# The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module
For CPV applications that have been the center of the study of the tandem cells with the robustness of spectrum issues, it was understood that the chromatic aberration of the concentrator optics enhanced the spectrum-mismatching loss [58; 59; 60; 61; 62]. However, such loss could be solved by the innovation of optics, including homogenizers and the secondary optical element (SOE) [63; 64]. The remaining problems of the spectrum-mismatching loss have been overcome by the adjustment of the spectral response of each sub-cell, including overlapping the absorption spectrum and broadening the absorption band to the zone of massive fluctuation. The model, theory, and advanced design of CPV, as well as innovations for solving the issue of spectrum loss in the real-world solar irradiance, were tried to be validated by outdoor energy yield monitoring. However, it was not very successful. One possible reason was that the performance of CPV was also sensitively affected by the tracking error and misalignment of the concentrator optics and the solar cell. However, this issue was solved by the series of innovations of the testing method of the misalignment [65], validation in the production line of the CPV module [66], and the analysis of the impact on the energy output [67; 68]. After solving uncertain factors, the influence of the spectrum change was re-examined. However, it was found that the standard model using air-mass (or the sun height) as the parameter of the solar spectrum, which has been used by many scientists and for more than 20 years, could not explain the seasonal trend of the performance by analysis [69] and the same results using variance (ANOVA) [70]. The new findings that directly and more strongly influence the spectrum than the air-mass was a fluctuation of atmospheric parameters. This was because the impact by the sun height appears strongly when the airmass value is more than 2, and both summer and winter have the early morning and the late evening time equally. Therefore, without consideration of atmospheric parameters, it is almost impossible to predict the annual energy yield; in other words, it is almost impossible to design the optimal tandem solar cells in yearly energy yield. Recently, tandem solar cells have been considered for use in non-concentrating applications, out of CPV, including vehicle-integrated photovoltaic (VIPV) and car-roof photovoltaics (PV) [71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82]. It was thought that most electric vehicles (EV) might be able to run by solar energy using tandem cells on the car roof [1]. The area of the car roof and other car-bodies are limited. Moreover, solar cells cannot be laminated to an undevelopable curved surface of the car body. It is difficult to cover the restricted area of the car-roof surface entirely. Therefore, extremely high performance that can be brought by tandem solar cells is highly required. The analysis of the spectrum sensitivity on CPV was done in our previous research [83; 84]. The calculation and analysis for CPV were more straightforward because we did not have to consider angular effects combined with the mixture of the direct and diffused components of the sunlight. Different from CPV applications, in which the cell is always perpendicularly illuminated by the sun using a solar tracker and only utilizes the direct sunlight, the typical application needs to use a diffused component of the sunlight from the sky, ground reflection, and skewed solar rays, with a combination of direct and diffused elements as a function of the sun orientation relative to the solar panel orientation. For an extension to non-concentrating applications, we need to solve the complicated coupling of spectrum and angles (Table 1). The key parameters are atmospheric parameters that are dependent on each other. For example, different incident angle modifier and different orientation lead to a diverse mixture of direct and diffused sunlight.