Studies On Performance Of CPCs With A Restricted Exit Angle

With the gradual depletion of fossil fuels in our planet and the emerging issue of environmental pollution resulting from the intensive use and exploitation of fossil fuels, the utilization and development of unexhaustible solar energy have receive more attention in recent years, especially the application of photovoltaic technology. However, the use of photovoltaic system(PV) is limited due to its high cost as compared to the conventional electricity generation, and the use of cheep optical concentrators in place of expensive solar cells in a PV system is commonly regarded to be one of effective techniques.Compound parabolic concentrator(CPC), consisted of two parabolic reflectors, is a typical non-imaging ideal concentrator. In recent years, CPCs have been widely tested for concentrating solar radiation on solar cells due to the advantages of its simple structure, convenient manufacturing and no need of tracking systems. Theoretically, for a CPC based photovoltaic module, the power output should be increased by a factor of its geometric concentration ratio(Ct) as compared to similar non-concentrating PV panel. However, the actual power output from a CPC based PV module was much less than the theoretical value. Apart from the optical loss resulting from the imperfect reflection on reflectors, it is a result of the optical loss partially resulting from the poor solar absorption of solar cells for radiation reflecting from the lower part of reflectors and the electrical loss partially resulting from uneven distribution of solar radiation on solar cells. In this work, an attempt was made to modify the common CPC(referred to CPC-90 from which the exit angle of solar rays is in 0-90o) by replacing the lower portion of parabola with a flat-plate reflector, forming the CPC with a restricted exit angle(referred to CPC-eθ from which the exit angle of solar rays is restricted within eθ), with the aim to improve the performance of CPC based PV systems. The proposed CPC based PV system shares the advantages of more unform distribution of solar radiation on the absorber to which solar cells are attached and more efficient photovoltaic concersion due to the incidence angle of solar rays on solar cells less than the desired value. The objective of this work is to theoretically and experimentally comapare the performance between CPC-eθ and CPC-90 so as to ascertain whether CPC-eθ is really better than CPC-90 for concentrating radiation on solar cells.First, the design principle and theory of CPCs is intriduced, the string method of CPC construction is presented, the optical and geometric characteristics of CPCs are summarized and requirments for determining structural and installing parameters of CPCs are discussed. Then mathamtical expressions to represent the dependence of optical efficiency on the projection incidence angle of solar rays on the cross-section of CPC-trough(⊥θ) is suggested, and a mathematical procedure to calculate the annual collectibe radiation on the absorber of CPC-eθ is developed based on the solar geometry and radiation theory. Calculation results indicate that, regardless of the tilt-angle adjustment mode to be employed, the annual collectible radiation on the absorber of CPC-90 is always slightly larger than that of CPC-eθ, indicating that CPC-90 is better than CPC-eθ for concentrating radiation on the solar cell provided that the solar cell is an isotropic receiver for solar radiation. Theoretical calculations indicate that the optimal acceptance half-angle of yearly fixed CPC-eθ tilted at the site latitude for maximizing the annual radiation collection is about 26o-27 o. For CPC-eθ with the tilt-angle of the aperture being yearly adjusted two times at two tilts, the optimal adjustment from the site latitude for each adjustment is about 22o; whereas for CPC-eθ with the tilt-angle of the aperture being yearly adjusted four times at three tilts, the optimal date when the tilt-angle adjustment is made is about 22 days from both equinoxes, and the optimal adjustment from the site latitude for each of four adjustments is 22-24 o.Mathematical expressions to represent the optical efficiecy of CPC-90 and CPC-eθ for concentrating radiation on the receiver with a restricted incidence angle(RWARIA, in short) are proposed and a mathmetaical procedure to calculate the annual radiation on RWARIA is developed. Calculations show that, for yearly fixed full CPC-90 and full CPC-eθ with identical acceptance half-angle(aθ), the CPC-eθ is slightly more efficient than CPC-90 for radiation concentration except the period of about 30 days before and after both equinoxes; whereas for truncated CPC-90 and CPC-eθ with identical geometric concentration factor(Ct) and aθ, the CPC-eθ is always more efficient in any day of a year. This shows that CPC-eθ is better than CPC-90 for concentrating radiation provided that solar cells can not accept the radiation incident at the angle larger thaneθ.The solar flux distribution on solar cells of CPCs is investigated by ray tracing simulation. Results show that the solar flux distribution on the absorber of CPC-eθ is more uniform as compared to CPC-90; the diffuse reflection on the semi-diffuse reflector of CPCs has not any positive effect on the solar flux distribution, in turn, leading the optical performance decrease greatly.In order to quantatively investigate the effect of diffuse reflection on CPCs’ reflectors on the energy collection., a mathematical procedure to predict the angular dependence of the optical efficiency of CPCs with semi-diffuse reflectors is suggested based on the theory of two-dimentional radiation transfer. Results show that the diffuse refection has a significant effect on the energy collection of CPCs and the optical performance is sharply deteriorated with the increase of diffuse reflectivity of semi-diffuse reflectors.To compare the photovoltaic performance of CPC-90 and CPC-65 based PV systems, two compound parabolic concentrators(CPC) were fabricated and tested for concentrating radiation on multi-crystalline solar cells. Both CPVs are identical in the acceptance half-angle(20o) and geometrical concentration factor(2 ×). Theoretical calculations show that CPV-90 annually concentrates about 3-5% more radiation on solar cells as compared to CPV-65. For the CPV-65, all radiation would arrive on the solar cells at the incidence angle less than 65 o, but for CPV-90, about 8-10% of annual collectible radiation would arrive on solar cells at the incidence angle larger than 65 o. Experimental results showed that the photovoltaic conversion efficiency of solar panels sharply decreased as the incidence angle of solar rays larger than 60o; compared to CPV-90, the power output at the maximum power points from CPV-65 were slightly higher, and increases of 2.1%, 5.4% and 8.17% were measured for θ⊥being 0o, 10 o and 16 o, respectively. The analysis showed that the incidence angle of solar rays on solar cells of CPV had a significant influence on the power output of CPVs, but solar flux distribution on solar cells had an insignificant effect. A further analysis indicated that the CPV-65 performed slightly better than the CPV-90 in terms of annual power output except in areas with poor solar resources where the annual power output from both systems was almost identical. This implied that CPV-65 performed better than CPV-90 in terms of annual electricity generation.