## 5 Conclusions  
Effective storage of solar energy is required because solar energy production is variable and depends on solar irradiance and weather conditions. The conversion of the StM system is proposed as a long-term method of solar energy storage. In a StM system, the hydrogenation of CO\({}_{2}\) was accomplished by utilizing the hydrogen extracted form solar power. An efficient StM system was operated outdoors during a field test at the University of Miyazaki, Japan. The StM system consisted of highly efficient CPV modules, DC/DC converter electrolyzer sets, directly applying hydrogen to the methanation system, and two adiabatic fixed-bed reactors with Ni-based catalysts. The CO\({}_{2}\) conversion to CH\({}_{4}\) was affected by reactor temperatures and the ratio of H\({}_{2}\) and CO\({}_{2}\). The inner temperature of reactor 1 (first reactor) increased over the operating temperature (260 \({}^{\circ}\)C) due to the exothermic reaction of CH\({}_{4}\) conversion. The StM's performance was analyzed and it was found that the highest conversion of CO\({}_{2}\) to CH\({}_{4}\) (97.6%) was observed at a reactor temperature of 260 \({}^{\circ}\)C and the stoichiometric ratio of H\({}_{2}\) and CO\({}_{2}\). This indicated that CO\({}_{2}\) hydrogenation reaction was favored at relatively low temperatures. Then, the total power consumption of the reactors was analyzed for the sunny and overcast conditions. A conversion efficiency 13.8% for solar to methane on a clear sunny day was obtained in our system. Natural gas composition often contains at least 80% of CH\({}_{4}\). Since our generated gas composition contained more than 80% of CH\({}_{4}\), the practical impact of our efficient StM system is significant. It is essential to optimize the system configuration and to increase the StM efficiency for reducing the production cost of CH\({}_{4}\) using the methanation system.  
Conceptualization, Y.O., M.S., and K.N.; methodology, S.W. and Y.O.; validation, S.W. and Y.O.; formal analysis, S.W. and Y.O.; data curation, S.W. and Y.O.; writing--original draft preparation, S.W. and Y.O.; writing--review and editing, S.W. and Y.O.; supervision, K.N. All authors have read and agreed to the published version of the manuscript.  
Part of this work was supported by JSPS KAKENHI Grant Number 18K05015 and a grant for Scientific Research on Priority Areas from the University of Miyazaki.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Input Energies**} & \multicolumn{2}{c}{**Produced Gases (Output)**} \\ \hline \(E_{\text{DNI}}\) & \(E_{\text{reactors}}\) & **Amount of H\({}_{2}\) during** & **Amount of CH\({}_{4}\) during** & **Stored Energy of** & \(\eta_{\text{StM}}\) \\ (**6 Wh**) & **(kWh)** & **Experimental Period** & **Experimental Period** & **Produced Methane** & \\  & & **(mol)** & **(mol)** & **(\&Wh)** \\ \hline
4.584 & 0.145 & 11.985 & 2.924 & 0.651 & 0.138 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of power input and output for the methanation system and conversion efficiency of solar energy to methane for sunny conditions (on 15 th November 2019).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\eta_{\text{CPV}}\) & \(\eta_{\text{DCDC}}\) & \(\eta_{\text{EC}}\) \\ \hline Sunny day & & & \\
15 th November & 27.4\% & 89.3\% & 70.2\% \\
2019 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: One-day elemental efficiencies on the system.  
**Acknowledgments:** We would like to thank [PERSON] and [PERSON] of Hitachi Zosen Corporation for supply of catalyst and many discussions on the methanation process using catalyst.  
**Conflicts of Interest:** The authors declare that there are no conflicts of interest.