J.M. Gordon

Time series analysis of daily horizontal solar radiation

An analysis of the stationary and sequential properties of daily global horizontal solar radiation, on a discrete monthly basis, is presented for a number of locations of widely varying climatic conditions. Such information is essential as input to analytic models for the long-term performance of solar energy systems and for the generation of synthetic daily radiation sequences that can serve as input to numerical simulations that model solar systems. The new aspects of our study include (1) analysis of a solar radiation database that is much larger than those considered heretofore and includes tropical low-latitude, as well as temperate middle-latitude, climates, (2) documentation of the magnitudes and correlations of generalized stationary and sequential radiation statistics for a wide range of climatic stations, (3) proposal of a simple functional form for the probability density function for daily radiation and comparison with actual data, (4) explicit consideration of confidence limits in predicting stationary radiation statistics from a limited number of years of data, (5) evidence that, contrary to the claims of most related studies, there do not seem to be universal values or universal correlations for either the persistence strengths or the persistence times of daily radiation, and, (6) discussion of the practical value of statistical studies of this nature for the design of solar energy systems.

High-flux photovoltaic solar concentrators with kaleidoscope-based optical designs

We propose, analyze and offer sample designs and results for a high-flux photovoltaic concentrator comprised of a large-aperture paraboloidal-dish primary concentrator, and a second-stage kaleidoscope flux homogenizer. The following key design aims are all satisfied: (1) highly uniform irradiance on the solar cell absorber; (2) maximum collection efficiency; and (3) not exceeding the prescribed target flux level (for illustrative purposes here taken to be 500 suns), despite the dish being capable of much higher concentration. As a result of recent advances in the low cost and ease of production of large dish concentrators, the kaleidoscope-based design offers an intriguing alternative to other high-concentration optical designs developed to date. Admissible kaleidoscope geometries are identified. We generate quantitative results for a compact practical design that incurs low optical losses, and produces a highly homogeneous flux map.

On optimized solar-driven heat engines

Abstract Heat engines will usually be designed somewhere between the two limits of (1) maximum efficiency, which corresponds to “Carnot” or reversible operation, albeit at zero power, and (2) maximum power point. Each of these limits implies a specific dependence of heat engine efficiency on the temperatures of the hot and cold reservoirs between which the heat engine operates. We illustrate that the energetically optimal operating temperature for solar-driven heat engines is relatively insensitive to the engine design point. This also pertains to solar collectors whose heat loss can range from predominantly linear (conductive/convective) to primarily radiative. Potential misconceptions are also discussed regarding the maximum power point and the Curzon-Ahlborn efficiency of “finite-time thermodynamics.”

Design, analysis and optimization of solar industrial process heat plants without storage

Abstract Solar industrial process heat applications which have a constant daytime load every day of the year permit optimal collector utilization, thus minimizing the cost of solar energy. In particular, one can avoid the cost and performance penalties associated with storage of solar heat, if the backup can operate at variable heating rate. Hence, these applications are particularly relevant for the near future when solar equipment is still relatively expensive and one is looking for solar applications with the lowest possible cost. This paper develops a method for designing and optimizing installations of this type, including a quick procedure for selecting the most cost effective collector and calculation of pumping energy. The economic optimum is shown to imply a slightly oversized collector field with dumping of excess energy during peak insolation. Using recently developed correlations for the annual energy collectible by the principal collector types, we state all results as explicit algebraic equations which are readily evaluated with a hand calculator. The accuracy is on the order of 3 percent if there is no uncertainty in the input variables. The method is illustrated by an example.

Central-station solar photovoltaic systems: field layout, tracker, and array geometry sensitivity studies

Abstract The optimal design of central-station photovoltaic (PV) systems depends, among other factors, on the field layout of PV arrays, PV array geometry, tracking constraints, and intermodule electrical connections. We illustrate the sensitivity of yearly PV system energy delivery losses that stem from inter-array shading as a function of key field, tracker, and array-related variables for flat-plates. The results turn out, to an excellent approximation, to be independent of site. We quantitatively assess the magnitude of series/parallel module connections, and bypass diode placement within arrays, on energy losses attributable to inter-array shading. The sensitivity to key design parameters is also found to be predicted accurately by calculations of collectible energy only. As such, the calculations are of general value for rapid yet accurate PV system analysis and optimization.

Tailored edge-ray concentrators as ideal second stages for Fresnel reflectors

For both linear and point-focus Fresnel reflectors, we present a new type of ideal nonimaging secondary concentrator, the tailored edge-ray concentrator, that can closely approach the thermodynamic limit of concentration. For large rim-angle heliostat fields, practical-sized secondaries with shapes that should be relatively easy to fabricate can achieve concentrations substantially above those of compound parabolic concentrators. This superiority stems from designing so as to accommodate the particular flux from the heliostat field. The edge-ray principle used for generating the new secondary dictates a heliostat tracking strategy that is different from the conventional one but is equally easy to implement.

Time series analysis of hourly global horizontal solar radiation

Abstract Accurate design and optimization of short response time solar energy systems with storage are sensitive to the stationary and sequential characteristics of hourly solar radiation. We perform monthly time series analyses of hourly global horizontal solar radiation for a wide range of climatic stations that span temperate and tropical conditions. The stationary statistics for individual hours are found to be very similar to the corresponding results for daily total global horizontal radiation, in keeping with a related fundamental observation of Liu & Jordan. Investigation of sequential properties shows that autocorrelation coefficients are, to a good approximation, independent of time of day and that persistence times are nearly as long as the entire daylight period, mainly due to the effect of very strong correlations at one-hour lag times. The isolated effect of two-hour and longer lag times, via the partial autocorrelation coefficients, is found to be negligible in most, but by no means all, instances. Finally, we find no universal correlation between hourly autocorrelation coefficients and monthly average radiation figures.

Reflector design for illumination with extended sources: the basic solutions

The goal of the optical design of luminaires and other radiation distributors is to attain the desired illumination on the target with a given source while minimizing losses. Whereas the required design procedure is well known for situations in which the source can be approximated as a point or as a line, the development of a general analytical design method for extended sources began only recently. One can obtain a solution for extended sources by establishing a one-to-one correspondence between target points and edge rays. Here the possible solutions in two dimensions (cylindrical sources) are identified, based on only one reflection for the edge rays. The solutions depend on whether the image on the reflector is bound by rays from the near or the far edge of the source. For each case there are two solutions that could be called converging and diverging by analogy with imaging optics. Counting the topological choices for the boundaries of the image we obtain a complete classification of the buildingblocks from which luminaires can be designed. One can construct interesting hybrid configurations by combining these building blocks. Thus one can gain a great deal of flexibility for tailoring designs to specific requirements. The differential equation for the reflector is shown to have an analytical solution. Explicit results are presented for symmetric configurations with the target at infinity.

A typical meteorological day (TMD) approach for predicting the long-term performance of solar energy systems☆

Abstract A method for predicting the long-term performance of solar energy systems, based on the analysis of system performance for one particular day—the typical meteorological day (TMD)—is presented. The TMD is constructed from the cumulative time distribution of insolation values on the collector aperture. The TMD method requires little calculational effort and a small data base relative to standard yearly computer simulations. Good agreement is found between the predictions of the new method and the corresponding results of the F -f-chart method. The TMD method is of particular value for cases that may often be treated inaccurately by simple calculational methods: (1) high threshold problems; (2) systems with short response times (e.g., due to small storage); and (3) systems in which collectors other than flat plates are used (the method is applicable to all solar collector types).

New high-flux two-stage optical designs for parabolic solar concentrators

Abstract We present a new two-stage optical design for parabolic dish concentrators that can realistically attain close to 90% of the thermodynamic limit to concentration with practical, compact designs (e.g., at parabola rim half-angles of around 45°). For comparison, the parabolic dish-plus-compound parabolic concentrator secondary design, at this rim angle, achieves no more than 50% of the thermodynamic limit. Our new secondary concentrator is tailored to accept edge rays from the parabolic primary, and incurs less than one reflection on average. It necessitates displacing the absorber from the parabolas focal plane, along the concentrators optic axis, toward the primary reflector, and constructing the secondary between the absorber and the primary. The secondary tailored edge-ray concentrators described here create new possibilities for building compact, extremely high flux solar furnaces and/or commercial parabolic dish systems.