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A diffusive solar cell window comprises a diffusion plate with TiO_{2} nanoparticles sandwiched between two glass layers. It is a simple, inexpensive, easy-to-made, and highly reliable transparent solar energy module. To improve its power generation efficiency as well as maintain indoor natural lighting, we examined the scattering mechanism in the diffusion plate with TiO_{2} nanoparticles within a diffusive solar cell window by Mie scattering simulations. In this work, a multiwavelength ASAP ray tracing model for a diffusive solar cell window with acceptable accuracy was developed to investigate the influence of the diffusion plate design parameter, mainly concentration of a diffusion plate with determined particle size distribution, on power generation efficiency and color shift of transmitted sun light. A concept of “effective average radius” was proposed to account for the equivalent scattering effect of a size distribution of quasispherical particles. Simulation results demonstrated that both the transmitted light and its correlated color temperature decreased as the concentration increased for a large-size diffusive solar cell window. However, there existed a maximum power generation efficiency at around 160 ppm concentration. The optimal design for a large-size diffusion plate inside a diffusive solar cell window by taking indoor lighting into account was suggested based on the simulation results.

Building integrated photovoltaic (BIPV) is an important application of future solar energy development. The integration of solar cells into windows must not only generate electrical power but also maintain indoor natural lighting. Various types of power generation on windows have been developed by the application of BIPV technology. In most cases, solar cells are directly placed on/in windows [

A 1 × 1 feet diffusive solar cell window prototype at work.

Schematic illustration of the basic structure of a diffusive solar cell window as well as various mechanisms of light transport inside.

Based on Mie theory of light scattering, optical simulations have been widely used to study light transport in diffusion plate, in tissues, in atmosphere, and in environment, and so forth, and have gained some ground in these research areas [

Generally, our devised diffusive solar cell window is made up of a diffusion plate—polycarbonate (PC) plate embedded with titanium dioxide (TiO_{2}) nanoparticles which was sandwiched between two glass plates. In practice, ethylene vinyl acetate (EVA) was used to laminate glass and PC. Accordingly, an ASAP ray tracing model was developed to simulate the measurement of a five-layer diffusive solar cell window in a solar simulator with acceptable accuracy. A typical cross-sectional dimension of a diffusive solar cell window structure for general purpose building applications implemented in simulations is shown in Figure

The implemented cross-sectional dimension (in proportion) for a typical diffusive solar cell window.

The optical simulations were divided into two main steps: (i) the construction of an accurate wavelength-dependent diffusion plate optical model and (ii) optimal design for a diffusive solar cell window.

In order to corroborate the five-layer diffusive solar cell window model, a prior work—the construction of an accurate wavelength-dependent optical model for the diffusion plate—was performed since the diffusion plate is the key component in a diffusive solar cell window. By simulating the transmittance spectra measurement of the diffusion plate using a spectrophotometer, a simplified ASAP model of transmittance spectra measurement for the diffusion plates with different concentrations of TiO_{2} nanoparticle was constructed. It consisted of a diffusion plate, a variable single-wavelength slit light source, and a detection surface that served as the entrance port opening of an integrating sphere. The densities of TiO_{2} and PC were assumed to be 4.0 g/cm^{3} and 1.2 g/cm^{3}, respectively. Given a radius of a nanoparticle, different concentrations of nanoparticle in a diffusion plate can be determined in simulations.

By Mie scattering theory, the aggregate of TiO_{2} nanoparticles in a diffusion plate was assumed to be spherical, isotropic, and uniform in size. In fact, there was a size distribution of around 200~300 nm for TiO_{2} nanoparticles implemented in this work, as shown in Figure _{2} nanoparticle size distribution were tested in the simulations of diffusion plate transmittance spectra measurement. The simulation results then were compared to the experimental measurements not only to validate the accuracy of the wavelength-dependent diffusion plate model but also to determine the operating “effective average radius” implemented in the diffusive solar cell window model. With resort to dynamic light scattering (DLS) measurements for the aggregate of TiO_{2} nanoparticles [

TEM image of the TiO_{2} nanoparticle aggregates.

As for the refractive indices (_{2}, and PC, they do vary with wavelength in the solar spectrum for silicon solar cell which is approximately from 400 to 1150 nm [

In the second step, there were two feasible approaches to perform the simulations for optimizing a diffusive solar cell window design by assigning the light source of the diffusive solar cell window model either to be one single operating wavelength or to be multiwavelength. Though single-wavelength approach could provide valuable information to improve the design of a diffusive solar cell window, but a more accurate model was needed in order to optimize its performance. Therefore, the multiwavelength approach was adopted in this work. An ASAP multiwavelength five-layer diffusive solar cell window measurement model was then developed. Simulations were performed to determine the power generation, transmittance, and transmitted light color of different-size diffusive solar cell window with given concentrations of TiO_{2} nanoparticle. The accuracy of this model was verified through the comparison between the simulation results and experimental data. Further simulations were performed to attain the optimal design for a large-size 640 × 640 mm diffusive solar cell window.

In the simulations of transmittance spectra measurements of the diffusion plate with TiO_{2} nanoparticles, the “effective average radius” of a TiO_{2} nanoparticle was determined to be 140 nm by the examination of all of the simulation results and comparison with experimental data. For this case, the transmittance spectra comparison between the simulation and the experiment demonstrated that the constructed diffusion plate model can exhibit acceptable accuracy across the whole silicon solar cell spectrum, as shown in Figure

Comparison of transmittance spectra of a diffusion plate with TiO_{2} nanoparticles between simulation and experiment. Solid line (—): simulation. Dash line (- - - -): experiment.

To validate the accuracy of the developed multiwavelength five-layer diffusive solar cell window measurement, we compared simulation results to the experimental measurements, as shown in Figure _{2} nanoparticles used, and 62%-T is for a 140 ppm one.

Comparison of power generation ratio of diffusive solar cell windows with different sizes between simulation and experiment in terms of (a) window area and (b) window perimeter.

In Figure

For future commercial applications, a 64 × 64 cm diffusive solar cell window, which was near a 2 × 2 ft size window, was simulated. The simulation results are shown in Figure

Simulation results of power generation ratio and transmittance for a 64 × 64 cm diffusive solar cell window with different concentrations of nanoparticle.

Simulation results of correlated color temperature variation of transmitted light for a 64 × 64 cm diffusive solar cell window with the increment of nanoparticle concentration.

We have developed an ASAP optical multiwavelength model for a diffusive solar cell window with acceptable accuracy which can be used to optimize the design for a large-size diffusive solar cell window. We also proposed a concept of “effective average radius” to account for the equivalent scattering effect of a size distribution of quasispherical particles. For a 64 × 64 cm diffusive solar cell window, there existed a maximum power generation ratio at around 160 ppm concentration in simulations. It did not increase with increasing particle concentration. The simulation also suggested that particle concentration of about 100 ppm was the optimal design parameter, given determined “effective average radius” of 140 nm, by taking indoor natural lighting into account. Its light transmittance can still maintain above 50%.

The authors ensure that there was no conflict of interests in this study.

This work was in part supported by the National Science Council (Grant no. NSC 102-2221-E-218-021) and by the Ministry of Economic Affairs (Grant no. 102-E0603), China.