## 2 Experimental Procedure  
Three highly efficient CPV modules (as shown in Figure 2a) were installed at the University of Miyazaki and connected in parallel with four sets of DC/DC converter EC cells (as shown in Figure 2b). Sunlight was converted to electricity by CPV modules and was supplied to EC cells. System performance is more than satisfactory on both sunny and cloudy days. This is a result of the efficient DC/DC converters connected to highly efficient CPV modules. For voltage matching between CPV modules and EC cells, DC/DC converters were used. Direct normal irradiance (DNI), which was input power in the system, was gauged by a pyrheliometer (EKO Instruments Co., Ltd., MS-56). The stored hydrogen energy was calculated by free energy of hydrogen (\(\Delta\)G\({}^{\circ}\) = -237 kJ/mol) and hydrogen generation rate (\(GR_{\text{H2}}\)), which was measured by a mass flow meter (MFM, Alicat Scientific M-2 SLM-D-25 COMP). Daily STH efficiencies of approximately 18% for sunny days and approximately 15% for cloudy days were achieved from this system [18]. The details of system configuration were shown in [18]. Disbanding of water molecules into H\({}_{2}\) and oxygen, and the subsequent addition of H\({}_{2}\) to CO\({}_{2}\), were attempted in the outdoor operation. The H\({}_{2}\) resulting from water splitting was subsequently reacted with CO\({}_{2}\) from the outside source. In the next step of the StM system, the Sabatier process, H\({}_{2}\) gas extracted from the electrolysis system was mixed with CO\({}_{2}\). The latter was introduced via a tank. The CO\({}_{2}\) hydrogenation or CO\({}_{2}\) reduction to CH\({}_{4}\) occurred within two reactors fed with Ni-based catalysts. Temperature is the next important parameter to achieve the highest CH\({}_{4}\) composition. Since the highest yield of CH\({}_{4}\) is obtained at a low temperature because of the exothermic nature of the reaction, the operating temperature must be below 300 \({}^{\circ}\)C [19]. Reverse-water, gas-shift reaction, and CO formation are favored when the temperature is above 500-800 \({}^{\circ}\)C [5,6]. To avoid catalyst deactivation due to sintering and carbon formation, the operating temperature should not exceed 500 \({}^{\circ}\)C [6,20]. Increasing temperature is an undesirable condition for CO\({}_{2}\) methanation because of the strongly exothermic reaction of CO\({}_{2}\). Higher pressures and lower temperatures are more favorable in thermodynamic methanation. At high temperatures, a high conversion can be maintained by increasing the pressures despite decreasing CH\({}_{4}\) generation and catalyst degradation. For lower-operating temperatures, an active catalyst is required, while the high-pressure operation is often uneconomical [21]. Since the methanation process is an extremely exothermic reaction, an effective method of temperature management is to cool the reactor inlet gas stream; this may cause undesired energy losses. Moreover, heat management in a fixed-bed reactor may be difficult, resulting in localized, hot spots. Use of an isothermal reaction in the fixed-bed reactor is an alternative cooling solution. In contrast, cooled reactors transfer the released heat from the reaction to a cooling medium. This may be difficult to manipulate within a single reactor. Therefore, at least two adiabatic reactors are needed to be connected in series for good control of reaction temperature in a fixed-bed reactor [9]. The design of the reactor is essential for thermal control of the system. In our system, the reaction was carried out in two adiabatic fixed-bed reactors in which the Ni-based ZrO\({}_{2}\) catalyst bed was fixed as shown in Figure 3. The two reactors were connected in series to maximize the CH\({}_{4}\) generation. The external electricity was applied to heaters of reactors and the reactor temperatures were controlled by a proportional, integral, derivative (PID) controller without cooling systems. Gas/liquid separators were used to filter the byproduct H\({}_{2}\)O to result in pure CH\({}_{4}\).