# The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module
## 4 Discussion
### Comparison Between 4T and 2T Configuration  
The annual performance of the 4T tandem module was calculated by the validated MS2E model. For comparison of robustness to the seasonal spectrum change, it is essential to introduce a normalized scale of the performance, because the area, nominal output, cell type, and power conversion efficiency are different. We used performance ratio \(PR\) and the ratio of the performance peak-to-peak \(R_{pp}\), which are defined by Equations (3) and (4).  
\[PR=\frac{(Outdoor\,efficiency)}{(Efficiency\,\,measured\,\,by\,\,STC)} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Measured** & **Estimated** & **Error** \\ \hline InGaP/GaAs on Si 1  & 39.6 Wh & 40.4 Wh & 1.9\% \\ InGaP/GaAs & 28.0 Wh & 28.9 Wh & 3.4\% \\ Si & 11.6 Wh & 11.4 Wh & 1.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison between measured and estimated (predicted by MS2E model) energy yield in a day (3 January 2019).  
Figure 6: Validation of the performance model (MS2E model) to 4T tandem module, decomposing performance in each output terminal (InGaP/GaAs top cell and Si bottom cell).  
\[R_{pp}=1-\frac{(\textit{peak to peak of PR in 4T})}{(\textit{peak to peak of PR in 2T})} \tag{4}\]  
Note that STC means the standard testing condition. The _PR_ value given by Equation (3) corresponds to how much power generation performance of the photovoltaic module drops in outdoor operation about the indoor testing result measured by the standard testing condition. The _Rpp_ value given by Equation (4) corresponds to the degree of suppression of the seasonal variation of performance of 4T configuration relative to standard 2T configuration. Both _PR_ and _Rpp_ values were integrated throughout the day, and their daily trend was plotted in time series. The result with contrast to 2T configuration is shown in Figure 6 and Table 3. Note that the peak-to-peak value of the _PR_ variation of 4T configuration was 0.084, and that of 2T was 0.139. The degree of improvement of seasonal variation _Rpp_ was 39.8% (Figure 7a). As a result, the annual energy yield per nominal power of 4T configuration increased to 1500 kWh/kW, and that of 2T was 1442 kWh/kW (Table 3). The improvement was mainly seen in the summer. It corresponded to the variation of water precipitation (Figure 7b). The bandgap of the bottom cell of Si is 1.11 eV, and the absorption edge is 1100 nm so that the performance of the Si bottom cell would not be affected by the water absorption typically seen in around 1200 nm.  
On the other hand, the InGaAs bottom cell with 1.0 eV bandgap is affected by the absorption of this band. In 2T configuration, the reduction of absorbed photons in this water band constrains the current output of series-connected entire junctions. In addition to the difference in numbers of terminals (4T or 2T), the difference of the bandgap of the bottom cell affected the degree of the seasonal variation.  
\begin{table}
\begin{tabular}{c c c} \hline  & **PR** & **Annual Energy Yields** \\  & **Peak-to-Peak Value** & **(kWh/kW)** \\ \hline InGaP/GaAs on Si 1  & 0.084 & 1500 \\ \hline InGaP/GaAs/InGaAs (2-terminal configuration) & 0.139 & 1442 \\ \hline \end{tabular}
\end{table}
Table 3: Summary of the outdoor performance of 4T on-Si tandem solar cell and normal 2T three-junction tandem solar cell.  
Figure 7: Comparison of the annual output between 4T configuration and 2T configuration affected by the variation of the atmospheric parameter: (**a**) Predicted seasonal fluctuation of the normalized energy yield of 4T (red and solid line) and 2T (black and dashed line) configuration; (**b**) Seasonal variation of precipitable water (optical depth) in our measurement that is likely to be responsible for the difference of behavior between 2T and 4T configuration. Note that this chart is identical to Figure 4b [99].