Model for Characterization and Optimization of Spectrally Selective Structures to Reduce the Operating Temperature and Improve the Energy Yield of Photovoltaic Modules

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 sub-bandgap light while still acting as an antireflection coating for higher energy photons. The sub-bandgap 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. Time-independent 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 1000× 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.