## 2 Methods
### How to Calculate the PV Output by MS2E Method
#### 2.3.3 Calculation of Power Output  
For the behavior of multijunction solar cells, Equation (7) was used as a simple and ideal model. The photocurrent density in each sub-cell was calculated from the global spectrum, \(I_{\rm gA\ all}\), recombined by the Equation (8),  
\[J_{\rm photo}=\int I_{\rm gA\ all}\cdot\frac{e}{\hbar c}\cdot\lambda\cdot{\rm EQE }_{\lambda}\cdot d\lambda\cdot\frac{\rm TSI}{\int I_{\rm gA\ all}\cdot d \lambda}\cdot\eta_{\rm opt}, \tag{8}\]\[J_{\text{sc without LC}}=\textbf{min}\Big{(}J_{\text{photo Top}},J_{\text{photo Middle}},J_{\text{photo Bottom}}\Big{)}, \tag{9}\]  
where \(\eta_{\text{opt}}\) is the optical efficiency of the incident angle modifier obtained from measurement data. Figure 3 shows the relationship between the incident angle and the optical efficiency of Si and IMM (InGaP/GaAs/InGaAs). A low-reflection textured surface was applied to Si, which reduced the surface reflectivity due to multiple reflections at the surface and improved the optical efficiency. The optical efficiency of IMM was worse than Si because the textured surface was not applied.  
In addition to absorbing light from the outside, a solar cell absorbs light emitted from the internally generated carriers. In the case of a multijunction solar cell, since different kinds of semiconductors are connected in a layer structure, light emission from the middle cell affects the bottom cell [27; 28; 29; 30]. This phenomenon is called luminescence coupling. In consideration of the luminescence coupling, the short-circuit current can be obtained by Equation (10),  
\[J_{\text{sc with LC}}=\textbf{min}\quad(J_{\text{photo Top}}\,J_{\text{photo Middle}},J_{\text{photo Bottom}}+\text{RCC}\] (10) \[\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad\qquad\qquad\qquad\qquad\qquad\  
where \(\beta_{\rm th}\) is the temperature coefficient of the \(V_{\rm occ}\), \(N_{\rm junction}\) is the number of junctions, \(N_{\rm series}\) is the number of cells in series, and \(V_{\rm t}\) is the thermal voltage (0.026V). Here, the cell temperature (\(T_{\rm cell}\)) was calculated by Equation (13),  
\[T_{\rm cell}=T_{\rm amb}+(\rm NOCT-20^{\circ}C)\cdot\frac{TSI}{800W/m^{2}}, \tag{13}\]  
where \(T_{\rm amb}\) is ambient temperature and NOCT is the nominal operation cell temperature. Equation (13) is widely used to estimate in a simple way cell temperature along year [33; 34].  
The current mismatching in multijunction solar cells improves the fill factor (\(FF\)) [35]. The current matching ratio (CMR) is obtained by Equation (14),  
\[\rm CMR=\frac{\textbf{min}\big{(}\textit{${I_{\rm photo\ Top}}$},\textit{${I_{ \rm photo\ Middle}}$},\textit{${I_{\rm photo\ Bottom}}$}\big{)}}{\textbf{mean} \big{(}\textit{${I_{\rm photo\ Top}}$},\textit{${I_{\rm photo\ Middle}}$}, \textit{${I_{\rm photo\ Bottom}}$}\big{)}}, \tag{14}\]  
where min and mean are the arithmetic minimum function and mean function. The \(FF\) was modeled by simple parabolic approximation from the degree of current mismatch between the sub-cells [36], shown in Equation (15),  
\[\Delta FF=\alpha+\beta\cdot(\rm CMR-CMR_{\rm Std})+\gamma\cdot(\rm CMR-CMR_{\rm Std })^{2}, \tag{15}\]  
where CMRstd is the calculated current matching ratio using the standard solar spectrum (ASTM G173 AM 1.5G) and the values of \(\alpha\), \(\beta\), \(\gamma\) are 0.904, 0.163, \(-\)0.717, respectively. The internal resistance in the cell was ignored. Finally, the \(FF\) was calculated by Equation (16),  
\[FF=FF_{\rm rate}+\Delta FF