Concentration-acceptance Product Research Articles

A practical upper-bound efficiency model for solar power plants

Abstract A generalized model for the maximum work rate extractable from the Sun is developed considering a reversible and an endoreversible system to define a more practical upper-bound efficiency for the conversion of solar radiation into work and power. This model is based on a photo-thermal work extractor in communication with a high-temperature radiation reservoir and a low-temperature heat sink. Following the model, a parametric analysis of the concentration acceptance product (ξ) and thermal conductance is performed to identify the interdependence of variables for the solar exergy. The results are compared with existing models to provide a practical baseline of work and power extractable from concentrated solar power plants (CSP) technologies. Therefore, it is possible to quantify the irreversibilities of an idealized thermodynamic system operating between the Sun and the absorber (via radiative transfer) and the environment (via convective transfer).

The gap angle as a design criterion to determine the position of linear Fresnel primary mirrors

A common choice for Linear Fresnel Reflector primary mirrors is the so-called uniform configuration, in which a constant value of mirror width – and their relative distances – is used. Often, it results in large relative mirror distances, leading to significant losses of etendue and concentration due to the light lost between the mirrors. In this paper a method to optimize the position of primary mirrors is presented with the goal of producing a more continuous primary optic, eventually closer to the theoretical limits of solar concentration. This calculation was done for two Linear Fresnel Reflector concentrators with uniform configurations, exploring how this method can improve the performance of such systems. This paper analyses the impact of such modifications on the overall optical performance of the collector, through the calculation of Concentration-Acceptance Product, Incidence Angle Modifier curves and an estimation of the total amount of collected energy for a specific location, Faro (Portugal). For the analyzed cases, the simulation results show that the proposed method produces denser primary fields, with an increase up to 21% in mirror area and collecting up to 14% more energy.

Design of leak-free sawtooth planar solar concentrator for daylighting system

Daylighting system installed on the roofs of commercial buildings is an effective measure for low-carbon green buildings. In order to further improve the efficiency and uniformity of daylighting system, this paper proposes an indoor daylighting system based on the design method of the solar concentrator with leak-free sawtooth lightguide. The mathematical model of the total internal reflection (TIR) lens array and lightguide is established. A plate of beam splitter plate is added to separate visible and non-visible light, and daylight and artificial light are used to provide indoor lighting. The factors affecting the optical concentration ratio and the concentration-acceptance product (CAP) value of solar concentrator are analyzed, which is helpful to design better daylighting system. When the optical concentrations ratio are 300, 800, and 1800, the acceptance angles are greater than ±0.17°, ±0.31° and ±0.45°, respectively. Simulation software is used to track the light. The results shows that the illumination uniformity of the system in the working plane reached 0.3, and the total efficiency of the daylighting system reached 65.36%. This design provides a new idea for commercial building lighting and greenhouse lighting applications, which has promising potential applications in the clean production.

Design method of a planar solar concentrator for natural illumination

This paper presents a design method of a natural light indoor illumination system using a planar solar concentrator as a daylighting module which can obtain high optical concentration ratios. In this design, the concentrator is composed of lens arrays, hemisphere-coupling structures, a lightguide, plate of beam splitters (PBS) and photovoltaic cells. The concentrated rays are divided into two parts by PBS, the visible rays for indoor illumination and the invisible rays for energy store. The converted electrical energy from invisible rays can drive the light emitting diodes (LEDs) at the entrance of the lightguide for illumination compensation in the condition of overcast and raining. Simulation results show that the proposed natural illumination system can achieve the illuminance more than 500 lx, which meets the commercial illumination requirement. In addition, the effects of collector width and parabolic coefficient on optical concentration ratio and concentration-acceptance product are discussed in detail. Finally, a prototype concentrator is constructed to demonstrate the viability of the proposed natural illumination system. The experimental measurements are in close agreement with simulation results. To the best of our knowledge, this is the first time that planar solar concentrators have been applied in the indoor illumination system, and our results can provide new insight into possible designs of novel natural illumination.

Algorithmically Optimized Hemispherical Dome as a Secondary Optical Element for the Fresnel Lens Solar Concentrator

The significance of this work lies in the development of a novel code-based, detailed, and deterministic geometrical approach that couples the optimization of the Fresnel lens primary optical element (POE) and the dome-shaped secondary optical element (SOE). The objective was to maximize the concentration acceptance product (CAP), while using the minimum SOE and receiver geometry at a given f-number and incidence angle (also referred to as the tracking error angle). The laws of polychromatic light refraction along with trigonometry and spherical geometry were utilized to optimize the POE grooves, SOE radius, receiver size, and SOE–receiver spacing. Two literature case studies were analyzed to verify this work’s optimization, both with a spot Fresnel lens POE and a spherical dome SOE. Case 1 had a 625 cm2 POE at an f-number of 1.5, and Case 2 had a 314.2 cm2 POE at an f-number of 1.34. The equivalent POE designed by this work, with optimized SOE radiuses of 13.6 and 11.4 mm, respectively, enhanced the CAP value of Case 1 by 52% to 0.426 and that of Case 2 by 32.4% to 0.45. The SOE’s analytical optimization of Case 1 was checked by a simulated comparative analysis to ensure the validity of the results. Fine-tuning this design for thermal applications and concentrated photovoltaics is also discussed in this paper. The algorithm can be further improved for more optimization parameters and other SOE shapes.

Optimizing the Fresnel-Lens Solar-Concentrator Design for Tracking Error Mitigation in Thermal Applications, Using a Statistical Algorithm

The driving motive of this work is to enhance the tolerability of a flat Fresnel-lens concentrator to tracking errors, without the use of secondary optics or sophisticated, and normally costly, meticulous tracking equipment. This is achieved by optimizing the prismatic geometry of the Fresnel lens through a statistical approach that incorporates laws of light refraction and trigonometry. The proposed design produces high focal heat flux that is more suitable for thermal applications. A comparative simulation analysis was conducted for two case studies from literature, each with a different design method for the Fresnel lens. On basis of equivalent geometric concentration ratio and f-number, the flat-spot lenses, designed by this study, returned higher values of the concentration acceptance product ( $$CAP$$ ). In case #1 of a 212× cylindrical lens with an f-number of unity, an equivalent flat lens by this work almost doubled the $$CAP$$ from 0.165 to 0.34. For the design case #2 of a 559× aspheric Fresnel lens made by simple geometrical optics, a 60.7% enhanced $$CAP$$ was achieved by this work’s lens, from 0.206 to 0.331, at an f-number of 0.83.

Two-stage solar concentrators based on parabolic troughs: asymmetric versus symmetric designs.

While nonimaging concentrators can approach the thermodynamic limit of concentration, they generally suffer from poor compactness when designed for small acceptance angles, e.g., to capture direct solar irradiation. Symmetric two-stage systems utilizing an image-forming primary parabolic concentrator in tandem with a nonimaging secondary concentrator partially overcome this compactness problem, but their achievable concentration ratio is ultimately limited by the central obstruction caused by the secondary. Significant improvements can be realized by two-stage systems having asymmetric cross-sections, particularly for 2D line-focus trough designs. We therefore present a detailed analysis of two-stage line-focus asymmetric concentrators for flat receiver geometries and compare them to their symmetric counterparts. Exemplary designs are examined in terms of the key optical performance metrics, namely, geometric concentration ratio, acceptance angle, concentration-acceptance product, aspect ratio, active area fraction, and average number of reflections. Notably, we show that asymmetric designs can achieve significantly higher overall concentrations and are always more compact than symmetric systems designed for the same concentration ratio. Using this analysis as a basis, we develop novel asymmetric designs, including two-wing and nested configurations, which surpass the optical performance of two-mirror aplanats and are comparable with the best reported 2D simultaneous multiple surface designs for both hollow and dielectric-filled secondaries.

Simultaneous Multiple Surface method for Linear Fresnel concentrators with tubular receiver

Linear Fresnel concentrators (LFR) are known for their potential cost-effectiveness, reliability and wide range of possible solar applications. However, this technology is still facing the challenge of increasing its overall performance, especially in the Concentrated Solar Power (CSP) field where Parabolic Trough and Central Tower Receiver concentrators are the predominant solutions. In order to increase the performance of conventional LFR concentrators it is necessary to increase their optical performance as these concentrators are still far from the theoretical limits of concentration. This paper presents a new Fresnel concentrator designed with the Simultaneous Multiple Surface (SMS) method for two reflective (X) surfaces (Fresnel XX SMS) and with a tubular receiver. This design also promotes a good light uniformity on the receiver. A comparison is made between this new Fresnel XX SMS and two present day available concentrators (a Fresnel with CPC (Compound Parabolic Concentrator) and a PT (Parabolic Trough) concentrator), as well as a calculation of the total amount of collected energy (kWh), before thermal losses, for a particular location, Faro (Portugal). Furthermore, a new definition of CAP (Concentration Acceptance Product) is proposed, as the standard definition does not fully take into account the optical nature of LFR concentrators. The paper ends with a discussion of the results obtained, their impact and possible applications in the future.

Infinitesimal etendue and Simultaneous Multiple Surface (SMS) concentrators for fixed receiver troughs

In order to increase the cost-effectiveness of conventional parabolic trough (PT) fields it is essential to reduce Capital Expenditure (Capex) as well as Operations and Maintenance (O&M) costs, in particular the need for flexible hosing or rotating joints, which are used because the tubular receiver also tracks in a solidary way with the trough. One possible alternative is to design a different type of optic with the center of mass on the center of the tubular receiver, generating the possibility of it being fixed, thereby dispensing with flexible hosing or rotating joints, without penalizing its overall efficiency or even concentration. In this work, two possible optical solutions, combining parabolic-type primaries with second-stage non-imaging optics concentrators for fixed receivers, are presented. These concentrators are designed using the Simultaneous Multiple Surface (SMS) design method and the infinitesimal etendue limit. A performance comparison with a conventional PT in terms of optical efficiency, CAP (Concentration-Acceptance Product) and other performance data are also presented, including an estimate of the total amount of yearly collected energy (kWh/m2 of entrance aperture) for one particular location – Faro (Portugal).

New second-stage concentrators (XX SMS) for parabolic primaries; Comparison with conventional parabolic trough concentrators

Parabolic Trough concentrators are the predominant Concentrated Solar Power (CSP) technology today. However this technology is facing substantial challenge from the need to reduce costs and/or increase performance. This paper address this challenge by exploring the room left from the fact this type of optic falls short from the theoretical limits of concentration, proposing a new solution enabling the design of larger troughs with higher concentration or larger acceptance angles, through the use of second stage concentration of a novel type. This new optic is designed with the Simultaneous Multiple Surface (SMS) method for two reflective (X) surfaces (XX SMS) Winston et al. (2005) – of which the primary is approximately parabolic – using a different assignation of the edge rays in order to significantly reduce the Fresnel losses around the glass cover of the evacuated tubes commonly used in CSP applications. To analyze the merits of this new optic, two different comparisons are made. The first one with the SMS Helmet concentrator through the calculation of CAP (Concentration–Acceptance Product) and the second one with a commercial Parabolic Trough concentrator, using an estimate of the total amount of collected energy (kWh) for one particular location, Faro (Portugal). The paper ends with a discussion of the results obtained, their impact and possible applications in the future.

Experimental characterization of Fresnel-Köhler concentrators

Most cost-effective concentrated photovoltaics (CPV) systems are based on an optical train comprising two stages, the first being a Fresnel lens. Among them, the Fresnel-Kohler (FK) concentrator stands out owing to both performance and practical reasons. We describe the experimental measurements procedure for FK concentrator modules. This procedure includes three main types of measurements: electrical efficiency, acceptance angle, and irradiance uniformity at the solar cell plane. We have collected here the performance features of two different FK prototypes (ranging different f -numbers, concentration ratios, and cell sizes). The electrical efficiencies measured in both prototypes are high and fit well with the models, achieving values up to 32.7% (temperature corrected, and with no antireflective coating on SOE or POE surfaces) in the best case. The measured angular transmission curves show large acceptance angles, again perfectly matching the expected values [measured concentration acceptance product (CAP) values over 0.56]. The irradiance pattern on the cell (obtained with a digital camera) shows an almost perfectly uniform distribution, as predicted by raytrace simulations. All these excellent on-sun results confirm the FK concentrator as a potentially cost-effective solution for the CPV market.