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Model for characterization and optimization of spectrally selective structures to reduce the operating temperature and improve the energy yield of photovoltaic modules Ian Slauch, Michael Deceglie, Timothy Silverman, and Vivian E. Ferry ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.9b00347 • Publication Date (Web): 16 Apr 2019 Downloaded from http://pubs.acs.org on April 19, 2019
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ACS Applied Energy Materials
Model for characterization and optimization of spectrally selective structures to reduce the operating temperature and improve the energy yield of photovoltaic modules Ian M. Slauch1, Michael G. Deceglie2, Timothy J Silverman2, and Vivian E. Ferry1* 1Department
of Chemical Engineering and Materials Science University of Minnesota 421 Washington Ave SE, Minneapolis, MN 55455 USA 2National *E-mail:
Renewable Energy Laboratory, Golden, Colorado 80401-3393 USA
[email protected] Abstract: Many existing commercially manufactured photovoltaic modules include a cover layer of glass, commonly coated with a single layer antireflection coating (ARC) to reduce reflection losses. As many common photovoltaic cells, including c-Si, CdTe, and CIGS, decrease in efficiency with increasing temperature, a more effective coating would increase reflection of subbandgap light while still acting as an antireflection coating for higher energy photons. The subbandgap reflection would reduce parasitic sub-bandgap absorption and therefore reduce operating temperature. This reduction under realistic outdoor conditions would lead to an increase in annual energy yield of a photovoltaic module beyond what is achieved by a single layer ARC. However, calculating the actual increase in energy yield provided by this approach is difficult without using time-consuming simulation. Here, we present a time-independent matrix model which can quickly determine the percentage change in annual energy yield of a module with a spectrally selective mirror by comparison to a baseline module with no mirror. The energy benefit is decomposed into a thermal component from temperature reduction, and an optical component from increased transmission of light above the bandgap, and therefore increased current generation. Timeindependent matrix model calculations are based on real irradiance conditions that vary with geographic location and module tilt angle. The absolute predicted values of energy yield improvement from the model are within 0.1% of those obtained from combined ray-tracing and time-dependent finite-element simulations and compute 1000x faster. Uncertainty in the model result is primarily due to effects of wind speed on module temperature. Optimization of the model result produces a 13-layer and a 20-layer mirror, which increase annual module energy yield by up to 4.0% compared to a module without the mirror, varying depending on the module location and tilt angle. Finally, we analyze how spectrally-selective mirrors affect the loss pathways of the photovoltaic module. Keywords: photonic structures, solar cells, photovoltaic modules, cooling, photovoltaic outdoor modeling, solar energy
INTRODUCTION Photovoltaic modules which are encapsulated with an outer layer of glass commonly include an antireflection coating (ARC) on the glass. When installed outdoors, the ARC decreases reflection 1 ACS Paragon Plus Environment
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at the module surface and increases the amount of sunlight reaching the cell. While ARC-coated modules do produce more energy than modules with bare glass, they also produce more waste heat and operate at higher temperature.1 For many common photovoltaic modules, including those based on c-Si, CdTe, and CIGS, cell efficiency drops as temperature rises,2 partially counteracting increases in energy yield provided by an ARC. Several methods of photovoltaic module cooling have been proposed,2 including water cooling,3,4 fin cooling,5 phase change materials,6,7 evaporative cooling8, and increased thermal emissivity. However, in modules with a cover glass layer, module cooling and increased energy yield can be achieved by replacing a single layer ARC with a spectrally selective mirror to reflect sub-bandgap light while also improving upon the antireflective effect above the bandgap. For c-Si in particular this method is promising as subbandgap light represents ~19% of the incident solar energy and c-Si has a relatively large temperature coefficient of cell efficiency at ~0.4%/K.9,10 Photovoltaic modules, however, experience a wide variety of irradiance and ambient weather conditions over the course of the day and the year, which much of the time are not similar to the standard test conditions at which a module is characterized. Modules installed at fixed tilt outdoors, for example, receive varying amounts of direct and diffuse sunlight from all angles of incidence, and operate at temperatures that are determined both by ambient conditions and the amount of waste heat produced.11 Evaluating and designing optical structures to maximize energy yield for modules therefore also requires methods for characterizing and predicting the resulting increase in efficiency and energy production under realistic conditions. Previously, we have shown that 1-D aperiodic stacks of dielectric materials at the air/glass interface can provide a ~1% increase in annual module energy yield compared to a module with a standard glass antireflection coating while simultaneously decreasing operating temperature.12,13 Calculating the benefits provided by such structures, however, is time-intensive, and requires the use of both a ray-tracing simulation to capture the optical properties and a finite-element simulation for the thermal and electrical output.10,14 A much simpler mathematical model which does not require computationally intensive calculations would be useful for further design of 1-D photonic structures, and could allow for modeling of more complex 2-D or 3-D photonic designs integrated into photovoltaic modules. Many simple models exist to calculate the power or operating temperature of a photovoltaic module,15–18 including those that model outdoor performance.19–22 For example, Sun et al.,23 Li et al.,9 and Vaillon et al.24 model the module temperature reduction from a given sub-bandgap reflective and mid-IR emissive coating on the module glass using a 1-D heat transfer equation9 or a heat balance on the entire module23,24. Finite-element simulations are also useful for calculating cell temperature25 or, as in our previous work,12,14,26 module operating temperature and output power. In this paper we develop a time-independent matrix model which accounts for outdoor irradiance conditions and predicts the benefit from selective reflectors on the overall energy yield of a photovoltaic module. We compare the results to the predictions of our previously developed timedependent full optical-electrical-thermal simulation14,26 at two different module tilts and 50 locations across the United States. The model presented is unique as it combines the wavelength 2 ACS Paragon Plus Environment
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ACS Applied Energy Materials
and angle-dependent optical response with real weather and irradiance data to calculate the benefit of a given spectrally selective mirror compared to a baseline case. It is especially important when considering spectrally selective coatings to include the current increase provided by antireflection and the influence that increased current has on operating temperature. We use this timeindependent matrix model to design two different, spectrally-selective mirrors to enhance the overall energy yield, and show how these mirrors modify the loss pathways inside the module. Figure 1 shows a schematic of the energy loss pathways considered in this paper, along with the general module layout that we consider. Ideally, the current-generating layers inside the photovoltaic module will absorb all light with energy greater than the bandgap into the cell, and none of the sunlight with energy less than the bandgap. However, materials commonly used to construct photovoltaic modules such as low-iron glass and ethylene vinyl acetate (EVA) absorb some sunlight above and below the Si bandgap, and especially in the near-UV spectral range, before it reaches the cell.27,28 Fresnel reflection at every material interface also limits the amount of light that enters the cell, and varies as a function of wavelength and angle of incidence. Finally, ~80% of the energy entering the cell is still not converted to electricity, but is instead wasted as heat. Thermalization of carriers to the bandgap, carrier recombination, resistive losses, subbandgap absorption at the metallic cell back contact, and absorption outside of the cell in the encapsulant and cover glass all contribute to heating the module. Each energetic pathway must be individually characterized, as all are affected by an optical modification such as addition of a 1-D spectrally-selective filter. In addition to detailed consideration of optical and electrical loss pathways, the time-independent matrix model also accounts for the real irradiance conditions experienced by the module. Operating outdoors, a photovoltaic module receives a time-dependent amount of radiation both directly from the sun and also as scattered diffuse radiation.29 Sunlight arrives at all angles of incidence, thus making modules which can effectively collect radiation over a wide range of angles beneficial.10 To avoid simulations which require stepping through time-series irradiance data, module energy yield and change in operating temperature are calculated from the total amount of energy received as a function of incidence angle. While the actual module operating temperature is also a function of ambient temperature and wind speed,30 with correlations linking these variables,31 this paper focuses on differences in module operating temperature arising from changes to module optical properties. Therefore, the model does not attempt to calculate an actual absolute operating temperature and does not require ambient temperature data or wind speed data. The effect of wind speed in particular on model accuracy is discussed in a later section and further in the Supporting Information.
THEORY A. Time-Independent Matrix Model Preparation To calculate wavelength and angle-dependent absorption of light in each of the layers of a c-Si solar module, the model requires in advance several matrices corresponding to fractions of incident light absorbed in a given module layer versus wavelength and angle of incidence. While the 3 ACS Paragon Plus Environment
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amount of light reaching a particular interface may change with the addition of a spectrallyselective mirror, these matrices do not change since the fraction is referenced to the light incident on that particular layer. The matrices correspond to absorption in the module glass, encapsulant, and cell. Each absorption matrix has one row for every wavelength considered and one column for every angle of incidence considered. In this paper, we consider 441 wavelengths equally spaced from 300 nm to 2500 nm and 90 angles equally spaced from 0° to 89°. For the glass and encapsulant layers, a matrix of absorbance fractions A can be calculated via Beer’s Law, shown below in eq. 1:
(
𝐴(𝜆,𝜃) = 𝑒𝑥𝑝 ―
4𝜋𝑘(𝜆)𝑑(𝜃) 𝜆
)
(1)
In the above equation, the absorbance is calculated as a function of the wavelength, λ, and free space angle of incidence, θ, where k is the wavelength-dependent imaginary index of refraction and d is the angle-dependent optical path length in the material. Real and imaginary indices n and k for glass and encapsulant are taken from the PV Lighthouse database27 and Vogt et al.,28 respectively. The geometric path length in the material, given by eq. 2, is calculated from the known thickness t, and angle θRef at which the refracted beam travels through the material, given in eq. 3: 𝑑=
𝑡
(2)
cos (𝜃𝑅𝑒𝑓)
𝜃𝑅𝑒𝑓 = sin ―1
(
sin (𝜃)𝑛𝐴𝑖𝑟 𝑛(𝜆)
)
(3)
The thicknesses of glass and encapsulant are 3.2 mm and 0.4 mm, respectively. The angle of refraction is calculated using nAir since the angle of incidence is the angle that the light, traveling in air, makes with the module normal. We take nAir = 1 for all calculations. The refractive index of the glass and encapsulant are very similar, so there is little refraction at this interface. Furthermore, reflection at this interface is ignored as it is
