0.431) to high annual clearness index (/(T = 0.723). In each case, the agreement between the theoretical predictions and the corresponding utilizability correlations based on the detailed hourly insolation data of 26 U.S. SOLMET stations[2, 3] is within the statistical fluctuation of these correlations. Because we are dealing with a quasi-first principles theory, the only climatic parameter required to calculate the annual utilizability curve for any concentrating col- lector in any climate is the annual average clearness index, /~T. Hence closed-form expressions can be used to generate results that normally require detailed hour- by-hour computer simulations. In Section 4, we note that the analytic expression for utilizability that should in principle pertain to the limit of very clear climates only, turns out to be quite accurate for all climates. Possible explanations for this fortuitous result are discussed. We conclude with a few summariz- ing remarks in Section 5. 2. REVIEW OF FORMALISM A. General points We begin by introducing the concepts necessary for the calculation of the utilizability function as discussed in Ref.[l]. In calculating the utilizability, a summation over all days of the year is approximated by an integral over the sunshine hours of one representative 12 hr day, equinox. The instantaneous beam radiation, I~"m(t), is represented by the clear day, time dependent insolation Ibe"m(t, clear day), modified by random fluctuations, f, lbeam(t) = /beam(t, clear day). f, (2.1) where t denotes the time relative to solar noon. Here, /beam(t, clear day) is the beam radiation seen by the collector array on a clear day (namely, incidence angle and shading effects are included). The fraction f(0-< f-< l) represents the fact that on different days, but at the same hour, radiation may be reduced below its clear day value owing to cloud cover, fog, pollution, etc. It is assumed that [ is a random variable, and that its prob- ability of occurrence is hence described by a distribution function P(f) given by[l, 6] P (f) = p " 3(f) + (1 - p )/3{exp(-/3f)}/{1 - exp(-/3)}, (2.2) rAnd Physics Department, Ben-Gurion University of the Negev, where /3 is a parameter to be determined from climatic Beersheva, Israel. variables, and p is the annual average fraction of day- 537