Analytic solutions for the optical and radiative properties of nonaccepted light radiation of V-trough concentrators

Knowledge of optical and radiative properties is often essential for the design and evaluation of V-trough solar energy collectors. Using the concept of reflection modes, we derived a set of functions associated with each mode; this allowed us to calculate the optical and radiative properties for rejected light radiation. These expressions, together with those for accepted light radiation published previously, were used to calculate the optical efficiency for beam radiation and the exchange factors (diffuse radiation) between aperture and absorber (accepted light) and between aperture and aperture (rejected light). Numerical results of these factors were obtained for various combinations of concentration ratio and vertex angle. Results are compared between a case in which the reflectivity is constant and one in which the reflectivity varies with incidence angle; the difference does not exceed 1% for a reflectivity of 0.8. Considering the reflectivity as a constant allows us to obtain analytic solutions for the exchange factors, expressed as a sum of trigonometric functions.     

Exact crossing rates of dual diversity over unbalanced correlated Rayleigh channels

General exact expressions for the level crossing rate of dual-branch selection, equal-gain, and maximal-ratio combiners operating over unbalanced correlated Rayleigh channels are derived. Sample numerical results are presented by specializing the general expressions to a space-diversity system with horizontally spaced omnidirectional antennas at the mobile station. It is observed that, whereas power imbalance is invariably prejudicial, fading correlation may be advantageous with closely spaced antennas arranged parallel to the direction of motion.     

Extreme total solar irradiance due to cloud enhancement at sea level of the NE Atlantic coast of Brazil

Extraterrestrial total solar irradiance, usually called Solar Constant, is attenuated by the atmosphere in different proportions, depending mainly on solar zenith angle and altitude of the measurement point. In this work, it is presented very high and extreme horizontal plane measurements of global solar irradiance that in some days overpassed the Solar Constant corrected by the actual Sun–Earth distance (CSC). They were obtained at sea level of the intertropical Atlantic coast, in the city of Recife, Brazil, in the period February 2008–January 2009. Extreme total solar irradiance values larger than CSC were measured during 3.4% of the days of the total registered period. This percentage increases to 7.4% for global solar irradiance within 95.1–100% of the CSC and to 15.3% within 90.1–95% of the CSC. The largest extreme total solar irradiance value, 1477 ± 30 W/m², was registered the 28th of March 2008 at 11:34 local time (UT – 3h). It overpassed by 7.9% the CSC value for this day (1369.4 W/m²) and by 42.3% the estimated value of the clear sky Iqbal C radiation model (1037.7 W/m²). The observation of extreme values should be taken into account in the study of solar radiation effects related to materials exposed to the outside, UV index and biological effects, among others. Also, the detailed knowledge of this interesting effect may contribute significantly to clarify physical aspects about the interaction of global solar radiation with the ecosystem and climate change.     

Improved solutions for temperature and thermal power delivery profiles in linear solar collectors

For the conversion of absorbed sunlight into useful thermal power, we demonstrate that the profiles of absorber temperature, fluid temperature and thermal power delivery along linear solar collectors can be solved in closed form even when the collector heat-loss coefficient is far from constant over the collector operating range. This analytic solution eliminates the errors inherent in earlier approximate solutions, and makes the dependence of collector performance on component properties transparent. An example for a realistic solar concentrator illustrates the improvement in prediction accuracy.     

Photovoltaic pumping systems driven by tracking collectors. Experiments and simulation

An experimental facility of a photovoltaic array mounted on a one-axis east–west tracker, coupled to a pumping system, was tested for several months, under two working conditions: fixed and tracking mode. Results show that the gain obtained in the daily water volume is higher than the one obtained for the collected irradiation. For values of hemispherical irradiation equal to 5000 and 6000 Wh/m², the irradiation collected by the tracker plane is 19 and 24% higher than the one collected by the fixed system. However, gains in water volume are equal to 37 and 41%. The reasons for the increase in pumped water volume being larger than the increase in collected irradiance are analyzed. To generalize the experimental results, a long term estimate of the water volume pumped by PV systems driven by tracking collectors was carried out via the utilizability method. As a result, we describe how the benefit ratio in pumped water volume is affected by the contributions due to collected irradiance, utilizability function and a factor Ω, related to the non-linearity of the characteristic curve. Finally, the influence of the critical irradiance (I_C) (minimum value of irradiance, necessary to start the water pump operation) on the benefit obtained in pumped water volume, by using tracking systems, is discussed. Numerical simulations show that the increase in pumped water volume, annual average, varies between 1.29 and 1.53 for (I_C) within the interval from 275 to 575 W/m².     

Second-order statistics for diversity-combining of non-identical correlated hoyt signals

In this paper, exact expressions for the level crossing rate (LCR) and average fade duration (AFD) for two-branch selection, equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, non-identical, correlated diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known. In passing, the joint bidimensional envelope-phase Hoyt distribution with arbitrary fading parameters is obtained.     

Solar energy resource assessment — Brazil

Appropriate information on solar resources is very important for a variety of technological areas, such as: agriculture, meteorology, forestry engineering, water resources and particularly for an innovating technology such as solar energy. In the market entry process of an innovating technology such as solar energy, the enlarged and sustained reproduction of this energy strongly depends on the economy and reliability of the demonstrative solar systems installed (within a restricted or wide scale). The economy and reliability of a system are the consequence of a well-prepared project, resulting from an accurate knowledge of the solar resource available. Therefore, knowing the potential of the solar resource accurately is not only a need, it is also an imperative for a larger diffusion and use of the solar energy.The existing sources of information on radiation in Brazil are quite varied, both at the institutional level and in different types of publications. At the institutional level these sources are: the National Institute of Meteorology, secretary of agriculture, research centers, universities, and electric power generating and distributing companies, among others. The publications with this information are project reports, internal reports of institutions or several magazines. Thus, the quality of the data varies considerably, the information presents spatial and temporal discontinuity and the instruments as well as the measurement units are not standardized.The general objective of this paper is to recover, qualify, standardize and make available the best information from the current existing solar resource in Brazil, either in the form of isoline charts of solar radiation, insolation, numeric tables or analytic summaries of a great part of the publications on the theme over the last forty years.     

Simulation model of a CPC collector with temperature-dependent heat loss coefficient

We describe a mathematical model for the optical and thermal performance of non-evacuated CPC solar collectors with a cylindrical absorber, when the heat loss coefficient is temperature-dependent. Detailed energy balance at the absorber, reflector and cover of the CPC cavity yields heat losses as a function of absorber temperature and solar radiation level. Using a polynomial approximation of those heat losses, we calculate the thermal efficiency of the CPC collector. Numerical results show that the performance of the solar collector (η vs. ΔT_f(0)/I_coll) is given by a set of curves, one for each radiation level. Based on the solution obtained to express the collector performance, we propose to plot efficiency against the relation of heat transfer coefficients at absorber input and under stagnation conditions. The set of characteristic curves merge, then, into a single curve that is not dependent on the solar radiation level. More conveniently, linearized single plots are obtained by expressing efficiency against the square of the difference between the inlet fluid temperature and the ambient temperature divided by the solar radiation level. The new way of plotting solar thermal collector efficiency, such that measurements for a broad range of solar radiation levels can be unified into a single curve, enables us to represent the performance of a large class of solar collectors, e.g. flat plate, CPC and parabolic troughs, whose heat loss functions are well represented by second degree polynomials.     

A methodology for the design of photovoltaic water supply systems

Photovoltaic pumping systems are used nowadays as a valuable alternative to supply water to communities living in remote rural areas. Owing to the seasonal variation and the stochastic behavior of solar radiation, at certain times the supply of water may not be able to meet demand. A study has been made of the relationship between water pumping capacity, reservoir size and water demand, for a given water deficit. As a result, curves of equal water deficit (iso‐deficit lines) can be obtained for various combinations of PV pumping capacity and reservoir size. A methodology to generate those curves is described, using as its main tool the characteristic curve of the system, that is, the relationship between water flow and collected solar radiation. The characteristic curve represents the combined behavior of the water pumping system and the well. The influence of the minimum collected solar radiation level, necessary to start the system's operation (the critical radiation level I_C), is also analyzed. Results show that PV pumping systems with different characteristic curves, but with the same critical levels, yield the same set of iso‐deficit lines. This drastically reduces the number of necessary solutions to those corresponding to a few values of I_C. Iso‐deficit lines, calculated for the locality of Recife (PE), Brazil, are used to illustrate the sizing procedure PV water supply systems. Copyright © 2001 John Wiley & Sons, Ltd.