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* Increased energy yield; decreased thrmal efficiency.
* Increased energy yield; decreased thrmal efficiency.


=== [http://www.sciencedirect.com/science/article/pii/S0038092X13000303 Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations - 2013]<ref>Boyd, M. 2013, 'Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations', ''Solar Energy'', vol. 91, pp. 79-92, ISSN 0038-092X, http://dx.doi.org/10.1016/j.solener.2013.01.015.</ref>
=== [http://www.sciencedirect.com/science/article/pii/S0038092X13000303 Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations - 2013]<ref>Boyd, M. 2013, 'Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations', ''Solar Energy'', vol. 91, pp. 79-92, ISSN 0038-092X, http://dx.doi.org/10.1016/j.solener.2013.01.015.</ref> ===
<small>'''Abstract'''-  An analytical model is formulated for the irradiance on a surface (collector) with a rear (opposite the sun) planar vertical diffuse reflector, as is common for a lower roof on a multi-story building. The vast majority of research on solar reflectors has been for specular, or mirror, reflectors, with any diffuse reflections modeled about the specular reflection angle. This model is capable of calculating incident and reflected direct, diffuse, and ground-reflected radiation using components borrowed from the Hay, Davies, Klucher, Reindl (HDKR) irradiance model, and is easily implemented in any computation programming software capable of numeric integration. The model accounts for reflector edge effects and shading of diffuse and ground-reflected radiation by the reflector, but it does not account for shading of beam radiation by the reflector.
<small>'''Abstract'''-  An analytical model is formulated for the irradiance on a surface (collector) with a rear (opposite the sun) planar vertical diffuse reflector, as is common for a lower roof on a multi-story building. The vast majority of research on solar reflectors has been for specular, or mirror, reflectors, with any diffuse reflections modeled about the specular reflection angle. This model is capable of calculating incident and reflected direct, diffuse, and ground-reflected radiation using components borrowed from the Hay, Davies, Klucher, Reindl (HDKR) irradiance model, and is easily implemented in any computation programming software capable of numeric integration. The model accounts for reflector edge effects and shading of diffuse and ground-reflected radiation by the reflector, but it does not account for shading of beam radiation by the reflector.



Revision as of 02:58, 26 January 2017

Contributors

S. Novia Berriel Anup Nair

Intro

The angle of incidence of solar rays is different at different latitudes. Therefore, using the same angle of inclination for concentrators will not help in acquiring best solar energy capture. What we aim to do in this project is obtain the optimal positioning of concentrators for 6 cases of latitude ranging from 10-60 degrees with an increment of 10 degrees. For each of the latitude cases, we will consider 9 inclination angles of the PV panels ranging from 0-90 degrees with an increment of 15 degrees and test the position of concentrators aiming to obtain best energy yield. We will simulate 6 angles for the concentrators ranging from 10-60 degrees with 10 degrees increment to find the optimal solution. We ultimately want to generate a thumb of rule from this experiment.

Searches

Google Scholar

  • low concentration solar reflectors
  • pv reflector for shaded panels
  • planar reflector for shaded solar panel

Literature Review

The papers reviewed for the completion of this project have been listed below in chronological order of publication. Included are brief summaries of each.

The use of planar reflectors for increasing the energy yield of flat-plate collectors - 1977[1]

Abstract- A mathematical model to simulate the performance of flat-plate collector-reflector systems is presented. First the collector energy balance is modified to account for the reflected energy. Then the exchange area for a diffuse reflector is obtained by integrating over both reflector and collector surfaces. For the specular reflector, the collector area exposed to reflected radiation is calculated from geometrical relations. Shading effects are also found from the system geometry. Fair agreement is obtained between the model and some experiments on a water heating collector in Brisbane, Australia. Finally, the model is used to predict the annual performance of a water heating system with several values of the reflector angle.

  • flat plate collectors tested (solar thermal collection)
  • diffuse reflectors found to have insignificant effect
  • mathematical calculation approach

Stationary reflector-augmented flat-plate collectors - 1981[2]

Abstract-A general procedure for determining the optimum geometry of a reflector-augmented solar collector which produces a desired pattern of flux-augmentation is described. The example used for illustration is a stationary collector whose winter performance is to be improved. Consideration of both a flat-plate collector with a bottom reflector and one with a top reflector led to distinct differences in their optimum configuration and performance being identified. Since either systems can be used to augment winter flux, a criterion for selecting the appropriate system is given. This criterion is based on the displacement in collector tilt from latitude inclination.

  • performance factors - reflector width ratio, reflector angle, panel tilt angle from latitude
  • performance curves to decide b/w top- and bottom-reflectors.
  • unity reflector width ration suggested.

Modeling daylight availability and irradiance components from direct and global irradiance - 1990[3]

Abstract - This paper presents the latest versions of several models developed by the authors to predict short time-step solar energy and daylight availability quantities needed by energy system modelers or building designers. The modeled quantities are global, direct and diffuse daylight illuminance, diffuse irradiance and illuminance impinging on tilted surfaces of arbitrary orientation, sky zenith luminance and sky luminance angular distribution. All models are original except for the last one which is extrapolated from current standards. All models share a common operating structure and a common set of input data: Hourly (or higher frequency) direct (or diffuse) and global irradiance plus surface dew point temperature. Key experimental observations leading to model development are briefly reviewed. Comprehensive validation results are presented. Model accuracy, assessed in terms of root-mean-square and mean bias errors, is analyzed both as a function of insolation conditions and site climatic environment.

  • Models for predicting relevant quantities like solar energy in short intervals and availability of light - can be used for specific user needs.
  • First model relates irradiance value to the light from sun/sky as comprehended by the human eye.
  • Second approximates illuminance and irradiance for horizontally surface tilted.
  • Third - angular distribution of light instead of the diffuse values.

A Comprehensive Physical Model for Light Reflection - 1991 [4]

Abstract - A new general reflectance model for computer graphics is presented. The model is based on physical optics and describes specular, directional diffuse, and uniform diffuse reflection by a surface. The reflected light pattern depends on wavelength, incidence angle, two surface roughness parameters, and surface refractive index. The formulation is self consistent in terms of polarization, surface roughness, masking/shadowing, and energy. The model applies to a wide range of materials and surface finishes and provides a smooth transition from diffuse-like to specular reflection as the wavelength and incidence angle are increased or the surface roughness is decreased. The model is analytic and suitable for Computer Graphics applications. Predicted reflectance distributions compare favorably with experiment. The model is applied to metallic, nonmetallic, and plastic materials, with smooth and rough surfaces.

  • Light reflection explained
  • Components of light reflection

External reflectors for large solar collector arrays, simulation model and experimental results - 1993[5]

Abstract - A model for the calculation of incident solar radiation from flat- and CPC-shaped external reflectors onto flat plate solar collector arrays has been developed. Assuming an infinite length of the collector/reflector rows, the basic calculations of incident radiation in the collector plane from the reflector become very simple. The direct radiation from the sun is projected into a vertical plane perpendicular to the collector and reflector plane. The incident radiation onto the collector, including corrections for shadowing and lost radiation above the collector, can then be calculated using 2-D geometry. For very short collector/reflector rows a 3-D model is given for correction for the loss of specular radiation in the east west direction. The diffuse radiation is assumed to be isotropic. The diffuse radiation in the collector plane is calculated using view factors. CPC-shaped reflectors can be treated with the same models by introducing an equivalent flat reflector. The incidence angle for the solar radiation from the reflector onto the collector is in most cases higher than the incidence angle for the radiation directly from the sun. Therefore the incidence angle characteristics of the collector glazing and absorber become more important in this application. Equations are given for the incidence angles for diffuse and beam radiation. An annual performance increase of over 30%, 100–120 kW h/m2, has been measured for aged (four operating seasons) flat reflectors in the Swedish climate. With a CPC-shaped reflector and new reflector materials, a performance increase of up to 170 kW h/m2 is not unrealistic. This means that the collector and ground area requirement can be reduced by more than 30% for a given load.

  • 2-D and 3-D models of panel/ reflector pairs
  • gives limiting angles for solar altitude for a particular reflector
  • four solar altitude cases for planar reflector, three for CPC

Modeling the solar irradiation on flat plate collectors augmented with planar reflectors[6]

Abstract - An analytical model has been developed and used to determine solar irradiation on flat collectors augmented with planar reflectors. The model uses measured insolation data from the NREL National Solar Radiation Data Base. In addition the model accounts for direct and reflected components of beam, diffuse and ground reflected insolation, considers finite length systems, accounts for shading of the collector by the reflector, and considers different configurations of the reflector relative to the collector. Thus the model represents an extension and refinement of many previous models. Computer simulations have been carried out over different time spans to assess the effects of including these features. In general, the addition of reflectors enhances the radiation received by the collector. Reflected beam radiation is the major contributor to the enhancement, although reflected sky diffuse and ground reflected radiation can be significant in many instances. To optimize effectively the design of the system with respect to selecting tilt angles and specifying a reflector-above or below-collector configuration requires proper modeling of the energy received by the collector system. Finite length analysis used in the model enables the optimization of reflector size relative to that of the collector. The model presented can be the basis of an analytical design tool for optimizing the design of a variety of reflector-enhanced solar energy collection systems.

  • Increase in irradiation with planar reflector - finite size system
  • Includes model for sky diffuse and ground reflected component, shading effects
  • top-reflector blocks sky diffuse and bottom-reflector blocks ground reflected

The enhancement of energy gain of solar collectors and photovoltaic panels by the reflection of solar beams - 2002[7]

Abstract - The use of reflecting panels for increasing energy gain, as demonstrated by use in greenhouses, was applied to conventional solar (thermal) collectors and photovoltaic panels. Several types of reflectors were considered in order of increasing sophistication, cost and enhancement coefficients. Calculations showed that the increase in energy gain ranged from 20 to 250%, depending on the type of equipment and season.

  • 5 types of flat-reflectors for increased reflected radiance. Heat and electricity not estimated.
  • Type1 - same dimension as receiving surface.
  • Type2 - incli. adjusted in type 1 so (x/a)=1.
  • Type3 - rotating axis for reflector; angle should be = (90+θ/2); θ=azimuth angle of sun; entire receiving surface not covered.
  • Type4 - Correction for type3; flaps for reflector; reflected beam width increased accordingly.
  • Type5 - receiver angle 90° wrt vertical inclination & sun's azimuth angle.
  • Rotating reflector better than changing inclination.

Feasibility study of one axis three positions tracking solar PV with low concentration ratio reflector - 2007[8]

Abstract - A new PV design, called “one axis three position sun tracking PV module”, with low concentration ratio reflector was proposed in the present study. Every PV module is designed with a low concentration ratio reflector and is mounted on an individual sun tracking frame. The one axis tracking mechanism adjusts the PV position only at three fixed angles (three position tracking): morning, noon and afternoon. This “one axis three position sun tracking PV module” can be designed in a simple structure with low cost. A design analysis was performed in the present study. The analytical results show that the optimal stopping angle β in the morning or afternoon is about 50° from the solar noon position and the optimal switching angle that controls the best time for changing the attitude of the PV module is half of the stopping angle, i.e. θH = β/2, and both are independent of the latitude. The power generation increases by approximately 24.5% as compared to a fixed PV module for latitude ϕ < 50°. The analysis also shows that the effect of installation misalignment away from the true south direction is negligible (<2%) if the alignment error is less than 15°. An experiment performed in the present study indicates that the PV power generation can increase by about 23% using low concentration (2X) reflectors. Hence, combining with the power output increase of 24.5%, by using one axis three position tracking, the total increase in power generation is about 56%. The economic analysis shows that the price reduction is between 20% and 30% for the various market prices of flat plate PV modules.

  • switching angle and stopping angle independent of latitude
  • reflectors at 60 degrees to panel
  • power increase with reflectors

Optimizing Reflection and Orientation for Bifacial Photovoltaic Modules - 2009[9]

Abstract - Currently, the world market for photovoltaic (PV) solar panel technology is expanding rapidly. The increasing market for PV panels reflects the increasing demand for a clean, reliable energy solution and indicates that PV panels may be the method of choice for supplementing today’s global energy needs. Although PV solar panel production is rising, PV panels are still a relatively new and high-priced technology. There remains a need for a commercially-viable method of implementing residential-scale photovoltaic systems for consumer homes. The purpose of this study is to ultimately maximize the irradiance (solar radiation energy) incident on a geometrically constrained 6.84-kilowatt photovoltaic array system, and thereby maximize the energy production. In this study, the optimum height and angle of bifacial (two-sided) PV modules are investigated both analytically and experimentally. Analytical methods utilize the sun’s position and average irradiance throughout the course of a day. Data is collected under actual, outdoor sunlight conditions. Furthermore, stationary flat reflectors with specular (mirror-like) and diffuse (light-scattering) reflection are used to experimentally characterize the amount of sunlight directed on the back face of the PV modules. By validating the theoretical results with experimental evidence, the analytical model can be used to accurately predict the optimum orientation and reflective material for any location and time of year. The findings suggest that a diffusely scattering reflector is a cost-efficient solution for the proposed PV array design.

  • discusses flat reflectors and partial shading
  • reduction in power output proportional to area in shade
  • adjusts reflector for time of year
  • need for uniform irradiance

Solar thermal collector augmented by flat plate booster reflector: Optimum inclination of collector and reflector - 2011[10]

Abstract - In this report we present a theoretical analysis of a solar thermal collector with a flat plate top reflector. The top reflector extends from the upper edge of the collector, and can be inclined forwards or backwards from vertical according to the seasons. We theoretically predicted the daily solar radiation absorbed on an absorbing plate of the collector throughout the year, which varies considerably with the inclination of both the collector and reflector, and is slightly affected by the ratio of the reflector and collector length. We found the optimum inclination of the collector and reflector for each month at 30°N latitude. An increase in the daily solar radiation absorbed on the absorbing plate over a conventional solar thermal collector would average about 19%, 26% and 33% throughout the year by using the flat plate reflector when the ratio of reflector and collector length is 0.5, 1.0 and 2.0 and both the collector and reflector are adjusted to the proper inclination.

  • opt. inclination yearlong (collector+flat top reflector) for 30°N - theoretically.
  • new graphical method for irradiation through reflection.
  • Angle of reflector inclination - forward in winter/backward in summer (less than 30°). Directly affected by ratio of collector & reflector length.
  • Collector Incli. - lower in summer/higher in winter. Not affected much by length ratio.

Model of loss mechanisms for low optical concentration on solar photovoltaic arrays with planar reflectors[11]

Abstract - The use of low optical concentration with planar reflectors represents a relatively simple method for improving solar photovoltaic (PV) specific efficiency. A coupled optical and thermal model was developed to determine the effects on yearly performance of a planar concentrator on array-scale solar PV installations. This model accounts for i) thermal, ii) angle of incidence, iii) reflectivity, and iv) string mismatch loss mechanisms in order to enable informed design of low optical concentration systems. A case study in Canada is presented using the model and the simulation results show that a planar reflector system installed on a traditional crystalline silicon-based PV farm can produce increases in electrical yield from 23-34% compared to a traditional optimized system and thus represents a potential method of achieving practical gains in PV system yield.

  • Framework for planar concentrator model - Independent of PV module.
  • Accounts for loss - includes thermal, incident angle, reflectivity and string mismatch
  • Case Study (with c-Si PV) - yield by 23-34%. Say better gains than tracking or parabolic concentrators.

Optimal position of flat plate reflectors of solar thermal collector-2011[12]

Abstract - In this paper the results of the influence of position of the flat plate reflectors made of Al sheet on thermal efficiency of solar thermal collector with spectrally selective absorber are presented. Analytical and experimental results on determination of the optimal position of flat plate solar reflectors during the day time over the whole year period are shown. Both numerical calculation and experimental measurements indicate that optimal angle position of the bottom reflector is the lowest (5°) in December and the highest (38°) in June for collector fixed at β = 45° position. The thermal efficiency of thermal collector without reflectors and with reflectors in optimal position has been determined. Though the thermal efficiency of thermal collector decreases slightly with the solar radiation intensity, the total thermal energy generated by thermal collector with reflectors in optimal position is significantly higher than total thermal energy generated by thermal collector without reflectors. These results show the positive effect of reflectors made of Al sheet and there is an energy gain in the range 35–44% in the summer period for thermal collector with reflectors, which is expected to reduce the cost pay back time.

  • Experiment Setup: top- and bottom- Al sheet reflectors; collector 45 degrees inclination. Coordinates (43°19′N, 21°54′E)
  • Analytical model for day time - whole year | Compared with and w/o reflectors
  • Total solar irradiation = direct radiation (collector) + reflected radiation (top & bottom) + diffuse radiation (mathematical equations given)
  • Increased energy yield; decreased thrmal efficiency.

Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations - 2013[13]

Abstract- An analytical model is formulated for the irradiance on a surface (collector) with a rear (opposite the sun) planar vertical diffuse reflector, as is common for a lower roof on a multi-story building. The vast majority of research on solar reflectors has been for specular, or mirror, reflectors, with any diffuse reflections modeled about the specular reflection angle. This model is capable of calculating incident and reflected direct, diffuse, and ground-reflected radiation using components borrowed from the Hay, Davies, Klucher, Reindl (HDKR) irradiance model, and is easily implemented in any computation programming software capable of numeric integration. The model accounts for reflector edge effects and shading of diffuse and ground-reflected radiation by the reflector, but it does not account for shading of beam radiation by the reflector.

The model shows good overall agreement with experimental tests, and is three percentage points more accurate than a standard radiation model for tilted surfaces. The model indicates that a planar vertical diffuse reflector increases the irradiance at high clearness indices and low reflector incidence angles, and decreases the irradiance otherwise. Increasing the reflector height and decreasing the collector pitch and distance between the collector and reflector increases the irradiance during clear periods, but decreases the irradiance, to a lesser absolute extent, during cloudy periods. Annual simulations show a gain in winter insolation and a loss in summer insolation for an average collector/reflector, with an increase in annual insolation for collectors near high albedo reflectors.

Photovoltaic System Performance Enhancement With Nontracking Planar Concentrators: Experimental Results and Bidirectional Reflectance Function (BDRF)-Based Modeling - 2013/2015 [14] [15]

Abstract - Nontracking planar concentrators are a low-cost method of increasing the performance of traditional solar photovoltaic (PV) systems. This paper presents new methodologies for properly modeling this type of system using a bidirectional reflectance function for nonideal surfaces rather than traditional geometric optics. This methodology allows for the evaluation and optimization of specular and nonspecular reflectors in planar concentration systems. In addition, an outdoor system has been shown to improve energy yield by 45% for a traditional flat glass module and by 40% for a prismatic glass crystalline silicon module when compared with a control module at the same orientation. When compared with a control module set at the optimal tilt angle for this region, the energy improvement is 18% for both systems. Simulations show that a maximum increase of 30% is achievable for an optimized system located in Kingston, ON, Canada, using a reflector with specular reflection and an integrated hemispherical reflectance of 80%. This validated model can be used to optimize reflector topology to identify the potential for increased energy harvest from both existing PV and new-build PV assets.

  • Two papers Same name - 2nd derived from 1st
  • new irradiance model - BRDF based
  • calculate irradiance-then module output (Isc) | obtain cell temperature-estimate power
  • 2nd paper - optimal module arrangement for Kingston (44.2312° N, 76.4860° W) - energy yield 18% up

Bibliography

  1. Grassie, S. & Sheridan, N. 1977 'The use of planar reflectors for increasing the energy yield of flat-plate collectors', Solar Energy, vol. 19, Issue 6, pp. 663-668, ISSN 0038-092X, http://dx.doi.org/10.1016/0038-092X(77)90027-5.
  2. H. Chiam, "Stationary reflector-augmented flat-plate collectors," Solar Energy, vol. 29, no. 1, pp. 65-69, 1982.
  3. R. Perez, P. Ineichen, R. Seals, J. Michalsky, and R. Stewart, "Modeling daylight availability and irradiance components from direct and global irradiance," Solar Energy, vol. 44, no. 5, pp. 271-289, 1990
  4. X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, "A comprehensive physical model for light reflection," SIGGRAPH Comput. Graph., vol. 25, no. 4, p. 175186, Jul. 1991
  5. Perers, B. & Karlsson, B. 1993, 'External reflectors for large solar collector arrays, simulation model and experimental results', Solar Energy, vol. 51, Issue 5, pp. 327-337, ISSN 0038-092X, http://dx.doi.org/10.1016/0038-092X(93)90145-E.
  6. .Joseph W. Bollentin, Richard D. Wilk, Modeling the solar irradiation on flat plate collectors augmented with planar reflectors, Solar Energy, Volume 55, Issue 5, 1995, Pages 343-354, ISSN 0038-092X, http://dx.doi.org/10.1016/0038-092X(95)00058-Y.
  7. M.D.J Pucar, A.R Despic, The enhancement of energy gain of solar collectors and photovoltaic panels by the reflection of solar beams, Energy, Volume 27, Issue 3, March 2002, Pages 205-223, ISSN 0360-5442, http://dx.doi.org/10.1016/S0360-5442(01)00081-0.
  8. B.J. Huang, F.S. Sun, "Feasibility study of one axis three positions tracking solar PV with low concentration ratio reflector", Energy Conversion and Management, vol. 48, Issue 4, pp. 1273-1280, April 2007.
  9. Dong, R 2009. Optimizing reflection and orientation for bifacial photovoltaic modules, honors thesis, Ohio State University, viewed 23 January 2017, <http://hdl.handle.net/1811/36981>.
  10. Hiroshi Tanaka, Solar thermal collector augmented by flat plate booster reflector: Optimum inclination of collector and reflector, Applied Energy, Volume 88, Issue 4, April 2011, Pages 1395-1404, ISSN 0306-2619, http://dx.doi.org/10.1016/j.apenergy.2010.10.032
  11. R. W. Andrews, N. Alazzam, J. M. Pearce, "Model of loss mechanisms for low optical concentration on solar photovoltaic arrays with planar reflectors", Proc. 40th Amer. Sol. Energy Soc. Natl. Sol. Conf., pp. 446-453, 2011
  12. L. T. Kosti, Z. T. Pavlovi, "Optimal position of flat plate reflectors of solar thermal collector", Energy Buildings, vol. 45, pp. 161-168, Feb. 2012.
  13. Boyd, M. 2013, 'Analytical model for solar irradiance near a planar vertical diffuse reflector – Formulation, validation, and simulations', Solar Energy, vol. 91, pp. 79-92, ISSN 0038-092X, http://dx.doi.org/10.1016/j.solener.2013.01.015.
  14. R. W. Andrews, A. Pollard and J. M. Pearce, "Photovoltaic System Performance Enhancement With Nontracking Planar Concentrators: Experimental Results and Bidirectional Reflectance Function (BDRF)-Based Modeling," in IEEE Journal of Photovoltaics, vol. 5, no. 6, pp. 1626-1635, Nov. 2015, doi: 10.1109/JPHOTOV.2015.2478064
  15. R. W. Andrews, A. Pollard and J. M. Pearce, "Photovoltaic system performance enhancement with non-tracking planar concentrators: Experimental results and BDRF based modelling," 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), Tampa, FL, 2013, pp. 0229-0234, doi: 10.1109/PVSC.2013.6744136
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