## 3 Results
### Validation of the Outdoor Operating Model for Non-Concentrating Multi-Junction Solar Cells  
The calculated energy generation trend was compared to the PV module prototype using three-junction tandem cell monitoring at the University of Miyazaki. The validation of the model (Table 1 and Figure 3) was carried out with the cooperation of the University of Miyazaki [92]. The detailed structure of the module and outdoor performance can be found in the publication of Ota [101; 102]. The solar cell used in the module was InGaP (1.88 eV)/GaAs (1.43 eV)/InGaAs (0.98 eV) inverted triple-junction solar cell. The InGaP top and the GaAs middle cell layers were grown on a GaAs substrate at first using metal organic chemical vapor deposition (MOCVD) technology, and then the InGaAs bottom cell (larger lattice-constant than GaAs) was grown. Deterioration of the crystal quality of the InGaP/GaAs layers was avoided before the growth of the buffer layer. After the growth of cell layers in an inverted order, cell layers were mounted on a handling substrate, and the GaAs substrate was removed. The module was assembled using these mounted cells, and its efficiency reached 31.17% under the standard testing condition [101; 102]. The general trend between the model and measurement is shown in Figure 6. Although the model trend was generated by the values of average years from the meteorological and solar irradiance database (METPV-11), the seasonal pattern matched the measured performance very well. Please note that the measured trend of the non-concentrating operation of the high-efficiency three-junction solar cell (31.17% efficiency) demonstrates a strange fluctuation of performance that could not be explained by the conventional model, as shown in the right chart in Figure 6; however, the calculated trend by the new model (Table 1 and Figure 5) successfully explains the strange behavior affected by spectrum change coupled with angular characteristics. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **CPV 1** & **Normal Installation** \\ \hline Solar spectrum & Only direct & A mixture of direct, diffused from the sky, and reflection \\ Angle & Always normal & Varies by time and seasons \\ Spectrum by angle & Constant (only normal) & Needs consider coupling to angle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The difference in performance modeling between concentrator PV and standard installation. Figure 5: Modeling performance of the non-concentrating multi-junction solar cells considering the complicated spectrum and angle interaction described in Table 1. In this study, we only considered the flat plate, so that correction to the curved surface in the integrated tool was not applied. In the validation of this model, the critical parameter related to the calculation in the super-multi-junction solar cell is the degree of luminescence coupling between the middle junction and the bottom junction. Note the degree of radiative coupling from the middle cell to the bottom cell (typically 15%) is the key to the validation of the model, and we must consider its coupling; otherwise, the model (Figure 2) could not meet to the outdoor validation (Figure 7). The level of the coupling ratio of the middle junction (GaAs) was measured by [PERSON] et al. as the function of the current level using a GaAs/GaInNAsSb two-junction cell, and the one corresponding to the non-concentration operation (14 mA/cm\({}^{2}\)) was about 15% [103]. Figure 6: Comparison between the measured and modeled seasonal trends of the performance of the PV module using multi-junction solar cells [96]. Performance ratio can be calculated by the formula defined as PR = Yf/Yr, where PR is performance ratio, and Yf is the integrated energy yield of one day, and Yr is the nominal energy yield of one day calculated by the standard testing condition (STC) module efficiency and total insolation.