Holographic Elements in Solar Concentrator and Collection Systems

Transcription

1 Holographic Elements in Solar Concentrator and Collection Systems Raymond K. Kostuk,2, Jose Castro, Brian Myer 2, Deming Zhang and Glenn Rosenberg 3 Electrical and Computer Engineering, Department University of Arizona, Tucson, AZ College of Optical Sciences, University of Arizona, Tucson, AZ Prism Solar Technologies, Tucson, AZ 8573 ABSTRACT Holographic elements have several unique features that make them attractive for solar collector and concentrator systems. These properties include the ability to diffract light at large deflection angles, Bragg selectivity, grating multiplexing, and angle-wavelength matching. In this presentation we review how these properties can be applied to solar collection and concentrator systems. An algorithm is presented for analyzing the energy collection properties of holographic concentrators in specific geometries and is applied to a planar collection format. Holographic elements are shown to have advantages for low concentration ratio solar concentrator systems. Keywords: solar concentrator, holographic filters, volume holograms, photovoltaic cells. INTRODUCTION Photovoltaic electrical energy generation is one of the most viable solar energy conversion processes. However the major problem associated with photovoltaic energy conversion is cost. One approach is to make large area sheets of photovoltaic material that can be mass produced at low cost, have conversion efficiencies of ~0%, and operate reliably for 5-0 years. A variety of material systems are being considered including thin film silicon, CdTe, CIGS, and organic PV cells [-3]. Although laboratory demonstrations of these cells have been encouraging, commercial products have not been forthcoming at the scale required to impact the energy problem. Another approach to reducing the cost of photovoltaic energy conversion is to use an optical concentrator in conjunction with multi-junction PV cells that are designed to work at high power levels with high conversion efficiency. This technique reduces the amount of expensive photovoltaic material used in the system. If the savings from this reduction is greater than the cost of the optics, tracking system, and additional heat sinking required for the concentrator PV system an overall cost saving is possible. High power concentrator systems appear best suited for centralized power distribution applications where the high initial cost can be amortized with many energy users. Holographic optical elements have long been suggested for use as solar concentrators [4]. They offer advantages in this application by providing complex optical functions in thin, low cost layers that can be integrated with other PV package components. A variety of designs have been suggested in the past [5-7]. In this paper we describe a design methodology for evaluating the properties of planar holographic concentrators. The affects of a moving, broad spectrum source on the diffraction efficiency of holographic components are investigated and used to estimate the energy collection properties of the concentrating system. 2. SOLAR ENERGY COLLECTION EFFICIENCY Analysis of the diffraction of light by a holographic optical element illuminated by a moving source with broad spectral content is a complex process. The position of the sun changes along two-axes corresponding to its daily and seasonal movement. Therefore as the sun moves the angle of incidence changes both along and perpendicular to the grating fringes (Fig. ). The most energetic range of the solar spectrum extends from approximately 350 nm to 2000 nm. The useable portion of the solar spectrum is limited by the spectral response of the photovoltaic (PV) cell. For a silicon cell this extends from about 375 nm to 50 nm. The useful energy spectrum that can be collected is the product of the solar and cell response spectra (Fig. 2). High and Low Concentrator Systems for Solar Electric Applications IV, edited by Lori E. Greene, Proc. of SPIE Vol. 7407, 74070E 2009 SPIE CCC code: X/09/$8 doi: 0.7/ Proc. of SPIE Vol E-

2 Seasonal Variation Daily Variation HPC Module Grating Planes PV Cell Fig.. Diagram showing the angle of incidence of the sun perpendicular and along the grating fringes of the holographic collector. A concentrator or collector can be considered 00% efficient if the full spectrum of available energy that illuminates the collector surface reaches the PV cell surface. If less than the full spectrum illuminates the PV cell surface then the energy collection efficiency is the ratio of the partial energy reaching the PV cell to the energy content of the full spectrum (solar and PV cell) Solar Combined Silicon Wavelength (nm) Fig. 2: Spectral energy distribution of the solar spectrum, a silicon PV cell, and the combined spectrum. Proc. of SPIE Vol E-2

3 3. HOLOGRAM ANALYSIS In order to determine the energy collection efficiency of a holographic concentrator both the direction and diffraction efficiency of the diffracted rays must be computed. In addition the analysis must be performed in three-dimensions since the angle of incidence of the sun varies both along and perpendicular to the grating fringes. The three-dimensional ray trace relations provide a straightforward set of equations for determining the direction of rays diffracted by the hologram: =, () 2 mp mi = q mc mo, (2) 2 ( lp li) q ( lc lo) ( ) ( ) 2 2 ni = li mi, (3) where l, m, and n are direction cosines in the x, y, and z directions. Subscripts c and o refer to the construction and object ray used to form the hologram, subscript p is the reconstruction ray and i is the diffracted ray. Rigorous coupled wave (RCW) relations provide the most accurate description of diffraction efficiency of a holographic grating [8]. However RCW theory is computationally intensive and does not lend itself to iterative design analysis. Approximate coupled wave theory can often be applied with reasonably accurate results and its analytical form can be readily incorporated into design algorithms [8,9]. The diffraction efficiency for a losses dielectric transmission hologram using the approximate two-wave model is given by: η = sin ( ν ξ ) + / ( + ξ / ν ), (4) where ν = πδnd / ( cos cos ) /2 h θ θ and ξ = ϑd h /2cosθ. Δn is the refractive index modulation, d h the 2 hologram thickness, and ϑ K cos( φ θ ) /2 2 K = 2 with K = 2 π / Λ, φ the slant angle of the grating, and n the 4π n refractive index of the grating material. For a reflection type grating the diffraction efficiency using two-wave approximate model is: = Δnd h / cos 2cos and ξ ϑd h /2cosθ ν π θ θ where ( ) / { ( ) ( ) } /2 η = / + ξ / ν /sinh ν ξ, (5) =. In the analysis a series of rays across the aperture of the hologram are diffracted using the ray trace equations and then weighted using the appropriate diffraction efficiency relation. Both the incident angle and wavelength are varied to simulate different sun angles and wavelengths of the solar spectrum. 4. ANGLE-WAVELENGTH MATCHING The angle-wavelength dispersion characteristic of holographic gratings plays an important role in the design of holographic concentrators. This matching property has two effects on hologram operation by indicating the direction of diffracted rays and the direction at which rays are diffracted with maximum diffraction efficiency. A hologram matches the incident and diffraction angles at specific wavelengths. This relation can be described using the two-dimensional grating equation. sinθ( ) sinθ2( ) sinθ( 2) sinθ2( 2) = =. (6) Λ 2 Proc. of SPIE Vol E-3

4 As shown in Fig. 3 if a hologram with a grating period Λ is illuminated at an incident angle θ( ) it will diffract a beam at an angle θ2( ) as determined by the grating equation. If the hologram was formed with angles θ( ) and θ2( ) the diffraction efficiency will also be a maximum when reconstructed with θ( ). x θ 2 ( ) Z θ ( 2 ) θ( ) θ 2 ( 2 ) S( ) S ( ) 2 x x 2 d Λ x' x' 2 η( ) η( ) 2 Object Plane Image Plane Fig. 3. Angle-wavelength matching property of grating diffraction. If the hologram is now reconstructed at an angle θ( 2) it will diffract at an angle 2( 2) θ. The diffraction efficiency will also be a maximum at this combination of wavelength and angle. This results as long as the K-vector closure condition as shown in Fig. 4 is satisfied. The propagation vectors used in this relation are given by: 2π n k [ sin ˆ i = θix+ cosθizˆ ], (7) i and the grating vector by K = k c k where k 2c c, k2care the propagation vectors used to form the hologram. n is the refractive index of the grating and i is the wavelength of light used to form the grating. This relation and vector diagram indicates that as long as the wavelength is shorter than max with 2π n K = 2 k i=,2;min = 2, the volume grating max can be reconstructed with high diffraction efficiency. However the angles will be different from those used to construct the hologram. If the angle of incidence is held constant and the wavelength is varied the diffraction efficiency will be high over a range of wavelengths and then decrease. When the angle of incidence changes a new set of wavelengths will be matched. This is the situation that exists with solar illumination. This property can be observed in Fig. 5 in the section on holographic planar concentrators. Proc. of SPIE Vol E-4

5 θ k 2 ( ) 2 k θ ( ) K k,min k 2 k 2,min k 22 Fig. 4. K-vector closure condition for volume grating Bragg matching. 5. ENERGY COLLECTION ALGORITHM An energy collection algorithm for a holographic concentrator was formulated in the following way: - The geometrical configuration for the holographic concentrator and PV cell is specified; - The parameters for constructing the hologram are selected (θ, θ 2, ); - The spectral responsivity of the PV cell is determined for the type of PV material; - A ray trace analysis of rays incident across the aperture of the hologram is performed to determine the percentage of rays that are captured by the PV cell aperture. The incident ray angles and wavelengths are varied to match values of the sun; - The diffraction efficiency for each ray that reaches the surface of the PV cell is computed and used to weight the value of the ray; and - The ratio of the weighted rays of the diffracted spectrum reaching the PV cell relative to the full solarresponsivity spectrum is computed. This quantity is used as the collection efficiency of the holographic concentrator. The collection efficiency represents the percentage of the energy diffracted by the hologram that reaches the surface of the PV cell relative to the energy that would be utilized if the hologram is replaced with a PV cell. This definition assumes that the conversion efficiency of the PV cell remains the same with low to moderate concentration ratios. For a planar concentrator the concentration ratio is the ratio of the hologram plus PV cell area to the PV cell area. 5. Energy Collection of a Holographic Planar Concentrator In order to assess the energy collection efficiency of holographic concentrators a holographic planar concentrator (HPC) is considered. The basic design for an HPC is shown in Fig. 5. θ inc Cover Glass n 2 Glass Substrate n PV Cell θ diff d D PVC D H Fig. 5. Schematic of a holographic planar concentrator. Proc. of SPIE Vol E-5

6 Collected Solar PWR nm 850 nm 750 nm 650 nm Sun Angle (deg) Fig. 6. Collected solar energy as function of incident angle with holograms formed at different wavelengths (indicated). Incident rays are diffracted by the hologram, totally internally reflected by the substrate, and illuminate the surface of the PV cell. The hologram can operate either as a transmission or reflection grating. The ray analysis for an HPC with DH = Dpvc = d with holograms formed with different construction wavelengths and 0 o /45 o construction angles is shown in Fig. 6. This shows the collected energy as a function of the in-plane movement of the sun relative to the plane of incidence (grating vector and surface normal). The ray trace plots show the collected solar energy assuming the diffraction efficiency is 00% for all wavelengths within the responsivity-solar spectrum. These plots represent the rays that intersect the PV cell surface after being diffracted by the holographic collector. In order to determine the actual energy collected, the rays intersecting the PV cell surface must be weighted by the diffraction efficiency. Figure 7 shows the diffraction efficiency as a function of wavelength for different angles of incidence to a reflection hologram in an HPC collector. The construction wavelength for this hologram is 750 nm and it has a thickness of 5 μm. The full width half maximum spectral bandwidth of the hologram is 75nm and varies across the useful range of the combined PV cell responsivity-solar spectral characteristic as the sun changes angular position. The diffracted spectral bandwidth can be increased either by cascading, multiplexing, or chirping the holographic gratings in the collector. Proc. of SPIE Vol E-6

7 o 0 o 20 o Diffraction Eff Wavelength (micrometers) Fig. 7. Diffracted energy spectrum with the sun incident at different angles with respect to the hologram normal. The calculation is for a reflection grating Collected Solar PWR Solar Seasonal Angle (deg) Fig. 8. Combined ray trace and diffraction efficiency analysis of collected solar energy. The combined energy collection efficiency taking into account both the ray directions and their diffraction efficiency is shown in Fig. 8. The result shown is for four, cascaded reflection gratings in an HPC collector that were constructed at 650 nm, 750 nm, 850 nm, and 950 nm. The result indicates that relatively high collection efficiency is possible over a wide range of incidence angles. Proc. of SPIE Vol E-7

8 6. CONCLUSIONS This paper outlines different aspects of modeling holographic elements for solar energy collection and concentration applications. An algorithm is described for modeling the reconstruction characteristics with solar illumination that includes, ray tracing, diffraction efficiency analysis, and geometrical considerations. It is shown that for planar holographic designs with cascaded gratings that it is possible to collect 20-45% of the available solar energy over an angular bandwidth for light diffracted within the plane of incidence to the hologram. REFERENCES [] Deng, X. and Schiff, W. A., "Amorphous silicon-based solar cells," in Handbook of Photovoltaic Science and Engineering, Luque, A. and Hegedus, S., eds. (Wiley, 2002), pp [2] Shafarman, W. N. and Stolt, L., "Cu(InGa)Se 2 Solar Cells," in Handbook of Photovoltaic Science and Engineering, Luque, A. and Hegedus, S., eds. (Wiley, 2002), pp [3] McCandless, B. E. and Sites, J. R., "Cadmium Telluride Solar Cells," in Handbook of Photovoltaic Science and Engineering, Luque, A. and Hegedus, S., eds. (Wiley, 2002), pp [4] Bloss, W. H., Griesinger, M. and Reinhardt, E. R., "Dispersive concentrating systems based on transmission phase holograms for solar applications," Appl. Opt., Vol. 2, (982). [5] Ludman, J. E., "Holographic solar concentrator," Appl. Opt., Vol. 2, (982). [6] Zhang, Y. W., Ih, C. S., Yan, H. F. and Chang, M. J., "Photovoltaic concentrator using a holographic optical element," Appl. Opt., Vol. 27, (988). [7] Quintana, J. A., Boj, P. G., Crespo, J., Pardo, M. and Satorre, M. A., "Line-focusing holographic mirrors for solar ultraviolet energy concentration," Appl. Opt., Vol. 36, (997). [8] Gaylord, T. K. and Moharam, M. G., "Analysis and applications of optical diffraction gratings," Proc. IEEE, 73, (985). [9] Kogelnik, H., "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J., 48, (969). Proc. of SPIE Vol E-8