Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I-100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

Measurement and simulation of solar radiation availability in relation to the growth of coffee plants in an agroforestry system with rubber trees

Solar radiation is an important factor for plant growth, being its availability to understory crops strongly modified by trees in an Agroforestry System (AFS). Coffee trees (Coffea arabica - cv. Obatã IAC 1669-20) were planted at a 3.4 x 0.9 m spacing inside and aside rows of monocrops of 12 year-old rubber trees (Hevea spp.), in Piracicaba-SP, Brazil (22º42'30" S, 47º38'00" W - altitude: 546m). One-year-old coffee plants exposed to 25; 30; 35; 40; 45; 80; 90; 95 and 100% of the total solar radiation were evaluated according to its biophysical parameters of solar radiation interception and capture. The Goudriaan (1977) adapted by Bernardes et al. (1998) model for radiation attenuation fit well to the measured data. Coffee plants tolerate a decrease in solar radiation availability to 50% without undergoing a reduction on growth and LAI, which was approximately 2m².m-2 under this condition. Further reductions on the availability of solar radiation caused a reduction in LAI (1.5m².m-2), thus poor land cover and solar radiation interception, resulting in growth reduction.

Intercepted solar radiation by maize crops subjected to different tillage systems and water availability levels

The objective of this work was to evaluate changes in the photosynthetic photon flux density (PPFD) interception efficiency and PPFD extinction coefficient for maize crop subjected to different soil tillage systems and water availability levels. Crops were subjected to no-tillage and conventional tillage systems combined with full irrigation and non-irrigation treatments. Continuous measurements of transmitted PPFD on the soil surface and incoming PPFD over the canopy were taken throughout the crop cycle. Leaf area index and soil water potential were also measured during the whole period. Considering a mean value over the maize cycle, intercepted PPFD was higher in the conventional tillage than in the no-tillage system. During the initial stages of plants, intercepted PPFD in the conventional tillage was double the PPFD interception in the no-tillage treatment. However, those differences were reduced up to the maximum leaf area index, close to tasseling stage. The lowest interception of PPFD occurred in the conventional tillage during the reproductive period, as leaf senescence progressed. Over the entire crop cycle, the interception of PPFD by the non-irrigated plants was about 20% lower than by the irrigated plants. The no-tillage system reduced the extinction coefficient for PPFD, which may have allowed a higher penetration of solar radiation into the canopy

Coffee water use in agroforestry system with rubber trees

Water uptake and use by plants are essentially energy processes that can be largely modified by percentage of soil cover, plant type; foliage area and its distribution; phenological stage and several environmental factors. Coffee trees (Coffea arabica - cv. Obatã IAC 1669-20) in Agrforestry System (AFS) spaced 3.4x0.9m apart, were planted inside and along rows of 12- year-old rubber trees (Hevea spp.) in Piracicaba-SP, Brazil (22 42'30" S, 47 38'00" W - altitude: 546m). Sap flow of one-year-old coffee plants exposed to 35; 45; 80; 95 and 100% of total solar radiation was estimated by the heat balance technique (Dynamax Inc.). Coffee plants under shade showed greater water loss per unit of incident irradiance. On the other hand, plants in monocrop (full sun) had the least water loss per unit of incident irradiance. For the evaluated positions average water use was (gH2O.m-2Leaf area.MJ-1): 64.71; 67.75; 25.89; 33.54; 27.11 in Dec./2002 and 97.14; 72.50; 40.70; 32.78; 26.13 in Feb./2003. This fact may be attributed to the higher stomata sensitivity of the coffee plants under more illuminated conditions, thus plants under full sun presented the highest water use efficiency. Express transpiration by leaf mass can be a means to access plant adaptation to the various environments, which is inaccessible when the approach is made by leaf area.

Methodology for Photovoltaic Modules Characterization and Shading Effects Analysis

This work describes the methodology, basic procedures and instrumental employed by the Solar Energy Laboratory at Universidade Federal do Rio Grande do Sul for the determination of current-voltage characteristic curves of photovoltaic modules. According to this methodology, I-V characteristic curves were acquired for several modules under diverse conditions. The main electrical parameters were determined and the temperature and irradiance influence on photovoltaic modules performance was quantified. It was observed that most of the tested modules presented output power values considerably lower than those specified by the manufacturers. The described hardware allows the testing of modules with open-circuit voltage up to 50 V and short-circuit current up to 8 A.