Simplified Calculational Procedure for Determining the Amount of Intercepted Sunlight in an Imaging Solar Concentrator

Abstract

In imaging solar concentrators, the solar radiation incident on a receiver surface depends upon both the overall concentrator shape and the angular distribution of light rays (sunshape) that reach the receiver. Calculation of the amount of sunlight incident on the receiver usually requires sophisticated computer programs. A simplified calculational procedure is presented to solve this problem for both one and two-dimensional concentrators, with the results presented in graphical form. The procedure first determines the amount of sunshape broadening resulting from optical scattering caused by reflector or glazing materials, surface slope errors, or other “mechanical” factors such as tracking errors or vibrations. These optical effects are combined into an effective error cone which is convoluted with measured sunshapes in order to obtain effective, broadened sunshapes. Broadened sunshapes for a variety of effective error-cone distributions are calculated and presented. It is found that when the root-mean-square (RMS) width of the effective error cone is greater than approximately two times the RMS width of the incident sunshape, the broadened sunshape can be adequately described by a circular normal distribution. A specific example is included which illustrates the calculational procedure discussed in the paper.

Progress in heliostat development

“…It can be solved numerically by Fourier transformation and polynomial expansion, (Biggs and Vittitoe, 1979) and (Walzel et al, 1977). A very simple solution is possible when the sun shape is considered to be a circular Gaussian distribution, see (Pettit et al, 1983b) and (Schwarzbözl et al, 2009). This simple convolution method requires less computational effort than the other methods but is also of lower accuracy.…”

Methodology for an Opto-Geometric Optimization of a Linear Fresnel Reflector for Direct Steam Generation

“…The intercept factor ideally should have a unit value; which would mean that all the radiation that enters the opening area (A) will be redirected entirely to the receiver; however, since the LFR is not an ideal (it should not be forgotten that a Fresnel reflector simulates the optical behavior of a parabolic channel, so in essence, it could not be a concentrator without optical losses) concentrator, there will be losses in this captured radiation. Although there are a great variety of methodologies to determine the intercept factor, such as directly applying the concept of the conservation of the étendue [29,30] or using an advanced ray-tracing technique [31], it is possible to use simpler methods such as that described by Pettit et al [32], or, in its simplest form, only the quotient between the area illuminated by the redirected rays and the area of the receiver, as stated in Equation 8and shown schematically in Figure 5. A pm = N m W m L m = 1500 m 2 : Effective area of the primary mirrors, A = W sf L m = 2100m 2 : Area of the LFR module.…”

Different Tracking Error Distributions and their Effects on the Long-Term Performances of Parabolic Dish Solar Power Systems

“…The effects of tracking errors on the optical performances of solar concentrators has been studied during the time by using both deterministic and statistical techniques (Wijeysundera, 1977;Biggs and Vittitoe, 1979;Bendt er al., 1979;Pettit et al, 1983; Collado er al., 1986, to quote only a few). Most of the authors which utilized statistical methods have modeled the tracking errors by time-independent Gaussian distributions (see e.g.…”